YouNotSneaky!

What are remittances used for?

2009-03-13T18:50:00.000-07:00

Here is a very thorough paper on remittances in Bangladesh. There's a lot of great info in it but I find Table 9 particularly interesting. I've written about remittances before here, and part of the point was that it was weird to expect poor families in developing countries to react to the receipt of remittances by investing all, or even most, of them. Understandably, low income people, just like anyone else, or hell, even more so, when faced with an increase in their income want to spend some of that extra money on consumption and things that make life worth living. The corollary being that all that worry about remittances inducing supposed "moral hazard" in recipients - making them work less or resulting in higher consumption rather than investment - is misplaced and, frankly, a bit patronizing. It demands of low income families in poor countries that they be more miserly and puritanical - save and work more (relative to their level of income) - than the people who have the fortune to live in richer parts of the world ever are (I mean, come on, look at US saving rates!).

But the data on remittances being way sketchy - mostly because a lot of them flow through unofficial channels, because poor countries which receive the inflows don't have the resources to keep track of them, and some of other statistical issues - it's actually pretty hard to say what remittances are being used for. That's where Prof. Siddiqui's paper comes in. Bangladesh is unique in that it actually has a government agency (BMET) which tries to keep close track of the inflow of remittances as well as, to some extent, on how these are used (and to its credit as a government agency, a significant part of its purpose seems to be to actually to figure out how best get the hell out of the way and just let the money flow). The main shortcoming here is that the remittances which BMET keeps track of are only the official ones sent by "short-term" migrants (mostly to select Middle East countries). So it misses both the remittances sent by migrants that wind up in Western countries as well as quite substantial flows sent through unofficial channels (and, roughly, estimates are that only about 50% of total remittance flows are through official channels). Still, even though the determinants of remittance flows may differ by host country and type of employment, it's fairly unlikely that their uses are affected by it. In other words there's no reason to expect that Table 9 in the paper does not accurately represent, at least approximately, the general use of remittances in Bangladesh. Here it is:

Here's my own quick aggregation into some basic categories:

What the table shows is the following:
1. To the extent that remittance receiving households spend them on consumption, it's mostly "basics" consumption. Almost 21% is spend on food and clothing. Only 6% is spend on other consumption (like furniture). And then 10% is spend on social ceremonies - weddings and the like. So out of total portion spent on consumption only 16.7% (that 16.7 of consumption, not total remittances) is spend on what could even remotely be considered "conspicuous consumption". Most of it is on necessities. And I hope nobody here's gonna begrudge anyone else a decent wedding. (Note: the amount of "conspicuous consumption" may be understated here since some of the unofficial remittance flows are in-kind)

2. The biggest investment categories are in land and migration. But this just means that the remittance receiving households are investing in the opportunities they are faced with. There probably aren't that many investment opportunities - for whatever reasons - in what folks in rich countries think of as "business". You invest in what makes sense in the economy you live in.

(Side note: I think this is a particular reflection of one of the themes in Dani Rodrik's book - for some countries the problem is not that savings rates are too low, but rather that saving rates are low because there's nothing to invest in. As a result, one would expect this tobe different for other countries. Different country, different recipe.)

And for people in countries which rely heavily on remittances, the investment with the highest return is to... send more people abroad to send back more remittances. Land (as well as construction on this land), on the other hand, is probably more of an investment in security. So taken together, these households are not just investing a lot, but they are investing wisely - they're diversifying their portfolios; spend some money on the high return and perhaps high risk investment of more migrants, and spend some of the money on the safe but low return of land.

3. Investment in "human capital" - health and education - is fairly low, though non-negligible. It's about 6% of the remittances. But here I can't help but shrug my shoulders. So what. The whole human capital thing has been more of a development-community/advisor fetish rather than something for which concrete evidence of return has been well documented (for example, see this classic). Given that these returns to human capital are fairly ethereal (and maybe ephemeral too!), 6% of remittance received spend on it is probably about right on the margin.

So the bottom line is that remittances are probably delivering lots of benefits and being used wisely, though not necessarily in the way that rich country advice-givers and would be do gooders would like. Tought nuggies.

A quick, uninformed, probably wrong, and completely unoriginal resolution to the "Brenner Paradox"

2009-01-31T00:34:00.000-08:00

In comments Jonathan points to a problem with the Domar explanation of reemergence of serfdom in Eastern Europe in the 16th/17th century. Because of real life responsibilities I've just gotten around to reading Jonathan's paper (From the part I've gotten through, it's highly recommended.) and it's gonna be a few days before Brenner's book arrives in the mail.

But steppin' back, asking' "what's the difference?", thinkin' "what's the simplest explanation?" and comin' up with something on the spur of the moment here's my answer to what I guess we can call (if we roughly buy into Domar's analysis) the "Brenner Paradox" (yes. I am aware of the fact that the preceding sentence has a lot of "s and 's which makes for a whole host of vertical lines). Note also that Krugman actually discusses this particular problem with Domar's explanation in his essay.

Ok, so what I'm calling the Brenner Paradox is the seemingly opposite effect that changes in the land/labor ratio had on the institutional development of Eastern and Western Europe.

According to Domar, an increase in the land/labor ratio raises the marginal product of labor in a competitive market, which means that, if competitive markets are the rules of the game, then labor wins and land(owner) loses. In turn, starting from a position of roughly competitive markets, or at least labor mobility - the ability of peasants to transfer between their employment between various landowners - what this means is that the incentive that landowners have to change the rules of the game, enact an institutional change and introduce some kind of a bonded-labor arrangement, increases.

16th century Polish-Lithuanian Commonwealth and late 16th/early 17th century Muscovy (Russia) both experienced a rise in the land/labor ratio, the first one through the opening up of the Ukrainian 'frontier' (and in fact, consistently with Domar's story, the Kresy region is where serfdom first began to reappear in PLC) and the second through eastward expansion (the beginning of what eventually turned into the exploration and settlement of Siberia) and a bit later also, through acquiring lands in the Ukraine. So the reappearance of serfdom in Eastern Europe is consistent with Domar's story.

The problem is that Western Europe also experienced an increase in the land/labor ratio, though a bit earlier, say 14th century, as a result of the Black Death. More land, less labor, due to the wiping out of roughly the third of (Western) Europe's population. But the trouble is that the same mechanism postulated by Domar - a rise in the land/labor ratio - has been used (by North and Thomas) to also explain the END of serfdom in Western Europe during this time.

Peoples need to make up their minds. Or listen to what I'm about to say. (Err..., see the title of the post first)

So how can we reconcile the two views while keeping the basic structure of Domar's explanation intact and without relying too much on non-robust just-so stories about exogenous institutional or cultural changes (at the moment, linking it up with the rise of Absolutist states in the West seems to be a bit ad hocish - but like I said, the book hasn't arrived yet)?

Well, I think the easiest way is to note that landowners' incomes in the pre-industrial world depend not just on the land/labor ratios but also on the relative number of landlords and peasants. Here's how (I'll lay out the 'model' first then discuss if some of the other historical facts match up with the explanation).

Suppose we have an economy with just two classes, laborers and landowners. Landowners don't work, they own the land and live off of the rents they receive. Laborers don't own land, they supply their labor in exchange for some kind of compensation from the landlord. The nature of this compensation depends on the institutional set up of the economy. Very very roughly speaking the institutional arrangement as how farm product gets split up can take three forms:
' a competitive labor (and land) market (I think one's gonna imply the other by Walras' Law in a general equilibrium set up. It also seems like Jonathan's paper relaxes or gets around this but I haven't gotten there yet). In that case workers get their marginal product and landowners get the marginal product of land without doing anything (lesson is: you can get what you're worth and still be exploited).
' a rough sharecropping (more precisely a fixed crop rent) arrangement where the product of the land gets split between the landowner and the workers according to some kind of institutionally-constrained contract agreed to under a system where there is NO labor mobility. Here basically a landowner takes a constant fraction of output and the rest goes to workers. Now, this would actually also be true with constant returns to scale and, say, a Cobb-Douglas production function, so what we assume here is that this share is greater than the share that the landowner would get under a competitive market
' a system where the workers get a fixed subsistence wage and landowners get everything else. The difference between this arrangement and the previous one is that if total output goes up, under the previous system peasants' incomes will still rise whereas here, any kind of increase is fully appropriated by the landlords.

In the back of my head I have a Malthusian view of these and if you play around with some fertility and mortality dynamics it turns out that there's some theoretical problems with analyzing the third kind of system (basically, it's either unstable, or ends up looking like the second one) and I also think it's empirically unsupported; there was a quite a bit of fluctuation in workers' wages (by pre Industrial world standards) which is inconsistent with a fixed wage rate and, as Clark notes, most societies seemed to have average incomes (which means peasants' incomes) quite above that required for bare subsistence.

So I'm going to focus on the difference between the institutional arrangement 1) and 2). In other words, I'm going to assume that under a bonded labor system landlords (in addition to getting all that stuff for free simply by virtue of owning land) can extract a portion of total output which is greater than that which they would obtain with competitive labor markets. But of course, if this was all there is to it then landlords would always prefer serfdom and then we'd have to recourse to those exogenous cultural and institutional factors that we want to avoid in order to provide an explanation. So what I'm going to assume is that there is some fixed cost to the landlords, per unit of time (though it could also be like a present discounted value cost of a one time institutional change), of keeping the peasants in bondage under serfdom. Now, this cost could be small and in fact it probably was. Jonathan quotes Moses Finley and it's worth repeating:

“[I]n the context of universal history, free labour, wage labour, is the
peculiar institution (historian Moses Finley, 1976).”

But if we were to assume otherwise we'd get a model where it's all serfdom all the time and part of what we want to explain is why in fact free labour, wage labour, emerged as an alternative to serfdom in Western Europe and why it disappeared in the East. So there's a cost to keepin' the people down. Furthermore, 'c' could represent all the monitoring cost associated with bad effort incentives under serfdom as well as the necessary expenditures required to enforce a more coercive legal environment.

I'm also going to assume that all landowners are identical to each other and the same for peasants. This is because I wish to explain things WITHOUT having to make the explanation depend on some particular distribution of land. In essence what this means is that there's constant returns to scale in land and labor (Jonathan's paper departs from this)- so we can treat a 'large' landowner as several 'small' landowners for purposes of analysis and we don't specify any kind of power dynamics between the big landowners and the small. So if T is the total amount of land in the economy and N is the number of landlords, T/N is the land per landowner. Also because landowners are identical, each one's going to hire/bondage L/N peasants where L is the total population of laborers.

Output of an individual farm is (and we will focus just on landowners' income here, in keeping with the spirit of Domar's paper):

With a competitive market the landlords have to pay the workers they hire a market wage, w, so their income is given by:

They maximize this income with respect to the number of workers they hire given the wage rate. This means that in equilibrium w=MPL, and solving for that, and plugging it back into landlords' incomes we have that it is:

Or in other words, in a competitive labor market landowners get share alpha of the output their farm (and workers) produces. Alpha, though a purely technical parameter, ends up being land's share in aggregate income. Plugging in T/N and L/N for T(i) and L(i) in the above equation we get each landlords' income as a function of TWO variables; the land labor ratio t=T/L and the landlord/peasant ratio phi=L/N:

Ok. Now, under a bonded labor system - serfdom (and ignoring some very important nuances) - we assume that the landlord just takes a share of total output, theta:

So it looks much like what happens with competitive markets but we assume that theta>alpha which captures the fact that laborers are screwed because they cannot move between farms. The difference in (gross) incomes for landlords between serfdom and the competitive is then just:

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But, as mentioned above, let's assume there's also a (possibly small) fixed cost 'c' to the landlords associated with making sure the peasants stay enserfed. Hence the net difference between landlords' income is actually:

To figure out which one they prefer, or in other words, the size of the landlords' incentive to adopt one system over the other, we first look at the situation in which they are indifferent. We set the above equation equal to zero and solve for t (land/labor ratio) as a function of phi (landowner/peasant ratio):

The figure below illustrates this relationship. It's immediately obvious that if t is above the curve in the picture then, since total output is larger with a higher land/labor ratio and landlords get to appropriate more of it under serfdom, in that case they will prefer serfdom. If t is below the curve on the other hand the extra portion of output that landlords could take away from the peasants under serfdom is just not justified by the cost of keeping serfdom in place.

The key - and this is the departure from Domar that makes this reconciliation of the paradox possible - is that phi, the labor/landlord ratio, also matters. Basically, if there's a lot of landlords around, this means low land per landlord and this means low landlord income regardless of whether you're in serfdom or a competitive world. But this means that moving from competition to serfdom is not going to increase incomes much and it might just not be worth it to the landlords.

Alright, now the 'steppin' back' part alluded to in the intro. What's the basic difference in how the land/labor changed in Eastern Europe in the 16th/17th century and how it changed in Western Europe in the 14th? Well, in Eastern Europe it went up because the numerator in T/L, T, went up (the opening up of Ukraine and lands to the east of Moscow). But in Western Europe it went up mostly because the denominator in T/L, L, went down (the deaths due to the Black Plague). But if L goes down this also means that L/N, phi, goes down as well. More precisely, what we need here is that the death rate of peasants due to the Black Death was greater than the death rate of landowners. I believe that somewhere someone (perhaps on my old Malthusian posts) said that that was indeed the case (if not, then the whole explanation in this post falls on its face).

So, it is possible that in Eastern Europe the land/labor ratio went up, labor became scarce (and hence, expansive in a competitive environment) but the relative numbers of peasants and landowners stayed the same. As a result, to prevent the erosion in their incomes the Slavic (and the East German ones too) landowners managed to carry out a change in institutional structure that was the reemergence of serfdom. This is the classic Domar explanation:

At the same time, the land/labor ratio went up in Western Europe a century or two earlier but for different reasons. But the shock also profoundly changed the relative number of landowners and laborers. While the decrease in the number of laborers put downward pressure on landlords' incomes, the fact that there were now fewer workers per landowner (hence per unit of land) and that there were some enforcement costs to keeping serfdom in place made it just not worth it to stick with a system of bonded labor:

According to this, Domar was essentially, though only partly right. If you just focus on Eastern Europe, as he did, then casting everything in terms of changes in the land labor ratio made sense since that's all that was changing. But expanding the model to Western Europe makes it appear to be wrong simply because the land labor ratio was NOT the only thing that was changing. There was something else going on at the same time. Ignoring the changes in the relative number of peasants and landlords (or, workers per land per landlord) creates the paradox.

Some notes:
Like I've tried to indicate, all of this could be bunk. In particular, I'm not exactly sure that the Black Death killed proportionately more peasants than landlords (in absolute numbers it did but what matters is the rates).

Also, whether or not this explanation is feasible depends on the 'initial' levels of t and phi.

Roughly speaking I think that even before the opening up of new land in Eastern Europe it tended to be relatively more land abundant than Western Europe. This was definietly true for Poland-Lithuania (with the Polish kings encouraging immigration from abroad as much as possible, at least prior to late 17th century, since there was all this fallow land laying around) and maybe true for the lands of former Kievan Rus though there the whole Mongol Yoke throws a wrench into the spokes of an easy answer. For other parts of Eastern Europe it was the expansion of the Ottoman Empire that wields a similar wrench, though at least for a few centuries Hungary was very similar to PLC. Bohemia had that whole Hussite War thing going which pretty much trumped all the other shocks (basically those were a big upward shock in phi but that was an effect not a cause so it doesn't apply - at least not until the Hapsburgs got a good hold on it). Overall, if we accept a higher t for Eastern Europe than for Western, that fits our explanation since a transition from free labor to serfdom is more likely if t is already high.

On the other hand, a transition from free labor to serfdom is also more likely if we start with a high phi - lots of peasants, few landlords. But my understanding is that if we go by the proportion of folks with noble titles to the masses without them then Eastern Europe had a much greater share of nobility in population. In Hungary between the beginning of Ottoman invasions and/or Austrians getting in there it reached as high as 20%. Poland had somewhere a bit above 10% of everyone running around calling themselves nobles, as did Lithuania (before the Union of Lublin). Moscow might've been different due to the simple fact that the Mongols shaved off a few of those percentage points. But of course having a noble title and/or being a member of the aristocracy is not the same thing as owning land. In fact there's some historical evidence for the prevelance of the 'landless noble' class in Eastern Europe during this time - folks who had their title and their ancestry, some cloths on their back and not much else. So maybe phi wasn't as high as one would think by looking at noble/peasant ratios.

In our modern world economic factors change quickly while institutions evolve slowly and sometimes lag behind. Given the previous post on the speed of convergence, in the Malthusian world and putting it together with this Domar style analysis, suggests that the opposite was the case in the Malthusian world. Economic pressures, while ever present, moved slowly and so institutions were given plenty of time to evolve and change and determine how the world was shaped.

Anyway. This is just meant to throw out a possible explanation which would necessarily involve an unnecessarily long blog post.

Re-Elect Gaius Baltar!

2009-01-25T22:18:00.001-08:00

The new seasons of Battlestar Galactica started. And we're all wondering; is Ellen really the Final Five? Or is she an older version of No. 6? Can Tigh be trusted as a human-wannabe-Cylon? Is Tyrol gonna go all Cylon or is he gonna be loyal to the fleet? Was that really Kara Thrace in the cockpit of that burned out raider or did she time travel?

But as an economist the one question in my mind is:

Why the hell was the MPK so low on New Caprica?

They had a year before the Cylons showed up. And after that year they were still living in freakin' tents. TENTS! After a year! Lazy ass bastards!

Now, the first explanation that comes to mind is that, you know, they just didn't have enough natural resources to work with. But that can't be. There's obviously woods around on New Caprica - where the search party from Galactica landed and the ambush took place. Cut down some of them trees and build some goddamn log cabins. You're in an virgin environment. Exploit it! You're in a world where diminishing returns have not set in. Take advantage! It took settlers in the American West less than two months to put up their cabin and that probably included plowing the land around it (I had a reference for that but lost it). What the hell where you people doing?

We are talking about a civilization that has FTL capability here! And they can't fashion tree trunks into adobes.

Also, there's obviously stone - where the execution of Roslin, Zarek and others was gonna take place. Now, if you take stones, and pile one on top of each other, at some point you make these things called *WALLS*. It's not a long shot from there to make a *CEILING*. And then you got a house. But when the Cylons showed up there was no *walls* or *ceiling* or *houses*, just freakin' tents.

And when the Cylons DID show up apparently they didn't have the same problems. They build a very large concrete building very quickly. Granted, them being Cylons, they build a prison. But they still build it. Why couldn't the New Caprica crew build a series of concrete buildings which, if they had been so inclined they could've called "apartments" (I think that word was mentioned somewhere in the Pythia prophecies). Was it just cuz they've all been feeling so sorry for themselves through out?

Alright, the obvious explanation here is the Presidency of Gaius Baltar. But as much of a shit as that guy is you just can't blame everything on him. Was Gaius Baltar really a *growth killing president*, say, like Robert Mugabe of the New Caprica?

It doesn't seem likely. From all indications Gaius just wanted pills, booze and hookers. In other words "non-distorting lump sum taxes". Or in yet in other words, do you really think that Gaius Baltar had the time to supervise the extraction of surplus from hard working New Capricans who were busy chopping down trees to build some comfy log cabins for themselves. No, in all likelihood he probably just collected enough lump sum taxes to fund the above mentioned activities and left everyone alone.

(As an aside, here I completely sympathize with the rabble rousing that Tyrol's union is about to do in the relevant episodes. Trade Unions make perfect sense - even more - when they're all anti-government in a government system. The Polish Solidarity being the prime example. The technical term for this is the *double marginalization problem*)

In fact, if you really think about it, then Laura Roslin seems like a much more of a "anti-development", "growth-killing" president than Gaius. She's got that 3rd grade autocratic marmish school teacher thing going and she knows what's best for everybody. Tom Zarek is not entirely wrong about her. Prime exhibit: the idea of randomly assigning people to tilium mining regardless of their background. I mean, even Lee Adama, who, like, plays the role of the "lovable dumbass" picked up on the fact that it's not really good to have English teachers, or cow farmers or ... people who turn logs into log cabins and stones into *walls* ... be miners.

You can't blame this one on Gaius. In fact I blame it on Roslin. She promised everyone she'd take care of them, they believed her and in the extraordinary circumstances it actually made sense for a while. People needed hope and change and then she gave it to them. And that's what she was good at. But once it settled into the nitty gritty the basic laws reasserted themselves. And ever since then she's been messing up the economy of the fleet, And they got all lazy.

They deserved it. Or if they didn't, it was Laura Roslin's fault.

Krugman and Domar go to Whitecastle

2009-01-19T02:43:00.000-08:00

Ay, Krugman and Domar are good.

Having written the last post I've re-read both the Evsey Domar paper and Paul Krugman's old article on it and was struck by how good both were. One amazing thing was how much old arguments get repeated over and over again even if they're, well, wrong.

Paul Krugman quotes James Surowiecki on the Black Death(and JS is in turn quoted by commentators on blogs all over);
" "The Black Death helped undermine feudalism. The population decline was so severe that the individual�s labor grew more valuable, which enabled serfs to abandon their lords and become tenant farmers or urban workers. "

and then Paul:

"That sounds plausible, but it's not the way it happened. According to Domar, serfdom actually withered away before the Black Death, as European population grew close to its Malthusian limit. The puzzle is why serfdom wasn't reinstituted after the Black Death. "

And then we go from there. The Domar paper really needs to be the basis for any kind of discussion of how political factors interacted with economic and demographic ones in the Malthusian world.

Speed of Convergence in the Malthusian World

2009-01-18T15:56:00.000-08:00

"Hola amigos. I know it's been a long time since I rapped at ya."

Alright, alright, might try getting back into this blogging thing despite lots of real life work, but let me start with something easy (yeah right); speed of convergence in the Malthusian world.

There's a review of Greg Clark's 'Farewell to Alms' in the new issue of Journal of Economic Literature by Robert Allen. Allen lists the the six claims made by FtA and argues that the data does not support any of the six claims:

1) the preindustrial world was in a Malthusian preventive check equilibrium
2) living standards were unchanging and above subsistence for the last 100,000 years
3) bad institutions were not the cause of economic backwardness
4) successful economic growth was due to the spread of "middle class" values from the elite to the rest of society for "biological" reasons
5) workers were the big gainers in the British Industrial Revolution
6) the absence of middle class values, for biological reasons, explains why most of the world is poor

I'm going to focus on the first two here since this is where, contra Allen, I think the data is actually the strongest in support of the claims (I also think claims 3 and 5 don't do too bad while evidence for the other two is at the moment at best circumstantial).

In fact the first portion of Allen's critical review reads like he's either actually providing evidence for the thesis of a Malthusian equilibrium and stagnation (g.e. standards of living after invention of agriculture were lower than before it) or nit picking details and statements not essential to the main thesis (in the book Clark says that post-agricultural incomes were "about the same" whereas Allen insists they were lower. He also mentions fertility was higher. But that's very much inline with the Malthusian model. Or Allen stresses frequently that even if there was some relationship between fertility and income other, social and historical factors had much more influence on the birth rate. But in fact, a fertility which is completely independent of income works even better in the Malthusian model (and that's what I'll have below) and Clark repeatedly stresses the various social custom, such as postponing marriage which were the main determinants of fertility in the Malthusian world).

But a frequent criticism of the Malthusian model of world history, which also shows up in Allen, that at various points in time income did seem to be significantly higher than at others. In other words that the claim #2 above is wrong. But the way the claim is presented is a straw man. FtA does not argue that there was never any change in incomes - in fact both the evidence on English laborers' wages (which doubled between roughly 1300 and 1450) and the historical comparison between wages in the ancient world in wheat pounds (Ancient Babylonia had about 2/3 the wages of Classical Athens, two times the wages of Roman Egypt and only slightly higher wages than 18th century England) shows exactly that kind of variation. The book simply argues that there is no long run trend, from 100,000 BC until the Industrial Revolution. Sometimes up, sometimes, down, but at the end of the day (or the millennia) all technological progress simply shows up in higher populations, not higher living standards.

Still, how does one reconcile the idea of "Malthusian stagnation" with the observation that incomes were significantly (though not by modern standards) higher in some places and at some times? One recourse would be to rely on differences in exogenous fertility and mortality rates which are not related to income to explain it. But as the book argues, and I think Allen would mostly agree, pretty much all pre industrial societies limited fertility in some way through social custom (be it getting folks to marry later, space the births within marriage more or simple infanticide). Basically, there just isn't enough variance in fertility rates (more specifically, birth rates) between regions to account for the variation in living standards. The other possibility is mortality rates but here the same problem arises. Could it really be true that Classical Athens had really high standards of living (unprecedented for the pre industrial world) simply because it had a ... really really high mortality rate?

Once you throw out the "Malthusian" explanations of fertility and mortality rates, how do you explain the dispersion of income in the pre industrial world? Well, there's technology, or land. But in the simple Malthusian story those factors are not supposed to matter - they get overwhelmed by the population pressures. To misquote Malthus, population grows geometrically while technology (and land) grow arithmetically. In fact, for example Kremer in a pretty famous paper (better link out there somewhere)assumes that the adjustment to the Malthusian equilibrium is instantaneous which is pretty essential for his empirical analysis.

So the question is, in the absence of large enough differences across regions and time in fertility and (exogenous) mortality, how does one explain persistent fairly large scale (by pre industrial standards) deviations from the Malthusian equilibrium? In other words, how can the world from 100,000 BC and the Industrial Revolution be both Malthusian and at the same time not be Malthusian at many points in time.

The answer to this lies in how fast the pre industrial economies adjust to their Malthusian steady states. Assuming roughly equal fertility and (exogenous) mortality rates for all pre Industrial Revoultion regions one can still obtain a dispersion of incomes at any point in time simply by assuming that the Malthusian adjustment take a long time. But in order for this explanation to work, we have to establish that in fact, these Malthusian pressures are in fact pretty slow.

The rest of this post tries to argue exactly that: the pre Industrial World was Malthusians but the Malthusian mechanisms took a long time to work. Over the millenniums, Malthusian pressures always dragged living standards down to those determined solely by demographics (fertility and mortality) and not by the availability of technology or land. But at the frequency of decades or even centuries technology (and land) could still play a very significant role in determining living standards.

Or in other words, both Clark and some of the more traditional historians who emphasize the riches of Ancient Rome or Classical Athens or 14th century China can be correct.

Ok, here's how the argument is going to work. First let's take a simple model of the Malthusian world in which there is SOME technological progress (or institutional improvements or land acquisition). From that we derive a simple condition which tells us whether or not we have Malthusian stagnation or not. Given that productivity growth in the pre industrial era was fairly low this condition is not of interest of itself, rather, it highlights an important phenomenon:

In the Malthusian world with some technological progress there is always a race between technology and demographic pressures. But this means we need to know the speed of demographic pressures. And this is the rate of convergence to the Malthusian stagnation. If the economy adjusts very quickly to the Malthusian equilibrium, then any kind of technological progress is going to get eaten up by more people rather than higher standards of living. If the economy adjusts slowly then technological progress can come into its own as an important (although not a consistent) determinant of living standards. Somewhere in between, we got somewhere in between.

Here's a Malthusian model with technological progress. Output per capita (living standards) is produced with technology and labor, there are diminishing returns to labor, and land is constant (which here means it's included in A):

while population grows according to:

(the mortality rate function m/y is not perfect as I've mentioned in my previous posts on the Malthusian model but for all relevant purposes it'll do here).

Let's suppose that productivity grows at a constant rate g or

Taking logs and time derivatives of the equation for living standards y we get the growth rate of per capita income:

If there is some level of income at which population growth is zero then it is:

A bunch of simple math can verify that in fact if the growth rate of productivity, g, is less than alpha*f, then the economy will converge to this level of per capita income. In that sense, the Malthusian model WITH technological growth is QUALITATIVELY NO different than the one WITHOUT technological growth in terms of its main predictions; long run stagnating incomes (quantitatively economies with higher g will have a higher LEVEL of income). But if somehow the rate of productivity growth is very high (relative to the birth rate and alpha) then output will grow without bound and we are no longer in the Malthusian trap. As it turns out for all intents and purposes growth rate of productivity (though not zero and even non trivial) in the Malthusian world was much lower than birth rate * alpha.

This means that the world before the Industrial Revolution really WAS in a Malthusian trap. But another question is how *tight* was that trap? How long did it take for a Malthusian economy to adjust to its Malthusian level, if it deviated from it?

To give away the punch line, the Malthusian economy took some time to adjust and so deviations from some kind of fertility/mortality determined subsistence living standard could persist for quite some time.

How can we get this? Well, one way to ask the question is to think about the HALF LIFE of a income deviation of a Malthusian economy: IF a Malthusian economy deviated from its long run equilibrium how long did it take to close HALF the gap between its current level and its ultimate, equilibrium, level?

Mathematically, if a variable X(t) grows at a constant rate b, then its half life is given by:

where t_HL is the number of years it takes to half the % distance to steady state and b is the (negative) growth rate. This is essentially the famous "Rule of 70" (since ln(2)=.69)) in reverse (shrinking in half rather than doubling).

So what we want is to write the growth rate of the living standards as a constant fraction of the % gap from its long run value:

The trouble is that in fact

which is a nonlinear function of the % gap. I.e., the convergence rate parameter which determines the half life "b" is NOT constant. BUT, following standard procedures (like those used to estimate the parallel parameter in the Solow model) we can approximate "b" by log-linearizing the actual g_y around its steady state to obtain a "b" that's gonna give us something pretty close to the half life.

Here's a graph of growth of y as a function of y:

Here's a linear approximation of growth of y by a tangent function around y*:

So, close to the steady state, the rate of convergence to the Malthusian eqiulibrium can be found by the slope of the tangent line. We get this from a Talor Expansion approximation:

(the "=" sign above is a "approximately equal" sign actually).

Now g_y evaluated at y* is obviously zero (i.e. in Malthusian equilibrium there is no growth in living standards). And we have that

So our approximation is:

I'm gonna leave it up to you to do all the basic calculus and algebra, but what you should get is:

Or, the "b" that we need for half life is exactly equal to alpha*f:

and in fact that is the rate of convergence to the Malthusian equilibrium.

This shouldn't be surprising. It's the reason why I considered the 'Malthusian model with technological progress' above. Again - in the Malthusian world there's a race between the rate of technological progress and the speed of Malthusian pressures. Above, we've assumed that technology changes at the rate g. Now, we've calculated the speed of the Malthusian pressures as alpha*f. And our condition for the world to be still Malthusian even in the presence of technological progress was

which is just another (fancy math) way of saying that Malthusian demographic pressures are faster than the growth of technology. (Generally economic "math talk" corresponds very well to intuitive verbal concepts with much less ambiguity).

Ok, but what does this mean? Well, we have that b=alpha*f and b give us the half life as t(HL)=.69/(alpha*f). If we got alpha and f then we can calculate the half life of a Malthusian economy and say something about how fast the adjustment takes place.

Alpha.
At the most basic level alpha measures the rate at which diminishing returns to land set in. If you got a competitive market in land (or by Walras' law) in labor) then alpha will equal the share of land in income - it will be the portion of total output that landlords appropriate. Now, of course, very few pre industrial (and a good number of ones today) economies had competitive markets in either land or labor. But some did have something approximating it (for example post serfdom England) and there's also other ways to estimate it. Without quoting a bunch of literature a not-unreasonable estimate for alpha is 1/4. It could be as low as 1/5 and as high as 1/3, depending on the institutional and land specific factors. But for the sake of a general description we'll take 1/4 here.

f
Strictly speaking, f, is not the fertility rate (number of births and average woman has over her lifetime) but the crude birth rate (number of births as a fraction of population). Fertility rate is actually easier to obtain and given the age structure of population and other demographic factors it's not actually straight forward to get a crude birth rate from a fertility rate. But what we're interested in here is an approximation. And one way to get it is to note that in a steady population, life expectancy equals the reciprocal of the birth rate (I'm leaving out why this is so). So we can get a rough birth rate by taking 1/Life Expectancy for a pre industrial economy. For pre industrial England life expectancy at birth was about 37 years and this seems to be roughly the mean/median for a lot of pre industrial economies (as mentioned above, there isn't THAT much variance in the fertility/birth rate). This would imply a crude birth rate of f=.027.

Combining the two we have the half life:

In other words:
If there was a shock to incomes in the Malthusian world, it would take about 103 years (or roughly 3 generations) for about half the effect of it to disappear. After about 6 generations, a quarter of the initial shock would still be present.

If these shocks occurred often enough (but not often enough to generate a long term trend - i.e. the g was still less than alpha*f) then in fact you can get a centuries long deviation from what should be a Malthusian equilibrium observed in historical data.

So the at the frequency of millenniums (or even several hundreds of years) the world was Malthusian. But on the order of a couple of generations or a century, innovations (broadly understood) mattered. We're reconciled the two seemingly contradictory views of history.

Some extrapolations.
Historians, by the nature of their subject, tend to focus on dramatic events (and that's what makes history interesting. It's also what makes the History of England the most boring kind of history one can study.) In other words they tend to focus on time periods when the pre industrial economies, almost by assumption, were deviating from their long run state, when they were getting shocked. For example, much has been written on the effect of Black Death in the 14th century (killing 1/3 or more of Europe's population) but very few make links between incomes in 16th century and the original (i.e. ignoring the subsequent "Little Black Deaths") shock - but this analysis suggests hundreds of years later it still mattered. For a historian what's interesting is wars, plagues, revolutions; times when history was deviating from its trend. The long, but ever present times in between where history took its inevitable march back to where it began are boring, but they are there.In that way, Clark's analysis reminds us to pay attention to long run effects and long run phenomenon - like the lack of trend in long run living standards between the emergence of modern man and the Industrial Revolution.

At the same time, acknowledging that the adjustments took place over multiple generations also allows us to reconcile two conflicting views of human history - that of stagnation and that of occasional periods of prosperity.

More importantly perhaps it makes economic sense. After all, if you're living in a Malthusian world, in which living standards are always determined by the fertility and (exogenous - i.e. socially determined) mortality what incentive is there to ever adopt new more productive technologies? You get the new technology, you have more children, diminishing returns mean that they will be just as poor as you.

So let's posit a form of "Malthusian Rational Expectations" - the people in the Malthusian world KNEW that they were living in a Malthusian World in which ultimately, over the long run, standards of living were determined by fertility and mortality. What point would they have in working harder, in adopting new technologies, in striving for better institutions?

They wouldn't, unless the transition period after the adoption was long enough.

So think about it this way. Say, you're a hunter gather that just stumbled upon this new technology called "agriculture" which will give you food security, increase the amount of food you can produce and generally increase your "standard of living". The only catch is you got to work a bit harder for it. Now, if you know the world is Malthusian, you know that these gains that this new technology "agriculture" promises are only going to be temporary.

But how temporary?

Higher standards of living means everybody will have more surviving children which means more people, which with diminishing returns ever present, means that everyone including your offspring will wind up right back where they started perhaps working harder for it.

But humans did switch to agriculture and people did continue to adopt advanced technologies, despite the fact that these produced no long run trend in living standards. Assuming some minimal cost to technology adoption, why did they do this?

If the demographic adjustment took place quickly there would have been no reason to do so (and in fact, in some societies and at many points in history people did resist new technologies even where these productivity enhancing - why bother when uncle Malthus will undo it anyway?). But if people's planning horizons stretched only to the next ... three?, four? generations (come on, how far is YOUR planning horizon?) then the above analysis implies that people adopted new technologies simply because the Malthusian equilibrium was too far away to matter for them.

Some quick afterthoughs:
(there's a testable prediction here - economies with higher land share or higher birth rates would adopt new technologies at a lower rate since in that case the half life would be lower and so any advantages of new technologies would be more short lived, so why bother?)

(there's some model of optimal technology adoption in the Malthusian world with a given birth rate and death rate here . Given how fast the adjustment takes place and how much extra work effort new technology requires whether or not new technology is adopted is going to depend on how much present generations value the well being of future generations (the income of their children). For a given rate of time preference the slower the adjustment the longer it takes for Malthus to disintegrate the benefits, the longer will the benefits of a better technology last the more incentive is there to adopt it.
Now, the interesting part is that this intersects with Clark's story about the spread of 'middle class values' - roughly speaking here, people becoming more patient over time. This means that over time the rate of time preference could go up which given the length of the adjustment process and all that other stuff, could make it more likely for folks to adopt a new technology. Basically more patient people would be willing to accept a faster adjustment time. Chicken and egg type of thing)

(Thinking about all this stuff it seems like there's a WEALTH of analysis yet to be done on the political economy of these questions. The one parameter which keeps popping up in all kinds of questions about the Malthusian economy is ALPHA - which, roughly is the share of land in income. But surely, in a feudal world this share is subject to all kinds of political, institutional and historical pressures. I readily admit that estimating it by land's share when markets are competitive is a bit of a cop out. But then we need to have some kind of a political model of how income shares get determined, which go beyond the standard Classical Ricardian analysis of land rents. I think the starting point for thinking about it is the very excellent article by Evsey Domar: ""The causes of slavery or serfdom: a hypothesis."" which Paul Krugman himself tried to get people interested in way back when (as far as I can tell, the response was "Oh, that's interesting but slightly weird, let's think about something else")

D-Temp

2008-11-06T04:11:00.000-08:00

Gabriel asks why Micro textbooks don't have as much of a data/empirical focus as Macro textbooks. Which is only partly true. "Micro" textbooks such as Mas-Collel-Whinston and Green are very theoretical as is Varian, and so on. "Macro" like Romer, or ... uh ... uh ... Carlin and Soskice (it's an undergrad book but grad programs currently using Romer could benefit from adopting it instead even though there's much less fancy math in it. Or is there?) have a lot of data/empirical work in them. At EI I speculated that part of it had to do with the insecurity of macro theory vs. micro. If in the back of your mind you know your theory, or in this context a lump of theories, a methodology, is schizophrenic (which Macro very much is) you're gonna throw up some numbers as barricades against obvious accusations. But the main - although related - reason for this phenomenon is that micro is simply much more specialized than macro. You pick up a Health (Micro)Economics textbook or a Labor(Micro)Economics textbook or a Sports(Micro)Economics textbook, it will be chuck full of data, I promise. But what are the specializations in Macro? (And how does that reflect on the status of this sub-discipline) Well... uh ... there used to be something called "Monetary Economics". Which got absorbed into "Money and Banking". Or maybe it was the other way around with M&B getting absorbed into ME once the finance people got purged and macroeconomists decided that somehow Central Banks have "preferences", i.e. "Monetary Rules"

Digression are these cardinal? ordinal? ordered subjective evaluations merely represented by a monotonic function invariant to affine transformations? Does BB wake up in the morning and say "I'd like to consume a little less inflation today" or where does this stuff come from?... It comes from people who insist on "Microfoundations" that's where it comes form. I did mention Schizophrenia, didn't I?

There's also the "growth and development" or "growth" and "development" specializations but even with quite impressive advances in both theory and data in these areas over the past twenty years they are still treated as "something we have to cover in ye ol' textbook but let's get it out of the way as quick as we can so we can start talking about business cycles" kinda way. Maybe it's the nature of the subject matter - and I don't think it is - but there's very little specialization in sub-disciplines in Macro (of course there's a good bit of specialization in the sense of running the same particular regression (or recalibratin') with minor tweaks over and over and over again) and well ... as Adam Smith told us, no specialization means low growth. From what I understand, these days fluctuations-Macro people specialize in explaining "puzzles".

And note that I haven't even brought up financial markets.

Consider another anomaly. Umm ... let's call it the "Data Theory Excess Methodology Puzzle" (D-Temp). At this point in time, Micro data is way way way better than Macro data. This is true even if you ignore all the aggregation issues and quibbles. To get at causation rather than correlation you need some really specific, well designed, and well collected, information and Micro is much closer to that than Macro which is still in the Torquemada stage of data gathering (i.e., torture and false confessions). Yet the standard Micro textbooks - assuming Gabriel's right here - focus on theory whereas the macro textbooks spend a lot more time on the data. Or, what I think I already said above, the determination of theory vs. data emphasis is simultaneous here. What gives? If you got good data then (assuming more data is a normal good) you should be more empirical. But if you look at the textbooks at first glance it looks like it's the bad-data-having-macro that has the more empirical approach.

This is the "D-Temp Puzzle".

Also note that most of the people who make the argument that "economics is too abstract", or "economics is too mathematical" or "economics as taught in grad school has nothing to do with the real world" or some convex combination of those three arguments, got their economics degrees like 15+ years ago. Give it about five more years and we'll start seeing (and I've been trying to do my part to start, resurrect, or more precisely reincarncate the trend) people talking about ad-hoc empirical estimations, causality, Lucas critique, structural econometrics and just the plain fact that the so called "Applied Micro" people are mostly making shit up and regressing the annual depreciation of your mother's slippers against your dog's fleas until it's significant (No. Really. That's really what they do. In fancy, statistical way but it's what they do. And then they call it "Letting the data speak for itself")

And when the pendulum swings I will feel a little better about being a Macroeconomist, even though a reluctant one.

I got a pair of deuces, what you got?

2008-10-29T21:46:00.000-07:00

... and what's the game we're playing, again?

Anyways. There comes a time when every macroeconomist needs to lay their cards on the table. Form their expectations, rational, adaptive or otherwise, but commit to something or other. Like a forecast.

And this time is obviously one of those times. All this crazy stuff happening, we should be able to say something about it. Something specific, in particular, to be precise, without qualifications. Most of the commentary so far has been on intermediate aspects, caveats, details, or theoretical nuances.

Yeah yeah yeah, credit crunch or not. Greenspan made some mistakes or maybe he was a Trotskyite saboteur. If only Friedman didn't advise the junta of Liechtenstein while Martin Luther was busy nailing his monetary thesis to the door of Wittenberg cathedral (i.e. on his "blog") Icelandics would've never settled Greenland. And then the Easter Island economy's money supply consisting of big statues of very important looking faces would've never collapsed, prompting a bailout of the Long Term Capital Management causing Cardinal Mazarin to scuttle the Bretton Woods system, Athos to become a drunk, Aramis to become a cynical advisor to McCain and Porthos wouldn't have died trying to hold up the whole edifice of the American financial system while Paulson cackled, Wasilla burned and Nemo fiddled. Rock the Vote against the Global Warming and for the Moderate Progress Within the Bounds of the Law!

But seriously. How much is GDP gonna fall? How high will unemployment get? When you say "worst since the Great Depression", do you mean like a 32.5% decline in output, .1% lower than that between 1929 and 1933? Or do you mean a 5% decline,.1% higher than the 1973-1975 recession? There's a lot of freakin' percentage points between 33% and 5%, which means there's worst and then there's worster, so let's get specific.

But of course I'm not gonna tell you. Well, I will but it should be immediately understood that the forecasts that follow are just based on half-monkey-butt guesses and quick algebra which I haven't double checked, but I think it's at least a way to clarify some of the issues and stop some of the crazy talk. Of course, we live in crazy times, so crazy talk might not be all that inappropriate. Hmm, I've already started with the qualifications.

Casey Mulligan has laid his cards on the table. Whatever you think of his estimates, at least he's estimating and doing what a macroeconomist should be doing in a situation like this. Predictin'. Forecastin'. Not evadin' the issue. Obviously he's new to blogging but I'm sure he'll learn soon (there's a lot more there).

My approach here is going to involve much more pulling stuff out of thin air, but it does have the potential misbenefit of being simpler.

So national income is composed of the financial sector and the non-financial sector. Here I take the financial sector to include the real estate sector, since it's more or less the same mess.

where Y is output at time t, F is the financial sector and NF is the non-financial sector.

Some data here. Better data around if you look.

In 2007, "Finance, insurance, real estate, rental, and leasing" (note that this does not include Construction which is a separate category. Real estate is people who buy and sell houses and other land for other people) was 20.68% of GDP. In 1998, it was 19.26% of GDP. Ok, here's the first problem. About 20% of the 'real economy' is 'unreal economy'. In other words, the financial sector + real estate are big enough in and of themselves that even if all negative effects from the present crisis are confined to that sector, it will still be big enough to show up as a decent recession. Suppose the financial sector shrinks by 10%. That's still a 2% drop in overall GDP which is larger than the last two recessions - basically, since Volcker.

10% shrinkage in the size of the financial sector is pretty huge actually. But anyway, we'll get to that soon enough. Ok, some simple accounting. Based on the equation above we have

or diving through by Y_t-1, re-arranging and all that, we get

where alpha_t=F_t/Y_t, or the share of the financial sector in GDP at time t. Factoring out the growth rate of the financial sector (or in this case, it's shrinkage) and letting g(.) denote growth rates ((dX/dt)/X) and dropping time subscripts on the alphas (which basically means going to continuous time - this doesn't matter significantly) we have

This is just accounting (true by definition) and it just means that the growth rate (or the fall in it) in output is a weighted average of the growth rate of the financial and non financial sectors where the weights are the shares of each in output. Like I said, it's just accounting. But here's where the economics come in - we can give an economic interpretation to the ratio

as the elasticity of the non-financial sector to the financial sector. In other words, this would be the effect that the trouble in the financial sector has on "mainstream", the "real economy" or whatever you want to call this. When you hear people talking about "how will this crisis affect main street?", they're really talking about that elasticity. Except so far it's not really an elasticity, I'm only pretending it is, so far it's only accounting. Still, at this point I can start putting some numbers on these variables and start figuring out how much of a decline in output can happen. Basically two variables got identified which will determine the recession, if any, that's gonna happen. And these are two variables that have been mentioned in a lot of the commentary directly or indirectly, but which here I am putting at the forefront, which I'm gonna slap some number on. Which allows me to put my pair of deuces on the table and look triumphantly at... well, nobody in particular. But it will be a really triumphant look. Because it's at least a forecast.

So ok. First question, how much will the financial sector shrink? In other words, what's . Above I said -10% or -.1. That was just an example, using a round number and all that. The truth is that neither I nor nobody else has any good idea of what that's going to be. We live in crazy times, as I said. But I'll try being rational in non-rational times, which is of course very irrational. Anyway. According to the data above, between 1998 and 2007 the Financial sector of the economy grew by about 7% more than overall GDP. So let's pretend that 1998 was a "normal year" and that if none of this crazy stuff happened the financial sector + real estate would've grown at about the same rate as overall GDP (I'm picking 1998 because it's far enough and close enough to "normal times". The share of the financial sector in GDP was increasing before that but 1) at least some of that increase DOES represent genuine innovation in the financial markets and 2) I'm too lazy to look for data that goes back before 1998). So our first monkey-guess is that the "correction" that's going on is going to involve the financial sector shrinking by 7%, down to where it was if that sector had grown at the same rate as overall output. So

This is actually the easy one. The tougher question is, what is going to be the spillover from the financial sector into "main street" or the non-financial sector, or what is . So far it's only really the ratio of the growth of the non-financial sector to the growth rate of the financial sector but if we assume it's some kind of a behavioral/social elasticity (i.e. do economics rather than accounting) then we can get some estimates. And here they are...

Oh wait. This is still too accounting based. Ok, let the size of the non-financial sector be a function of the F sector (which provides credit to the NF sector, as well uses up resources which have alternative uses in the NF sector) and a whole bunch of other stuff that we'll call A:

We could include a lag here and let it be a function of F_(t-1) but that would just unnecessarily complicate things. Let's also assume that the "whole bunch of other stuff", whatever that is, grows at a constant rate, g. So growth of A is g. In that case, the growth of the non-financial sector's going to be

where now is the spillover of financial markets to non-financial markets (rather than just an accounting ratio), g is an exogenous growth rate of the non-financial sector due to productivity increases which have nothing to do with the financial markets (technological progress and the like) and is how much the non-financial sector grows due to these productivity increases. In fact, at this point it's not too crazy to assume which would be equivalent to assuming the functional form (even if one objects to this formulation, it's still that data-wise phi*g would be the actual estimated growth rate of the non-financial sector which is not due to changes in the financial sector, which is what we actually care about here. Yes. It is difficult to write economics in a non-confusing manner. That's why there was comedy at the beginning of this post. To soften you up). So now our equation for the size of the recession becomes:

or

which is very similar to what we had previously except for that now we have an extra term (1-a)g, which represent increases in output due to exogenous growth in the non-financial sector and, more importantly, our interpretation of epsilon has changed - now it is truly an elasticity which measures the effect of changes in the financial sector on the main street economy.

Ok, but we still need to know what that epsilon is. I don't know. I know "g" though. If your horizon is a year than I'd say it's between 1% and 2%. Let's not be too optimistic and say it's actually .5% but now that we have actual formulas we can calculate the recession for various levels. Hmmm,... epsilon.

The epsilon or the how the financial crisis will affect the size of the "real economy". Thinking about it there's couple heuristics we can use here. First, there's a lot of talk about how the financial sector is too big and too bloated. A lot of that is crazy talk from people who ascribe to the Thomas Aquinas view that interest rate should be zero, but in these particular times there's probably something to it. What this means is that epsilon cannot be THAT big. I'd say less than one, and significantly so. Second, note that it can be positive or negative.

If epsilon > 0 this means that when the financial sector contracts, the non-financial sector does as well. The straightforward interpretation here is that as the financial sector collapses, the non-financial sector gets denied credit. And I'm sure you've been hearing stories about that.

A more counter-intuitive case would be that epsilon < 0, which you don't hear as much about. But this has a natural interpretation too. As a particular sector of the economy contracts, it releases resources, in terms of workers, capital, knowledge and yes, even re-directed credit, which can than be used by the non-financial sector. In fact, for most industries, this is exactly what happens when one industry contracts and another expands (and it is at least partly what Casey Mulligan's talking about in his post). That means that as the financial sector shrinks, the non-financial sector is given more resources to grow. So the elasticity is negative (which is good news for us here).

Additionally, in the long run (yes yes yes, I know that in the long run "we're all dead" but if you never think about the long run then when it comes it's gonna suck, and so will the medium run which comes around while you're still alive. (Rock the Vote against the metempsychosis of good quotes into empty cliches!)) insolvent financial institutions will be replaced by new, solvent ones, or their business overtaken by old, solvent ones. And that means the credit will resume and the negative aspects of epsilon will be reduced.

There's another aspect that should keep epsilon down in absolute terms ...

Oh.

The forecasts. Where are they? Hold up, hold up. Would anyone try to bluff by telling you they got a pair of deuces? They're coming.

... and that's the fact that by many accounts banks are withholding credit for two reasons. One, they wanna hoard because they're worried that they might go insolvent themselves. Two, they wanna hoard because they're worried that whoever they lend to will go insolvent and won't pay back. The first one applies generally. The second one though should not be a problem in terms of lending to non-financial institutions - provided that most "main street" firms are fine. Which if they're not, then we're in big trouble, but then, why are we worrying about the financial crisis in particular anyway? So while the supply side of credit may be a problem here, there shouldn't be much of a problem on the "effective" demand side - i.e. banks should be able to find non-financial firms to lend to.

Note that this DOES NOT apply to the trouble that's currently starting in many emerging markets, as noted in some places, where many firms are potentially insolvent. In that case, both the number of potential supply of lenders and decent borrowers are low so ... well, this post is getting long and you probably want your forecasts, but yeah, much bigger trouble.

Anyways. I pick:

In the short run; epsilon = .3, in other words, if the financial system shrinks by 10%, the non-financial system shrinks by 3% due to lack of credit. I also pick g (exogenous growth in non-financial sector) g=0, reflecting, well, the short run.

In the medium run; epsilon = 0. I'm just gonna assume that the positive and negative effects described above offset each other. I'll let g=.005 in this case.

In the long run; epsilon = -.2. For symmetry I wanna go with -.3 but I also want to be a bit pessimistic. So if the financial system initially shrinks by 10%, it releases enough resources (I do wish I had some input/output tables here. It's true, people don't do that enough anymore) for the non-financial sector to increase by 2%. Going along with the pessimist I'll keep g at .5%.

What does that gives us?
Well, here's the values based on all this stuff above:
g_F - exogenous shrinkage in the financial system due to the present crisis = -.07
alpha - share of the financial sector in gdp, rounding it up = .2
g - exogenous improvements in the non financial sector = 0 in short run, .005 in medium and long run.
epsilon - .3 in short run, 0 in medium run, -.2 in long run.

Which means:
In short run

In other words a drop, peak to trough, in GDP of slightly more than 3%. How bad is this? Well, it's basically the second part of the Volcker recession. So not as bad as all of the Volcker recession of the early 80's (the whole thing was 5%+). But worse than the last two recessions we've had. If you want some good news, then there's the schadenfreude that the drop in the "main street" economy this implies is only about 2.1%

In the medium run:

Or something that looks like the 2000's recession if it looks like anything at all. You'll be able to see it if you squint really hard, but it will be there.

In the long run:

which means a slight gain due to the fact that the over bloated financial sector gets rid of some excess weight and due to the fact there's some productivity increases in the non-financial sector. Note that the productivity increases in the non-financial sector are assumed to be 1/2 of a percent, which would normally show up as .4% growth in GDP so this still represents some drag on the increases in incomes that would otherwise happen.

So there you go. There's my pair of dueces. They may not be much but they're spades.

But wait! We're not done actually.

One more thing we can do, since we're totally into the monkey-guess-ad-hoc-macro-make-up-elasticity-values territory (BTW. An empirical question related to a previous post. Did any of the efforts in macroeconomics to try and deal with the Lucas Critique and estimate the "deep" parameters actually lead to better forecasts? Or did they just lead to changes in the assumed utility functions/adjustment costs of capital/pushed back the ad-hociness another level? In other words, did they deal with Friedman?). It's called Okun's Law, which relates changes in output to changes in unemployment:

Usually u* is taken to be "natural rate" of unemployment but here we can just take it to be the present rate of unemployment. And xi is usually estimated to be between 2 and 3. And current unemployment rate is 6.1. Then the relevant unemployment rates we'll see according to the estimates above are:

Short run: Lower 6.1+(3.08)/3=7.13, Upper 6.1+(3.08)/2=7.64
Medium run: Lower 6.1+1/3=6.43, Upper 6.1+1/2=6.6
Long run: Lower 6.1-.12/3=6.06, Upper 6.1-.12/2=6.04

Alright, almost over. But obviously in these circumstances Bob's your uncle and the guesses above are just guesses although based on some assumptions. So here are some tables which allow you to question me (remember that this is all based on accounting and the behavioral assumptions are free) - maybe you think the crisis will cause a much greater fall in the size of the financial sector or maybe you think that epsilon's greater/smaller/insane. Here's some tables which do the calculations for you. I highlighted some values which I thought were relevant (click to enlarge).

The recession:

The effect on main street:

And the resulting unemployment rate:

Oh yeah. These were calculated under the assumption that g=0. Which means that if g=.005 - there's a 1/2 % improvement in productivity of the non financial sector - add .004 to the estimated growth rates of output. And then use Okun's Rule again. Basically this makes things a little bit, but not much, better.

Additional stuff:
* Ugh, now I gotta look for the links to anything that's relevant in all that crap I wrote above.
* This is also a useful framework to use when thinking about the bailout plan. What is it trying to achieve? Is it trying to contain the shrinkage of the financial sector? Well, that means less recession in short run, but less positive adjustment in the long run. Sure, it may be worth it. Or is trying to target the epsilon, the spillover from the financial sector to the non-financial sector? This also has some short run vs. long run implications (even if one's not a liquidationist - see previous post). Or is it just throwing money around hoping that it will hit something somewhere?
* I'm actually very much in favor of "moderate progress within the bounds of the law". In fact, I think that's my political bliss point. I still think that's pretty funny though. There's a difference between aesthetics/humor and ethics/politics.
* This stuff's peak to trough. If someone forces me to forecast the time frames as well I'd say; short run = 1 year, medium run = 1.5 years, long run = 2 years+
* I kept the Visigoths out of this

Minsky, Austrians and the MMT

2008-10-26T21:52:00.000-07:00

In the discussion of the present crisis two kinds of theories are generally being invoked as applicable or as "having foreseen it", by two different groups of people. Interestingly enough they lie on opposite ends of the political spectrum. Minsky's "Financial Instability Hypothesis" is generally associated with a pretty left wing version of "radical Keynesianism", while the "Fed driven malinvestment" story comes courtesy of the Austrian school. There is of course a fundamental difference between the two - the Keynesian view sees fluctuations and bubbles as inherent to the capitalist system, while the Austrians think it's all created by sloppy government/Fed policy - but, aside from that, both of these stories can be reconciled with the present events. (And here is a bit of a synthesis though done from the Austrian side)

At this point I should probably say that my knowledge of both of these approaches is pretty superficial and I'm perfectly happy to be corrected.

To make both stories make sense we need to add in the role of monetary policy in the present crisis. Daniel Davies (among others) has argued (somewhat along the Austrian view, surprisingly) that it was Fed policy to "engineer" the housing bubble as part of its 2000/2001 recession fighting strategy.

So let's accept for the moment that monetary policy was bad. How does the Minsky view contrast with the Austrian view?

In Minsky, as I understand it, waves of euphoria in good times lead to speculative bubbles which then crash resulting in a credit crunch and ensuing bad times. Now, it's partly the job of the Central Bank to step in and try to smooth this "slow movement" by cooling down the euphoria with high interest rates in the good times and expanding credit with low interest rates once the bubble pops (plus regulation and the like). Assuming the above view of monetary policy, the Fed did not do its job in this regard, letting the euphoria and the bubble grow until we got into the present mess. On the face of it, this view roughly fits.

So, to sum up, Minsky:
Naturally occurring speculative bubbles + Fed fails at its role = crisis.

How is the Austrian view different? Well basically it is:
Fed naturally screws up -> artificial speculative bubble = crisis.

You can sort of see why both stories can plausibly fit the present scenario here. In the Austrian view the Central Bank keeps interest rates artificially low, which causes "malinvestment" or in this context the real estate bubble, eventually this policy induced bubble collapses and all those bad investments have to be "liquidated" with a resulting recession.

One significant difference between the two views is how to deal with the situation. In the Minsky view, since these bubbles are inherent to the market, the role of the Fed once the crisis is under way is to provide liquidity. So even though the Fed failed at stopping the bubble in the first place, now that the bubble popped the Fed's job is to continue with the policy of cheap credit until good times return. The same policy that caused the bubble in the first place is the one necessary to get out of the crisis.

In the Austrian view the "liquidation" of "malinvestment" is necessary and even desirable, if the economy is to get back on its track. Hence, the Fed should not provide cheap credit but keep it at its normal level and let the thing sort itself out. Otherwise the "malinvestments" will continue leading to an even bigger necessary "correction" later on.

So while both these theories can offer a somewhat convincing story of how we got here, their fundamental assumptions imply completely different policy actions. And at that point it's basically a confused look and a "who knows".

Let's step back though and think about a "what if" scenario? What if the Fed had raised the interest rates and 'smoothed the euphoria' in the Minsky view or not lowered the interest rates and not caused the bubble in the Austrian view? Well, the most apt reference point here is that of Japan in the early 90's, which also had a real estate bubble (whether naturally occurring or caused by previous lax monetary policy on the part of BoJ). The Japanese Central Bank DID pop that one. And the result was ten years of economic stagnation. We've yet to see how the present situation unfolds and how it compares to that particular outcome.

Anyways. Where does this leave Mainstream Macroeconomic Theory (MMT), which is neither Austrian nor Radically Keynesian? Not applicable, irrelevant, out of touch? After all, in your basic MMT, too lax of a monetary policy just leads to higher inflation which then puts a drag on long term growth (Austrians also have this part). But bubbles and crises aren't a part of it. And inflation hasn't been a problem (yet). So yeah, for present purposes MMT doesn't seem to do us any good in understanding this crisis.

Is that a damning failure? Umm, yes and no. The 'yes' side seems pretty straight forward and basically that's what all the stuff written above is about. On the 'no' side, I think it's important to realize two things about MMT. First, it seeks to describe how the economy operates during "normal times", is in fact pretty good at that aspect (which is where it gets that first 'M' in its acronym), and it just happens that we aren't living in "normal times". Second, and relatedly, the MMT developed in particular historical circumstances and in response to particular historical events. And almost by definition, first-M-in-the-acronym kind of theories are going to change much more slowly than events on the ground. Theory builds on what came before it, it changes slowly, it is "sticky". It evolves rather than jumps. When the world goes out of wack that affects the direction in which the theory evolves but very rarely will it cause a complete overhaul of the theory (a possible exception: General Theory, the Great Depression, and the development of Macro itself). New ideas, new hypothesis, radical new explanations occasioned by crises and unforeseen events even when they seem plausible need to be tested by real life experience, filtered by repeated natural experiments and thoroughly examined on the basis of their yet unexplored assumptions. All this takes time and expecting MMT to be able to explain something unprecedented is like expecting your (fixed) capital stock to instantaneously adjust to its long run level in your basic growth model.

And this of course is what opens up the door for more radical theories like the two mentioned above. The thing is that even though both of them may be able to offer plausible stories about the current events, overall... well, overall, they're wrong. The Minsky "movements" of euphoria driven bubbles seem to be rare. Between 1987 and 2000 too be generous, and 1982 and the present to not be, the theory seemed to have next to no applicability. That's between 13 and 26 years where these kind of fluctuations just weren't there. Similarly, in the same time period, despite very widely different Central Bank monetary policies (or maybe because of it) the 'malinvestment' cycles don't really seem to be either.

When the crisis hits, yeah, you're gonna reach for the shelf and pull down the first bottle labeled "crisis theory" since that's what you need. But when there is no crisis you'll hardly notice that shelf and those bottles are there, and with good reason. Part of the difficulty here is that 'normal times' are, well, normal, while crises only come around once in awhile. This means that you will have a lot more data to test the 'normal times' theory and only a few observations which can be used to sort among possible crisis theories. So the MMT, which is, which needs to be, based on a thorough empirical footing is going to be based on all the data available for normal times and that is what it is going to explain well. But once a crisis hits it will be irrelevant since the observations of crises, within the context of that theory are pretty much bound up to be considered "outliers", being few, in between, and extreme. And being few, in between, and extreme these outliers are not even going to be particularly useful in figuring out which crisis theory is correct. And that's how both the Minsky view and the Austrian view can both wind up providing plausible explanations for what's happening now, even though fundamentally they are very different.

But like I said, when the world goes out of wack that can, and should, influence the direction in which MMT is evolving, even if it cannot make it instantaneously adjust to offer a good explanation. So here's my suggestion. Traditionally Macroeconomics is divided into two branches - Long Run Growth and Short Run Fluctuations. Perhaps the impact of this crisis on Macroeconomics-as-she-is-done is that it really should have three branches; Long Run Growth, Short Run Fluctuations and Crisis Managment. As it is currently, crises, of whatever kind, don't really have much of a place in either LRG or SRF though there is some exceptions/precedents (Krugman's (and others) currency crisis theory for example. Or the whole 'coordination game' approach. All in all, the point is that these approaches probably could use a greater emphasis within the general Macro framework ). This is why MMT doesn't have much of an explanation for all this mess, and why you got to reach for the shelf with the 'extreme' (though not necessarily wrong) theories. Given that I don't think Macroeconomics is really capable of integrating 'crisis theory' into either LRG or SRF - particularly since it is not really capable of integrating these two approaches themselves, whether out of the inherent difficulty or just plain ol' unwillingness to try, something I've complained about before - the next best scenario might be that crises get their own sub-branch within Macro.

Friedman vs. Microfoundations

2008-10-22T19:10:00.000-07:00

MACROECONOMIST! Stand up, lend your ear, and listen! The very reason for your existence is under question once again (last link, only in the comments). It is said that you are no more than a subspecies of a superior form (can we please have a Google or some other search engine that is "net" of Wiki pages?), one which you should aspire too but have not yet achieved. Your discipline, your raison d’etre (well, I am going to use it as long as it's here), is called ethereal and treated like some aboriginal culture which needs to be civilized by those who claim superior status. This process has been well underway by well meaning but clueless colonizers for some time. And it is time. It is time you rejected their do-gooder inroads, their insistence on assimilation, and the patronizing misunderstandings they carry before their Gods as offerings. Their temptations of Maximization (seriously, if maximization was all there was to 'microfoundations' shouldn't we all be studying evolutionary models anyway. That's a critique of both btw). Their phony Dynamics which were always implicit in your own dogmas. Their substitution of ritual for true hermeneutics.

What have they brought us? It is true that our texts were fallible. And it is true that, in the beginning, their critiques shone light upon our misunderstandings. But we mistook a lighting of a candle for a conflagration of divine knowledge. And ecstatic with a small dose of illumination we threw our books upon Savoranola’s fire. Even Michelangelo himself threw his Madonnas onto the pyre (find a relevant link yourself. All I get is wiki).

Yet in end, their promises fizzled once the glow of the ambers died. Having abandoned our faith we were left with trying to build a house out of ashes – micro founded ashes – rather than ad-hoc oaken beams. It is time. It is time we returned to the practical knowledge which had allowed us to built a shelter, no matter how shabby, but which could stand up well in the hail storms, even if we did not understand the engineering principles involved. A good pool player knows how to sink the final ball in its pocket at the end of the game, avoiding the eight ball. The knowledge of the laws of physics is immaterial. Perhaps if the game was played on a table with no friction our detractors would have had something useful to say.

But we have been in the wilderness for a long time. We are weak. It is the truth and let us admit it, our spirits have been starved of intellectual substance for some time. And they may be for some time yet. But our path is righteous. And if we are going to ever get back upon it we need to first assert our own existence. We are MACROECONOMISTS! We have insights which cannot be derived from the cult of Some-kind-of-Maximization-somewhere-by-somebody-for-some-reason (and who knows who or what) = Microfoundations.

MACROECONOMIST! Stand up and listen because you need a weapon. A holy weapon! Or an unholy one perhaps! One forged in the fires of battles of yore’. One, which even the detractors fear. One, which they claim to worship as much as we do. Only the cold steel which is mutually respected can shatter their sanctimonious presumptions. Too many times, too many battles, have the detractors fought against faux foes with their faux epees. Yet, those easy skirmishes have dulled their senses. Since we both have arisen from the same Promethean fire, in order to strike at our brothers’ usurpation we need that which contains our mutual essence.

And here I will give it to you, that sacred weapon which can turn the tide. The task will not be easy, but if we are to persevere it is necessary. You, each one of you, will need a printer. An ink jet or a laser jet, it matters not which. Some stock of paper, the heavier the better. Turn on your printer, oh MACROECONOMIST! Let the incantations begin.

First, you will need to download this file, although it is quite possible that you may have this ancient text in your archives already. If so, retrieve it! Next, comes the mystical part of forging words into weapons. Take the essay, convert it into a text file through whatever magic you are suited to best. Once it is in a text format, the hardest, most tedious, most excruciating part begins. What you need to do, OH MACROECONMIST, is to format the text so that each letter of the mystical incantation corresponds to only one page. That is, one page = one letter of Friedman’s “Essay in Positive Economics”. All in all it seems there are about 10,135 words in that essay. Assuming average word length to be about 5 letters that amounts to 50,675 pages. I know, I know, it’s gonna cost you a lot of printer ink, but come on, this is a mystical weapon we’re talking about. Print that sucker out. And then wield it.

Your next task, OH MACROECONOMIST, is to seek out your foes. Attend a conference and purposefully present a paper which is just pure Macro. If need be, put a Phillips Curve in it. And then wait for your adversary, your prey, your would be patron, to ask you about … microfoundations.

Raise your ancient mystical weapon! 50,675 pages of Friedman. They will cower upon its revelation. Do not be afraid of your own wrath, let not mercy enter into your heart!. If need be, think of Charleston Heston smashing the Tablets of the Covenant in 10 Commandments or of William Jennings Bryan being crucified upon the cross of gold in that cartoon Macro Principles books always include! But strike down hard. Slap that faux-macroeconomist who insists upon microfoundations with your fury.

Smite!

Smite!

Smite the microeconomists who say that macro is but a sub field of micro. Smite them with your 50,675 pages of Friedman, which say:

Misunderstanding about this apparently straightforward process centers on the phrase "the class of phenomena the hypothesis is designed to explain." The difficulty in the social sciences of getting new evidence for this class of phenomena and of judging its conformity with the implications of the hypothesis makes it tempting to suppose that other, more readily available, evidence is equally relevant to the validity of the hypothesis-to suppose that hypotheses have not only "implications" but also "assumptions" and that the conformity of these "assumptions" to "reality" is a test of the validity of the hypothesis different from or additional to the test by implications. This widely held view is fundamentally wrong and productive of much mischief. Far from, providing an easier means for sifting valid from invalid hypotheses, it only confuses the issue, promotes misunderstanding about the significance of empirical evidence for economic theory, produces a misdirection of much intellectual effort devoted to the development of positive economics, and impedes the attainment of consensus on tentative hypotheses in positive economics.

Now, just substitute "microfoundations" for "assumptions" and your weapon of great power is ready. It is not the assumptions of a model that matter. And THAT, you freakin’ monkeys (this is spoken in an ominous Friedman voice, not my voice, I’m just channeling here you know), applies to macro or micro assumptions. It is how good the model is at actually describing and predicting reality. One can have a macro model founded on good micro foundations predicting crap. Like all these “puzzles” that generate papers in present day macroeconmics without ever wondering “hey! Maybe it’s the assumption of complete markets that screws everything up!”. Or one can have a perfectly good macro model, reduced form and all of that, no worry about microfoundations, which predicts stuff that actually happens. Why have you forgotten? Why? Why? Why?”

----

All I’m saying, 50,675 pages of Friedman outta be enough to convince any neoclassical economist.

----

In trying to link to relevant stuff in this post, it occurs to me that the whole freakin' problem with Wikipedia is not enough supply (or substitutes) rather than too much demand. That and deviation from median person's preferences. Really, detailed info on Savoranola just really ain't there on the internets just like it's he/it's not something/someone you can just bring up in a normal conversation. Wiki gets criticized for having too many goofy articles on whether Skeletor had ears or not but honestly, that's what people wanna read about. Nothing wrong with that, though personally I'd rather read about Savoranola. But you gotta take the good of the capitaleesm with the bad of the capitaleesm. Same thing for democracy.

Obligatory Post on Krugman's Nobel

2008-10-13T13:59:00.000-07:00

In Econ Grad Student Lore (which is as often false as true) it is said that when Maurice Allais got his Nobel prize he said "About freakin' time!", or at least something close to that, maybe in French. Paul Krugman actually seems genuinely surprised to have gotten one, but I'm with Maurice on this one.

Oh yeah, I've never met Krugman (though I've met some other laureates. George Akerlof in particular seems like a very nice person) but I did pass him in the hallway at the AEA meetings when I was on the job market. "Hey that guy's Paul Krugman!" I thought to myself. And then; "Wow, he's sort of short".

Additional thought (added later): And yeah, Krugman was the economist that got me first interested in economics with his popular books. But I expect a lot of people are going to be saying that now (and some of it may be true).

You know those charts which graph your political ideologies in a two dimensional space?

2008-10-12T04:07:00.000-07:00

I was trying really hard to write a post on how Macroeconomics should, should not, has, and has not been done. It got long. But in the process of trying to organize my thoughts I drew this graph to help me think. In the end the graph was better than the long winded rant, so I dumped the post and kept the graph. Not as good as XKCD but the self reflection did illuminate some surprising things I never realized about myself before. I am really, really, really bothered by Platypusai.

Click to enlarge and all that.

Please note that if you were try to draw some indifference curves through that creepy/cheesy space, you'd get to the problem of non convex preferences, and possibly satiation point, very quickly (I'm not sure of what I'd like more of; Uriah Heep or Alaric the Visigoth).

UPDATE: This one's updated to be more about economics:

The "Sweeteners"

2008-10-02T13:43:00.000-07:00

So after voting "no" before, enough lawmakers might now vote "yes" on the new bailout plan because:

1. Mental health provisions in insurance plans.
2. State and local sales tax deductions.
3. Subsidies to rural counties
4. Relief for victims of natural disasters
5. Business tax breaks
6. Energy subsidies

and all that for a measly 120 billion on top of the 700 billion already in there.

So, ok, raising the FDIC limit to 250,000 may be a good idea in the present circumstances. But other than that, what 1-6 above have in common is that

THEY HAVE NOTHING IN COMMON WITH THE FINANCIAL CRISIS!!!!!!!

(and did anyone notice how in the debates McCain kept referring to this situation as a "Fiscal Crisis"? No John, a "Fiscal Crisis" is when the government's broke and can't borrow. What we have is a "Financial Crisis". Two different things, buddy. I know, I know, he's not the only one confusing things.)

Alright, so maybe you gotta cut some deals to pass the darned thing and that's where we get the above. But the list also reflects how seriously our lawmakers are taking this plan - basically, who cares about the plan itself, let's see how many pet projects we can coat tail on it. If you want those things, fine, but try to get'em passed when there isn't a big crisis going on. If the plan sucked before it sucks worse now.

And of course there's this whole thing about how the taxpayers will not actually have to pay the 700 billion (I'm assuming that no one's been brazen enough to argue the same for the additional 120 billion but who knows), and hey, maybe they'll even make a profit. Whoa! Government makes profit for the taxpayers! Hey, why didn't we do this before? Why not in fact, do it all the time, crisis or no crisis. I mean, Profit's good! With a bailout plan every year, pretty soon the government will be able to close that deficit and pay off the debt. I know, I know, I'm being uncharitable, but the amount of crap that we're being told on this whole thing is overwhelming and it's almost enough by itself to oppose it.

Economic Logic is also mad. (via Gabriel)

Here's Casey Mulligan on the lack of the link between Wall Street and Main Street.

UPDATE: Here's Ken Rogoff, via Mark Thoma:

"Does such nitpicking fail to recognize the urgency of fixing the financial system? Isn’t any plan better than none? I, for one, am not convinced. Efficient financial systems are supposed to promote growth in the real economy, not impose a huge tax burden. And the US financial sector, in greasing the wheels of the real economy, has been soaking up an astounding 30% of corporate profits and 10% of wages. ... Isn’t it possible, then, that rather than causing a Great Depression, significant shrinkage of the financial sector, particularly if facilitated by an improved regulatory structure, might actually enhance efficiency and growth?"

Free Clay Davis!

2008-10-01T20:22:00.000-07:00

I know, I know, Economics.

Anyways, the DVD of the 5th season of the Wire arrived and I've been re-watching it (and apparently it just ended airing in the UK - this one's a ping back). One scene/development struck out which I haven't noticed before.

So you know how Herc 'steals' Marlo's cell phone number from Levy's Rolodex which he then passes on to Carver making the (illegal) wiretapping of Marlo by Lester possible (with some sketchy help from McNulty). If you read the boards (like at Television Without Pity - is there such a thing as a Wire-nerd?) while the show was airing, that one act on Herc's part was lauded as a single redeeming feature of an otherwise useless and incompetent existence (though possibly just coming up with the fake informer name "Fuzzy Dunlop" might also qualify).

Watching it again though, I got the impression that actually Levy purposefully set Herc up. So redeeming it might have been, but here Herc was also a pawn in a larger plan (i.e. as dumb as ever). Levy obviously knew that Herc lost his police job because of Marlo, Marlo rubbed it in when he saw Herc working for Levy ("ever find that camera?", "cost me the job", evil chuckle), and Levy could've realistically expected that Herc would try to get back at Marlo.

What's in it for Levy? Well, what suggests that it's a setup is that when Levy puts Marlo's number in his Rolodex he does so with great flourish, eyes Herc and then pronounces "I have a feeling Marlo's going to bring us a lot of business" and then explains that the fact that Marlo's using a cell phone means that sooner or later it's going to get wire tapped and that means a lot of extra work and pay for the law firm. He almost suggests to Herc that he steal and pass the number along so that it gets wire tapped.

Additional evidence: Marlo and Snoop and that third guy are first seen talking to Levy about that third guy taking a charge for someone else. Once they're done discussing the details Marlo tells Levy "take me off your clock". Levy looks annoyed and then, after Marlo leaves proceeds to set Herc up as described above.

Also noteworthy is that Clay Davis implies to Lester in the next to last episode that Levy knew about the scam he, Clay, pulled on Stringer Bell (with greasing the approval for Stringer's developments) and was in fact part of the con. So him setting up one of his clients, in this case Marlo, is not unprecedented. Principal-agent problem and all that.

Of course this show's so good that you sort of want to look for stuff that's not really there and read too much into it.

And I know that I should post something on the bailout and all but in fact I think this Wire t-shirt might sum it up perfectly.
There's also the one in the title of this post.

More Wire economics: when Michael suspects that Snoop is setting him up he goes to the meeting place early to observe the situation - just as Chris and Snoop taught him. Being young and car-less but not careless, he's watching Snoop from a taxi. After seeing what he needs to see he asks the taxi driver to take him somewhere else. The driver replies:
"I see no Medium of Exchange", after which Michael slips him a few bills.
Hey, that guy took a Principles of Macro class and remembered one of the functions of money!

Physiological Foundations of the Investiture Controversy

2008-09-21T14:47:00.000-07:00

Whenever I see "scientific" articles like this one (via Michael. ), which purport to document "innate" differences between conservatives and liberals (of course, usually ignoring the possibility that other political ideologies may exist) I think about how great it would be if we could gather up a bunch of psychologists and political scientists, stick'em all into a time machine and send them to... oh, I dunno, the 12th century, and let them study the people there.

Then they'd write an article with an abstract like this:

Support for Pope and Emperor Varies with Physiological Traits

Although views on the Investiture Controversy have been thought to arise largely from individuals' experiences, recent research suggests that they may have a biological basis. We present evidence that variations in support for the Pope vs. the Emperor, correlate with physiological traits. In a group of 46 adult participants with strong allegiance to either the Guelph or the Ghibelline faction, individuals with measurably lower physical sensitivities to sudden noises (like Church bells) and threatening visual images (Dragons, Saracens, washing oneself with water) were more likely to support simony, mundus, Phillip of Swabia, agricultural interests and capital punishment, whereas individuals displaying measurably higher physiological reactions to those same stimuli were more likely to favor auctoritas, ecclesia, Lombard League, Otto of Brunswick, mercantile interests and capital punishment. Thus, the degree to which individuals are physiologically responsive to threat appears to indicate the degree to which they advocate policies that protect the existing social structure from both the (external) existing social structure and (internal) existing social structure. Or at least favor Pisa over Genoa.

Of course the main benefit of this experiment, aside from the extra addition to our knowledge of social phenomenon, would be that we'd get to leave all those psychologists and political scientists in the 12th century.

UPDATE: Here's Reason's Hit and Run on the same study. Some of the comments are pretty funny.

What should the Top Unsolved Problems in Economics Be?

2008-09-16T21:05:00.000-07:00

This one's straight up for the econ geeks and it is a bit old, in internet time, but I've been busy so I'm just getting around to commenting on it. Mike Moffat points to the Wikipedia list of "Unsolved Problems in Economics" and says that while he likes the idea he's not so sure about the choices made by the Wiki community. I hold a similar view though for different reasons. Here's the list, without the commentary (which of course will come later):

* What caused the Industrial Revolution?
* What is the proper size and scope of government?
* How can heterogeneous production goods be included in a mathematically tractable intertemporal equilibrium construction?
* What truly caused the Great Depression?
* Can we explain the Equity Premium Puzzle?
* How is it possible to provide causal explanations using the purely logical constructions of mathematical economics?
* Can we create an equivalent of Black-Scholes for futures contract pricing?
* What is the microeconomic foundation of inflation?
* Is the money supply endogenous?
* How does price formation occur? Why do some markets achieve Pareto efficiency?
* What causes the variation of income among ethnic groups?

Mike appears to object to the fact that many of these questions don't really have a single particular answer. It is doubtful if the Industrial Revolution had a single cause. Or at least I think so and so does Mike. But I don't think that's a case for rejection - interesting questions often have multiple solutions, just ask the mathematician (ok, ok, that's a bit semantic). The job of economic researchers, particularly the empirical guys (guided by the theoretical gals), is to figure out the appropriate relative weights and likelihoods of various explanations. Maybe the Great Depression was 62% due to Monetary factors, 34% due to Animal Spirits 17% due to Real Shocks, 13% due to the radio broadcast of The War of the Worlds, and the rest we can ascribe to measurement error. We need to estimate those numbers.

But here's another Top, perhaps Unsolved, question - What constitutes a Top Unsolved Question in Economics (this is as good a place as any to link to this)? What criteria should be used?

There's the, possibly apocryphal, piece of econ grad student lore which tells of how D. McCloskey used to terrorize students which were unfortunate to have him (back then) on their dissertation committee with the "So What" question. Your assumptions could be realistic, your algebra pristine and your statistical analysis robust (without any reference to statistical significance). But you had better also be able to answer the "So What?" question. Or in other words, at the end of the day, why does the subject and the question posed in the dissertation matter?

I can think of three categories/criteria that I think are relevant here, listed in the increasing order of how I think McCloskey would've accepted them (i.e. the first probably wouldn't be all that satisfactory, etc.)

1. Some problems are intrinsically interesting and they excite human curiosity.
2. Some problems tell us something about ourselves and the, uh, human condition, even when they have no obvious practical implications.
3. The consequence for policy, and essentially for human welfare.

Now, I'm actually a lot more sympathetic to (1) than a lot, most even, economists would admit. Some problems are just plain ol' interesting to work on and it's just going be human nature to work on them. Additionally, sometimes no-immediate-practical-implication solutions to esoteric problems can turn out to really matter for everyday bread and butter (or so my Topologist friends tell me. Of course, they would say that, wouldn't they?). And as a former History student I've filled my head with all kinds of facts that really, I mean, really, have no bearing whatsoever on life as she's lived these days (that thing about being doomed to repeat History if you don't know it? Not true. You gonna repeat it whether you know it or not. To the extent that history does actually repeat itself. Which it doesn't). But perhaps History teaches us something about who we are... maybe. But lots of stuff does that and if that's all there was to it folks'd be right to scoff at History. No, lots of History matters simply because it is an intrinsically interesting area of study. And if Historians can study History for its own stake, then I'm cool with Economists studying Economics for Economics' sake.

(2) is essentially the whole reason we have the field of Behavioral Economics (of course (1) could apply here as well). Behaviorals deal with, essentially, the irrational or intransitive aspects of human behavior. And since it's impossible, almost by definition, to say what it is that irrational people really want, there's no clear policy implications (even ignoring the fact that these biases apply to governments and private markets alike).

This criteria/reason, in my opinion, is a worthy endeavor as well. In some fundamental sense it's what got those pre historic humans on the Savannah 100,000 years ago thinking about stuff - stuff as in more than survival - and what of course has culminated in this post right here. Or maybe that's actually do to some genetic mismutation (or "malmutation" if you're an Austrian).

But you know what I mean; the wondering about who we are and how we are has had many culminations and one of those has been the very existence of Social Science itself. That and the existence of "America's Next Top Model" (can't bring myself to put in a link for that one).

Of course (3) is the obvious one so let's be brief. But it is actually surprising how often we forget about it. And - here's where I move to the actual discussion of items on that list - one thing you'll notice about the Wikipedia numbers is the almost complete absence of Growth and Development topics. I mean, the reasons for the Industrial Revolution and the variation of income among ethnic groups (why the hell is that word "ethnic" in there? Why not "national"? Or just "groups"? Or better yet, why not just "individuals"? I actually suspect some subtle (racist) POV pushing here) are somewhat tangentially related. And "proper scope for government" might have big implications for human welfare but in this particular case Mike's right in that the answer is 92% subjective, 13% objective, with the rest being the sum of our ignorance.

There's actually a fairly widespread bias in Macro in studying stuff that doesn't matter that much for human welfare, in relative terms - economic fluctuations (yes, even in these dark times) - though some (via Gabriel) have pointed this out. And this list's along the same lines.

Take the "Can we create an equivalent of Black-Scholes for futures contract pricing?" problem. I'm sure it satisfies (1), if that's where your kinky inclinations lead you. If you really push it you could argue that it would tell us a bit more about how this one sub market (futures) of a sub market (derivatives) of a sub market (financial assets) in a sub market (developed countries) works and that bit of knowledge teaches us a bit of about ourselves and fits in with (2). Just maybe you can generalize it to some other facet of observed phenomenon. And then you can pat yourself on your head.

The "Equity Premium Puzzle" does fit in with (1) (if you ever start thinking about it it'll get in your head for awhile) and (2) (since it has to do with risk aversion and related phenomenon) and it maybe, in its general implications, rather than the narrow focus on the US (or developed country) stock market have some modest implications for welfare. But... personally I think the Equity Premium Puzzle has already been solved (in fact I think Reitz had it back in '88. This may be one of those instances where the crietria (1) is so strong that folks are loath to give up on such a fun, productive and paper-generating research topic, despite the fact that there may be not much left there.

So, in my book, the list fails, not because the possibility of multiple answers to complicated problems, but quite simply because most of the items on the list don't really answer McCloskey's "So What" question satisfactorily. Most of them probably satisfy (1), a fewer number (2) and only two or three (IR, GD) have serious implications for human welfare.

In interest of being constructive and not just critical I'm gonna throw up my own (actually it's also Robert Lucas') "Top Unsolved Question": why are poor countries poor and what can we do about it? I think that one satisfies (1), (2) and (3).

Europe travels - monetary economics

2008-09-07T23:52:00.000-07:00

I've spent the last month traveling across Europe. That, and some other stuff has kept this blog fairly quite. Anyway. Here's some observations on how this Money thing works over there.

1. Optimum coin to note ratio.
We started off in Britain. The thing about British money is that there's a lotta coins. In fact, all small and medium sized purchases involve change and change means coins. So you wind up with a buttload of coins in your pocket which, after awhile becomes sort of unnerving. They jingle more than you'd like. They're heavy. They tend to fall out of your pockets when you pull something else out, like a lighter.
So of course you try to get rid of them, paying in multiple coins when you could pay with a 5 pound note or something. But this does not work. Because the prices tend to be quirky as well (something along the lines of the super annoying x.99 cents pricing in US). All that does for you is get you smaller denomination coins - five and two pences - which you receive as change, instead of getting rid of the annoying little discs all together. Soon enough you wind up with a pocketful of jingly small denomination coins that neither you, nor the merchant you're transacting with wants. Your only option is to annoy the merchant by purchasing a few-pound priced good with 2 and 5 pence coins. Understandably quite a few of them refuse.

Then we went to Poland and the Czech R. There local currency still triumphs. But there is a particular social norm left over from the bad old days - everyone insists on exact change. It used to be worse, I remember going back in 96, purchasing stuff worth something like 17.85, handing over a 20 zloty note and being told "This ain't America brother, exact change please!". Now most places just ask you for it but enough of them will reluctantly make change if it is not too bothersome. This whole insistance on exact change however has the perverse general equilibrium effect that hardly anyone ever has exact change. You end up carrying very few coins and small denominations (since you've used it up satisfying the exact change requirement) and all kinds of large bills. Everybody hordes the little denomination coins - in the complete opposite of UK - and those go out of circulation. So it's not uncommon for merchants to tell you "I can't make change for that, go find somewhere else and break down your money". And this isn't some kind of one off transaction we're talking about but just your regular grocery, newspaper, beer buying. And there's obvious transaction costs to that, the very ones that the institution of money is meant to alleviate.

The Euro seems to have achieve that nice middle ground between excessive coins and lack of them. There's still some inefficiencies related to weird pricing but like in US, most of these could be eliminated simply by phasing the very small coin denominations out of circulation.

Yes, get rid of the US penny PLEASE and get rid of the analogous denominations for the Euro.As for UK and Poland, well, it's gonna take some time.
Persistence and all that.

Question for the Theorists

2008-06-25T01:47:00.000-07:00

all the hoopla

Where would you like to see your favorite piece of Economic Theory in, say, 50 years time? If you're into the General Equilibrium thing what kind of progress do you think needs to be made? If you're a Game Theory fool, what else can be said? Where is DSGE going to go that doesn't involve just another tweak of parameters/assumptions that we all only half heartedly believe in? I'm not asking for specific theorems (or applications)... well, maybe for conjectures. More along the lines of a road map. Not quite like Hilbert's program because I'm sure we all can agree that would be asking too much at this point. But a goal. What would an ideal economic methodology look like? At least in a specialized kind of way, within your favorite approach?

Ok, ok, it is possible that there may be some who think that their preferred method, whatever it is, already describes actually existing economies, Sraffa Shrugged and all, and nothing more needs to be said. I'm asking the other peoples.

And mind you, this is meant to be a question for the theorists. So answers like "we will be able to model agent learning better" are not satisfactory since they deal with a specific problem within a methodological approach (mostly DSGE in this case) rather than the big questions that have been forgotten in these past years. If it's about learning, for example, than it's gotta be something that criss crosses the methodological approaches.

We can bring in the applied folks in on this (of whom I am one, just sort of keeping an eye on the theory as I think all applied folks should) - what kind of theoretical results do you think would have a big impact on that Kudzu sub field of economics called "Applied Micro"? In the sense that it would stop a lot of people from doing it. As long as we're on this topic, what is your Bayesian estimate of the optimal ratio of theory to empirics? In our hearts of hearts, that little place where our irrationality resides, we know that "there's no theory without data"! Of course in our soul of souls we also know that "empirical work unbacked by theory is just data mining"! But if you leave those special places then you do realize that - since we're all economists here - it's probably an interior solution. So what's the break down? Gimme a number folks.

(As an aside, I'm sort of pessimistically rooting for the whole Agent-Based-Modeling approach. Rooting for it cuz I think it does have potential - integrate it with standard GE! And maybe it can get at some of the questions that Alex keeps asking about dynamics and so on. Pessimistically because even at this early stage (and my knowledge of the field is slightly greater than epsilon) I think it seems pretty obvious that it's bound to run into all the standard problems of other methodological approaches; indeterminacy, arbitrariness (there's a million ways to be heterogeneous. Why pick a particular one?) and ultimately, well, hopefully, generality.)

Americans are right - soccer is a ridiculous game

2008-06-12T14:35:00.000-07:00

"the ball bounces around randomly for about an hour an a half, then suddenly it hits some guy's head and accidentally goes into the net, everybody goes crazy, and somebody's lost really bad and somebody's achieved a great victory" - a paraphrase of an American columnist, possibly PJ O'Rourke, describing their attempt at trying to appreciate soccer, done from memory.

Austria:Poland - 1:1

The setup: Euro 2008. Poland has lost to Germany. Austria has lost to Croatia. The looser of the Poland/Austria game is eliminated from the competition. Austria dominates for first 30 minutes. The Poles get a lucky, though very elegant goal ... which might have been an offside (similar situation occurs in the Poland-Germany game with Poland the worse off). Energized by the goal the Poles control the rest of the game although they do not manage to score again. In the 92nd minute, at the very very very end of injury time, the ball is kicked into the Polish penalty box and an Austrian player very clearly either slips or takes a dive. The referee awards a spurious penalty kick to the Austrians which they take advantage off to tie it up. The Poles, or at least this one, feel totally cheated and for all practical purposes both teams are eliminated.

In American football, basketball or baseball, a bad decision by a referee will give one team a slight advantage (in critical situations perhaps a crucial slight advantage) in terms of winning the game. In soccer a bad decision by a referee not only can very easily determine the outcome of a match but in many cases the entire standing in a group/division and even advancement to the next round (i.e. play offs). There are huge discontinuities in terms of the marginal effects of a referee's decisions.

To be exciting games we like to watch and play need a mixture of uncertainty and reward to skill and effort, unless one's a gambling sort who thinks that roulette is an intellectually sophisticated game. In this respect however soccer is worse than pinball. True, skill plays a role - you can rely on Argentina to beat up on The United Arab Emirates every time. But if the teams are even remotely evenly matched in terms of the randomness/skill content it's not even a pinball game. It's a pinball game with broken flippers, a roulette wheel where a referee occasionally decides to magically and arbitrarily move the silver ball closer or farther from the number you picked.

The great power wielded by the referee and the impossibility of double checking his decision (by design, since the technology exists to do this and American Football, for example, has managed to implement it successfully) also creates great potential for corruption. And any honest assessment of team sports is pretty much bound to conclude that FIFA and its various national counterparts are rife with it. From how locations are chosen, to how groups are selected, to how matches are adjudicated.

In addition to corruption there's other problems that this huge amount of uncertainty combined with power of no appeal on part of the refs creates (in addition to the fact that soccer refs are the least respected among their type/proffesion across the sports). First there's an obvious incentive for players to learn how to "game the ref" rather than focus on skill - the dives, the fake injuries, the prima donna acting that characterizes many a "star" team. Second, since with this much uncertainty it really is hard to objectively rank teams in terms of their skill, the all to human referees come to rely on certain rules-of-thumb, strength of tradition, and "I think thats right because it seems to have been right in the past". Germany, Brazil, Argentina, Italy win because... well, they're supposed to win, particularly if in terms of fundamental objective skill the game's close.

Of course this begs the question - why is soccer popular in the rest of the world, but not so much in US? Here everyone's got their favorite answers which either boil down to assertions that Americans are too crude and brutish to appreciate the grace and beauty of the game, or, on the other side to mistaken assessments that "soccer is a game for teenage girls" (as anyone who's ever played it knows, soccer is as physically demanding as American football, probably more than basketball, and certainly more than baseball). But the simple truth is that it's all about tribalism - in its national or regional forms. Without the tribalism the game of soccer looses most of its appeal. It can best be seen as either a very beautiful excercise in synchronization -in which case it should be judged in the same way as ice skating competitions and water ballet. Or as a simple spin of a roulette wheel. Or perhaps both - a spin of a very beautiful, ornamented and elegant roulette wheel.

And US is a very non-tribal place. While some folks in the South may still smart about those damn Yankees, for the most part a Wyomingian, or a Rhode Islander tend to have fairly weak connections to their place of residence. This is compounded by the fact that often times, for real tribalism to be strong, a Nebraskan-of-Guatemalan-origin would have to feel very strongly about Nebraska, a Delawerian-of-Vietnamese-descent very strongly about Delaware and a some white bread Oregon hippy about Oregon. To be sure, these kinds of feelings do exist but compared to ROW they are very muted, for fairly obvious reasons.

The outcome of the Austria-Poland game wasn't even that unfair. Both teams played well and they were ... evenly matched. Both goals had a good bit of arbitrariness about them (though of course I think the Poles were "border line offsides" when they scored their goal whereas the Austrian penalty kick was clearly undeserved). But the game was a really good illustration of why soccer is a very ridiculous sport.

Some notes:
1. American College football competition actually shares some of the defects of soccer competitions - mostly due to the institutional design where the (top 25) winners are chosen by voting by folks who obviously have vested interest in the outcome. And given the large number of college football team you get intrinsic intransitivity (haha - alliterative joke alert) - A beats B, B beats C, C beats A, so who's 1st, 2nd and 3rd?. As a result, much like refs in soccer, the NCAA voters choose teams who are "supposed to win" (or in this case, be ranked high) even when facts on the ground - given that there's room for interpretation - speak otherwise. So USC, Florida, Ohio State ... a few others ... are pretty much always guaranteed spots in Top 10/Bowls even if they get stumped once or twice by gutsy underdogs (which actually happens quite often in college football, which makes it more exciting than soccer (which is too random) and NFL football (which is too predetermined)).

2. I don't mean to imply above that there's a HUGE amount of corruption in soccer competitions, or in particular in regard to this particular game. I don't think the ref was "bought" or even incompetent or anything like that. I do think there is enough corruption in it, created by the nature of the incentives of the game as she is practiced today, and enough uncertainty which makes this corruption possible to pretty much make it a coin flip.

3. I got a post on the difference between games that we enjoy playing and watching and the games that game theorists analyze coming up, but I think I need to cool down a bit. Go outside and smoke three more cigarettes in a row or something. So later.

4. Sorry, Michael, though I don't know if this is your thing.

5. Also note that what American Football, Baseball and Basketball all have in common is that there's a lot more "points" scored in each game than in a soccer game. From point of view of Economics of Sports this makes a lot sense. If each "point scored" is a random draw from some distribution (which could favor one team over another) then with the absolute outcome of a game depending on a large number of points scored that outcome is more likely (by sort of wavy-handy law of large numbers) to reflect the "true" underlying skill of the two competing teams. Of course if the number of points required/time allowed is too large, then not only do we as spectators loose our attention span, but the outcome becomes too predetermined. You want some variance in there to make it exciting. But soccer's got too much of it.

Remittances

2008-05-31T21:41:00.000-07:00

For a while there it seemed like "Remittances" were going to be the next big panacea in development economics. You know, you've all heard the stories about how Haiti's remittances are more than 100% of its GDP or how remittances trump the flow of private foreign aid in Uzbekistan, or how in Lilliputan nobody works anymore, they all live off remittances now.

And there's a lot of truth in that in the sense that it's definitely a phenomenon that is of a magnitude that begs for careful study. But honestly I've actually been a bit disappointed with a good bit of the relevant literature.

On one hand you've got the remittance cheerleaders who extol the great virtues of these cross border transfers. They're actually right to do so in fact but they tend to miss the point - I'll explain what I mean in a second, and in fact that is what this post is all about. On the other hand, it's almost too easy to say "hey, poor people are getting sent money now so they're better off". So people look for "counter intuitive" effects of remittance flows because "counter intuitive" effects are all the rage these days. As a result you get a somewhat sizable literature on the moral hazard effects of remittances. For example, this IMF working paper takes this position. The New Economist blog discussed similar results awhile back here (and btw that is a really good blog). The basic idea here is that when workers in destination countries send money back home to grandma in Azerbaijan, grandma doesn't work as much anymore... ha ha you foolish grandson, grandma got one over on you!

So let's dispose of the latter, "Remittances are bad" argument first since that's more straight forward. The basic problem here is that it doesn't pass the common sense test. Yeah, of course when folks send money to their grandma, she'll work less. That maybe the whole point. In fact, based on personal experience of a family which has sent much money back to the old world, this ain't "moral hazard". Quite simply, it's remittances doing what they're supposed to do. And while it's definitely possible to set up a model where it is moral hazard which leads to a decline in labor supply of remittance recipients, it is even more straightforward to set up a model where a fall in labor supply is the purpose that the remittance sender is trying to achieve. Since, empirically, all we observe is that (sometimes) labor supply falls when remittances go up there really isn't a way to distinguish between these two models and it certainly is no evidence for the "moral hazard" story.

Also, please note that the paper linked to above develops a model where an increase in the LEVEL of remittances is supposed to generate a decrease in the per capita growth rate (under some assumptions). Yet, the researchers find no evidence of that so they skip very quickly to a regression of the effect of the CHANGE in remittance flows on the level of growth. Which is a different thing all together. (pg 18 for model specification. I'm not sure what the offered explanation: "This specification better captures the dynamics of private transfers" actually means in this context. Table 4 shows the lack of relationship between level of remittances and growth. Table 5 shows the fudged model where there is a negative relationship between change in remittances and change in output (could it be that when output grows faster, wage differentials get smaller, so there's less of a need to send remittances?).

Ok. But what about the argument that remittances are all biscuits and gravy with tiny bits of sausage in it? Welllll, no. Sort of. I mean, yes, but, let's think about things more carefully here. (This is basically the gist of this WB report, which doesn't mean that agree with everything in it)

Bottom line is that most of the so called "gains from remittances" are straight up gains from IMMIGRATION. Or in other words, they are gains from the fact that some person from a poor household in a poor county has managed to make their way to a rich country and now has a richer income. Strictly speaking the gain from remittances is just the gain from INTER-HOUSEHOLD reallocation of income between the migrant and those who stay behind, not the overall increase in household income due to migration.

Let's illustrate this with some standard econ graphs. Take a household which is comprised of two individuals, say, brothers. And suppose that initially both brothers live in a poor country where they both earn the poor country wage of W(P). Now, we're going to take "household utility" as out metric here, and assuming that each brother's utility has diminishing returns to income and that each brother cares about the other we basically get that the two brothers should divide their total income (2*W(P)) equally between themselves (this is sufficient, not necessary. All we need is that there is some altruism between household members here). This is illustrated in a standard budget constraint/indifference curve below, where the utility of brother 1 is on the x-axis and the utility of brother 2 is on the y-axis;

Now suppose one of the brothers has the good luck to be able emigrate to a richer country where he earns the wage w(Rich). If there is no possibility of remittances here what is the highest utility level that the two brother household can attain here? Welp, it's represented by the indifference curve which crosses the new endowment point;

But we got that new blue budget constraint there - which illustrates the possible income/utility levels which are attainable IF there is a costless way to transfer resources from the lucky immigrant brother to the unlucky stay at home brother. Hence, if remittances are allowed the household will be able to reach a higher utility level as illustrated below;

Given all that we can actually decompose the benefit "from remittances" into that which is due to immigration of a particular household member and that which is due to, well, actual remittance flows:

All that basically means that the observed benefits from remittances that people rave so much about are mostly just straight up benefits from LABOR MIGRATION. Which are huge, but somehow that just isn't being said.

Now. I actually think the pure gains from remittances (moving from u2 to u3 in the graph above) are actually quite substantial as well. But it is important to keep two things in mind here:
1. These gains would not be possible without the migration of some household members in the first place. Hence, the ability to MIGRATE is a necessary condition for the REMITTANCE benefits to take place. The graphical analysis above misses this fact but it's there.
2. The size of the two effects are complementary. The bigger the gain from migration, the greater the disparity between those who migrate and those who stay behind. If there is diminishing returns to income, this means the gains from reallocation from the lucky migrants to those who stay behind are greater as well.

But all of this seems extremely simplified. I'm basically assuming that all these wages that people make are just consumption. But a strand of this literature emphasizes the fact that remittances can serve as basis for capital for households in poor countries. Something like; the lucky immigrant sends money to your grandma back in Lesotho and she invests that and starts her own business and boom, growth in Lesotho happens.

Again. There's some truth to that. But there's also problems with that kind of logic. First, we can take the above analysis and extent it to some kind of a dynamic setting where investment today pays of in growth in the future. But we're not missing much (I actually think there's all kinds of good reasons for economists to stay with static models - very often there's a simple way to reduce a dynamic model to a static one). So let's say that the sending of remittances is not just a pure transfer of resources but it also increases the income of the brother left behind. Maybe it provides funds for him to invest in a personal business etc. This is basically a shift/kink of the budged constraint above, and only a change in our labeling of our axis from "one period income" to "lifetime income":

So yeah, there's some additional benefits there to be had if the household members back home are more credit constrained (in very broad definition of that phrase) then the ... migrants in destination countries ... ? But wait a minute! Does that really make sense? After all, if anything, the return to investment, just like the return to labor tends to be higher in destination countries than in source countries. If the return in the destination country is higher then why shouldn't migrant invest in a business in his new found home, make more money, and then send it back? A hot dog stand in New York will make an immigrant more money than a similar business venture back in Nairobi. So why not invest in "capital" in the destination country for the household as a whole rather than using up resources in a relatively inefficient (compared to what you can get in US or EU) start up venture run back home? And then send the proceeds back so that all can enjoy it?

Again. There may be some truth to the view that remittances can facilitate investment back home. Usually a successful investment requires a good amount of local/tacit knowledge. Hence a newly arrived immigrant might not be able to take advantage of the investment opportunities in the host countries. You don't know how to speak English so you can't take advantage of the high rate of return to investment in US. But, if you send enough money back to Moldova, your relatives back home (who know the local language and economy well) will be able to turn that money into a productive business.

Except that the difference in rates of return is too huge to really make that story make sense. Again. Yeah, sometimes. For some people. Occasionally. But on average the brother who has been lucky enough to migrate is also likely to be the one lucky enough to have more and better investment opportunities.

And all that means is that most likely the majority of "remittances" flows that we observe are in fact meant to facilitate consumption. In other words, they're there for grandmas and brothers in poorer countries to be able to enjoy a standard of living which otherwise would be unattainable. And if you increase somebody's income they might work less (since there's no change in the wages they face this would be a pure income effect). But that's a good thing. In a similar way, the recipients may not spend their received remittances on investment (rationally, since the return to these investments in typical home countries is low) but instead buy themselves a cell phone or just some extra food. Is there anything wrong with that?

Finally, two caveats. First, you might actually see a spike in investment due to remittances if these are used to finance construction of new homes. I remember visiting a village in my own home country in the early 90's and it seemed like everyone there was building themselves a new house. The typical explanation offered by the relatives was "they got family abroad". But of course this is more of a consumption of a durable good rather than "investment" as that word is commonly used.

Second, there might actually be additional benefits from remittances (to consumption) which are not captured above. The graphs above all implicitly assume that both brothers face the same price levels in host and home countries. But of course the Balassa-Samuelson theorem (which is well supported empirically) tells us that price levels are lower in poor countries. Hence a dollar sent back to Bolivia, when converted to local currency, can go farther than if that dollar were to be spent in US. The graph below illustrates this:

(There's some caveats and details here - basically it matters how you label the axis (utility or income) and what is the exact shape of each individual's utility. I was too lazy to redraw the whole thing and basically it works out as illustrated above).

Oh and by the way, all the above generalizes easily to the case where the household welfare function assigns unequal weights to the two brothers, or where the household is comprised of more than two individuals, only few of whom are migrants, and other possible extensions.

Economists and their non-Economics hobbies

2008-05-01T00:45:00.000-07:00

Keeping up with the theme of the last post.

So, Danny Quah kicks innocent wooden boards for the sake of global equality, and Kenneth Rogoff (former Chief Economist at the World Bank) is an International Grandmaster in Chess (and former under 21 US Chess Champion) (I recall seeing one or two of his games in the British Times a few years back as one of the "Chess puzzles"). William Baumol, as it turns out is a pretty good artist. Here's his cover of Thijs ten Raa's "The Economics of Input-Output Analysis" (thanks to Daniel for being enough of a pain to make me get that book):

Here's Baumol's art page. (www.econ.nyu.edu/user/baumolw) It loads weird, at least for me. Basically, you wait for it to load and then it disappears. But if you click on a particular (absent) image while it's loading you get it and then just navigate from there. I think the stuff is really good and it certainly looks fitting on an economics book cover - the one on the ten Raa book makes me think of people standing on the shoulders of other people in order to put something up, which makes me think of intermediate inputs into production and also fits in very well with the idea behind (some of) input/output analysis that ultimately labor is the only factor of production (i.e., as far as I can tell, none of them folks are standing on any machines, "neoclassical" capital). On the other hand some of the pictures on that website look like they loose something in the translation into a computer format or maybe Baumol got a little carried away with photoshop at some point.

The picture in the upper right of this blog, right under "About Me", is a portrait of Amadeo Modigliani. The non-economic Modigliani. Then came grad school, then came job, so maybe after tenure I'll have time to bust out the oil tubes again. Also, if you paint in oils you pretty much get it on everything, it doesn't come off, and you smell like turpentine all the time, which'd probably get you weird looks at conferences. Also at one point I had a 2000+ rating on Yahoo Chess, but that's Yahoo Chess.

Randy Wright, of the Search Models With Monetary Stuff In'Em fame, is a hesher and also has the Contractions.

Now everyone else needs to fess up. My suspicion is that Mark Thoma could track a butterfly in a snowstorm while living off of roots, berries and Oregon mushrooms.

Kung Fu Development Economics

2008-04-18T11:27:00.000-07:00

I just wanted to link to this post by Danny Quah, which in addition to being really interesting and informative (and helpful when you get into internet fights with people who assert, with no backing data, that the growth in China and India "has only benefited the rich there and multinational corporations") also has Kung Fu Development Economics in it!

(Alright, alright, I don't know exactly which martial art Danny practices (actually I think it's Taekwondo) but Kung Fu Development Economics just sounds, you know, TOUGH.)

In fact, just in general I wanted to recommend Danny Quah's blog which is excellent and which as soon as I get around to updating my bloglist I'll add there along with a couple of others (and some are getting the boot!)

Update: Yes, it's Taekwondo.

Malthusian Simulation

2008-04-17T17:34:00.000-07:00

The model in the simulation is as follows:

Per capita income at time t is

where A is land/technology, L is amount of labor and alpha<1. A grows at the rate g (possibly 0) so

Growth of population is births minus deaths or

where f is the crude birth rate (CBR) and m/m+y is the crude death rate. So here we're assuming that the fertility rate is independent of income (which isn't too much at odds with empirical evidence) and the mortality rate is a declining function of income. If per capita income is zero, everybody dies and if per capita income income is very very large then very very few people die. Each period.

That's pretty much the model and if we got numbers for the parameters we can simulate it. Some parameters, like the fertility rate we can get more or less from the data. Right at the start we can pick a value for alpha, or labor's share in output. Others we can pin down by using observed data and assuming that at particular points in time the economy is at its long run steady state. To do that we need to solve for it:

The change in per capita income from one period to next is given by

If technological progress is slow enough relative to rate at which the population adjustment takes place (whole another post - but the condition will be evident in a second) then in steady state per capita income will be constant even with on going technological progress. So dy=0, or

or winding that puppy backwards

where L(0) is the initial level of population (assuming we start out in steady state) and L(t) is our final level of population (assuming we end in steady state). So from that we can calculate/calibrate the annual growth rate of technological progress as

Then we calculate the steady state level of per capita income from the population growth equation:

solving for y (and dropping the time sub script since this is steady state per capita income) we have

where

from which you can also see the necessary condition for the steady state to exist (if g is too high then you will get ever increasing income) and with a bit of thought can also figure out the approximate rate of convergence to the steady state.

From this, if we know the steady state income at some point in time (basically you want to pick to points in time where income is the same and which are far enough apart so that any kind of transitory shocks, like, um, the Black Death, have time to sort themselves out) we can calibrate m, the mortality rate parameter. Alternatively if we observe a mortality level in what we think is a steady state year than we can calibrate the income. In practice the former turns out to be easier. In particular if we only care about the magnitude of changes rather the magnitude of levels (as in the previous post) we can just "normalize" the steady state level of income to 1 and see how much of a rise we can get in % terms with various shocks.

Then all that's left is to calibrate the initial level of technology which is easy if we have steady state income:

And that's pretty much it.

The nature of this calibration excercise and the model is that if we shock the model (by, say, killing off a third of population of England in 1350) and then leave it alone then it will be pretty good in matching the population data.

But this is pretty much by construction so it doesn't really constitute a "test" of the model. The problem, as noted in the post below, is that it is pretty much impossible to match the 100% increase in per capita incomes (or wages, but that might be even worse) that occurred between 1350 and 1480. Here's what it looks like with just an initial shock of wiping out a third of the population:

The fact that in the model the shock has an immediate impact on incomes while this doesn't happen until 130 years later historically is not that important. You know, sticky wages, market frictions and all that, means that we shouldn't expect an immediate adjustment. The important aspect is that at its peak income rises only 14.5% above its steady state level, rather than the 100% seen in the data.

Like I said below, you can try to mess with it in order to get those higher incomes;
1. Increase mortality rate or decrease the fertility rate. But then you'll screw up that nice match up of population data in the above graph, winding up with way too few people in 1570 and on.
2. Increase the technological growth rate. But then you'll screw up that nice match up of population data in the above graph, winding up with way too many people in 1570 and on.

Of course you can try a combination of these to try to match it up. Or play with the other parameters. That's why here is the Excel file used for the simple simulations (Thanks to Gabriel).

There was too much fluctuation in incomes in the Malthusian world.

2008-04-13T18:33:00.000-07:00

Updates:
In this discussion of Greg Clark's book a similar point comes up (among many others) but without the maths.
Another, um, blogger, links to this paper by Ron Lee (which is also discussed in the above ssha link). This is a JSTOR version but I think I recall seeing an ungated version somewhere which I'll try to find.

This particular graph from Clark's "Farewell to Alms" has been bothering me for awhile:

To see why, let's recap some of the basic ideas behind the pre-industrial Malthusian economy. According to Clark the Malthusian economy was characterized by:

1. Low growth rate of technology.
2. Per capita income at any point in time being a negative function of population size due to diminishing returns to labor which combined with standard "Malthusian pressures" in turn meant that over the "long run",
3. Fertility and mortality rates were the major, if not only, determinants of per capita income.

More specifically, in the context of the above graph we also have that:

1. There was little or no change in real wages between 1200 and 1800 in England.
2. The "hump", or the increase in real wages in England between roughly 1350 and 1600 was due to the Black Death (and the "little Black Deaths" that followed it).

In a qualitative sense (the sign and direction of changes) the Clark story actually matches up pretty well with the data, which is a good portion of the reason why the Malthusian model is a compelling description of the pre-industrial world. But once you start thinking about it, the quantitative implications (the magnitude of these changes) of the Malthusian model are quite a bit at odds with the data.

Specifically, the above graph of the real wages in England has two problematic features (and I'm gonna keep going with the numbered lists here):

1. A doubling of real wages as seen in England between roughly 1350 and, I don't know, 1480, as seen in the graph, is pretty much impossible in the Malthusian world, given some plausible parameter values. To get that order of magnitude would require either a very high rate of technological growth (ruled out by Malthusian Assumption 1) or a HUGE drop in population. Now, of course Black Death, which wiped out perhaps a third of Europe's/England's population at a stroke, may seem to the casual observer like a HUGE shock. But I mean really HUGE. In the Malthusian model (again, assuming some plausible parameter values) something like 7/8 of England's population would have to disappear at a stroke to double incomes. Even with an initial shock which kills 1/3 of population and recurring "after shocks" this pretty much couldn't happen.

The reason for this is that the very logic of Malthusian economy which relies on diminishing returns to labor (Malthusian Assumption 2) basically precludes this kind of an increase (given a reasonable estimate for labor's share in output).

2. The fact that farm laborer's wagers are higher than construction laborer's wages throughout the period. This one I'm not so sure about and folks with more knowledge of historical details may correct me at will. But, if one thinks of farm laborers as the workers located in rural areas and construction laborers as workers located in urban areas (of course this has to be true only roughly, on average) then the fact that the Black Death affected urban areas to a greater extent than rural areas is quite at odds with the above data series. If more city folk died than farm folk, then we should see a greater increase in construction worker's wages than farm laborer's wages. But if anything we see a rise in the farm/construction premium which also sort of implies a fall in the urban/rural premium - the opposite of what we would expect if the Black Death affected urban areas more than rural ones.

This particular criticism is weaker than the first one. For example it could be that an ongoing migration from the countryside into the cities (as was the case) equalized the wages between the two areas so that the mortality difference was "split" between the farm and the city and hence we really shouldn't expect any difference in wages between rural and urban workers in pre industrial England (I can write you down a model where this happens but I'm not going to bother right now). Still, the fact that the series implies a different outcome than the Malthusian model with a Black Death shock would imply is a bit troublesome.
In what follows I'm gonna ignore this second criticism (because a full Malthusian model with rural-urban migration is too messy for a blog post) and focus on the first one.

Alright, so what would it take for wages to double in the Malthusian world? In this world, at any point in time wages depend on the size of the population, land and technology level (and we ignore the role of capital since this is pre industrial world. See also Oxonomics on the work by Reed and Frazer, with h/t to Gabriel). Since the amount of available land doesn't change much (well, there's the Dutch and their "fake" land...) we lump in technology and land together. Specifically let the total output of a pre-Industrial economy equal;

where y(t) is per capita income, A(t) is a "catch-all" factor which includes land, stock of capital and the level of technology, L(t) is population and alpha<1 measures the degree of diminishing returns (if you got a market in land 1-alpha will be land's share in output).

So. How big of a shock was the Black Death? Or, in other words, how big of a shock - in terms of its affect on per capita income - was the wiping out of a third of population of England?

Not much. Because of diminishing returns.

Let y(bbd) be the income before the sudden unset of the Black Death and the y(abd) be the per capita income after the Black Death. We're not gonna be sticklers here and require that the 1/3 drop in population immediately translates into higher wages. But it should translate into the observed doubling at some point within the next 250 years. Can that happen?

Assume that technological growth is low (again, Malthusian Assumption 1) so that there's negligible change in A before and after the shock. Then the ratio of the after-BD and pre-BD incomes is given by

Since we're assuming technology growth is negligble this just comes down to the ratio of populations pre and after Black Death.

The key parameter here is alpha which measures the rate of diminishing returns to labor. If you've got a labor market then alpha will be the share of total output which goes to labor and 1-alpha the share that is "appropriated" by landowners. Standard estimates for land's share in the pre-Malthusian economy put it t somewhere between 25% and 40%. So let's pick a medium value of 1/3. This means that if population after the black death was 2/3 of that before the black death the ratio of per capita incomes pre and after would be 1.1445.

Or in other words, this "huge" shock - Black Death - would increase percapita incomes by only about 15%. Even if we take land's share to be a very high 50% that still gives us only a 22.5% increase in per capita incomes. Ay. Even with alpha close to zero, a 2/3 shock to population increases per capita incomes by 50%, not by 200%.

Ok. But you wouldn't expect the impact to be immediate and what about those "after shocks"? Perhaps a better model of the shocks would be an initial wiping out of a third or half of England's population, and an overall increase in the mortality rate. This increase would mean that not only would there be an increase in income initially, but also the "steady state" level of per capita income will go up as well. For example if the growth rate of population is given by

Then in steady state y=m/f, so y(abd)/y(bbd)=m(abd)/m(bbd), so all you would need is a doubling of the mortality rate (at initial level of income). If you want to get a bit more realistic a more plausible function for growth rate of population would be

since in this case the mortality rate is bounded between 0 and 1. In this case y=m*(1-f)/f, but with no changes in fertility, y(abd)/y(bbd) still equals m(abd)/m(bbd). Here the mortality rate wouldn't quite double (assuming that pre Black Death income was at its old steady state value and evaluating the mortality rate at that income means that the ratio of pre and after mortality rates would be 2/(1+f)). Close enough.

What does that mean? First let's consider how much would population have to drop in order to get that doubling of per capita incomes:

which means, that with no technological growth, one way or another (i.e. combining the initial shock to population with a higher mortality rate) you need population to drop by 7/8. In other words, for incomes in 1480 to be twice of those in 1348, the population of England in 1480 needs to be 1/8 of that in 1348. Which of course isn't what happened. In fact, English population in 1480 was slightly higher than in 1348 (about 4 mil compared to 3.5 mil pre Black Death)

But what if there was some technological progress in the intervening years, wouldn't it be possible for incomes to double in those 130 years? Well, if the Malthusian assumption that tech progress (which includes capital accumulation and land expansion here) is slow enough so that over the long period incomes stagnate (between 1348 and 1800) then most of that tech progress would just go into higher populations with only small, if any, impact on per capita incomes. But even ignoring that it's doubtful that tech progress was fast enough to generate these kind of magnitudes.

There's several ways to get an idea of why this won't work. First is to let the labor ratio between 1480 and 1348 be what it was - about 1.15 or just for the sake of argument, about the same (which makes it easier to double the wages), and ask how how much technological progress would be needed to double them wages.

Too skip more equation-editing in blogger let's just assume that 1480 minus 1348 is approximately 140 and then use the good ol' "rule of 70" (actually 72) in which case the time it takes for income to double is 70/g where g is the growth rate. So here this would imply a technological growth rate of about 1/2 percent per year. Compared to the modern world where we see tech growth rates between 1 and 2 % per year this seems paltry. But for the Malthusian world this is huge!

If we assume that England was at steady state in 1348 and again at a steady state in 1811 (i.e. all the adjustment to shocks like the Black Death and its aftermath has worked itself out in that period) then we can estimate the average annual growth rate of technology over the whole period from:

or a measly 0.00066=.066%

But even if technological growth was .5% per year you wouldn't see much of it show up income. Instead it would go into population growth. And in fact this technological growth is the very reason why you have 4 million people in 1480 rather than 3.75, or why you have 9.5 million around 1810 rather than 3.75.

You could keep finanglin' here. Maybe model the Black Death as an initial drop of 1/3 in population followed by an increase in mortality rates until 1450 or so, after which mortality returns to normal. Or maybe later than 1450. But this won't work either. What ends up happening is that you can either match the population levels (but for that you need essentially a stable mortality parameter, higher rate of tech progress won't do it) but not income levels, or you can match the income (with changes in mortality, after shocks to L) but not the population levels (if you increase m or periodically decrease L you will wind up with way too few people in England in 1480, 1601 and 1821.

Of course since this is historical, hence pretty imprecise data, you gotta give it a good bit of leeway. Still a doubling of wages is a lot more than a 15% increase in them so the magnitude is quite a ways off (like I said, I think qualitatively it matches up).

All of which suggests, that if you do believe the numbers in that figure at least somewhat, something else must've been going on in the period 1348 to 1480. Changes in fertility? Maybe, but here you'll run into the same problem as when you monkey around with the mortality rate - too few people if you want high enough income. Acceleration in technological progress during this time? But why 1348 to 1480 as opposed to 100 years later when Enlightenment is beginning to take hold? And even then, the dynamics of the Malthusian economy very strongly suggest that even this higher tech growth would not show up in higher incomes but get eaten up by higher population (you would way over predict population level in 1480). Land expansion? Same as with tech growth and remember that this is before the discovery of the new world? Maybe a change in the share of output going to land and labor respectively - alpha? I wouldn't rule this one out, actually.

(alpha is one parameter that economists don't like to mess with. But it makes a lot more sense to mess with it in the pre-industrial, half-feudal world than in the modern one)

Anyways. I've got a simple excel file which lets you simulate your own toy Malthusian economy based on this which I'll post as soon as I can make it user friendly enough and figure out how to link to excel files.

(Note: There's probably a whole bunch of typos in the above)

I have some really deep insights on the present Housing Crisis

2008-04-07T00:21:00.000-07:00

and they're right HERE. The key is the Surburban market.

and Milo is another proof that it's punk rock to have a PhD.

UPDATE: This post originally had one less "b" in it!!!

Socrates would've taught the Solow model!

2008-04-03T13:48:00.001-07:00

There's some discussion going around as to the usefulness of the Solow model:

The initial question and initial response over at William Polley's blog here.
The response by EclectEcon here.
Some comments from Gavin Kennedy here.
More from EcletEcon here.
Gabriel commenting here.
Mike commenting here.

Then there's also Robert posting a quote by Kaldor which argues that the "whole structure" of neoclassical economics crumbles once one introduces increasing returns which also turned into a somewhat related discussion of constancy of factor shares, the validity/belief in JB Clark's marginal productivity theory of income distribution and the relevance of the Solow models in the comments (as with most sites that do the heterodox economics thing some of the comments are good and some of them are just nonsense).

Anyway. I'm in the You Should Teach The Solow Model crowd.
Why? Because Socrates would've taught it.

Socrates thought there were two, maybe three, kinds of people in the world and that you could arrange them in a hierarchy;

1. Those who don't know but think they know.
2. Those who don't know but know they don't know.

and then maybe some lucky ones;

3. Those who know and know they know.

There aren't many people in the 3rd category. But for some reason we always expect our models to move us from the 2nd category to the 3rd. And we're not satisfied if the movement is from the 1st to the 2nd.

The Solow model basically says that "it ain't capital accumulation" which is the cause of sustained growth, it's something else, the magical so called "Solow residual" which could include technology, policy, CHANGE in institutions etc. (I think a lot of people get confused here. Institutions, almost by definitions, don't change quickly. So they can only affect the LEVEL of income or, alternatively create CONDITIONS for growth. For example, property rights are great. But they don't cause growth by themselves. It's the higher investment which property rights cause that causes growth (and in Solow that ain't gonna work in long run. You gotta have something else))

There've been many people over the years that've concluded that since the Solow model doesn't "explain" growth (because it lumps its major cause into an exogenous residual) it is useless and only an excercise in mathematics.

But people! When you thought you knew (it's capital accumulation!) and then you learn that you don't know (it can't be capital accumulation!) you've learned something just as important and valid as if you've acquired a "positive knowledge".

And before Solow, lots of people DID think that all it took for growth to take place was a higher saving rate and more investment. Lots of development economists, planners in socialist countries, planners in third world countries, advisors from international organizations and so on.

It's good to know that you can get milk from cows. But it's also good to know that you can't get milk from chickens - particularly if you were under the mistaken impression that you could.

How to read The Economist

2008-03-14T15:31:00.001-07:00

So Dani Rodrik (I know I know I pick on him too much but only because he's one of my favorite economists) asks whether he should start reading the Economist again and Henry at Crooked Timber comments. Sort of ironic, since Dani is the one that is probably responsible for yours truly getting mentioned in those esteemed pages (either him or Mark Thoma).

But anyway. Before one decides on whether to read anything one must know the proper way to read it. So I'm here to help out. Here's how I read The Economist:

1. Skip the entire US section.

2. Look in Europe section. Anything about Eastern Europe (which also includes the Balkans and Turkey)?
If so read it, if not skip it.

3. Look at Economics Focus. Is it about Finance or Social Security?
If so skip it, if not, read it.

4. Read the Obituary

5. Read the Africa, Asia and Latin America sections.
Unless it's about the Palestinian-Israeli conflict, Hugo Chavez or, well ... China.

6. Read the science section.

7. Look at the titles of articles and books and authors/artists in the Arts and Lit section.
Is it about Victorian crap? Skip it.
If it's about books by USish or British writers read it with a 10% probability.
Otherwise instantly make up my mind whether a particular book/art sounds like stupid crap or possibly interesting, which usually means reading a given article on non-Victorian, non-US, non-Brit lit or art topic with a probability of about 25%

8. Read the Letters to the Editor.
Verbalize out loud the "Dear Sir" that each letter starts with in an accent that is supposed to be, but is not, appropriate to the apparent ethnicity/nationality of the author.

And since I'm bloggin' again, lemme just note that Dani Rodrik is the Watcher

2008-03-03T00:31:00.000-08:00

I've had reservations about posting this, mostly because I was not able to find a photograph which would conclusively prove it. But I think the two pictures below leave it beyond the shadow of the doubt that Dani Rodrik is the Watcher:

So. Who's the Slayer?

Monopolies and price stability

2008-03-01T21:55:00.000-08:00

Ok, ok. Economics. With maths. And graphs.
Let us nerd out brothers!

(Update: Typos have been fixed. Thanks guys!)

Anyway. Here's something that at one point in grad school, when I thought about going into IO, I though about pursuing but then it never really went anywhere and I got interested in other stuff instead. I got reminded of it recently when trying to look up my electricity bill on line, having a buttload of trouble and eventually winding up at a webpage which as it's header had the sentence:

"Our purpose is to serve our customers by guaranteeing price stability"

I'm not gonna say which electricity company it was, but hey, I'm pretty sure they're all the same even if they're not as explicit about the fact that they're ripping you off. Of course "price stability" here means "stability of consistently higher prices". But there is an interesting economic question here, just from a purely positive point of view - are prices more stable in a monopolistic market or a competitive one? Is there any justification for the obviously self serving claim of a (government granted) monopolist?

And being even more generous, I can sort of see it. When prices change a lot, it's a pain. On the simplest level, you show up to the store, having had optimized your optimal money holdings (i.e. the cash in your pocket you took with you) and the fact that the actual price is way different from what you expected means you gotta make another run to the ATM machine or forgo something. Probably less explicitly but more importantly, when prices keep changing on you it means you've gotta recalculate your optimal allocations of expenditure again. You gotta set up a new Lagrangian, take the damn first order conditions and figure out if making out the adjustments in your optimal consumption basket - given your income - are worth it. What? You don't think that way? You don't set up constrained Lagrangians every time there's a change in prices and compute your Kuhn-Tucker conditions? Well, actually you do, And so do most people. It's just they do on the intuitive level what economists formalize in (semi) fancy maths (they're really not that fancy, believe me). But the "bounded rationality" people have a point here. It's a pain in the ass expanding mental computation resources on dealing with this sort of thing.

So how do we figure it out? Well, consider a simple set up with linear market demand and constant marginal costs (I worked it out with increasing, quadratic, costs which is probably the more realistic case - particularly for the oligopoly case below - and it works roughly the same way), where firms are Cournot competitors (this makes it easier to compare competitive markets and oligopolistic/monopolistic markets). In that case an individual firm's profits are given by

where

and

so profit max implies

By symmetry, all firms produce the same amount of output so that the q's are all the same. This means that sum of q's is just q*N and we can drop the i subscript. So

and

Plugging this back into our inverse demand function P(Q) we get

c$">

This means that as the number of firms gets really large (N goes to infinity) price goes to marginal cost.

which is known as the "Cournot Theorem" and here I will take this to represent the "perfect competition" case. In that case, or in the parallel case of Bertrand competition with a homogeneous good, or the textbook example of a competitive market (except here the supply curve would be a flat line at c. Like I said, this pretty much works with a quadratic cost function in which case you get the usual upward sloping market supply curve), the variance of the price will be just the variance of marginal costs:

What will the variance of prices be under a monopoly or under oligopoly? Well, first consider the simplest case where all fluctuations in price are due to cost shocks. Then

So in this particular case, yes, prices would be less volatile under Monopoly than under competition. In fact, increasing the number of the firms in the market would increase price volatility. Here's a graph of that:

Here's a graphical representation of what's up in this case. Remember from your basic econ that a monopoly will never operate on the inelastic portion of its demand since then by decreasing output it could both cut costs and raise revenues. So it's gotta be on the elastic, or "flat" portion of its demand (in % terms of course, since this is linear demand). This in turn means that the monopolist is willing to absorb some of the cost shocks rather than passing them fully onto the consumers:

But what if price fluctuations result only from changes in demand?

Well in that case in a perfectly competitive market, with constant marginal cost, there will be no change in price, so the volatility of prices under monopoly must be greater than in a competitive market (again, this generalizes to quadratic cost functions and upward sloping supply curves as long as the shocks are to the intercept and not to the slope).

So the first lesson is:
If the fluctuations in price are due to shocks to firms' costs then the fluctuations in price will be less under a monopoly then in a competitive market.
If the fluctuations in price are due to shocks to consumers' demand then the fluctuations in price will be greater under a monopoly then in a competitive market.

How much does that generalize to the case where there are shocks both to costs and demand?
The above price equation tells us that then the variance of prices will be

Again to keep things simple lets assume that the cost shocks and the demand shocks are uncorrelated so that Cov(a,c)=0. Then we have

So is the variance of price increasing or decreasing in the number of firms?
Taking the derivative with respect to N we get

vs. 0

or

N vs.

(Addition, since I screwed up last time: If V(c) is large then for price volatility to be increasing in N, you need a small N.

Or here's another way

vs.

Which means that volatility under an oligopoly is less than volatility under perfect competition if

V(a)<2NV(c) i.e. if shocks come mostly from cost side)

Which once again says that if the shocks come mostly from the cost side then the volatility of prices will decrease with number of firms - monopoly is good for price stability. But if most of the shocks come from the demand side then price volatility will decline as the number of firms in the market decreases.

Also. Neurosis after "Souls at Zero" is not worth listening to.

Ok, Obama

2008-02-22T20:49:00.000-08:00

I like McCain but the simple fact of it is that Republicans pretty much need to be punished for the last 8 years. So sorry John, I'd vote for you in any other election and you got my respect but I think it's gonna be (via Dani Rodrik):

And note the words "Por Nuestra Nacion" and "En Estra Gran Nacion", both indicating the close association of the author with the US of A. On his terms. This is assimilation in the good sense of the word. Assimilation as in folks identifying with the polity and the general public good of where they're at. So what if it's expressed in Spanish?

Viva Obama!
Viva!

Mitt Romney has me almost convinced

2008-02-03T13:09:00.001-08:00

So... apparently McCain:
- is "bad" on taxes because he voted against Bush's tax cuts twice.
- is "bad" on torture because he opposed waterboarding.
- is "bad" on immigration because he proposed an "amnesty"

and on top of that McCain is catching a lot of hell from none other than Rick Santorum (I'm not even gonna link anything here) and happens to be one of only two candidates (along with Clinton) that doesn't start foaming at the mouth at the mention of "China" or cynically exploiting xenophobic/populist misinformed fears of some.

And here I was thinking "Obama or Hillary?" This puppy's now in the race in my head.

Trivia question for the Wire affecionados

2008-01-24T00:12:00.000-08:00

In which episode of The Wire does the longest "Sheeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeet", as articulated by everyone's favorite corrupt politician, Clay Davis, occur?

I'm thinking that one episode in Season 2 where Daniels and Davis have a confrontation. But the current season, what with Davis' indictment and all, might be well posed to beat that record.

http://www.hbo.com/thewire/cast/characters/clay_davis.shtml

Recycling old stuff

2007-12-22T15:09:00.001-08:00

As long as we're on the topic, here's a thing I wrote during the last election on this one blog thingy for friends. Since I don't have much time to post, you get leftovers. And yes, it's (partly) tongue in cheek:

-------------------------------------------------------------------------------

For the sake of all that's decent please don't vote tomorrow

First of all, only people who own at least 2 cows should be allowed to vote. We can't have just any ol' cowless yokel votin'. Plato recognized this long time ago in his famous book called "The Republicans". Thomas Hobbyist also saw the problem in his also famous book called "Levitation".

Second, given that we gonna have voting for all, including yokels with less than two cows each, we should have a right to sell our damned, mostly useless votes, to the highest bidder. (I'm an Anarcho-Monarchist after all). As that lead singer for The Cure, Albert Camus, said "What better way to enslave a man, then to give him a vote and call him free?". Well, Mr. Cow-moo, if we can sell our votes then it ain't free is it?

Some people might thing that this will result in "bought" elections. To these people I would say...well, I wouldn't say anything I'd just let our ol' pal Reality give'em a few good slaps. At least this way the money would go to poor cowless yokels rather than to PAC lobbyists, advertising executives, and butthead campaign managers (who according to D-Ante inhabit the fourth level of hell).

But wouldn't that mean that people's wishes are not respected? Well first of all I know a lot of people whose wishes should NOT be respected, at all, since that would imply some very silly things like teachin' in schools that we are NOT descedent from monkeys. Since monkeys are cool and cute and mischevious at the same time, this would just be wrong. We should be proud of our simian ancestors. Anyway I digress. The answer to the dilemma is known as "price discrimination". This is where you charge different prices to different people based on their, or your own preferences. Like you know you'd charge a higher price for heroin to a fiend then just a casual user. Cuz the fiend needs it that much more. So if you can sell your vote you should;
1) price it higher to the more desperate candidate and
2) if you don't like Democrats, don't sell your vote to a democrat, and same if you don't like Republicans. Or at least charge the bastards you hate higher prices. This is elementary economics. If you're gonna sell out, make sure you get a decent price.

In the end though voting is just a clumsy way of society trying to make us feel like we matter and like it cares about us - it's a personalized Oprah show for all of us without the decency to own a cow or two. But every reasonable brain cell in your cerebellum will tell you that it society, Oprah included (I betcha Oprah does own at least two cows), don't give a damn and that even if it did, there's so many cowless yokels out there that there's no freakin' way a single can make a difference. Even in Bush vs. Gore a single vote couldn't've made difference. This result is called Mathematics and it was handed down long ago to the ancient Egyptians by the aliens that "seeded" them here on earth. Can't mess with that.
And that's assuming that there's candidates worthy of choosing between!

So please, tomorrow, on voting day, stay home, drink some beer, and look into the present market price of cows, since when I take over it's only gonna be folks with at least two cows that get to vote.

Voter turnout's already too high - leave it alone!

2007-12-22T14:06:00.000-08:00

Mark Thoma links (but disagrees with) to a an article by some Australian do-gooder who thinks that people should be forced to vote. Gabriel also comments. I've already left some comments there but here I wanted to say a bit more about the argument that voting is a public good subject to the free-rider problem. So first, let us just note that the author of the article doesn't really know what a free-rider problem is and equates with "when other people don't do what I want them to do".

But anyway. Is higher voter turnout better? Aside from some amorphous and ill defined appeals to 'good citizenship' I really don't see why. Voting is supposed to be a mechanism which takes individual preferences and somehow aggregates them into a social outcome. If the outcome of the voting process is the same whether 20% of those eligible vote, or 60% do so, what's the difference? Most of these arguments are just a smoke screen for the self-interested motives that knows that a different % of voters (this goes both ways) would deliver a different outcome. But this means that what people care is that the outcome resemble their preferences, not how many people vote per se.

Suppose it's gonna be Obama vs. Giuliani. And suppose that 20 million people prefer Giuliani and 20 million + 1 prefer Obama. If 40 million people stayed at home on election day and only that one guy who prefers Obama shows up, what's the problem? The system worked even with .00000256 % voter turn out. And if there is some, even very small cost, to people of voting then there are potentially huge savings from having those folks stay at home.

Or think about it another way. Suppose that choice of our glorious leader is not made in the voting booth, but instead, the government sends out pollsters (who for the sake of argument, are 100% reliable and trustworthy) to ask people who they prefer. "You want Barack or Rudy?" This is exactly the same as voting except from you having to go to the government, the government comes to you. And suppose that there's some small cost of sending the pollster to each individual citizen.

How many people should be polled? Obviously sending a pollster to every single citizen would be very super expensive (but somehow the voting-fetishists don't mind if that cost would be born by individuals). Welp, those ol' buddies the Central Limit Theorem and the Law of Large Numbers tell us you don't need a large sample (*) to be able to estimate the relevant voting shares and preferences. Something like 10% would work, 15% would be golden (and of course that's how the stations are able to fairly accurately predict winners. If they had bigger budgets and could actually get 10% to 15% they'd get it spot on almost every time). So in this case, polling only 10% or 15% of the eligible citizens would work just fine and would save the government oodles of money relative to asking, say 60% or 70% of the population, and accuracy would increase only a tad (I'm gonna keep this a post without any serious maths).

In fact polling 64% of the eligible voters seem ridiculous from that perspective. And that's what the voter turnout was in the 2004 election.

At this point the counter argument is usually something about how we're all members of the polity and voting gives us a sense of belonging. Ok, fine. That's probably why you get that crazy 64% number rather than something much more reasonable and lower. But there's no externality here. If it gives you a sense of belonging you go vote. If it doesn't you stay at home. End of story. And it's not like you can force people to 'feel' like they belong just by making them do something they don't want to.

And like I said before. Only people who own at least two heads of cattle should have the right to vote anyway.

(*) Of course this requires the sample be random. In a sense the sample of those who actually vote from the universe of eligible voters is not random. It's self selected. It's people who have strong feelings (and sometimes even, yes, better information) about the outcome. But that's the way it should be. Do you want people flipping coins in the voting booth?

(So I tend to think that having a small cost of voting is a good thing as it discourages those who only care marginally (in the non-economic sense of the word). Part of the problem with voting as a social-choice mechanism is exactly that it's one person one vote - it doesn't account for the intensity of preferences. If I only care a little I have the same weight in the process as someone who cares a lot. Having a small cost (which could be just the opportunity cost of time it takes to vote) dampens this problem as it eliminates some borderline indifferent voters.

But there's another problem. 'Caring a lot' about an a outcome, or having very intense preferences about it are not always good either. And some of the people with very intense preferences should also be somehow taxed on their voting. For an obvious example take that crazy guy in Iowa who asked Edwards about OJ. Obviously he feels very strongly about something. He's also a total nut case who probably won't be dissuaded from voting his nut case ideas in the booth by a small cost. This is of course a typical problem in a democracy but here overall I think it just falls into that Churchill quote about democracy being the worst possible system except for all the others, and I don't really see an objective way of solving this problem)

Monoposonistic Labor Markets, Minimum Wages and Employment - the Laffer Curve of Leftist Economics?

2007-11-19T14:30:00.000-08:00

After having written this I realize that I think that the Laffer curve is still crazier of the two.

The Laffer Curve, of course is the idea that the relationship between tax revenue and the tax rate is reverse-u shaped, with end points at 0 and 1. If tax rate is 0, then there's no tax revenue. If the tax rate is 1 (100%) then no one wants to work (legally) and hence no revenue is collected. This leads to the conclusion that there is some "optimal" tax rate between 0 and 1 which will maximize tax revenues, and as a corollary, that if the current tax rates are higher than that then cutting taxes can actually INCREASE tax revenue. This is used by some on the crazy right as an argument that "tax cuts pay for themselves". However, even though the theory is sound and all, there's little to no indication that there are actual economies which have tax rates high enough so that cutting them would result in revenue increases. Maybe Sweden in the 80's, maybe really rich people in the early 1960's US. Maybe. Bottom line is that most serious economists don't think the Laffer curve idea matters for all practical purposes - you cut tax rates, you get lower tax revenues. (There should be a caveat here about demand side vs. supply side effects of tax cuts which maybe I'll write about later).

What does this have to do with the debate on minimum wages, which pops up with regularity of a sinusoid function? Well these debates usually go something like this:

Econ 101 - Higher minimum wages lead to lower employment because they raise the price of labor and when you raise the price of something folks buy less of it.

HetEcon - Oh please. Show me the empirical evidence. Oh, and Card and Krueger.

(a short, abusive, impolite and snarky conversation ensues about Card and Krueger and the potential shortcoming of it as well as that of follow ups and other studies)

HetEcon - Anyway. MONOPSONY!

And it's true. If you have a Monosponistic labor market then higher minimum wages COULD increase employment.

Basically, in a competitive market the marginal cost curve coincides with the labor supply curve and at the end of the day wages are equal to the value of marginal product. Mathematically, if firms take wages as given, and if Q(L) is firm's output as a function of amount of labor it hires and p is the price it receives for its product then its profit is given by:

Taking the first order condition we get

which is the usual 'nominal wage equals the value of marginal product'

All this implies is that if wages are set above the market wage then firms have to adjust their hiring so that the VMPL above matches the set minimum wage. How do you get VMPL to equal a higher wage rate? Well, if there's diminishing returns to labor, you hire less workers, so that the 'marginal worker's' product is higher than it would otherwise be.

However, if firms have wage-setting power (and this doesn't just mean that firms can choose wages. It means that their choice is not constrained by competition with other firms) then the profit is written as

where now the wage rate is a function of amount of labor hired, w(L), since a monopsonist faces an upward sloping labor supply curve.

The firms choose the amount of labor to maximize their profits which mathematically means that they set the derivative of p*Q(L) (marginal revenue product of labor) to the derivative of w(L)*L (marginal cost):

Dividing through by w, rearranging and setting

where epsilon is the elasticity of labor supply, we get

which is a standard 'mark up' equation (parallel to a similar one for a monopolist).

The graph below illustrates this.

In fact we can write monospony wages as a fraction of competitive wages - the wages that would prevail in a competitive market:

where w^M are wages in a monopsonistic market and w^C are wages in a competitive market.

Note however that the mere existence of monopsony power does not guarantee that higher minimum wages will always lead to higher employment (as should be intuitively freakin' obvious). In fact, there's a limited range over which employment increases with minimum wages - between the original monopsony wage and the competitive wage:

After that it's downhill again. In fact, what we get again, just as with the Laffer curve is a reverse-u shape. The graph below shows how employment varies with the minimum wage in a monosponistic market:

So only if the minimum wage is somewhere between the monopsony and the competitive wage can increasing minimum wages increase employment. However, all this so far is pretty good news for minimum wage advocates. Let's go back to the equation

'Standard' estimates of epsilon - the elasticity of labor supply - indicate that it is fairly small, mostly less than 1 (this however is subject of some controversy). Even taking epsilon to equal one you can set minimum wages up to twice that of monopsony wages and still get increases in employment. So if the monopsony wage for unskilled workers in US is, say, 5$, you could set the minimum wages up as high as 10$ and get away with it.

Of course, there's a problem. The situation described above is that of a true "company town" where there's only single employer (*cough* gobemen *cough*) and it's work for'em or starve. But if you think about most unskilled jobs there seems to be plenty of competition. Even a very small town usually has five or six fast food joints, video rental places, coffee shops, retailers as well as a big box store or two. It'd would be quite a stretch to argue that that each corner McDonald's is a monopsonist in the market for unskilled labor, just like the Burger King that's sitting right across the street from it. So we need to modify the above equation to something more realistic, something like "monopsonistic competition" (by parallel with 'monopolistic competition')

(note that all through out this post we're playing along with the idea that labor markets are characterized by monopsony power and only considering to what extent)

There is one strand in literature which points to 'search costs' as a source of monopsony power, even when there's lots of employers. Workers have to physically search for jobs, be matched with their employers, search is costly, and once you're hired quitting your job is costly since it'll take you some time to find your next job. Well, as a former member of the minimum wage fast food industry, I seriously doubt that search plays a big role in these kinds of jobs. Once I literally quit my job at a Burger King (without giving 2 wks notice I might add. A bit crappy, but the manager was a real schmucko which is why I quit), walked across the street to a Wendy's, filled out an application and started my first shift the very same day.

'Search' and 'matching' actually probably are far more important for highly skilled jobs where both the (relative to other markets) number of potential employers and the number of potential employees are small. Academic jobs are a good example. Medicine, law firms... all these are probably better candidates for this kind of monopsony than the industries actually affected by minimum wages.

(As a side note, let me be clear here. I don't mean to advocate any kind of minimum wages for academics. In fact I think a better model here is that of a double monopoly which means the distortions could off set each other).

But alright, alright. Can't we still have monopsony power even with lost of firms? Well, yeah. Here's the set up. Now the market wages depend not on the labor demanded by any one firm but all firms together. Say there's N firms in this market. An individual firm's profit function is then given by:

Taking derivatives with respect to L_i, setting it to zero and all that magic, we get:

So as not to get into all kinds of caveats let's just suppose that all firms have the same VMPL's (whether through productivity or prices or both). Then we can sum that sucker above over j and get

or

where now VMPL is sort of an average (across firms) value of the marginal product, and epsilon is the elasticity of TOTAL labor supply (rather than that faced by any one firm) with respect to wages. In effect, when moving from a 'company town' to a 'oligopsony' or 'monopsonistic competition' (that's the MC above) framework, the estimated elasticity of labor gets multiplied by the number of firms in the market. So now you can get convergence to competitive wages not just with a perfectly elastic labor supply curve (epsilon = infinity) (i.e. perfect competition) but also with a large number of firms in the market (N getting really large).

So now, if the monopsony wage is 5$, labor elasticity is 1 and there's 10 firms in the market (probably too low) then the maximum minimum wage which can be set without adverse effects on employment is 5.50$. With a, perhaps, more realistic labor elasticity of 1/2 it can go up to 6$.

Looking at it this way leaves very little room for minimum wages to increase employment, if at all, and even granting that labor markets are characterized by some amount of monopsony power.

So is this idea as bad as the Laffer curve? Probably not quite so much. One thing the minimum wage advocates might, just might, have on their side is 'standard' estimates of labor supply which are quite low (even though some folks argue that these are underestimated when using traditional methods. In fact I saw Edward Prescott start one of his lectures by saying "labor elasticity is 2". And there's other newer work which finds that that epsilon is much higher than previously thought).

But both ideas - the Laffer curve and the minimum-wages-raise-employment - are characterized by a lot of wishful thinking and a lot of unwarranted assumptions.

(and there are a couple studies, by Barro for example, which claim to have uncovered Laffer effects for some income groups in the 80's, which on the face of it are no more 'out there' than Card and Krueger).

(one other thing. The whole monopsony-as-reason-for-minimum-wage argument assumes that it's the market for unskilled labor which is most characterized by monopsony. But, as I partly indicated above, there's good many reasons to think that if you find monopsony somewhere, it's elsewhere. Which could, just could possibly be an argument for industry-specific minimum wages. And in fact, that's how them Europeans do it. But a general, blunt, un-targeted, federally mandated minimum wage law still wouldn't make much sense).

(I might have spelled monopsony as mono-s-pony above somewhere, since the spell checker don't know either one. Which is a market with only a single Equus Caballus, not a market with only one buyer. Sorry.)

One Economics, Many Recipes Seminar at Crooked Timber

2007-11-13T22:21:00.000-08:00

In case you're missing it.

With comments by (in reverse order of posting):

Mark Thoma (Economist's View)

John Quiggin (non CT blog)

Henry Farrell (non working link to game theory subpage that's probably good)

David Warsh (online column)

Daniel Davies (dsquared digest)

Jack Knight (no wait not this ... this)

Daniel Drezner (the world famous)

Adam Przeworski (you should at the very least read this paper)

and a response from Dani Rodrik (also world famous).

All ... almost all ... comments by the discussants are really good. In fact, they're sort of exhaustive in the sense that it's really hard to think of anything to add. Except that the whole "heterodox vs. orthodox, or maybe heterodox or orthodox" debate is pretty tired by now and there ain't no point in having it again. Also, since I let my opinions out of the bag a bit already, I might as well add that as far as the discussion goes it's something like David Warsh and Mark Thoma tied for 1st. For me. But other folks are interested in other aspects. So you should read all of them.

As a general note, I've been quite busy this term with work and so on. Still am, especially now when the quarter is coming to an end. Perhaps frequent posting will joyously resume in the near future. Until then it's eternal tears of sorrow for you. (Sorry, it's not really a video).

Dani Rodrik is a Liar

2007-11-03T00:50:00.001-07:00

He's a First-Best Economist, That's what he is !!!! I know this because I read his book

Crooked Timber is planning on doing a seminar on Dani Rodrik's book "One Economics, Many Recipes". Go Buy The Goddamn Book!

In the meantime I'm gonna jump the gun. Because I'm sort of upset. We do economics because we like precision, objectivity and the ability to disagree with each other while maintaining respect for our fellow economists whatever crazy notions they may hold at one time another (um... we all have exceptions). They at least have thought it through.

Which is why we should make certain terms precise. What exactly is a "second best economist" as opposed to a "first best economist"?
I thought there was a difference there, and maybe there still is, but after going though the book all I can say is that I agree.

But. This is Dani's basic framework;

You should identify the areas where the DIRECT distortion are the biggest and focus on those.

( Added: As Dani notes in comments, I should be clearer (leave it to me to be imprecise in a post where I ask for precision). By "biggest" I mean those with the highest shadow price in terms of welfare loss. Those are not necessarily the same as the ones where there is the largest gap between marginal social benefit and marginal private benefit. The example in the book is one of opening up the capital account )

The not so implicit warning is that if you try to reform some other distortions the theory says that either a) the likely gains are going to be small or b) while you make things better in one area you might screw things up in another. Or a or b. If you at least focus on the biggest distortions, you might, just might, get it right (though actually choosing among the probabilities in this uncertain world (and the uncertainty of the world is what Danny Rodrik stresses)) is exactly what makes this hard.

As far as practical advice goes it's about as good as you can get unless you're the sort who goes for Utopian visions.

It's a humble message which is what economics as a field of study should aim for. But it's not "second best economics". It's still "first best". It just says that you should be careful in your thinking about what constitutes first best.

And that's why I get upset.

A First-Best Economist uses basic economic theory to guide her decision. Yes, even "Econ 101" theory sometimes. But this is same approach behind "Growth Diagnostics".

A Second-Best Economics is a different animal. She's is not the fauna that Dani hopes for. It's not about identifying a menu of options, choosing from that menu, considering how one choice affects another and how the feedback mechanisms work ... arghhhh I quite dislike putting this into prose. George Goddamn Akerloff and Kenneth Freaking Arrow are both First Best Economists! They're the First among the First Best Economists!

A Second Best Economist insists, and keeps on insisting, that no matter what, INTRODUCING MORE DISTORTIONS CAN MAKE THINGS BETTER!!!

AND THE MORE DISTORTIONS THE BETTER!!!! They want to up the lambda's just like the Washington Consensus folks don't even pay attention to the magnitude of lambda!

The politics:

There's a big difference between saying that;
a) reform everything everywhere in accordance with neoclassical economic theory
b) DOWN WITH NEOCLASSICAL ECONOMIC THEORY!!! Do the opposite of what it says. Distortion everywhere. Therefore distort MORE!!!!
c) Heavy Metal!!!!!!
d) Think about it

Obviously any thinking person would choose c) ... wait...

Um. It's a loaded question. Obviously c), wait no, d) is the right answer

Inequality

2007-10-30T10:25:00.000-07:00

I think a bit of the point of the last (next to last?) post got lost by bringing the US vs. EU into it. Here's another way to think about it.

Suppose there are 250 economies in the world, each with exactly the same, really large, number of people. Furthermore these economies are exact replicas of each other. Every person in economy 1 has 249 exact twins in all the other economies all of whom have the same identical income. So the distribution of income in each economy is EXACTLY the same. And in each of these 250 economies the distribution of income is given by a logistic distribution with parameters mu and sigma (again, same for all 250 of'em).

Now say you're a researcher who's interested in studying the relationship between economic development, as measured by mean income, and inequality, as measured by the Gini coefficient. Problem for you is that you do not get to observe the entire income distribution in each of the 250 economies at your disposal (in a way, if you COULD observe the entire income distribution for all 250 economies, why would you be interested in the mean and the Gini anyway? Those are descriptive statistics, which means they leave information out). So you don't know that all these 250 economies are identical (which also means that even if you did know you couldn't estimate the relationship between development and inequality anyway since you'd have no variation in the data. A single observation).

Instead, what you do have is the ability to select 1000 people from each of these economies, compute sample means and sample Ginis and base your inference about development and inequality on this data. Of course, since you're a scrupulous researcher you want to ensure that each of your samples of 1000 is random.

Well, in that case what you're gonna get is exactly what I got in the previous post; a positive relationship between inequality and mean income and you will erroneously conclude (as the paper cited below did) that as countries become more developed they become more unequal, EVEN THOUGH ALL THE ECONOMIES ARE REALLY IDENTICAL.

Economic Investigations has nicer graphics:

(They're much nicer over there)

From this faulty conclusions all kinds of wrong policy implications and conclusions can follow. That more inequality is the price you have to pay for higher standards of living (right wing). That growth of income doesn't matter because it's only the rich who benefit (left wing). And so on.

So what's left? Are we prevented from saying anything about the relationship between inequality and development because we don't know what distributions the underlying data come from? Well, no, but there should be a lot more caution with regard to the data and a lot less conclusions drawn from regressions of the form
Inequality = a + b*income

and even (or especially)
Inequality = a + b*income + c*income^2

For example, it would be silly to try to argue that an economy with an average income of 2000$ per year comes from the same distribution (or is identical too, and the difference in sample mean accounted for by randomness) as an economy with an average income of 30000$. Likewise an economy with a Gini of .6 is very very unlikely to be the same (or have the same "structure") as one with a Gini of .3 (interpreting the magnitude of Gini coefficients was part of my motivation for looking at this stuff).

In fact, here's the distribution of the mean income across the 250 economies from the original simulation:

Of course, by the Central Limit Theorem as the number of your economies increases the distribution of the mean income will converge to a normal distribution with the "true" mean of means. Going by the sample standard deviation above this means that an economy with an observed per capita income of 40,000$ is about (roughly, sort of, hold on a second ...) only 5% likely to come from a lognormal distribution with mean of 36,000$.

Here's the distribution for the Gini

So here the sample minimum and max are .41 and .48 which means that it's possible for our estimate of inequality to vary quite a lot even when the true Gini is .44. On the other hand the good news is that most of the observations fall within (.42,.46) interval and anything outside of that is unlikely to have come from that distribution.

Of course what really matters is the JOINT distribution of mean income and the gini. But it should be possible to compute the probability that any two observed economies come from the same distribution. I haven't done it yet. I'm working on it.

Here are some other "fake" relationships found in the generated data:

Share of top 1% earners vs. avg income (this also fits the observed pattern for US and EU):

So this follows the pattern with the Gini for pretty much the same reason, but because for the y-axis variable you're only looking at the portion of the distribution there's more dispersion around the regression line.

Here's poverty vs. log income:

This one's a bit harder to explain since the poverty (measured by headcount ratio with the poverty line set at 10000$) does not depend on the Bill Gates effect. But it's sort of the same thing locally at the left tail of the distribution (you get some lucky draws which both increase average income and decrease poverty, since the lognormal density is increasing for values below the median) so the strength of the relationship is much weaker. Also it's going to be very sensitive to where one sets the poverty line.

Finally, Amartya Sen proposed the following measure of Social Welfare:
SW = (1-G) * y, where G is gini and y is average income. Since here G and y are positively related, when G goes up, (1-G) goes down but y goes up. So there's two offsetting effects on SW and this is essentially a measure of which one dominates. Here it looks like higher income is associated with lower welfare (because of higher inequality, so the change in inequality dominates (which is why some folks love this measure)). But again, remember that these are all identical economies:

Ok. That's it for now. Be suspicious of people claiming that there's strong relationship(s) between inequality and growth/income.

Update on inequality...

2007-10-28T13:46:00.000-07:00

I plan on adding a few comments to my previous post soon (pretty busy with real work currently). But for now I just wanted to note that Gabriel wrote the Mathematica code which you can use to run your own simulations.

Here's a paper which I can't access right now but which looks like it falls into the trap outlined in the previous post. Abstract:

Recent research has posited that, in advanced economies, there is a positive correlation between in- come inequality and development. Using a new unbalanced panel dataset for 71 countries from 1961 to 1992, we present evidence that supports this conjecture. Although many factors may be contributing to this renewed positive relationship between growth and inequality, one plausible explanation rests on the shift away from a manufacturing base towards a service base in most advanced economies.

(My emphasis)

Inequality and the Bill Gates effect

2007-10-21T15:38:00.000-07:00

(Note: I haven't gotten all the kinks worked out in what follows below. So maybe I've missed something or said something wrong)

The recurrent topic of which economy's dad can beat up which economy's dad - the US' or the EU's - recently popped up again here and there. Roughly speaking, the US has lots of inequality but higher per capita income, whereas the EU (here, as often, basically meaning France, Italy and Germany) has lower per capita income but a lot less inequality. In fact if you take the OECD countries, minus the late joiners, and slap'em up on a scatter plot what you'll see is a (pretty rough - there's all kinds of measurment issues here) positive relationship between per capita income and the level of inequality as measured by the Gini coefficient.

These differences start people talking about the Anglo-Saxon vs. European models of the economy, how the US and Europe have different economic structures which produce these results and how either Europe is quickly falling into the dustbin of history, or the US is becoming a place where folks starve in the gutter because they have no access to health insurance and evil capitalist stole their puppies. A possible question one might ask however is whether this kind of relationship - high income and inequality in US, low income and inequality in Europe - could arise simply by chance. To do that let's delve a bit deeper into the measurement of inequality and income distributions. What I'm gonna argue is that despite the fact that it may not seem like it, this kind of relationship could very well arise by chance and that relatedly, there probably isn't that much of a difference between the economic structure of the US and that of the EU. In fact, a positive relationship between per capita income and inequality is PRECISELY what you would expect if THERE ARE NO DIFFERENCES in the underlying structure of these economies (given certain assumptions of course).

Ok, so the Gini coefficient is a measure of inequality and it is given by:

where y_i is the income of person i and the y's are arranged in an ascending order, that is:

The Gini has the familiar interpretation as twice the area between the diagonal and the Lorenz curve, and it is equal to 0 if everyone has the same income, and 1 if one person has all the income. Higher levels of G indicate higher inequality.

One of the key properties of the Gini (or any half way decent measure of inequality for that matter) is that it is scale independent. What this means is that if we multiply everyone's income by some positive number (say double everyone's income) then the amount of inequality, as measured by the Gini, will not change. In other words, richer economies are not automatically considered to be more unequal than poor ones. (It also means that the Gini is a unit-less measure, independent of whether we measure incomes in US dollars or rupees or World of Warcraft gold or whatever)

Mathematically it means that G is a function homogenous of degree 0 in all the y's

0 $">

So, you would expect that if you have a whole bunch of economies, all of which have the same "underlying economic structure" then, on average, there should be no relationship between per capita income and inequality. Some economies might randomly end up with high inequality and high per capita income, some randomly end up with high inequality and low per capita income, some with low income/low inequality and some with low income/high inequality. But on average there should be no pattern for "similar" economies.

In fact there's a whole literature on the relationship between inequality and economic development (as measured by level of per capita income) going back to Nobel prize winner Simon Kuznets. Kuznets, famously claimed to have discovered the so called Kuznets curve which says that the relationship between inequality and per capita income is reversed n-shape. That is, in poor countries everyone's dirt poor but they're all equally dirt poor. As the economy begins to develop and per capita income rises however, some portion of the population begins pulling away from everyone else and inequality rises. In developed economies the rest of the population has increasing incomes along with the very top and inequality actually falls. There's been a lot of work looking into whether the Kuznets curve actually exists in the data (it sort of looks like it, except that most middle income countries tend to be in Latin America which has high inequality for historical reasons, hence the relationship might not be driven by changes in income), controlling for reverse causality and other factors. A typical approach is to run a regression like this

where G is the gini, y_A is per capita income, x is a set of control variables and the betas and gammas are parameters to be estimated. Then if the estimation produces beta_1>0 and beta_2<0 then this is taken as evidence in support of the Kuznets hypothesis.

Relatedly, we might expect that if we were to do a regression such as the one above and get beta_1=beta_2=0 then all the economies in the sample have roughly the same "underlying economic structure" (except for variation in the x's) and the differences among them in per capita income and inequality have arisen purely by chance.

But this expectation is actually wrong. The reason for this is that both statistics - the Gini and the per capita income - are themselves constructed from the same underlying data, the individual level or household level incomes, which themselves are produced through some partly random process.

To explain and illustrate it's actually easier to do a simulation (and like I said, I haven't worked out all the kinks).

I'm assume here that within each economy (simulation) individual incomes are draws from a log-normal distribution with parameters mu and sigma where

Why a log normal distribution? Well, for most real life economies the income distribution is skewed to the left (meaning median income is less than average income) and generally a log normal is a pretty good fit. Another potential candidate could be the Pareto distribution but that actually turns to be "too skewed" - overall it's something like mostly log-normal with Pareto at the very top. At any rate, what actually matters is that the incomes are generated by a data generating process which is left skewed.

(See here. Actually, I had a better reference somewhere but managed to loose it among my bookmarks)

I'm gonna keep stressing this throughout but the key is that all the simulated economies have incomes generated by the SAME process, that is the same mu and sigma.

So we generate, say a 1000 draws from a log normal distribution and then repeat this, say, 250 times (should do more than 1K but that was enough to considerably slow down my computer and anyway 1K obs might very well be more than what you have to work with in the real world when calculating Gini's). Then, for each economy (each set of 1K draws) we calculate the Gini, per capita income and some other statistics. Then we look at the relationship between the Gini and per capita income. And we see something like this...

(mu=10.3, sigma=.7, implying on average median income of about 29K, per capita income of 38K and an average Gini of .378)

or something like this...

(mu=10.15, sigma=.8307; I was trying to calibrate these roughly to US and European data but admittedly there's so many measurement issues here that's pretty hard to actually know what the median income of ... individuals?, households?, workers? ... is).

So. What we end up getting is a POSITIVE relationship between inequality and per capita income EVEN THOUGH we assumed that all the economies had the same "underlying economic structure". What "randomness" produces here is not a lack of a relationship but a fairly strong positive one. By this interpretation it could very well be pure luck that US ended up with higher per capita income and higher inequality than Europe, rather there being any actual "structural" differences between them.

But what is the intuition for these results? Well, it's Bill Gates. With a log normal distribution (or any left skewed one) once in a while, PURELY BY CHANCE, you will get a Bill Gates in your economy. A really really rich person out in the right tail end of the distribution. His appearance is purely random, but given enough economies to observe we should observe Bill Gates' in at least some of them.

What happens when a Bill Gates (in real life, a few thousand of them) appears? Well, a very very rich person has the effect of pulling up the average income in an economy but leaving the median income unchanged. And with a log normal distribution the resulting Gini is in large part a measure of the difference between the median and the average. In fact if we regress the ginis from out simulations on the means and the medians (or their ratio) we can explain 2/3 of the variation in the gini:

If instead the data generating process which throws up the initial incomes was symmetric (or close to it) then for every Bill Gates, on average, there'd be an anti-Bill Gates, a really really poor person in the left tail of the distribution to offset the effect of the other on the mean (more precisely there'd be on average same amounts of really really rich and really really poor). In that case you WOULD actually expect no relationship between income and gini for similar economies. But if the individual incomes comes from a skewed distribution then you will get a positive relationship.

Ok, so what does it mean and is it plausible? Well, unless I'm missing something, first thing it means is that there's plenty of reason to be suspicious of all them studies which regress ginis on incomes to uncover relationships between inequality and development. For the topic at hand it could mean that there isn't that much *real* difference between US and EU. By pure chance, in US a few hundred more Bill Gates appeared than in EU and as a result both per capita income and level of inequality got pulled up.

We have this tendency to look for "structural" explanations when confronted with patterns in the data. And so we start talking about the "Anglo-Saxon model" or "European social democracy" but we forget that these patterns could be purely random. Add to that the fact that usually these kind of debates serve ideological and political purposes and it's easy to see why folks are so quick to jump to conclusions. But the above would actually be bad news for both Euro-bashers - lower incomes in Europe is just a matter of luck - and US-haters - higher inequality in US would also not be a result of some rat race soulless system (at least not any less soulless than the European one) but again, an artifact of random chance.

And once you pause and think about it this way you realize that the European economies and the "Anglo-Saxon" ones have way way more in common with each other than they do with all the other economies in the world. They're all rich, essentially capitalist (don't kid yourself, European economies are capitalist, Scandinavia included) economies and hence any real differences between them are bound to be minimal.

(Note also that the above explanation is pretty inline with the paper and comments cited at Marginal Revolution linked to above)

A bit more on the effects of "job protection" on unemployment rates

2007-09-16T18:18:00.000-07:00

I screwed up in the initial algebra. The correction is below. You guys are supposed to check this for me!

In the comments to the last post Jane points out that whether higher unemployment benefits increase or decrease labor force participation and hence unemployment rate depends on whether the getting of benefits is tied to job search or not. In US at least, in order to qualify for the benefits a person must essentially list themselves as "unemployed" rather than "not in labor force" which WOULD actually increase the unemployment rate. On the other hand, even in US there are many benefits which are a function solely of income and not labor force status which would likely operate in the manner described in the last post. In addition some countries guarantee a "minimum subsistence income" which is also independent of whether one is job seeking or not. The overall point I guess is still that the crazy applied labor economists shouldn't just slap "unemployment rate" on the y-axis and "unemployment benefits" on the x-axis and try to draw some regression line through the scatter plot (and Greg Mankiw shouldn't do it in the new edition of his book) and pretend that it means something without considering carefully the actual institutional structure and how these benefits really affect incentives to 1) enter the labor force, 2) time spent looking for a job as opposed to just stating that one is looking for a job (this seems to be one of these instances where economists are forgetting one of their favorite adages that one should look at what people actually do rather than what they say they do). This is also one of the points of the HBGS paper linked to in the last post and it's a step in the right direction even though I still feel like they're playing along too much with "how's it been done so far".

Anyway, all that actually leads us to an empirically testable hypothesis. In economies where unemployment benefits are not tied to labor force participation and there is generous outside government assistance (say, housing subsidies for low income families etc.) unemployment rate would be LOWER than in economies which tie income subsidies to looking for a job (the effect may be small however since if income subsidies which are tied to looking for a job induce greater LFPR that would enter in both the denominator and numerator of the unemployment rate). This would actually be somewhat of a test as to whether people lie about looking for jobs just to qualify for unemployment benefits in the latter type of economies.

But I know that what you really want out of my posts is maths. So I'm gonna address a different aspect of the whole "job protection" issue - the prohibition, or more generally the increase in the costs, of firing workers. I'm gonna do it at a pretty low level of analysis - a reduced form model if you'd like, because if I could do it better I'd write a full paper about it, not a blog post.

If you think about it, and as derrida derider says over in CT comments, the effect of increasing costs of firing workers on the unemployment rate may actually go either way. On the one hand, the fact that it will be costly to fire some deadbeat workers once hired may make an employer less willing to hire workers in the first place and so cut back on the number of hires increasing the unemployment rate. On the other hand, all them deadbeats that do somehow end up being hired cannot be fired and hence stay out of the pool of unemployed workers decreasing the unemployment rate.

So suppose that at any point in time there's just two types of workers, those employed E(t) and those looking for a job, or searchers, S(t). We normalize the total population for simplicity to 1 so that dE/dt=-dS/dt or the inflow of workers into unemployment equals, obviously, the outflow of workers from the search pool. Here's a graph (I know you guys like these too);

So the change in the number of searchers is

where f is the rate at which employed workers are fired, q is the rate at which existing workers voluntarily quit their jobs, h is the rate at which job searchers are hired and E(t) and S(t) are the stocks of the employed and searchers at any given point in time. I'm assuming that f, q and h are exogenous because like I said, this is a reduced form model. What you'd wanna do ideally is to endogenize these fine members of the Arabic alphabet by deriving them from some profit/utility maximization set up.

But anyway, assuming a steady state where the number of job searchers (unemployed) and employed is constant (again, you'd wanna specify how this happens, that it's stable and all that) we have

or

where we dropped the time argument since these are steady state values. Using the fact that total labor force is constant at 1 and so S=1-E we have the employment rate:

and the unemployment rate:

Now, the proposition that implementation of "job protection" in terms of prohibition on firing results in employers being more reluctant to hire workers but also unable to fire some of the workers they've already hired means that:

or in other words that both the firing and hiring of workers has fallen.

Taking a total derivative of the unemployment rate we get:

or

(the reason both dh and df have minus signs in their paranthases is that both of'em are negative). So whether a prohibition on firing increases or decreases the unemployment rate depends on whether

is greater or less than

CORRECTION, LOST A FREAKIN' 1:

Interestingly, if there are no voluntary quits in this economy then the effect on the unemployment rate is always positive - more "job protection" means more unemployment. But for a high enough rate of voluntary separations (which again, here is exogenous) job protection could actually protect jobs in the sense of lowering the unemployment rate (at the cost of keeping a lot of unproductive workers employed, but that's another story). This also suggests that "job protection" of this sort would only decrease the unemployment rate in economies with already low rates of unemployment (high q/U) but not in economies with high rates of unemployment.

If there are no voluntary quits in this economy then the effect on the unemployment rate depends just on the relative magnitude of % changes in h and f. For a given levels of dh and df however, a higher quit rate makes it more likely that the change in the unemployment rate due to this policy is negative. That is the "job protection" policy is likely to lower the unemployment rate when the quit rate is high. Also if you start out in an economy with an already high unemployment rate, the effect of the policy would be to increase the unemployment rate. I hope I didn't flip a sign now that I found my 1.

Finally, and obviously, the unemployment rate would increase if the negative effect on hiring is large relative to the negative effect on firing.

Anyway. The larger point I think is that in a world where there's all kinds of institutional incentives to be or not to be in the labor force, to misreport oneself as looking for a job (hence as "unemployed") simply to acquire benefits, where employers are essentially forced to subsidize workers that they would not otherwise keep on their payroll (think of it as government outsourcing the job of providing a minimum standard of living out to the private sector), where the institutional details of how unemployment assistance and other benefits are provided play havoc with incentives in all kinds of different directions, and of course, all them other things, the unemployment rate is not really a meaningful statistics by which to compare economies by.

What are these crazy applied labor economists talking about?

2007-09-14T16:09:00.000-07:00

or, how HIGHER unemployment benefits LOWER the unemployment rate.

Disclaimer: Am I missing something?

Dani Rodrik links to a paper by Baker, Howell, Glyn and Schmitt and Henry of Crooked Timber picks up on it, about how more "protective" labor market institutions do not necessarily, contra conventional wisdom, cause higher unemployment in Europe. The paper (which I haven't gotten all the way through) makes some good points about measurement and definitional issues and claims that when one corrects for these the supposed association between "rigid labor markets" and unemployment disappears. Which doesn't necessarily mean that there is no relationship but just that the presently available data are not of sufficient quality to allow us to discern what exactly, if anything is going on.

Ok. Fine. But. Speaking of definitional issues.

Why would anyone ever think that higher unemployment benefits lead to higher unemployment rates?!?!???

(actually there are some, like two, reasons why, which I'll hopefully get to at the end of this post).

Now, certainly one would expect that higher unemployment benefits would lead to FEWER PEOPLE WORKING (or hours or whatever) and result in lower LABOR FORCE PARTICIPATION RATE but why it would lead to higher unemployment rates is beyond me (uh... again, except for them two reasons I'll get to. So maybe more like "next to me").

So let's get this straight.
You're UNEMPLOYED if - you ain't got a job but you want one or are at least actively looking for one.
You're NOT IN THE LABOR FORCE if - you ain't got a job and you don't want nor are looking for one.

Among all the talk of definitional issues (the fact that unemployment might be defined differently in Europe or in US, that unemployment benefits are not measured comprehensively, that coverage and enforcement differs, etc.) the above distinction is never made. Now, this isn't necessarily the authors' (HBGS) fault. From what I understand, and from some of the studies they refer to in their paper, it seems like these two get conflated in the literature all the time. At the very least the OECD and couple of other organizations seem to be guilty of this confusion. So HBGS are just following (a faulty) convention.

What you typically get in these studies is a graph like one below:

where some kind of measure of unemployment benefits is on the x axis and the unemployment rate is on the y axis. The difference between HBGS and older studies is that the older studies tend to find a positive relationship while HBGS argue that with new and improved data there is no or even a negative relationship and that hopefully when better data emerges we'll get a clearer picture.

Well, I hope that the better data emerges soon and that it confirms "standard theory" which is to say SHOW A STRONG NEGATIVE RELATIONSHIP BETWEEN UNEMPLOYMENT RATE AND UNEMPLOYMENT BENEFITS. That is after all what "standard theory" (most of it, except for those two famous exceptions) says.

So what does the standard theory say? Well, the most standard of the standard theories - that of a competitive market with wages which adjust to equilibrium - doesn't, cannot, have unemployment in it. The wage clears the market and everyone who wants a job at the market wage gets one. So the level of unemployment benefits doesn't matter for the unemployment rate (though it does for the labor force participation rate). So we need a less standard theory which has unemployment in it.

Easy. Slap in some "labor market rigidity" which puts wages above equilibrium level. This could be a high enough level of minimum wages, unions, efficiency wages or whatever. Whatever your favorite culprit, with above market wages, the demand for jobs will exceed the demand for workers and there will be unemployment. This is Econ 101 Principles stuff.

Now what happens when you increase the level of unemployment benefits? Welp, that would affect the labor supply curve. For a given wage, the opportunity cost of not-working is lower so less labor will be supplied. Some folks will drop out of the labor force. Labor supply curve will shift up and back. However, keeping that higher than equilibrium wage in place, the demand for jobs will not change. Ergo, the number of unemployed - the difference between labor supply and labor demand at the higher wage - has to go down. Of course labor force participation will also decline. So which way does the unemployment RATE move? Down. But before we get there consider this graph which illustrates how a sufficiently generous level of unemployment benefits can get rid of ALL unemployment in your economy:

Ok, but how do we know that, in the context of this model, the unemployment RATE will always fall?
Well, the unemployment rate is defined as

where w* is the above equilibrium wage and b is the level of unemployment benefits. Of course we expect that labor supply, LS, decreases with the level of unemployment benefits (labor supply shifts up) so

Differentiating the UNRate we then get

So explain to me again why are people expecting to find a positive relationship between unemployment rate and unemployment benefits?

Ok, now to those two reasons why higher unemployment might raise the unemployment rate.
First is JOB SEARCH. If you're getting higher benefits while unemployed (and unemployed means you're busy searching for a new job) you might take your time with your search and cherry pick your job offers. Hence you will be unemployed for a longer period of time which means that at any given point in time there will likely be more people unemployed and searching for jobs which means higher unemployment rates. You could probably get at examining whether increased job search length is behind higher European unemployment rates by looking at vacancy and turn over data (if it were available) but I'm guessing this is probably not the case. Anyway, strictly speaking this isn't "structural unemployment" which is what Europe gets blamed for, but "frictional unemployment" (if a meaningful distinction can be made).

Second we've got the HYSTERESIS idea which is usually associated with Oliver Blanchard and some others. The argument here would roughly say, ok, increased unemp benefits initially increase labor force particiaption rate not unemployment. But this means some folks drop out of the labor market. And a lot of skill are of the "learning by doing" type so by not having a job (because they're not looking for one) these folks' skill atrophy, become obsolete or just generally don't improve. Consequently, when and if these folks reenter the labor market they're likely to be lower skilled, and have a harder time finding a job. This, BTW, is what leads folks to look at the long term unemployment rate and unemployment benefits.

Both of these are plausible stories (though I don't think the first one is that important in this context). However, even if they are true empirically, the initial "standard theory" story about decreased unemployment rate which I told above is also true. So the two (three) effects could offset each other and you'd just end up getting weak results from the data. Huh. That seems to be exactly what we're getting from the data in fact.

So to sum up. No, I don't think higher unemployment benefits are the cause of higher unemployment rates in Europe. "Standard theory" doesn't think so either. If anything, these higher unemployment benefits hide the extent of the problem by lowering labor force participation rates. The "standard theory" suggests that if unemployment benefits in Europe (btw, Europe here mostly refers to Ger, Fra, Bel, Ita and uh ... Spa I think, where the UnRate really is high. Of course it refers to Western Europe, why would you think otherwise? Just like no one ever dummies for "former Ottoman colony", only "former British colony" and "former French colony" when studying the effect of colonialism on economic growth)... so ... uh ... yeah, if benefits in Europe resembled US levels their unemployment rates would be even higher.

Now, the story with other "labor market rigidities" is of course different.

As a final comment, I just wanted to note that the otherwise good Principles of Macroeconomics textbook by John Taylor, after really really carefully defining what is meant by "unemployment rate" and "labor force participation rate" makes this same mistake - mixing up labor force participation and unemployment - in its "Case Study" section which purports to explain the higher unemployment rates in Europe. So again, I don't blame HBGS for following a sketchy precedent.

Hello, I'm a first best economist.

2007-08-06T18:41:00.000-07:00

Actually, I’m not quite sure if I really am a first best economist. But I find it notable that so far no one has come forward and said “well, I’m one of them first best economists that you’ve been hearing about, what's going on here?”

Tyler Cowen has come the closest but even he thought it wise to hedge his bets (“better-than-first-best economist”). Rather the typical response has been “oh yeah, I’m definitely in the second-best camp, no question” and then “me too, I’m also with the sophisticated, nuanced, second besters!”. This of course brings out my natural contrariness and makes me want to be the first person to officially declare as a first best economist. The First First Best Economist. That way, when other first best economists come forward, if and whenever they deviate from the party line to, like, first-and-three-sevenths best economics, I will have the moral authority to give’em demerits. Of course it could just happen that I end up demeritting only myself.

As far as the substantial foundations for my claim I DO happen to think that if the world could be put on “autopilot” and the policymakers, the authorities, and the monkey that pulls the levers had to either automatically follow the directive:

a) "Do exactly what "Econ 101" tells you too!"

or the directive

b) "Assume all the potential market failures that could occur are in fact occurring! Implement Econ 340 solutions to all potential market failures immediately and simultaneously!"

I think we'd still wind up with a better world in a) than b). And that's assuming that the monkey doesn't have a lever, c), labeled "get more bananas for monkey while pretending to be doing b)" (an elaboration on Dani's third counter argument to second best economics). Which is I guess what makes me a first best economist.

Now of course economists of the >1 best school will counter that that's not a fair comparison. What they advocate is not mindless government regulation, micro overmanaging, problem fixing and excessive lever pulling. What they advocate is looking at each problem in detail and figuring things out on case by case basis, all carefully, reasonably and all. In other words that what I'm doing above is just ... GASP ... setting up a straw-man (a straw-man with perhaps a shade of truth to it. After all straw-men only work if they somewhat resemble actual humans)

Whatever could've suggested that course of action to me?

----
I think I like Michael Greinecker's classification system better (and I'm sorry to drag him into this):

I think one may be able to sort economists by how much they believe in the merits of both markets and governments.

Tyler Cowen - Believes in both markets and government.

David Friedman - Believes in markets but not in government.

Joseph Stigliz - Believes in government but not in markets.

John Roemer - Believes neither in government nor in markets.

It´s hard to find a ideological pattern here.

The last sentence is particularly true. Theoretically I think I most agree with John Roemer. But he's also the person on that list that I'm the farthest from politically. I probably agree the least-theoretically-but-most-politically with Tyler (given that these are correct summations of these fine folks' views).

-----

Other links:
Ezra Klein
Crooked Timber
and here's a guy who definitely beat me to it but telling you that at the beginning would've ruined the, uh, aesthetic point and I would've missed the opportunity to make that stupid demerit joke above.

This guy too (thanks to Robert for pointer)

Two things related to music

2007-08-04T16:32:00.000-07:00

1. Brian May gets a PhD in Astrophysics.

2. You might have seen this around before: Worst Album Covers. I just wanted to publicly fess up to actually owning records by one of these artists. And liking it.

Via God of The Machine.

Just so you know

2007-08-01T21:12:00.000-07:00

Someone somewhere asked me about my own professional research, rather than the annoying crap I post here. Welp here it is;

Mexicans who wind up back in Mexico after being in US - whether through their own choice or cause they got their asses deported - earn 20% more than the Mexicans who've never been to US.

20% more. That's like the equivalent of going to college, without actually having gone to college, by just putting your little foot over the imaginary crystal frontier . This is evidence for two possible hypothesis:

1. Self-selection - it takes a lot of freakin' guts to migrate to US, there's a lot of physical hardship, not to mention the emotional costs of being separated from one's family etc. and as a result only those who think they can *make it* come here. And these are the exactly the kind of people you'd want. As that old SNL skit said:
"you got a strong back? we could use you!" (as an aside, if it's true that Mexican immigrants primarily lower the wages of the lowest skilled native workers, how come the lowest skilled native workers aren't complaining? Mostly I just see some middle class movie critics and upper class Harvard professors who have a problem with it. And folks who worry about brown people having too many children. FOP.)

2. There are human-capital-accumulation possibilities available in US that are simply not there in Mexico. The ex-migrants come back to Mexico with a lot more skills than they have left.

This is one of those things that empirically it's gonna be really hard to tell apart. Another interesting aspect of all this is that the wage premium (us wages vs. mexican wages) IS NOT the highest for the poorest parts of Mexico. An immigrant from Chiapas or Oaxaca gets a big bonus compared to what they were making back home, but once you control for education and skill level, an immigrant from Mexico City actually gets, in percentage terms, way way more.

Bottom line = American institutions + Mexican work ethic - Lazy Americans "natives" who've been here for generations = fuck you China, Europe, come over here, let me slap your around a bit. We'll own this world for a few more centuries. Because WE DON'T get crazy about immigration. We're an idea (a wonderful, wonderful idea), not a people. Franks or whatever. And you people that have been here for generations, you're getting lazy, getting spoiled, if you don't look out you'll wind up like'em Europeans over there.

Here you go, we immigrants upraciate this much more than you spoiled monkeys:

All American!

Do Americans work more because of status concerns? Maybe, but in all honesty, it's hard to tell

2007-07-30T15:59:00.000-07:00

This case is more complicated than the status effects/savings case presented below. There's basically two reasons for this.

First, how much people want to work - labor supply - can be all kinds of weird, even without assuming any kind of "status effects". Labor supply curves can slope downwards (if the income effect dominates the substitution effect), they can bend backwards (same, except different at different wage levels), they can be discontinuous because of household specialization, and relatedly, there's two margins that people operate on when it comes to labor supply. Whether to play in the labor market in the first place (labor force participation) and then, if so, how much (hours worked). Add to that the various institutional structures which constrict the flexibility of labor supply and you can get pretty much anything.

The second reason why this is more complicated than the savings case is that now we have two "goods" (things which are desirable) which are subject to the "status effect" to a different degree. With saving and consumption the trade-off was between keeping up with the Joneses today, or keeping up with the Joneses tomorrow. In both periods there were status effects. However, the usual story with respect to work time is told differently:

Your annoying neighbor Jones works more and with his extra income goes out and purchases a Cadillac ("he means a Lexus but he don't know it") with a vanity license plate that says "YouAintGot1". At this point you start thinking "maybe I should have one" but the only way to afford it - given that you want to keep your level of savings constant so that we don't mix up our various "status effects" here - is to work more, slave like an ant and buy a Cadillac too. What ends up happening is that you end up working more than you'd like to just to keep up with the Joneses and you consume a (sub-optimal) amount of leisure.

The difference between this story and the one about consumption/saving one is that what is being implicitly assumed is that only one type of good - consumption of physical goods - is subject to "status effects". The other good - leisure - is not a "status good". Right at the start this is sketchy. Why couldn't leisure be a status good too? Obviously if I can show off to my neighbors that "I don't have to work hard for my income" by goofing off in conspicuous ways, why doesn't that involve status? Mr. Veblen, I'll see your Conspicuous Consumption and raise you some InYourFace Conspicuous Leisure! From what I understand (according to my reading of Victorian novels) that's how "status goods" used to play out. The merchant that was richer than an aristocrat was still looked down upon because, well, he still had to work for his money, whereas the aristocrat simply inherited it.

But never mind. From a theoretical point of view, the difference is that now not all goods are subject to the "status effect". Before, both "consumption today" and "consumption tomorrow" were both subject to status. In fact if both consumption of physical goods and leisure are status goods then we can just relabel:

consumption today = consumption of physical goods
consumption tomorrow = consumption of leisure

and then everything in the last post goes through - i.e. status effects essentially don't matter.

So let's consider the case where one good - consumption of physical goods - is a "status good", but the other - leisure - is not. If people for some goofy reasons are driven to compete in terms of their consumption of physical goods are they going to supply more or less labor? Will they work more or less?

Here it is actually plausible that the answer is "more", but not necessarily. Which is why a model which incorporates status effects on labor supply needs to be empirically tested. Them parameters need to be estimated. How do you know if some peoples care about status, rather than just having a lower disaffection for work (i.e. a lower marginal utility of leisure)?. The point here is that it's gonna be pretty much impossible to estimate this kind of thing.

Alright, so how do we go about analyzing this? Well, let's suppose that we've got a person whose welfare depends on their level of leisure, their consumption of some physical good ("trinkets") and also the consumption of trinkets by other people.
Specifically;

or

where c denotes consumption, l denotes leisure and c_J denotes the consumption of them annoyin' Joneses. Since our person has no power over how the Joneses choose their consumption level she regards c_J as a parameter and optimizes u over c and l.

Her consumption is equal to her income which is given by

where h is amount of hours worked and w is the wage. Normalizing the time endowment to 1, h=1-l, so

Graphing that sucker in consumption/leisure space you get your usual budget constraint:

The fact that both leisure and consumption are desirable, and assuming that there's diminishing marginal utility to both gives us a standard indifference curve. Since no one person has power over what average consumption is, c_J is just an argument in the utility function:

This means that one way to analyze what happens if people care about status in consumption is to see how the indifference curve changes when other people's consumption (here average consumption) changes. In other words, what happens to the slope of the indifference curve when, say, average consumption goes up. There's two possibilities. The indifference curve either gets flatter or steeper. If it gets flatter then the amount of leisure will fall and consumption will rise. If it gets steeper then the opposite will happen:

On the other hand it could be the case that your consumption gets "crowded" or "congested" by the status seeking of others. Every time you buy a damn Cadillac, Jones does too and you get no utility from it (this is another way of saying that other people's purchases mess with your marginal utility of consumption of physical goods). At some point you might decide to not bother and switch to the one good that is not affected by others' choices - leisure. In that case your indifference curve will become steeper rather than flatter and you will increase your leisure and decrease your consumption:

So which one is it? Well, to see what happens we can look at how the slope of the indifference curve changes when there's a rise in average (Jones') consumption. Of course if someone doesn't care about status at all then there won't be a change. Your econ 101 (or maybe 201 in some places) tells you that the slope of the indifference curve is given by the ratio of marginal utilities:

where the top is the marginal utility of leisure and the bottom the marginal utility of own consumption. To see the role of status effects we take a total derivative of (absolute value) that with respect to average consumption:

If that equation above is negative then we have the first case with the indifference curve gettin' flatter. If it's positive then we have the second case, with an increase in average consumption INCREASING leisure.

Of course
and

are just cross derivatives of leisure and consumption with other people's consumption:

Are these guys positive or negative? If Jones buys his Cadillac how does that affect your enjoyment of leisure? On the other hand it's somewhat plausible that your MARGINAL utility of consumption would go up if c_J increases - you not only get the extra benefit of consumption for its own sake but also you catch up with the Joneses. But it' not clear. Still, I'm willing to concede here that the relevant parameters work out so that the net effect of an increase in average consumption is to raise labor supply. But that's exactly why this is the sort of thing that you'd wanna estimate empirically. And that's gonna be messy.

To illustrate, take a simple specification of utility with own consumption, others' consumption and leisure:

where c is own consumption, c_J is others' consumption, h is own hours worked, w is own wage, h_J is others' hours worked and w_J is others' wage. Gamma measures the dis utility of work effort. Phi, like before, measures the extent of the "status effect".

Maximizing that sucker wrt to h gives you a labor supply function:

If phi=0 - no status effects - then this would just collapse to

at which point you could just log that monkey and run some regressions in order to estimate alpha and gamma.

This is what it looks like for the average person (Jones):

and if you can find some variation in h and w then you could, at least in theory run a regression like this:

The problem with this is that both gamma - the disutility of work - and phi - the status effect - all wind up in the constant. In other words, there's no way to know - even if you can estimate this thing - whether people in a given economy work more because they care more about status, or because they just dislike working less. If you got some taxes, or labor market distortions running around that's gonna be in there too. And it could be very well the case that what looks like "Americans work more because they care about status" is really "the freakin' income taxes are lower". Or maybe Americans are just "more hardworking" for them, anthropological, sociological, psychological, and English Studies reasons. How would you know?

We can actually use the equation above for average/Jones' hours worked to plug into any ol' person's labor supply function. In that case we get a very nonlinear equation. We could still estimate it - to be honest I'm not up to my nonlinear econometrics - but I'm pretty sure you'd get the same problem. Work it through yourself. What you'll get is that with nonlinear methods you can estimate two parameters but you've got three variables you care about. In other words, one of your parameters will be a (nonlinear) combination of alpha and gamma, and the other a (nonlinear) combinations of alpha and phi. Which, again, means that even when you get all kinds of fancy statistically it's next to impossible to separate the "status effect" (phi) from just plain ol' "don't like to work effect" (gamma).

So how would you know? And anyway, isn't worry about "status" an Old World type of thing?

A final note here. You could get some estimates by considering some kind of variation in wages and labor supply levels. But this is going to get you thinking about exactly what kind of status people worry about. You could estimate the above equation across different countries. But that brings up the alpha/gamma problem mentioned above. You could assume that people care about status within their own status, zip code or county. Or maybe educational groups. At each point the same issue will arise. I could explain all this better, but god damn, I'm tired after writing all this.

Do Americans save so little because of status concerns? Nah.

2007-07-30T14:43:00.000-07:00

Suppose you live next door to an annoying family named the Joneses. One day Mr. Jones goes out and buys a boat, which he then displays prominently in front of his house, washes it all the time, puts cute little ribbons around it and names it "NotYours". This rubs you the wrong way, you feel like your "status" has decreased and it gets you thinking that maybe you too should go out and buy yourself a boat. Maybe you should save less, consume more and keep up with the Joneses.

This is the usual story told of how "status effects" can lead to (sub-optimal) level of saving on the part of folks, why Americans don't save and how consumerism is going to be the death of us all.

But wait a minute. Suppose that, instead of buying that boat in order to keep up with the Joneses now you ... SAVE more money, get it back with interest in few years and buy... an even bigger boat! That'll show the Joneses! Maybe "status effects" lead to increased savings!?

The point missed by the usual story is that saving is just postponed consumption (I like the Buy-Nothing-Day. I like the Day-After-Buy-Nothing-Day where you spend all the money you didn't spend on BNT even more), so if you ARE trying to keep up with the Joneses you face a trade off: Keep up today, or keep up tomorrow. How you gonna play it? (hint: it might depend on your marginal rate of intertemporal substitution)

You also have to consider that the Joneses are playing the same game. They go through exactly the same logic. In fact, they might even anticipate that if they purchase a boat, you will purchase one too (or a bigger one) in order to keep up and any benefits of "status" will not materialize. Hence they will probably not buy the boat - unless of course they happen to enjoy going out on the lake in the summer and fishing, which is after all the primary, the overwhelming, if not the only reason people buy freakin' boats.

The end result might very well be that EVEN IF people care about status this has no effect whatsoever on their behavior.

Ok, here's the maths. I've got two cases - the first has a plausible "standard" representation of utility (people's preferences) which includes the fact that people care about status. But this case is boring. For a good reason. Nothing happens. It looks exactly like the case where people don't care about status. The second case has some more interesting dynamics, but, to be perfectly honest, from a purely theoretical point of view it's a bit sketchy (7 bonus points if you can tell me why).

The basis for all this is the Ramsey model of saving. In the standard model consumers have a utility function like this:

where c(t) is consumption at time t and theta measures the degree of intertemporal substitution mentioned above. The consumers discount future consumption at the rate and face the interest rate r.

The optimal path of consumption (hence, saving) is solved for by setting up the Hamiltonian, finding the first order order conditions, differentiating them wrt time and solving out. What you get at the end is the following differential equation for growth rate of consumption over time:

growth rate of consumption = g(c) =

Then in the long run the economy converges to a steady state such that the real interest rate is equal to subjective discount rate and consumption is constant, g(c)=0 (here we're assuming no technological growth ).

Alright. We modify the above utility function to include the possibility that consumers care not only about their own consumption but also about that of others. The simplest way to do this here is to include average consumption as an argument in their utility function.

Case 1.

where c_i(t) is person i's consumption at time t, c_a(t) is average consumption at time t, phi measures the strength of the "status effect" and it is less than 1 (more bonus points for telling me why).
The first order condition is then (omitting time arguments):

where
is the Hamiltonian multiplier for person i. Taking logs and differentiating wrt time we have:

The second first order condition (wrt to the state variable) tells us that:

Note the lack of i subscript on the real interest rate r. This means that we're assuming that all agents face the same interest rate. Since we want to examine the "pure" effect of status on consumption and saving rather than that of credit market imperfections this is a natural assumptions in this context. Of course if different consumers face different r's things get more complicated (and more ad hocy)

Setting the two FOC's equal we get:

Solving for g(c_i) we get:

which is POTENTIALLY different from the simple we had above. Note that if phi is zero than that equation becomes the standard equation in the model without "status effects". However, the second term on the RHS shows that how AVERAGE consumption changes has the potential effect of affecting how any one person's consumption changes. But is it up, down, or do the effects cancel out? Well, to solve it out, we could assume that all consumers are identical, blah blah blah, and then solve out for the "representative" consumer, but we don't have to. What we can do is to solve the above diff equation for the average consumer, then plug in that growth rate of consumption into the equation for any ol' person i. This means that we are NOT assuming that consumers are all identical. These malchiks can be as heterogenous as they wanna be. Replacing the i subscript by a above we get:

which means that the AVERAGE person's consumption follows the path which is the same as in the model without "status effects" - for the average person it washes out. This is not surprising if you think about it. Now that we have g(c_a) we can plug that into the equation for g(c_i) and get any person's consumption path. The algebra is straight forward and what you get at the end is:

for all i. In other words, same as the model without status effects.

This is what I meant by the fact that this version is boring. After all that math you get back to exactly what you had if there were no "status" effect. Boring, but instructive, I guess.

(Note also that the way the whole thing works we could replace the average person with the median person - the most common growth of consumption - and it would still work. In fact, if everyone in this society compares themselves to Bob, where Bob's growth rate of consumption is given by g_bob, all this still works).

Case 2.

Here, instead we'll assume that the utility function which represents person i's preferences is given by:

where the notation is same as before and phi is still the "status effect" and is still less than one (the case where it's >1 is actually fun to work out from a mathematical point of view in the Ramsey model with Cobb-Douglas Production Function though it's empirically/economically implausible. Outward spirals and all. Which don't matter because of the transversality condition which I haven't even mentioned.)

Now the first order condition is:

Logs, time derivatives, second FOC same as before and all that gets you:

Again, note that if phi is zero, this is the same as the "standard" model. I'll save you the long story and just note that for roughly similar reason as above, the growth of any person's consumption, g(c_i), winds up being the same as the growth rate of the average person's consumption, g(c_a). Here however, this matters. Specifically, dropping the i and a subscripts and just denoting growth of consumption for anybody by g(c) we get:

which IS different from the standard model (). So, is the growth of consumption higher, lower, or the same? Obviously it depends on theta (you can also see in the above, if you play around a little why we need phi<1). Theoretically, theta, the reciprocal of the rate of intertemporal substitution, can be between 0 and infinity. If theta = 1 then utility is logarithmic and we get the standard model - "status effects" don't matter. If theta<1 then consumption will grow slower without the "status effect" than with it. If theta>1 then consumption will grow slower with the "status effect" than without it. In steady state, where rho=r, it doesn't matter.

Empirical estimates of theta are in fact all over the place. Roughly speaking it depends on whether you're looking at micro studies or macro studies. Saving behavior over time in most economies suggests a theta above 1 but somewhat less than 2 (Barro and Sala-i-Martin) which would mean that "Keeping Up with the Joneses" economies would have HIGHER saving rates than those where people don't care about status - flying in the face of the simple story I started this whole post with. On the other hand, micro studies - some of them actually looking at labor supply which is also related to theta (see next post, if I write it) tend to find much lower values of theta, so it could go the other way. Theta also measures the extent of risk aversion, and if you think that there's something to the equity premium puzzle other than pure weirdness than you'd also think theta is >1. At any rate, theta=1 is not implausible. So... again, status effects don't matter, even with this sketchy formulation

(answer to the bonus question about why this formulation is sketchy - "status effect" formulation of utility should mean that if you increase a person's consumption but keep their status constant by increasing average consumption as well then their utility should not decline. Case 1 has this property for all c_i and c_a, as long as phi<1. This case does not).

Final note: I don't really buy into the Duesenberry Hypothesis. Maybe at this point, I should note that I really like Robert Frank's article on the homo economicus with a conscience (jstor req), but I think he's wrong on this topic. I readily confess that I haven't read the original but only read the representations of DH that one can find around. The whole thing to me seems to ... dare I say it? ... lack microfoundations. I.e. It COULD be that status concerns increase present consumption. On the other hand it could go the other way and in fact probably shouldn't matter. And estimations of a Duesenberry style consumption functions are subject to the usual critiques of consumption function estimation and then some. Ok, if I feel like it next post is on "status effects" and labor supply.

Another final note: You can set this up in a two period model with "consumption today" and "consumption tomorrow", discrete time and all that but you still get the same results.

Non Tariff Barriers

2007-07-23T22:05:00.000-07:00

(or how trade “protection” really works, or, the reason why the border is "wide")

Here’s a translation of a two recent news stories from the Polish press – Polish travelers carrying goods into Belarus are now required to bring condoms with them or else! And Belarus has its first declared millionaire.

---

Going into Belarus? Only if you bring … protection!
A Polish driver traveling to Belarus is required to bring with him a first aid kid. And now, also some condoms. Alexander Lukaszenko’s border guards will not lift the border barrier (szlagan?) until they see the required box of condoms.
Most of the Poles crossing the Poland-Belarus border regard the new regulations as ridiculous whose aim is only to make life more difficult. “What do I need condoms for?” – complains an irate Marcin Zlotnicki, a truck driver for a export firm from Lublin – “I’m not going there to have sex. I just want to deliver my load. It’s not enough that at every stop you have to pay bribes, now we’re supposed to find some place that’ll sell us condoms before the border”

The strange requirements of the border are not known to everyone yet. Many truck drivers think it’s a joke. But it’s not. One person who did not laugh was a local priest who wanted to cross the border in order to see of his parishioners on the other side of the arbitrary line, the Lublin cleric Piotr Mrozik: “Because of this new regulation all I had was trouble. Because, obviously, I didn’t have any condoms, they grabbed me, put me up against the wall and searched me. Then I had to go to the nearest gas station, and in my clerical garb ask the obviously embarrassed attendant for a pack of condoms just so I could cross the border. It was a ridiculous situation!”

Polish custom guards say they don’t know anything officially about the new requirements. “We’ve only heard about this from annoyed truck drivers. Initially we didn’t believe it ourselves” says Marcin Czajka from (some complicated name for a Polish Customs office) in (an even more complicated name of a Polish border town). “Supposedly the Belorussian border guards say that it’s for reasons of “safety and security”, so now all first aid kits which cross the border are required to include condoms. I guess it’s just in case or something”.

Aleksander Koncki, the Belorussian consul in Bialej Podlaskies, asked by our journalists about the subject is himself surprised. “No one told me anything. I don’t know if that regulation really exists. I think it’s just a rumor”.

The news about the new requirements of the customs guards has spread quickly among the border villages which engage in much trade with their Belorussian neighbors. Some villagers have been quick to realize upon the business opportunity. Aside the standard fruit and vegetable sellers one normally sees along the roads there have appeared mobile condom-sellers. At the gas stations near the border the supply of condoms has run out.

Grzegorz Gorczyca from the local Chelm Autoclub (like a local AAA) explains that even before this latest regulation, the requirements of crossing the border have always been arbitrary. “They always, for some reason, ask about condoms. And if you got condoms then they ask about something else. It’s just another pretext to extort another bribe. Now it seems the Belorussian border guards systematized it and made it official. I’m not especially surprised. If you’re going east, you expect these sorts of things.”

----

Depending on how you wanna look at it, here’s something on a more upbeat note:

A sensation among our neighbors! Belarus has it’s first millionaire!

This is the first time that the Belorussian economy has seen such a thing! Belarus has its first millionaire. A real millionaire, counting the income in dollars. So far no one has managed to accumulate a wealth of more than few hundred thousands. After all, Alexander Lukaszenko is a communist who, like Janosik, gives to the poor after taking way from the … somewhat less poor.

The information about the first ever Belorussian millionairehas been leaked out by the Belorussian Tax Office (Belorussian IRS). Apparently Belorussians tax official could not believe their eyes when they saw that some Belorussian had the courage to report an income of 20 billion rubles (9 million dollars). Obviously the Tax Office did not release the name of the magnate. But it did not hesitate to report the occurrence to the proper authorities (i.e. the “security police”,the KGB, i.e. the whatever version of Gestapo). Now the job of inspecting the person in question has been turned over to the agents, inspectors, controllers, bureaucrats and other person in government.

Most likely, if it turns out that the person in question is a (communist) party member and one of the friends of President Lukaszenko, who only got his millions “following orders” then the Belorussian Tax Office will leave him alone. On the other hand if it happens to be the case that some Belorussian had the nerve to have a decent business idea and got rich selling some product that Belorussians actually wanted, it would be better for him if he got his things together and left the country right now.

It’s not like Belarus is known for its friendly business atmosphere. Tax audits can last for many years, basically until the person investigated pays up what is demanded of him. If a “fault” is found then the punishment is severe. Someone who “misreported” their income pays, at the very least 150% of their income.

-----

Added (also corrected spelling):

Here's some rocking Belorussian tunes.

Daniel's post over at Crooked Timber

2007-07-22T20:51:00.000-07:00

Here it is, no comment necessary but further repostings would probably be good:

-------
IMPORTANT: Time to do the right thing by our Iraqi friends
Posted by Daniel

I’ve written on this in the past (as has John, and Jim Henley, and it’s been in the New Republic), but the situation is now urgent as well as serious – there is a very grave danger that the UK is preparing to sell its local employees in Iraq down the river, and the time to do something about it is now.

Iraqi interpreters used by the British Army and CPA South have already been hunted down by death squads. The British forces in and around Basra are no longer really sufficient to protect themselves, let alone their employees, as Channel 4 news details.

There really is no way of keeping these people safe while they are in Iraq, and they need to be kept safe. Quite apart from what one would call a “debt of honour” (the phrase is somewhat pompous, but accurately describes the situation), it never makes sense to get a reputation for abandoning one’s friends. Therefore, the Iraqi staff used by the British in Iraq need to be given asylum in the UK, along with their families.

This is not the current policy of the UK. The Home Office has simply suggested that Iraqis put at risk by their work for the British “register with the appropriate UN refugee agency”, joining the mountain of 2 million-plus refugees and IDPs already caused by the war. This simply isn’t good enough; the safety of Iraqis who are marked out as traitors by the insurgency can’t be guaranteed in the refugee camps either.

Denmark has already done the right thing, giving asylum to all 200 Iraqis who worked alongside their forces. The vast majority of the people concerned are already fluent English speakers and number only a few thousand, so we are not talking about a huge burden on the UK’s asylum system here – certainly nothing like the scale of the Ugandan Asian asylum operation, which is itself generally recognised to have been a massive net positive for the British economy and society.

British readers of CT ought to write to their MPs to ask them what they plan to do about this problem. It is best if you can write an individual letter, perhaps based on the set of bullet points over the fold, but if not, then the form letter on Dan Hardie’s blog is better than nothing (Update: the entire form letter is now also below the fold, after a burst of realism about how many readers you lose per click). I’ve also emailed my small set of contacts in the media about this story – as the links above show, to a large extent the “MSM” is already working on it, but anything we can do to keep it on the front pages will help. American readers of CT, well I guess you probably need to be thinking about how to organise something similar when your politicians start doing the same thing.

(other CT authors – can we leave this one up at the top of the page during Monday UK daytime please?)

bullet points for a letter to an MP (Dan H wrote these):

* It is morally unacceptable that Britain should abandon people who are at risk because they worked for British soldiers and diplomats.

* This country will be shamed if any more Iraqis are murdered for the ‘crime’ of having supported UK forces.

* Iraqis who worked for British forces should not be told to leave Iraq and throw themselves on the mercy of United Nations relief agencies in Arab countries: these agencies are already being overwhelmed by the outflow of Iraqi refugees, and Iraqi refugees who have worked for British diplomats or troops may well be targeted by local jihadists.

* There is plentiful evidence that armed groups in Iraq kill the families of those they consider ‘enemies’: for this reason we must extend the right of asylum to the families of those who worked for us.

* It is entirely practical for this country’s troops in Iraq, and its embassies in neighbouring countries, to take in Iraqis who have worked for us and fly them to the UK. Indeed, there is already considerable anger among British servicemen that Iraqis are being abandoned in this way.

* This country is large enough and rich enough to accommodate several thousand Iraqi refugees. Denmark has already given asylum to all 200 Iraqis who worked for its smaller occupying force.

* It does not matter what your MP’s views (or what your views) are on the invasion and subsequent occupation of Iraq. People who risked their lives for this country’s soldiers are now being abandoned by the British Government. Their lives can and must be saved by their being granted the right of asylum in this country.

* This policy should be implemented regardless of whether British soldiers stay in Iraq or are soon withdrawn. But it must be introduced soon: applications for asylum cannot be processed in a lengthy fashion, as the security situation in Basra is deteriorating rapidly, and delay is likely to lead to further killings of Iraqis who worked for British troops.

and here’s the form letter, and a repeat of the Write To Them link.

Dear (MP’s name)

As your constituent, I am writing to discover your views on the treatment of Iraqi citizens who are working, or have worked, for the British Army, t he Coalition Provisional Authority, and contractors working for both organisations in the South of Iraq. In particular, I would like to know if you support the right of these people to indefinite asylum in the United Kingdom. I strongly suggest that they do indeed have this right. They have, by definition, put their lives at risk by the support they have given to British soldiers who were sent to war by a vote of the House of Commons.

Whether you- or I- supported or opposed the invasion and occupation of Iraq is immaterial. The risk run by Iraqis working for British troops is even greater than that run by the soldiers themselves. British soldiers are now suffering very high casualties in Iraq, and are continuing to serve bravely- but the ir local staff are obliged to live among neighbours who will, in many cases, be sympathetic to or even belong to the armed groups fighting the British army. We owe these people a clear moral debt. We cannot allow them to be murdered for the ‘crime’ of helping our service men and women.

The most effective way of helping these brave Iraqis is to offer them indefinite right to remain in the United Kingdom. There is plentiful evidence that armed groups in Iraq make a practice of murdering not only their ‘enemies’ but their families too: and for this reason we must extend the right of asylum to the families of those who have worked with us. This policy should be enacted immediately whether our forces stay in Iraq or are soon withdrawn. Applications for asylum cannot be ‘processed’ in a lengthy fashion: the situation in Basra is deteriorating, the ability of British soldiers to protect those that work for them is seriously compromised and any delay is likely to lead to the murder of Iraqis who have worked for the British military.

I would appreciate your views on this matter.

Yours sincerely
NAME

MINDME

2007-07-15T11:24:00.000-07:00

Mark Thoma takes the Free Exchange blog to task for mis attributing views to him. In his response the following sentence jumped out at me:

Mark Thoma:
Please quit implying my ideology drives my economics, it doesn't.

Can I get that on a T-shirt or a bumper sticker? Or maybe it should be made into one of those internet age acronyms like IMHO, ROTFL, AFFAIK, etc. so that it doesn't have to be typed out every time it's relevant.

MIDNDME?

MINDME is more aesthetic but it's grammatically incorrect.

(and anyway, even if it did, it wouldn't be the end of the world, or the debate for that matter. As Shumpeter said, just because it's ideology, doesn't mean it's wrong)

Doxy Wars II

2007-07-12T15:17:00.000-07:00

Max Sawicky - who last time around pretty much stated that the only good kind of Economics is a left wing Economics (when he was warning fellow heterodoxists against trusting too much in Behavioral Economics because it too could be "reactionary") - has a pretty little smear job over at TPM Cafe. I guess I could use a nicer phrase to describe his article, but since in the fairly recent past Max has not found it in his heart to give others a charitable reading, I don't see why I should extend him that courtesy. And this is part of a theme. Last time this whole heterodox vs. orthodox economics thing went around the Internets I walked away with a distinct feeling that many of the mainstream economists (Brad DeLong, Mark Thoma, Tyler Cowen, if he can be called mainstream) where bending over backwards to find something nice to say about the heterodoxists (I believe the only one who called them whiners and said mean things (though probably true) about them was Henry Gintis, a fellow heterodoxist), while most of the heterodox behaved like assholes or spoiled little brats with a sense of entitlement (I'll leave it alone at that). Let me note the exceptions that pop in my head immediately- Barkley Rosser was as always calm, reasonable and with many interesting things to say. Robert was esoteric, cryptic and, uh, less than clear as always but polite. There were probably a few others but anyways... no more Mr. Nice Mainstream Economist.

Let's go through Max's list. (Also read the comments on Max's site. It's true. I insulted what he said (which I think is fair game in these kinds of debates). He on the other hand goes straight for the personal. "Toady". "Comedian". I'm surprised that it hasn't been suggested that I take money from Evil Corporations. Did I mention the word "asshole"?)

1. Supply and demand, 1. This celebrated and most basic economic model while in principle multidimensional in practice obscures anything interesting that affects market conditions. It bespeaks militant, ideologically-based reductionism. A good illustration is the minimum wage debate. In the usual supply and demand model, a minimum wage can only reduce employment. Nothing else is logically possible.

Bunkum. In the "usual" supply and demand model the consequences of a minimum wage can be:
1. Unemployment if the min wage is set high.
2. No effect if the min wage is set low.
3. Higher wages with no effect on employment if the labor demand curve is inelastic.

Now, the 3rd one is pretty "unusual" in that it probably doesn't happen very much. But Max's speaking of logical possibilities. What is a weasel word like "usual" doing in an enumeration of logical consequences? It's there so he can BS his way out if called on it.

2. S&D, 2. The outcome in an supply and demand model in principle has no inherently attractive qualities, in and of itself, since it depends on the distribution of ability to pay. If Oliver Twist has no money to buy a crust of bread, his zero allotment is "efficient." The lack of any normative foundation is typically glossed over.

Well first, you need a positive model before you can start making normative judgments. And the equilibrium of the "usual" S&D model does have one attractive feature - no waste, no money left on the table. Okay, lemme explain slowly the concept of Pareto Efficiency here because folks is confused.

Suppose there's a total of 100$ in the economy and two people, Meriadoc and Pippin. If all of that 100 bucks is in some way fully divided between the two, then regardless of who gets what, the outcome is said to be Pareto Efficient. Not fair. Not just. Just efficient. But suppose that only 80$ gets divided between Meriadoc and Pippin with, say, Mary getting 79$ and Pip getting 1$. The other 20$ just lies there on the sidewalk rotting. Then we have inefficiency. We could pick up the 20$ and give it to Pip, or give it to Mary or split it up between them two. Even if we give it all to Mary, so that now he's got 99$ and Pip only 1$, assuming Pip and Mary don't care about relative status, only more money, then we can all agree that (Mary=99, Pip=1) is "better" or, more precisely, "more efficient", then (Mary=79, Pip=1). (If they do care about status or whatever, you can reformulate the problem in equivalent terms)

Of course we may care about income distribution, inequality and all those other things. But that comes later. The PO criteria just says, if there's 20$ laying on the side, for goodness sake, pick it up and give it to someone, anyone. And that's the attractive property that a "usual" S&D equilibrium has - no 20$ left lying around rotting.

3. Gross Domestic Product (GDP). Add up all the quantities in the supply and demand models over the year ("final goods and services") and you get GDP. Solemn assurances that GDP is not synonymous with economic welfare fall easily by the wayside. More GDP (and less leisure time, less environmental quality, a less sustainable economic future) is always better. If terrorists knock down the Empire State Building, GDP could go up. More! Better! Comrade Stalin would approve.

This one's dumb in several ways. In fact it's so dumb it's embarassing - Max doesn't seem to even know what GDP measures. First, measurement or the definition of GDP HAS NOTHING TO DO WITH FREAKIN' SUPPLY AND DEMAND! It is simply adding up everything that has been produced by an economy in a given year. True, there are practical issues in what weights to use when constructing this measure - the prices - and a lot of sweat has been poured out over tackling that issue but for one if all you care about how GDP changes over time, a lot of those problems go away. And that's not what Max is talking about anyway. Second, the part about "assurances..fall easily by the wayside" is just pulled out of thin air. And um, for a given amount of leisure, and a level of environmental quality, more GDP is better. If you want something that measures other things then look at another measure.

Third, and perhaps most tellingly, the statement about GDP going up if terrorists destroy the Empire State building is a classic example of the Broken Window Fallacy, and anyone minimally trained in economics should know better. Presumably Max thinks that GDP would go up because you'd have to use firemen, policemen to deal with it, and construction workers to rebuild it. Of course the firemen, policemen and construction workers employed to deal with the terrorist strike are firemen, policemen and construction workers who would otherwise be employed in some other endeavor and so GDP WOULD NOT go up.

But suppose that through some weird, complex, effects, GDP could go up because of a terrorist strike. So freakin' what? DO YOU REALLY SERIOUSLY THINK THAT THE US GDP, OR THE EUROPEAN GDP, OR THE GDP FOR ANY FREAKIN' COUNTRY IN THE WORLD HAS INCREASED OVER TIME BECAUSE OF AN INCREASE IN TERRORIST ATTACKS? Or because of car accidents (Nader used that line once when I saw him speak)??? NO! It has increased over time because of investment and technological growth. This is misleading shyster-ness at its worst.

4. Commerce versus The Market. Forgetting about boring concerns of economic justice, the idea of a competitive, functioning market is actually very rigorous. So much so, there are hardly any good examples of such things. (The example often used is grain, undoubtedly by people who have never seen the back end of a cow.) When the Federal government tries to organize markets with the buzzword of "competitive sourcing," the results are even more comical. There is plenty of commerce, but there are very few markets, even though economists pretend they solve most of our problems.

I'm not gonna say much about this one because it's too ambiguous to really know what he's talking about. Let me just 1) suggest that Max looks through the, I dunno, last five years, of top economic journals and see what small percentage of articles actually assumes perfectly competitive markets, and 2) note that if you have a badly designed government auction then you get bad outcomes and if you have a well designed government auction you have good outcomes. How do you get a well designed auction? Yo hire some mainstream economists trained in game theory friend.

And having spend a lot of time on the farm as a kid let me just note that I've seen plenty cows but never this much bullsh... never mind.

5. In Search Of: The profit motive. Professors tell their gullible students that business firms maximize profits. This induces efficient use of resources and fortuitous allocation of capital. But if you study the economics of firms, even under orthodox auspices, you find out they don't maximize profits.

Because I'm getting lazy I'm gonna skip this one too. But what is it that firms do anyway? Maximize the number of ponies per capita? All the stuff on the principal agent problem, role of managers, market shares, has been part of mainstream, even in undergrad teaching for years.

6. The deficit's gonna getcha. Years of braying about the evils of budget deficits have failed to be borne out by the purported consequence -- high interest rates. The entire traditional macro apparatus fails to allow for the interventions of large foreign lenders who aren't dumb enough to believe what the textbooks say.

So apparently Max is with Dick Cheney on this one. Hey, cut'em taxes George, deficits are nothing to worry about. (I'll go out on a limb here and guess that Max thinks deficits are not a problem if they're produced by high spending by left wing presidents, but are a problem if produced by low taxes under right wing presidents) More substantially, you might not see higher interest rates as a consequence of budget deficits if the Fed doesn't want to see'em, since that's ultimately where interest rates get set. But since Max has put my mind at rest here, I've learned to stop worrying and learned to love the deficit.

7. Capital fundamentalism. As with reductionism of the S&D model, growth modeling zeroes in on private capital accumulation, even though a) other factors are demonstrably important and beg for attention; and b) private capital accumulation may be a consequence of other factors, rather than a cause and appropriate object for policy. Out of an obsession with this premise, the International Monetary Fund has screwed up a lot of countries too weak to ignore its advice.

This is another one that's particularly dumb. The story of Growth Theory in the past ... 25 years ... has been all about looking at "other factors that are demonstrably important". In fact, if it wasn't for that past 25 years of mainstream theory we might still be putting too much emphasis on capital accumulation today (and worrying too much about stuff like the CCC). Either Max hasn't read a Growth paper in the past 25 years or he's making stuff up for an audience that may not know any better. As far as b) goes, why the heck do you think all them Growth Regressions (to take an example, other approaches do the same thing) go to all these lengths to control for "endogeneity of investment". Same for human capital (ever heard of Bils and Klenow?). What you get at the end of the day is that once the growth-as-a-cause-of-investment (rather than vice versa) is controlled for, there's still some room for investment playing a role. But see answer to a) on that.

8. Every import is sacred. Regulation of markets is allowed, unless the market includes parties from different countries. Then it is strictly verboten.

Huh? Oh yeah, I remember a while back EPI was estimating "job loss due to trade" by counting every unit of imports as displacing exactly one unit of domestic production. Even Paul Krugman made fun of them for it.

9. The unnatural rate of unemployment. Economists used to say it was 6.0, maybe 5.5 percent. Lower would give rise to ruinous inflation. The huge social benefits of another couple of percentage points less unemployment were -- are -- implicitly discounted. Current rate is 4.5. 'Nuff said.

This particular one may have some truth to it. But it's a "smart after the fact" kind of thing. If the Fed was trying to get unemployment down to 4.5 in say 1978, not only would it had not been able too, but inflation would've been very high. Oh wait. It actually was very high.

10. "Power? You want the political science dept." Power looms over economic transactions, except in economic theory. Workers do not hire capitalists. Consumers do not choose merchants. Shareholders do not choose managers. Voters do not choose elected officials.

Maybe workers do not hire capitalists. But they do choose what employers they work for. Hey, I worked 12 years in the food industry, about half at minimum wage and I quit my job plenty of times. And seriously, "Consumers do not choose merchants"????? Is that actually said with a straight face? Is this heterodox wisdom that we've been missing? It happens to be summer and so I'm spending some time with the family. Always, always, my folks insist on telling me about where they shop, which stores have the best deals for the best items, and how they...um...choose the merchants they patronize. Again, I can't believe this is said in any kind of seriousness. Same freakin' thing for the voters - though I'm guessing here Max has the political lobby's and so on in mind. Maybe he's right. Maybe he knows better. After all he works for one.

Here's some folks who are nicer about it. Me? I just don't have it in me to put up with personal insults and arguments-in-bad-faith without hitting back a bit.

Thank you Alex Tabarrok

2007-07-11T14:53:00.000-07:00

This is a very good piece of commentary on the stupidity of this article.

And I'm really starting to wonder what the hell is David Card talking about. I'm thinking of the previous "I lost some friends over the minimum wage research" quote too - maybe he did. But seriously, Card is a top-notch, widely respected, as celebrated-within-the-profession as they come economist, so where's all the whinnying coming from? Card, Krueger, Blinder, Stiglitz, Akerloff, Krugman - not to mention the old liberal guard of Arrow, Samuelson, Solow, Tobin, Modigiliani and Icouldgoon, - are some of the most successful and respected economists out there, and at the same time not folks one would really call "pro free market".

I think this all has to do with perspective or framing. Every other freakin' department on campus, that isn't science or enginneering, is out on the loony left. So when the economics department has the nerve to be left-center or moderate or balanced, or "leftist-but-sometimes-markets-do-work-you-know" the economists seem like wild eyed libertarian radicals to the rest of the intelligentsia (actually, you know what, you other folks can keep that label, with all the pretensions and phony sophism that goes with it).

And that NY Times article is proof that the barbarians are real.

Graphical explanation for empirical studies of immigrant's impact on wages (with some unavoidable maths)

2007-07-03T12:09:00.000-07:00

Note to the heterodox readers, if any: This post is unabashedly neoclassical.

Note to everyone else; this post is a bit of a mess. I could go through and clean up notation, label all the graphs, add in relevant links and edit it for readability and um, make it more inflammatory, but after drawing all the graphs and typing in all the formulas in LaTex I'm just feeling too lazy right now.

Here's some relevant links:
George Borjas
Brad DeLong
Mark Thoma

Ok.

Solow Model:

On the x-axis is capital per worker, K/L. The bright blue line represents the addition to capital stock per worker, the saving rate times per capita output, s*Y/L. The dark blue line is output per worker as a function of capital per worker. The red line represents the subtraction from capital per worker due to capital depreciation and maybe (native) population growth, (n+d)*K/L. Where subtraction from capital per worker equals addition to capital per worker, capital per worker is constant (for simplicity I'm assuming there's no technological growth which would drive additional capital accumulation). This is the long run steady state of this economy. On the y-axis we can read of the level of output per capita (as well as things like total savings and consumption per capita).

Now we want to relate wages to per capita output. If we take the commonly used Cobb Douglas aggregate production function to represent the relationship between capital, labor and output;

so that per capita output is

where K is capital, L is labor (later on, an index of labor input) and Y is aggregate output.

and assume labor gets paid its marginal product then we'll have an equation for wages

Inverting that (so we can line up our graphs nicely) we have

This is shown below:

The reason why the slope of the green line is greater than 1 is because some of the per capita output goes to capital owners rather than workers. Parameter a generally measures the extent of diminishing returns to capital but here it also turns out to represent the share of total output going to capital owners. The higher the share a, the steeper the green line, the lower the wages. Additionally we can find the return on capital, r, by looking at the purple line tangent to the production function (dark blue curve - in the graph I tangented the wrong curve and I don't feel like redrawing it). Since all the debate has been about immigration's impact on wages, I'm not gonna worry too much about r for the rest of the post.

So how does immigration come in? Well, the simplest way to introduce it is to assume it represents and increase in the number of workers. As the number of workers increases due to immigration capital per worker (K/L) falls and so does output per worker (Y/L). We find the new Y/L (in graphs denoted by lower case y, just like K/L is k) by moving down the dark blue production function, come over to the graph on the left and find the new, lower wage level.

This is essentially what some really old, "naive", studies of the effects of immigration on wages did. But it isn't the end of the story. Because now K/L is below it's steady state value, return to capital is higher and as a result addition to capital per worker is greater than subtraction per worker. So the process of capital accumulation starts again and K/L returns over time to its old level, as does Y/L and as do wages.

(note for the mathematically savvy; you can actually linearize the system of differential equations around the steady state and compute the rate of convergence from which one could estimate how fast wages recover to their pre-immigration levels)

This is equivalent to estimating the elasticity of labor demand. But here I can just tell you what it is. It's alpha, or if you believe that capital's share in output is 1/3, it's 1/3. So this simple analysis would say that for every 10% increase in the number of workers due to immigration, wages would fall, on impact by 3.3% and then slowly go back to where they were. The whole process is illustrated below. This is where you're gonna hafta start clicking on the images to enlarge'em.

But like I said, this is a fairly naive approach. That's because it implicitly assumes that all workers, foreign and domestic, skilled and unskilled are perfect substitutes for each other. This doesn't mean that workers are of the same quality, it's just that quality is related linearly. One engineer equals three doctors equals five lawyers equals a hundred construction workers equals six hundred and sixty six economists. For the purposes of production, if you're a firm, it doesn't matter whether you hire the five lawyers or the six hundred sixty six economists.

Obviously that's not very good. So let's start differentiating workers. First let's just differentiate them by skill level. Suppose that now L is not the number of workers but an index of a labor input, composed of skilled and unskilled workers. Specifically let's assume that the labor input index is constant elasticity of substitution and is given by:

where U is number of unskilled workers, S is number of skilled workers and rho measures the elasticity of substitution in production between'em.

Then, again assuming that each kind of worker gets paid her marginal product we get wages:

and inverting again we have

where the last part follows after some simple algebra. This means we have two green lines - one that relates skilled workers' wages to per capita ... we actually got to be careful now, it's no longer per capita output, it's output per unit of labor input, but the two are related in a straight forward manner so I might slip in what follows. Likewise now it's capital per unit of labor input rather than capital per worker ... anyway, two green lines, one for the unskilled and one for the skilled workers.

So what happens now when there's immigration, which here I'll take to be an increase in the number of unskilled workers? Well, as before, each worker (or unit of labor input) has less capita to work with so Y/L goes down as before. But note that now the slopes of the green lines depend on the the number of workers, skilled and unskilled. I'll let you take the derivatives (it's simple for the skilled since there only L changes, but for the unskilled both L and U change). Anyway if you do that, you'll get that how the lines shift depends on rho - which measures the elasticity of substitution between skilled and unskilled workers.

Well, most estimates of rho suggest that skilled and unskilled workers are complements. To build a house you need some relatively unskilled construction workers, but you also need skilled architects, surveyors, etc. You can't build the house if you don't have one group or the other. This means that rho is negative (and it's a pain to always worry about a negative parameter, but there you go). If you took your derivatives correctly you'll see that this means that the slope of the green line for the skilled workers shifts downward, while the green line for the unskilled workers shifts upward. This means that the effect on unskilled workers' wages is acerbated but skilled workers gain from immigration. If you were to do an empirical study based on the simple model based above, rather than this one, then the gains to skilled workers would instead show up, incorrectly, as gains to capital (if it wasn't just a complete mess).

Here's the graph, and to avoid clutter I'm omitting labels - think of it as one of those puzzles where you have to fill in the missing parts.

Of course, once the shock occurs, the process of capital accumulation starts up again, which the graph illustrates. Now the green lines are permanently shifted, but output per ... indexed labor, starts going back to its old level. This means that now both wages of unskilled and skilled start rising. So the wages of the unskilled recover somewhat (math can tell you that it's not all the way) while the wages of the skilled keep on rising. The purple arrows in the upper graphs indicate how wages move, while the red lines in the lower graphs show the time path of wages for the two worker groups.

Here's the same thing with good old supply and demand, but it's less pretty and you don't see everything that's going on:

The increase in the number of unskilled workers is a shift in labor supply in the upper graph represented by a shift in the blue line. This lowers the wage rate for unskilled workers. But through complementarity effects it also increases the demand for skilled labor, increasing their wages as seen in the lower graph. Then capital accumulates and the demands for both kinds of labor shift up. (Again, I omitted all the labels out of laziness. Wages are on the y-axis, amount of each type of labor is on the x-axis).

Of course all this begs the question; who are the skilled workers? Well, if you look at Ottaviano and Peri, then for the US, the answer seems to be "anyone's who graduated from high school", which means most workers see some gains in the short run and even larger gains in the long run. But it's true, the very bottom would be hurt. Or would it?

Well, this kind of study is still fairly basic. I guess you could call these kinds of studies "second generation" - they estimate the effects separately for various skill levels of workers and allow for capital accumulation that might result. But they still differentiate workers only very coarsely.

The above mentioned Ottaviano and Peri goes much further and differentiates workers by skill level, occupation and whether they're immigrants or not. It's not implausible that foreign born and native born workers, even when they have the same education and are employed in the same industry would not be perfectly substitutable for each other. It'd be too much work here to go through all the differentiations possible. Let's just differentiate between three types of workers here: skilled-native, unskilled-native, and unskilled-immigrant. So we're assuming a labor index like this:

Where now S is number of skilled native workers, U_n is number of unskilled native workers and I is number of immigrants. Now rho measures elasticity of substitution between skilled and unskilled workers and epsilon measures elasticity of substitution between foreign and native workers.

Let's define the unskilled labor index as:

Since we've got three groups now, we'll have three green lines. The equations for the wages are now:

And if we invert these we'll get the three green lines.

Now we increase the number of immigrants. The effect on native-skilled workers is pretty straight forward because it is essentially the same as the effect on skilled workers in the model right above. The green line shifts down and skilled workers gain today and even more in the future. The effect on PREVIOUS immigrants is also pretty straightforward - above we were increasing the number of unskilled workers, here we're increasing the number of immigrants, so the effect on previous immigrant's wages when the new ones come is to decrease their wages on impact, which then gradually recover somewhat over time.

The difference is in what happens to native unskilled workers. Again, if you do the math, you'll see that it depends on elasticities of substitution (now rho and epsilon) and which one is bigger. So theoretically, now, the answer is "it depends". The green line for native-unskilled workers could shift up or it could shift down. It could even shift down enough so that even unskilled workers gain, today and in the future. For this to be true however, there would have to be a lot of complementarity between native and foreign unskilled workers (epsilon would have to be negative and large in absolute value). Here again is a stripped down graph:

So like I said, for the native unskilled workers it could go either way. They could loose some and then recover or they could gain and then gain some more. What it depends on is the relative magnitudes of elasticity of substitution between native-unskilled and foreign-unskilled and the elasticity between the unskilled as a group and skilled as a group. As it turns out most estimates suggest that the complementarity between skill groups is larger than between foreign and native (note that actually you don't need complementarity. You need enough less-than-perfect substitutability) which means that the loose-then-recover-some scenario is more plausible for the unskilled (again here roughly meaning "high school drop outs"). But it's not that much larger. In fact what the estimates suggest is that the green line for unskilled workers shift down though not quite enough to offset the fall in wages due to decreased capital per worker. What this means is that the likely effect on unskilled workers' wages is "small loss in short run, slight gain in the long run", or, more or less 0.

0.

And in fact, that's roughly speaking (in terms of orders of magnitude) what Ottaviano and Peri find although that study being more detailed is not directly comparable to all them graphs above. As often is the case The World doesn't really feel like providing unambiguous, strong, one sided evidence that would make taking an ideological stance easy (until you think about the gains to the migrants themselves).

In a way the bottom line here, if you've read this far, is that the main people that immigrants are hurting through their effect on wages are those most like them. In other words, previous immigrants.

HAPPY FOURTH OF JULY!

Who owns the Satus Quo?

2007-07-02T18:47:00.000-07:00

Over at Marginal Revolution Alex Tabarrok has a mildly provocative post where he likens trade protectionists to slave owners. It's a good analogy. Well... maybe it's just meant to get people's panties up in a twist. But the point is serious, and it's that there are always implicit winners and losers from any policy or environmental (not in the "nature" sense, but the social and physical structure within which we operate) change. Even more than that. There are implicit winners and losers from the ABSENCE of any policy or environmental change.

By not removing a trade barrier over shoes a shoe producer gets a higher price and the shoe consumer pays a higher price. There's a winner and a looser. By removing the trade barrier the shoe producer gets a lower price and the shoe consumer gets a lower price. There's a winner and a looser. Either way "Someone, somewhere, always gets screwed". That's why the Kaldor-Hicks criteria - which says "do it!" if the winners gain enough so that they could THEORETICALLY compensate the losers - makes sense EVEN IF that compensation never takes place. Because we shouldn't presume that there's someone who "owns" the status quo.

Now of course there may be other reasons why the winners should compensate the losers when a policy change is being implemented. There may also be other reasons why the potential losers should compensate the potential winners when a policy change is NOT implemented. Roughly speaking, these two situations correspond to the concepts of Compensating Variation and Equivalent Variation.

These reasons may be pragmatic - if the potential losers have enough political power they can block a Kaldor-Hicks policy change, in which case it is to the benefit of potential winners to them buy off - sometimes it is just better to pay the Mafia wise guy to leave you alone.

They may be Rawlsian or Utilitarian. But note here that it doesn't matter what the status quo is, the only thing that matters is how the less well off fare under the two alternatives. This is a different consideration than one that says that compensation to a shoemaker must take place when a tariff on shoes is removed as a matter of "justice".

Because most commentators are really thinking about the other reasons they miss the point. And the point is that nobody owns the status quo so there's no sense to talk of "justice" here.

And if we're going to get egaliterian here why shouldn't Mary the Shoemaker compensate Poor Boy Paul (track 23, here, one of my all time favorite songs) for keeping the tariffs in place? Actually the answer to that is; because Poor Boy Paul would gain more than Mary the Shoemaker would loose and, other considerations aside, we cannot presume that Mary owns the status quo. So remove'em.

Here are the relevant lyrics (which apparently you can't find on through Google. what the hell are The Kids these days listening too?!):

I got patches on my knees cuz my pants are worn out
Holes in my shoes and my toes are stickin' out
Buttons on my shirt don't match at all
That's why they call me Poor Boy Paul
Hop pop poddity ditty wop pop pop.....

12 (faux) principles of (Political) Economics

2007-06-18T20:52:00.000-07:00

It's true. This side does not get enough attention in mainstream economics these days. And the heterodox mumble.

Here's mine, the goofy ones;

1. The answer to most questions in economics is usually “It depends”.
2. People respond to incentives, but incentives are determined in their own head and who knows what goes on in there.
3. But on average, masses of people respond in fairly predictable ways and these predictable ways, embodied in the so-called “Econ 101” thinking, are pretty useful guides. They are not absolutes however.
4. “On one hand … on the other hand” is about as good as you can do in a complicated world.
5. All economic models boil down to two (occasionally three) curves on a blackboard that cross. If it’s more than that or if you can't draw it that way, then your model stinks.
6. First Fundamental Theorem of Economics: Where the two curves cross, it’s important.
7. Game theory accidentally teaches us that outcomes are very sensitive to the structure of interaction. Small changes in the rules of the game can produce vastly different outcomes.
8. A logical, aesthetically compelling, story is important, even if the assumptions are crazy. Check it with math.
9. Anyone who makes exaggerated claims about their pet theories, ideas, or solutions, be they mainstream or heterodox, either doesn’t know what they’re talking about, hasn’t done their homework or is trying to sell you something. “Our results SUGGEST…” is a good indicator that a person has thought hard about their subject. At least as far as these things go. A thorough method combined with some humility should invite more attention than extraordinary claims of genius. Scientific progress takes place at the margin.
10. When an economic idea about how things work pops into your head, your very next question should be “why is that wrong?”. It’s useful to simulate competition among ideas in your brains so that only the truly good ones survive. Success, however, is not guaranteed.
13. “I don’t know” is often the best answer that can be given.

More on immigration - of the intergalactic kind

2007-05-28T18:19:00.002-07:00

Gabriel links to a webpage which has tools for teaching economics. Some of it's good, some goofy, and pretty much a lot of it of the kind that prompts some people to cry that "neoclassical brainwashing" is going on (essentially because you're teaching kids about scarcity and there are theories of economics out there which are not based on the idea of scarcity which are not getting equal treatment). Anyway, I did think this one was funny:

Concept: Opportunity cost, comparative advantage What's wrong with this picture? It's nice of Superman to rescue a kitten, but has he considered the opportunity cost of doing so? Rescuing kittens is so easy that children often do it. With all the accidents, crimes, and natural disasters that occur in the world, surely he could spend his time more productively. The concept of comparative advantage suggests that Superman should focus on tasks that others can't do well, like stopping runaway trains or transporting nuclear weapons into deep space so they can detonate safely.

(isn't it just like an economist to ruin all the fun? typical!)

But it makes you wonder. The guy can fly so fast around the earth that he can make it rotate backwards. Surely then he would have the time to, I don't know, build everyone in the world a car. And a house. And saw (sew?) like 500 t-shirts for everybody in the world. And plant a bunch of sugar cane. And write some script. And answer some telephone calls in India. And mow my lawn. Then he get can get back to chasing those goofy looking villains.

And why doesn't the Fraternal Order of Police ever complain that Superman is taking away their jobs and lowering their wages? Surely as much crime as that guy fought and defeated there must've been huge layoffs in the law enforcment/crime fighting industry and who's ever left is making a pittance. You know that if this stuff was for real people'd be organizing and demanding that Superman get deported to wherever he came from.

Now of course in the world of Middle Earth it's perfectly understandable why someone like Gandalf wouldn't use his superpowers to increase output. He'd know, being wise, that he was living in a Malthusian world and an increase in output would just result in more hobbits with no change in hobbit standard of living. And the last thing he'd want to do is lower the hobbit mortality rate since that would actually reduce hobbit income per capita.

Yeah, Dani Rodrik's right

2007-05-24T11:31:00.000-07:00

That was the first thought that occured to me when I woke up this morning. What can I say in my defense? Sometimes I'm slow and I have to sleep on it (and of course I'm not sneaky). Basically, the first-order/second-order impacts of tariff reduction on efficiency and producer surplus means that it is always possible to draw your supply and demand curves so that the efficiency gain from tariff reduction is arbitrarily small. Not zero, but as small as you want it. On the other hand it is NOT possible to draw your supply (and demand, but this doesn't play a role) curve in a way so that the change in producer surplus is small:

You can draw the above curves to make the blue triangles really small. But, given a change in prices due to change in tariff, you cannot make that red rectangle go away.

Of course if the efficiency gains are small and positive and loss to producers is large than this means that the change in consumer surplus has to be large. This is another way of saying that most of the benefits of tariff reduction are diffused over the millions of people who purchase a given good, while the costs of tariff reduction are concentrated within the particular industry - the group of producers, both workers and capital owners.

I also vaguely recall some floatin', shrinkin', shriekin' Harberger triangles from my dreams.

How much of a jerk do you have to be to oppose immigration?

2007-05-22T17:34:00.000-07:00

Update: Don't Trip Up does a similar calculation for Britain and EE

Both Alex Tabarrok and Dani Rodrik have come out in favor of immigration into US on the basis that the relevant "moral community" one should consider is the world and not just the US natives. It might be the case that immigration from Mexico into US lowers the wages of the unskilled workers here (the extent of this effect is subject to some controversy, see the previous post on Ottaviano and Peri). However, the increase in the migrants' wages is so large that support for immigration is still justified.

This kind of argument provokes the expected response from the expected folks, roughly along the lines that we should care more about native workers - the citizens - then the migrants - the non-citizens. Ok. But how much more? Let's put on our annoying-economist hat and consider the question; if you consider a foreign national to be only 1/2 a human being (alright, alright, only 1/2 as "important") as a native citizen, are you justified in opposing immigration? After all, it takes a real jerk to argue that foreign people's welfare should not count at all. Suppose the foreigners are only 1/10th as important? Surely, if natives' welfare counts for ten times as much as that of foreigners, we would be justified in banning immigration since it may adversely affect the wages of the unskilled in US? Well, let's see...

Suppose we transfer one person from Mexico to United States (illegally or otherwise). As a result his wages increase compared to what he was making in Mexico. Let us also suppose that as a result of this transfer the wages of some unskilled worker in US fall. Furthermore we will ignore the aggregate gains from immigration that occur and which all economists, including Borjas admit exist. We do this to make our job harder, not easier.

How much do you have to weight the native's welfare relative to that of the Mexican immigrant in order to oppose moving this migrant into US?

Well, in the standard framework we have ourselves a Social Welfare Function - in this case a utiliterian one with unequal weights attached to the welfare of natives and immigrants. The key is actually that there's decreasing marginal utility of wealth. Let be the weight attached to the well being of the native. So the weight attached to the well being of the immigrant is . Let
be the wage rate of the native worker before migration and
be the wage rate of the native worker after migration.
Here we're assuming that w_{N,New}$">

Similiarly let be the wage rate of the immigrant worker before migration (in Mexico) and be the wage rate of the immigrant worker after migration (in US).

Of course

Let utility be a CES function of wage/income:

Then welfare before migration is given by:

and after migration:

Setting these equal and solving for lambda tells us how much you have to weight the well being of native workers in order to be indifferent between migration and no migration. If your lambda is less than this value (and that's up to you) then you should support the migration, if your lambda is greater then go ahead an oppose the migration. We get:

To calculate the "jerk factor" lambda we have to get some estimates of how much wages change for both migrants and natives.

Let's get crazy and accept the Borjas results, which say that in the long run the migration will depress a native unskilled worker's wages by 5% (note this isn't exact translation of the Borjas findings but close enough). Of course these kinds of estimates are in the aggregate but it makes things simpler here (and doesn't do much injustice to reality) to assume that there's some one particular native worker who bears the full brunt of moving a Mexican worker into US.

In addition, let's use the findings from here that a migrant's wages increase from $2.56 to $9.34 after migration. In fact to make things simple, suppose that once the Mexican worker migrates, the wages of the unskilled native are equal to $9.34 (this assumes there's no premium for being a native, for speaking English, etc. Again, this makes my job harder, not easier). So

which simplifies the above lambda equation to:

Finally, if the migration decreases the natives' wage rate by 5% this means that originally his wage rate was (1.05)*9.34=9.81. So

This still depends on theta which measures the extent of diminishing marginal utility of income. There's various estimates for this. Theta=1 is nice and easy to use because then the utlity function is logarithmic, simplifying many things. On the other hand some macro studies and the equity premium suggest much higher values for theta. At any rate, here's a table of lambda against various values of theta and the implications for the jerk factor - how much more you have to weight natives' welfare than that of potential migrants (click to enlarge):

So, for example, with the implausibly low value of theta=1/2 one would have to consider the welfare of the native worker to count about 20 as much as that of the potential migrant. With logarithmic utility (theta=1) each native worker counts about 26 and a half times as much as a migrant. With a (what I consider more plausible) theta=2 you need 55 and some migrants to make up one native.

Here's the same in a graph:

Clearly one doesn't need to be a rootless cosmopolitan to reject these kinds of weights. One only need not be a jerk.

-- What about the immigrants crowding our schools? Using our health care system? Living on welfare? What about crime? Well. First, most of that is bunk. Most studies which look into the amount of tax money that (illegal) immigrants put into the collective kitty find that it's much more than what they take out in terms of benefits - one obvious reason is that illegal immigrants usually pay a lot in payroll taxes but never collect Social Security or medicare. Likewise the statistics for crime are ambigous to say the least. Illegal immigrants, by and large, are afraid of getting deported which means that they try to stay out of trouble as much as they can. However, even if these things were true in essence this would be a change in the post-migration wage rate (adjusted for externalities) of the native. Given the change in the wages of the migrant, this is not going to affect the results that much.

-- This post has already been edited for civility. What incivility remains pretty much belongs here.

The Economics of The Wire

2007-05-21T17:37:00.001-07:00

*Possible spoilers below*

I'm really surprised that no one's has mentioned the Economics of the HBO show "The Wire" (though there have been discussions as to whether a show embraces a libertarian or a socialist ethos). The series is bursting with economic concepts, and it mostly gets them right which I guess is somewhat surprising. First, because it's TV and TV usually does not get that stuff right, and second because of the political leanings of its creator. But nope, they get it pretty much spot on.

In fact, you could probably base an entire course in Industrial Organization on episodes of the Wire. Stringer Bell is actually taking an economics class in the show, in order to figure out how to boost the profits of his drug organization (gets an A- on his paper).

Like I said, there's a lot there but the part which I find really interesting is the various forms of competition that do or can take place between the various drug gangs.

First you got the obvious competition over turf - who controls the corners where drugs are sold. This immediately screams "Hotelling location model!". While this kind of competition can be, and occasionally does become very deadly, most of the time on the show there's a sort of a semi-stable equilibrium. Proposition Joe controls the drug corners of East Baltimore and the Barksdale Crew controls West Baltimore, and aside for the annual basketball game they stay out of each other's way, like two firms in a linear city which move to the corners. There are two 'shocks' which upset this balance. One is the entry of the third firm, Marlo. The other is the cooperative solution reached by Prop Joe and Stringer Bell which involves a trade off of turf for quality product.

Which brings us to the second type of competition which is in quality of the product. Prop Joe has the quality drugs which beat out that of his rivals. After Avon's arrest the Barksdales are hit with disruptions in their supply chain and are forced to put out very diluted drugs. At this point the difference becomes great enough so that "there's a steady flow of fiends from West to East". The difference in the price/quality ratios is greater than the transportation cost for the consumers, the drug fiends, and Prop Joe ends up 'stealing' most of Barksdales' demand. Stringer Bell responds with some ad hoc solutions which rely on the bounded rationality of his customers - he re-brands low quality drugs under a new name - but he's well aware that this is only a temporary measure. Stringer knows that this trick can only work for awhile and that ultimately even drug fiends are rational consumers (the other trick is to engage in some 'make-pretend' competition among different brands which are both controlled by the same supplier). As a result he is forced to share some of Barksdales best turf and location with East Baltimore.

And this is where the rare instance of true price competition appears. Like firms in real world, the drug organizations seem to try to avoid price competition at all costs. They would rather shoot it out over who owns what corner than have two drug crews under cutting each other on price. In a way it makes sense. When Stringer forces Bodie to let some of Prop Joe's people into the towers, the rival crews start playing Bertrand very quickly. There is a scene where Bubbles, who used to buy from Bodie, switches to Cheese's drug due to lower prices. Bodie runs up and offers Bubbles a buy one get one free deal to which Cheese responds with a price cut of his own. One can think of this situation as an instance in the Hotelling game where the two firms are located too close together and as a result price competition completely erodes the profit margins.

There is of course a lot more. The double marginalization problem of a downstream and upstream monopolists. Brands as imperfect signals of quality. Barriers to entry, pecuniary and lethal. Contestable markets. The stock of reputation as value in itself (Omar!). The incentives that police officers face ("That's what you get for giving a fuck when it's not your turn to give a fuck"). Rational addiction. Political economy and public choice theory. Outsourcing of certain tasks to better suited outsiders (obviously Brother Muzone took some local Baltimore enforcer's job!). Asymmetric information. The optimal time to defect in a repeated game (why did Avon and Stringer set up each other when they did? And why both at the same time?). The sustainability of a cooperative/collusive arrangement (Prop Joe's drug Co-op). The economics and politics of Unions (including that of labor substituting technological change). Law and economics. And of course elasticities:
"What you're thinking is that we have an inelastic product here. But what we have here is an elastic product"

How much inequality would Plato tolerate?

2007-05-14T18:59:00.000-07:00

This is a version of a problem I gave to my students on their last midterm.

Part I
(Ha! I'm like the television series. Endless suspense with no resolution.)

UPDATE: Gabriel has some really nice graphs on this. And no, I'm not a Platonist. If anything, I'm more of an Epicurean.

In his Laws Plato states that no man should own more than five times the land of any other man. Of course in this statement Plato is pretty much ignoring the incomes/wages of common laborers and slaves. But let's do some quick, rough exercises to see how much income inequality, in terms of the Gini coefficient, this can generate. Are the economies of the Platonic ideal comparable to present day economies? Was the ancient world more equal to the one today, albeit poor? Or was it just a bunch of wanna-be King Arthurs opressing the autonoumous collectives with the violence inherent in the system? What kind of assumptions matter?

Since we're talking about the pre-modern world let's make the Classical assumption and do the analysis in terms of "classes" of people. We can change the number of classes and the proportion of each in population to see how inequality measure varies. Part of the point of the exercise is that the Gini coefficient hides a lot of information about the income distribution.

First, let's suppose that there's just two classes in the economy. The income of a lower class person is Y_n and that of a higher class person is Y_x. In fact let

Let the proportion of lower class people in the economy be p.

The Lorenz curve and the Gini in this case are illustrated below:

Then a quick calculation ("quick calculation" means that I'm too lazy to try to write the math in blogger's version of Latex. Nothing more nor less. See the misuse of the word "trivial" in mathematics) of the Gini index of inequality gives us:

Obviously if every body's poor then p=1 and the Gini is 0 and likewise, if every body's rich then p=0 and Gini is also 0 since we have perfect equality in both cases.

Since we're interested in the maximum amount of inequality that Plato would tolerate we can maximize this with respect to d, the fraction of rich folks' income that the poor receive. After some messy algebra and the like we get

Then we plug that back into our Gini and we get (after some more algebra):

Now here's where subtleties of "What did the Master really mean?" come into play. If Plato simply meant that no person should have more than 5 times the income than another person than p is simply 1/5. Plugging that into the G_max gives us a Gini of about .38. This is somewhere between the present day Gini for Ireland and Israel. In other words Plato would be mostly ok with the kind of inequality we find in the world today.

However, I'm pretty sure that the richest person in Ireland or Israel today has way way way way more than five times the income of the poorest person in those countries. This is another way of saying that a lot of the action is in the middle of the income distribution. To put it yet another way, beware of inequality measure which compare the top 1% to the bottom 1%, or the top decile to the bottom quintile, or the top deci-trie-ile to the bottom quatri-platy-pus-ile etc.

But wait! What about diminishing returns to land, which are a standard assumption of the pre-modern, industrial economic analysis? Under some (essentially, wrong) assumptions this means that if the ratio of land ownership is

then

where a measures the extent of diminishing returns to land. If you got yourself an aggregate production function for this pre-modern economy then this a will actually correspond to the income share of land in total income. As it happens we do have some measures of this variable. Hansen and Prescott use a =.25 in their calibration of a growth model. More generally Clark looks at the share of land rents in output and finds it at between .25 in medieval England to somewhere a bit below .5 in parts of 17th century China. The Chinese data actually probably overstate a because they're derived from farm-level data (this is important for what follows below), so let's say .4 as an upper bound. In this case the max-income to the min-income ratio would be between 1.5 and 1.9. Plugging these into our G-max we get that it is between .1 and .15 - a low level of inequality not found in today's world! Could it be that Plato, or the world he was speaking of, was a radical (authoritarian) egalitarian?

Well, no. Like I said, the above has some very wrong implicit assumptions. What it really assumes is that each landowner works her own land and has the same level of productivity and uses no laborers or slaves. In other words, this is a model of just one class and of inequality variation within that class. What we need to do is to put the peasants - a separate class, back into the analysis.

But this means 3 classes at which point the analysis gets more complicated. We could assume however that each landlord doubles as both a worker and a land owner. Making another extreme assumption that the market for labor is competitive...

(I'd actually guess that this was more true in Plato's time than in medieval Europe - Greek system of slavery essentially amounted to a slave paying a fixed payment to his owner and then for all intents and purposes pretty much being left alone - and even that kept getting reformed with slaves' and poor people's debts being cancelled - anyway this essentially worked like a lump sum tax, a pure transfer not affecting any marginal conditions. On the other hand the feudal system extracted a PERCENTAGE of output hence affected marginal conditions and incentives driving a wedge between marginal products and wages. I vaguely recall reading Joan Robinson somewhere making the point that essentially this should be the basis for a theory of exploitation rather than the whole Marxist "surplus labor", "labor theory of value" approach.)

... so that we can keep the analysis contained to one class but allowing for labor input. Welp, in that case land owners live off their land rents but they also hire labor to work the land (some of the labor could be their own). But this means they will hire labor to the point where the marginal product of labor equals the wage rate. Given a total supply of the fixed input labor this means that a landlord's rents will be strictly proportional to the amount of labor she owns. If there are constant returns to scale in both factors - land and labor - then this means that a poor landlord's income is the same fraction of a rich landlord's income as his land is. Another words, we're back to

and the .38 Gini coefficient we got above.

Some notes:

No, I don't really torture my students like this. The problem I gave'em was a lot more stylized and straight forward. A good number of them picked up on the basic point.

The (see below) that was above and now that you see below essentially depends on the market structure of the economy. The assumption that each landowner only works his own land and hires no labor means that essentially there is no labor market. However if there is SOME kind of a labor marker (and it need not be competitive) then this means that the land ratios of the landlords will equalize (in imperfect markets approximate) the income ratios. This is how we go from "ratio of incomes" = "some root of land ownerships" to "ratio of incomes" = "ratio of land ownership"

The part II will contain the analysis with three classes - these could be {peasants, small landowners, large landowners}, or if you wanna compare pre-modern world inequality with modern inequality then {peasants, capitalists, landowners} - the point of the latter being that inequality actually decreased with the Industrial Revolution. Even though "capitalists" gained, "workers-used-to-be-peasants" gained much more. The folks who got really screwed by the technological changes of the IR were the aristocratic landowners. Which gives you hope for this world. Karma and all that. And even honest Marxist oughta sympathize.