Relative vs. Absolute Poverty

Here's Tim Worstall.
Here's a graph for Western European countries plus Canada, without UK (which does badly on every measure of poverty and inequality):



Not that this is statistically significant or anything, but it should give one a pause. Basically income and inequality, for developed countries (UK aside) tend to be positively related. Income is negatively related to absolute poverty. And relative poverty is essentially just inequality. So you get this relationship. No causal mechanisms are implied.

Costs of Inflation

A while back there was some discussion over at Gabriel's on the long run costs of inflation. The standard culprits here are shoeleather costs, menu costs, price signal costs or inflation induced distortions in the financial markets. But the first two just can't be that big, the third is hard to quantify and fuzzy and I don't put much stock in the magnitude of the fourth, given the existance of many inflation hedging instruments (though I'm no finance guy so this is based more on a gut feeling then anything rigorous).

But this past weekend I saw a nice paper presented by Randall Wright of Penn State. It's basically a combination of a monetary model with a search/matching model. Fusing together RBC style models with search and matching models seems to be the new thing (probably not that new, I'm pretty out of touch with this aspect of Macro) in this field. This is a good thing.

The argument is simple:
Inflation is just a tax on holding money.
Money greases the exchange of goods and services by eliminating double coincidence of wants.
If money is getting taxed households switch out of money holdings and money can't do its proper job. As a result the amount of transactions in the goods market declines.
This then feeds into the labor market etc.
(I know this sounds a good bit like the shoeleather cost story but trust me, it's better)

I think this is the most common sense and straight forward explanation for high costs of inflation I've seen yet. Another nice aspect is that one can actually use the model to calculate the magnitude of these costs. And they're non-trivial. Going from a 10% inflation to a 0% would be the same as having a 1% permanent increase in productivity growth which is nothing to sneeze at (though I'm sure this sort of thing is highly nonlinear).

Another interesting implication of the paper is that while in general the Friedman Rule of 0% inflation is optimal, if fiscal policy (for example with respect to unemployment benefits) is suboptimal then a small positive inflation rate is better. Basically this is an instance of the theory of second best where one distortion is used to offset and neutralize an already existing distortion.

Wright also has an article on the topic in the forthcoming New Palgrave Dictionary of Economics.

See more along the same lines here.

I'm gonna be a jerk because I can't hold it in any longer

Who's got the worse comments section, Brad DeLong or Mark Thoma?
(ignore for the sake of argument the overlap between the commentators)

Both have generally interesting high quality posts (many of which I disagree with) but the comments sections are imported straight from the Daily Kos or something (of course there are many notable exceptions). Crooked Timber on the other hand is probably to the left of both those guys but the comments are far better and it's possible to have an intelligent discussion there (as well as a nasty fight, with other commentators or the posters).

Nash's Dancing with a Pretty Girl Game

Consider the following game:
There are P prizes and N players. Each player’s strategy is to “choose” a prize (a dance with a pretty girl). If he (economic feminists, I told you to stop reading!) is the only one to choose that prize he gets it. If there are other players who choose the same prize, he gets it with probability 1/n(p), where n(p) is the total number of players (including this guy) who have chosen the same prize p. Let the (adjusted, Von-Neumann, etc.) values of the prizes be V(p) and WLOG assume that V(p)>V(p+1). Also WLOG we’ll assume that the players are indexed by n and that the smaller n’s end up with the smaller p’s. So we’ll list the payoffs of players as ( V(1)/n(1), …, V(2)/n(2),…).

Below is an illustration of the two player, two prize version of the game:


This game, depending on parameters will have either a single equilibrium – both players going for the higher value Prize 1, or two symmetric equilibria where one player goes for the higher value prize and the other one for the, uh, the other one. In general in this game efficiency requires that ‘no prize is left untaken’. This means that in this game if the parameters are such that the game is the one with the two equilibria, then the outcome is efficient. Otherwise both players exhaust themselves trying to win the attention of the prettier girl but only one can succeed. Ex-post then, given that only one wins, the loser would’ve been better off going after the somewhat less pretty girl. What then, are the parameters that will guarantee efficient outcome? Well, this is intuitive. Suppose that a dance with either girl is equally desirable – there’s no difference between the prizes. Then the only equilibrium is the separating one where each player pairs of with a different girl. It’s efficient. More generally, if the difference between the value of the two prizes is not too great then the outcome will be efficient – in this particular case we need that the value of the first prize cannot be greater then twice the value of the second prize.

How does this generalize to those P prizes and N players? And what happens if we keep P fixed but increase N? First note that if there are more prizes then players then only the N first prizes will play any role (given they’re ordered by decreasing values). So we can ignore games where P>N. Then, note that if there are exactly the same number of players as prizes then the condition for efficiency (where every prize is chosen by at least one player) requires that the player with the worse-valued prize has no incentive to switch to a two person competition with the player with the best-valued prize. In other words we need that the value of the best prize is less then twice the value of the worst prize (which can be seen in the 2x2 example above). But things get better as we increase the number of players.

The diagrams below illustrate the set of parameters which guarantee the efficient outcome (again, “no prize left untaken”) for the game where there are 3 prizes. I’ve normalized the value of the worst prize to 1 (can’t normalize it to 0 since 0/n=0). The colored areas are the values of prizes 1 and 2 for which the outcome will be efficient. The blue area represents the addition to that set as you increase the number of players.



The recursive formula for the size of the set of parameters which guarantee efficiency is given by
An=An-1+(n-2)/2
Which, with the initial value of A3=1/2 comes to



Obviously this goes to infinity as N goes to infinity which means that with a large number of players it's quite likely that one will get the efficient solution.

Another way to see the limit result is to consider a continuum of players. In this case each player will perceive himself to have no effect upon the probability of winning the prize. In turn this means that in equilibrium each player has to be indifferent between all prizes:



Summing over j we get payoffs per player



and summing again over players we get that total payoffs = , which means the equilibrium is efficient.

In general the idea of "competition" needs to be distinguished from the idea of "non-cooperation" (which in turn does not imply absence of cooperation which could be self-enforcing). In a Bertrand model with just two people one gets a "competitive outcome" while one can have a monopolistic competition with a large number of players and a "uncompetitive outcome". Probably the best definition of competition is that of Makowski and Ostroy- that of PEDS (Perfectly Elastic Demand and Supply). (Here's the link if you've got JEL subscription)

Lithuania:France 0:0 as I type this

So awhile back, while I was busy with work and making plans to get all sick and miserable (which finally materialized this past week), both Michael and Robert were busy pickin’ on Steven Landsburg for his comments on the movie about John Nash, “A Beautiful Mind”. Now, both Michael and Robert are correct but I say give Steven a bit of a break! He gets some of the details wrong but his basic point is correct. And he’s writing a column of limited length in which he’s trying to convey a complex economic/ mathematical idea to laymen audience (I call this “The Krugman Defense”).

The point concerns the scene in the movie where Nash and two of his buddies are at a bar and they see three young women, one of which, apparently by universal agreement, is prettier then the other two. One of the buddies proclaims that it’s “every men for himself” but then Nash has his “brilliant” insight – if they all go for the same prettiest woman they all may loose (or at least two of them will) while if they cooperate and each takes his chance with a different girl they all can win. The implication is supposed to be that competition is inefficient compared to cooperation.

This scene is annoying for at least two reasons (for economists, feminists may find a couple reasons more (and feminist economists should not watch this scene or the movie under any circumstances, they have enough stress and frustration in their lives as it is)). First the scene seems to mix up two of Nash’s concepts – the idea of a Nash Equilibrium and that of the Nash Bargaining Solution. The first applies to non-cooperative games, while the second is a solution concept for cooperative games (BTW don't be too trusting of Wiki on this either). But this can be essentially excused on the grounds of the same “Krugman Defense” that I think should apply to Landsburg – the movie is trying to portray sophisticated concepts to the uninitiated in a limited amount of time so it’s okay if it cuts some corners (a far more annoying scene is the one where Nash’s advisor tells him “You know you just disproved everything Adam Smith ever said!” or something equally silly as that).

However, the second irksome aspect of the scene is that it doesn’t illustrate what it tries to illustrate. That is, the non-cooperative solution of the game the three friends seem to be engaged in can actually be efficient! There may be no need for cooperation anyway! What’s more, even if the original outcome is inefficient, if the number of pretty girls one can try for a dance with (I think that’s all that the guys in the movie were after, honestly) stays constant, but you increase the number of potential suitors then the likelihood (loosely speaking) that the efficient result obtains increases! In other words you get sort of a limit/Cournot theorem result that as the number of players goes to infinity, efficiency becomes more and more likely and is guaranteed at infinity.

Details coming up in the next post.

Taking a short break

Been traveling and in the course of these travels I've managed to catch a very nasty cold. And I have some more traveling to do soon. Hence the sparsity of posts. Be back soon.

Poets, Writers, Historians and the Spanish Civil War

Stephen Schwartz has a very very good article on the Marxist historian Eric Hobsbawm's take on the Spanish Civil War, George Orwell and general Stalinist apologetics. This is via Brad DeLong and Stephen's comment in that thread is also very much worth reading.

The sentence which made me chuckle in Stephen's article is actually somewhat peripheral to the general topic, but nonetheless all too true. It is in regard to Pablo Neruda, who's always annoyed me:

Neruda was a Stalinist agent and is highly overrated as a poet, mainly the object of devotion by teenagers in the Hispanic world and illiterates elsewhere.




But wait! There's more excellent literary criticism there. On Hemingway, whose only readable book is Old Man and the Sea, mainly due to its moderate length:

Hobsbawm cites Hemingway ... – a “macho” admirer of Stalin and a compulsive liar – who wrote two of the worst books imaginable on the Spanish war

Graveyard of old economic ideas - Balanced and Unbalanced Growth

I had a student from some other class come in asking me about "unbalanced growth". Apparantly he was referred to me by the professor running the other class (Econ History I believe). It actually took me a few minutes to connect two and two together and figure out what this was all about (the fact that he really mumbled the names Hirschman and Rosenstein-Rodan (saying something that sounded like "I read Ishmensteiennodan". Who?) didn't help much) but I'm a push over for this sort of thing so I ended up writing up a fairly lenghty response to him. I figure I might as well make it do double work as a blog post while I'm busy writing the final exam.

He basically had three questions:

1. What is “balanced” and “unbalanced growth”?
2. How is it perceived by economists today?
3. What was the role, if any, of unbalanced growth in the industrial revolution in England?

1. Here’s what I know about balanced and unbalanced growth theories.

Basically this was a big area of research in the 50’s so much that some people even talked of the “Balanced Growth Controversy”. Very roughly speaking, on one side you had people associated with Rosenstein-Rodan who argued that a successful development/industrialization strategy needed to “attack on all fronts”, that is aim for increases in productivity and investment in all sectors of the economy at once. On the other there was Hirschman who argued that it was better to focus on a few key industries. These would create demand for inputs (backward linkages) and serve as inputs to other industries themselves (forward linkages) and would spur development economy wide. However, this literature, along with a good chunk of development economics pretty much died in the 60’s. Paul Krugman has a good essay on this which you can find here (it’s a bit broader then just the story of development economics):

http://www.pkarchive.org/theory/dishpan1.html

To Krugman’s explanations for why this avenue of research was abandoned (i.e. it’s hard to formally model economies of scale and imperfect competition) I’d add two that I think are also relevant:

i) Solow’s publication of his model in 1956 which basically argued that differences in capital stocks could account for very little of the differences in standards of living, and correspondingly that it was technological progress not capital accumulation which was the engine of growth. As a result since the 1960’s many development/growth economists became less interested in capital and capital based models of development. The New Growth Theory of the 1980’s (Paul Romer and others) essentially tried to account for where technological progress comes from. Since both the Rodan-Rosenstein model and the Hirschman theory are essentially models of investment driven development, they were probably abandoned for this reason as well.

ii) The fact that the RR and Hirschman were not fully explicit formal models made them difficult to test empirically. Furthermore, even non-formally, some of the concepts employed were not easy to relate to real world experience. I know some folks tried to evaluate Hirschman’s ideas by identifying backward and forward linkages with the extent to which a particular industry was an input for other industries and how many different inputs itself it used but I don’t think any of these efforts were overtly successful.

The second point above I think explains why one has a hard time finding “real world examples” of balanced or unbalanced growth. One could argue that the import substitution/industrialization policies followed by many developing countries in the 60’s and 70’s were examples of Rosenstein-Rodan’s theory applied to practice. However many of these experiments ended in disappointment which may or may have not had anything to do with the validity of the RR story. More recently RR’s ideas were revived and formalized by Murphy, Schleifer and Vishny as the “Big Push” model. The paper is here

http://www.economics.harvard.edu/faculty/shleifer/papers.html

under “Industrialization and the Big Push”.

This paper here claims to have found evidence for the Big Push/RR model of industrialization in East Asia and Eastern Europe
http://economicsbulletin.vanderbilt.edu/2003/volume15/EB-03O40005A.pdf

I attach list some other relevant papers at the bottom. The 1973 Demery and Demery paper is probably closest to a thorough empirical investigation of the issues. Note they’re all pretty old.

2. Today “balanced growth” is pretty much associated with the “Big Push” model by contemporary economists. The Big Push model is itself in a class of models which rely on economies of scale and strategic complementarities to generate poverty traps and where a coordinated action by the government can push the economy out of the trap and into a better, higher growth equilibrium. Another important paper in this area is Kremer’s O-Ring model:

http://ideas.repec.org/a/tpr/qjecon/v108y1993i3p551-75.html

I’d say that while most contemporary development and growth economists are somewhat favorable to the Balanced Growth/RR/Big Push models many think that other factors (institutions, political systems, geography) are more important. This is a remnant of the Solow idea that it isn’t capital accumulation (which is what the Big Push entails) that drives growth.

3. As for the role of unbalance in England’s industrialization. Well, basically theories of the industrial revolution are a dime a dozen. Some of these implicitly incorporate some of the ‘unbalanced growth’ ideas others do not. But these are sort of two different questions. Rosenstein-Rodan and Hirschman were trying to figure out what the proper government policy should be to make a poor country industrialize in the heyday of state sponsored planning and development programs (most of which failed). 19^th century England, as well as most presently-rich countries, seems to have industrialized/developed without any concerned coordinated government intervention at all, aside from the establishment of property rights and rule of law. The exceptions here might be 19^th century Prussia and Meji Japan so they’re probably better candidates to look at in terms of balanced and unbalance growth theories.

To the extent that ‘unbalances’ played a role though, different authors have stressed different industries as being “key” to England’s industrialization. David Landes (Wealth and Poverty of Nations) for example argues that it was the innovation in the textiles industry which raised incomes, which in turn raised demand and which then allowed other sectors of the British economy to develop – which depending on how you read it sounds either like a Big Push story (without government intervention), or a backwards and forwards linkages Hirschman story. Other authors have stressed the labor saving productivity advances in agriculture which released rural labor to be employed in factories and textile mills, which also has aspects of “unbalanced growth”. However, Greg Clark in his forthcoming book “Farewell to Alms” and previous papers has argued that the productivity growth during the industrial revolution was occurring in many sectors at once; textiles, manufactures, agriculture, transportation – i.e. balanced growth. Other authors have argued that balanced growth and unbalanced growth are essentially empirically indistinguishable. Under Balanced growth you have spontaneously occurring productivity growth and industrialization across many sectors. Under Unbalanced growth you have a few key industries grow but this quickly translates into overall economic growth as the backward and forward linkages establish themselves. Either way a detached observer/researcher would see essentially the same thing happen. I think one of the papers below makes this point in the context of England.

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

More speculatively, 40 years from now, what are going to be the forgotten, abandoned, orphaned research areas in economics? Will RBC be just a footnote in a book no one reads? (yeah, I'm trying to rile Gabriel up a bit)? Behavioral economics (I'm sure at least of its aspects will be)?

And if you go strictly by the title of this post, does it mean that the "Big Push" model is just a Balanced-Growth-Zombie?

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

Some refs (no particular order)

V. V. Bhatt, 1965, "Some Notes on Balanced and Unbalanced Growth", The Economic Journal, Vol. 75

David Demery and Lionel Demery, 1973, "Cross-Section Evidence for Balanced and Unbalanced Growth", The Review of Economics and Statistics, Vol. 55.

Gawande, Li and Sauer, (2003), "Big push industrialization: some empirical evidence for East
Asia and Eastern Europe", Economics Bulletin, Vol 15.

J. R. T. Hughes, 1959, "Foreign Trade and Balanced Growth: The Historical Framework", The American Economic Review, Vol. 49, No. 2, Papers and Proceedings of the Seventy-first
Annual Meeting of the American Economic Association.

P. N. Rosenstein-Rodan, "Problems of Industrialisation of Eastern and South-Eastern Europe"
The Economic Journal, Vol. 53, No. 210/211.

Paul Streeten, 1959, "Unbalanced Growth", Oxford Economic Papers, New Series, Vol. 11, No. 2.

Robert B. Sutcliffe, 1964, "Balanced and Unbalanced Growth", The Quarterly Journal of Economics, Vol. 78, No. 4.

Pan A. Yotopoulos and Jeffrey B. Nugent, "A Balanced-Growth Version of the Linkage Hypothesis: A Test" The Quarterly Journal of Economics, Vol. 87, No. 2.
(note the different citation style - as in original)

Stop the Dumping, end "Foreign Aid"!

So we're finishing up the term in Principles of Macro with discussion of international trade and policy, including Anti-Dumping policy (as it works with relation to the Department of Commerce and the International Trade Commission). Before that we had a class or two on growth and development (we covered some of this at the beginning too), including foreign aid. There's this hippy-ish girl who sits in the first row, is majoring in Psych and always has this suspicious look on her face as in "I don't buy all this Economics stuff". Yesterday she asked a question:

"Wait, if the foreigners give you stuff for free it's called 'Foreign Aid' but if they try to sell it to you for slightly more than free all of sudden it's called 'Dumping' and they have to pay penalties. I don't understand!"

Can't say I do either.

Here's Bruce Blonigen's page on dumping. He's sorta THE Dumping guy.

Nine lives and then some

I realize that picking on the letters to the editor of your local paper is like challanging a one legged turtle to a 100 meter race, but this one provoked a pretty weird train of thought in my head and it was made the "Letter of the Day".

Some lady from the Humane Society writes in to protest the practice of trapping and euthanizing feral cats. She asserts that

"Years of trapping and euthanizing feral cats have failed to control their numbers"

However

"Trap-Neuter-Return programs...have been successful in...reducing the numbers [of feral cats]"

Whoa! How could this be? I can think of two possible ways to account for the difference in results between the two approaches:

1. Economic explanation: Cats respond to incentives. They are rational economic agents. Presumably they prefer gettin' clipped to getting helped along to cat heaven. As a result they invest less resources in avoiding getting trapped when the policy is trap-neuter then when it's trap-bye-bye-kitty. So with trap-neuter more cats are trapped.

or

2. Preferred explanation: The numbers under trap-euthenize don't go down because all them dead kitties come back as ZOMBIE CATS!!!

Which isn't to say that putting feral cats to sleep is more humane then neutering'em (though how do we know this?). But people on a moral crusade will lie to you at a greater frequency then people who are just plain ol' tryin' to sell you somethin'.


For more economics of the undead see here
and here.

Update 2 - More realistic preferences, or, mixing up egalite with fraternite


The basic set up is same as before except now we assume there’s 3 groups of people in society; the poor, the middle class and the rich. The pre-tax income of the poor is y_p, and that of the middle class is y_c. Let gamma denote the fraction of the population which is poor, and delta the fraction which is rich. Furthermore also assume that the median voter is no longer a "pure altruist" but a "egaliterian altruist" in the sense that she cares about the income levels of the poor and the middle class, but not of the rich. Here I'm gonna assume that the weight she attaches to the incomes of these two groups is the same, b. The indirect utility function is then





From this we get the median voter's most preferred tax rate:



What happens to t* as b changes? It depends on whether the median voter is a member of the poor or a member of the middle class:




where (some crap)>0. So if the median voter is a member of the middle class then y_m=y_c and the non crap part simplifies to



but if she is a member of the poor we have y_m=y_p and




So the poorer the median voter the more that altruism will tend to make her anti-redistributionist. Which seems counterintuitive, but it's not. The basic point, which I think is fairly general, is that if the median voter (or whoever makes policy decisions in this society) is altruistic towards at least some people with an income above their own then this altruism will dampen the redistribution that the voter would favor given their income position.

Update 1 to previous post on fraternite and egalite

Michael and Gabriel both respond to my post about altruism and redistribution of wealth. Here I will quickly respond to both of them in turn. I also plan on posting a slightly different version of that model to emphasize the point.

Michael says:

The argument is crystal clear, yet kinda unconvincing.

Homo oeconomicus does care a lot about redistribution, namely how much of the cake goes to himself. Radeks altruist doesn't care about distribution at all. I don't think there are mamy altruists of this kind out there at all.

Maybe, I should add that with any realistic parameters, one would get complete redistribution. Single dimensional issue spaces are of no use in explaining redistributive politics.

(link in the original)

Actually the agent in the model does care about redistribution and how much cake she gets. The utility is a weighted sum of her own post tax income and that of society. Now, the assumption that the agent puts the same weight on all other citizen’s is most likely unrealistic. Do I really care about Bill Gates’ post tax income when deciding what kind of tax rates to support? Nah. But then again I’m no “pure altruist” (and perhaps there ain’t many out there). On the other hand when I read in the newspaper that Poland’s GDP went up, I get some utility out of that even though it has no effect what so ever on my own income. So maybe it’s not so crazy after all. Regardless, the point of the model is not to realistically describe real life altruists but to, well, make a point. IF people were “pure altruists” (rather than a mix of altruism and egalitarianism) then they would prefer less redistribution. I think some folks some times confuse the two notions of altruism and egalitarianism and it’s good to be reminded that the two can work in opposite directions.

Also I think the result is more general then the simple model suggests in a sense that altruistic considerations can tamper redistributionist tendencies. More on that later.

As far as the Roemer paper, I’m not sure it’s relevant here. There’s some significant differences in the set up. First, and perhaps most importantly there’s no leaky bucket/excess burden. Roemer writes:

Nevertheless, twentieth-century universal suffrage has not engendered the expropriation of the rich through the tax system, and a variety of reasons have been offered in explanation, including the following. (1) Voters recognize that there would be adverse dynamic effects to expropriating the rich… In this article, I will propose another possible explanation for the non-expropriation of the rich in democracies

In other words the two dimensional policy space is a complementary explanation for lack of expropriation to that of a leaky bucket. Second, Roemer’s model is not the Downsian model of the median voter theorem which I use. One can argue about which model is more appropriate but to make a general point I think one can have their pick.

Finally “Single dimensional issue spaces are of no use in explaining redistributive politics” is too much of a blanket statement (and I think it misrepresents what Roemer is saying). Acemoglu and Robinson most definitely squeeze out a lot out of a model pretty similar to what I have, in explaining how democracy does or does not come about (though one could argue that their model is not exactly single dimensional since in addition to the linear tax rate there’s the choice of whether to democratize or not)

Gabriel says:

I’d rather avoid, if at all possible, having agents with preferences over the size of the economy or the distribution of income. Not only does it sounds “common sense” alarms, which might not matter, but the critical point for me is the difficulty of going to the data.

As for “altruism”, I’d rather study it within the regular model of rational choice. The agent has an income which can be spent on various uses, including other people. If I remember correctly, there is considerable altruism, but it’s mostly within the household.

It depends on the purpose of the model. I want to see what happens to desire for redistribution as a person becomes more altruistic (in the sense of having a preference of over the size of the economy) and the model tells me pure altruists would be less redistributionist. I think this is a somewhat counterintuitive aspect of altruism that most people don’t think about. I don’t think the set up is THAT unrealistic but even if this isn’t meant to be taken to the data. It’s stripped down and unclothed to focus on a particular issue – effect of altruism on redistribution. I’m not proposing that the model actually predicts real life tax rates with any degree of accuracy.
Also if you think that “altruism” can be studied in a regular model of rational choice then…wait…this is a regular model of rational choice, just with respect to voting and public choice rather than individual consumption of altruism. If you’re ok with one, why not the other? I agree that most altruism in the real world occurs with respect to family members, friends, compatriots etc. (in decreasing order). There’s a paper along the lines of your second post by what’s-his-name which looks at Ricardian Equivalence in that context. But the issue which gave rise to this whole thing was the contention that societies with more immigration would be less redistributative because the natives care only about the welfare of other natives and not that of immigrants. But this makes it necessary to model this altruism of natives towards other natives in a public choice context to see if that statement actually makes sense. So Friedman’s statement has, implicitly, a model very much like this one behind it.
Also you seem to call for a rational choice model but in the rest of that first post stray into behavioral territory (and the relationship between altruism and paternalism)