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

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:



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.