Author Archives: afinetheorem

The Economics of John Nash

I’m in the midst of a four week string of conferences and travel, and terribly backed up with posts on some great new papers, but I can’t let the tragic passing today of John Nash go by without comment. When nonacademics ask what I do, I often say that I work in a branch of applied math called game theory; if you say you are economist, the man on the street expects you to know when unemployment will go down, or which stocks they should buy, or whether monetary expansion will lead to inflation, questions which the applied theorist has little ability to answer in a satisfying way. But then, if you mention game theory, without question the most common way your interlocutor knows the field is via Russell Crowe’s John Nash character in A Beautiful Mind, so surely, and rightfully, no game theorist has greater popular name recognition.

Now Nash’s contributions to economics are very small, though enormously influential. He was a pure mathematician who took only one course in economics in his studies; more on this fortuitous course shortly. The contributions are simple to state: Nash founded the theory of non-cooperative games, and he instigated an important, though ultimately unsuccessful, literature on bargaining. Nash essentially only has two short papers on each topic, each of which is easy to follow for a modern reader, so I will generally discuss some background on the work rather than the well-known results directly.

First, non-cooperative games. Robert Leonard has a very interesting intellectual history of the early days of game theory, the formal study of strategic interaction, which begins well before Nash. Many like to cite von Neumann’s “Zur Theorie der Gesellschaftsspiele” (“A Theory of Parlor Games”), from whence we have the minimax theorem, but Emile Borel in the early 1920’s, and Ernst Zermelo with his eponymous theorem a decade earlier, surely form relevant prehistory as well. These earlier attempts, including von Neumann’s book with Morganstern, did not allow general investigation of what we now call noncooperative games, or strategic situations where players do not attempt to collude. The most famous situation of this type is the Prisoner’s Dilemma, a simple example, yet a shocking one: competing agents, be they individuals, firms or countries, may (in a sense) rationally find themselves taking actions which both parties think is worse than some alternative. Given the U.S. government interest in how a joint nuclear world with the Soviets would play out, analyzing situations of that type was not simply a “Gesellschaftsspiele” in the late 1940s; Nash himself was funded by the Atomic Energy Commission, and RAND, site of a huge amount of important early game theory research, was linked to the military.

Nash’s insight was, in retrospect, very simple. Consider a soccer penalty kick, where the only options are to kick left and right for the shooter, and to simultaneously dive left or right for the goalie. Now at first glance, it seems like there can be no equilibrium: if the shooter will kick left, then the goalie will jump to that side, in which case the shooter would prefer to shoot right, in which case the goalie would prefer to switch as well, and so on. In real life, then, what do we expect to happen? Well, surely we expect that the shooter will sometimes shoot left and sometimes right, and likewise the goalie will mix which way she dives. That is, instead of two strategies for each player, we have a continuum of mixed strategies, where a mixed strategy is simply a probability distribution over the strategies “Left, Right”. This idea of mixed strategies “convexifies” the strategy space so that we can use fixed point strategies to guarantee that an equilibrium exists in every finite-strategy noncooperative game under expected utility (Kakutani’s Fixed Point in the initial one-page paper in PNAS which Nash wrote his very first year of graduate school, and Brouwer’s Fixed Point in the Annals of Math article which more rigorously lays out Nash’s noncooperative theory). Because of Nash, we are able to analyze essentially whatever nonstrategic situation we want under what seems to be a reasonable solution concept (I optimize given my beliefs about what others will do, and my beliefs are in the end correct). More importantly, the fixed point theorems Nash used to generate his equilibria are now so broadly applied that no respectable economist should now get a PhD without understanding how they work.

(A quick aside: it is quite interesting to me that game theory, as opposed to Walrasian/Marshallian economics, does not derive from physics or other natural sciences, but rather from a program at the intersection of formal logic and mathematics, primarily in Germany, primarily in the early 20th century. I still have a mind to write a proper paper on this intellectual history at some point, but there is a very real sense in which economics post-Samuelson, von Neumann and Nash forms a rather continuous methodology with earlier social science in the sense of qualitative deduction, whereas it is our sister social sciences which, for a variety of reasons, go on writing papers without the powerful tools of modern logic and the mathematics which followed Hilbert. When Nash makes claims about the existence of equilibria due to Brouwer, the mathematics is merely the structure holding up and extending ideas concerning the interaction of agents in noncooperative systems that would have been totally familiar to earlier generations of economists who simply didn’t have access to tools like the fixed point theorems, in the same way that Samuelson and Houthakker’s ideas on utility are no great break from earlier work aside from their explicit incorporation of deduction on the basis of relational logic, a tool unknown to economists in the 19th century. That is, I claim the mathematization of economics in the mid 20th century represents no major methodological break, nor an attempt to ape the natural sciences. Back to Nash’s work in the direct sense.)

Nash only applies his theory to one game: a simplified version of poker due to his advisor called Kuhn Poker. It turned out that the noncooperative solution was not immediately applicable, at least to the types of applied situations where it is now commonplace, without a handful of modifications. In my read of the intellectual history, noncooperative games was a bit of a failure outside the realm of pure math in its first 25 years because we still needed Harsanyi’s purification theorem and Bayesian equilibria to understand what exactly was going on with mixed strategies, Reinhard Selten’s idea of subgame perfection to reasonably analyze games with multiple stages, and the idea of mechanism design of Gibbard, Vickers, Myerson, Maskin, and Satterthwaite (among others) to make it possible to discuss how institutions affect outcomes which are determined in equilibrium. It is not simply economists that Nash influenced; among many others, his work directly leads to the evolutionary games of Maynard Smith and Price in biology and linguistics, the upper and lower values of his 1953 results have been used to prove other mathematical results and to discuss what is meant as truth in philosophy, and Nash is widespread in the analysis of voting behavior in political science and international relations.

The bargaining solution is a trickier legacy. Recall Nash’s sole economics course, which he took as an undergraduate. In that course, he wrote a term paper, eventually to appear in Econometrica, where he attempted to axiomatize what will happen when two parties bargain over some outcome. The idea is simple. Whatever the bargaining outcome is, we want it to satisfy a handful of reasonable assumptions. First, since ordinal utility is invariant to affine transformations of a utility function, the bargaining outcome should not be affected by these types of transformations: only ordinal preferences should matter. Second, the outcome should be Pareto optimal: the players would have to mighty spiteful to throw away part of the pie rather than give it to at least one of them. Third, given their utility functions players should be treated symmetrically. Fourth (and a bit controversially, as we will see), Nash insisted on Independence of Irrelevant Alternatives, meaning that if f(T) is the set of “fair bargains” when T is the set of all potential bargains, then if the potential set of bargains is smaller yet still contains f(T), say S strictly contained by T where f(T) is in S, then f(T) must remain the barganing outcome. It turns out that under these assumptions, there is a unique outcome which maximizes (u(x)-u(d))*(v(x)-v(d)), where u and v are each player’s utility functions, x is the vector of payoffs under the eventual bargain, and d the “status-quo” payoff if no bargain is made. This is natural in many cases. For instance, if two identical agents are splitting a dollar, then 50-50 is the only Nash outcome. Uniqueness is not at all obvious: recall the Edgeworth box and you will see that individual rationality and Pareto optimality alone leave many potential equilibria. Nash’s result is elegant and surprising, and it is no surprise that Nash’s grad school recommendation letter famously was only one sentence long: “This man is a genius.”

One problem with Nash bargaining, however. Nash was famously bipolar in real life, but there is an analogous bipolar feel to the idea of Nash equilibrium and the idea of Nash bargaining: where exactly are threats in Nash’s bargain theory? That is, Nash bargaining as an idea completely follows from the cooperative theory of von Neumann and Morganstern. Consider two identical agents splitting a dollar once more. Imagine that one of the agents already has 30 cents, so that only 70 of the cents are actually in the middle of the table. The Nash solution is that the person who starts with the thirty cents eventually winds up with 65 cents, and the other person with 35. But play this out in your head.

Player 1: “I, already having the 30 cents, should get half of what remains. It is only fair, and if you don’t give me 65 I will walk away from this table and we will each get nothing more.”

Player 2: “What does that have to do with it? The fair outcome is 50 cents each, which leaves you with more than your originally thirty, so you can take your threat and go jump off a bridge.”

That is, 50/50 might be a reasonable solution here, right? This might make even more sense if we take a more concrete example: bargaining over wages. Imagine the prevailing wage for CEOs in your industry is $250,000. Two identical CEOs will generate $500,000 in value for the firm if hired. CEO Candidate One has no other job offer. CEO Candidate Two has an offer from a job with similar prestige and benefits, paying $175,000. Surely we can’t believe that the second CEO will wind up with higher pay, right? It is a completely noncredible threat to take the $175,000 offer, hence it shouldn’t affect the bargaining outcome. A pet peeve of mine is that many applied economists are still using Nash bargaining – often in the context of the labor market! – despite this well-known problem.

Nash was quite aware of this, as can be seen by his 1953 Econometrica, where he attempts to give a noncooperative bargaining game that reaches the earlier axiomatic outcome. Indeed, this paper inspired an enormous research agenda called the Nash Program devoted to finding noncooperative games which generate well-known or reasonable-sounding cooperative solution outcomes. In some sense, the idea of “implementation” in mechanism design, where we investigate whether there exists a game which can generate socially or coalitionally preferred outcomes noncooperatively, can be thought of as a successful modern branch of the Nash program. Nash’s ’53 noncooperative game simply involves adding a bit of noise into the set of possible outcomes. Consider splitting a dollar again. Let a third party tell each player to name how many cents they want. If the joint requests are feasible, then the dollar is split (with any remainder thrown away), else each player gets nothing. Clearly every split of the dollar on the Pareto frontier is a Nash equilibrium, as is each player requesting the full dollar and getting nothing. However, if there is a tiny bit of noise about whether there is exactly one dollar, or .99 cents, or 1.01 cents, etc., when deciding whether to ask for more money, I will have to weigh the higher payoff if the joint demand is feasible against the payoff zero if my increased demand makes the split impossible and hence neither of us earn anything. In a rough sense, Nash shows that as the distribution of noise becomes degenerate around the true bargaining frontier, players will demand exactly their Nash bargaining outcome. Of course it is interesting that there exists some bargaining game that generates the Nash solution, and the idea that we should study noncooperative games which implement cooperate solution concepts is without a doubt seminal, but this particular game seems very strange to me, as I don’t understand what the source of the noise is, why it becomes degenerate, etc.

On the shoulders of Nash, however, bargaining progressed a huge amount. Three papers in particular are worth your time, although hopefully you have seen these before: Kalai and Smorodinsky 1975 who retaining the axiomatic approach but drop IIA, Rubinstein’s famous 1982 Econometrica on noncooperative bargaining with alternative offers, and Binmore, Rubinstein and Wolinsky on implementation of bargaining solutions which deals with the idea of threats as I did above.

You can read all four Nash papers in the original literally during your lunch hour; this seems to me a worthy way to tip your cap toward a man who literally helped make modern economics possible.

“The Power of Communication,” D. Rahman (2014)

(Before getting to Rahman’s paper, a quick note on today’s Clark Medal, which went to Roland Fryer, an economist at Harvard who is best known for his work on the economics of education. Fryer is no question a superstar, and is unusual in leaving academia temporarily while still quite young to work for the city of New York on improving their education policy. His work is a bit outside my interests, so I will leave more competent commentary to better informed writers.

The one caveat I have, however, is the same one I gave last year: the AEA is making a huge mistake in essentially changing this prize from “Best Economist Under 40″ to “Best Applied Microeconomist Under 40″. Of the past seven winners, the only one who isn’t obviously an applied microeconomist is Levin, and yet even he describes himself as “an applied economist with interests in industrial organization, market design and the economics of technology.” It’s not that Saez, Duflo, Levin, Finkelstein, Chetty, Gentzkow and Fryer are doing bad work – their research is all of very high quality and by no means “cute-onomics” – but simply that the type of research they do is a very small subset of what economists work on. This style of work is particularly associated with the two Cambridge schools, and it’s no surprise that all of the past seven winners either did their PhD or postdoc in Cambridge. Where are the macroeconomists, when Europe is facing unemployment rates upwards of 30% in some regions? Where are the finance and monetary folks, when we just suffered the worst global recession since the 1930s? Where are the growth economists, when we have just seen 20 years of incredible economic growth in the third world? Where are the historians? Where are the theorists, microeconomic and econometric, on whose backs the applied work winning the prizes are built? Something needs to change.)

Enough bellyaching. Let’s take a look at Rahman’s clever paper, which might be thought as “when mediators are bad for society”; I’ll give you another paper shortly about “when mediators are good”. Rahman’s question is simple: can firms maintain collusion without observing what other firms produce? You might think this would be tricky if the realized price only imperfectly reflects total production. Let the market price p be a function of total industry production q plus an epsilon term. Optimally, we would jointly produce the monopoly quantity and split the rents. However, the epsilon term means that simply observing the market price doesn’t tell my firm whether the other firm cheated and produced too much.

What can be done? Green and Porter (1984), along with Abreu, Pearce and Stacchetti two years later, answered that collusion can be sustained: just let the equilibrium involve a price war if the market price drops below a threshold. Sannikov and Skrzypacz provided an important corollary, however: if prices can be monitored continuously, then collusion unravels. Essentially, if actions to increase production can be taken continuously, the price wars required to prevent cheating must be so frequent that join profit from sometimes colluding and sometimes fighting price wars is worse than joint profit than from just playing static Cournot.

Rahman’s trick saves collusion even when, as is surely realistic, cheaters can act in continuous time. Here is how it works. Let there be a mediator – an industry organization or similar – who can talk privately to each firm. Colluding firms alternate who is producing at any given time, with the one producing firm selling the monopoly level of output. The firms who are not supposed to produce at time t obviously have an incentive to cheat and produce a little bit anyway. Once in a while, however, the mediator tells the firm who is meant to produce in time t to produce a very large amount. If the price turns out high, the mediator gives the firm that was meant to produce a very large amount less time in the future to act as the monopolist, whereas if the price turns out low, the mediator gives that firm more monopolist time in the future. The latter condition is required to incentivize the producing firm to actually ramp up production when told to do so. Either a capacity constraint, or a condition on the demand function, is required to keep the producing firm from increasing production too much.

Note that if a nonproducing firm cheats and produce during periods you were meant to be producing 0, and the mediator happens to secretly ask the temporary monopolist firm to produce a large amount, you are just increasing the probability that the other firm gets to act as the monopolist in the future while you just get to produce zero. Even better, since the mediator only occasionally asks the producing firm to overproduce, and other firms don’t know when this time might be, the nonproducing firms are always wary of cheating. That is, the mediator’s ability to make private recommendations permits more scope for collusion than firms who only options are to punish based on continuously-changing public prices, because there are only rare yet unknown times when cheating could be detected. What’s worse for policymakers, the equilibrium here which involves occasional overproduction shows that such overproduction is being used to help maintain collusion, not to deviate from it; add overproduction to Green-Porter price wars as phenomena which look like collusion breaking down but are instead collusion being maintained.

Final working paper (RePEc IDEAS). Final version published in AER 2014. If you don’t care about proof details, the paper is actually a very quick read. Perhaps no surprise, but the results in this paper are very much related to those in Rahman’s excellent “Who will Monitor the Monitor?” which was discussed on this site four years ago.

“Editor’s Introduction to The New Economic History and the Industrial Revolution,” J. Mokyr (1998)

I taught a fun three hours on the Industrial Revolution in my innovation PhD course this week. The absolutely incredible change in the condition of mankind that began in a tiny corner of Europe in an otherwise unremarkable 70-or-so years is totally fascinating. Indeed, the Industrial Revolution and its aftermath are so important to human history that I find it strange that we give people PhDs in social science without requiring at least some study of what happened.

My post today draws heavily on Joel Mokyr’s lovely, if lengthy, summary of what we know about the period. You really should read the whole thing, but if you know nothing about the IR, there are really five facts of great importance which you should be aware of.

1) The world was absurdly poor from the dawn of mankind until the late 1800s, everywhere.
Somewhere like Chad or Nepal today fares better on essentially any indicator of development than England, the wealthiest place in the world, in the early 1800s. This is hard to believe, I know. Life expectancy was in the 30s in England, infant mortality was about 150 per 1000 live births, literacy was minimal, and median wages were perhaps 3 to 4 times subsistence. Chad today has a life expectancy of 50, infant mortality of 90 per 1000, a literacy of 35%, and urban median wages of roughly 3 to 4 times subsistence. Nepal fares even better on all counts. The air from the “dark, Satanic mills” of William Blake would have made Beijing blush, “night soil” was generally just thrown on to the street, children as young as six regularly worked in mines, and 60 to 80 hours a week was a standard industrial schedule.


The richest places in the world were never more than 5x subsistence before the mid 1800s

Despite all of this, there was incredible voluntary urbanization: those dark, Satanic mills were preferable to the countryside. My own ancestors were among the Irish that fled the Potato famine. Mokyr’s earlier work on the famine, which happened in the British Isles after the Industrial Revolution, suggest 1.1 to 1.5 million people died from a population of about 7 million. This is similar to the lower end of the range for percentage killed during the Cambodian genocide, and similar to the median estimates of the death percentage during the Rwandan genocide. That is, even in the British Isles, famines that would shock the world today were not unheard of. And even if you wanted to leave the countryside, it may have been difficult to do so. After Napoleon, serfdom remained widespread east of the Elbe river in Europe, passes like the “Wanderbucher” were required if one wanted to travel, and coercive labor institutions that tied workers to specific employers were common. This is all to say that the material state of mankind before and during the Industrial Revolution, essentially anywhere in the world, would be seen as outrageous deprivation to us today; palaces like Versailles are not representative, as should be obvious, of how most people lived. Remember also that we are talking about Europe in the early 1800s; estimates of wages in other “rich” societies of the past are even closer to subsistence.

2) The average person did not become richer, nor was overall economic growth particularly spectacular, during the Industrial Revolution; indeed, wages may have fallen between 1760 and 1830.

The standard dating of the Industrial Revolution is 1760 to 1830. You might think: factories! The railroad! The steam engine! High Britannia! How on Earth could people have become poorer? And yet it is true. Brad DeLong has an old post showing Bob Allen’s wage reconstructions: Allen found British wages lower than their 1720 level in 1860! John Stuart Mill, in his 1870 textbook, still is unsure whether all of the great technological achievements of the Industrial Revolution would ever meaningfully improve the state of the mass of mankind. And Mill wasn’t the only one who noticed, there were a couple of German friends, who you may know, writing about the wretched state of the Working Class in Britain in the 1840s as well.

3) Major macro inventions, and growth, of the type seen in England in the late 1700s and early 1800s happened many times in human history.


The Iron Bridge in Shropshire, 1781, proving strength of British iron

The Industrial Revolution must surely be “industrial”, right? The dating of the IR’s beginning to 1760 is at least partially due to the three great inventions of that decade: the Watt engine, Arkwright’s water frame, and the spinning jenny. Two decades later came Cort’s famous puddling process for making strong iron. The industries affected by those inventions, cotton and iron, are the prototypical industries of England’s industrial height.

But if big macro-inventions, and a period of urbanization, are “all” that defines the Industrial Revolution, then there is nothing unique about the British experience. The Song Dynasty in China saw the gun, movable type, a primitive Bessemer process, a modern canal lock system, the steel curved moldboard plow, and a huge increase in arable land following public works projects. Netherlands in the late 16th and early 17th century grew faster, and eventually became richer, than Britain ever did during the Industrial Revolution. We have many other examples of short-lived periods of growth and urbanization: ancient Rome, Muslim Spain, the peak of the Caliphate following Harun ar-Rashid, etc.

We care about England’s growth and invention because of what followed 1830, not what happened between 1760 and 1830. England was able to take their inventions and set on a path to break the Malthusian bounds – I find Galor and Weil’s model the best for understanding what is necessary to move from a Malthusian world of limited long-run growth to a modern world of ever-increasing human capital and economic bounty. Mokyr puts it this way: “Examining British economic history in the period 1760-1830 is a bit like studying the history of Jewish dissenters between 50 B.C. and 50 A.D. At first provincial, localized, even bizarre, it was destined to change the life of every man and women…beyond recognition.”

4) It is hard for us today to understand how revolutionary ideas like “experimentation” or “probability” were.

In his two most famous books, The Gifts of Athena and The Lever of Riches, Mokyr has provided exhausting evidence about the importance of “tinkerers” in Britain. That is, there were probably something on the order of tens of thousands of folks in industry, many not terribly well educated, who avidly followed new scientific breakthroughs, who were aware of the scientific method, who believed in the existence of regularities which could be taken advantage of by man, and who used systematic processes of experimentation to learn what works and what doesn’t (the development of English porter is a great case study). It is impossible to overstate how unusual this was. In Germany and France, science was devoted mainly to the state, or to thought for thought’s sake, rather than to industry. The idea of everyday, uneducated people using scientific methods somewhere like ar-Rashid’s Baghdad is inconceivable. Indeed, as Ian Hacking has shown, it wasn’t just that fundamental concepts like “probabilistic regularities” were difficult to understand: the whole concept of discovering something based on probabilistic output would not have made sense to all but the very most clever person before the Enlightenment.

The existence of tinkerers with access to a scientific mentality was critical because it allowed big inventions or ideas to be refined until they proved useful. England did not just invent the Newcomen engine, put it to work in mines, and then give up. Rather, England developed that Newcomen engine, a boisterous monstrosity, until it could profitably be used to drive trains and ships. In Gifts of Athena, Mokyr writes that fortune may sometimes favor the unprepared mind with a great idea; however, it is the development of that idea which really matters, and to develop macroinventions you need a small but not tiny cohort of clever, mechanically gifted, curious citizens. Some have given credit to a political system, or to the patent system, for the widespread tinkering, but the qualitative historical evidence I am aware of appears to lean toward cultural explanations most strongly. One great piece of evidence is that contemporaries wrote often about the pattern where Frenchmen invented something of scientific importance, yet the idea diffused and was refined in Britain. Any explanation of British uniqueness must depend on Britain’s ability to refine inventions.

5) The best explanations for “why England? why in the late 1700s? why did growth continue?” do not involve colonialism, slavery, or famous inventions.

First, we should dispose of colonialism and slavery. Exports to India were not particularly important compared to exports to non-colonial regions, slavery was a tiny portion of British GDP and savings, and many other countries were equally well-disposed to profit from slavery and colonialism as of the mid-1700s, yet the IR was limited to England. Expanding beyond Europe, Dierdre McCloskey notes that “thrifty self-discipline and violent expropriation have been too common in human history to explain a revolution utterly unprecedented in scale and unique to Europe around 1800.” As for famous inventions, we have already noted how common bursts of cleverness were in the historic record, and there is nothing to suggest that England was particularly unique in its macroinventions.

To my mind, this leaves two big, competing explanations: Mokyr’s argument that tinkerers and a scientific mentality allowed Britain to adapt and diffuse its big inventions rapidly enough to push the country over the Malthusian hump and into a period of declining population growth after 1870, and Bob Allen’s argument that British wages were historically unique. Essentially, Allen argues that British wages were high compared to its capital costs from the Black Death forward. This means that labor-saving inventions were worthwhile to adopt in Britain even when they weren’t worthwhile in other countries (e.g., his computations on the spinning jenny). If it worthwhile to adopt certain inventions, then inventors will be able to sell something, hence it is worthwhile to invent certain inventions. Once adopted, Britain refined these inventions as they crawled down the learning curve, and eventually it became worthwhile for other countries to adopt the tools of the Industrial Revolution. There is a great deal of debate about who has the upper hand, or indeed whether the two views are even in conflict. I do, however, buy the argument, made by Mokyr and others, that it is not at all obvious that inventors in the 1700s were targeting their inventions toward labor saving tasks (although at the margin we know there was some directed technical change in the 1860s), nor it is even clear that invention overall during the IR was labor saving (total working hours increased, for instance).

Mokyr’s Editor’s Introduction to “The New Economic History and the Industrial Revolution” (no RePEc IDEAS page). He has a followup in the Journal of Economic History, 2005, examining further the role of an Enlightenment mentality in allowing for the rapid refinement and adoption of inventions in 18th century Britain, and hence the eventual exit from the Malthusian trap.

“The Contributions of the Economics of Information to Twentieth Century Economics,” J. Stiglitz (2000)

There have been three major methodological developments in economics since 1970. First, following the Lucas Critique we are reluctant to accept policy advice which is not the result of directed behavior on the part of individuals and firms. Second, developments in game theory have made it possible to reformulate questions like “why do firms exist?”, “what will result from regulating a particular industry in a particular way?”, “what can I infer about the state of the world from an offer to trade?”, among many others. Third, imperfect and asymmetric information was shown to be of first-order importance for analyzing economic problems.

Why is information so important? Prices, Hayek taught us, solve the problem of asymmetric information about scarcity. Knowing the price vector is a sufficient statistic for knowing everything about production processes in every firm, as far as generating efficient behavior is concerned. The simple existence of asymmetric information, then, is not obviously a problem for economic efficiency. And if asymmetric information about big things like scarcity across society does not obviously matter, then how could imperfect information about minor things matter? A shopper, for instance, may not know exactly the price of every car at every dealership. But “Natura non facit saltum”, Marshall once claimed: nature does not make leaps. Tiny deviations from the assumptions of general equilibrium do not have large consequences.

But Marshall was wrong: nature does make leaps when it comes to information. The search model of Peter Diamond, most famously, showed that arbitrarily small search costs lead to firms charging the monopoly price in equilibrium, hence a welfare loss completely out of proportion to the search costs. That is, information costs and asymmetries, even very small ones, can theoretically be very problematic for the Arrow-Debreu welfare properties.

Even more interesting, we learned that prices are more powerful than we’d believed. They convey information about scarcity, yes, but also information about other people’s own information or effort. Consider, for instance, efficiency wages. A high wage is not merely a signal of scarcity for a particular type of labor, but is simultaneously an effort inducement mechanism. Given this dual role, it is perhaps not surprising that general equilibrium is no longer Pareto optimal, even if the planner is as constrained informationally as each agent.

How is this? Decentralized economies may, given information cost constraints, exert too much effort searching, or generate inefficient separating equilibrium that unravel trades. The beautiful equity/efficiency separation of the Second Welfare Theorem does not hold in a world of imperfect information. A simple example on this point is that it is often useful to allow some agents suffering moral hazard worries to “buy the firm”, mitigating the incentive problem, but limited liability means this may not happen unless those particular agents begin with a large endowment. That is, a different endowment, where the agents suffering extreme moral hazard problems begin with more money and are able to “buy the firm”, leads to more efficient production (potentially in a Pareto sense) than an endowment where those workers must be provided with information rents in an economy-distorting manner.

It is a strange fact that many social scientists feel economics to some extent stopped progressing by the 1970s. All the important basic results were, in some sense, known. How untrue this is! Imagine labor without search models, trade without monopolistic competitive equilibria, IO or monetary policy without mechanism design, finance without formal models of price discovery and equilibrium noise trading: all would be impossible given the tools we had in 1970. The explanations that preceded modern game theoretic and information-laden explanations are quite extraordinary: Marshall observed that managers have interests different from owners, yet nonetheless are “well-behaved” in running firms in a way acceptable to the owner. His explanation was to credit British upbringing and morals! As Stiglitz notes, this is not an explanation we would accept today. Rather, firms have used a number of intriguing mechanisms to structure incentives in a way that limits agency problems, and we now possess the tools to analyze these mechanisms rigorously.

Final 2000 QJE (RePEc IDEAS)

“Identifying Technology Spillovers and Product Market Rivalry,” N. Bloom, M. Schankerman & J. Van Reenen (2013)

How do the social returns to R&D differ from the private returns? We must believe there is a positive gap between the two given the widespread policies of subsidizing R&D investment. The problem is measuring the gap: theory gives us a number of reasons why firms may do more R&D than the social optimum. Most intuitively, a lot of R&D contains “business stealing” effects, where some of the profit you earn from your new computer chip comes from taking sales away from me, even if you chip is only slightly better than mine. Business stealing must be weighed against the fact that some of the benefits of knowledge a firm creates is captured by other firms working on similar problems, and the fact that consumers get surplus from new inventions as well.

My read of the literature is that we don’t have know much about how aggregate social returns to research differ from private returns. The very best work is at the industry level, such as Trajtenberg’s fantastic paper on CAT scans, where he formally writes down a discrete choice demand system for new innovations in that product and compares R&D costs to social benefits. The problem with industry-level studies is that, almost by definition, they are studying the social return to R&D in ex-post successful new industries. At an aggregate level, you might think, well, just include the industry stock of R&D in a standard firm production regression. This will control for within-industry spillovers, and we can make some assumption about the steepness of the demand curve to translate private returns given spillovers into returns inclusive of consumer surplus.

There are two problems with that method. First, what is an “industry” anyway? Bloom et al point out in the present paper that even though Apple and Intel do very similar research, as measured by the technology classes they patent in, they don’t actually compete in the product market. This means that we want to include “within-similar-technology-space stock of knowledge” in the firm production function regression, not “within-product-space stock of knowledge”. Second, and more seriously, if we care about social returns, we want to subtract out from the private return to R&D any increase in firm revenue that just comes from business stealing with slightly-improved versions of existing products.

Bloom et al do both in a very interesting way. First, they write down a model where firms get spillovers from research in similar technology classes, then compete with product market rivals; technology space and product market space are correlated but not perfectly so, as in the Apple/Intel example. They estimate spillovers in technology space using measures of closeness in terms of patent classes, and measure closeness in product space based on the SIC industries that firms jointly compete in. The model overidentifies the existence of spillovers: if technological spillovers exist, then you can find evidence conditional on the model in terms of firm market value, firm R&D totals, firm productivity and firm patent activity. No big surprises, given your intuition: technological spillovers to other firms can be seen in every estimated equation, and business stealing R&D, though small in magnitude, is a real phenomenon.

The really important estimate, though, is the level of aggregate social returns compared to private returns. The calculation is non-obvious, and shuttled to an online appendix, but essentially we want to know how increasing R&D by one dollar increases total output (the marginal social return) and how increasing R&D by one dollar increases firm revenue (marginal private return). The former may exceed the latter if the benefits of R&D spill over to other firms, but the latter may exceed the former is lots of R&D just leads to business stealing. Note that any benefits in terms of consumer surplus are omitted. Bloom et al find aggregate marginal private returns on the order of 20%, and social returns on the order of 60% (a gap referred to as “29.2%” instead of “39.2%” in the paper; come on, referees, this is a pretty important thing to not notice!). If it wasn’t for business stealing, the gap between social and private returns would be ten percentage points higher. I confess a little bit of skepticism here; do we really believe that for the average R&D performing firm, the marginal private return on R&D is 20%? Nonetheless, the estimate that social returns exceed private returns is important. Even more important is the insight that the gap between social and private returns depends on the size of the technology spillover. In Bloom et al’s data, large firms tend to do work in technology spaces with more spillovers, while small firms tend to work on fairly idiosyncratic R&D; to greatly simplify what is going on, large firms are doing more general R&D than the very product-specific R&D small firms do. This means that the gap between private and social return is larger for large firms, and hence the justification for subsidizing R&D might be highest for very large firms. Government policy in the U.S. used to implicitly recognize this intuition, shuttling R&D funds to the likes of Bell Labs.

All in all an important contribution, though this is by no means the last word on spillovers; I would love to see a paper asking why firms don’t do more R&D given the large private returns we see here (and in many other papers, for that matter). I am also curious how R&D spillovers compare to spillovers from other types of investments. For instance, an investment increasing demand for product X also increases demand for any complementary products, leads to increased revenue that is partially captured by suppliers with some degree of market power, etc. Is R&D really that special compared to other forms of investment? Not clear to me, especially if we are restricting to more applied, or more process-oriented, R&D. At the very least, I don’t know of any good evidence one way or the other.

Final version, Econometrica 2013 (RePEc IDEAS version); the paper essentially requires reading the Appendix in order to understand what is going on.

“Entrepreneurship: Productive, Unproductive and Destructive,” W. Baumol (1990)

William Baumol, who strikes me as one of the leading contenders for a Nobel in the near future, has written a surprising amount of interesting economic history. Many economic historians see innovation – the expansion of ideas and the diffusion of products containing those ideas, generally driven by entrepreneurs – as critical for growth. But we find it very difficult to see any reason why the “spirit of innovation” or the net amount of cleverness in society is varying over time. Indeed, great inventions, as undeveloped ideas, occur almost everywhere at almost all times. The steam engine of Heron of Alexandria, which was used for parlor tricks like opening temple doors and little else, is surely the most famous example of a great idea, undeveloped.

Why, then, do entrepreneurs develop ideas and cause products to diffuse widely at some times in history and not at others? Schumpeter gave five roles for an entrepreneur: introducing new products, new production methods, new markets, new supply sources or new firm and industry organizations. All of these are productive forms of entrepreneurship. Baumol points out that clever folks can also spend their time innovating new war implements, or new methods of rent seeking, or new methods of advancing in government. If incentives are such that those activities are where the very clever are able to prosper, both financially and socially, then it should be no surprise that “entrepreneurship” in this broad sense is unproductive or, worse, destructive.

History offers a great deal of support here. Despite quite a bit of productive entrepreneurship in the Middle East before the rise of Athens and Rome, the Greeks and Romans, especially the latter, are well-known for their lack of widespread diffusion of new productive innovations. Beyond the steam engine, the Romans also knew of the water wheel yet used it very little. There are countless other examples. Why? Let’s turn to Cicero: “Of all the sources of wealth, farming is the best, the most able, the most profitable, the most noble.” Earning a governorship and stripping assets was also seen as noble. What we now call productive work? Not so much. Even the freed slaves who worked as merchants had the goal of, after acquiring enough money, retiring to “domum pulchram, multum serit, multum fenerat”: a fine house, land under cultivation and short-term loans for voyages.

Baumol goes on to discuss China, where passing the imperial exam and moving into government was the easiest way to wealth, and the early middle ages of Europe, where seizing assets from neighboring towns was more profitable than expanding trade. The historical content of Baumol’s essay was greatly expanded in a book he edited alongside Joel Mokyr and David Landes called The Invention of Enterprise, which discusses the relative return to productive entrepreneurship versus other forms of entrepreneurship from Babylon up to post-war Japan.

The relative incentives for different types of “clever work” are relevant today as well. Consider Luigi Zingales’ new lecture, Does Finance Benefit Society? I can’t imagine anyone would consider Zingales hostile to the financial sector, but he nonetheless discusses in exhaustive detail the ways in which incentives push some workers in that sector toward rent-seeking and fraud rather than innovation which helps the consumer.

Final JPE copy (RePEc IDEAS). Murphy, Schleifer and Vishny have a paper, also from the JPE in 1990, on the topic of how clever people in many countries are incentivized toward rent-seeking; their work is more theoretical and empirical than historical. If you are interested in innovation and entrepreneurship, I uploaded the reading list for my PhD course on the topic here.

“Designing Efficient College and Tax Policies,” S. Findeisen & D. Sachs (2014)

It’s job market season, which is a great time of year for economists because we get to read lots of interesting papers. The one, by Dominik Sachs from Cologne and his coauthor Sebastian Findeisen, is particularly relevant given the recent Obama policy announcement about further subsidizing community college. The basic facts of marginal college students are fairly well-known: there is a pretty substantial wage bump for college grads (including ones who are not currently attending but who would attend if college was a little cheaper), many do not go to college even given this wage bump, there are probably externalities both in the economic and social realm from having a more education population though these are quite hard to measure, borrowing constraints bind for some potential college students but don’t appear to be that important, and it is very hard to design policies which benefit only marginal college candidates without also subsidizing those who would go whether or not the subsidy existed.

The naive thought might be “why should we subsidize college in the absence of borrowing constraints? By revealed preference, people choose not to go to college even given the wage bump, which likely implies that for many people studying and spending time going to class gives negative utility. Given the wage bump, these people are apparently willing to pay a lot of money to avoid spending time in college. The social externalities of college probably exist, but in general equilibrium more college-educated workers might drive down the return to college for people who are currently going. Therefore, we ought not distort the market.”

However, Sachs and Findeisen point out that there is also a fiscal externality: higher wages equals higher tax revenue in the future, and only the government cares about that revenue. Even more, the government is risk-neutral, or at least less risk-averse than individuals, about that revenue; people might avoid going to college if, along with bumping up their expected future wages, college also introduces uncertainty into their future wage path. If a subsidy could be targeted largely to students on the margin rather than those currently attending college, and if those marginal students see a big wage bump, and if government revenue less transfers back to the taxpayer is high, then it may be worth it for the government to subsidize college even if there are no other social benefits!

The authors write a nice little structural model. People choose to go to college or not depending on their innate ability, their parent’s wealth, the cost of college, the wage bump they expect (and the variance thereof), and their personal taste or distaste for studying as opposed to working (“psychic costs”). All of those variables aside from personal taste and innate ability can be pulled out of U.S. longitudinal data, performance on the army qualifying test can proxy for innate ability, and given distributional assumptions, we can identify the last free parameter, personal taste, by assuming that people go to college only if their lifetime discounted utility from attendance, less psychic costs, exceeds the lifetime utility from working instead. A choice model of this type seems to match data from previous studies with quasirandom variation concerning the returns to college education.

The direct benefit to the government from higher tax revenue from a subsidy policy, then, is the cost of the subsidy times the number subsidized, minus the proportion of subsidized students who would not have gone to college but for the subsidy times the discounted lifetime wage bump for those students times government tax revenue as a percent of that wage bump. The authors find that a general college subsidy program nearly pays for itself: if you subsidize everyone there aren’t many marginal students, but even for those students the wage bump is substantial. Targeting low income students is even better. Though the low income students affected on the margin tend to be less academically gifted, and hence to earn a lower (absolute) increase in wages from going to college, subsidies targeted at low income students do not waste as much money subsidizing students who would go to college anyway (i.e., a large percentage of high income kids). Note that the subsidies are small enough in absolute terms that the distortion on parental labor supply, from working less in order to qualify for subsidies, is of no quantitative importance, a fact the authors show rigorously. Merit-based subsidies will attract better students who have more to gain from going to college, but they also largely affect people who would go to college anyway, hence offer less bang for the buck to government compared to need-based grants.

The authors have a nice calibrated model in hand, so there are many more questions they ask beyond the direct partial equilibrium benefits of college attendance. For example, in general equilibrium, if we induce people to go to college, the college wage premium will fall. But note that wages for non-college-grads will rise in relative terms, so the net effect of the grants discussed in the previous paragraph on government revenue is essentially unchanged. Further, as Nate Hilger found using quasirandom variation in income due to layoffs, liquidity constraints do not appear to be terribly important for the college making decision: it is increasing grants, not changing loan eligibility, that will do anything of any importance to college attendance.

November 2014 working paper (No IDEAS version). The authors have a handful of other very interesting papers in the New Dynamic Public Finance framework, which is blazing hot right now. As far as I understand the project of NDPF, essentially we can simplify the (technically all-but-impossible-to-solve) dynamic mechanism problem of designing optimal taxes and subsidies under risk aversion and savings behavior to an equivalent reduced form that essentially only depends on simple first order conditions and a handful of elasticities. Famously, it is not obvious that capital taxation should be zero.

“Competition, Imitation and Growth with Step-by-Step Innovation,” P. Aghion, C. Harris, P. Howitt, & J. Vickers (2001)

(One quick PSA before I get to today’s paper: if you happen, by chance, to be a graduate student in the social sciences in Toronto, you are more than welcome to attend my PhD seminar in innovation and entrepreneurship at the Rotman school which begins on Wednesday, the 7th. I’ve put together a really wild reading list, so hopefully we’ll get some very productive discussions out of the course. The only prerequisite is that you know some basic game theory, and my number one goal is forcing the economists to read sociology, the sociologists to write formal theory, and the whole lot to understand how many modern topics in innovation have historical antecedents. Think of it as a high-variance cross-disciplinary educational lottery ticket! If interested, email me at kevin.bryanATrotman.utoronto.ca for more details.)

Back to Aghion et al. Let’s kick off 2015 with one of the nicer pieces to come out the ridiculously productive decade or so of theoretical work on growth put together by Philippe Aghion and his coauthors; I wish I could capture the famous alacrity of Aghion’s live presentation of his work, but I fear that’s impossible to do in writing! This paper is based around writing a useful theory to speak to two of the oldest questions in the economics of innovation: is more competition in product markets good or bad for R&D, and is there something strange about giving a firm IP (literally a grant of market power meant to spur innovation via excess rents) at the same time as we enforce antitrust (generally a restriction on market power meant to reduce excess rents)?

Aghion et al come to a few very surprising conclusions. First, the Schumpeterian idea that firms with market power do more R&D is misleading because it ignores the “escape the competition” effect whereby firms have high incentive to innovate when there is a large market that can be captured by doing so. Second, maximizing that “escape the competition” motive may involve making it not too easy to catch up to market technological leaders (by IP or other means). These two theoretical results imply that antitrust (making sure there are a lot of firms competing in a given market, spurring new innovation to take market share from rivals) and IP policy (ensuring that R&D actually needs to be performed in order to gain a lead) are in a sense complements! The fundamental theoretical driver is that the incentive to innovate depends not only on the rents of an innovation, but on the incremental rents of an innovation; if innovators include firms that already active in an industry, policy that makes your current technological state less valuable (because you are in a more competitive market, say) or policy that makes jumping to a better technological state more valuable both increase the size of the incremental rent, and hence the incentive to perform R&D.

Here are the key aspects of a simplified version of the model. An industry is a duopoly where consumers spend exactly 1 dollar per period. The duopolists produce partially substitutable goods, where the more similar the goods the more “product market competition” there is. Each of the duopolists produces their good at a firm-specific cost, and competes in Bertrand with their duopoly rival. At the minimal amount of product market competition, each firm earns constant profit regardless of their cost or their rival’s cost. Firms can invest in R&D which gives some flow probability of lowering their unit cost. Technological laggards sometimes catch up to the unit cost of leaders with exogenous probability; lower IP protection (or more prevalent spillovers) means this probability is higher. We’ll look only at features of this model in the stochastic distribution of technological leadership and lags which is a steady state if there infinite duopolistic industries.

In a model with these features, you always want at least a little competition, essentially for Arrow (1962) reasons: the size of the market is small when market power is large because total unit sales are low, hence the benefit of reducing unit costs is low, hence no one will bother to do any innovation in the limit. More competition can also be good because it increases the probability that two firms are at similar technological levels, in which case each wants to double down on research intensity to gain a lead. At very high levels of competition, the old Schumpeterian story might bind again: goods are so substitutable that R&D to increase rents is pointless since almost all rents are competed away, especially if IP is weak so that rival firms catch up to your unit cost quickly no matter how much R&D you do. What of the optimal level of IP? It’s always best to ensure IP is not too strong, or that spillovers are not too weak, because the benefit of increased R&D effort when firms are at similar technological levels following the spillover exceeds the lost incentive to gain a lead in the first place when IP is not perfectly strong. When markets are really competitive, however, the Schumpeterian insight that some rents need to exist militates in favor of somewhat stronger IP than in less competitive product markets.

Final working paper (RePEc IDEAS) which was published in 2001 in the Review of Economic Studies. This paper is the more detailed one theoretically, but if all of the insight sounds familiar, you may already know the hugely influential follow-up paper by Aghion, Bloom, Blundell, Griffith and Howitt, “Competition and Innovation: An Inverted U Relationship”, published in the QJE in 2005. That paper gives some empirical evidence for the idea that innovation is maximized at intermediate values of product market competition; the Schumpeterian “we need some rents” motive and the “firms innovate to escape competition” motive both play a role. I am actually not a huge fan of this paper – as an empirical matter, I’m unconvinced that most cost-reducing innovation in many industries will never show up in patent statistics (principally for reasons that Eric von Hippel made clear in The Sources of Innovation, which is freely downloadable at that link!). But this is a discussion for another day! One more related paper we have previously discussed is Goettler and Gordon’s 2012 structural work on processor chip innovation at AMD and Intel, which has a very similar within-industry motivation.

“Forced Coexistence and Economic Development: Evidence from Native American Reservations,” C. Dippel (2014)

I promised one more paper from Christian Dippel, and it is another quite interesting one. There is lots of evidence, folk and otherwise, that combining different ethnic or linguistic groups artificially, as in much of the ex-colonial world, leads to bad economic and governance outcomes. But that’s weird, right? After all, ethnic boundaries are themselves artificial, and there are tons of examples – Italy and France being the most famous – of linguistic diversity quickly fading away once a state is developed. Economic theory (e.g., a couple recent papers by Joyee Deb) suggests an alternative explanation: groups that have traditionally not worked with each other need time to coordinate on all of the Pareto-improving norms you want in a society. That is, it’s not some kind of intractable ethnic hate, but merely a lack of trust that is the problem.

Dippel uses the history of American Indian reservations to examine the issue. It turns out that reservations occasionally included different subtribal bands even though they almost always were made up of members of a single tribe with a shared language and ethnic identity. For example, “the notion of tribe in Apachean cultures is very weakly developed. Essentially it was only a recognition
that one owed a modicum of hospitality to those of the same speech, dress, and customs.” Ethnographers have conveniently constructed measures of how integrated governance was in each tribe prior to the era of reservations; some tribes had very centralized governance, whereas others were like the Apache. In a straight OLS regression with the natural covariates, incomes are substantially lower on reservations made up of multiple bands that had no pre-reservation history of centralized governance.

Why? First, let’s deal with identification (more on what that means in a second). You might naturally think that, hey, tribes with centralized governance in the 1800s were probably quite socioeconomically advanced already: think Cherokee. So are we just picking up that high SES in the 1800s leads to high incomes today? Well, in regions with lots of mining potential, bands tended to be grouped onto one reservation more frequently, which suggests that resource prevalence on ancestral homelands outside of the modern reservation boundaries can instrument for the propensity for bands to be placed together. Instrumented estimates of the effect of “forced coexistence” is just as strong as the OLS estimate. Further, including tribe fixed effects for cases where single tribes have a number of reservations, a surprisingly common outcome, also generates similar estimates of the effect of forced coexistence.

I am very impressed with how clear Dippel is about what exactly is being identified with each of these techniques. A lot of modern applied econometrics is about “identification”, and generally only identifies a local average treatment effect, or LATE. But we need to be clear about LATE – much more important than “what is your identification strategy” is an answer to “what are you identifying anyway?” Since LATE identifies causal effects that are local conditional on covariates, and the proper interpretation of that term tends to be really non-obvious to the reader, it should go without saying that authors using IVs and similar techniques ought be very precise in what exactly they are claiming to identify. Lots of quasi-random variation generates that variation along a local margin that is of little economic importance!

Even better than the estimates is an investigation of the mechanism. If you look by decade, you only really see the effect of forced coexistence begin in the 1990s. But why? After all, the “forced coexistence” is longstanding, right? Think of Nunn’s famous long-run effect of slavery paper, though: the negative effects of slavery are mediated during the colonial era, but are very important once local government has real power and historically-based factionalism has some way to bind on outcomes. It turns out that until the 1980s, Indian reservations had very little local power and were largely run as government offices. Legal changes mean that local power over the economy, including the courts in commercial disputes, is now quite strong, and anecdotal evidence suggests lots of factionalism which is often based on longstanding intertribal divisions. Dippel also shows that newspaper mentions of conflict and corruption at the reservation level are correlated with forced coexistence.

How should we interpret these results? Since moving to Canada, I’ve quickly learned that Canadians generally do not subscribe to the melting pot theory; largely because of the “forced coexistence” of francophone and anglophone populations – including two completely separate legal traditions! – more recent immigrants are given great latitude to maintain their pre-immigration culture. This heterogeneous culture means that there are a lot of actively implemented norms and policies to help reduce cultural division on issues that matter to the success of the country. You might think of the problems on reservations and in Nunn’s post-slavery states as a problem of too little effort to deal with factionalism rather than the existence of the factionalism itself.

Final working paper, forthcoming in Econometrica. No RePEc IDEAS version. Related to post-colonial divisions, I also very much enjoyed Mobilizing the Masses for Genocide by Thorsten Rogall, a job market candidate from IIES. When civilians slaughter other civilians, is it merely a “reflection of ancient ethnic hatred” or is it actively guided by authority? In Rwanda, Rogall finds that almost all of the killing is caused directly or indirectly by the 50,000-strong centralized armed groups who fanned out across villages. In villages that were easier to reach (because the roads were not terribly washed out that year), more armed militiamen were able to arrive, and the more of them that arrived, the more deaths resulted. This in-person provoking appears much more important than the radio propaganda which Yanigazawa-Drott discusses in his recent QJE; one implication is that post-WW2 restrictions on free speech in Europe related to Nazism may be completely misdiagnosing the problem. Three things I especially liked about Rogall’s paper: the choice of identification strategy is guided by a precise policy question which can be answered along the local margin identified (could a foreign force stopping these centralized actors a la Romeo Dallaire have prevented the genocide?), a theoretical model allows much more in-depth interpretation of certain coefficients (for instance, he can show that most villages do not appear to have been made up of active resistors), and he discusses external cases like the Lithuanian killings of Jews during World War II, where a similar mechanism appears to be at play. I’ll have many more posts on cool job market papers coming shortly!

“The Rents from Sugar and Coercive Institutions: Removing the Sugar Coating,” C. Dippel, A. Greif & D. Trefler (2014)

Today, I’ve got two posts about some new work by Christian Dippel, an economic historian at UCLA Anderson who is doing some very interesting theoretically-informed history; no surprise to see Greif and Trefler as coauthors on this paper, as they are both prominent proponents of this analytical style.

The authors consider the following puzzle: sugar prices absolutely collapse during the mid and late 1800s, largely because of the rise of beet sugar. And yet, wages in the sugar-dominant British colonies do not appear to have fallen. This is odd, since all of our main theories of trade suggest that when an export price falls, the price of factors used to produce that export also fall (this is less obvious than just marginal product falling, but still true).

The economics seem straightforward enough, so what explains the empirical result? Well, the period in question is right after the end of slavery in the British Empire. There were lots of ways in which the politically powerful could use legal or extralegal means to keep wages from rising to marginal product. Suresh Naidu, a favorite of this blog, has a number of papers on labor coercion everywhere from the UK in the era of Master and Servant Law, to the US South post-reconstruction, to the Middle East today; actually, I understand he is writing a book on the subject which, if there is any justice, has a good shot at being the next Pikettyesque mainstream hit. Dippel et al quote a British writer in the 1850s on the Caribbean colonies: “we have had a mass of colonial legislation, all dictated by the most short-sighted but intense and disgraceful selfishness, endeavouring to restrict free labour by interfering with wages, by unjust taxation, by unjust restrictions, by oppressive and unequal laws respecting contracts, by the denial of security of [land] tenure, and by impeding the sale of land.” In particular, wages rose rapidly right after slavery ended in 1838, but those gains were clawed back by the end of 1840s due to “tenancy-at-will laws” (which let employers seize some types of property if workers left), trespass and land use laws to restrict freeholding on abandoned estates and Crown land, and emigration restrictions.

What does labor coercion have to do with wages staying high as sugar prices collapse? The authors write a nice general equilibrium model. Englishmen choose whether to move to the colonies (in which case they get some decent land) or to stay in England at the outside wage. Workers in the Caribbean can either take a wage working sugar which depends on bargaining power, or they can go work marginal freehold land. Labor coercion rules limit the ability of those workers to work some land, so the outside option of leaving the sugar plantation is worse the more coercive institutions are. Governments maximize a weighted combination of Englishmen and local wages, choosing the coerciveness of institutions. The weight on Englishmen wages is higher the more important sugar exports and their enormous rents are to the local economy. In partial equilibrium, then, if the price of sugar falls exogenously, the wages of workers on sugar plantations falls (as their MP goes down), the number of locals willing to work sugar falls, hence the number of Englishman willing to stay falls (as their profit goes down). With few plantations, sugar rents become less important, labor coercion falls, opening up more marginal land for freeholders, which causes even more workers to leave sugar plantations and improves wages for those workers. However, if sugar is very important, the government places a lot of weight on planter income in the social welfare function, hence responds to a fall in sugar prices by increasing labor coercion, lowering the outside option of workers, keeping them on the sugar plantations, where they earn lower wages than before for the usual economic reasons. That is, if sugar is really important, coercive institutions will be retained, the economic structure will be largely unchanged in response to a fall in world sugar prices, and hence wages will fall, but if sugar is only of marginal importance, a fall in sugar prices leads the politically powerful to leave, lowering the political strength of the planter class, thus causing coercive labor institutions to decline, allowing workers to reallocate such that wages approach marginal product; since the MP of options other than sugar may be higher than the wage paid to sugar workers, this reallocation caused by the decline of sugar prices can cause wages in the colony to increase.

The British, being British, kept very detailed records of things like incarceration rates, wages, crop exports, and the like, and the authors find a good deal of empirical evidence for the mechanism just described. To assuage worries about the endogeneity of planter power, they even get a subject expert to construct a measure of geographic suitability for sugar in each of 14 British Caribbean colonies, and proxies for planter power with the suitability of marginal land for sugar production. Interesting work all around.

What should we take from this? That legal and extralegal means can be used to keep factor rents from approaching their perfect competition outcome: well, that is something essentially every classical economist from Smith to Marx has described. The interesting work here is the endogeneity of factor coercion. There is still some debate about much we actually know about whether these endogenous institutions (or, even more so, the persistence of institutions) have first-order economic effects; see a recent series of posts by Dietz Vollrath for a skeptical view. I find this paper by Dippel et al, as well as recent work by Naidu and Hornbeck, are the cleanest examples of how exogenous shocks affect institutions, and how those institutions then affect economic outcomes of great importance.

December 2014 working paper (no RePEc IDEAS version)

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