Author Archives: afinetheorem

“Ranking Firms Using Revealed Preference,” I. Sorkin (2015)

Roughly 20 percent of earnings inequality is not driven by your personal characteristics or the type of job you work at, but by the precise firm you work for. This is odd. In a traditional neoclassical labor market, every firm should offer to same wage to workers with the same marginal productivity. If a firm doesn’t do so, surely their workers will quit and go to firms that pay better. One explanation is that since search frictions make it hard to immediately replace workers, firms with market power will wind up sharing rents with their employees. It is costly to search for jobs, but as your career advances, you try to move “up the job ladder” from positions that pay just your marginal product to positions that pay a premium: eventually you wind up as the city bus driver with the six figure contract and once there you don’t leave. But is this all that is going on?

Isaac Sorkin, a job market candidate from Michigan, correctly notes that workers care about the utility their job offers, not the wage. Some jobs stink even though they pay well: 80 hour weeks, high pressure bosses, frequent business travel to the middle of nowhere, low levels of autonomy, etc. We can’t observe the utility a job offers, of course, but this is a problem that always comes up in demand analysis. If a Chipotle burrito and a kale salad cost the same, but you buy the burrito, then you have revealed that you get more utility from the former; this is the old theory of revealed preference. Even though we rarely observe a single person choosing from a set of job offers, we do observe worker flows between firms. If we can isolate workers who leave their existing job for individual reasons, as distinct from those who leave because their entire firm suffers a negative shock, then their new job is “revealed” better. Intuitively, we see a lot of lawyers quit to run a bed and breakfast in Vermont, but basically zero lawyers quitting to take a mining job that pays the same as running a B&B, hence the B&B must be a “better job” than mining, and further if we don’t see any B&B owners quitting to become lawyers, the B&B must be a “better job” than corporate law even if the pay is lower.

A sensible idea, then: the same worker may be paid different amounts in relation to marginal productivity either because they have moved up the job ladder and luckily landed at a firm with market power and hence pay above marginal product (a “good job”), or because different jobs offer different compensating differentials (in which case high paying jobs may actually be “bad jobs” with long hours and terrible work environments). To separate the two rationales, we need to identify the relative attractiveness of jobs, for which revealed preference should work. The problem in practice is both figuring out which workers are leaving for individual reasons, and getting around the problem that it is unusual to observe in the data a nonzero number of people going from firm A to firm B and vice versa.

Sorkin solves these difficulties in a very clever way. Would you believe the secret is to draw on the good old Perron-Frebonius theorem, a trusted tool of microeconomists interested in network structure? How could that be? Workers meet firms in a search process, with firms posting offers in terms of a utility bundle of wages plus amenities. Each worker also has idiosyncratic tastes about things like where to live, how they like the boss, and so on. The number of folks that move voluntarily from job A to job B depends on how big firm A is (bigger firms have more workers that might leave), how frequently A has no negative productivity shocks (in which case moves are voluntary), and the probability a worker from A is offered a job at B when matched and accepts it, which depends on the relative utilities of the two jobs including the individual idiosyncratic portion. An assumption about the distribution of idiosyncratic utility across jobs allows Sorkin to translate probabilities of accepting a job into relative utilities.

What is particularly nice is that the model gives a linear restriction on any two job pairs: the relative probability of moving from A to B instead of B to A depends on the relative utility (abstracting from idiosyncratic portions) adjusted for firm size and offer probability. That is, if M(A,B) is the number of moves from A to B, and V(A) is a (defined in the paper) function of the non-idiosyncratic utility of job A, then

M(A,B)/M(B,A) = V(B)/V(A)

and hence

M(A,B)V(A) = M(B,A)V(B)

Taking this to data is still problematic because we need to restrict to job changes that are not just “my factory went out of business”, and because M(A,B) or M(B,A) are zero for many firm pairs. The first problem is solved by estimating the probability a given job switch is voluntary using the fact that layoff probability is related to the size and growth rate of a firm. The second problem can be solved by noting that if we sum the previous equation over all firms B not equal to A, we have

sum(B!=A)M(A,B)*V(A) = sum(B!=A)M(B,A)*V(B)

or

V(A) = sum(B!=A)M(B,A)*V(B)/sum(B!=A)M(A,B)

The numerator is the number of hires A makes weighted for the non-idiosyncratic utility of firms the hires come from, and the denominator is the number of people that leave firm A. There is one such linear restriction per firm, but the utility of firm A depends on the utility of all firms. How to avoid this circularity? Write the linear restrictions in matrix form, and use the Perron-Frebonius theorem to see that the relative values of V are determined by a particular eigenvector as long as the matrix of moves is strongly connected! Strongly connected just means that there is at least one chain of moves between employers that can get me from firm A to B and vice versa, for all firm pairs!. All that’s left to do now is to take this to the data (not a trivial computation task, since there are so many firms in the US data that calculating eigenvectors will require some numerical techniques).

So what do we learn? Industries like education offer high utility compared to pay, and industries like mining offer the opposite, as you’d expect. Many low paying jobs offer relatively high nonpay utility, and many female-dominated sectors do as well, implying the measured earnings inequality and gender gaps may be overstating the true extent of utility inequality. That is, a teacher making half what a miner makes is partly reflective of the fact that mining is a job that requires compensating differentials to make up for long hours in the dark and dangerous mine shaft. Further, roughly two thirds of the earnings inequality related to firms seems to be reflecting compensating differentials, and since just over 20% of earnings inequality in the US is firm related, this means that about 15% of earnings inequality is just reflecting the differential perceived quality of jobs. This is a surprising result, and it appears to be driven by differences in job amenities that are not easy to measure. Goldman Sachs is a “good job” despite relatively low pay compared to other finance firms because they offer good training and connections. This type of amenity is hard to observe, but Sorkin’s theoretical approach based on revealed preference allows the econometrician to “see” these types of differences across jobs, and hence to more properly understand which jobs are desirable. This is another great example of a question – how does the quality of jobs differ and what does that say about the nature of earnings inequality – that is fundamentally unanswerable by methodological techniques that are unwilling to inject some theoretical assumptions into the analysis.

November 2015 Working Paper. Sorkin has done some intriguing work using historical data on the minimum wage as well. Essentially, minimum wage changes that are not indexed to inflation are only temporary in real terms, so if it costly to switch from labor to machines, you might not do so in response to a “temporary” minimum wage shock. But a permanent increase does appear to cause long run shifts away from labor, something Sorkin sees in industries from apparel in the early 20th century to fast food restaurants. Simon Jäger, a job candidate from Harvard, also has an interesting purely empirical paper about friction in the labor market, taking advantage of early deaths of German workers. When these deaths happen, working in similar roles at the firm see higher wages and lower separation probability for many years, whereas other coworkers see lower wages, with particularly large effects when the dead worker has unusual skills. All quite intuitive from a search model theory of labor, where workers are partial substitutes for folks with the same skills, but complements for folks with firm-specific capital but dissimilar skills. Add these papers to the evidence that efficiency in the search-and-matching process of labor to firms is a first order policy problem.

“Estimating Equilibrium in Health Insurance Exchanges,” P. Tebaldi (2016)

After a great visit to San Francisco for AEA and a couple weeks reading hundreds of papers while hiding out in the middle of the Pacific, it’s time to take a look at some of the more interesting job market papers this year. Though my home department isn’t directly hiring, I’m going to avoid commenting on work by candidates being flown out to Toronto in general, though a number of those are fantastic as well. I also now have a fourth year of data on job market “stars” which I’ll present in the next week or so.

Let’s start with a great structural IO paper by Pietro Tebaldi from Stanford. The Affordable Care Act in the United States essentially set up a version of universal health care that relies on subsidizing low income buyers, limiting prices via price caps and age rating limits (the elderly can only be charged a certain multiple of what the young are charged), and providing a centralized comparison system (“Bronze” or “Silver” or whatever plans essentially cover the same medical care, with only the provider and hospital bundle differing). The fundamental fact about American health care is less that it is a non-universal, privately-provided system than that it is enormously expensive: the US government, and this is almost impossible to believe until you look at the numbers, spends roughly the same percentage of GDP on health care as Canada, even though coverage is universal up north. Further, there is quite a bit of market power both on the insurer side, with a handful of insurers in any given market, and on the hospital side. Generally, there are only a handful of hospitals in any region, with the legacy of HMOs making many insurers very reluctant to drop hospitals from their network since customers will complain about losing “their” doctor. Because of these facts, a first-order concern for designing a government health care expansion must be controlling costs.

Tebaldi points out theoretically that the current ACA design inadvertently leads to high insurer markups. In nearly all oligopoly models, markup over costs depends on the price elasticity of demand: if buyers have inelastic demand in general, markups are high. In health care, intuitively young buyers are more price sensitive and have lower expected costs than older buyers; many young folks just won’t go to the doctor if it is too pricey to do so, and young folks are less likely to have a long-time doctor they require in their insurance network. Age rating which limits the maximum price difference between young and old buyers means that anything that leads to lower prices for the young will also lead to lower prices for the old. Hence, the more young people you get in the insurance pool, the lower the markups are, and hence the lower the cost becomes for everyone. The usual explanation for why you need young buyers is that they subsidize the old, high-cost buyers; the rationale here is that young buyers help even other young buyers by making aggregate demand more elastic and hence dragging down oligopoly insurer prices.

How can you get more young buyers in the pool while retaining their elastic demand? Give young buyers a fixed amount subsidy voucher that is bigger than what you give older buyers. Because buyers have low expected costs, they will only buy insurance if it cheap, hence will enter the insurance market if you subsidize them a lot. Once they enter, however, they remain very price sensitive. With lots of young folks as potential buyers, insurers will lower their prices for young buyers in order to attract them, which due to age rating also lowers prices for older buyers. It turns out that the government could lower the subsidy given to older buyers, so that total government subsidies fall, and yet out of pocket spending for the old would still be lower due to the price drop induced by the highly elastic young buyers entering the market.

Now that’s simply a theoretical result. Tebaldi also estimates what would happen in practice, using California data. Different regions of California have different age distributions. you can immediately see that prices are higher for young folks in regions where there are a lot of potential old buyers, and lower in regions with a fewer potential old buyers, for exactly the elasticity difference plus age rating reason given above. These regional differences permit identification of the demand curve, using age-income composition to instrument for price. The marginal costs of insurance companies are tougher to identify, but the essential idea just uses optimal pricing conditions as in Berry, Levinsohn and Pakes. The exact identification conditions are not at all straightforward in selection markets like insurance, since insurer marginal costs depend on who exactly their buyers are in addition to characteristics of the bundle of services they offer. The essential trick is that since insurers are pricing to set marginal revenue equal to marginal cost, the demand curve already estimated tells us whether most marginal customers are old or young in a given region, and hence we can back out what costs may be on the basis of pricing decisions across regions.

After estimating marginal costs and demand curves for insurance, Tebaldi can run a bunch of counterfactuals motivated by the theory discussed above. Replacing price-linked subsidies, where buyers get a subsidy linked to the second-lowest priced plan in their area, with vouchers, where buyers get a fixed voucher regardless of the prices set, essentially makes insurers act as if buyers are more price-elastic: raising insurance prices under price-linked subsidies will also raise the amount of the subsidy, and hence the price increase is not passed 1-for-1 to buyers. Tebaldi estimates insurance prices would fall $200 on average if the current price-linked subsidies were replaced with vouchers of an equivalent size. Since young buyers have elastic demand, coverage of young buyers increases as a result. The $200 fall in prices, then, results first from insurers realizing that all buyers are more sensitive to price changes when they hold vouchers rather than pay a semi-fixed amount determined by a subsidy, and second from the composition of buyers therefore including more elastic young buyers, lowering the optimal insurer markup. The harm, of course, is that vouchers do not guarantee year-to-year that subsidized buyers pay no more than a capped amount, since in general the government does not know every insurer’s cost curve and every buyer’s preferences.

Better still is to make vouchers depend on age. If young buyers get big vouchers, even more of them will buy insurance. This will drag down the price set by insurers since aggregate elasticity increases, and hence old buyers may be better off as well even if they see a reduction in their government subsidy. Tebaldi estimates that a $400 increase in subsidies for those under 45, and a $200 decrease for those over 45, will lead to 50% more young folks buying insurance, a 20% decrease in insurer markup, a post-subsidy price for those over 45 that is unchanged since their lower subsidy is made up for by lower insurer prices, and a 15% decrease in government spending since decreased subsidies for the old more than make up for increased subsidies for the young. There is such a thing as a free lunch!

Now, in practice, governments do not make changes around the margins like this. Certain aspects of the subsidy program are, crazily, set by law and not by bureaucrats. Note how political appearance and equilibrium effect differ in Tebaldi’s estimates: we decrease subsidies for the old and yet everyone including the old is better off due to indirect effects. Politicians, it goes without saying, do not win elections on the basis of indirect effects. A shame!

January 2016 working paper. The paper is quite concisely written, which I appreciate in our era of 80-page behemoths. If you are still reluctant to believe in the importance of insurer market power, Tebaldi and coauthors also have a paper in last year’s AER P&P showing in a really clean way the huge price differences in locations that have limited insurer competition. On the macro side, Tebaldi and network-extraordinaire Matt Jackson about deep recessions making a simple point. In labor search models, the better the boom times, the lower productivity workers you will settle for hiring. Thus, when negative economic shocks follow long expansions, they will lead to more unemployment, simply because there will be more relatively low productivity workers at every firm. Believable history-dependence in macro models is always a challenge, but this theory makes perfect sense.

Douglass North, An Economist’s Historian

Sad news today arrives, as we hear that Douglass North has passed away, living only just longer than his two great compatriots in Cliometrics (Robert Fogel) and New Institutional Economics (Ronald Coase). There will be many lovely pieces today, I’m sure, on North’s qualitative and empirical exploration of the rise of institutions as solutions to agency and transaction cost problems, a series of ideas that continues to be enormously influential. No economist today denies the importance of institutions. If economics is the study of the aggregation of rational choice under constraints, as it is sometimes thought to be, then North focused our mind on the origin of the constraints rather the choice or its aggregation. Why do states develop? Why do guilds, and trade laws, and merchant organizations, and courts, appear, and when? How does organizational persistence negatively affect the economy over time, a question pursued at great length by Daron Acemoglu and his coauthors? All important questions, and it is not clear that there are better answers than the ones North provided.

But North was not, first and foremost, a historian. His PhD is in economics, and even late in life he continued to apply the very most cutting edge economic tools to his studies of institutions. I want to discuss today a beautiful piece of his, “The Role of Institutions in the Revival of Trade”, written jointly with Barry Weingast and Paul Milgrom in 1990. This is one of the fundamental papers in “Analytic Narratives”, as it would later be called, a school which applied formal economic theory to historical questions; I have previously discussed here a series of papers by Avner Greif and his coauthors which are the canonical examples.

Here is the essential idea. In the late middle ages, long distance trade, particularly at “Fairs” held in specific places at specific times, arose again in Western Europe. Agency problems must have been severe: how do you keep people from cheating you, from stealing, from selling defective goods, or from reneging on granted credit? A harmonized body of rules, the Merchant Law, appeared across many parts of Western Europe, with local courts granting judgments on the basis of this Law. In the absence of nation-states, someone with a negative judgment could simply leave the local city where the verdict was given. The threat of not being able to sell in the future may have been sufficient to keep merchants fair, but if the threat of future lost business was the only credible punishment, then why were laws and courts needed at all? Surely merchants could simply let it be known that Johann or Giuseppe is a cheat, and that one shouldn’t deal with them? There is a puzzle here, then: it appears that the set of punishments the Merchant Law could give are identical to the set of “punishments” one receives for having a bad reputation, so why then did anybody bother with courts and formal rules? In terms of modern theory, if relational contracts and formal contracts can offer identical punishments for deviating from cooperation, and formal contracts are costly, then why doesn’t everyone simply rely on relational contracts?

Milgrom, North and Weingast consider a simple repeated Prisoner’s Dilemma. Two agents with a sufficiently high discount rate can sustain cooperation in a Prisoner’s Dilemma using tit-for-tat: if you cheat me today, I cheat you tomorrow. Of course, the Folk Theorem tells us that cooperation can be sustained using potentially more complex punishment strategies in infinitely repeated games with any number of players, although a fundamental idea in the repeated games literature is that it may be necessary to punish people who do not themselves punish when they are meant to do so. In a repeated prisoner’s dilemma with an arbitrary number of players who randomly match each period, cooperation can be sustained in a simple way: you cheat anyone you match with if they cheated their previous trading partner and their previous trading partner did not themselves cheat their partner two rounds ago, and otherwise cooperate.

The trick, though, is that you need to know the two-periods-back history of your current trading partner and their last trading partner. Particularly with long-distance trade, you might frequently encounter traders you don’t know even indirectly. Imagine that every period you trade with someone you have never met before, and who you will never meet again (the “Townsend turnpike”, with two infinite lines of traders moving in opposite directions), and imagine that you do not know the trading history of anyone you match with. In this incomplete information game, there is no punishment for cheating: you cheat the person you match with today, and no one you meet with tomorrow will ever directly or indirectly learn about this. Hence cooperation is not sustained.

What we need, then, is an institution that first collects a sufficient statistic for the honesty of traders you might deal with, that incentivizes merchants to bother to check this sufficient statistic and punish people who have cheated, and that encourages people to report if they have been cheated even if this reporting is personally costly. That is, “institutions must be designed both to keep the traders adequately informed of their responsibilities and to motivate them to do their duties.”

Consider an institution LM. When you are matched with a trading partner, you can query LM at cost Q to find out if there are any “unpaid judgments” against your trading partner, and this query is common knowledge to you and your partner. You and your partner then play a trading game which is a Prisoner’s Dilemma. After trading, and only if you paid the query cost Q, when you have been cheated you can pay another cost C to take your trading partner to trial. If your partner cheated you in the Prisoner’s Dilemma and you took them to trial, you win a judgment penalty of J which the cheater can either voluntarily pay you at cost c(J) or which the cheater can ignore. If the cheater doesn’t pay a judgment, LM lists them as having “unpaid judgments”.

Milgrom, North and Weingast show that, under certain conditions, the following is an equilibrium where everyone always cooperates: if you have no unpaid judgments, you always query LM. If no one queries LM, or if there are unpaid judgments against your trading partner, you defect in the Prisoner’s Dilemma, else you cooperate. If both parties queried LM and only one defects in the Prisoner’s Dilemma, the other trader pays cost C and takes the cheater to the LM for judgment. The conditions needed for this to be an equilibrium are that penalties for cheating are high enough, but not so high that cheaters prefer to retire to the countryside rather than pay them, and that the cost of querying LM is not too high. Note how the LM equilibrium encourages anyone to pay the personal cost of checking their trading partner’s history: if you don’t check, then you can’t go to LM for judgment if you are cheated, hence you will definitely be cheated. The LM also encourages people to pay the personal cost of putting a cheater on trial, because that is the only way to get a judgment decision, and that judgment is actually paid in equilibrium. Relying on reputation in the absence of an institution may not work if communicating reputation of someone who cheated you is personally costly: if you need to print up posters that Giuseppe cheated you, but can otherwise get no money back from Giuseppe, you are simply “throwing good money after bad” and won’t bother. The LM institution provides you an incentive to narc on the cheats.

Note also that in equilibrium, the only cost of the system is the cost of querying, since no one cheats. That is, in the sense of transactions costs, the Law Merchant may be a very low-cost institution: it generates cooperation even though only one piece of information, the existence of unpaid judgments, needs to be aggregated and communicated, and it generates cooperation among a large set of traders that never personally interact by using a single centralized “record-keeper”. Any system that induces cooperation must, at a minimum, inform a player whether their partner has cheated in the past. The Law Merchant system does this with no other costs in equilibrium, since in equilibrium, no one cheats, no one goes for judgment, and no resources are destroyed paying fines.

That historical institutions develop largely to limit transactions costs is a major theme in North’s work, and this paper is a beautiful, highly formal, explication of that broad Coasean idea. Our motivating puzzle – why use formal institutions when reputation provides precisely the same potential for punishment? – can be answered simply by noting that reputation requires information, and the cost-minimizing incentive-compatible way to aggregate and share that information may require an institution. The Law Merchant arises not because we need a way to punish offenders, since in the absence of the nation-state the Law Merchant offers no method for involuntary punishment beyond those that exist in its absence; and yet, in its role reducing costs in the aggregation of information, the Law proves indispensable. What a beautiful example of how theory can clarify our observations!

“The Role of Institutions in the Revival of Trade” appeared in Economics and Politics 1.2, March 1990, and extensions of these ideas to long distance trade with many centers are considered in the papers by Avner Greif and his coauthors linked at the beginning of this post. A broad philosophical defense of the importance of transaction costs to economic history is North’s 1984 essay in the Journal of Institutional and Theoretical Economics. Two other titans of economics have also recently passed away, I’m afraid. Herbert Scarf, the mathematician whose work is of fundamental importance to modern market design, was eulogized by Ricky Vohra and Al Roth. Nate Rosenberg, who with Zvi Griliches was the most important thinker on the economics of invention, was memorialized by Joshua Gans and Joel West.

“Valuing Diversity,” G. Loury & R. Fryer (2013)

The old chair of my alma mater’s economics department, Glenn Loury is, somehow, wrapped up in a kerfuffle related to the student protests that have broken out across the United States. Loury, who is now at Brown, wrote an op-ed in the student paper which to an economist just says that the major racial problem in the United States is statistical discrimination not taste-based discrimination, and hence the types of protests and desired recourse of the student protesters is wrongheaded. After being challenged about “what type of a black scholar” he is, Loury wrote a furious response pointing out that he is, almost certainly, the world’s most prominent scholar on the topic of racial discrimination and potential remedies, and has been thinking about how policy can remedy racial injustice since before the student’s parents were even born.

An important aspect of his work is that, under statistical discrimination, there is huge scope for perverse and unintended effects of policies. This idea has been known since Ken Arrow’s famous 1973 paper, but Glenn Loury and Stephen Coate in 1993 worked it out in greater detail. Imagine there are black and white workers, and high-paid good jobs, which require skill, and low-paid bad jobs which do not. Workers make an unobservable investment in skill, where the firm only sees a proxy: sometimes unskilled workers “look like” skilled workers, sometimes skilled workers “look like” unskilled workers, and sometimes we aren’t sure. As in Arrow’s paper, there can be multiple equilibria: when firms aren’t sure of a worker’s skill, if they assume all of those workers are unskilled, then in equilibrium investment in skill will be such that the indeterminate workers can’t profitably be placed in skilled jobs, but if the firms assume all indeterminate workers are skilled, then there is enough skill investment to make it worthwhile for firms to place those workers in high-skill, high-wage jobs. Since there are multiple equilibria, if race or some other proxy is observable, we can be in the low-skill-job, low-investment equilibrium for one group, and the high-skill-job, high-investment equilibrium for a different group. That is, even with no ex-ante difference across groups and no taste-based bias, we still wind up with a discriminatory outcome.

The question Coate and Loury ask is whether affirmative action can fix this negative outcome. Let an affirmative action rule state that the proportion of all groups assigned to the skilled job must be equal. Ideally, affirmative action would generate equilibrium beliefs by firms about workers that are the same no matter what group those workers come from, and hence skill investment across groups that is equal. Will this happen? Not necessarily. Assume we are in the equilibrium where one group is assumed low-skill when their skill in indeterminate, and the other group is assumed high-skill.

In order to meet the affirmative action rule, either more of the discriminated group needs to be assigned to the high-skill job, or more of the favored group need to be assigned to the low-skill job. Note that in the equilibrium without affirmative action, the discriminated group invests less in skills, and hence the proportion of the discriminated group that tests as unskilled is higher than the proportion of the favored group that does so. The firms can meet the affirmative action rule, then, by keeping the assignment rule for favored groups as before, and by assigning all proven-skilled and indeterminate discriminated workers as well as some random proportion of proven-unskilled discriminated workers, to the skilled task. This rule decreases the incentive to invest in skills for the discriminated group, and hence it is no surprise that not only can it be an equilibrium, but that Coate and Loury can show the dynamics of this policy lead to fewer and fewer discriminated workers investing in skills over time: despite identical potential at birth, affirmative action policies can lead to “patronizing equilibria” that exacerbate, rather than fix, differences across groups. The growing skill difference between previously-discriminated-against “Bumiputra” Malays and Chinese Malays following affirmative action policies in the 1970s fits this narrative nicely.

The broader point here, and one that comes up in much of Loury’s theoretical work, is that because policies affect beliefs even of non-bigoted agents, statistical discrimination is a much harder problem to solve than taste-based or “classical” bias. Consider the job market for economists. If women or minorities have trouble finding jobs because of an “old boys’ club” that simply doesn’t want to hire those groups, then the remedy is simple: require hiring quotas and the like. If, however, the problem is that women or minorities don’t enter economics PhD programs because of a belief that it will be hard to be hired, and that difference in entry leads to fewer high-quality women or minorities come graduation, then remedies like simple quotas may lead to perverse incentives.

Moving beyond perverse incentives, there is also the question of how affirmative action programs should be designed if we want to equate outcomes across groups that face differential opportunities. This question is taken up in “Valuing Diversity”, a recent paper Loury wrote with recent John Bates Clark medal winner Roland Fryer. Consider dalits in India or African-Americans: for a variety of reasons, from historic social network persistence to neighborhood effects, the cost of increasing skill may be higher for these groups. We have an opportunity which is valuable, such as slots at a prestigious college. Simply providing equal opportunity may not be feasible because the social reasons why certain groups face higher costs of increasing skill are very difficult to solve. Brown University, or even the United States government as a whole, may be unable to fix the persistence social difference in upbringing among blacks and whites. So what to do?

There are two natural fixes. We can provide a lower bar for acceptance for the discriminated group at the prestigious college, or subsidize skill acquisition for the discriminated group by providing special summer programs, tutoring, etc. If policy can be conditioned on group identity, then the optimal policy is straightforward. First, note that in a laissez faire world, individuals invest in skill until the cost of investment for the marginal accepted student exactly equates to the benefit the student gets from attending the fancy college. That is, the equilibrium is efficient: students with the lowest cost of acquiring skill are precisely the ones who invest and are accepted. But precisely that weighing of marginal benefit and costs holds within group if the acceptance cutoff differs by group identity, so if policy can condition on group identity, we can get whatever mix of students from different groups we want while still ensuring that the students within each group with the lowest cost of upgrading their skill are precisely the ones who invest and are accepted. The policy change itself, by increasing the quota of slots for the discriminated group, will induce marginal students from that group to upgrade their skills in order to cross the acceptance threshold; that is, quotas at the assignment stage implicitly incentivize higher investment by the discriminated group.

The trickier problem is when policy cannot condition on group identity, as is the case in the United States under current law. I would like somehow to accept more students from the discriminated against group, and to ensure that those students invest in their skill, but the policy I set needs to treat the favored and discriminated against groups equally. Since discriminated-against students make up a bigger proportion of those with a high cost of skill acquisition compared to students with a low cost of skill acquisition, any “blind” policy that does condition on group identity will induce identical investment activity and acceptance probability among agents with identical costs of skill upgrading. Hence any blind policy that induces more discriminated-students to attend college must somehow be accepting students with higher costs of skill acquisition than the marginal accepted student under laissez faire, and must not be accepting students whose costs of skill acquisition were at the laissez faire margin. Fryer and Loury show, by solving the relevant linear program, that we can best achieve this by allowing the most productive students to buy their slots, and then randomly assigning slots to everyone else.

Under that policy, very low cost of effort students still invest so that their skill is high enough that buying a guaranteed slot is worth it. I then use either a tax or subsidy on skill investment in order to affect how many people find it worth investing in skill and then buying the guaranteed slot, and hence in conjunction with the randomized slot assignment, ensuring that the desired mixture across groups that are accepted is achieved.

This result resembles certain results in dynamic pricing. How do I get people to pay a high price for airplane tickets while still hoping to sell would-be-empty seats later at a low price? The answer is that I make high-value people worried that if they don’t buy early, the plane may sell out. The high-value people then trade off paying a high price and getting a seat with probability 1 versus waiting for a low price by maybe not getting on the plane at all. Likewise, how do I induce people to invest in skills even when some lower-skill people will be admitted? Ensure that lower-skill people are only admitted with some randomness. The folks who can get perfect grades and test scores fairly easily will still exert effort to do so, ensuring they get into their top choice college guaranteed rather than hoping to be admitted subject to some random luck. This type of intuition is non-obvious, which is precisely Loury’s point: racial and other forms of injustice are often due to factors much more subtle than outright bigotry, and the optimal response to these more subtle causes do not fit easily on a placard or a bullhorn slogan.

Final working paper (RePEc IDEAS version), published in the JPE, 2013. Hanming Fang and Andrea Moro have a nice handbook chapter on theoretical explorations of discrimination. On the recent protests, Loury and John McWhorter have an interesting and provocative dialog on the recent student protests at Bloggingheads.

Angus Deaton, 2015 Nobel Winner: A Prize for Structural Analysis?

Angus Deaton, the Scottish-born, Cambridge-trained Princeton economist, best known for his careful work on measuring the changes in wellbeing of the world’s poor, has won the 2015 Nobel Prize in economics. His data collection is fairly easy to understand, so I will leave larger discussion of exactly what he has found to the general news media; Deaton’s book “The Great Escape” provides a very nice summary of what he has found as well, and I think a fair reading of his development preferences are that he much prefers the currently en vogue idea of just giving cash to the poor and letting them spend it as they wish.

Essentially, when one carefully measures consumption, health, or generic characteristics of wellbeing, there has been tremendous improvement indeed in the state of the world’s poor. National statistics do not measure these ideas well, because developing countries do not tend to track data at the level of the individual. Indeed, even in the United States, we have only recently begun work on localized measures of the price level and hence the poverty rate. Deaton claims, as in his 2010 AEA Presidential Address (previously discussed briefly on two occasions on AFT), that many of the measures of global inequality and poverty used by the press are fundamentally flawed, largely because of the weak theoretical justification for how they link prices across regions and countries. Careful non-aggregate measures of consumption, health, and wellbeing, like those generated by Deaton, Tony Atkinson, Alwyn Young, Thomas Piketty and Emmanuel Saez, are essential for understanding how human welfare has changed over time and space, and is a deserving rationale for a Nobel.

The surprising thing about Deaton, however, is that despite his great data-collection work and his interest in development, he is famously hostile to the “randomista” trend which proposes that randomized control trials (RCT) or other suitable tools for internally valid causal inference are the best way of learning how to improve the lives of the world’s poor. This mode is most closely associated with the enormously influential J-PAL lab at MIT, and there is no field in economics where you are less likely to see traditional price theoretic ideas than modern studies of development. Deaton is very clear on his opinion: “Randomized controlled trials cannot automatically trump other evidence, they do not occupy any special place in some hierarchy of evidence, nor does it make sense to refer to them as “hard” while other methods are “soft”… [T]he analysis of projects needs to be refocused towards the investigation of potentially generalizable mechanisms that explain why and in what contexts projects can be expected to work.” I would argue that Deaton’s work is much closer to more traditional economic studies of development than to RCTs.

To understand this point of view, we need to go back to Deaton’s earliest work. Among Deaton’s most famous early papers was his well-known development of the Almost Ideal Demand System (AIDS) in 1980 with Muellbauer, a paper chosen as one of the 20 best published in the first 100 years of the AER. It has long been known that individual demand equations which come from utility maximization must satisfy certain properties. For example, a rational consumer’s demand for food should not depend on whether the consumer’s equivalent real salary is paid in American or Canadian dollars. These restrictions turn out to be useful in that if you want to know how demand for various products depend on changes in income, among many other questions, the restrictions of utility theory simplify estimation greatly by reducing the number of free parameters. The problem is in specifying a form for aggregate demand, such as how demand for cars depends on the incomes of all consumers and prices of other goods. It turns out that, in general, aggregate demand generated by utility-maximizing households does not satisfy the same restrictions as individual demand; you can’t simply assume that there is a “representative consumer” with some utility function and demand function equal to each individual agent. What form should we write for aggregate demand, and how congruent is that form with economic theory? Surely an important question if we want to estimate how a shift in taxes on some commodity, or a policy of giving some agricultural input to some farmers, is going to affect demand for output, its price, and hence welfare!

Let q(j)=D(p,c,e) say that the quantity of j consumed, in aggregate is a function of the price of all goods p and the total consumption (or average consumption) c, plus perhaps some random error e. This can be tough to estimate: if D(p,c,e)=Ap+e, where demand is just a linear function of relative prices, then we have a k-by-k matrix to estimate, where k is the number of goods. Worse, that demand function is also imposing an enormous restriction on what individual demand functions, and hence utility functions, look like, in a way that theory does not necessarily support. The AIDS of Deaton and Muellbauer combine the fact that Taylor expansions approximately linearize nonlinear functions and that individual demand can be aggregated even when heterogeneous across individuals if the restrictions of Muellbauer’s PIGLOG papers are satisfied to show a functional form for aggregate demand D which is consistent with aggregated individual rational behavior and which can sometimes be estimated via OLS. They use British data to argue that aggregate demand violates testable assumptions of the model and hence factors like credit constraints or price expectations are fundamental in explaining aggregate consumption.

This exercise brings up a number of first-order questions for a development economist. First, it shows clearly the problem with estimating aggregate demand as a purely linear function of prices and income, as if society were a single consumer. Second, it gives the importance of how we measure the overall price level in figuring out the effects of taxes and other policies. Third, it combines theory and data to convincingly suggest that models which estimate demand solely as a function of current prices and current income are necessarily going to give misleading results, even when demand is allowed to take on very general forms as in the AIDS model. A huge body of research since 1980 has investigated how we can better model demand in order to credibly evaluate demand-affecting policy. All of this is very different from how a certain strand of development economist today might investigate something like a subsidy. Rather than taking obversational data, these economists might look for a random or quasirandom experiment where such a subsidy was introduced, and estimate the “effect” of that subsidy directly on some quantity of interest, without concern for how exactly that subsidy generated the effect.

To see the difference between randomization and more structural approaches like AIDS, consider the following example from Deaton. You are asked to evaluate whether China should invest more in building railway stations if they wish to reduce poverty. Many economists trained in a manner influenced by the randomization movement would say, well, we can’t just regress the existence of a railway on a measure of city-by-city poverty. The existence of a railway station depends on both things we can control for (the population of a given city) and things we can’t control for (subjective belief that a town is “growing” when the railway is plopped there). Let’s find something that is correlated with rail station building but uncorrelated with the random component of how rail station building affects poverty: for instance, a city may lie on a geographically-accepted path between two large cities. If certain assumptions hold, it turns out that a two-stage “instrumental variable” approach can use that “quasi-experiment” to generate the LATE, or local average treatment effect. This effect is the average benefit of a railway station on poverty reduction, at the local margin of cities which are just induced by the instrument to build a railway station. Similar techniques, like difference-in-difference and randomized control trials, under slightly different assumptions can generate credible LATEs. In development work today, it is very common to see a paper where large portions are devoted to showing that the assumptions (often untestable) of a given causal inference model are likely to hold in a given setting, then finally claiming that the treatment effect of X on Y is Z. That LATEs can be identified outside of a purely randomized contexts is incredibly important and valuable, and the economists and statisticians who did the heavy statistical lifting on this so-called Rubin model will absolutely and justly win an Economics Nobel sometime soon.

However, this use of instrumental variables would surely seem strange to the old Cowles Commission folks: Deaton is correct that “econometric analysis has changed its focus over the years, away from the analysis of models derived from theory towards much looser specifications that are statistical representations of program evaluation. With this shift, instrumental variables have moved from being solutions to a well-defined problem of inference to being devices that induce quasi-randomization.” The traditional use of instrumental variables was that after writing down a theoretically justified model of behavior or aggregates, certain parameters – not treatment effects, but parameters of a model – are not identified. For instance, price and quantity transacted are determined by the intersection of aggregate supply and aggregate demand. Knowing, say, that price and quantity was (a,b) today, and is (c,d) tomorrow, does not let me figure out the shape of either the supply or demand curve. If price and quantity both rise, it may be that demand alone has increased pushing the demand curve to the right, or that demand has increased while the supply curve has also shifted to the right a small amount, or many other outcomes. An instrument that increases supply without changing demand, or vice versa, can be used to “identify” the supply and demand curves: an exogenous change in the price of oil will affect the price of gasoline without much of an effect on the demand curve, and hence we can examine price and quantity transacted before and after the oil supply shock to find the slope of supply and demand.

Note the difference between the supply and demand equation and the treatment effects use of instrumental variables. In the former case, we have a well-specified system of supply and demand, based on economic theory. Once the supply and demand curves are estimated, we can then perform all sorts of counterfactual and welfare analysis. In the latter case, we generate a treatment effect (really, a LATE), but we do not really know why we got the treatment effect we got. Are rail stations useful because they reduce price variance across cities, because they allow for increasing returns to scale in industry to be utilized, or some other reason? Once we know the “why”, we can ask questions like, is there a cheaper way to generate the same benefit? Is heterogeneity in the benefit important? Ought I expect the results from my quasiexperiment in place A and time B to still operate in place C and time D (a famous example being the drug Opren, which was very successful in RCTs but turned out to be particularly deadly when used widely by the elderly)? Worse, the whole idea of LATE is backwards. We traditionally choose a parameter of interest, which may or may not be a treatment effect, and then choose an estimation technique that can credible estimate that parameter. Quasirandom techniques instead start by specifying the estimation technique and then hunt for a quasirandom setting, or randomize appropriately by “dosing” some subjects and not others, in order to fit the assumptions necessary to generate a LATE. If is often the case that even policymakers do not care principally about the LATE, but rather they care about some measure of welfare impact which rarely is immediately interpretable even if the LATE is credibly known!

Given these problems, why are random and quasirandom techniques so heavily endorsed by the dominant branch of development? Again, let’s turn to Deaton: “There has also been frustration with the World Bank’s apparent failure to learn from its own projects, and its inability to provide a convincing argument that its past activities have enhanced economic growth and poverty reduction. Past development practice is seen as a succession of fads, with one supposed magic bullet replacing another—from planning to infrastructure to human capital to structural adjustment to health and social capital to the environment and back to infrastructure—a process that seems not to be guided by progressive learning.” This is to say, the conditions necessary to estimate theoretical models are so stringent that development economists have been writing noncredible models, estimating them, generating some fad of programs that is used in development for a few years until it turns out not to be silver bullet, then abandoning the fad for some new technique. Better, the randomistas argue, to forget about external validity for now, and instead just evaluate the LATEs on a program-by-program basis, iterating what types of programs we evaluate until we have a suitable list of interventions that we feel confident work. That is, development should operate like medicine.

We have something of an impasse here. Everyone agrees that on many questions theory is ambiguous in the absence of particular types of data, hence more and better data collection is important. Everyone agrees that many parameters of interest for policymaking require certain assumptions, some more justifiable than others. Deaton’s position is that the parameters of interest to economists by and large are not LATEs, and cannot be generated in a straightforward way from LATEs. Thus, following Nancy Cartwright’s delightful phrasing, if we are to “use” causes rather than just “hunt” for what they are, we have no choice but to specify the minimal economic model which is able to generate the parameters we care about from the data. Glen Weyl’s attempt to rehabilitate price theory and Raj Chetty’s sufficient statistics approach are both attempts to combine the credibility of random and quasirandom inference with the benefits of external validity and counterfactual analysis that model-based structural designs permit.

One way to read Deaton’s prize, then, is as an award for the idea that effective development requires theory if we even hope to compare welfare across space and time or to understand why policies like infrastructure improvements matter for welfare and hence whether their beneficial effects will remain when moved to a new context. It is a prize which argues against the idea that all theory does is propose hypotheses. For Deaton, going all the way back to his work with AIDS, theory serves three roles: proposing hypotheses, suggesting which data is worthwhile to collect, and permitting inference on the basis of that data. A secondary implication, very clear in Deaton’s writing, is that even though the “great escape” from poverty and want is real and continuing, that escape is almost entirely driven by effects which are unrelated to aid and which are uninfluenced by the type of small bore, partial equilibrium policies for which randomization is generally suitable. And, indeed, the best development economists very much understand this point. The problem is that the media, and less technically capable young economists, still hold the mistaken belief that they can infer everything they want to infer about “what works” solely using the “scientific” methods of random- and quasirandomization. For Deaton, results that are easy to understand and communicate, like the “dollar-a-day” poverty standard or an average treatment effect, are less virtuous than results which carefully situate numbers in the role most amenable to answering an exact policy question.

Let me leave you three side notes and some links to Deaton’s work. First, I can’t help but laugh at Deaton’s description of his early career in one of his famous “Notes from America”. Deaton, despite being a student of the 1984 Nobel laureate Richard Stone, graduated from Cambridge essentially unaware of how one ought publish in the big “American” journals like Econometrica and the AER. Cambridge had gone from being the absolute center of economic thought to something of a disconnected backwater, and Deaton, despite writing a paper that would win a prize as one of the best papers in Econometrica published in the late 1970s, had essentially no understanding of the norms of publishing in such a journal! When the history of modern economics is written, the rise of a handful of European programs and their role in reintegrating economics on both sides of the Atlantic will be fundamental. Second, Deaton’s prize should be seen as something of a callback to the ’84 prize to Stone and ’77 prize to Meade, two of the least known Nobel laureates. I don’t think it is an exaggeration to say that the majority of new PhDs from even the very best programs will have no idea who those two men are, or what they did. But as Deaton mentions, Stone in particular was one of the early “structural modelers” in that he was interested in estimating the so-called “deep” or behavioral parameters of economic models in a way that is absolutely universal today, as well as being a pioneer in the creation and collection of novel economic statistics whose value was proposed on the basis of economic theory. Quite a modern research program! Third, of the 19 papers in the AER “Top 20 of all time” whose authors were alive during the era of the economics Nobel, 14 have had at least one author win the prize. Should this be a cause for hope for the living outliers, Anne Krueger, Harold Demsetz, Stephen Ross, John Harris, Michael Todaro and Dale Jorgensen?

For those interested in Deaton’s work beyond what this short essay, his methodological essay, quoted often in this post, is here. The Nobel Prize technical summary, always a great and well-written read, can be found here.

“Inventing Prizes: A Historical Perspective on Innovation Awards and Technology Policy,” B. Z. Khan (2015)

B. Zorina Khan is an excellent and underrated historian of innovation policy. In her new working paper, she questions the shift toward prizes as an innovation inducement mechanism. The basic problem economists have been grappling with is that patents are costly in terms of litigation, largely due to their uncertainty, that patents impose deadweight loss by granting inventors market power (as noted at least as far back as Nordhaus 1969), and that patent rights can lead to an anticommons which in some cases harms follow-on innovation (see Scotchmer and Green and Bessen and Maskin for the theory, and papers like Heidi Williams’ genome paper for empirics).

There are three main alternatives to patents, as I see them. First, you can give prizes, determined ex-ante or ex-post. Second, you can fund R&D directly with government, as the NIH does for huge portions of medical research. Third, you can rely on inventors accruing rents to cover the R&D without any government action, such as by keeping their invention secret, relying on first mover advantage, or having market power in complementary goods. We have quite a bit of evidence that the second, in biotech, and the third, in almost every other field, is the primary driver of innovative activity.

Prizes, however, are becoming more and more common. There are X-Prizes for space and AI breakthroughs, advanced market commitments for new drugs with major third world benefits, Kremer’s “patent buyout” plan, and many others. Setting the prize amount right is of course a challenging project (one that Kremer’s idea partially fixes), and in this sense prizes run “less automatically” than the patent system. What Khan notes is that prizes have been used frequently in the history of innovation, and were frankly common in the late 18th and 19th century. How useful were they?

Unfortunately, prizes seem to have suffered many problems. Khan has an entire book on The Democratization of Invention in the 19th century. Foreign observers, and not just Tocqueville, frequently noted how many American inventors came from humble backgrounds, and how many “ordinary people” were dreaming up new products and improvements. This frenzy was often, at the time, credited to the uniquely low-cost and comprehensive U.S. patent system. Patents were simple enough, and inexpensive enough, to submit that credit for and rights to inventions pretty regularly flowed to people who were not politically well connected, and for inventions that were not “popular”.

Prizes, as opposed to patents, often incentivized the wrong projects and rewarded the wrong people. First, prizes were too small to be economically meaningful; when the well-named Hippolyte Mège-Mouriès made his developments in margarine and garnered the prize offered by Napoleon III, the value of that prize was far less than the value of the product itself. In order to shift effort with prizes, the prize designer needs to know both enough about the social value of the proposed invention to set the prize amount high enough, and enough about the value of alternatives that the prize doesn’t distort effort away from other inventions that would be created while relying solely on trade secrecy and first mover advantage (I discuss this point in much greater depth in my Direction of Innovation paper with Jorge Lemus). Providing prizes to only some inventions may either generate no change in behavior at all because the prize is too small compared with the other benefits of inventing, or cause inefficient distortions in behavior. Even though, say, a malaria vaccine would be very useful, an enormous prize for a malaria vaccine will distort health researcher effort away from other projects in a way that is tough to calculate ex-ante without a huge amount of prize designer knowledge.

There is a more serious problem with prizes. Because the cutoff for a prize is less clear cut, there is more room for discretion and hence a role for wasteful lobbying and personal connection to trump “democratic invention”. Khan notes that even though the French buyout of Daguerre’s camera patent is cited as a classic example of a patent buyout in the famous Kremer QJE article, it turns out that Daguerre never actually held any French patent at all! What actually happened was that Daguerre lobbied the government for a sinecure in order to make his invention public, but then patented it abroad anyway! There are many other political examples, such as the failure of the uneducated clockmaker John Harrison to be granted a prize for his work on longitude due partially to the machinations of more upper class competitors who captured the ear of the prize committee. Examining a database of great inventors on both sides of the Atlantic, Khan found that prizes were often linked to factors like overcoming hardship, having an elite education, or regional ties. That is, the subjectivity of prizes may be stronger than the subjectivity of patents.

So then, we have three problems: prize designers don’t know enough about the relative import of various ideas to set price amounts optimally, prizes in practice are often too small to have much effect, and prizes lead to more lobbying and biased rewards than patents. We shouldn’t go too far here; prizes still may be an important part of the innovation policy toolkit. But the history Khan lays out certainly makes me more sanguine that they are a panacea.

One final point. I am unconvinced that patents really help the individual or small inventor very much either. I did a bit of hunting: as far as I can tell, there is not a single billionaire who got that way primarily by selling their invention. Many people developed their invention in a firm, but non-entrepreneurial invention, for which the fact that patents create a market for knowledge is supposedly paramount, doesn’t seem to be making anyone super rich. This is even though there are surely a huge number of inventions each worth billions. A good defense of patents as our main innovation policy should really grapple better with this fact.

July 2015 NBER Working Paper (RePEc IDEAS). I’m afraid the paper is gated if you don’t have an NBER subscription, and I was unable to find an ungated copy.

“Buying Locally,” G. J. Mailath, A. Postlewaite & L. Samuelson (2015)

Arrangements where agents commit to buy only from selected vendors, even when there are more preferred products at better prices from other vendors, are common. Consider local currencies like “Ithaca Hours”, which can only be used at other participating stores and which are not generally convertible, or trading circles among co-ethnics even when trust or unobserved product quality is not important. The intuition people have for “buying locally” is to, in some sense, “keep the profits in the community”; that is, even if you don’t care at all about friendly local service or some other utility-enhancing aspect of the local store, you should still patronize it. The fruit vendor, should buy from the local bookstore even when her selection is subpar, and the book vendor should in turn patronize you even when fruits are cheaper at the supermarket.

At first blush, this seems odd to an economist. Why would people voluntarily buy something they don’t prefer? What Mailath and his coauthors show is that, actually, the noneconomist intuition is at least partially correct when individuals are both sellers and buyers. Here’s the idea. Let there be a local fruit vendor, a supermarket, a local bookstore and a chain bookstore. Since the two markets are not perfectly competitive, firms earn a positive rent with each sale. Assume that, tomorrow, the fruit vendor, the local book merchant, and each of the chain managers draw a random preference. Each food seller is equally likely to need a book sold by either the local or chain store, and likewise each bookstore employee is equally likely to need a piece of fruit sold either by the local vendor or the supermarket; you might think of these preferences as reflecting prices, or geographical distance, or product variety, etc. In equilibrium, prices of each book and each fruit are set equally, and each vendor expects to accrue half the sales.

Now imagine that the local bookstore owner and fruit vendor commit in advance not to patronize the other stores, regardless of which preference is drawn tomorrow. Assume for now that they also commit not to raise prices because of this agreement (this assumption will not be important, it turns out). Now the local stores expect to make 3/4 of all sales, since they still get the purchases of the chain managers with probability .5. Since the markup does not change, and there is a constant profit on each sale, then profits improve. And here is the sustainability part: as long as the harm from buying the “wrong product” is not too large, the benefit for the vendor-as-producer of selling more products exceeds the harm to the vendor-as-consumer of buying a less-than-optimal product.

That tradeoff can be made explicit, but the implication is quite general: as the number of firms you can buy at grows large, the benefit to belonging to a buy local arrangement falls. The harm of having to buy from a local producer is big because it is very unlikely the local producer is your first choice, and the price firms set in equilibrium falls because competition is stronger, hence there is less to gain for the vendor-as-producer from belonging to the buy local agreement. You will only see “buy local” style arrangements, like Ithaca Hours, or social shaming, in communities where vendors-as-consumers already purchase most of what they want from vendors-as-producers in the same potential buy local group.

One thing that isn’t explicit in the paper, perhaps because it is too trivial despite its importance, is how buy local arrangements affect welfare. Two possibilities exist. First, if in-group and out-of-group sellers have the same production costs, then “buy local” arrangements simply replace the producer surplus of out-of-group sellers with deadweight loss and some, perhaps minor, surplus for in group members. They are privately beneficial yet socially harmful. However, an intriguing possibility is that “buy local” arrangements may not harm social welfare at all, even if they are beneficial to in-group members. How is that? In-group members are pricing above marginal cost due to market power. A “buy local” agreement increases the quantity of sales they make. If the in-group member has lower costs than out of group members, the total surplus generated by shifting transactions to the in-group seller may be positive, even though there is some deadweight loss created when consumers do not buy their first choice good (in particular, this is true whenever the average willingness-to-pay differential for people who switch to the in-group seller once the buy local group is formed exceeds the average marginal cost differential between in-group and out-of-group sellers.)

May 2015 working paper (RePEc IDEAS version)

On the economics of the Neolithic Revolution

The Industrial and Neolithic Revolutions are surely the two fundamental transitions in the economic history of mankind. The Neolithic involved permanent settlement of previously nomadic, or at best partially foraging, small bands. At least seven independent times, bands somewhere in the world adopted settled agriculture. The new settlements tended to see an increase in inequality, the beginning of privately held property, a number of new customs and social structures, and, most importantly, an absolute decrease in welfare as measured in terms of average height and an absolute increase in the length and toil of working life. Of course, in the long run, settlement led to cities which led to the great inventions that eventually pushed mankind past the Malthusian bounds into our wealthy present, but surely no nomad of ten thousand years ago could have projected that outcome.

Now this must sound strange to any economist, as we can’t help but think in terms of rational choice. Why would any band choose to settle when, as far as we can tell, settling made them worse off? There are only three types of answers compatible with rational choice: either the environment changed such that the nomads who adopted settlement would have been even worse off had they remained nomadic, settlement was a Pareto-dominated equilibrium, or our assumption that the nomads were maximizing something correlated with height is wrong. All might be possible: early 20th century scholars ascribed the initial move to settlement to humans being forced onto oases in the drying post-Ice Age Middle East, evolutionary game theorists are well aware that fitness competitions can generate inefficient Prisoner’s Dilemmas, and humans surely care about reproductive success more than they care about food intake per se.

So how can we separate these potential explanations, or provide greater clarity as to the underlying Neolithic transition mechanism? Two relatively new papers, Andrea Matranga’s “Climate-Driven Technical Change“, and Kim Sterelny’s Optimizing Engines: Rational Choice in the Neolithic”, discuss intriguing theories about what may have happened in the Neolithic.

Matranga writes a simple Malthusian model. The benefit of being nomadic is that you can move to places with better food supply. The benefit of being sedentary is that you use storage technology to insure yourself against lean times, even if that insurance comes at the cost of lower food intake overall. Nomadism, then, is better than settling when there are lots of nearby areas with uncorrelated food availability shocks (since otherwise why bother to move?) or when the potential shocks you might face across the whole area you travel are not that severe (in which case why bother to store food?). If fertility depends on constant access to food, then for Malthusian reasons the settled populations who store food will grow until everyone is just at subsistence, whereas the nomadic populations will eat a surplus during times when food is abundant.

It turns out that global “seasonality” – or the difference across the year in terms of temperature and rainfall – was extraordinarily high right around the time agriculture first popped up in the Fertile Crescent. Matranga uses some standard climatic datasets to show that six of the seven independent inventions of agriculture appear to have happened soon after increases in seasonality in their respective regions. This is driven by an increase in seasonality and not just an increase in rainfall or heat: agriculture appears in the cold Andes and in the hot Mideast and in the moderate Chinese heartland. Further, adoption of settlement once your neighbors are farming is most common when you live on relatively flat ground, with little opportunity to change elevation to pursue food sources as seasonality increases. Biological evidence (using something called “Harris lines” on your bones) appears to support to idea that nomads were both better fed yet more subject to seasonal shocks than settled peoples.

What’s nice is that Matranga’s hypothesis is consistent with agriculture appearing many times independently. Any thesis that relies on unique features of the immediate post-Ice Age – such as the decline in megafauna like the Woolly Mammoth due to increasing population, or the oasis theory – will have a tough time explaining the adoption of agriculture in regions like the Andes or China thousands of years after it appeared in the Fertile Crescent. Alain Testart and colleagues in the anthropology literature have made similar claims about the intersection of storage technology and seasonality being important for the gradual shift from nomadism to partial foraging to agriculture, but the Malthusian model and the empirical identification in Matranga will be much more comfortable for an economist reader.

Sterelny, writing in the journal Philosophy of Science, argues that rational choice is a useful framework to explain not only why backbreaking, calorie-reducing agriculture was adopted, but also why settled societies appeared willing to tolerate inequality which was much less common in nomadic bands, and why settled societies exerted so much effort building monuments like Gobekli Tepe, holding feasts, and participating in other seemingly wasteful activity.

Why might inequality have arisen? Settlements need to be defended from thieves, as they contain stored food. Hence settlement sizes may be larger than the size of nomadic bands. Standard repeated games with imperfect monitoring tell us that when repeated interactions become less common, cooperation norms become hard to sustain. Hence collective action can only be sustained through mechanisms other than dyadic future punishment; this is especially true if farmers have more private information about effort and productivity than a band of nomadic hunters. The rise of enforceable property rights, as Bowles and his coauthors have argued, is just such a mechanism.

What of wasteful monuments like Gobekli Tepe? Game theoretic deliberate choice provides two explanations for such seeming wastefulness. First, just as animals consume energy in ostentatious displays in order to signal their fitness (as the starving animal has no energy to generate such a display), societies may construct totems and temples in order to signal to potential thieves that they are strong and not worth trifling with. In the case of Gobekli Tepe, this doesn’t appear to be the case, as there isn’t much archaeological evidence of particular violence around the monument. A second game theoretic rationale, then, is commitment by members of a society. As Sterelny puts it, the reason a gang makes a member get a face tattoo is that, even if the member leaves the gang, the tattoo still puts that member at risk of being killed by the gang’s enemies. Hence the tattoo commits the member not to defect. Settlements around Gobekli Tepe may have contributed to its building in order to commit their members to a set of norms that the monument embodied, and hence permit trade and knowledge transfer within this in-group. I would much prefer to see a model of this hypothesis, but the general point doesn’t seem impossible. At least, Sterelny and Matranga together provide a reasonably complete possible explanation, based on rational behavior and nothing more, of the seemingly-strange transition away from nomadism that made our modern life possible.

Kim Sterelny, Optimizing Engines: Rational Choice in the Neolithic?, 2013 working paper. Final version published in the July 2015 issue of Philosophy of Science. Andrea Matranga, “Climate-driven Technical Change: Seasonality and the Invention of Agriculture”, February 2015 working paper, as yet unpublished. No RePEc IDEAS page is available for either paper.

“Bonus Culture: Competitive Pay, Screening and Multitasking,” R. Benabou & J. Tirole (2014)

Empirically, bonus pay as a component of overall renumeration has become more common over time, especially in highly competitive industries which involve high levels of human capital; think of something like management of Fortune 500 firms, where the managers now have their salary determined globally rather than locally. This doesn’t strike most economists as a bad thing at first glance: as long as we are measuring productivity correctly, workers who are compensated based on their actual output will both exert the right amount of effort and have the incentive to improve their human capital.

In an intriguing new theoretical paper, however, Benabou and Tirole point out that many jobs involve multitasking, where workers can take hard-to-measure actions for intrinsic reasons (e.g., I put effort into teaching because I intrinsically care, not because academic promotion really hinges on being a good teacher) or take easy-to-measure actions for which there might be some kind of bonus pay. Many jobs also involve screening: I don’t know who is high quality and who is low quality, and although I would optimally pay people a bonus exactly equal to their cost of effort, I am unable to do so since I don’t know what that cost is. Multitasking and worker screening interact among competitive firms in a really interesting way, since how other firms incentivize their workers affects how workers will respond to my contract offers. Benabou and Tirole show that this interaction means that more competition in a sector, especially when there is a big gap between the quality of different workers, can actually harm social welfare even in the absence of any other sort of externality.

Here is the intuition. For multitasking reasons, when different things workers can do are substitutes, I don’t want to give big bonus payments for the observable output, since if I do the worker will put in too little effort on the intrinsically valuable task: if you pay a trader big bonuses for financial returns, she will not put as much effort into ensuring all the laws and regulations are followed. If there are other finance firms, though, they will make it known that, hey, we pay huge bonuses for high returns. As a result, workers will sort, with all of the high quality traders will move to the high bonus firm, leaving only the low quality traders at the firm with low bonuses. Bonuses are used not only to motivate workers, but also to differentially attract high quality workers when quality is otherwise tough to observe. There is a tradeoff, then: you can either have only low productivity workers but get the balance between hard-to-measure tasks and easy-to-measure tasks right, or you can retain some high quality workers with large bonuses that make those workers exert too little effort on hard-to-measure tasks. When the latter is more profitable, all firms inefficiently begin offering large, effort-distorting bonuses, something they wouldn’t do if they didn’t have to compete for workers.

How can we fix things? One easy method is with a bonus cap: if the bonus is capped at the monopsony optimal bonus, then no one can try to screen high quality workers away from other firms with a higher bonus. This isn’t as good as it sounds, however, because there are other ways to screen high quality workers (such as offering lower clawbacks if things go wrong) which introduce even worse distortions, hence bonus caps may simply cause less efficient methods to perform the same screening and same overincentivization of the easy-to-measure output.

When the individual rationality or incentive compatibility constraints in a mechanism design problem are determined in equilibrium, based on the mechanisms chosen by other firms, we sometimes called this a “competing mechanism”. It seems to me that there are quite a number of open questions concerning how to make these sorts of problems tractable; a talented young theorist looking for a fun summer project might find it profitable to investigate this as-yet small literature.

Beyond the theoretical result on screening plus multitasking, Tirole and Benabou also show that their results hold for market competition more general than just perfect competition versus monopsony. They do this through a generalized version of the Hotelling line which appears to have some nice analytic properties, at least compared to the usual search-theoretic models which you might want to use when discussing imperfect labor market competition.

Final copy (RePEc IDEAS version), forthcoming in the JPE.

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.

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