“Incentives for Unaware Agents,” E.L. von Thadden & X. Zhao (2012)

There is a paradox that troubles a lot of applications of mechanism design: complete contracts (or, indeed, conditional contracts of any kind!) appear to be quite rare in the real world. One reason for this may be that agents are simply unaware of what they can do, an idea explored by von Thadden and Zhao in this article as well as by Rubinstein and Glazer in a separate 2012 paper in the JPE. I like the opening example in Rubinstein and Glazer:

“I went to a bar and was told it was full. I asked the bar hostess by what time one should arrive in order to get in. She said by 12 PM and that once the bar is full you can only get in if you are meeting a friend who is already inside. So I lied and said that my friend was already inside. Without having been told, I would not have known which of the possible lies to tell in order to get in.”

The contract itself gave the agent the necessary information. If I don’t specify the rule that patrons whose friend is inside are allowed entry, then only those who are aware of that possibility will ask. Of course, some patrons who I do wish to allow in, because their friend actually is inside, won’t know to ask unless I tell them. If the harm to the bar from previously unaware people learning and then lying overwhelms the gain from allowing unaware friends in, then the bar is better off not giving an explicit “contract”. Similar problems occur all the time. There are lots of behavioral explanations (recall the famous Israeli daycare which was said to have primed people into an “economic relationship” state of mind by setting a fine for picking kids up late, leading to more lateness, not less). But the bar story above relies on no behavioral action aside from agents having a default (ask about the friend clause if aware, or don’t ask if unaware) which can be removed if agents are informed about their real possible actions when given a contract.

When all agents are unaware, the tradeoff is simple, as above: I make everyone aware of their true actions if the cost of providing incentive rents is exceeded by the benefit of agents switching to actions I prefer more. Imagine that agents can not clean, partially clean, or fully clean their tools at the end of the workday (giving some stochastic output of cleanliness). They get no direct utility out of cleaning, and indeed get disutility the more time they spend cleaning. If there is no contract, they default to partially cleaning. If there is a contract, then if all cleaning pays the same the agent will exert zero effort and not clean. The only reason I might offer high-powered incentives, then, is if the benefit of getting agents to fully clean their tools exceeds the IC rents I will have to pay them once the contract is in place.

More interesting is the case with aware and unaware agents, when I don’t know which agent is which. The unaware agents gets contracts that pay the same wage no matter what their output, and the aware agents can get high-powered incentives. Solving the contracting problem involves a number of technical difficulties (standard envelope theorem arguments won’t work), but the solution is fairly intuitive. Offer two incomplete wage contracts w(x) and v(x). Let v(x) just fully insure: no matter what the output, the wage is the same. Let w(x) increase with better outputs. Choose the full insurance wage v low enough that the unaware agents’ participation constraint just binds. Then offer just enough rents in w(x) that the aware agents, who can take any action they want, actually take the planner preferred action. Unlike in a standard screening problem, I can manipulate this problem by just telling unaware agents about their possible actions: it turns out that profits only increase by making these agents aware if there are sufficiently few unaware agents in the population.

Some interesting sidenotes. Unawareness is “stable” in the sense that unaware agents will never be told they are unaware, and hence if we played this game for two periods, they would remain unaware. It is not optimal for aware agents to make unaware agents aware, since the aware earn information rents as a result of that unawareness. It is not optimal for the planner to make unaware agents aware: the firm is maximizing total profit, announcements strictly decrease wages of aware agents (by taking their information rents), and don’t change unaware agents rents (they get zero since their wage is always chosen to make their PC bind, as is usual for “low types” in screening problems). Interesting.

2009 working paper (IDEAS). Final version in REStud 2012. The Rubinstein/Glazer paper takes a slightly different tack. Roughly, it says that contract designers can write a codex of rules, where you are accepted if you satisfy all the rules. An agent made aware of the rules can figure out how to lie if it involves only lying about one rule. A patient, for instance, may want a painkiller prescription. He can lie about any (unverifiable) condition, but he is only smart enough to lie once. The question is, which codices are not manipulable?

Talk: Carnegie Mellon, April 12 2013

A quick housekeeping note: if you are at Carnegie Mellon, I will be presenting a new paper (joint with Jorge Lemus, also here at Northwestern) in Posner Hall, room 388, from 12 to 1 this Friday. Come by and say hi!

The paper I’m presenting is actually quite cool, and we have pretty high hopes for it. Take the standard models of patent races or sequential innovation. The problem in those models is, do firms exert the socially optimal amount of effort on R&D? But this is not the only problem, as the title of the classic 1962 “Rate and Direction of Inventive Activity” NBER volume makes clear. The amount of effort may be fine, but firms may be working on the wrong projects. The intuition here we know from statements like “Firms do not do enough basic research.” What we’ve done is write out a totally general model of research direction which, for applied folks, is usable as long as you are familiar with standard sequential innovation models. We shut down all the already-known sources of inefficiency, and find that the interaction of direction choice and sequential innovation creates three qualitatively novel sources of inefficiency. Fixing these inefficiencies can be difficult; for example, broad patents for early inventors can actually make inefficiency worse.

Both Jorge and I would love your comments, so come on by!

“The Economic Benefits of Pharmaceutical Innovations: The Case of Cox-2 Inhibitors,” C. Garthwaite (2012)

Cost-benefit analysis and comparative effectiveness are the big buzzwords in medical policy these days. If we are going to see 5% annual real per-capita increases in medical spending, we better be getting something for all that effort. The usual way to study cost effectiveness is with QALYs, Quality-Adjusted Life Years. The idea is that a medicine which makes you live longer, with less pain, is worth more, and we can use alternative sources (such as willingness to accept jobs with higher injury risk) to get numerical values on each component of the QALY.

But medicine has other economic effects, as Craig Garthwaite (from here at Kellogg) reminds us in a recent paper of his. One major impact is through the labor market: the disabled or those with chronic pain choose to work less. Garthwaite considers the case of Vioxx. Vioxx was a very effective remedy for long-term pain, which (it was thought) could be used without the gastrointestinal side effects of ibuprofen or naproxen. It rapidly become very widely prescribed. However, evidence began to accumulate which suggested that Vioxx also caused serious heart problems, and the pill was taken off the market in 2004. Alternative joint pain medications for long term use weren’t really comparable (though, having taken naproxen briefly for a joint injury, I assure you it is basically a miracle drug.)

We have a great panel on medical spending called MEPS which includes age, medical history, prescriptions, income, and labor supply decisions. That is, we have everything we need for a quick diff-in-diff. Take those with joint pain and those without, before Vioxx leaves the market and after. We see parallel trends in labor supply before Vioxx is removed (though of course, those with joint pain are on average older, more female, and less educated, hence much less likely to work). The year Vioxx is removed, labor supply drops 10 percent among those with joint pain, and even more if we look ahead a few periods after Vioxx is taken off the market.

For more precision, let’s do a two-stage IV on the panel data, first estimating use of any joint pain drug conditioning on the Vioxx removal and the presence of joint pain, then labor supply conditional on use of an joint pain drug. Use of any joint pain drug fell about 50% in the panel following the removal of Vioxx. Labor supply of those with joint pain is about 22 percentage points higher when Vioxx is available in the individual fixed effects IV, meaning a 54% decline in probability of working for those who were taking chronic joint pain drugs before Vioxx was removed. How big an economic effect is this? About 3% of the work force are elderly folks reporting some kind of joint pain, and 20% of them found the pain serious enough to have prescription joint pain medication. If 54% of that group leaves the labor force, this means overall labor supply changed by .35 percentage points because of Vioxx (accounting for spillovers to related drugs), or $19 billion of labor income disappeared when Vioxx was taken off the market. This is a lot, though of course these estimates are not too precise. The point is that medical cost effectiveness studies, in cases like the one studied here, can miss quite a lot if they fail to account for impacts beyond QALYs.

Final working paper (IDEAS page). Paper published in AEJ: Applied 2012.

“Contractability and the Design of Research Agreements,” J. Lerner & U. Malmendier (2010)

Outside research has (as we discussed yesterday) begun to regain prominence as a firm strategy. This is particularly so in biotech: the large drug firms generally do not do the basic research that leads to new products. Rather, they contract this out to independent research firms, then handle the development, licensing and marketing in-house. But such contracts are tough. Not only can do I have trouble writing an enforceable contract that conditions on the effort exerted by the research firm, but the fact that research firms have other projects, and also like to do pure science for prestige reasons, means that they are likely to take my money and use it to fund projects which are not entirely the most preferred of the drug company.

We are in luck: economic theory has a broad array of models of contracting under multitasking worries. Consider the following model of Lerner and Malmendier. The drug firm pays some amount to set up a contract. The research firm then does some research. The drug firm observes the effort of the researcher, who either worked on exactly what the drug company prefers, or on a related project which throws off various side inventions. After the research is performed, the research firm is paid. With perfect ability to contract on effort, this is an easy problem: pay the research firm only if they exert effort on the projects the drug company prefers. When the research project is “tell me whether this compound has this effect”, it might be possible to write such a contract. When the research project is “investigate the properties of this class of compounds and how they might relate to diseases of the heart”, surely no such contract is possible. In that case, the optimal contract may be just to let the research firm work on the broader project it prefers, because at least then the fact that the research firm gets spillovers means that the drug firm can pay the researcher less money. This is clearly second-best.

Can we do better? What about “termination contracts”? After effort is observed, but before development is complete, the drug firm can terminate the contract or not. Payments in the contract can certainly condition on termination. How about the following contract: the drug firm terminates if the research firm works on the broader research project, and it takes the patent rights to the side inventions. Here, if the research firm deviates and works on its own side projects, the drug company gets to keep the patents for those side projects, hence the research firm won’t do such work. And the drug firm further prefers the research firm to work on the assigned project; since termination means that development is not completed, the drug firm won’t just falsely claim that effort was low in order to terminate and seize the side project patents (indeed, on equilibrium path, there are few side patents to seize since the research firm is actually working on the correct project!). The authors show that the contract described here is always optimal if a conditional termination contract is used at all.

Empirically, what does this mean? If I write a research contract for more general research, I should expect more termination rights to be reserved. Further, the liquidity constraint of the research firms matter; if the drug firm could make the research firm pay it back after termination, it would do so, and we could again achieve the first best. So I should expect termination rights to show up particularly for undercapitalized research firms. Lerner and Malmendier create a database from contract data collected by a biotech consulting firm, and show that both of these predictions appear to be borne out. I read these results as in the style of Maskin and Tirole; even when I can’t fully specify all the states of the world in a contract, I can still do a good bit of conditioning.

2008 Working paper (IDEAS version). Final paper in AER 2010. Malmendier will certainly be a factor in the upcoming Clark medal discussion, as she turns 40 this year. Problematically, Nick Bloom (who, says his CV, did his PhD part time?!) also turns 40, and both absolutely deserve the prize. If I were a betting man, I would wager that the just-published-in-the-QJE Does Management Matter in the Third World paper will be the one that puts Bloom over the top, as it’s really the best development paper in many years. That said, I am utterly confused that Finkelstein won last year given that Malmendier and Bloom are both up for their last shot this year. Finkelstein is a great economist, no doubt, but she works in a very similar field to Malmendier, and Malmendier trumps her by any conceivable metric (citations, top cited papers, overall impact, etc.). I thought they switched the Clark Medal to an every-year affair just to avoid such a circumstance, such as when Athey, List and Melitz were all piled up in 2007.

I’m curious what a retrospective Clark Medal would look like, taking into account only research that was done as of the voting year, but allowing us to use our knowledge of the long-run impact of that research. Since 2001, Duflo 2010 and Acemoglu 2005 are locks. I think Rabin keeps his in 2001. Guido Imbens takes Levitt’s spot in 2003. List takes 2007, with Melitz and Athey just missing out (though both are supremely deserving!). Saez keeps 2009. Malmendier takes 2011. Bloom takes 2012. Raj Chetty takes 2013 – still young, but already an obvious lock to win. What’s interesting about this list is just how dominant young folks have been in micro (especially empirical and applied theory); these are essentially the best people working in that area, whereas macro and metrics are still by and large dominated by an older generation.

“Patent Alchemy: The Market for Technology in U.S. History,” N. Lamoreaux, K. Sokoloff & D. Sutthiphisall (2012)

It may appear that the world of innovation looks very different today than it used to. Large in-house R&D outfits – the Bell Labs of the past – are being replaced by small firms who sell the results of their research on to producers. Venture capital funding of research appears more and more important, both for providing capital to inventors and to linking the inventors up with potential buyers. Patent trolls hound the innocent, suing them for patent violations they weren’t even aware of. The speed with which patents are evaluated has slowed to a crawl, and the number of patents being granted continues to grow. Many patents are merely defensive, acquired solely to keep someone else from acquiring them.

Lamoreaux et al, building on earlier work by Lamoreaux and Sokoloff as well as Tom Nicholas’ interesting recent research, point out that none of the above is strange. The rise of in-house R&D is a phenomenon that doesn’t show up in great number in America until well into the twentieth century, only becoming dominant after the Second World War. Around the turn of the century, most innovation was done by small, independent inventors, or by small research firms like Edison’s outfit. A series of intermediaries, principally but not always patent lawyers, served both to file the proper paperwork and to link inventors with potential buyers; the authors provide a bunch of juicy historical stories, derived from lawyer diaries during this period, on exactly how such transactions took place. Railroads were frequently being hounded by patent trolls who tried to catch them unaware, and traveling patentbuyers crossed the Midwest and South suing farmers for using unlicensed barbed wire or milk buckets. Patents took an average of three years to be processed by the early 1900s, and the patenting rate was near an all time high. Firms regularly bought patents just so their competitors wouldn’t have them.

This is all to say that, to the extent we are worried about certain aspects of the patent system today, looking to history may be a useful place to begin. “Submarine patents”, acquired by trolls and kept unused until a particularly juicy potential violator has started to earn large profits, don’t appear to have been too prominent at the turn of the century – given how lucrative this business appears, perhaps an investigation of why they only appear in the present would be worthwhile. The role of a patent as a saleable piece of knowledge, allowing non-producers to do useful research and then sell that research to a firm who finds it useful, surely has some role, as Arrow pointed out in his famous 1962 essay. When patents instead simply add transaction costs or result in thickets, discouraging activity by true innovators, something has gone awry. And when something goes wrong in the world, it is rarely the case that history can offer us no useful guidance.

2012 working paper (No IDEAS version). Prof. Sokoloff passed away from cancer at a young age in 2007, so this may become his final published paper – it incorporates a great number of ideas he worked on throughout his career, so that would be a fitting tribute.

“Recruiting for Ideas: How Firms Exploit the Prior Inventions of New Hires,” J. Singh & A. Agrawal (2011)

Firms poach engineers and researchers from each other all the time. One important reason to do so is to gain access to the individual’s knowledge. A strain of theory going back to Becker, however, suggests that if, after the poaching, the knowledge remains embodied solely in the new employer, it will be difficult for the firm to profit: surely the new employee will have an enormous amount of bargaining power over wages if she actually possesses unique and valuable information. (As part of my own current research project, I learned recently that Charles Martin Hall, co-inventor of the Hall-Heroult process for aluminum smelting, was able to gather a fortune of around $300 million after he brought his idea to the company that would become Alcoa.)

In a resource-based view of the firm, then, you may hope to not only access a new employer’s knowledge, but also spread it to other employees at your firm. By doing this, you limit the wage bargaining power of the new hire, and hence can scrape off some rents. Singh and Agrawal break open the patent database to investigate this. First, use name and industry data to try to match patentees who have an individual patent with one firm at time t, and then another patent at a separate firm some time later; such an employee has “moved”. We can’t simply check whether the receiving firm cites this new employee’s old patents more often, as there is an obvious endogeneity problem. First, firms may recruit good scientists more aggressively. Second, they may recruit more aggressively in technology fields where they are already planning to do work in the future. This suggests that matching plus diff-in-diff may work. Match every patent to another patent held by an inventor who never switches firms, attempting to find a second patent with very similar citation behavior, inventor age, inventor experience, technology class, etc. Using our matched sample, check how much the propensity to cite the mover’s patent changes compares to the propensity to the cite the stayer’s patent. That is, let Joe move to General Electric. Joe had a patent while working at Intel. GE researchers were citing that Intel patent once per year before Joe moved. They were citing a “matched” patent 1 times per year. After the move, they cite the Intel patent 2 times per year, and the “matched” patent 1.1 times per year. The diff-in-diff then suggests that moving increases the propensity to cite the Intel patent at GE by (2-1)-(1.1-1)=.9 citations per year, where the first difference helps account for the first type of endogeneity we discussed above, and the second difference for the second type of endogeneity.

What do we find? It is true that, after a move, the average patent held by a mover is cited more often at the receiving firm, especially in the first couple years after a move. Unfortunately, about half of new patents which cite the new employee’s old patent after she moves are made by the new employee herself, and another fifteen percent or so are made by previous patent collaborators of the poached employee. What’s worse, if you examine these citations by year, even five years after the move, citations to the pre-move patent are still highly likely to come from the poached employee. That is, to the extent that the poached employee had some special knowledge, the firm appears to have simply bought that knowledge embodied in the new employee, rather than gained access to useful techniques that quickly spread through the firm.

Three quick comments. First, applied econometrician friends: is there any reason these days to do diff-in-diff linearly rather than using the nonparametric “changes-in-changes” of Athey and Imbens 2006, which allows recovery of the entire distribution of effects of treatment on the treated? Second, we learn from this paper that the mean poached research employee doesn’t see her knowledge spread through the new firm, which immediately suggests the question of whether there are certain circumstances in which such knowledge spreads. Third, this same exercise could be done using all patents held by the moving employee’s old firm – I may be buying access to general techniques owned by the employee’s old firm rather than the specific knowledge represented in that employee’s own pre-move patents. I wonder if there’s any difference.

Final Management Science version (IDEAS version). Big thumbs up to Jasjit Singh for putting final published versions of his papers up on his site.

“Chinese Economic Performance in the Long Run,” A. Maddison (2007)

Many economists know the rough contours of Western economic history well. Real income of unskilled laborer and farmer households was at no time and in no place more than, at best, three times subsistence income (see Scheidel for a nice summary of this evidence). Peaks in per capita GDP were reached in the heyday of ancient Rome and the early Arab caliphate. Regional regression was nothing strange – Europe in 1000 was using less advanced technology in many cases than the Romans had, credit markets were essentially nonexistent, long-distance or even regional trade had dried up, and no city in Europe existed with a population of even 10,000 people at the turn of the millennium. Living standards begin to rise slowly after the Black Death, first in Renaissance Italy, and then in the Netherlands and England. The Industrial Revolution finally severs the Malthusian noose by the mid-1800s, when living standards for most members of society begin to rise from their historical norm.

But what of China? Before he died, one of Angus Maddison’s final projects was compiling data on historic China. In Chinese culture, the classic periods in history are the Tang and Song dynasties, roughly from the 7th to the 12th centuries, with brief interludes, and perhaps the late Yuan and early Ming, from the late 13 to the late 1400s. Did China escape the Malthusian curse? They also did not. It seems likely that incomes were roughly at subsistence until the Tang dynasty in the 9th century, when income per capita rose perhaps 30 percent. That peak would not be seen again until around 1970!

Now, in a Malthusian world, you can still grow, or be more advanced economically, but that growth is eaten up by population growth. The main pattern in China seems to be a massive shift in population density in the south, meaning south of the Yangtse, after the beginning of the Song dynasty. Woodblock printing, allowing for the dissemination of guides to more productive agriculture, appeared in this era. Chinese agriculture appears to have been much more advanced that that of Europe or India; indeed, more of China’s farmland was irrigated in 1400 than America’s today, and not until the 20th century did Europe reach grain yields seen in China in 1400. If you know your Joseph Needham, you know much of this is driven by Chinese agricultural inventions like the curved mouldboard and the use of crop rotation (not seen in Europe until the eighteenth century!). Population rose ten-fold from 1400 to 1950 despite little change in per capita income. A nontrivial increase in caloric yield per acre of farmland came from the introduction of new world crops like maize and the sweet potato, which appear in China during the Ming dynasty. Nonagricultural rural work also appears to have been much more developed than in medieval Europe, with William Skinner’s “hexagonal trade” existent during nearly all of the post-Tang dynasties. Such trade allowed cities to develop – around 1000, China had almost 100 cities with population above 10,000, as compared to none in Europe!

More recently, industrialization gets a late start. The 1800s are a giant disaster for China, with wars against Europeans, Russians and Japanese (China lost essentially all of these), the Taiping rebellion that kills tens of millions in the nation’s heartland, Muslim rebellions in the Northwest, and a near complete lack of institutional modernization of the type seen in Japan. By 1890, only 10 miles of rail are found in the whole country, and modern industry makes up only one-half percent of the economy. Despite some fits and starts during the Republican era (especially in Shanghai and Japanese-controlled Manchuria), by the end of World War 2 and the Chinese Civil War, per capita income is no higher than it was during the Tang dynasty. Perhaps the non-vilification of Mao in today’s China has to do with the fact that, even with near-complete autarky, the Great Leap Forward and the Cultural Revolution, per capita income still nearly doubled during the Maoist era, and the industrial share of GDP rose up to match the agricultural share. That is, despite all of the human rights disasters, the Maoist economic performance was simply unheard of in Chinese history. Nearly all of this growth came from capital deepening and (especially) increases in labor supply and the human capital embodied in that labor supply; literacy rose from 20 percent to about 80 percent. And, of course, the economic history since 1976 is well-known – in only three years of the past 37 has GDP per capita grown slower than six percent, an unprecedented streak in the history of the globe.

http://browse.oecdbookshop.org/oecd/pdfs/product/4107091e.pdf
(Full PDF version of the published book – big thumbs up to the OECD for making these public. If you are a Chinese speaker, prepare to be annoyed by Maddison’s habit of using Wade-Giles transliteration, i.e., Cheng Ho instead of Zheng He, Yung-lo Emperor instead of the Yangle Emperor, Kwangtung for Guangdong, Tseng Kuo-fan for Zeng Guofan. Speaking of Maddison, his historic income tables (.XLS) are a great way to while away a rainy afternoon. Who knew Australia was once the world’s richest place, or that Sri Lanka was historically a particularly wealthy part of Asia, or that Venezuela was wealthier per capita than all of Western Europe in the middle of the 20th century?)

“Returns to Scale in Research & Development: What Does the Schumpeterian Hypothesis Imply?,” F. Fisher & P. Temin (1973)

Schumpeter famously argued for the economic importance of market power. Even though large firms cause static inefficiency, they had dynamic benefits in that large firms demand more invention since they can extract more revenue from each new product. Further, they supply more invention, Schumpeter hypothesized, since the rate of invention has increasing returns to scale in the number of inventors, and in the number of other employees at the firm. (Axioms A and B). The second part of that statement may be for many reasons; for instance, if the output of a research project could be many potential products, a larger firm has the ability to capitalize on many of those new projects, whereas a small firm might have more limited complementary capabilities. Often, this hypothesis has been tested by checking whether larger firms are more research intensive, meaning that larger firms have a higher percentage of their workforce doing research (Hypothesis 1). Alternatively, a direct reading of Schumpeter is that a 1% increase in the non-research staff of a firm leads to a more than 1% increase in total R&D output of a firm, where output is just the number of research workers times each worker’s average output as a function of firm size (Hypothesis 2).

And here is where theory comes into play. Are axioms A and B necessary or sufficient for either hypothesis 1 or 2? If they don’t imply hypothesis 1, then the idea of testing the Schumpeterian axioms about increasing returns to scale by examining researcher employment is wrong-headed. If they don’t imply hypothesis 2, then Schumpeter’s qualitative argument is incomplete in the first place. Fisher and Temin (that’s Franklin Fisher and Peter Temin, two guys who, it goes without saying, have had quite some careers since they wrote this paper in the early 70s!) show that, in fact, for both hypotheses the axioms are neither necessary nor sufficient.

An even more basic problem wasn’t noticed by Fisher and Temin, but instead was pointed out by Carlos Rodriguez in a 1979 comment. If Axiom 1 holds, and the average product per researcher is increasing in the number of researchers, then marginal product always exceeds average product. If market equilibrium means I pay all research workers their marginal product, then I will be making a loss if I operate at the “optimal” quantity. Hence I will hire no research workers at all. So step one to interpreting Schumpeter, then, is to restate his two axioms. A weaker condition might be that if the number of research and the number of nonresearch workers increase at the same rate, then average product per research worker is increasing. This is implied by Axioms A and B, but doesn’t rely on always-increasing average product per research worker (Axiom C). This is good for checking our two hypotheses, since anything that would have been implied by Axioms A and B is still implied by our more theoretically-grounded axiom C.

So what does our axiom imply about the link between research staff size and firm size? Unsurprisingly, nothing at all! Surely the optimal quantity of research workers depends on the marginal product of more research workers as firm size grows, and not on the average product of those workers. Let’s prove it. Let F(R,S) is the average product per research worker as a function of R, the number of researchers, and S, the number of other employees at the firm. I hire research workers as long as their marginal product exceeds the researcher wage rate. The marginal product of total research output is the derivative of R*F(R,S) with respect to R, or F+R*dF/dR. As S increases, this marginal product goes up if and only if dF/dS+R*dF^2/dRdS>0. That is, I hire more research workers in equilibrium if my non-research staff is bigger according to a function that depends on the second derivative of the average output per researcher. But my axioms had only to do with the first derivative! Further, if dF/dS+R*dF^2/dRdS>0, then larger firms have a larger absolute number of scientists than smaller firms, but this implication is completely independent of the Schumpeterian axioms. What’s worse, even that stronger assumption involving the second derivative does not imply anything about the share of research workers on the staff.

The moral is the same one you were probably taught you first day of economics class: using reasoning about averages to talk about equilibrium behavior, so dependent on marginals, can lead you astray very quickly!

1971 working paper; the final version was published in JPE 1973 (IDEAS). Related to the comment by Rodriguez, Fisher and Temin point out here that the problem with increasing returns to scale does not ruin their general intuition, for the reasons I stated above. What about the empirics of Schumpeter’s prediction? Broadly, there is not much support for a link between firm size and research intensity, though the literature on this is quite contentious. Perhaps I will cover it in another post.

“The Meaning of Utility Measurement,” A. Alchian (1953)

Armen Alchian, one of the dons from UCLA’s glory days, passed away today at 98. His is, for me, a difficult legacy to interpret. On the one hand, Alchian-Demsetz 1972 is among the most famous economics papers ever written, and it can fairly be considered the precursor to mechanism design, the most important new idea in economics in the past 50 years. People produce more by working together. It is difficult to know who shirks when we work as a team. A firm gives a residual claimant (an owner) who then has an incentive to monitor shirking, and as only one person needs to monitor the shirking, this is much less costly than a market where each member of the team production would need somehow to monitor whether other parts of the team shirk. Firms are deluded if they think that they can order their labor inputs to do whatever they want – agency problems exist both within and outside the firm. Such an agency theory of the firm is very modern indeed. That said, surely this can’t explain things like horizontally integrated firms, with different divisions producing wholly different products (or, really, any firm behavior where output is a separable function of each input in the firm).

Alchian’s other super famous work is his 1950 paper on evolution and the firm. As Friedman would later argue, Alchian suggested that we are justified treating firms as if they are profit maximizers when we do our analyses since the nature of competition means that non-profit maximizing firms will disappear in the long run. I am a Nelson/Winter fan, so of course I like the second half of the argument, but if I want to suggest that firms partially seek opportunities and partially are driven out by selection (one bit Lamarck, one bit Darwin), then why not just drop the profit maximization axiom altogether and try to write a parsimonious description of firm behavior which doesn’t rely on such maximization?

It turns out that if you do the math, profit maximization is not generally equivalent to selection. Using an example from Sandroni 2000, take two firms. There are two equally likely states of nature, Good and Bad. There are two things a firm can do, the risky one, which returns profit 3 in good states and 0 in bad states, and a risk-free one, which always returns 1. Maximizing expected profit means always investing all capital in the risky state, hence eventually going bankrupt. A firm who doesn’t profit maximize (say, it has incorrect beliefs and thinks we are always in the Bad state, hence always takes the risk-free action) can survive. This example is far too simple to be of much worth, but it does at least remind us of lesson in the St. Petersburg paradox: expected value maximization and survival have very little to do with each other.

More interesting is the case with random profits, as in Radner and Dutta 2003. Firms invest their capital stock, choosing some mean-variance profits pair as a function of capital stock. The owner can, instead of reinvesting profits into the capital stock, pay out to herself or investors. If the marginal utility of a dollar of capital stock falls below a dollar, the profit-maximizing owner will not reinvest that money. But a run of (random) losses can drive the firm to bankruptcy, and does so eventually with certainty. A non-profit maximizing firm may just take the lowest variance earnings in every period, pay out to investors a fraction of the capital stock exactly equal to the minimum earnings that period, and hence live forever. But why would investors ever invest in such a firm? If investment demand is bounded, for example, and there are many non profit-maximizing firms from the start, it is not the highest rate of return but the marginal rate of return which determines the market interest rate paid to investors. A non profit-maximizer that can pay out to investors at least that much will survive, and all the profit maximizers will eventually fail.

The paper in the title of this post is much simpler: it is merely a very readable description of von Neumann expected utility, when utility can be associated with a number and when it cannot, and the possibility of interpersonal utility comparison. Alchian, it is said, was a very good teacher, and from this article, I believe it. What’s great is the timing: 1953. That’s one year before Savage’s theory, the most beautiful in all of economics. Given that Alchian was associated with RAND, where Savage was fairly often, I imagine he must have known at least some of the rudiments of Savage’s subjective theory, though nothing appears in this particular article. 1953 is also two years before Herbert Simon’s behavioral theory. When describing the vN-M axioms, Alchian gives situations which might contradict each, except for the first, a complete and transitive order over bundles of goods, an assumption which is consistent with all but “totally unreasonable behavior”!

1953 AER final version (No IDEAS version).

“The Oligopoly Solution Concept is Identified,” T. Bresnahan (1980)

Here’s a classic, super-simple paper. I think I can give you the idea in two paragraphs. I know price and quantity sold for some good. I know supply and demand must equate. I use whatever method I like to deal with simultaneity of the supply and demand functions (say, a cost shifter approach). How can I identify whether the industry is acting as if it had market power? That is, how can I separate collusive behavior from competitive behavior?

A numerical example will help. Let marginal costs and demand be linear. Let demand be P=11-Q. Shift demand and supply (meaning shift the intercept) however you like. The price-quantity bundle you see under monopoly with MC constant and equal to 1 will be identical to the price-quantity bundle you see under perfect competition with MC increasing and equal to 1+Q. For instance, price=6 and quantity=5 is found by letting P=MC for MC=1+Q or by letting MR=MC for MR=11-2Q. And demand shifters don’t help us! If demand shifts to P=R-Q, where R is any y-intercept, then under perfect competition with MC=1+Q, we have equilibrium price such that 1+Q=R-Q, or Q=(R-1)/2, and equilibrium price under monopoly with MC=1 such that MC=MR, or R-2Q=1, or Q=(R-1)/2. Supply shifters are equally unhelpful: for inverse demand P=11-Q, shifting the y-intercept for the cost curve of both the hypothetical monopolist and the hypothetical perfectly competitive market changes equilibrium quantity by exactly the same amount. So what to do? The simplest method is to assume, a priori, something about the nature of marginal costs in the industry; if they are constant, the the price patterns we saw in the numerical example can only be explained by monopoly/collusive behavior. But Bresnahan points out that we don’t even need to make this assumption. Just note that a rotation of the demand curve through some equilibrium point affects those with market power and those without differently. Since rotating the demand curve retains the P=MC equilibrium condition under perfect competition, such a rotation only affects equilibrium price and quantity if competition is not perfect. If I have, say, demand-side instruments, one of which only affects the y-intercept and one of which affects the slope (and perhaps also the intercept), then not only can I identify whether perfect competition exists, but I can even identify the degree to which behavior is monopolistic. Useful.

Final version from Economic Letters 1982 (IDEAS)