A Fine Theorem

August 14, 2017
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It seems this weblog has become an obituary page rather than a simple research digest of late. I am not even done writing on the legacy of Ken Arrow (don’t worry – it will come!) when news arrives that yet another product of the World War 2 era in New York City, an of the CCNY system, has passed away: the great scholar of entrepreneurship and one of my absolute favorite economists, William Baumol.

But we oughtn’t draw the line on his research simply at entrepreneurship, though I will walk you through his best piece in the area, a staple of my own PhD syllabus, on “creative, unproductive, and destructive” entrepreneurship. Baumol was also a great scholar of the economics of the arts, performing and otherwise, which were the motivation for his famous cost disease argument. He was a very skilled micro theorist, a talented economic historian, and a deep reader of the history of economic thought, a nice example of which is his 2000 QJE on what we have learned since Marshall. In all of these areas, his papers are a pleasure to read, clear, with elegant turns of phrase and the casual yet erudite style of an American who’d read his PhD in London under Robbins and Viner. That he has passed without winning his Nobel Prize is a shame – how great would it have been had he shared a prize with Nate Rosenberg before it was too late for them both?

Baumol is often naively seen as a Schumpeter-esque defender of the capitalist economy and the heroic entrepreneur, and that is only half right. Personally, his politics were liberal, and as he argued in a recent interview, “I am well aware of all the very serious problems, such as inequality, unemployment, environmental damage, that beset capitalist societies. My thesis is that capitalism is a special mechanism that is uniquely effective in accomplishing one thing: creating innovations, applying those innovations and using them to stimulate growth.” That is, you can find in Baumol’s work many discussions of environmental externalities, of the role of government in funding research, in the nature of optimal taxation. You can find many quotes where Baumol expresses interest in the policy goals of the left (though often solved with the mechanism of the market, and hence the right). Yet the core running through much of Baumol’s work is a rigorous defense, historically and theoretically grounded, in the importance of getting incentives correct for socially useful innovation.

Baumol differs from many other prominent economists of innovation because is at his core a neoclassical theorist. He is not an Austrian like Kirzner or an evolutionary economist like Sid Winter. Baumol’s work stresses that entrepreneurs and the innovations they produce are fundamental to understanding the capitalist economy and its performance relative to other economic systems, but that the best way to understand the entrepreneur methodologically was to formalize her within the context of neoclassical equilibria, with innovation rather than price alone being “the weapon of choice” for rational, competitive firms. I’ve always thought of Baumol as being the lineal descendant of Schumpeter, the original great thinker on entrepreneurship and one who, nearing the end of his life and seeing the work of his student Samuelson, was convinced that his ideas should be translated into formal neoclassical theory.

A 1968 essay in the AER P&P laid out Baumol’s basic idea that economics without the entrepreneur is, in a line he would repeat often, like Hamlet without the Prince of Denmark. He clearly understood that we did not have a suitable theory for oligopoly and entry into new markets, or for the supply of entrepreneurs, but that any general economic theory needed to be able to explain why growth is different in different countries. Solow’s famous essay convinced much of the profession that the residual, interpreted then primarily as technological improvement, was the fundamental variable explaining growth, and Baumol, like many, believed those technological improvements came mainly from entrepreneurial activity.

But what precisely should the theory look like? Ironically, Baumol made his most productive step in a beautiful 1990 paper in the JPE which contains not a single formal theorem nor statistical estimate of any kind. Let’s define an entrepreneur as “persons who are ingenious or creative in finding ways to add to their wealth, power, or prestige”. These people may introduce new goods, or new methods of production, or new markets, as Schumpeter supposed in his own definition. But are these ingenious and creative types necessarily going to do something useful for social welfare? Of course not – the norms, institutions, and incentives in a given society may be such that the entrepreneurs perform socially unproductive tasks, such as hunting for new tax loopholes, or socially destructive tasks, such as channeling their energy into ever-escalating forms of warfare.

With the distinction between productive, unproductive, and destructive entrepreneurship in mind, we might imagine that the difference in technological progress across societies may have less to do with the innate drive of the society’s members, and more to do with the incentives for different types of entrepreneurship. Consider Rome, famously wealthy yet with very little in the way of useful technological diffusion: certainly the Romans appear less innovative than either the Greeks or Europe of the Middle Ages. How can a society both invent a primitive steam engine – via Herod of Alexandria – and yet see it used for nothing other than toys and religious ceremonies? The answer, Baumol notes, is that status in Roman society required one to get rich via land ownership, usury, or war; commerce was a task primarily for slaves and former slaves! And likewise in Song dynasty China, where imperial examinations were both the source of status and the ability to expropriate any useful inventions or businesses that happened to appear. In the European middle ages, incentives shift for the clever from developing war implements to the diffusion of technology like the water-mill under the Cistercians back to weapons. These examples were expanded to every society from Ancient Mesopotamia to the Dutch Republic to the modern United States in a series of economically-minded historians in a wonderful collection of essays called “The Invention of Enterprise” which was edited by Baumol alongside Joel Mokyr and David Landes.

Now we are approaching a sort of economic theory of entrepreneurship – no need to rely on the whims of character, but instead focus on relative incentives. But we are still far from Baumol’s 1968 goal: incorporating the entrepreneur into neoclassical theory. The closest Baumol comes is in his work in the early 1980s on contestable markets, summarized in the 1981 AEA Presidential Address. The basic idea is this. Assume industries have scale economies, so oligopoly is their natural state. How worried should we be? Well, if there are no sunk costs and no entry barriers for entrants, and if entrants can siphon off customers quicker than incumbents can respond, then Baumol and his coauthors claimed that the market was contestable: the threat of entry is sufficient to keep the incumbent from exerting their market power. On the one hand, fine, we all agree with Baumol now that industry structure is endogenous to firm behavior, and the threat of entry clearly can restrain market power. But on the other hand, is this “ultra-free entry” model the most sensible way to incorporate entry and exit into a competitive model? Why, as Dixit argued, is it quicker to enter a market than to change price? Why, as Spence argued, does the unrealized threat of entry change equilibrium behavior if the threat is truly unrealized along the equilibrium path?

It seems that what Baumol was hoping this model would lead to was a generalized theory of perfect competition that permitted competition for the market rather than just in the market, since the competition for the market is naturally the domain of the entrepreneur. Contestable markets are too flawed to get us there. But the basic idea, that game-theoretic endogenous market structure, rather than the old fashioned idea that industry structure affects conduct affects performance, is clearly here to stay: antitrust is essentially applied game theory today. And once you have the idea of competition for the market, the natural theoretical model is one where firms compete to innovate in order to push out incumbents, incumbents innovate to keep away from potential entrants, and profits depend on the equilibrium time until the dominant firm shifts: I speak, of course, about the neo-Schumpeterian models of Aghion and Howitt. These models, still a very active area of research, are finally allowing us to rigorously investigate the endogenous rewards to innovation via a completely neoclassical model of market structure and pricing.

I am not sure why Baumol did not find these neo-Schumpeterian models to be the Holy Grail he’d been looking for; in his final book, he credits them for being “very powerful” but in the end holding different “central concerns”. He may have been mistaken in this interpretation. It proved quite interesting to give a careful second read of Baumol’s corpus on entrepreneurship, and I have to say it disappoints in part: the questions he asked were right, the theoretical acumen he possessed was up to the task, the understanding of history and qualitative intuition was second to none, but in the end, he appears to have been just as stymied by the idea of endogenous neoclassical entrepreneurship as the many other doyens of our field who took a crack at modeling this problem without, in the end, generating the model they’d hoped they could write.

Where Baumol has more success, and again it is unusual for a theorist that his most well-known contribution is largely qualitative, is in the idea of cost disease. The concept comes from Baumol’s work with William Bowen (see also this extension with a complete model) on the economic problems of the performing arts. It is a simple idea: imagine productivity in industry rises 4% per year, but “the output per man-hour of a violinist playing a Schubert quarter in a standard concert hall” remains fixed. In order to attract workers into music rather than industry, wages must rise in music at something like the rate they rise in industry. But then costs are increasing while productivity is not, and the arts looks “inefficient”. The same, of course, is said for education, and health care, and other necessarily labor-intensive industries. Baumol’s point is that rising costs in unproductive sectors reflect necessary shifts in equilibrium wages rather than, say, growing wastefulness.

How much can cost disease explain? Because the concept is so widely known by now that it is, in fact, used to excuse stagnant industries. Teaching, for example, requires some labor, but does anybody believe that it is impossible for R&D and complementary inventions (like the internet, for example) to produce massive productivity improvements? Is it not true that movie theaters now show opera live from the world’s great halls on a regular basis? Is it not true that my Google Home can, activated by voice, call up two seconds from now essentially any piece of recorded music I desire, for free? Speculating about industries that are necessarily labor-intensive (and hence grow slowly) from those with rapid technological progress is a very difficult game, and one we ought hesitate to play. But equally, we oughtn’t forget Baumol’s lesson: in some cases, in some industries, what appears to be fixable slack is in fact simply cost disease. We may ask, how was it that Ancient Greece, with its tiny population, put on so many plays, while today we hustle ourselves to small ballrooms in New York and London? Baumol’s answer, rigorously shown: cost disease. The “opportunity cost” of recruiting a big chorus was low, as those singers would otherwise have been idle or working unproductive fields gathering olives. The difference between Athens and our era is not simply that they were “more supportive of the arts”!

Baumol was incredibly prolific, so these suggestions for further reading are but a taste: An interview by Alan Krueger is well worth the read for anecdotes alone, like the fact that apparently one used to do one’s PhD oral defense “over whiskies and sodas at the Reform Club”. I also love his defense of theory, where if he is very lucky, his initial intuition “turn[s] out to be totally wrong. Because when I turn out to be totally wrong, that’s when the best ideas come out. Because if my intuition was right, it’s almost always going to be simple and straightforward. When my intuition turns out to be wrong, then there is something less obvious to explain.” Every theorist knows this: formalization has this nasty habit of refining our intuition and convincing us our initial thoughts actually contain logical fallacies or rely on special cases! Though known as an applied micro theorist, Baumol also wrote a canonical paper, with Bradford, on optimal taxation: essentially, if you need to raise $x in tax, how should you optimally deviate from marginal cost pricing? The history of thought is nicely diagrammed, and of course this 1970 paper was very quickly followed by the classic work of Diamond and Mirrlees. Baumol wrote extensively on environmental economics, drawing in many of his papers on the role nonconvexities in the social production possibilities frontier play when they are generated by externalities – a simple example of this effect, and the limitations it imposes on Pigouvian taxation, is in the link. More recently, Baumol has been writing on international trade with Ralph Gomory (the legendary mathematician behind a critical theorem in integer programming, and later head of the Sloan Foundation); their main theorems are not terribly shocking to those used to thinking in terms of economies of scale, but the core example in the linked paper is again a great example of how nonconvexities can overturn a lot of our intuition, in the case on comparative advantage. Finally, beyond his writing on the economics of the arts, Baumol proved that there is no area in which he personally had stagnant productivity: an art major in college, he was also a fantastic artist in his own right, picking up computer-generated art while in his 80s and teaching for many years a course on woodworking at Princeton!

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