The site you are currently reading would violate SOPA and PIPA: I link almost exclusively to ungated copies of work whose copyright has generally been transferred to a journal. Though many journals essentially ignore the fact that authors place copies of their articles on personal websites without the journal’s permission, the fact remains that such articles are being backed up by their authors in violation of the journal’s copyright, absurd as this may be. Beyond simple academic research blogs, huge swathes of fast-growing internet firms from the past 15 years, such as Youtube, would never have appeared in a SOPA/PIPA world.

Until a recent uproar, these bills were sailing through Congress. I recently consulted for a white paper on a similarly wrongheaded bill, the Research Works Act, which would vastly limit your access to new research papers. In doing so, I had to read the records of Congressional hearings on these bills. Aside from a handful of congressmen, the people voting on issues related to invention, science and the internet have very limited knowledge of these issues; this is no surprise, as only four out of 535 congressmen hold a research doctorate, an average age in the Senate of 63, and technology firms have a relatively tiny lobbying presence compared to old media companies. The major movie and recording industry lobbyist groups also form one of Washington’s most notorious revolving doors: the MPAA head is former senator Chris Dodd, and the federal judge at the venue of choice for suits related to the music industry is herself a former RIAA lobbyist.

Economists and academics really need to make themselves heard on these bills and on other bills related to innovation. If nearly every major politician country frequently said that “we all agree that we need to ensure steelworkers get paid” with little concern for the broader welfare effects of tariffs, economists would surely bring up the vast amount of research that exists on Ricardian advantage, trade wars, the tradeoffs inherent in protectionism, etc. Yet politicians also say “we all agree that we need to ensure content creators get paid” even though, from the perspective of social welfare, that is completely unimportant. As social planners dealing with innovation, we need to worry about policies that both limit the creation of new content and inventions while simultaneously not expanding consumption of existing products enough to overcome that first decrease. It is striking that in Congressional testimony on copyright issues, no one arguing for SOPA and PIPA even pretends to argue that access to film and music and books and newspapers has decreased – it is clearly a Golden Age for access – or that the amount of new film or music or text has decreased. Given those facts, even though content creators, and particularly middlemen, may find it more difficult to extract rents from their work, as economists we realize that this “era of piracy” has probably led to massive social welfare gains. This is a perspective that, when economists have made it in the past, has been largely ignored, but nonetheless it is one we need to continue to make.

Two final things. First, I note, if only to myself, the following quote from Peirce to be used in a future research paper of my own: “Economical science is particularly profitable to science; and that of all the branches of economy, the economy of research is the most profitable.” Second, check out where this essay was published: the annual report of the U.S. government Coast Survey of 1879! No wonder it has been overlooked. If you know anything of the biography of Peirce, though, there is not much surprising in this odd location. Peirce was supposedly such a nut that, despite obvious brilliance, he was repeatedly blackballed from academic appointments by future colleagues around the country!

Wible claims, and I also know of no earlier such work, that this Peirce essay is the earlier mathematical work on the theory of invention. And given the intellectual history, this seems almost certain to be so. The essay was written right at the cusp of the marginal revolution and mathematical political economy, Peirce is known to have been familiar with the few scraps of earlier mathematical economics like Cournot’s famous 1838 essay, and Peirce is the father of a philosophical school for which selecting the best line of research to examine in order to learn inductively was a pressing concern. If you’ve ever read economics articles from the middle of the 19th century, this one will shock you: in style, I think it is essentially publishable today. It looks like 21st century economics. There are marginal tradeoffs. There is social science done by mathematical manipulation of heavily abstracted concepts. There is even a Marshallian diagram! It’s phenomenal. Since this looks like modern economics, let’s discuss it like modern economics; what does Peirce’s theory say?

As he introduced it, “I considered this problem. Somebody furnished a fund to be expended upon research without restrictions. What sort of researches should it be expended upon?” Essentially, there are some scientific problems which we understand only vaguely; you may think of this purely qualitatively, or as meaning something is measured to within some confidence interval. There are diminishing returns to science, so that while decreasing error can be done at linear cost, the utility gained from such reduction is concave (the inverse is quadratic in Peirce’s formulation). There is a total fixed research budget. What should be worked on first? Note that this paper was first written in 1876: there is no stochastic learning or any such thing, as the mathematics to discuss bandits and related objects was not yet developed. Learning is purely deterministic here.

Solving that constrained maximization problem gives the now-familiar, but then-nonexistent, result that we should compare ratios of MU/MC across different projects. Peirce called this ratio of marginal utility to marginal cost the “economic urgency” of a given line of research. He notes that, given that functional form assumptions, new research fields where we know very little are particularly worthwhile investments: the gains from increasing our knowledge are exponential in ignorance, whereas the cost is linear. As an example, an early chemist with simple vials is able to provide results with more social utility than a thousand chemists working in Peirce’s day with all sorts of modern equipment. Peirce also derives a result concerning sampling which is a bit opaque for modern readers given that it is couched in terms of “accidental probable error” rather than confidence intervals; nonetheless, it is very Wald-esque in that it explicitly argues that optimal sample size in experiments depends crucially on the budget, the costs of sampling and the utility of learning inferences from that sampling. Such considerations are absolutely ignored in a lot of research design even today!

http://books.google.com/books?id=ux79s_IhpFYC (Both Peirce’s original essay and Wible’s commentary appear in “Science Bought and Sold,” edited by Mirowski and Sent. The Google Books Preview is generous enough here for you to read the entirety of both essays; I do not see any other ungated copies of either online.)

Hume is first and foremost a philosopher and historian, but his social science is not unknown to us economists. Many economists, I imagine, know Hume as the guy who first wrote down the quantity theory of money (more on this shortly). A smaller number, though I hope a nontrivial number, also know Hume as Adam Smith’s best friend, with obvious influence on the Theory of Moral Sentiments and less obvious but still extant influence on The Wealth of Nations. Given Hume’s massive standing in philosophy – was Hume the Paul Samuelson of philosophers, or Samuelson the Hume of economists? – I want to jot down a few notes on particularly interesting comments of his. Readers particularly interested in this topic who have already read the Treatise and the Enquiry might want to pick up the newest edition of Rotwein’s collection of Hume essays on economics, as without such a collection his purely economic content is rather scattered.

First, on money. Hume claims prices are determined by the ratio of circulating currency to the number of goods, and lays out what we now call the specie-flow mechanism: an inflow of specie causes domestic prices to rise, causing imports to become more attractive, causing specie to flow out. He doesn’t say so explicitly, as far as I can tell, but this is basically a long-run equilibrium concept. The problem with Hume as monetarist, as pointed out by basically everyone who has ever written on this topic, is that Hume also has passages where he notes that during a monetary expansion, people are (not become! Remember Hume on causality!) more industrious, increasing the national product. Arguments that Hume is basically modern – money is neutral in the long run and not the short – are not terribly convincing.

Better, perhaps, to note that Hume has a strange understanding of the role of money creation. On many questions of moral behavior, Hume stresses the role of conventions and particularly the role of government in establishing conventions. He therefore treats different types of monetary expansions differently. An exogenous increase in the monetary supply, from a silver discovery or other temporary inflow of specie, does not affect conventions about the worth of money, but an increase in money supply deriving from excess credit creation by banks and sovereigns can affect conventions, hence affecting moral behavior, hence affecting the real economy. The above interpretation of Hume’s monetary writings is by no means universal, but I think, at least, it is an important framework to keep in the back of the mind.

Concerning methodology of social science, Hume makes one particularly striking claim: the human sciences are in a sense easier than natural sciences. A more common argument – due to Comte, perhaps, though my memory fails me – is that physics is simpler than chemistry, which is simpler than biology, then again simpler than psychology, and then social sciences, because each builds upon the other. I understand how particles work, hence understand physics, but I need to know how they interact to understand chemistry, how molecules affect lifeforms for biology, how the brain operates to understand psychology, and how brains and bodies interact with each other and history to understand social science. Hume flips this around entirely. He is an empiricist, and notes that to the extent we know anything, it is through our perceptions, and our own accounts as well as those of other humans are biased and distorted. To interpret perceptions of the natural world, we must first generalize about the human mind: “the science of man is the only solid foundation.” Concerning the social world, we are able to observe the actions and accounts of many people during our lives, so if we are to use induction (and this is Hume, so of course we are wary here), we have many examples from which to draw. Interesting.

https://dspace.stir.ac.uk/bitstream/1893/3167/1/2009%20Hume%20and%20Modern%20Economics.pdf (Working paper – final version in Capitalism and Society, 2009)

Moser, Voena and Waldinger: “German-Jewish Emigres and U.S. Invention.”
A ton of German-Jewish scientists moved overseas, including to the U.S. in the 30s and 40s: the Manhattan Project gang is a famous example. We often think of research worker productivity as involving important spillovers. Are high-knowledge immigrants good for domestic scientists? From a sample of 500 or so German-Jewish chemists, the authors collect data on future patents given to those who stayed in Germany (losing their academic position, of course), who moved to the U.S., and who moved to another country like the U.K. They note the subfield of each of those patents – 166 subfields in total based on patent classification – and examine the 2 million US patents in those fields. The scientists who moved to the US were not that productive ex-ante, since super high-profile Jewish scientists tended to receive university placements in the UK after leaving Germany, so selection is not a huge concern. Over the next few decades, subfields with emigres to the US see at least a 30 percent increase in patents by domestic American inventors, while there is no change in subfields where emigres did not come to the US. This holds even controlling for the attractiveness of a given area by, for example, including patents in a given class by foreigners as an regressor. Interesting indeed, and carefully done, but I can’t help but feel the numbers are just too big to be plausible. I just can’t believe that a single, average-quality, young, German-Jewish chemist can lead to an annual increase of 50 patents by domestic workers in the subfield he works in. That’s much bigger than the biggest agglomeration spillovers I have ever seen. I definitely look forward to the promised followup where the exact method by which this huge spillover takes place is investigated further. It’s also less clear to me how much we learn about modern day immigration: the German-Jewish immigrants brought over chemistry techniques that simply weren’t known by any US scientists, whereas a modern scientist from China, say, may be an expert in some area but such knowledge is probably more substitutable with current domestic worker skills.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1910247 (December 2011 working paper)

Myerson, AAEA Schultz Memorial Lecture
Roger Myerson, ur-theorist, somehow was invited to give the Agricultural and Applied Economics Association lecture this year. Recently, he has been particularly interested in questions of political theory. Myerson is incredibly bright and has, I think, a much better grasp of history than many other theorists; surely, this lecture must have been the only one at AEA to cite Xenophon’s Education of Cyrus! The basic point of the lecture, which built on a number of his recent papers, was the following: are elections enough for democratic accountability? The answer is no, and for a simple reason. Voters will only punish the corrupt to the extent that they believe the next potential president will be less corrupt. But how are they to know who will steal and who will not? Myerson argues that strong local governments – federalism, basically – are an important method for potential national leaders to show off their quality and to build reputation. There was a lot of further talk about constitutional structure, local elite buy-in and other related topics, but the above equilibrium argument was federalism was new to me and certainly relevant to Pakistan (where strong local governments have over and over been shut down by the central leaders once they were growing strong enough to be a proving ground for future leaders), Afghanistan (with a strong central leader but little provincial control), Burma (embarking on glasnost and perestroika in a state that ought be much more multipolar) and many others.

http://home.uchicago.edu/rmyerson/research/lahore.pdf (Lecture notes not available online, but here is a recent article of Myerson’s on a similar topic)

Aghion, Farhi and Kharoubbi: “Monetary Policy, Liquidity and Growth”
We often separate questions of monetary policy which affects the business cycle from questions of long-term growth in our models. Aghion and his coauthors give a simple story where it matters: liquidity constrained companies facing an accommodative central bank need to purchase fewer liquidity-granting assets because when future credit crunches will be moderated. This gives them more money to invest. This allows their sector to grow quicker. To test whether countries with strongly countercyclical policies allow quicker growth in liquidity constrained industries, they try to get around reverse causality using the same technique as in Zingales-Rajan: country-wide monetary policy versus sectoral growth, using an international dataset. The theoretical story above can absolutely be seen in the data, and in a manner robust to a number of different specifications. I’d like to see some more comment on the politics here: if sectoral growth is heterogeneously affected by monetary policy, different sectors surely will lobby differently. Also, I highly recommend seeing Phillipe Aghion present if you get the chance: he is an exhausting – though entertaining! – whirlwind of energy.

http://isites.harvard.edu/fs/docs/icb.topic1003175.files/aghion_112111.pdf (November 2011 working paper)

Chetty, Friedman & Saez: “Using Differences in Knowledge Across Neighborhoods to Estimate the Impact of EITC on Earnings.”
This was definitely the most careful and clever work I saw presented, and it’s no surprise with Raj Chetty’s name on the front page: I take it everyone agrees that if weren’t so young, he would already have his Clark Medal? Chetty and coauthors want to know how tax changes affect behavior. Many older papers look at behavior right after a tax change is enacted, but this is problematic because many people don’t react right away to the tax change, potentially because they don’t know about it right away. So the estimates from looking at the immediate effects will be different from the steady-state impact of a tax change. For instance, does the EITC cause labor supply to increase or decrease among the poor? It would be great if we knew exactly who knew about the tax change and when, since then we can avoid the above problem. This paper is super clever here: they realize that some areas learn about changes before others: perhaps urban areas have denser information networks, or tax preparers and government bureaucrats are more likely to tell you you are eligible, or the local newspaper heavily promotes the policy. Also, lots of people cheat on their taxes, particularly the self-employed since they have no workplace telling the government how much they made. For a given family size, there is an income which maximizes the EITC rebate. It turns out that you can see a huge and obvious number of self-employed people reporting precisely that amount of income – the distribution of income is much smoother for wage earners who are not self-employed. The size of this spike proxies for knowledge about EITC in a community. Chetty showed a bunch of checks here as well: people who move from low information areas to high info areas became much more likely to cheat the next year, tax preparers are probably helping spread tax code information, there is heterogeneity even at the state level, etc. With this measure of knowledge about the tax code in hand, we can counterfactually investigate labor responses of the policy once the whole country learns about the tax code change, a process that took over a decade for the EITC. Interesting technique – and it also doesn’t hurt that Chetty and coauthors were given access to over a decade of every American tax return!
http://obs.rc.fas.harvard.edu/chetty/eitc_nbhd_slides.pdf (Slides)

Henry and Ponce consider a very simple example first. Let there be three firms, one of whom has invented something. If I sell it myself, I earn p1 in profits each year. If two of us are selling, we earn p2<.5p1 profits each in the duopoloy. If three of us all sell, we earn p3<.67p2 in triopoly profits. It costs K to reverse engineer, and K<p3, so in the absence of markets for knowledge, everyone imitates immediately, and all earn triopoly profits. This is the standard "if we don't give patent protection, inventions will be imitated" story.

But what if I can sell knowledge that I hold? Think about what happens in the subgame once two firms have the knowledge: since it is worthwhile for firm 3 to reverse engineer, she will do so unless once of us sells her knowledge for less than K. But since she is going to enter whether she is sold knowledge or not, we are all going to earn triopoly profits going forward. So we should both try to sell her the knowledge we have and earn triopoly profts plus the gains from selling the knowledge – but since we both know this, the knowledge will sell to the third firm for 0 since the two firms already holding knowledge will Bertrand compete it away.

What happens, then, when only one firm, the original inventor, holds knowledge? She sets a price for the knowledge equal to exactly K. The two other firms must be playing a mixed strategy as to when to buy the knowledge (or when to pay K and reverse engineer), since if the other firm will buy knowledge at time t, I know I can immediately buy that knowledge epsilon later for 0 given the logic in the last paragraph. That is, both firms want to get knowledge and start earning profits as early as possible, but they also would love to get the knoweldge for free by waiting until the other firm buys it. Therefore, each firm buys the knowledge at a time dependent on a mixed strategy; precisely, they buy according to an exponential distribution that looks basically the same as the solution to your usual war of attrition game (discounting future profits is essential here, of course). Note that the original inventor earns triopoly profits after a random delay before the first entrant, but monopoly profits until that point, and a profit of K at the time the knowledge is first sold; this is much better for the firm than triopoly profits from time 0 onward, the best case for the imitator, as well as the profits earned in the world without markets for selling knowledge.

What if we increase the number of potential imitators? With more imitators, the delay before the first imitator buys knowledge increases; this is because the profit from entering falls from p3 to pN, where N is the number of potential imitators, and because there are a lot more other imitators that I think may enter before me, letting me get knowledge for free. Under some conditions on K, p1, p2, p3 and p4, inventor expected profit in this knowledge sale market may be equal to monopoly profit forever. Note that this secrecy payoff is better for the inventor than even a patent, since patents involve disclosure of knowledge and last only for a limited time. The authors hypothesize that more well-developed markets for licensing knowledge may explain why secrecy has, over time, become more important for IP protection compared to patents.

A simple proof you can read in the original paper notes that the result does not change if it is possible to change the knowledge sales contract such that I can sell knowledge and make it so the recipient cannot then resell: it turns out that we can ignore this since, in equilibrium, the inventing firm will never want to insist on such a condition. The paper also ignores sequential innovation, but hypothesizes that such chains may make the example above more stark, an intuition that seems reasonable to me. Note also that many of the results above hold even when K, the cost of imitating, is very small.

At the very least, following this result, I expect statements in the theory literature along the lines of “in the absence of patent protection, firms are immediately imitated and profits are Bertrand competed away” to disappear. That is a poor way to discuss interesting issues surrounding patents.

econ.sciences-po.fr/sites/default/files/file/ehenry/carlos.pdf (April 2011 working paper – final version in the October 2011 JPE)

Kohlberg and Mertens were writing in the heyday of the equilibrium refinement literature – theirs was one of the last well-known refinements of Nash. Consider constructing a “reasonable set” of equilibria to a game. What properties might you like such a set to have? Best would, of course, be to define a set of axioms on “reasonableness” then show what this implies about the equilibrium, but the authors says “we do not yet feel ready for such an approach; we think the discussion…will abundantly illustrate the difficulties involved.” More on this point in the last paragraph of this post.

What non-axiomatic properties, then, might you like? Backwards induction is fairly reasonable, as has been discussed ad nauseum in an earlier philosophy and decision theory literature. Admissibility is another good one, also with roots in decision theory: all equilibria in the players’ reasonable sets should be undominated. Three other properties have to do with the game form itself. Existence of all least one equilibrium, surely, is a property we want if we only want to restrict ourselves to “reasonable sets” of potential equilibia. Invariance of equilibria to the game form in the sense of some 1950s authors also seems reasonable: I don’t want to get different reasonable sets simply by changing the way I write down a game tree if such a change has no effect on the normal form of the game (there is a technical qualification here that I ignore); one argument here is that the equilibria of a game should not depend on whether I give instructions to a computer on how I should play in every situation before the game begins, or whether I play through the game tree myself. Finally, if I delete a dominated strategy from game G to create game G’, I don’t want any equilibria to disappear from the reasonable set.

Here Kohlberg and Mertens propose their well-known KM stable set. The proofs are of limited interest except to those of you really up on your differential geometry; I assume theorems like “p-bar is homotopic to a homeomorphism” are not of broad interest to readers of this site. In any case, a KM stable set is a closed set of Nash equilibria such that, for any set of completely mixed strategies for all players, if I perturb the strategies of each player by some small delta to that set of completely mixed strategies, the perturbed game has equilibria epsilon close to the the original equilibrium (close in terms of the strategy simplex, as usual). Every game has at least one equilibrium in a KM stable set, but there may be multiple such sets. This definition is hard to work with, of course, but it satisfies all of desired properties except backward induction. Kohlberg and Mertens note in the conclusion that it would be great if someone could make a small modification such that backward induction were also captured (I believe Hillas did this, though I’ve not read his paper)

What is most interesting about this paper is how far afield the refinement literature got itself. I think the problem is evident in the list of non-axioms/properties listed by Kohlberg and Mertens. There are many properties you might think are reasonable for the solution to a game of strategic interaction. Some of them are decision-theoretic (Type 1). Some of them involve robustness to errors of logic, or limited reasoning capacity, or minor mistakes (Type 2). Some of them involve equilibria definitions that can handle problems in the way the game form are written (Type 3), as the invariance property here attempts to do.

Attempting to do all of the above simultaneously is going to be problematic. We ought first agree on a canonical game form, and given the form, ought describe errors explicitly in the game form (Type 2), then deal axiomatically with the decision theoretic issues. Looking back from 2012, I think that Type 2 has been dealt with suitably, and negatively, by papers discussed previously on this site. Essentially, if there are a set of Nash Equilibria, I can make every one of them a strict Nash Equilibria by altering super-high-order knowledge in a way that is fairly uncontroversial once you accept that reasoning with higher-order knowledge may be limited or that people make mistakes in applying such knowledge. That is, all NE would need to be part of any “reasonable set” if we are to leave the world of perfectly rational agents.

I actually think Type 3 robustness is not fully explored, though, which brings us back to Kreps and Scheinkman. I don’t think their conclusion – that the squabble about Cournot and Bertrand can be in some sense solved by suitably changing Bertrand such that information about other agents’ potential production is known when I choose price – is enough. Rather, there is a potential problem with the idea of how Nash Equilibrium treats payoffs, a problem made most clear in games with continuous action spaces where the payoffs depend on a system of variables, some of which can be solved for if we know the others. This is a bit opaque, but I hope to have more to say on that point in the near future.

http://www.dklevine.com/archive/refs4445.pdf (Final Econometrica version – big thumbs up to David Levine for his continuing acts of giving a different finger up to copyright maximalism.)

Lattices are wholly familiar to economists at this stage, but it is worth recapping that they can be formulated in two identical ways: either as a set of elements plus two operations satisfying commutative, associative and absorption laws, which together ensure the set of elements is a partially ordered set (the standard “axiomatic” definition), or else as a set in which each subset has a well-defined infimum and supremum, from which the meet and join operators can be defined and shown to satisfy the laws mentioned above. We use lattices all the time in economic theory: proofs involving preferences, generally a poset, are an obvious example, but also results using monotone comparative statics, among many others. In mathematics more generally, proofs using lattices unify results in a huge number of fields: number theory, projective geometry, abstract algebra and group theory, logic, and many more.

With all these great uses of lattice theory, you might imagine early results proved these important connections between fields, and that the axiomatic definition merely consolidated precisely what was assumed about lattices, ensuring we know the minimum number of things we need to assume. This is not the case at all.

Ernst Schroder, in the late 19th century, noted a mistake in a claim by CS Peirce concerning the axioms of Boolean algebra (algebra with 0 and 1 only). In particular, one of the two distributive laws – say, a+bc=(a+b)(a+c) – turns out to be completely independent from the other standard axioms. In other interesting areas of group theory, Schroder noticed that the distributive axiom was not satisfied, though other axioms of Boolean algebra were. This led him to list what would be the axioms of lattices as something interesting in their own right. That is, work on axiomatizing one area, Boolean algebra, led to an interesting subset of axioms in another area, with the second axiomatization being fundamentally creative.

Dedekind (of the famous cuts), around the same time, also wrote down the axioms for a lattice while considering properties of least common multiples and greatest common divisors in number theory. He listed a set of properties held by lcms and gcds, and noted that distributive laws did not hold for those operations. He then notes a number of interesting other mathematical structures which are described by those properties if taken as axioms: ideals, fields, points in n-dimensional space, etc. Again, this is creativity stemming from axiomatization. Dedekind was unable to find much further use for this line of reasoning in his own field, algebraic number theory, however.

Little was done on lattices until the 1930s; perhaps this is not surprising, as the set theory revolution hit math after the turn of the century, and modern uses of lattices are most common when we deal with ordered sets. Karl Menger (son of the economist, I believe) wrote a common axiomatization of projective and affine geometries, mentioning that only the 6th axiom separates the two, suggesting that further modification of that axiom may suggest interesting new geometries, a creative insight not available without axiomatization. Albert Bennett, unaware of earlier work, rediscovered the axiom of the lattice, and more interestingly listed dozens of novel connections and uses for the idea that are made clear from the axioms. Oystein Ore in the 1930s showed that the axiomatization of a lattice is equivalent to a partial order relation, and showed that it is in a sense as useful a generalization of algebraic structure as you might get. (Interesting for Paul Samuelson hagiographers: the preference relation foundation of utility theory was really cutting edge math in the late 1930s! Mathematical tools to deal with utility in such a modern way literally did not exist before Samuelson’s era.)

I skip many other interesting mathematicians who helped develop the theory, of which much more detail is available in the linked paper. The examples above, Schlimm claims, essentially filter down to three creative purposes served by axiomatics. First, axioms analogize, suggesting the similarity of different domains, leading to a more general set of axioms encompassing those smaller sets, leading to investigation of the resulting larger domain – Aristotle in Analytica Posteriora 1.5 makes precisely this argument. Second, axioms guide the discovery of similar domains that were not, without axiomatization, thought to be similar. Third, axioms suggest modification of an axiom or two, leading to a newly defined domain from the modified axioms which might also be of interest. I can see all three of these creative acts in economic areas like decision theory. Certainly for the theorist working in axiomatic systems, it is worth keeping an open mind for creative, rather than summary, uses of such a tool.

http://axiom.vu.nl/cmsone/SchlimmOnline.pdf (2009 working paper – final version in Synthese 183)

We economists know common knowledge via the mathematical rigor of Aumann, but priority for the idea goes to a series of linguists in the 1960s and to the superfamous philosopher David Lewis and his 1969 book “Conventions.” Even within philosophy, the formal presentation of Aumann has proven more influential. But the economic conception of common knowledge is subject to some serious critiques as a standard model of how we should think about knowledge. One, it is equivalent to an infinite series of epistemic iterations: I know X, know you know that I know X, and so on. Second, and you may know this argument via Monderer and Samet, the standard “common knowledge is created when something is announced publicly” is surely spurious: how do I know that you heard correctly? Perhaps you were daydreaming. Third, Aumann-style common knowledge is totally predicated on deductive reasoning: every agent correctly deduces the effect of every new piece of information on their own knowledge partition. This is asking quite a bit, to say the least. The first objection is not too worrying: any student of game theory knows the self-evident event definition of common knowledge, which implies that epistemic iteration definition. Indeed, you can think of the “I know, know that you know, know you know that I know, etc.” iterations as the consequence of knowing some public event. Paternotte gives the great example of any inductive proof in mathematics: knowing X holds for the first element and X holding for element i implies it holds for i+1 is not terribly cognitively demanding, but knowing those two facts implies knowledge of an infinite string of implications. The second objection, fallibility, has been treated with economists using p-belief: assign a probability distribution to the state space, and talk about having .99-common belief rather than common knowledge. The third, it seems, is less readily handled.

But how did Lewis think of common knowledge? And can we formalize his ideas? What is then represented? This paper is similar to Cubitt and Sugden (2003, Economics and Philosophy), though it strikes me as the more interesting take. Lewis said the following:

It is common knowledge among a population that X iff some state of affairs holds such that
1: Everyone has reason to believe that A holds
2: A indicates to everyone that everyone has reason to believe that A holds, and
3: A indicates to everyone that X.

Note that the Lewisian definition is not susceptible to the three arguments noted above. Agents don’t necessarily believe something, but rather just have reason to do so. They know how each other reason, but the method of reasoning is not necessarily deductive. Let’s try to formalize those conditions in a standard state space world. Let B(p,i)E be the belief operator of agent i: B(.7,John):”It rains today” means John believes with probability .7 that it will rain today. Condition 1 in Lewis looks like claiming that all agents believe with p>.5 that A holds (have a “reason to believe A”). The word “A indicate X” should mean that there is a reasoning function of agent i, f(i), such that if A is believed with p>.5, then so is X (we will need some technical conditions here to ensure the function f(i) is defined uniquely for a given reasoning standard).

What is interesting is that this definition is tightly linked to standard Monderer-Samet common p-belief. For every common p-belief, p>.5, there are a set of parameters for which Lewisian common knowledge exists. For every set of parameters where Lewisian common knowledge exists, there is at least .5-common belief. Thus, though Lewisian common knowledge appears to be not that strict, it in fact is in a strong sense equivalent to common p-belief, and thus implies any of the myriad results published using that simpler concept. What an interesting result! I take this to mean that many common complaints about common knowledge are not that serious at all, and that p-belief, quite standard these days in economics, is much more broadly applicable than I previously believed.

http://www.springerlink.com/content/n81219v23334n610/ (GATED. Philosophy community: you have to do something about the lack of working papers freely accessible! Final version in Synthese 183.2 – if you are a micro theorist, you should definitely be reading this journal, as it is definitely the top journal in philosophy publishing analytic, formal results in theory of knowledge.)

Richter and Streb consider the German machine tool industry in its own early days: 1877 to the 1930s. A quick case study of J.E. Reinecker, a major tool producer, show that firm buying machines from more advanced US firms from 1873 onward, first replicating parts then replicating whole machines. German law at the time did not give patent protection within Germany to foreign inventions not manufactured in Germany. By the late 1800s, Reinecker was creating many novel inventions on its own, applying for patents in both Europe and the US. During World War I, nonmilitary R&D essentially came to a halt in Germany, and the German firms fell behind once again, leading to a decade where imitation of foreign machines once again predominated. When German firms were innovative, the German government assisted them in getting protection overseas: for instance, after 1909, American toolmakers were exempt from the rule that they had to manufacture in Germany, a rule that presumably would lead to more favorable treatment of German patents by US authorities. Further, the extra delay incurred by patent applicants from overseas versus German firms waxed and waned depending on the innovativeness of German firms; at times of imitation, there were long delays for foreign applicants, while in times of novel invention, foreign firms were not treated so harshly.

Using a custom dataset of German tool patents that are “valuable” (renewal fees were paid for at least 10 years), Richter and Streb show a similar pattern across toolmakers as a whole in Germany: imitation early on, then a series of valuable novel patents, then a collapse in WW1 followed by imitation for another few years. Firm level data is not specific enough, except at the level of a case study, to know how important imitation was to the growth of future successful German tool firms, but the evidence presented is at least suggestive of the fact that German firms who imitated (as listed in a complaint by a US industry lobby) produced many of the future valuable patents in their industry.

This paper is just historical evidence, but it does provide a great example of a more general rule: intellectual property rarely follows the same logic as traditional Ricardian trade. There is no particular reason in standard trade theory why IP rules need be harmonized. Indeed, were I (or essentially any economist who has looked at IP) were to advise a third world government, I would absolutely tell them to enforce much weaker IP than that in Europe or the US. Learning by doing matters.

http://eh.net/eha/system/files/Richter.pdf (Aug 2010 Working Paper – final version in most recent issue of the Journal of Economic History)

Mokyr provides what seems to me the most cogent answer. Roughly, the IR is special not only because new techniques were invented – things were being invented continuously throughout history – but because the process of cumulative invention did not peter out. He suggests that there are two types of knowledge, prescriptive and propositional, which tell us how to do something and why that how works. The two types of knowledge feed back onto one another: seeing a machine work gives us reason to search for why, and knowing why a process operates lets us develop new techniques using that process. The Industrial Revolution exploded with greatest force when there was a process for doing scientific research, whose results were accepted as “true”, whose results were communicated to the broader politic, which were then transformed into products by tinkerers and other non-research inventors. Much of Mokyr’s book, especially chapters 2 and 3, provide low-level and heavily-cited evidence for such claims. You should read the whole thing, so the rest of this post is just notes on other arguments I found interesting.

1) Knowledge being “tight” and well-justified helps science become accepted, but such tightness is not necessary for progress. Consider sanitation in the 1800s: cleanliness helped reduce germ-borne illness, especially from the water supply, but the justification for cleanliness campaigns was by and large the now-discredited miasma theory (“sickness is in the air”).

2) Selection of “true” techniques may operate sometimes on firms, but certainly won’t operate on households. Households need to be persuaded that a given fact is true in order to change behavior. Cue Latour and Ziman on socially constructed facts. Beyond households, non-market selection of technology is also prevalent in many other areas since politics shapes market outcomes. For instance, in 2001, the Netherlands got 4% of power from nuclear, versus 56% in next-door Belgium.

3) Useful new technology is often resisted, and not for Mancur Olson style rent-seeking reasons. Law is often xenophobic (Ming and Qing-era China), corporate leaders can be conservative while having market power (Henry Ford did not like radial tires), etc.

4) Sometimes resistance is justified by uncertainty. Consider this amazing anecdote about the engineer Thomas Midgley, from General Motors. In 1921, Midgley invented tetraethyl lead for gasoline, which helped engine performance; of course, it also polluted terribly. In 1928, he invented CFCs, a miracle chemical which also turned out to be awful for the environment. After being stricken by polio, Midgley invented a series of pulleys to help himself get out of bed – well, you know how this ends: the poor guy ended up strangling himself with his own invention by accident!

5) “Caldwell’s Law” says that creative states are only super creative for a short time. This isn’t merely a result of rent-seeking taking over, though. Top-down invention systems like those in Song-era China can be very productive, while political fragmentation may halt invention due to wars and instability (Sweden after 1700, Netherlands after 1580). Rather, certain types of inventions may be more amenable to certain types of institutions, and if institutions are rigid over time, a given state can be super inventive in one era and less so in another. And institutions are not rigid arbitrarily: “Institutions are there for a reason; they were not imposed on poor countries by an evil spirit (p. 283).”

This is a book well worth reading.

http://books.google.com/books?hl=en&lr=&id=alOdfmgXaEoC (Google Books preview – grab the full text from your nearest library!)