A Beautiful Theory Falls to Ugly Data

My latest paper, A Test of the Coase Conjecture Using Prices of Electronic Books, with the excellent Tim Groseclose, has just been published. The Coase Conjecture is another one of Coase’s little ideas — the original paper is six pages — that has spawned hundreds of follow-up papers and thousands of citations.

The idea is simple. A monopolist of a durable good has a time-inconsistency problem. Set the monopoly price in period 1 and he will be tempted in period 2 to cut the price and mop up the customers whose valuations sit between the period-1 price and MC. But the same logic applies in period 2, and again in period 3, and so on — eventually the price unravels to MC. Consumers see this coming, the monopolist knows the consumers see it coming, and so the monopolist cuts price to MC in period 1. And since a “period” is just the interval between price changes, the whole unraveling happens — in Coase’s phrase — “in the twinkling of an eye.”

The theorists, most notably Gul, Sonnenschein and Wilson and Fudenberg, Levine and Tirole, formalized Coase’s insight and showed that under quite general conditions the logic goes through. Which is rather surprising, since, as Tim and I point out, Coase’s conjecture implies that many patents and copyrights are essentially worthless — a prediction wildly at variance with the facts. Other theorists, including Stokey, Ausubel and Deneckere, and Board and Pycia, have offered variants under which the Coase outcome does and does not obtain.

For all this theory, there have been almost no direct tests of the Coase Conjecture apart from a handful of lab experiments. Ours is one of the first papers to take the conjecture to the real world. We look at e-books, an unusually clean setting: digital goods are durable, marginal costs are low, resale is limited, and prices can be changed quickly. Using the prices of e-books that are in the public domain as a proxy for marginal cost, we ask: (a) do prices rapidly fall to MC, and (b) does the market clear in the first period? The answer to both is no. E-book prices begin well above MC, sales continue over many periods, and prices don’t even decline monotonically.

We reject the Coase Conjecture decisively.

The paper has an interesting history. The theorists (or the referees we guessed were theorists) praised the paper for taking the theory seriously but inevitably had a fillip to offer, distinguishing the world of pure theory from empirical tests. The empiricists, on the other hand, said our tests were too simple since no one takes the theory that seriously. It’s good to see the paper find a home!

We reject the Coase Conjecture decisively, but it remains to say why. We can rule out some explanations — it’s not rising MC, and it’s not the finiteness of buyers (which can support a perfectly price-discriminating Pac-Man equilibrium).

Two theories remain: 1) sellers can commit not to lower prices, and 2) the outside-options model of Board and Pycia. I prefer the former, my co-author prefers the latter. To me, commitment just isn’t that hard. The standard story is that profits are like cookies on the table and the monopolist can’t resist — but at least the people tempted by cookies get to eat the cookies! The Coase profits are illusory: the monopolist races to MC in period 1 precisely because they know they won’t resist later and as a result they don’t even get a taste of profit! Too clever by half. I say, show some backbone. Firms are *all about* commitment — to workers, consumers, contractors. Why not to a price? My co-author points out, however, that this is more Tabarrok-vibe than carefully laid out theory.

Tim likes the Board and Pycia model which begins with the plausible idea that consumers have outside options — if they don’t buy the book today, they will buy another book, rent the movie, or borrow from the library — and crucially, once they take the outside option, the consumer never returns to the market. You might think outside options would make it *harder* for the firm to set a high price, but Board and Pycia show in a very clever but extended argument that when you carefully work out the full equilibrium the opposite holds: outside options give firms a time-consistent incentive to set and keep a high price. Tim explains the argument further here (see also our paper for an intuitive breakdown).

In any case, the Coase Conjecture — at least as modelled by the theorists — fails in an environment most conducive to it.

A beautiful theory falls to ugly data.