How Does A System Of Competitive Markets Equilibrate (If At All)?

.Scarf

(From an economics blog)

General equilibrium theory in economics, and asset pricing theory in particular, assumes that markets somehow equilibrate. It is generally little appreciated that economists have no credible (read: scientifically valid) theory to support this claim. The typical textbook description that markets have got to equilibrate is that, if prices are too high, excess supply will push them down, while if prices are too low, there is excess demand, and prices will increase. It is long known that this Walrasian story of equilibration won't do the job. The story is easy and intuitive when there are only two goods or assets (say, money and a bond). But once there are more than two, there exist robust counter-examples of equilibrium convergence. (The picture on this web page depicts a famous one, namely the "Scarf example.")

Fortunately, the Walrasian story is not true. Together with Charles Plott, our group studied price and allocation dynamics in a situation where we knew markets eventually reached the competitive equilibrium. (So, this was a nice case!) What we found was that prices in one market not only reacted to its own excess demand (or supply), but to excess demands (and supplies) in ALL markets. These cross-market effects had never been documented. And they exhibited an interesting feature: there appeared to be a relationship between the direction of reaction of prices in one market to excess demand in another one that could be traced to how the good/asset in the other market affected marginal utility in the first one. This feature makes the markets system stable. The results were published in the Journal of Financial Markets (the article won a best-paper award). A copy can be found here.

We are now working on explanations for these cross-market effects. We published some preliminary findings based on new experiments. In collaboration with Elena Asparouhova and John Ledyard, we have embarked on a dialogue between theory and experiments. We are getting sharper results, so that we hope to soon provide a full theory of equilibration... which at the same time may resolve an old puzzle: why do centralized, anonymous continuous double auctions manage to equilibrate while other "free market" systems (like over-the-counter-like, decentralized markets) have difficulty?

Interestingly for asset price modeling, our equilibration theory makes predictions about the cross-sectional behavior of expected returns similar to those from equilibrium theories like CAPM. As such, economists' hesitance to move away from equilibrium thinking "because otherwise we won't have anything to say" appears to be unfounded.