Comment on ‘Large stock price changes: volume or liquidity?’, by Weber and Rosenow

Supply and demand is one of the central concepts in economics. In my introductory economics course the notion that the price was the point where the supply and demand curves met was presented more or less as a fact. When queried as to how the price ever got there the professor had no good answer. He admitted that it might not arrive there instantly, but could not say anything about the time scale for this to happen. He could produce neither convincing empirical evidence nor theoretical arguments that it had to do so. I concluded that economics was speculation misleadingly presented as science and quit attending the class. Needless to say, I did not do very well in the course. I now know that understanding how prices actually come to equilibrium is a long-standing problem, which goes under the name of tatonnement. The state of the art from a theoretical point of view is summarized in Franklin Fisher’s 1983 book Disequilibrium Foundations of Equilibrium Economics. A perusal of this book makes the problem clear: in order to give an account of how prices might or might not reach equilibrium, it is necessary to tackle the difficult job of modelling how the market actually functions, which involves introducing strong and very specific assumptions about market structure and enormously complicates the theoretical problem. The literature on this subject is not very convincing and the resulting theories have little empirical content. I now have more sympathy for my professor. The lack of a convincing theory of tatonnment leaves us without any guarantee that prices actually converge to equilibrium, which is an embarrassing situation for economic theory: if the rate at which prices approach equilibrium is slower than the rate at which the equilibrium shifts, then prices won’t approach equilibrium at all. Even if the rate of tatonnement is faster than that of equilibrium shifts, unless we have a way to estimate their relative time scales we don’t know whether to expect prices to deviate from their equilibrium values by one percent or a factor of ten. Because it is impossible to know the correct equilibrium price, from an empirical point of view so far these matters have proven to be difficult to test. If we accept that the limit order book is the true representative of supply and demand, then transaction prices produced in a continuous double auction are by definition clearing prices. Of course the limit order book typically does not represent all the supply and demand in the market, but only what is revealed at a particular instant in time—see the discussion in the next to last paragraph of this comment. However, even if we accept that the limit order book represents everything, the view presented by Weber and Rosenow is still qualitatively different than that presented in a typical introductory class. In particular, they show that the depth of the limit order book exhibits large variations, which are associated with liquidity, and are very important in price formation. Although the role of liquidity versus volume in price formation is usually discussed as a market microstructure problem, the distinction exists even in the standard market clearing framework. Let qð pÞ 1⁄4 P i qi be the aggregate demand at price p, where qi is the demand of agent i. Assume that dq=dp < 0. Suppose only one agent alters her demand at a time, by an amount q, while everyone else holds their demand constant. The new market clearing condition is qð p0Þ þ q 1⁄4 qð pÞ. Let p 1⁄4 p0 p be the change in the clearing price. Under the assumption that q is differentiable and p is small, *Email: jdf@santafe.edu