Methods of Estimation for Models of Markets with Bounded Price Variation

Abstract

[Introduction] There has been a considerable amount of literature on the estimation of models which are in disequilibrium (see Fair and Jaffe [1972], Fair and Kelejian [1974], Amemiya [1974], Maddala and Nelson [1974], Goldfeld and Quandt [1975], Laffont and Garcia [1977], Bowden [1978] etc.). The main feature of these models is that there is a demand function, a supply function, a "Min condition", and (in some models) a price adjustment equation. The "cornerstone" equation in these models is Q1=Min(D1, S,) where: D_t = Quantity demanded at time t ; S_t = Quantity supplied at time t ; Q_t = Quantity transacted at time t. This equation, which says that the short-side of the market always prevails separates the sample points into those belonging to demand and those belonging to supply. One can classify the models into two categories: those with sample separation known and those with sample separation unknown. But, the important point is that the "min" condition implies, under the usual assumptions that the probability of equilibrium is zero for any t. However, there are many practical cases where some of the observations refer to equilibrium points and some to disequilibrium points. This is because trading in many markets is confined to some limits on price and the disequilibrium occurs only when these limits are violated. There are minimum wage laws in labor markets, usury laws in credit markets, and trading limits in commodity markets. In all such cases, the markets are sometimes in equilibrium and sometimes in disequilibrium. The present paper discusses methods of estimation for models of such markets.

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