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A Likelihood Approach to Estimating Market Equilibrium Models

Graduate School of Business, Stanford University, Stanford, California 94305-5015.
Kellogg School of Management, Northwestern University, Evanston, Illinois 60208-2001.
draganska_michaela{at}gsb.stanford.edu
d-jain{at}kellogg.northwestern.edu

This paper develops a new likelihood-based method for the simultaneous estimation of structural demand-and-supply models for markets with differentiated products. We specify an individual-level discrete-choice model of demand and derive the supply side assuming manufacturers compete in prices. The proposed estimation method considers price endogeneity through simultaneous estimation of demand and supply, allows for consumer heterogeneity, and incorporates a pricing rule consistent with economic theory.

The basic idea behind the proposed estimation procedure is to simulate prices and choice probabilities by solving for the market equilibrium. By repeating this many times, we obtain an empirical distribution of equilibrium prices and probabilities. The empirical distribution is then smoothed and used in a likelihood procedure to estimate the parameters of the model. The advantage of this method is that it avoids the need to perform a transformation of variables. If the tastes of consumers are independent across market periods, our approach yields maximum likelihood estimates; otherwise, it yields consistent but not fully efficient partial likelihood estimates.

Key Words: price endogeneity; competitive strategy; maximum likelihood
History: Received: April 1, 2002;

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