Solving for Market Equilibrium using Random Coefficient Random Utility Models

In this paper we develop a likelihood based approach for estimating the joint equilibrium parameter distribution in random coefficient-random utility models. Under this demand specification and a profit maximizing supply specification, the equilibrium distribution of prices and quantities has an intractable likelihood function that cannot be directly analyzed. We solve this problem by adding a small, stochastic error to our demand and pricing equations. We then simulate the equilibrium parameter distributions using Markov Chain Monte Carlo simulation on this complex, nonlinear model. We show how to incorporate unobserved quality characteristics via instrumental variables and estimate a market equilibrium model for the U.S. automobile market. We compare estimation results and corresponding elasticities of our joint system to those from an instrumental-variables estimation of a logit specification and those of a random-coefficient random utility specification of demand only. The joint system provides significantly better estimation results both in terms of parameter values and in terms of substitution patterns. We conclude by discussing methodological extensions to include demographic information that has proven beneficial in other random coefficient applications.