The Empirical Likelihood MPEC Approach to Demand Estimation

The family of Generalized Empirical Likelihood (GEL) estimators provide a number of potential advantages relative to Generalized Method of Moments (GMM) estimators. While it is well known these estimators share an asymptotic distribution, the GEL estimators may perform better in finite sample, particularly in the case of many weak instruments. A relatively new literature has documented that finite-sample bias in the demand estimation problem of Berry, Levinsohn, and Pakes (1995) is often large, especially in the absence of exogenous cost shifting instruments. This paper provides a formulation for a computationally tractable GEL estimator based on the MPEC method of Su and Judd (2012) and adapts it to the BLP problem. When compared to GMM, the GEL estimator performs substantially better, reducing the bias by as much as 90%. Furthermore, it is possible to use analytic bias correction to reduce the bias even more and obtain accurate estimates with relatively small numbers of markets