Likelihood inference for some non-regular econometric models

Victor Chernozhukov

In this paper we study inference for a conditional model with a jump in the conditional density, where the location and size of the jump are described by regression lines. This interesting structure is shared by several structural econometric models. Two prominent examples are the standard auction model where density jumps from zero to a positive value, and the equilibrium job search model, where the density jumps from one level to another, inducing kinks in the cumulative distribution function. This paper develops the asymptotic inference theory for likelihood based estimators of these models - the Bayes and maximum likelihood estimators. Bayes and ML estimators are useful classical procedures. While MLE is transformation invariant, Bayes estimators offer some theoretic and computational advantages. They also have desirable efficiency properties. We characterize the limit likelihood...