Identification and Asymptotic Approximations: Three Examples of Progress in Econometric Theory

In empirical economics, the size and quality of datasets and computational power has grown substantially, along with the size and complexity of the econometric models and the population parameters of interest. With more and better data, it is natural to expect to be able to answer more subtle questions about population relationships, and to pay more attention to the consequences of misspecification of the model for the empirical conclusions. Much of the recent work in econometrics has emphasized two themes: The first is the fragility of statistical identification. The other, related theme involves the way economists make large-sample approximations to the distributions of estimators and test statistics. I will discuss how these issues of identification and alternative asymptotic approximations have been studied in three research areas: analysis of linear endogenous regressor models with many and/or weak instruments; nonparametric models with endogenous regressors; and estimation of partially identified parameters. These areas offer good examples of the progress that has been made in econometrics.