Three Essays in Microeconometrics

Abstract

Traditional econometric methods can perform poorly in applications. The poor performance is usually due to challenges faced by researchers conducting empirical data analysis, yet overlooked by large sample reasonings that depend on stringent conditions. Such lack of robustness can be detrimental to economic decision making and prescribing policy recommendations. This dissertation consists of three connected chapters on important issues in microeconometric theory, with a particular emphasis on developing robust inference procedures in program evaluation and other microeconomic settings.

The first chapter discusses the implications of small probability weights entering the inverse probability weighting estimator, and proposes an inference procedure that is robust to not only small probability weights but also a wide range of trimming choices. Robustness is achieved by combining resampling techniques with a novel bias correction method. This chapter is based on the working paper “Robust Inference Using Inverse Probability Weight- ing” (Ma and Wang, 2019).

In an important class of two-step semi-parametric models, the second chapter provides estimation and inference procedures that are robust to including high-dimensional covariates in the first-step estimation. Robustness is achieved by the jackknife bias correction, and the bootstrap is employed for statistical inference. This chapter is based on the paper “Two-Step Estimation and Inference with Possibly Many Included Covariates” (Cattaneo, Jansson and Ma, 2018d).

The third chapter develops a non-parametric estimator of probability density functions based on local polynomial techniques. The proposed estimator is easy to implement and is robust to discontinuities in the underlying density – an important concern in empirical research. This chapter is based on the working paper “Simple Local Polynomial Density Estimators” (Cattaneo, Jansson and Ma, 2019b).