On Nonparametric and Semiparametric Partitioning-Based Methods in Applied Microeconomics

Abstract

This dissertation concerns estimation and inference using partitioning-based least squares estimators in nonparametric and semiparametric models.

Chapter II studies the large sample properties of partitioning-based estimators in a standard nonparametric regression model. First, a general characterization of their leading asymptotic bias is obtained, based on which several bias-corrected estimators are proposed. Second, integrated mean squared error (IMSE) approximations for the point estimator are established for principled tuning parameter selection. Third, pointwise and uniform inference methods are developed with and without bias correction techniques. In particular, the uniform inference results rely on novel uniform distributional approximations for the undersmoothed and robust bias-corrected t-statistic processes. In the univariate case, they require seemingly minimal rate restrictions and improve on the approximation rates known in the literature.

Chapter III examines binscatter, a particular application of partitioning-based methods to semiparametric partial linear models. An array of theoretical and practical results is offered, including principled number of bins selection, confidence intervals and bands, hypothesis tests for parametric and shape restrictions of the regression function, and several other new methods applicable to canonical binscatter and higher-order polynomial, covariate-adjusted, and smoothness-restricted extensions.

Chapter IV concerns the methodology for implementing these results. I first discuss several commonly used basis expansions. Their leading approximation errors are presented, which can be used for tuning parameter selection and bias-corrected inference. Subsequently, I give a more detailed IMSE approximation for the special case of a tensor-product partition. Using these results, I propose two data-driven procedures (rule-of-thumb and direct plug-in) for tuning parameter selection. Finally, an empirical example and simulation evidence are provided.