Essays in robust estimation and inference in semi- and nonparametric econometrics.

Summary In the introductory chapter, we provide a comparative survey of approaches in econometrics and statistical learning on the issues of estimation and inference in statistics.In the second chapter, we focus on a general class of nonparametric instrumental variable models. We generalize the estimation procedure of Otsu (2011) by adding a regularization term. We prove the convergence of our estimator for the Lebesgue L2 norm.In the third chapter, we show that when the data are not independent and identically distributed (i.i.d.) but simply joint exchangeable, a modified version of the empirical process converges weakly to a Gaussian process under the same conditions as in the i.i.d. case. We obtain a similar result for an adapted version of the empirical bootstrap process. We deduce from our results the asymptotic normality of several nonlinear estimators as well as the validity of the bootstrap-based inference. Finally, we revisit the empirical paper by Santos Silva and Tenreyro (2006).In the fourth chapter, we address the issue of inference for ratios of expectations. We find that when the denominator does not tend too quickly to zero as the number of observations n increases, the nonparametric bootstrap is valid for asymptotic inference. In a second step, we complete an impossibility result of Dufour (1997) by showing that when n is finite, it is possible to construct confidence intervals that are not pathological are certain conditions on the denominator.In the fifth chapter, we present a Stata command that implements the estimators proposed by de Chaisemartin and d'Haultfoeuille (2018) to measure several types of treatment effects that are widely studied in practice.