Essays on estimation and inference in semiparametric models

This dissertation can be divided in two parts. The first part (Chap. 1) concerns estimation and inference in partially identified semiparametric models, and the second part (Chap. 2 & 3) focus on data-driven methods for estimation and testing of point identified models. In Chapter 1, I investigate a specific partial identification structure in the semiparametric moment equation models, that is, the parameter of interest becomes identified when fixing the nuisance parameters. Such structure enables us to transform the nonstandard problems to standard ones. Uniform weak convergence of the set estimates are established and are in turn used to develop set inference and hypothesis tests of interest. A practically convenient multiplier-type bootstrap is proposed to approximate the asymptotic distribution. I also extend the classical over-identification test to the semiparametric partially identified setting, and use this test to construct confidence region for the true parameter value.;Chapter 2 introduces automatic data-driven tests for the correct specification of a Vector Autoregression (VAR) model. The particular feature of the proposed tests is the automatic selection of the order of the residual serial correlation tested. The proposed tests present several attractive characteristics: simplicity, robustness and high power in finite samples. The tests are simple to implement since the researcher does not need to specify the order of the autocorrelation tested. In addition, the test is robust to the presence of conditional heteroskedasticity of unknown form, and accounts for estimation uncertainty without requiring the computation of inverses of near-to-singularity covariance matrices.;Chapter 3 proposes a simple fully data-driven version of Powell's (2001) two-step semiparametric estimator for the sample selection model. The main feature of the proposal is that the bandwidth used to estimate the infinite-dimensional nuisance parameters is chosen optimally by minimizing the mean squared error of the fitted semiparametric model. We introduce the concept of asymptotic normality, uniform in the bandwidth, and show that the proposed estimator achieves this property for a wide range of bandwidths.