Essays On Non Parametric And High Dimensional Econometrics
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Essays on Nonparametric and High-Dimensional Econometrics
This dissertation studies questions related to identification, estimation, and specification testing of nonparametric and high-dimensional econometric models. The thesis is composed by two chapters. In Chapter 1, I propose specification tests for two formally distinct but related classes of econometric models: (1) semiparametric conditional moment restriction models dependent on conditional expectation functions, and (2) a class of high-dimensional unconditional moment restriction models dependent on high-dimensional best linear predictors. These classes may be motivated by economic models in which agents make choices under uncertainty and therefore have to predict payoff-relevant variables such as the behavior of other agents. The proposed tests are shown to be both asymptotically correctly sized and consistent. Moreover, I establish a bound on the rate of local alternatives for which the test for high-dimensional unconditional moment restriction models is consistent. These results allow researchers to test the specification of their models without introducing additional parametric, typically ad hoc, assumptions on expectations. In Chapter 2, I show that it is possible to identify and estimate a generalized panel regression model (GPRM) without imposing any parametric structure on (1) the function of observable explanatory variables, (2) the systematic function through which the function of observable explanatory variables, fixed effect, and disturbance term generate the outcome variable, or (3) the distribution of unobservables. I proceed with estimation using a series maximum rank correlation estimator (SMRCE) of the function of observable explanatory variables and provide conditions under which L2-consistency is achieved. I also provide conditions under which both L2 and uniform convergence rates of the SMRCE may be derived.
Essays in Honor of Cheng Hsiao
Author: Dek Terrell
language: en
Publisher: Emerald Group Publishing
Release Date: 2020-04-15
Including contributions spanning a variety of theoretical and applied topics in econometrics, this volume of Advances in Econometrics is published in honour of Cheng Hsiao.
Essays on Non-parametric and High-dimensional Econometrics
Chapter 1 studies the instrument validity for local average treatment effects. we provide a testable implication for instrument validity in the local average treatment effect (LATE) framework with multivalued treatments. Based on this testable implication, we construct a nonparametric test of instrument validity in the multivalued treatment LATE framework. The test is asymptotically consistent. The size of the test can be promoted to the nominal significance level over much of the null, indicating a good power property. Simulation evidence is provided to show the good performance of the test in finite samples. Chapter 2 constructs improved nonparametric bootstrap tests of Lorenz dominance based on preliminary estimation of a contact set. Our tests achieve the nominal rejection rate asymptotically on the boundary of the null; that is, when Lorenz dominance is satisfied, and the Lorenz curves coincide on some interval. Numerical simulations indicate that our tests enjoy substantially improved power compared to existing procedures at relevant sample sizes. Chapter 3 proposes a sieve focused GMM (SFGMM) estimator for general high-dimensional semiparametric conditional moment models in the presence of endogeneity. Under certain conditions, the SFGMM estimator has oracle consistency properties and converges at a desirable rate. We then establish the asymptotic normality of the plug-in SFGMM estimator for possibly irregular functionals. Simulation evidence illustrates the performance of the proposed estimator.