Three Essays in Inference and Computational Problems in Econometrics

Abstract

This dissertation is organized into three independent chapters. In Chapter 1, I consider the selection of weights for averaging a set of threshold models. Existing model averaging literature primarily focuses on averaging linear models, I consider threshold regression models. The theory I developed in that chapter demonstrates that the proposed jackknife model averaging estimator achieves asymptotic optimality when the set of candidate models are all misspecified threshold models. The simulations study demonstrates that the jackknife model averaging estimator achieves the lowest mean squared error when contrasted against other model selection and model averaging methods. In Chapter 2, I propose a model averaging framework for the synthetic control method of Abadie and Gardeazabal (2003) and Abadie et al. (2010). The proposed estimator serves a twofold purpose. First, it reduces the bias in estimating the weights each member of the donor pool receives. Secondly, it accounts for model uncertainty for the program evaluation estimation. I study two variations of the model, one where model weights are derived by solving a cross-validation quadratic program and another where each candidate model receives equal weights. Next, I show how to apply the placebo study and the conformal inference procedure for both versions of my estimator. With a simulation study, I reveal that the superior performance of the proposed procedure. In Chapter 3, which is co-authored with my advisor Professor Youngki Shin, we provide an exact computation algorithm for the maximum rank correlation estimator using the mixed integer programming (MIP) approach. We construct a new constrained optimization problem by transforming all indicator functions into binary parameters to be estimated and show that the transformation is equivalent to the original problem. Using a modern MIP solver, we apply the proposed method to an empirical example and Monte Carlo simulations. The results show that the proposed algorithm performs better than the existing alternatives.