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https://hdl.handle.net/2142/120349
Description
Title
Three essays in econometrics
Author(s)
Chen, Hongqi
Issue Date
2023-04-06
Director of Research (if dissertation) or Advisor (if thesis)
Lee, Ji Hyung
Doctoral Committee Chair(s)
Lee, Ji Hyung
Committee Member(s)
Medeiros, Marcelo Cunha
Shao, Xiaofeng
Chung, EunYi
Department of Study
Economics
Discipline
Economics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
quantile methods
high-dimensional econometrics
time-series, network data
Abstract
This dissertation contains three chapters which focus on quantile methods with different data structures. In the first chapter, we study the theoretical properties of K-step and t-threshold quantile forward regressions in a linear quantile regression model with high-dimensional covariates. The model under our investigation is assumed potentially misspecified and we consider the best sparse approximation using quantile forward regressions. We provide non-asymptotic prediction bounds for both methods, and show asymptotic convergence results and the asymptotic efficacy of K-step quantile forward regression. In our asymptotic framework, we allow the number of covariates and the number of steps to diverge at different rates with the sample size. We demonstrate superior finite sample performance of quantile forward regressions to commonly-used penalization methods in terms of prediction accuracy and variable selection through extensive Monte Carlo simulations. We illustrate the usage of quantile forward regressions by two empirical applications: growth-at-risk forecasting and testing the convergence hypothesis of international economic growth.
The second chapter investigates a variable screening approach to study growth-at-risk (GaR) forecasting with high-dimensional predictors. Unlike the existing studies focusing on a few predictors, we use a high-dimensional Fred-QD dataset that can retain useful information on GaR forecasting. To do this, we refine and extend the quantile partial correlation (QPC) based variable screening method by Ma et al. (2017) so that the method can employ time series data. A set of Monte Carlo simulations confirms the validity of QPC under weak dependence, and the empirical application on variable selection for GaR forecasting illustrates the benefit of the method. Some labor market factors are shown to be particularly useful in predicting GaR.
In the third chapter, we study a robust inference procedure for the linear quantile regression estimator with a dyadic data structure. We investigate the asymptotic distribution of the quantile regression estimator when dependence exists between any pair of dyads with common nodes in a network. We also provide the consistency results for the covariance matrix estimator and show asymptotic distributions for the corresponding t-statistic and Wald statistic under univariate and joint hypothesis testing scenarios. To showcase the effectiveness of our proposed method, we present numerical simulations and an empirical application using international trade data. Our results demonstrate the excellent performance of the robust t-statistic and Wald statistic in quantile regression inference with dyadic data.
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