Date of Award
Doctor of Philosophy (PhD)
high dimensionality, structural changes
Social and Behavioral Sciences
This dissertation consists of three essays on estimating and testing structural changes in high dimensional econometrics models. These essays are based on three working papers joint with Prof. Badi Baltagi and Prof. Chihwa Kao. The first essay considers estimating the date of a single common change in the regression coefficients of a heterogeneous large N and large T panel data model with or without strong cross- sectional dependence. The second essay considers estimating a high dimensional factor model with an unknown number of latent factors and a single common change in the number of factors and/or factor loadings. The third essay considers estimating a high dimensional factor model with an unknown number of latent factors and multiple common changes in the number of factors and/or factor loadings, and also testing procedures to detect the presence and number of structural changes.
The first essay studies the asymptotic properties of the least squares estimator of the common change point in large heterogeneous panel data models under various sets of conditions on the change magnitude and N-T ratio, allowing N and T to go to infinity jointly. Consistency and limiting distribution are established under general conditions. A general Hajek-Renyi inequality is introduced to calculate the order of the expectation of sup-type terms. Both weak and strong cross-sectional dependence are considered. In the former case the least squares estimator is consistent as the number of subjects tends to infinity while in the latter case a two step estimator is proposed and consistency can be recovered once estimated factors are used to control the cross-sectional dependence. The limiting distribution is derived allowing the error process to be serially dependent and heteroskedastic of unknown form, and inference can be made based on the simulated distribution.
The second essay tackles the identification and estimation of a high dimensional factor model with unknown number of latent factors and a single common break in the number of factors and/or factor loadings. Since the factors are unobservable, the change point estimator is based on the second moments of the estimated pseudo factors. This essay shows that the estimation error of the proposed estimator is bounded in probability as N and T go to infinity jointly. This essay also shows that the proposed estimator has a high degree of robustness to misspecification of the number of pseudo factors. With the estimated change point plugged in, consistency of the estimated number of pre and post- break factors and convergence rate of the estimated pre and post-break factor space are then established under fairly general assumptions. Finite sample performance of the proposed estimators is investigated using Monte Carlo experiments.
The third essay considers high dimensional factor models with multiple common structural changes. Based on the second moments of the estimated pseudo factors, both joint and sequential estimation of the change points are considered. The estimation error of both estimators is bounded in probability as the cross-sectional dimension N and the time dimension T go to infinity jointly. The measurement error contained in the estimated pseudo factors has no effect on the asymptotic properties of the estimated change points as N and T go to infinity jointly, and no N-T ratio condition is needed. The estimated change points are plugged in to estimate the number of factors and the factor space in each regime. Although the estimated change points are inconsistent, using them asymptotically has no effect on subsequent estimation. This essay also proposes (i) tests for the null of no change versus the alternative of l changes and (ii) tests for the null of l changes versus the alternative of l + 1 changes. These tests allow us to make inference on the presence and number of structural changes. Simulation results show good performance of the proposed estimation and testing procedures.
Wang, Fa, "Essays on structural changes in high dimensional econometric models" (2016). Dissertations - ALL. 458.