Econometrics
Applied Econometrics
Macroeconomics

Econometrics
Applied Econometrics
Statistics
Macroeconomics

May 1998 (Oral) Econometrics and Macroeconomics
Aug 1997 (Written) Microeconomic and Macroeconomic Theory

Econometric Analysis of Bootstrap Performance

Professor Donald W. K. Andrews
Professor Peter C. B. Phillips
Professor Donald Brown

May 2003

M. Phil., Yale University, 1999
M.A., Yale University, 1997
M.A., Seoul National University, 1996
B.A., Seoul National University, 1994

Yale University Fellowship, 1997-2000
Scholarship of Honors, Seoul National University, 1994-1995
Graduation cum laude, Seoul National University, 1994

Teaching Assistant, Econometrics I (Graduate course), Yale University, Spring 2002
Teaching Assistant, Introduction to Econometrics and Data Analysis (Undergraduate Course), Yale University, Fall 2001, Fall 2000, Fall 1999
Teaching Assistant, Econometrics III (Graduate course), Yale University, Spring 2000
Teaching Assistant, Macroeconomics (Undergraduate course), Yale University, Spring 1999

Research Assistant, Professor Donald W. K. Andrews, 1999

"Higher-Order Improvements of the Restricted Parametric Bootstrap for Tests," Yale University, 2002, mimeographed.

"Higher-Order Improvements of Block Bootstraps for LM tests Based on Extremum Estimators, 2001, mimeographed.

This dissertation analyzes higher-order properties of parametric and non-parametric bootstrap methods for testing hypotheses. With advances in computer technology, various bootstrap methods have been receiving attention in econometric analysis and applications. The foremost attraction of bootstrap methods in testing hypotheses and confidence interval construction is its capability for achieving higher-order improvements over the standard procedures based on first-order asymptotics. These improvements are justified by the analytical tools of Edgeworth expansions.

While recent developments in Edgeworth expansion theory, especially for sums of weakly dependent time series, have broadened the horizon for bootstrap methods in econometric analysis, most existing studies have been devoted to the non-parametric iid and block bootstraps. Even for the non-parametric bootstrap, theory has not been developed to cover some of the widely adopted testing procedures such as LM tests of nonlinear restrictions. The central goal of this dissertation is to widen those areas of econometric analysis in which bootstrap methods are readily applicable and to include some of the testing procedures for which higher-order improvements of bootstrap methods are currently unavailable. The goal is pursued in two directions; implementation of bootstrap methods for LM tests of nonlinear restrictions and higher-order improvements from the restricted parametric bootstrap in comparison with those from the unrestricted parametric and non-parametric bootstrap.

The first chapter of the dissertation studies the non-parametric iid and block bootstraps for LM tests, based on extremum estimators. Compared with Wald tests of nonlinear restrictions, LM tests are in many cases preferable, due to their use of restricted estimators that are often easier to compute. The main issues include constructing a correctly recentered bootstrap LM statistic so that its conditional distribution resembles the null non-bootstrap distribution of the test statistic, and making a modification to the correction factor in the bootstrap test statistic to adjust the discrepancy in its covariance term due to block bootstrapping the resample. The results obtained show that the (non-parametric) block bootstrap for LM tests achieves higher-order improvements that are comparable to previous asymptotic improvement results for Wald tests (Hall and Horowitz (1996) and Andrews (2002)). Simulations in the chapter show that the block bootstrap for Wald and LM tests yields asymptotic improvements and tends to have smaller finite sample rejection probabilities compared with standard non-bootstrap tests.

The second chapter is devoted to the restricted parametric bootstrap for percentile-t tests, Wald tests, and LM tests. The results for the unrestricted parametric bootstrap are established in Andrews (2001), but without results for LM tests. The main idea is to take full advantage of the parametric model and the null hypothesis in use. This is done by utilizing the asymptotic orthogonality between the (aymptotically) efficient estimator and an inefficient but consistent estimator, as was first suggested in the bootstrap context by Davidson and McKinnon (1999). By establishing Edgeworth expansions uniformly in a compact subset of the parameter space and by adopting the approach of Hall (1988, 1992), it is shown that the restricted parametric bootstrap tests obtain the same higher-order improvements for dependent observations as the improvements established for the unrestricted parametric and non-parametric bootstrap for iid observations. This contrasts with the asymptotic improvement results for the (non-parametric) block bootstrap. It is also shown that the asymptotic improvements of the restricted parametric bootstrap are even greater for one-sided and equal-tailed percentile t tests than the improvements of the unrestricted parametric and non-parametric bootstrap for iid observations. Particularly for equal-tailed tests, this means that asymptotic improvements from the bootstrap are now available. In addition, the results cover Wald tests and LM tests with sharper bounds on the errors in rejection probabilities than were previously available for dependent observations.