Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators

TLDR

Monte Carlo experiments reveal that GMM‑based tests frequently exhibit true rejection rates that deviate substantially from nominal levels when asymptotic critical values are used. The paper establishes conditions under which bootstrap procedures provide asymptotic refinements to the critical values of t‑tests and overidentifying‑restriction tests. For dependent data, the bootstrap must resample blocks and the resulting test‑statistic formulas differ from those applied to the original data. Monte Carlo results show that the bootstrap generally reduces level errors relative to first‑order asymptotic theory and offers an indication of the accuracy of those asymptotic critical values.

Abstract

Monte Carlo experiments have shown that tests based on generalized-method-ofmoments estimators often have true levels that differ greatly from their nominal levels when asymptotic critical values are used. This paper gives conditions under which the bootstrap provides asymptotic refinements to the critical values of t tests and the test of overidentifying restrictions. Particular attention is given to the case of dependent data. It is shown that with such data, the bootstrap must sample blocks of data and that the formulae for the bootstrap versions of test statistics differ from the formulae that apply with the original data. The results of Monte Carlo experiments on the numerical performance of the bootstrap show that it usually reduces the errors in level that occur when critical values based on first-order asymptotic theory are used. The bootstrap also provides an indication of the accuracy of critical values obtained from first-order asymptotic theory.