Robust Fixed-b Inference in the Presence of Time-Varying Volatility

Abstract

Time-varying volatility arises in many macroeconomic and financial applications. While “fixed-$b$” arguments provide refinements in the use of estimators for the asymptotic variance of GMM estimators, the resulting fixed-$b$ distributions of test statistics are not pivotal under time-varying volatility. Three approaches to robustify inference are investigated: (i) wild bootstrapping, (ii) time transformations and (iii) selection of test statistics and critical values according to the outcome of a pretest for heteroskedasticity. Simulations quantify the distortions from using the original fixed-$b$ approach and compare the effectiveness of the proposed corrections. Overall, the wild bootstrap is to be recommended. An empirical application to the Fama & French five factor model illustrates the relevance of the procedures.