Bootstrapping GMM Estimators for Time Series

Atsushi Inoue and Mototsugu Shintani

No 129, Vanderbilt University Department of Economics Working Papers from Vanderbilt University Department of Economics

Abstract: This paper establishes that the bootstrap provides asymptotic refinements for the generalized method of moments estimator of overidentified linear models when autocorrelation structures of moment functions are unknown. When moment functions are uncorrelated after finite lags, Hall and Horowitz (1996) showed that errors in the rejection probabilities of the symmetrical t test and the test of overidentifying restrictions based on the bootstrap are O(T-1). In general, however, such a parametric rate cannot be obtained with the heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimator since it converges at a nonparametric rate that is slower than T-1/2. By taking into account the HAC covariance matrix estimator in the Edgeworth expansion, we show that the bootstrap provides asymptotic refinements when kernels whose characteristic exponent is greater than two are used. Moreover, we find that the order of the bootstrap approximation error can be made arbitrarily close to o(T-1) provided moment conditions are satisfied. The bootstrap approximation thus improves upon the first-order asymptotic approximation even when there is a general autocorrelation. A Monte Carlo experiment shows that the bootstrap improves the accuracy of inference on regression parameters in small samples. We apply our bootstrap method to inference about the parameters in the monetary policy reaction function.

Keywords: Asymptotic refinements; block bootstrap; dependent data; Edgeworth expansions; instrumental variables (search for similar items in EconPapers)
JEL-codes: C12 C22 C32 (search for similar items in EconPapers)
Date: 2001-12, Revised 2003-08
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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http://www.accessecon.com/pubs/VUECON/vu01-w29R.pdf Revised version, 2003 (application/pdf)

Related works:
Journal Article: Bootstrapping GMM estimators for time series (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:van:wpaper:0129

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