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Bootstrapping GMM Estimators for Time Series

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  • Atsushi Inoue

    ()
    (North Carolina State University)

  • Mototsugu Shintani

    ()
    (Department of Economics, Vanderbilt University)

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.

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File URL: http://www.accessecon.com/pubs/VUECON/vu01-w29R.pdf
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Bibliographic Info

Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0129.

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Date of creation: Dec 2001
Date of revision: Aug 2003
Handle: RePEc:van:wpaper:0129

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Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

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Keywords: Asymptotic refinements; block bootstrap; dependent data; Edgeworth expansions; instrumental variables;

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  1. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
  2. Lahiri, Soumendra Nath, 1996. "On Edgeworth Expansion and Moving Block Bootstrap for StudentizedM-Estimators in Multiple Linear Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 42-59, January.
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  16. Donald W.K. Andrews, 2000. "Equivalence of the Higher-order Asymptotic Efficiency of k-step and Extremum Statistics," Cowles Foundation Discussion Papers 1269, Cowles Foundation for Research in Economics, Yale University.
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