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Bootstrapping GMM estimators for time series

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  • Inoue, Atsushi
  • Shintani, Mototsugu

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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Suggested Citation

  • Inoue, Atsushi & Shintani, Mototsugu, 2006. "Bootstrapping GMM estimators for time series," Journal of Econometrics, Elsevier, vol. 133(2), pages 531-555, August.
  • Handle: RePEc:eee:econom:v:133:y:2006:i:2:p:531-555
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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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