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Bootstrapping GMM Estimators for Time Series

  • Atsushi Inoue

    ()

    (North Carolina State University)

  • Mototsugu Shintani

    ()

    (Department of Economics, Vanderbilt University)

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
File Function: Revised version, 2003
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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
Contact details of provider: Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

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  1. Kenneth D. West & Whitney K. Newey, 1995. "Automatic Lag Selection in Covariance Matrix Estimation," NBER Technical Working Papers 0144, National Bureau of Economic Research, Inc.
  2. Sílvia Gonçalves & Halbert White, 2002. "Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models," CIRANO Working Papers 2002s-41, CIRANO.
  3. Hall, Alastair R, 1994. "Testing for a Unit Root in Time Series with Pretest Data-Based Model Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 461-70, October.
  4. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  5. John Y. Campbell & Robert J. Shiller, 1989. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," NBER Working Papers 3153, National Bureau of Economic Research, Inc.
  6. Andrews, Donald W.K., 2002. "EQUIVALENCE OF THE HIGHER ORDER ASYMPTOTIC EFFICIENCY OF k-STEP AND EXTREMUM STATISTICS," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1040-1085, October.
  7. 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.
  8. Kenneth D. West, 1986. "Dividend Innovations and Stock Price Volatility," NBER Working Papers 1833, National Bureau of Economic Research, Inc.
  9. Donald W.K. Andrews, 1999. "Higher-Order Improvements of a Computationally Attractive-Step Bootstrap for Extremum Estimators," Cowles Foundation Discussion Papers 1230, Cowles Foundation for Research in Economics, Yale University.
  10. Hahn, Jinyong, 1996. "A Note on Bootstrapping Generalized Method of Moments Estimators," Econometric Theory, Cambridge University Press, vol. 12(01), pages 187-197, March.
  11. 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.
  12. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 115(1), pages 147-180.
  13. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  14. Runkle, David E., 1991. "Liquidity constraints and the permanent-income hypothesis : Evidence from panel data," Journal of Monetary Economics, Elsevier, vol. 27(1), pages 73-98, February.
  15. Rothenberg, Thomas J., 1984. "Approximating the distributions of econometric estimators and test statistics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 15, pages 881-935 Elsevier.
  16. Tauchen, George, 1986. "Statistical Properties of Generalized Method-of-Moments Estimators of Structural Parameters Obtained from Financial Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(4), pages 397-416, October.
  17. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
  18. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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