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Bootstrapping GMM estimators for time series

  • Inoue, Atsushi
  • Shintani, Mototsugu

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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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 133 (2006)
Issue (Month): 2 (August)
Pages: 531-555

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Handle: RePEc:eee:econom:v:133:y:2006:i:2:p:531-555
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. 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.
  2. Clarida, Richard & Galí, Jordi & Gertler, Mark, 1998. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," CEPR Discussion Papers 1908, C.E.P.R. Discussion Papers.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
  8. 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.
  9. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  10. 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.
  11. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  12. 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.
  13. Ng, S. & Perron, P., 1994. "Unit Root Tests ARMA Models with Data Dependent Methods for the Selection of the Truncation Lag," Cahiers de recherche 9423, Universite de Montreal, Departement de sciences economiques.
  14. 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.
  15. 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.
  16. Hahn, Jinyong, 1996. "A Note on Bootstrapping Generalized Method of Moments Estimators," Econometric Theory, Cambridge University Press, vol. 12(01), pages 187-197, March.
  17. Kenneth D. West, 1986. "Dividend Innovations and Stock Price Volatility," NBER Working Papers 1833, National Bureau of Economic Research, Inc.
  18. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  19. repec:cup:etheor:v:12:y:1996:i:1:p:187-97 is not listed on IDEAS
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