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Bootstrapping GMM Estimators for Time Series

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Author Info
Atsushi Inoue () (North Carolina State University)
Mototsugu Shintani () (Department of Economics, Vanderbilt University)

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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.vanderbilt.edu/Econ/wparchive/workpaper/vu01-w29R.pdf
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File Function: Revised version, 2003
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Paper provided by Department of Economics, Vanderbilt University in its series 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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Related research
Keywords: Asymptotic refinements; block bootstrap; dependent data; Edgeworth expansions; instrumental variables;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May. [Downloadable!] (restricted)
    Other versions:
  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
    Other versions:
  3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  4. 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, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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  5. 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. [Downloadable!]
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  6. Kenneth D. West, 1988. "Dividend Innovations and Stock Price Volatility," NBER Working Papers 1833, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  7. repec:cup:etheor:v:12:y:1996:i:1:p:187-97 is not listed on IDEAS
  8. Hahn, Jinyong, 1996. "A Note on Bootstrapping Generalized Method of Moments Estimators," Econometric Theory, Cambridge University Press, vol. 12(01), pages 187-197, March. [Downloadable!]
  9. 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. [Downloadable!] (restricted)
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  10. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules And Macroeconomic Stability: Evidence And Some Theory," The Quarterly Journal of Economics, MIT Press, vol. 115(1), pages 147-180, February. [Downloadable!] (restricted)
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  11. Newey, Whitney K & West, Kenneth D, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Blackwell Publishing, vol. 61(4), pages 631-53, October. [Downloadable!] (restricted)
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  12. 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.
  13. 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.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Javed Iqbal & Robert Brooks & Don U.A. Galagedera, 2008. "Multivariate tests of asset pricing: Simulation evidence from an emerging market," Monash Econometrics and Business Statistics Working Papers 2/08, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  2. Valentina Corradi & Norman R. Swanson, 2003. "Evaluation of Dynamic Stochastic General Equilibrium Models Based on Distributional Comparison of Simulated and Historical Data," Departmental Working Papers 200320, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  3. W. Härdle & J. Horowitz & J.-P. Kreiss, . "Bootstrap Methods For Time Series," Sonderforschungsbereich 373 2001-59, Humboldt Universitaet Berlin.
  4. Valentina Corradi & Norman R. Swanson, 2003. "Bootstrap Conditional Distribution Tests In the Presence of Dynamic Misspecification," Departmental Working Papers 200311, Rutgers University, Department of Economics. [Downloadable!]
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  5. Diana N. Weymark & Mototsugu Shintani, 2004. "Measuring Inflation Pressure and Monetary Policy Response: A General Approach Applied to US Data 1966 - 2001," Working Papers 0424, Department of Economics, Vanderbilt University. [Downloadable!]
  6. Valentina Corradi & Norman R. Swanson, 2003. "Bootstrap Specification Tests for Diffusion Processes," Departmental Working Papers 200321, Rutgers University, Department of Economics. [Downloadable!]
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  7. Oliver Blaskowitz & Helmut Herwartz, 2008. "Testing directional forecast value in the presence of serial correlation," SFB 649 Discussion Papers SFB649DP2008-073, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  8. Diana N. Weymark & Mototsugu Shintani, 2006. "Quantifying Inflation Pressure and Monetary Policy Response in the United States," Levine's Bibliography 321307000000000321, UCLA Department of Economics. [Downloadable!]
  9. Eric Ghysels & João Pereira, 2003. "On Portfolio Choice, Liquidity, and Short Selling: A Nonparametric Investigation," CIRANO Working Papers 2003s-27, CIRANO. [Downloadable!]
  10. Inoue, Atsushi & Kilian, Lutz, 2005. "How Useful is Bagging in Forecasting Economic Time Series? A Case Study of US CPI Inflation," CEPR Discussion Papers 5304, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  11. Zisimos Koustas & Jean-Francois Lamarche, 2009. "Comment on ``Interest Rate Setting and Inflation Targeting: Evidence of a Nonlinear Taylor Rule for the United Kingdom''," Working Papers 0903, Brock University, Department of Economics, revised Apr 2009. [Downloadable!]
  12. Lutz Kilian & Atsushi Inoue, 2004. "Bagging Time Series Models," Econometric Society 2004 North American Summer Meetings 110, Econometric Society. [Downloadable!]
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  13. Silvia Goncalves & Halbert White, 2002. "Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models," University of California at San Diego, Economics Working Paper Series 2000-32R, Department of Economics, UC San Diego. [Downloadable!]
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  14. Jason Allen & Allan W. Gregory & Katsumi Shimotsu, 2008. "Empirical Likelihood Block Bootstrapping," Working Papers 08-18, Bank of Canada. [Downloadable!]
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  15. Valentina Corradi & Norman Swanson, 2004. "Predective Density and Conditional Confidence Interval Accuracy Tests," Departmental Working Papers 200423, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  16. Norman Swanson & Valentina Corradi, 2006. "Nonparametric Bootstrap Procedures for Predictive Inference Based on Recursive Estimation Schemes," Departmental Working Papers 200618, Rutgers University, Department of Economics. [Downloadable!]
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  17. Yixiao Sun & Peter C.B. Phillips, 2008. "Optimal Bandwidth Choice for Interval Estimation in GMM Regression," Cowles Foundation Discussion Papers 1661, Cowles Foundation, Yale University. [Downloadable!]
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