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Published online by Cambridge University Press:  02 October 2014

Daniel Wilhelm*
*Address correspondence to Daniel Wilhelm, Department of Economics, University College London, 30 Gordon St, London WC1H 0AX, United Kingdom; e-mail:


A two-step generalized method of moments estimation procedure can be made robust to heteroskedasticity and autocorrelation in the data by using a nonparametric estimator of the optimal weighting matrix. This paper addresses the issue of choosing the corresponding smoothing parameter (or bandwidth) so that the resulting point estimate is optimal in a certain sense. We derive an asymptotically optimal bandwidth that minimizes a higher-order approximation to the asymptotic mean-squared error of the estimator of interest. We show that the optimal bandwidth is of the same order as the one minimizing the mean-squared error of the nonparametric plugin estimator, but the constants of proportionality are significantly different. Finally, we develop a data-driven bandwidth selection rule and show, in a simulation experiment, that it may substantially reduce the estimator’s mean-squared error relative to existing bandwidth choices, especially when the number of moment conditions is large.

Copyright © Cambridge University Press 2014 

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Anatolyev, S. (2005) GMM, GEL, serial correlation, and asymptotic bias. Econometrica 73(3), 9831002.CrossRefGoogle Scholar
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59(3), 817858.CrossRefGoogle Scholar
Andrews, D.W.K. & Monahan, J.C. (1992) An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60(4), 953966.CrossRefGoogle Scholar
Goldstein, L. & Messer, K. (1992) Optimal plug-in estimators for nonparametric functional estimation. Annals of Statistics 20(3), 13061328.CrossRefGoogle Scholar
Götze, F. & Hipp, C. (1978) Asymptotic expansions in the central limit theorem under moment conditions. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 42, 6787.CrossRefGoogle Scholar
Guggenberger, P. (2008) Finite sample evidence suggesting a heavy tail problem of the generalized empirical likelihood estimator. Econometric Reviews 27(4), 526541.CrossRefGoogle Scholar
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and Its Applications. Academic Press.Google Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50(4), 10291054.CrossRefGoogle Scholar
Hansen, L.P., Heaton, J., & Yaron, A. (1996) Finite-sample properties of some alternative GMM estimators. Journal of Business and Economic Statistics 14(3), 262280.Google Scholar
Imbens, G.W., Spady, R.H., & Johnson, P. (1998) Information theoretic approaches to inference in moment condition models. Econometrica 66(2), 333357.CrossRefGoogle Scholar
Jansson, M. (2002) Consistent covariance matrix estimation for linear processes. Econometric Theory 18, 14491459.CrossRefGoogle Scholar
Jun, B.H. (2007) Essays in econometrics. Ph.D. thesis, University of California, Berkeley.
Kiefer, N. & Vogelsang, T. (2002a) Heteroskedasticity-autocorrelation robust standard errors using the Bartlett kernel without truncation. Econometrica 70(5), 20932095.CrossRefGoogle Scholar
Kiefer, N. & Vogelsang, T. (2002b) Heteroskedasticity-autocorrelation robust testing using bandwidth equal to sample size. Econometric Theory 18, 13501366.CrossRefGoogle Scholar
Kiefer, N. & Vogelsang, T. (2005) A new asymptotic theory for heteroskedasticity-autocorrelation robust tests. Econometric Theory 21, 11301164.CrossRefGoogle Scholar
Kinal, T.W. (1980) The existence of moments of k-class estimators. Econometrica 48(1), 241249.CrossRefGoogle Scholar
Kitamura, Y. & Stutzer, M. (1997) An information-theoretic alternative to generalized method of moments estimation. Econometrica 65(4), 861874.CrossRefGoogle Scholar
Kunitomo, N. & Matsushita, Y. (2003) Finite Sample Distributions of the Empirical Likelihood Estimator and the GMM Estimator. Discussion paper F-200, CIRJE.
Magdalinos, M.A. (1992) Stochastic expansions and asymptotic approximations. Econometric Theory 8(3), 343367.CrossRefGoogle Scholar
Nagar, A.L. (1959) The bias and moment matrix of the general k-class estimators of the parameters in simultaneous equations. Econometrica 27(4), 575595.CrossRefGoogle Scholar
Newey, W.K. & McFadden, D. (1994) Large sample estimation and hypothesis testing. In Engle, R.F. & McFadden, D.L. (eds.), Handbook of Econometrics, vol. IV, pp. 21112245. Elsevier Science B.V.Google Scholar
Newey, W.K. & Smith, R.J. (2004) Higher order properties of GMM and generalized empirical likelihood estimators. Econometrica 72(1), 219255.CrossRefGoogle Scholar
Newey, W.K. & West, K. (1994) Automatic lag selection in covariance matrix estimation. Review of Economic Studies 61(4), 631653.CrossRefGoogle Scholar
Owen, A.B. (1988) Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75(2), 237249.CrossRefGoogle Scholar
Parzen, E. (1957) On consistent estimates of the spectrum of a stationary time series. Annals of Mathematical Statistics 28(2), 329348.CrossRefGoogle Scholar
Powell, J.L. & Stoker, T.M. (1996) Optimal bandwidth choice for density-weighted averages. Journal of Econometrics 75, 291316.CrossRefGoogle Scholar
Qin, J. & Lawless, J. (1994) Empirical likelihood and general estimating equations. Annals of Statistics 22(1), 300325.CrossRefGoogle Scholar
Rilstone, P., Srivastava, V.K., & Ullah, A. (1996) The second-order bias and mean squared error of nonlinear estimators. Journal of Econometrics 75(2), 369395.CrossRefGoogle Scholar
Robinson, P.M. (1991) Automatic frequency domain inference on semiparametric and nonparametric models. Econometrica 59(5), 13291363.CrossRefGoogle Scholar
Rothenberg, T. (1984) Approximating the distributions of econometric estimators and test statistics. In Griliches, Z. & Intriligator, M.D. (eds.), Handbook of Econometrics, vol. II, pp. 881935. Elsevier Science Publishers B.V.Google Scholar
Sargan, J.D. (1958) The estimation of economic relationships using instrumental variables. Econometrica 26(3), 393415.CrossRefGoogle Scholar
Sargan, J.D. (1959) The estimation of relationships with autocorrelated residuals by the use of instrumental variables. Journal of the Royal Statistical Society, Series B (Methodological) 21(1), 91105.Google Scholar
Stock, J.H., Wright, J.H., & Yogo, M. (2002) A survey of weak instruments and weak identification in generalized method of moments. Journal of Business and Economic Statistics 20(4), 518529.CrossRefGoogle Scholar
Sun, Y. & Phillips, P.C.B. (2008) Optimal Bandwidth Choice for Interval Estimation in GMM Regression. Discussion paper 1661, Cowles Foundation, Yale University.
Sun, Y., Phillips, P.C.B., & Jin, S. (2008) Optimal bandwidth selection in heteroskedasticity-autocorrelation robust testing. Econometrica 76(1), 175194.CrossRefGoogle Scholar
Tamaki, K. (2007) Second order optimality for estimators in time series regression models. Journal of Multivariate Analysis 98, 638659.CrossRefGoogle Scholar
White, H. & Domowitz, I. (1984) Nonlinear regression with dependent observations. Econometrica 52(1), 143162.CrossRefGoogle Scholar
Xiao, Z. & Phillips, P.C.B. (1998) Higher-order approximations for frequency domain time series regression. Journal of Econometrics 86, 297336.CrossRefGoogle Scholar
Zaman, A. (1981) Estimators without moments: The case of the reciprocal of a normal mean. Journal of Econometrics 15(2), 289298.CrossRefGoogle Scholar