GMM, GEL, Serial Correlation, and Asymptotic Bias
Abstract
For stationary time series models with serial correlation, we consider generalized method of moments (GMM) estimators that use heteroskedasticity and autocorrelation consistent (HAC) positive definite weight matrices and generalized empirical likelihood (GEL) estimators based on smoothed moment conditions. Following the analysis of Newey and Smith (2004) for independent observations, we derive second order asymptotic biases of these estimators. The inspection of bias expressions reveals that the use of smoothed GEL, in contrast to GMM, removes the bias component associated with the correlation between the moment function and its derivative, while the bias component associated with third moments depends on the employed kernel function. We also analyze the case of no serial correlation, and find that the seemingly unnecessary smoothing and HAC estimation can reduce the bias for some of the estimators.
Citing Literature
Number of times cited according to CrossRef: 43
- Ke-Li Xu, Inference of local regression in the presence of nuisance parameters, Journal of Econometrics, 10.1016/j.jeconom.2020.04.028, (2020).
- Fei Jin, Lung-fei Lee, EFFICIENT TWO-STEP GENERALIZED EMPIRICAL LIKELIHOOD ESTIMATION AND TESTS WITH MARTINGALE DIFFERENCES, Econometric Theory, 10.1017/S0266466620000249, (1-40), (2020).
- Jia Zhang, Haoming Shi, Lemeng Tian, Fengjun Xiao, Penalized generalized empirical likelihood in high-dimensional weakly dependent data, Journal of Multivariate Analysis, 10.1016/j.jmva.2018.12.010, (2019).
- Davide La Vecchia, Alban Moor, Olivier Scaillet, A Higher-Order Correct Fast Moving-Average Bootstrap for Dependent Data, SSRN Electronic Journal, 10.2139/ssrn.3515288, (2019).
- Haiqi Li, Rui Fan, Sung Y. Park, Generalized empirical likelihood specification test robust to local misspecification, Economics Letters, 10.1016/j.econlet.2018.07.024, 171, (149-153), (2018).
- Fei Jin, Lung-fei Lee, GEL estimation and tests of spatial autoregressive models, Journal of Econometrics, 10.1016/j.jeconom.2018.07.007, (2018).
- Alain Guay, Jean-François Lamarche, Structural change tests for GEL criteria, Econometric Reviews, 10.1080/00927872.2016.1178893, 37, 9, (1000-1032), (2016).
- Pierre Chaussé, Dinghai Xu, GMM estimation of a realized stochastic volatility model: A Monte Carlo study, Econometric Reviews, 10.1080/07474938.2016.1152654, 37, 7, (719-743), (2016).
- Márcio Poletti Laurini, Luiz Koodi Hotta, GMC/GEL estimation of stochastic volatility models, Communications in Statistics - Simulation and Computation, 10.1080/03610918.2016.1213282, 46, 9, (6828-6844), (2016).
- Jonathan B. Hill, Artem Prokhorov, GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference, Journal of Econometrics, 10.1016/j.jeconom.2015.09.001, 190, 1, (18-45), (2016).
- Ke-Li Xu, Inference of Local Regression in the Presence of Nuisance Parameters, SSRN Electronic Journal, 10.2139/ssrn.2992157, (2016).
- Seojeong Lee, Asymptotic refinements of a misspecification-robust bootstrap for GEL estimators, Journal of Econometrics, 10.1016/j.jeconom.2015.11.003, 192, 1, (86-104), (2016).
- Eric S. Lin, Ta-Sheng Chou, Finite-sample refinement of GMM approach to nonlinear models under heteroskedasticity of unknown form, Econometric Reviews, 10.1080/07474938.2014.999499, 37, 1, (1-28), (2015).
- Márcio Poletti Laurini, Luiz Koodi Hotta, Generalized moment estimation of stochastic differential equations, Computational Statistics, 10.1007/s00180-015-0598-2, 31, 3, (1169-1202), (2015).
- Jinyuan Chang, Song Xi Chen, Xiaohong Chen, High dimensional generalized empirical likelihood for moment restrictions with dependent data, Journal of Econometrics, 10.1016/j.jeconom.2014.10.011, 185, 1, (283-304), (2015).
- Alastair R. Hall, Econometricians Have Their Moments: GMM at 32, Economic Record, 10.1111/1475-4932.12188, 91, (1-24), (2015).
- Alain Guay, Florian Pelgrin, Using Implied Probabilities to Improve the Estimation of Unconditional Moment Restrictions for Weakly Dependent Data, Econometric Reviews, 10.1080/07474938.2014.966630, 35, 3, (344-372), (2014).
- Daniel Wilhelm, OPTIMAL BANDWIDTH SELECTION FOR ROBUST GENERALIZED METHOD OF MOMENTS ESTIMATION, Econometric Theory, 10.1017/S026646661400067X, 31, 5, (1054-1077), (2014).
- Yi Hu, Xiaohua Xia, Ying Deng, Dongmei Guo, Higher Order Mean Squared Error of Generalized Method of Moments Estimators for Nonlinear Models, Discrete Dynamics in Nature and Society, 10.1155/2014/324904, 2014, (1-8), (2014).
- Paulo M.D.C. Parente, Richard J. Smith, Recent Developments in Empirical Likelihood and Related Methods, Annual Review of Economics, 10.1146/annurev-economics-080511-110925, 6, 1, (77-102), (2014).
- Seojeong Jay Lee, Asymptotic Refinements of a Misspecification-Robust Bootstrap for GEL Estimators, SSRN Electronic Journal, 10.2139/ssrn.2393191, (2014).
- PETER McADAM, ALPO WILLMAN, Technology, Utilization, and Inflation: What Drives the New Keynesian Phillips Curve?, "Journal of Money, Credit and Banking", 10.1111/jmcb.12062, 45, 8, (1547-1579), (2013).
- Yoshihide Kakizawa, Frequency domain generalized empirical likelihood method, Journal of Time Series Analysis, 10.1111/jtsa.12043, 34, 6, (691-716), (2013).
- Alain Guay, Jean-François Lamarche, STRUCTURAL CHANGE TESTS BASED ON IMPLIED PROBABILITIES FOR GEL CRITERIA, Econometric Theory, 10.1017/S0266466612000114, 28, 6, (1186-1228), (2012).
- Guido M. Kuersteiner, Kernel-weighted GMM estimators for linear time series models, Journal of Econometrics, 10.1016/j.jeconom.2012.05.013, 170, 2, (399-421), (2012).
- Nikolay Gospodinov, Taisuke Otsu, Local GMM estimation of time series models with conditional moment restrictions, Journal of Econometrics, 10.1016/j.jeconom.2012.05.017, 170, 2, (476-490), (2012).
- Patrik Guggenberger, Joaquim J.S. Ramalho, Richard J. Smith, GEL statistics under weak identification, Journal of Econometrics, 10.1016/j.jeconom.2012.05.009, 170, 2, (331-349), (2012).
- Mikio Ito, Akihiko Noda, The GEL estimates resolve the risk-free rate puzzle in Japan, Applied Financial Economics, 10.1080/09603107.2011.613761, 22, 5, (365-374), (2011).
- Richard J. Smith, GEL CRITERIA FOR MOMENT CONDITION MODELS, Econometric Theory, 10.1017/S026646661100003X, 27, 6, (1192-1235), (2011).
- Jason Allen, Allan W. Gregory, Katsumi Shimotsu, Empirical likelihood block bootstrapping, Journal of Econometrics, 10.1016/j.jeconom.2010.10.003, 161, 2, (110-121), (2011).
- VASCO J. GABRIEL, LUIS F. MARTINS, The Cost Channel Reconsidered: A Comment Using an Identification‐Robust Approach, "Journal of Money, Credit and Banking", 10.1111/j.1538-4616.2010.00361.x, 42, 8, (1703-1712), (2010).
- Alastair R. Hall, Generalized Method of Moments (GMM), Encyclopedia of Quantitative Finance, 10.1002/9780470061602, (2010).
- Luis F. Martins, Vasco J. Gabriel, New Keynesian Phillips Curves and potential identification failures: A Generalized Empirical Likelihood analysis, Journal of Macroeconomics, 10.1016/j.jmacro.2009.01.003, 31, 4, (561-571), (2009).
- Kenneth D. West, Ka-fu Wong, Stanislav Anatolyev, Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments, Econometric Reviews, 10.1080/07474930802467241, 28, 5, (441-467), (2009).
- Francesco Bravo, Blockwise generalized empirical likelihood inference for non‐linear dynamic moment conditions models, The Econometrics Journal, 10.1111/j.1368-423X.2009.00286.x, 12, 2, (208-231), (2009).
- Emma M. Iglesias, Garry D.A. Phillips, Asymptotic bias of GMM and GEL under possible nonstationary spatial dependence, Economics Letters, 10.1016/j.econlet.2007.09.015, 99, 2, (393-397), (2008).
- Stanislav Anatolyev, Method-of-moments estimation and choice of instruments: Numerical computations, Economics Letters, 10.1016/j.econlet.2008.01.015, 100, 2, (217-220), (2008).
- Allan Gregory, Katsumi Shimotsu, Empirical Likelihood Block Bootstrapping, SSRN Electronic Journal, 10.2139/ssrn.1134869, (2008).
- Alain Guay, Jean-Francois Lamarche, The Information Content of Implied Probabilities to Detect Structural Change, SSRN Electronic Journal, 10.2139/ssrn.1291915, (2008).
- Alain Guay, Florian Pelgrin, Using Implied Probabilities to Improve Estimation with Unconditional Moment Restrictions, SSRN Electronic Journal, 10.2139/ssrn.1077584, (2007).
- Stanislav Anatolyev, OPTIMAL INSTRUMENTS IN TIME SERIES: A SURVEY, Journal of Economic Surveys, 10.1111/j.1467-6419.2007.00501.x, 21, 1, (143-173), (2007).
- Fernanda P. M. Peixe, Alastair R. Hall, Kostas Kyriakoulis, The Mean Squared Error of the Instrumental Variables Estimator When the Disturbance Has an Elliptical Distribution, Econometric Reviews, 10.1080/07474930500545488, 25, 1, (117-138), (2007).
- Ivan Fernandez-Val, Bias Correction in Panel Data Models with Individual Specific Parameters, SSRN Electronic Journal, 10.2139/ssrn.869104, (2005).
