Dovonon, Prosper and Gonçalves, Sílvi (2017) Bootstrapping the GMM overidentification test under firstorder underidentification. Journal of Econometrics . ISSN 03044076 (In Press)
Preview 
Text (application/pdf)
1MBdovonon2017.pdf  Accepted Version Available under License Spectrum Terms of Access. 
Official URL: http://dx.doi.org/10.1016/j.jeconom.2017.06.021
Abstract
The main contribution of this paper is to study the applicability of the bootstrap to estimating the distribution of the standard test of overidentifying restrictions of Hansen (1982) when the model is globally identified but the rank condition fails to hold (lack of firstorder local identification). An important example for which these conditions are verified is the popular test of common conditionally heteroskedastic features proposed by Engle and Kozicki (1993). As Dovonon and Renault (2013b) show, the Jacobian matrix for this model is identically zero at the true parameter value, resulting in a highly nonstandard limiting distribution that complicates the computation of critical values.
We first show that the standard GMM bootstrap fails to consistently estimate the distribution of the overidentification restrictions test under lack of firstorder identification. We then propose a new bootstrap method that is asymptotically valid in this context. The modification consists of adding an additional term that recenters the bootstrap moment conditions in a way as to ensure that the bootstrap Jacobian matrix is zero when evaluated at the GMM estimate.
Divisions:  Concordia University > Faculty of Arts and Science > Economics 

Item Type:  Article 
Refereed:  Yes 
Authors:  Dovonon, Prosper and Gonçalves, Sílvi 
Journal or Publication:  Journal of Econometrics 
Date:  9 August 2017 
Funders: 

Digital Object Identifier (DOI):  10.1016/j.jeconom.2017.06.021 
ID Code:  982759 
Deposited By:  Danielle Dennie 
Deposited On:  15 Aug 2017 13:25 
Last Modified:  01 Aug 2018 00:00 
References:
D.W.K. Andrews Higherorder improvements of a computationally attractive kstep bootstrap for extremum estimators Econometrica, 70 (2002), pp. 119–262Andrews, D.W.K., Guggenberger, P., 2015. Identificationand singularityrobust inference for moment condition, Cowles Foundation Discussion Paper No. 1978.
J. Bochnak, M. Coste, M.F. Roy Real Algebraic Geometry Springer Verlag, Berlin Heidelberg (1998)
B. Brown, K.W. Newey Generalized method of moments, efficient bootstrapping, and improved inference J. Bus. Econom. Statist., 20 (2002), pp. 507–510
F.A. Bugni, I.A. Canay, S. Shi Specification tests for partially identified models defined by moment inequalities J. Econometrics, 185 (2015), pp. 259–282
G. Cheng, J.Z. Huang Bootstrap consistency for general semiparameteric Mestimation Ann. Statist., 38 (2010), pp. 2884–2915
J.G. Cragg, S.G. Donald Inferring the rank of a matrix J. Econometrics, 76 (1997), pp. 223–250
P. Dovonon, A.R. Hall The Asymptotic Properties of GMM and Indirect Inference Under SecondOrder Identification, Concordia University and University of Manchester (2015)
P. Dovonon, E. Renault GMM Overidentification Test with First Order Underidentification, Department of Economics, Concordia University, Montreal, Canada (2009)
P. Dovonon, E. Renault Supplement to ‘testing for common conditionally heteroskedastic factors’: extensions and proofs
Econometrica Suppl. Mater., 81 (2013) http://www.econometricsociety.org/ecta/supmat/10082_proofs.pdf
P. Dovonon, E. Renault Testing for common conditionally heteroskedastic factors Econometrica, 81 (2013), pp. 2561–2586
C. Doz, E. Renault Factor volatility in mean models: a GMM approach Econometric Rev., 25 (2006), pp. 275–309
R.F. Engle, S. Kozicki Testing for common features J. Bus. Econom. Statist., 11 (1993), pp. 369–395
G. Fiorentini, E. Sentana, N. Shephard Likelihoodbased estimation of latent generalized arch structures Econometrica, 72 (2004), pp. 1481–1517
E. Giné, J. Zinn Bootstrapping general empirical measures Ann. Probab., 18 (1990), pp. 851–869
S. Goņcalves, H. White Maximum likelihood and the bootstrap for nonlinear dynamic models J. Econometrics, 119 (2004), pp. 199–220
J. Hahn A note on bootstrapping generalized method of moments estimators Econometric Theory, 12 (1996), pp. 187–197
P. Hall, J. Horowitz Bootstrap critical values for tests based on generalizedmethodofmoments estimators Econometrica, 64 (1996), pp. 891–916
L.P. Hansen Large sample properties of generalized method of moments estimators Econometrica, 50 (1982), pp. 1029–1054
C. He, T. Teräsvirta Properties of moments of a family of GARCH processes J. Econometrics, 92 (1999), pp. 173–192
A. Inoue, M. Shintani Bootstrapping GMM estimators for time series J. Econometrics, 133 (2006), pp. 531–555
M.R. Kosorok Introduction to Empirical Processes and Semiparametric Inference Springer, New York (2008)
S. Lee Asymptotic refinements of a misspecificationrobust bootstrap for generalized method of moments estimators J. Econometrics, 178 (2014), pp. 398–413
J.H. Lee, Z. Liao On Standard Inference for GMM with Local Identification Failure of Known Forms University of Illinois and UC Los Angeles (2016)
E. Madsen GMMBased Inference in the AR(1) Panel Data Model for Parameter Values Where Local Identification Fails Centre for Applied Microeconometrics, Department of Economics, University of Copenhagen, Copenhagen, Denmark (2009)
W.K. Newey, D.L. McFadden Large sample estimation and hypothesis testing in: R. Engle, D.L. McFadden (Eds.), Handbook of Econometrics, vol. 4, Elsevier Science Publishers, Amsterdam, The Netherlands (1994), pp. 2113–2247
D. Pollard Convergence of Stochastic Processes Springer, New York (1984)
A. Rotnitzky, D.R. Cox, M. Bottai, J. Robins Likelihoodbased inference with singular information matrix Bernoulli, 6 (2000), pp. 243–284
J.D. Sargan Identification and lack of identification Econometrica, 51 (1983), pp. 1605–1633
B. Sen, M. Banerjee, M. Woodroofe Inconsistency of the bootstrap: The Grenander estimator Ann. Statist., 38 (2010), pp. 1953–1977
Sentana, E., 2009. Finite Underidentification, CEMFI, Working Paper No. 1508, Madrid, Spain.
A.W. van der Vaart Asymptotic Statistics Cambridge University Press, Cambridge (1998)
A.W. van der Vaart, J.A. Wellner Weak Convergence and Empirical Processes Springer Verlag, NewYork (1996)
J.H. Wright Detecting lack of identification in GMM Econometric Theory, 19 (2003), pp. 322–330
Repository Staff Only: item control page