Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-27T14:26:04.042Z Has data issue: false hasContentIssue false
  • English
  • Français

GEL CRITERIA FOR MOMENT CONDITION MODELS

Published online by Cambridge University Press:  19 September 2011

Richard J. Smith
Richard J. Smith*
Affiliation:
cemmap, U.C.L. and I.F.S. and University of Cambridge
*
*Address correspondence to Richard J. Smith, Faculty of Economics, University of Cambridge, Austin Robinson Building, Sidgwick Ave., Cambridge CB3 900, U.K.; email: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

GEL methods that generalize and extend previous contributions are defined and analyzed for moment condition models specified in terms of weakly dependent data. These procedures offer alternative one-step estimators and tests that are asymptotically equivalent to their efficient two-step GMM counterparts. The basis for GEL estimation is via a smoothed version of the moment indicators using kernel function weights that incorporate a bandwidth parameter. Examples for the choice of bandwidth parameter and kernel function are provided. Efficient moment estimators based on implied probabilities derived from the GEL method are proposed, a special case of which is estimation of the stationary distribution of the data. The paper also presents a unified set of test statistics for overidentifying moment restrictions and combinations of parametric and moment restriction hypotheses.

Type
ARTICLES
Information
Econometric Theory , Volume 27 , Issue 6 , December 2011 , pp. 1192 - 1235
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aitchison, J. (1962) Large-Sample restricted parametric tests. Journal of the Royal Statistical Society (Series B) 24, 234–250.Google Scholar
Altonji, J.G. & Segal, L.M. (1996) Small sample bias in GMM estimation of covariance structures. Journal of Business and Economic Statistics 14, 353–366.Google Scholar
Anatolyev, S. (2005) GMM, GEL, Serial correlation and asymptotic bias. Econometrica 73, 983–1002.CrossRefGoogle Scholar
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.CrossRefGoogle Scholar
Andrews, D.W.K. & Monahan, J.C. (1992) An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60, 953–966.CrossRefGoogle Scholar
Antoine, B., Bonnal, H., & Renault, E. (2007) On the efficient use of the informational content of estimating equations: Implied probabilities and euclidean empirical likelihood. Journal of Econometrics 138, 461–487.CrossRefGoogle Scholar
Back, K. & Brown, D.P. (1993) Implied probabilities in GMM estimators. Econometrica 61, 971–975.CrossRefGoogle Scholar
Brown, B.W. & Newey, W.K. (1998) Efficient semiparametric estimation of expectations. Econometrica 66, 453–464.CrossRefGoogle Scholar
Brown, B.W. & Newey, W.K. (2002) Generalized method of moments, efficient bootstrapping, and improved inference. Journal of Business and Economic Statistics 20, 507–517.CrossRefGoogle Scholar
Chesher, A. & Smith, R.J. (1997) Likelihood ratio specification tests. Econometrica, 65, 627–646.CrossRefGoogle Scholar
Corcoran, S.A. (1998) Bartlett adjustment of empirical discrepancy statistics. Biometrika 85, 967–972.CrossRefGoogle Scholar
Cressie, N. & Read, T. (1984) Multinomial goodness-of-fit tests. Journal of the Royal Statistical Society, Series B 46, 440–464.Google Scholar
Gouriéroux, C. & Monfort, A. (1989) A general framework for testing a null hypothesis in a “Mixed Form.” Econometric Theory, 5, 63–82.CrossRefGoogle Scholar
Gradshteyn, I.S. & Ryzhik, I.M. (1980) Tables of Integrals, Series and Products. Academic Press.Google Scholar
Grenander, U. & Rosenblatt, M. (1984) Statistical Analysis of Stationary Time Series. Chelsea.Google Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.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, 262–280.Google Scholar
Imbens, G.W. (1997) One-Step estimators for over-identified generalized method of moments models. Review of Economic Studies 64, 359–383.CrossRefGoogle Scholar
Imbens, G.W., Johnson, P., & Spady, R.H. (1998) Information theoretic approaches to inference in moment condition models. Econometrica. 66, 333–357.CrossRefGoogle Scholar
Jansson, M. (2002) Consistent covariance matrix estimation for linear processes. Econometric Theory 18, 1449–1459.CrossRefGoogle Scholar
Kitamura, Y. (1997) Empirical likelihood with weakly dependent processes. Annals of Statistics 25, 2084–2102.CrossRefGoogle Scholar
Kitamura, Y. (2007) Empirical likelihood methods in econometrics: Theory and practice. In Blundell, R.W., Newey, W.K., & Persson, T. (eds.), Advances in Economics and Econometrics, Theory and Applications: Ninth World Congress of the Econometric Society, vol. 3, Econometric Society Monograph Series, ESM 43, Chap. 8, pp. 174–237. Cambridge University Press.Google Scholar
Kitamura, Y., & Stutzer, M. (1997) An information-theoretic alternative to generalized method of moments estimation. Econometrica 65, 861–874.CrossRefGoogle Scholar
Newey, W.K. (1985a) Generalized method of moments specification testing. Journal of Econometrics. 29, 229–256.CrossRefGoogle Scholar
Newey, W.K. (1985b) Maximum likelihood specification testing and conditional moment tests. Econometrica 53, 1047–1070.CrossRefGoogle Scholar
Newey, W.K. & McFadden, D. (1994) Large sample estimation and hypothesis testing. Chap. 36 in Engle, R.F. & McFadden, D. (eds.), Handbook of Econometrics, vol. 4, pp. 2111–2245. North Holland.Google Scholar
Newey, W.K. & Smith, R.J. (2004) Higher order properties of GMM and generalized empirical likelihood estimators. Econometrica 72, 219–255.CrossRefGoogle Scholar
Newey, W.K. & West, K.D. (1987) A simple, positive semi-definite heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica. 55, 703–708.CrossRefGoogle Scholar
Neyman, J. (1959) Optimal asymptotic tests of composite statistical hypotheses. In Grenander, U. (ed.), Probability and Statistics. Wiley.Google Scholar
Qin, J. & Lawless, J. (1994) Empirical likelihood and general estimating equations. Annals of Statistics 22, 300–325.CrossRefGoogle Scholar
Rao, C.R. & Mitra, S.K. (1971) Generalized Inverse of Matrices and Its Applications. Wiley.Google Scholar
Sargan, J.D. (1980) Some tests of dynamic specification for a single equation. Econometrica 48, 879–897.CrossRefGoogle Scholar
Schennach, S. (2007) Point Estimation with Exponentially Tilted Empirical Likelihood. Annals of Statistics 35, 634–672.CrossRefGoogle Scholar
Seber, G.A.F. (1964) The linear hypothesis and large sample theory. Annals of Mathematical Statistics 35, 773–779.CrossRefGoogle Scholar
Smith, R.J. (1987) Alternative asymptotically optimal tests and their application to dynamic specification. Review of Economic Studies 54, 665–680.CrossRefGoogle Scholar
Smith, R.J. (1997) Alternative semi-parametric likelihood approaches to generalized method of moments estimation. Economic Journal 107, 503–519.CrossRefGoogle Scholar
Smith, R.J. (2000) Empirical likelihood estimation and inference. In Salmon, M. & Marriott, P. (eds.), Applications of Differential Geometry to Econometrics, Chap. 4, pp. 119–150. Cambridge University Press.CrossRefGoogle Scholar
Smith, R.J. (2005) Automatic positive semidefinite HAC covariance matrix and GMM estimation. Econometric Theory 21, 158–170.CrossRefGoogle Scholar
Smith, R.J. (2007) Weak instruments and empirical likelihood: A discussion of the papers by D.W.K. Andrews and J.H. Stock and Y. Kitamura. In Blundell, R.W., Newey, W.K., & Persson, T. (eds.), Advances in Economics and Econometrics, Theory and Applications: Ninth World Congress of the Econometric Society, vol. 3, Econometric Society Monograph Series, ESM 43, Chap. 8, pp. 238–260. Cambridge University Press.Google Scholar
Szroeter, J. (1983) Generalized Wald methods for testing nonlinear implicit and overidentifying restrictions. Econometrica 51, 335–353.CrossRefGoogle Scholar
Tauchen, G. (1985) Diagnostic testing and evaluation of maximum likelihood models. Journal of Econometrics 30, 415–443.CrossRefGoogle Scholar
White, H. (1984) Asymptotic Theory for Econometricians. Academic Press.Google Scholar