Hostname: page-component-74656f9884-54qdv Total loading time: 0 Render date: 2026-11-09T22:31:04.387Z Has data issue: false hasContentIssue false
  • English
  • Français

GEL METHODS FOR NONSMOOTH MOMENT INDICATORS

Published online by Cambridge University Press:  30 April 2010

Paulo M.D.C. Parente  and
Richard J. Smith
Paulo M.D.C. Parente*
Affiliation:
University of Exeter
Richard J. Smith
Affiliation:
Centre for Microdata Methods and Practice, University College London and Institute for Fiscal Studies, and University of Cambridge
*
*Address correspondence to Paulo M.D.C. Parente, Department of Economics, University of Exeter, Streatham Court, Rennes Drive, Exeter EX4 4PU, UK; e-mail: p.m.parente@exeter.ac.uk.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

This paper considers the first-order large sample properties of the generalized empirical likelihood (GEL) class of estimators for models specified by nonsmooth indicators. The GEL class includes a number of estimators recently introduced as alternatives to the efficient generalized method of moments (GMM) estimator that may suffer from substantial biases in finite samples. These include empirical likelihood (EL), exponential tilting (ET), and the continuous updating estimator (CUE). This paper also establishes the validity of tests suggested in the smooth moment indicators case for overidentifying restrictions and specification. In particular, a number of these tests avoid the necessity of providing an estimator for the Jacobian matrix that may be problematic for the sample sizes typically encountered in practice.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 27 , Issue 1: SPECIAL ISSUE ON EMPIRICAL LIKELIHOOD AND RELATED METHODS , February 2011 , pp. 74 - 113
Copyright
Copyright © Cambridge University Press 2010

References

REFERENCES

Andrews, D.W.K. (1994) Empirical process methods in econometrics. In Engle, R.F. & McFadden, D.L. (eds.), Handbook of Econometrics, vol. 4, pp. 2247–2294. North Holland.Google Scholar
Andrews, D.W.K. (1997) A stopping rule for the computation of generalized method of moments estimators. Econometrica 65, 913–931.CrossRefGoogle Scholar
Bowman, A.W. & Azzalini, A. (1997) Applied Smoothing Techniques for Data Analysis. Oxford University Press.Google Scholar
Brown, B.W. & Newey, W.K. (2002) Generalized method of moments, efficient bootstrapping and improved inference. Journal of Business Economics and Statistics 20, 507–517.Google Scholar
Buchinsky, M. (1995) Estimating the asymptotic covariance matrix for quantile regression models. A Monte Carlo study. Journal of Econometrics 68, 303–338.Google Scholar
Chernozhukov, V. & Hong, H. (2003) A MCMC approach to classical estimation. Journal of Econometrics 115, 293–346.Google Scholar
Christoffersen, P., Hahn, J., & Inoue, A. (1999) Testing, Comparing and Combining Value at Risk Measures. Working paper, University of Pennsylvania.Google Scholar
Corcoran, S. (1998) Bartlett adjustment of empirical discrepancy statistics. Biometrika 85, 965–972.Google Scholar
Cressie, N. & Read, T. (1984) Multinomial goodness-of-fit tests. Journal of the Royal Statistical Society Series B, 46, 440–464.Google Scholar
Daniels, H. (1961) The asymptotic efficiency of a maximum likelihood estimator. In Fourth Berkeley Symposium on Mathematical Statistics and Probability. pp. 151–163. University of California Press.Google Scholar
Davidson, R. & MacKinnon, J. (1983) Small sample properties of alternative forms of the Lagrange multiplier test. Economics Letters 12, 269–275.CrossRefGoogle Scholar
Dorsey, R. & Mayer, W. (1995) Genetic algorithms for estimation problems with multiple optima, non-differentiability and other irregular features. Journal of Business, Economics and Statistics 13, 53–66;CrossRefGoogle Scholar
Fitzenberger, B. (1997) The moving blocks bootstrap and robust inference for linear least squares and quantile regressions. Journal of Econometrics 82, 235–287.CrossRefGoogle Scholar
Guggenberger, P. & Smith, R.J. (2005) Generalized empirical likelihood estimators and tests under partial, weak and strong identification. Econometric Theory 21, 667–709.Google Scholar
Hansen, L. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.Google Scholar
Hansen, L., Heaton, J., & Yaron, A. (1996) Finite-sample properties of some alternative GMM estimators. Journal of Business and Economic Statistics 14, 262–280.Google Scholar
Hoeffding, W. (1965) Asymptotically optimal tests for multinomial distributions (with discussion). Annals of Mathematical Statistics 36, 369–408.CrossRefGoogle Scholar
Hogg, R. (1979) Statistical robustness: One view of its use in applications today. American Statistician 33, 108–116.Google Scholar
Honore, B. & Hu, L. (2004) On the performance of some robust instrumental variables estimators. Journal of Business Economics and Statistics 22, 30–39CrossRefGoogle Scholar
Horowitz, J. (1992) A smooth maximum score estimator for the binary response model. Econometrica 60, 505–531.Google Scholar
Horowitz, J. (1998) Bootstrap methods for median regression models. Econometrica 66, 1327–1351.Google Scholar
Houck, C., Joines, J., & Kay, M. (1995) A Genetic Algorithm for Function Optimization: A Matlab Implementation. NSCU IE TR 95-09, North Carolina State University. http://www.ie.ncsu.edu/mirage/GAToolBox/gaot.Google Scholar
Huber, P. (1967) The behavior of maximum likelihood estimates under nonstandard condition. In Fifth Berkeley Symposium on Mathematical Statistics and Probability, pp. 221–233. University of California Press.Google Scholar
Imbens, G. (1997) One-Step estimators for over-identified generalized method of moments models. Review of Economic Studies 64, 359–383.Google Scholar
Imbens, G., Spady, R., & Johnson, P. (1998) Information theoretic approaches to inference in moment condition models. Econometrica 66, 333–357.CrossRefGoogle Scholar
Johnson, N. & Kotz, S. (1972) Distributions in Statistics: Continuous Univariate Distributions-2. Wiley.Google Scholar
Kemp, G.C.R. (2005) GEL Estimation and Inference with Non-Smooth Moment Indicators and Dynamic Data. Working paper, University of Essex.Google Scholar
Kitamura, Y. (2001) Asymptotic optimality of empirical likelihood for testing moment restrictions. Econometrica 69, 1661–1672.Google Scholar
Kitamura, Y. & Stutzer, M. (1997) An information-theoretic alternative to generalized method of moments estimation. Econometrica 65, 861–874.Google Scholar
Koenker, R. (1997) Rank tests for linear models. In Rao, C.R. & Maddala, G.S. (eds.), Handbook of Statistics, vol. 15. North Holland.Google Scholar
Koenker, R. (2005) Quantile Regression. Cambridge University Press.Google Scholar
Koenker, R. & Bassett, G. (1978) Regression quantiles. Econometrica 46, 33–50.CrossRefGoogle Scholar
Koenker, R. & Bassett, G. (1982) Tests for linear hypotheses and L1 estimation. Econometrica 50, 1577–1583.CrossRefGoogle Scholar
Magnus, J.R. & Neudecker, H. (1999) Matrix Differential Calculus with Applications in Statistics and Econometrics. Wiley.Google Scholar
Newey, W.K. (1985) Maximum likelihood specification testing and conditional moment tests. Econometrica 53, 1047–1070.Google Scholar
Newey, W.K. & McFadden, D.L. (1994) Large sample estimation and hypothesis testing. In Engle, R.F. & McFadden, D.L. (eds.), Handbook of Econometrics, vol. 4, pp. 2111–2245. North Holland.Google Scholar
Newey, W.K. & Powell, J.L. (1987) Asymmetric least squares estimation and testing. Econometrica 55, 819–847.Google Scholar
Newey, W.K., Ramalho, J.J.S., & Smith, R.J. (2005) Asymptotic bias for GMM and GEL estimators with estimated nuisance parameters. In Andrews, D.W.K. & Stock, J.H. (eds.), Identification and Inference in Econometric Models: Essays in Honor of Thomas J. Rothenberg, pp. 245–281. Cambridge University Press.CrossRefGoogle Scholar
Newey, W.K. & Smith, R.J. (2004) Higher order properties of GMM and generalized empirical likelihood estimators. Econometrica 219–255.CrossRefGoogle Scholar
Newey, W.K. & West, K. (1987) Hypothesis testing with efficient method of moments estimation. International Economic Review 28, 777–787.Google Scholar
Nolan, D. & Pollard, D. (1987) U-Processes: Rates of convergence. Annals of Statistics 15, 780–799.Google Scholar
Otsu, T. (2008) Conditional empirical likelihood estimation and inference for quantile regression models. Journal of Econometrics 142, 508–538.CrossRefGoogle Scholar
Owen, A. (1988) Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75, 237–249.Google Scholar
Owen, A. (1990) Empirical likelihood ratio confidece regions. Annals of Statistics 18, 90–120.Google Scholar
Owen, A. (2001) Empirical Likelihood. Chapman and Hall.Google Scholar
Pakes, A. & Pollard, D. (1989) Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027–1057.Google Scholar
Parente, P.M.D.C. & Smith, R.J. (2008) GEL Methods for Non-Smooth Moment Indicators. CWP 19/08, cemmap, I.F.S. and U.C.L.CrossRefGoogle Scholar
Pollard, D. (1984) Convergence of Stochastic Processes. Springer-Verlag.Google Scholar
Pollard, D. (1985) New ways to prove central limit theorems. Econometric Theory 1, 295–314.CrossRefGoogle Scholar
Powell, J.L. (1984) Least absolute deviation estimation for censored regression model. Journal of Econometrics 25, 303–325.CrossRefGoogle Scholar
Powell, J.L. (1986) Censored regression quantiles. Journal of Econometrics 32, 143–155.CrossRefGoogle Scholar
Qin, J. & Lawless, J. (1994) Empirical likelihood and general estimating equations. Annals of Statistics 22, 300–325.Google Scholar
Ramalho, J.J.S. (2001) Alternative Estimation Methods and Specification Tests for Moment Condition Models. Ph.D. thesis, University of Bristol.Google Scholar
Ramalho, J.J.S. & Smith, R.J. (2004) Goodness of Fit Tests for Moment Conditions Models. Working paper, University of Warwick.Google Scholar
Rao, C.R. & Mitra, S.K. (1971) Generalized Inverse of Matrices and Its Applications. Wiley.Google Scholar
Smith, R.J. (1997) Alternative semi-parametric likelihood approaches to generalized method of moments estimation. Economic Journal 107, 503–519.Google Scholar
Smith, R.J. (2000) Empirical likelihood estimation and inference. In Marriott, P. & Salmon, M. (eds.), Applications of Differential Geometry to Econometrics, pp. 119–150. Cambridge University Press.Google Scholar
Smith, R.J. (2001) GEL Method for Moment Condition Models. Revised version CWP 19/04, cemmap, I.F.S., and U.C.L., available at http://cemmap.ifs.org.uk/wps/cwp0419.pdf.Google Scholar
Tauchen, G. (1985) Diagnostic testing and evaluation of maximum likelihood models. Journal of Econometrics 30, 415–443.CrossRefGoogle Scholar
Van der Vaart, A. (1998) Asymptotic Statistics. Cambridge University Press.CrossRefGoogle Scholar
Weiss, A. (1991) Estimating nonlinear dynamic models using least absolute error estimation. Econometric Theory 7, 46–68.CrossRefGoogle Scholar
Whang, Y. (2003) Smoothed Empirical Likelihood Methods for Quantile Regression Models. Working paper, Korea University.Google Scholar
Zhang, J. & Gijbels, I. (2003) Sieve empirical likelihood and extensions of the generalized least squares. Scandinavian Journal of Statistics 30, 1–24.Google Scholar