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STRUCTURAL CHANGE TESTS BASED ON IMPLIED PROBABILITIES FOR GEL CRITERIA

Published online by Cambridge University Press:  21 May 2012

Alain Guay  and
Jean-François Lamarche
Alain Guay*
Affiliation:
Université du Québec à Montréal
Jean-François Lamarche
Affiliation:
Brock University
*
*Address correspondence to Alain Guay, Département de sciences économiques, Université du Québec à Montréal, Québec, Canada; e-mail: [email protected].
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Abstract

This paper proposes Pearson-type statistics based on implied probabilities to detect structural change. The class of generalized empirical likelihood estimators (see Smith 1997, The Economic Journal107, 503–519) assigns a set of implied probabilities to each observation such that moment conditions are satisfied. The proposed test statistics for structural change are based on the information content in these implied probabilities. We consider cases of structural change with unknown breakpoint that can occur in the parameters of interest or in the overidentifying restrictions used to estimate these parameters. We also propose a structural change test based on implied probabilities that is robust to weak identification or cases in which parameters are completely unidentified. The test statistics considered here have competitive size and power properties. Moreover, they are computed in a single step, which eliminates the need to compute the weighting matrix required for generalized method of moments estimation.

Type
Articles
Information
Econometric Theory , Volume 28 , Issue 6 , December 2012 , pp. 1186 - 1228
Copyright
Copyright © Cambridge University Press 2012 

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References

REFERENCES

Anatolyev, S. (2005) GMM, GEL, serial correlation, and asymptotic bias. Econometrica 73(3), 983–1002.CrossRefGoogle Scholar
Andrews, D.W.K. (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821–856.Google Scholar
Andrews, D.W.K. & Ploberger, W. (1994) Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 1383–1414.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
Caner, M. (2007) Bounded pivotal structural change tests in continuous updating GMM with strong, weak identification and completely unidentified cases. Journal of Econometrics 137, 28–67.CrossRefGoogle Scholar
Caner, M. (2008a) Exponential Tilting and Weak Instruments: Estimation and Testing. Working paper, North Carolina State University.Google Scholar
Caner, M. (2008b) Nearly-singular design in GMM and generalized empirical likelihood estimators. Journal of Econometrics 144, 511–523.Google Scholar
Cressie, N. & Read, T. (1984) Multinomial goodness-of-fit tests. Journal of the Royal Statistical Society B 46, 440–464.Google Scholar
Gallant, A.R. & White, H. (1988) A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models. Basil Blackwell.Google Scholar
Ghysels, E., Guay, A., & Hall, A. (1997) Predictive tests for structural change with unknown breakpoint. Journal of Econometrics 82, 209–233.Google Scholar
Ghysels, E. & Hall, A. (1990) Are consumption-based intertemporal capital asset pricing models structural. Journal of Econometrics 45, 121–139.CrossRefGoogle Scholar
Gregory, A.W., Lamarche, J.-F., & Smith, G.W. (2002) Information-theoretic estimation of preference parameters: Macroeconomic applications and simulation evidence. Journal of Econometrics 107, 213–233.Google Scholar
Guay, A. (2003) Optimal predictive tests. Econometric Reviews 22(4), 379–410.CrossRefGoogle Scholar
Guay, A. & Lamarche, J.-F. (2009) Structural Change Tests for GEL Criteria. Working paper 0904, Brock University.Google Scholar
Guay, A. & Pelgrin, F. (2007) Using Implied Probabilities to Improve Estimation in Unconditional Moment Models: Re-assessing the New Keynesian Phillips Curve, Manuscript.Google Scholar
Guggenberger, P., Ramalho, J.J.S., & Smith, R.J. (2007) GEL Pearson-type Statistics under Weak Identification. Manuscript.Google Scholar
Guggenberger, P. & Smith, R.J. (2008) Generalized empirical likelihood tests in time series models with potential identification failure. Journal of Econometrics 142, 134–161.Google Scholar
Hall, A.R., Inoue, A., & Peixe, F.P.M. (2003) Covariance matrix estimation and the limiting behavior of the overidentifying restrictions test in the presence of neglected structural instability. Econometric Theory 19, 962–983.CrossRefGoogle Scholar
Hall, A.R. & Sen, A. (1999) Structural stability testing in models estimated by generalized methods of moments. Journal of Business and Economic Statistics 17, 335–348.Google Scholar
Hall, P. & Horowitz, J.L. (1996) Bootstrap critical values for tests based on generalized-method-of-moments estimators. Econometrica 64, 891–916.CrossRefGoogle Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.Google 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., Spady, R.H., & Johnson, P. (1998) Information theoretic approaches to inference in moment condition models. Econometrica 66, 333–357.Google Scholar
Kitamura, Y. (2001) Asymptotic optimality of empirical likelihood for testing moment restrictions. Econometrica 69, 1661–1672.CrossRefGoogle Scholar
Kitamura, Y. & Stutzer, M. (1997) An information-theoretic alternative to generalized method of moments estimation. Econometrica 65, 861–874.CrossRefGoogle Scholar
Kullback, S. & Leibler, R.A. (1951) On information and sufficiency. Annals of Mathematical Statistics 22, 79–86.Google Scholar
Li, H. & Müller, U.K. (2009) Valid inference in partially unstable generalized method of moments models. Review of Economic Studies 76, 343–365.CrossRefGoogle Scholar
Mittelhammer, R.C., Judge, G.G., & Miller, D.J. (2000) Econometric Foundations, 1st ed. Cambridge University Press.Google Scholar
Newey, W.K. & Smith, R.J. (2004) Higher order properites of GMM and generalized empirical likelihood estimators. Econometrica 72, 219–256.Google Scholar
Newey, W.K. & West, K.D. (1994) Automatic lag selection in covariance matrix estimation. Review of Economic Studies 61, 631–654.CrossRefGoogle Scholar
Otsu, T. (2006) Generalized empirical likelihood inference for nonlinear and time series models under weak identification. Econometric Theory 22, 513–527.CrossRefGoogle Scholar
Pollard, D. (1984) Convergence of Stochastic Processes. Springer-Verlag.CrossRefGoogle Scholar
Qin, J. & Lawless, J. (1994) Empirical likelihood and general estimating equations. Annals of Statistics 22, 300–325.CrossRefGoogle Scholar
Ramalho, J.J.S. & Smith, R.J. (2005) Goodness of Fit Tests for Moment Condition Models. Working paper 5_2005, University of Évora.Google Scholar
Rossi, B. (2005) Optimal tests for nested model selection with underlying parameter instability. Econometric Theory 21, 962–990.Google Scholar
Schennach, S.M. (2007) Point estimation with exponetially tilted empirical likelihood. Annals of Statistics 35, 634–672.Google Scholar
Shannon, C.E. (1948) Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy. IEEE Transactions on Information Theory 26, 26–37.Google Scholar
Smith, R.J. (1997) Alternative semi-parametric likelihood approaches to generalized method of moments. The Economic Journal 107, 503–519.CrossRefGoogle Scholar
Smith, R.J. (2000) Empirical likelihood estimation and inference. In Salmon, M. and Marriott, P. (eds.), Applications of Differential Geometry to Econometrics. pp. 119–150. Cambridge University Press.CrossRefGoogle Scholar
Smith, R.J. (2004) GEL Criteria for Moment Condition Model. CEMMAP Working Paper CWP19/04.CrossRefGoogle Scholar
Sowell, F. (1996a) Optimal tests of parameter variation in the generalized method of moments framework. Econometrica 64, 1085–1108.CrossRefGoogle Scholar
Sowell, F. (1996b) Test for Violations of Moment Conditions. Manuscript, Carnegie Mellon University.Google Scholar
Stock, James H. & Wright, J.H. (2000) GMM with weak identification. Econometrica 68, 1055–1096.CrossRefGoogle Scholar