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Encompassing and Specificity

Published online by Cambridge University Press:  11 February 2009

Jean-Pierre Florens ,
David F. Hendry  and
Jean-François Richard
Jean-Pierre Florens
Affiliation:
Toulouse University
David F. Hendry
Affiliation:
Nuffield College
Jean-François Richard
Affiliation:
University of Pittsburgh
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Abstract

A model M is said to encompass another model N if the former can explain the results obtained by the latter. In this paper, we propose a general notion of encompassing that covers both classical and Bayesian viewpoints and essentially represents a concept of sufficiency among models. We introduce the parent notion of specificity that aims at measuring lack of encompassing. Tests for encompassing are discussed and the test statistics are compared to Bayesian posterior odds. Operational approximations are offered to cover situations where exact solutions cannot be obtained.

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 4 , October 1996 , pp. 620 - 656
Copyright
Copyright © Cambridge University Press 1996

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References

REFERENCES

Berger, J. (1990) Robust Bayesian analysis: Sensitivity to the prior. The Journal of Statistical Planning and Inference 25, 303–328.CrossRefGoogle Scholar
Billingsley, P. (1968) Convergence of Probability Measures. New York: John Wiley and Sons.Google Scholar
Blackwell, D. (1951) Comparison of experiments. In Proceedings of the Second Berkeley Symposium of Mathematical Statistics and Probability, pp. 93–102. Berkeley: University of California Press.Google Scholar
Blackwell, D. (1953) Equivalent comparison of experiments. The Annals of Mathematical Statistics 24, 265–272.Google Scholar
Csiszar, I. (1967) On information type measures of difference of probability distributions and indirect observations. Studia Scientiarum Mathematicarum Hungria 2, 299–318.Google Scholar
Davidson, J.E.H., Hendry, D.F., Srba, F., & Yeo, S. (1978) Econometric modelling of the aggregate time-series relationship between consumers' expenditure and income in the United Kingdom. Economic Journal 88, 661–692.CrossRefGoogle Scholar
Dellacherie, C. & Meyer, P.A. (1975) Probability et Potentiel. Paris: Hermann. (English translation, 1978, Probabilities and Potential, New York: North-Holland.)Google Scholar
Florens, J.P., Larribeau, S., & Mouchart, M. (1994) Bayesian encompassing test of a unit root hypothesis. Econometric Theory 10, 747–763.CrossRefGoogle Scholar
Florens, J.P. & Mouchart, M. (1989) Bayesian specification tests. In Cornet, B. & Tulkens, H. (eds.), Contributions to Operations Research and Econometrics, pp. 467–490. Cambridge, Massachusetts: MIT Press.Google Scholar
Florens, J.P. & Mouchart, M. (1993) Bayesian testing and testing Bayesians. In Maddala, G.S., Rao, C.R., & Vinod, H.D. (eds.), Handbook of Statistics, vol. 11: Econometrics, pp. 303–334. Amsterdam: North-Holland.CrossRefGoogle Scholar
Florens, J.P., Mouchart, M., & Rolin, J.-M. (1990) Elements of Bayesian Statistics. New York: Marcel Dekker.Google Scholar
Florens, J.P. & Richard, J.-F. (1989) Encompassing in Finite Parametric Spaces. Mimeo, Duke University.Google Scholar
Florens, J.P. & Scotto, S. (1984) Information Value and Econometric Modelling. Southern European Economic Discussion Paper Series, 17, GREQE, University of Aix-Marseille.Google Scholar
Goel, P.K. & DeGroot, M.H. (1979) Comparison of experiments and information measures. Annals of Statistics 7 (5), 1066–1077.Google Scholar
Gourieroux, C. & Monfort, A. (1995) Testing non-nested hypotheses. In Engle, R.F. & McFadden, D.L. (eds.), Handbook of Econometrics, vol. 4, pp. 2585–2637. Amsterdam: North-Holland.Google Scholar
Gourieroux, C, Monfort, A., & Trognon, A. (1983) Testing nested or nonnested hypotheses. Journal of Econometrics 38, 73–90.Google Scholar
Gourieroux, C, Monfort, A., & Trognon, A. (1984) Pseudo-maximum likelihood methods: Theory. Econometrica 52, 681–700.CrossRefGoogle Scholar
Govaerts, B., Hendry, D.F., & Richard, J.-F. (1994) Encompassing in stationary linear dynamic models. Journal of Econometrics 63, 245–270.CrossRefGoogle Scholar
Hendry, D.F. & Richard, J.-F. (1982) On the formulation of empirical models in dynamic econometrics. Journal of Econometrics 20, 3–33. (Reprinted 1990, in C.W.J. Granger (ed.)F Modelling Economic Series, Oxford: Clarendon Press.)Google Scholar
Hendry, D.F. & Richard, J.-F. (1983) The econometric analysis of economic time series (with discussion). International Statistical Review 51, 111–163.CrossRefGoogle Scholar
Hendry, D.F. & Richard, J.-F. (1989) Recent developments in the theory of encompassing. In Comet, B. & Tulkens, H. (eds.), Contributions to Operations Research and Econometrics. The XXth Anniversary of CORE, pp. 393–440. Cambridge, Massachusetts: MIT Press.Google Scholar
Huber, P.J. (1967) The behavior of maximum likelihood estimates under non-standard conditions. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 221–233. Berkeley: University of California Press.Google Scholar
Kiefer, N. & Richard, J.F. (1987) Decision Theory, Estimation Strategies and Model Choice. CAE working paper 87–08, Cornell University.Google Scholar
Lavine, M. (1991) Sensitivity and Bayesian statistics: The prior and the likelihood. Journal of the American Statistical Association 86, 396–399.CrossRefGoogle Scholar
LeCam, L. (1964) Sufficiency and approximate sufficiency. Annals of Mathematical Statistics 35, 1419–1455.Google Scholar
Mizon, G.E. (1984) The encompassing approach in econometrics. In Hendry, D.F. & Wallis, K.F. (eds.), Econometrics and Quantitative Economics, pp. 135–172. Oxford: Basil Blackwell.Google Scholar
Mizon, G.E. & Richard, J.-F. (1986) The encompassing principle and its application to non-nested hypothesis tests. Econometrica 54, 657–678.CrossRefGoogle Scholar
Neveu, J. (1970) Bases Mathematiques des Probability, 2nd ed.Paris: Masson. (English translation, 1965, Mathematical Foundations of the Calculus of Probability, San Francisco: Holden-Day.)Google Scholar
Raiffa, H. & Schlaifer, R. (1961) Applied Statistical Decision Theory. Boston: Division of Research, Harvard Business School.Google Scholar
Sawa, T. (1978) Information criteria for discriminating among alternative regression models. Econometrica 46, 1273–1292.Google Scholar
Torgensen, E.N. (1976) Comparison of statistical experiments. Scandinavian Journal of Statistics 3, 186–208.Google Scholar
White, H. (1982) Maximum likelihood estimation of misspecified models. Econometrica 50, 1–26.Google Scholar
Zellner, A. (1971) An Introduction to Bayesian Inference in Econometrics. New York: John Wiley.Google Scholar