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Variable Augmentation Specification Tests in the Exponential Family

Published online by Cambridge University Press:  11 February 2009

Shiferaw Gurmu  and
Pravin K. Trivedi
Shiferaw Gurmu
Affiliation:
University of Virginia
Pravin K. Trivedi
Affiliation:
Indiana University
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Abstract

This paper motivates, exposits, and develops the variable augmentation specification test (VAST) approach from the perspective of generalized linear exponential family, which includes several parametric families widely used in applied econometrics and statistics. The approach is equivalent to score tests and link tests and serves to both unify and simplify the computation of score tests in such models using the Engle-Davidson-MacKinnon technique of artificial regression. Specification tests for both the mean and the variance components are treated symmetrically. Several theoretical applications are discussed.

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Type
Articles
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Econometric Theory , Volume 9 , Issue 1 , January 1993 , pp. 94 - 113
Copyright
Copyright © Cambridge University Press 1993

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References

1.Barndorff-Nielsen, O. & Blaesild, P.. Exponential models with affine foliations. Annals of Statistics 3 (1983): 753–769.Google Scholar
2.Barndorff-Nielsen, O. & Blaesild, P.. Reproductive exponential families. Annals of Statistics 3 (1983): 770–782.Google Scholar
3.Basawa, I.V. Neyman-Le Cam tests based on estimating functions. In Le Cam, L.M. & Olshen, R.A. (eds.), Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, Vol. II, pp. 811–825. Monterey: Wadsworth, 1985.Google Scholar
4.Breusch, T. & Pagan, A.R.. A simple test of heteroskedasticity and random coefficient variation. Econometrica 47 (1979): 1287–1294.Google Scholar
5.Davidson, R. & MacKinnon, J.G.. Convenient specification tests for logit and probit models. Journal of Econometrics 21 (1984): 241–262.Google Scholar
6.Davidson, R. & MacKinnon, J.G.. Specification tests based on artificial regressions. Journal of the American Statistical Association 85 (1990): 220–227.Google Scholar
7.Efron, B.Double exponential families and their use in generalized linear regression. Journal of the American Statistical Association 81 (1986): 709–721.Google Scholar
8.WaldEngle, R.F. Engle, R.F. Likelihood Ratio, and Lagrange multiplier tests in econometrics. In Griliches, Z.I. & Intriligator, M.D. (eds.), Handbook of Econometrics, II, pp. 775–826. Amsterdam: Elsevier Science Publishers B.V., 1983.Google Scholar
9.Engle, R.F. & Bollerslev, T.. Modeling the persistence of conditional variances. Econometric Reviews 5 (1986): 1–50.Google Scholar
10.Godfrey, L.G.Misspecification tests in econometrics: the Lagrange multiplier principle and other approaches. Cambridge: Cambridge University Press, 1988.Google Scholar
11.Godfrey, L.G., McAleer, M. & McKenzie, C.R.. Variable addition and Lagrange multiplier tests for linear and logarithmic regression models. Review of Economics and Statistics LXX (1988): 492–503.CrossRefGoogle Scholar
12.Godfrey, L.G. & Wickens, M.R.. Testing linear and log-linear regressions for functional form. Review of Economic Studies 48 (1981): 487–496.Google Scholar
13.Gourieroux, C., Monfort, A. & Trognon, A.. Pseudo-maximum likelihood methods: theory. Econometrica 52 (1984a): 681–700.Google Scholar
14.Gourieroux, C., Monfort, A. & Trognon, A.. Pseudo-maximum likelihood methods: applications to Poisson models. Econometrica 52 (1984b): 701–720.Google Scholar
15.Jaggia, S. & Trivedi, P.K.. Joint and separate score tests of state dependence and unobserved heterogeneity. Indiana University, Manuscript, 1991. Paper presented at the North American Meetings of the Econometric Society, 1989, Ann Arbor, Michigan (forthcoming in Journal of Econometrics).Google Scholar
16.Jorgenson, B.Exponential dispersion models. Journal of the Royal Statistical Society, Seriesn B 49 (1987): 127–162.Google Scholar
17.McCullagh, P.Quasi-likelihood functions. The Annals of Statistics 11 (1983): 59–67.Google Scholar
18.McCullagh, P.On the asymptotic distribution of Pearson's statistic in linear exponential family models. International Statistical Review 53 (1985): 61–67.Google Scholar
19.McCullagh, P.The conditional distribution of goodness of fit statistics for discrete data. Journal of the American Statistical Association 81 (1986): 104–107.CrossRefGoogle Scholar
20.McCullagh, P. & Nelder, J.A.. Generalized Linear Models, 1st ed., 2nd ed.London: Chapman and Hall, 1983, 1989.Google Scholar
21.Moon, C.-G.Simultaneous specification test in a binary logit model: skewness and heteroskedasticity. Communications in Statistics 17 (1988): 3361–3387.Google Scholar
22.Nelder, J.A. & Pregibon, D.. An extended quasi-likelihood function. Biometrika 74 (1987): 221–232.CrossRefGoogle Scholar
23.Pagan, A.R. Model evaluation by variable addition. In Hendry, D.F. & Wallis, K.F. (eds.), Econometrics and Quantitative Economics, pp. 103–133. Oxford: Blackwell, 1984.Google Scholar
24.Pagan, A.R. & Ullah, A.. The econometric analysis of models with risk terms. Journal of Applied Econometrics 3 (1988): 87–106.Google Scholar
25.Pregibon, D.Goodness of link tests for generalized linear models. Applied Statistics 29 (1980): 15–24.Google Scholar
26.Pregibon, D. Score tests in GLIM with applications. In Gilchrist, R. (ed.), GLIM82: Proceedings of the International Conference on Generalized Linear Models, pp. 87–97. New York: Springer-Verlag, 1982.Google Scholar
27.Pregibon, D. Link tests. In Kotz, J. & Johnson, N.L. (eds.), Encyclopedia of Statistical Sciences, pp. 82–85. New York: Wiley, 1985.Google Scholar
28.Ramsey, J.B. Classical model selection through specification error tests. In Zarembka, P. (ed.), Frontiers in Econometrics, pp. 13–47. New York: Academic Press, 1974.Google Scholar
29.Smyth, G.K.Generalized linear models with varying dispersion. Journal of the Royal Statistical Society, Series B 51 (1989): 47–60.Google Scholar
30.Stukel, T.Generalized logistic models. Journal of the American Statistical Association 83 (1988): 426–431.Google Scholar
31.Wooldridge, J.M.On the application of robust, regression-based diagnostics to models of conditional means and variances. Journal of Econometrics 47 (1991): 5–46.CrossRefGoogle Scholar
32.Zeger, S.L. & Qaqish, B.. Markov regression models for time-series: a quasi-likelihood approach. Biometrics 44 (1988): 1049–1060.Google Scholar