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A Unified Approach to Robust, Regression-Based Specification Tests

Published online by Cambridge University Press:  11 February 2009

Jeffrey M. Wooldridge
Jeffrey M. Wooldridge
Affiliation:
Massachusetts Institute of Technology
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Abstract

This paper develops a general approach to robust, regression-based specification tests for (possibly) dynamic econometric models. A useful feature of the proposed tests is that, in addition to estimation under the null hypothesis, computation requires only a matrix linear least-squares regression and then an ordinary least-squares regression similar to those employed in popular nonrobust tests. For the leading cases of conditional mean and/or conditional variance tests, the proposed statistics are robust to departures from distributional assumptions that are not being tested, while maintaining asymptotic efficiency under ideal conditions. Moreover, the statistics can be computed using any √T-consistent estimator, resulting in significant simplifications in some otherwise difficult contexts. Among the examples covered are conditional mean tests for models estimated by weighted nonlinear least squares under misspecification of the conditional variance, tests of jointly parameterized conditional means and variances estimated by quasi-maximum likelihood under nonnormality, and some robust specification tests for a dynamic linear model estimated by two-stage least squares.

Type
Articles
Information
Econometric Theory , Volume 6 , Issue 1 , March 1990 , pp. 17 - 43
Copyright
Copyright © Cambridge University Press 1990

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References

1.Bollerslev, T. & Wooldridge, J.M.. Quasi-maximum likelihood estimation of dynamic models with time-varying covariances. MIT Department of Economics Working Paper No. 505, 1988.Google Scholar
2.Breusch, T.S. & Pagan, A.R.. A simple test for heteroskedasticity and random coefficient variation. Econometrica 47 (1979): 1287–1294.Google Scholar
3.Breusch, T.S. & Pagan, A.R.. The Lagrange Multiplier statistic and its application to model specification in econometrics. Review of Economic Studies 47 (1980): 239–253.CrossRefGoogle Scholar
4.Davidson, R. & MacKinnon, J.G.. Several tests of model specification in the presence of alternative hypotheses. Econometrica 49 (1981): 781–793.CrossRefGoogle Scholar
5.Davidson, R. & MacKinnon, J.G.. Heteroskedasticity-robust tests in regression directions. Annales de I'INSEE 59/60 (1985): 183–218.Google Scholar
6.Domowitz, I. & White, H.. Misspecified models with dependent observations. Journal of Econometrics 20 (1982): 35–58.CrossRefGoogle Scholar
7.Engle, R.F.Autoregressive conditional heteroskedasticity with estimates of United Kingdom inflation. Econometrica 50 (1982): 987–1008.CrossRefGoogle Scholar
8.Engle, R.F. Wald, Likelihood Ratio, and Lagrange Multiplier tests in econometrics. In Griliches, Z. and Intriligator, M. (eds.), Handbook of Econometrics, Vol. II, Amsterdam: North Holland (1984): 775–826.Google Scholar
9.Godfrey, L.G.Testing for multiplicative heteroskedasticity. Journal of Econometrics 8 (1978): 227–236.Google Scholar
10.Hansen, L.P.Large sample properties of generalized method of moments estimators. Econometrica 50 (1982): 1029–1054.Google Scholar
11.Hausman, J.A.Specification tests in econometrics. Econometrica 46 (1978): 1251–1271.Google Scholar
12.Hsieh, D.A.A heteroskedasticity-consistent covariance matrix estimator for time series regressions. Journal of Econometrics 22 (1983): 281–290.Google Scholar
13.Kennan, J. & Neuman, G.R.. Why does the information matrix test reject too often? University of Iowa Department of Economics Working Paper No. 88–4, 1988.Google Scholar
14.Koenker, R.A note on studentizing a test for heteroskedasticity. Journal of Econometrics 17(1981): 107–112.Google Scholar
15.Newey, W.K.Maximum likelihood specification testing and conditional moment tests. Econometrica 53 (1985): 1047–1070.CrossRefGoogle Scholar
16.Newey, W.K.Efficient estimation of semiparametric models via moment restrictions. Manuscript. Princeton University.Google Scholar
17.Neyman, J. Optimal asymptotic tests of composite statistical hypotheses. In Grenander, U. (ed.), Probability and Statistics, Stockholm: Almquist and Wiksell (1959): 213–234.Google Scholar
18.Pagan, A.R. & Hall, A.D.. Diagnostic tests as residual analysis. Econometric Reviews 2 (1983): 159–218.CrossRefGoogle Scholar
19.Pagan, A.R., Trivedi, P.K., & Hall, A.D.. Assessing the variability of inflation. Review of Economic Studies 50 (1983): 585–596.Google Scholar
20.Tauchen, G.Diagnostic testing and evaluation of maximum likelihood models. Journal of Econometrics 30 (1985): 415–443.CrossRefGoogle Scholar
21.White, H.A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48 (1980): 817–838.Google Scholar
22.White, H.Nonlinear regression on cross section data. Econometrica 48 (1980): 721–746.Google Scholar
23.White, H.Maximum likelihood estimation of misspecified models. Econometrica 50 (1982): 1–26.CrossRefGoogle Scholar
24.White, H.Asymptotic Theory for econometricians. New York: Academic Press, 1984.Google Scholar
25.White, H. Specification testing in dynamic models. In Bewley, T. (ed.), Advances in Econometrics-Fifth World Congress, Vol. I, New York: Cambridge University Press (1987): 1–58.Google Scholar
26.Wooldridge, J.M. Asymptotic properties of econometric estimators. UCSD Ph.D. dissertation, 1986.Google Scholar
27.Wooldridge, J.M. A regression-based Lagrange Multiplier statistic that is robust in the presence of heteroskedasticity. MIT Department of Economics Working Paper No. 478, 1987.Google Scholar
28.Wooldridge, J.M. Specification testing and quasi-maximum likelihood estimation. MIT Department of Economics Working Paper No. 479, 1987.Google Scholar
29.Wooldridge, J.M. A C(α) Version of the Newey-Tauchen-White Test. Manuscript, MIT Department of Economics, 1989.Google Scholar