Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-29T01:15:21.462Z Has data issue: false hasContentIssue false
  • English
  • Français

Testing for Consistency using Artificial Regressions

Published online by Cambridge University Press:  18 October 2010

Russell Davidson  and
James G. MacKinnon
Russell Davidson
Affiliation:
Queen's University, Ontario, Canada and GREQE, Ecole des Hautes Etudes en Sciences Sociales, Universités d'Aix-Marseille ll et ll Centre de la Vieille Charité, France
James G. MacKinnon
Affiliation:
Queen's University, Ontario, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider several issues related to Durbin-Wu-Hausman tests; that is, tests based on the comparison of two sets of parameter estimates. We first review a number of results about these tests in linear regression models, discuss what determines their power, and propose a simple way to improve power in certain cases. We then show how in a general nonlinear setting they may be computed as “score” tests by means of slightly modified versions of any artificial linear regression that can be used to calculate Lagrange multiplier tests, and explore some of the implications of this result. In particular, we show how to create a variant of the information matrix test that tests for parameter consistency. We examine the conventional information matrix test and our new version in the context of binary-choice models, and provide a simple way to compute both tests using artificial regressions.

Type
Articles
Information
Econometric Theory , Volume 5 , Issue 3 , December 1989 , pp. 363 - 384
Copyright
Copyright © Cambridge University Press 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Amemiya, T.Advanced econometrics. Cambridge, Massachusetts: Harvard University Press, 1985.Google Scholar
2.Bera, A.K. & McKenzie, C.R.. Alternative forms and properties of the score test. Journal of Applied Statistics 13 (1986): 13–25.CrossRefGoogle Scholar
3.Boothe, P. & MacKinnon, J.G.. A specification test for models estimated by GLS. Review of Economics and Statistics 68 (1986): 711–714.CrossRefGoogle Scholar
4.Breusch, T.S. & Goldfrey, L.G.. Data transformation tests. Economic Journal 96 (1986): 47–58.CrossRefGoogle Scholar
5.Chesher, A.Testing for neglected heterogeneity. Econometrica 52 (1984): 865–872.CrossRefGoogle Scholar
6.Chesher, A. & Spady, R.. Asymptotic expansions of the information matrix test statistic. Presented at the Econometric Study Group meeting, Bristol, June 1988.Google Scholar
7.Das Gupta, S. & Perlman, M.D.. Power of the noncentral F test: effect of additional variates on Hotelling's T2 test. Journal of the American Statistical Association 69 (1974): 174–180.Google Scholar
8.Davidson, R., Godfrey, L.G., & MacKinnon, J.G.. A simplified version of the differencing test. International Economic Review 26 (1985): 639–647.CrossRefGoogle Scholar
9.Davidson, R. & MacKinnon, J.G.. Small-sample properties of alternative forms of the Lagrange multiplier test. Economics Letters 12 (1983): 269–275.CrossRefGoogle Scholar
10.Davidson, R. & MacKinnon, J.G.. Model specification tests based on artificial linear regressions. International Economic Review 25 (1984): 485–502.CrossRefGoogle Scholar
11.Davidson, R. & MacKinnon, J.G.. Convenient specification tests for logit and probit models. Journal of Econometrics 25 (1984): 241–262.CrossRefGoogle Scholar
12.Davidson, R. & MacKinnon, J.G.. Testing linear and log-linear regressions against Box-Cox alternatives. Canadian Journal of Economics 25 (1985): 499–517.CrossRefGoogle Scholar
13.Davidson, R. & MacKinnon, J.G.. Heteroskedasticity-robust tests in regression directions. Annales de I'INSÉE 59/60 (1985): 183–218.CrossRefGoogle Scholar
14.Davidson, R. & MacKinnon, J.G.. Implicit alternatives and the local power of test statistics. Econometrica 55 (1987): 1305–1329.CrossRefGoogle Scholar
15.Davidson, R. & MacKinnon, J.G.. Testing for consistency using artificial regressions. Queen's University Institute for Economic Research, Discussion Paper No. 679, 1987.Google Scholar
16.Davidson, R. & MacKinnon, J.G.. Double-length artificial regressions. Oxford Bulletin of Economics and Statistics 50 (1988): 203–217.CrossRefGoogle Scholar
17.Davidson, R. & MacKinnon, J.G.. A new form of the information matrix test. Queen's University Institute for Economic Research, Discussion Paper No. 724, 1988.Google Scholar
18.Durbin, J.Errors in variables. Review of the International Statistical Institute 22 (1954): 23–32.CrossRefGoogle Scholar
19.Engle, R.F.A general approach to Lagrange multiplier model diagnostics. Journal of Econometrics 20 (1982): 83–104.CrossRefGoogle Scholar
20.Engle, R.F. Wald, Likelihood-ratio, and Lagrange multiplier tests in econometrics. In Griliches, Z. and Intriligator, M. (ed.), Handbook of Econometrics. Amsterdam: North Holland, 1984.Google Scholar
21.Fisher, G.R. & Smith, R.J.. Least-squares theory and the Hausman specification test. Queen's University Institute for Economic Research, Discussion Paper No. 641, 1985.Google Scholar
22.Godfrey, L.G. & Wickens, M.R.. Testing linear and log-linear regressions for functional form. Review of Economic Studies 48 (1981): 487–496.CrossRefGoogle Scholar
23.Hall, A.The information matrix test for the linear model. Review of Economic Studies 54 (1987): 257–263.CrossRefGoogle Scholar
24.Hausman, J.A.Specification tests in econometrics. Econometrica 46 (1978): 1251–1272.CrossRefGoogle Scholar
25.Holly, A.A remark on Hausman's specification test. Econometrica 50 (1982): 749–759.CrossRefGoogle Scholar
26.Kennan, J. & Neumann, G.R.. Why does the information matrix test reject too often? A diagnosis of some Monte Carlo symptoms. Hoover Institution, Stanford University, Working Papers in Economics E-88–10, 1988.Google Scholar
27.Lancaster, T.The covariance matrix of the information matrix test. Econometrica 52 (1984): 1051–1053.CrossRefGoogle Scholar
28.Nakamura, A. & Nakamura, M.. On the relationships among several specification error tests presented by Durbin, Wu, and Hausman. Econometrica 49 (1981): 1583–1588.CrossRefGoogle Scholar
29.Newey, W.K.Maximum-likelihood specification testing and conditional moment tests. Econometrica 53 (1985): 1047–1070.CrossRefGoogle Scholar
30.Orme, C.The calculation of the information matrix test for binary-data models. University of York, mimeo., 1987.Google Scholar
31.Orme, C.The small sample performance of the information matrix test. University of York, mimeo., 1987.Google Scholar
32.Plosser, C.I., Schwert, G.W., & White, H.. Differencing as a test of specification. International Economic Review 23 (1982): 535–552.CrossRefGoogle Scholar
33.Ramsey, J.B.Tests for specification errors in classical linear least-squares regression analysis. Journal of the Royal Statistical Society, Series B 31 (1969): 350–371.Google Scholar
34.Ruud, P.A.Score tests of consistency. University of California at Berkeley, mimeo., 1982.Google Scholar
35.Ruud, P.A.Tests of specification in econometrics. Econometric Reviews 3 (1984): 211–242.CrossRefGoogle Scholar
36.Thursby, J.G. & Schmidt, P.. Some properties of tests for specification error in a linear regression model. Journal of the American Statistical Association 72 (1977): 635–641.CrossRefGoogle Scholar
37.White, H.A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48 (1980): 817–838.CrossRefGoogle Scholar
38.White, H.Maximum-likelihood estimation of misspecified models. Econometrica 50 (1982): 1–25.CrossRefGoogle Scholar
39.Wu, D.Alternative tests of independence between stochastic regressors and disturbances. Econometrica 41 (1973): 733–750.CrossRefGoogle Scholar