Abstract
We present a numerically convenient procedure for computing Wald criteria for nested hypotheses. Similar to Szroeter’s (1983) generalized Wald test, the suggested procedure does not require explicit derivation of the restrictions implied by the null hypothesis and hence its use might eliminate an intricate step in testing linear and nonlinear hypotheses. We show that the traditional Wald test, Szroeter’s (1983) generalized Wald test and our procedure are asymptotically equivalent under H0. A class of nonlinear transformations of the restrictions for which the Wald statistic is asymptotically invariant is discussed. Finally, we illustrate the use of our procedure for testing the common factor restrictions in a dynamic regression model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Almon, S. (1965): “The distributed lag between capital appropriations and expenditures”,Econometrica, 30, 178–196.
Billingsley, P. (1968):Convergence of Probability Measures, New York, John Wiley.
Gouriéroux, C., Monfort, A., and A. Trognon (1985): “Moindres carrés asymptotiques”,Annales de l’INSEE, 58, 91–122.
Gouriéroux, C., and A. Monfort (1987): “A general framework for testing a null hypothesis in a ‘mixed’ form”, Institut National de Statistique et des Etudes Economiques, Paris, Document de travail 8711.
Holly, A., and A. Monfort (1985): “Some useful equivalence properties of Hausman’s test”, Cahiers de recherches économiques, 8505, Université de Lausanne.
Hoffman, D.L., and P. Schmidt (1981): “Testing the restrictions implied by the rational expectations hypothesis”,Journal of Econometrics 15, 265–287.
Kodde, D.A., Palm F.C. and G.A. Pfann (1987): “Asymptotic least squares estimation: efficiency considerations”, Research-memorandum, University of Limburg.
Mizon, G.E., and D.F. Hendry (1980): “An empirical application and Monte Carlo analysis of tests of dynamic specification”,The Review of Economic Studies, 47, 21–46.
Rudin, W. (1976):Principles of Mathematical Analysis, 3rd edit., Tokyo, McGraw-Hill.
Sargan, J.D. (1977): “Dynamic specification for models with autoregressive errors. Vector autoregressive case”, Discussion paper, London School of Economics.
Sargan, J.D. (1980a): “Some tests of dynamic specification for a single equation”,Economitrica, 48, 879–898.
Sargan, J.D. (1980b): “The consumer price equation in the postwar British economy: An exercise in equation specification testing”,The Review of Economic Studies, 47, 113–136.
Stroud, T.W.F. (1971): “On obtaining large-sample tests from asymptotically normal estimators”,The Annals of Mathematical Statistics, 42, 1412–1424.
Szroeter, J. (1983): “Generalized Wald methods for testing nonlinear implicit and overidentifying restrictions”,Econometrica, 51, 335–353.
Wald, A. (1943): “Tests of statistical hypotheses concerning several parameters when the number of observations is large”,Transactions of the American Mathematical Society, 54, 426–482.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Palm, F.C., Kodde, D.A. Computing Wald criteria for nested hypotheses. Statistical Papers 29, 169–190 (1988). https://doi.org/10.1007/BF02924523
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02924523