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Davidson

Publications

Testing for Consistency using Artificial RegressionsJournal articleRussell Davidson et James G. MacKinnon, Econometric Theory, Volume 5, Issue 03, pp. 363-384, 1989

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.
Double Length Artificial RegressionsJournal articleRussell Davidson et James G. MacKinnon, Oxford Bulletin of Economics and Statistics, Volume 50, Issue 2, pp. 203-17, 1988

Artificial linear regressions often provide a convenient way to calculate test statistics and estimated covariance ma trices. This paper discusses one family of these regressions called d ouble length because the number of observations in the artificial reg ression is twice the actual number of observations. These double-leng th regressions can be useful in a wide variety of situations. They ar e quite easy to calculate, and, in contrast to the more widely applic able OPG regression, seem to have good properties when applied to sam ples of modest size. The authors first discuss how they are related t o the familiar Gauss-Newton and squared-residuals regressions for non linear regression models, then show how they may be used to test for functional form, and finally discuss several other ways in which they may be useful in applied econometric work. Copyright 1988 by Blackwell Publishing Ltd
Implicit Alternatives and the Local Power of Test StatisticsJournal articleRussell Davidson et James G. MacKinnon, Econometrica, Volume 55, Issue 6, pp. 1305-29, 1987

The local power of test statistics is analyzed by considering sequences of data-generating processes (DGPs) that approach the null hypothesis without necessarily satisfying the alternative. The three classical test statistics-LR, Wald, and LM-are shown to tend asymptot ically to the same random variable under all such sequences. The powe r of these statistics depends on the null, the alternative, and the sequence of DGPs in a geometrically intuitive way. This implies that, for any statistic that is asymptotically chi-squared under the null, there exists an "implicit alternative hypothesis" against which that statistic will have highest power. Copyright 1987 by The Econometric Society.
Spatial aspects of housing quality, density, and maintenanceJournal articleRussell Davidson, Richard Arnott et David Pines, Journal of Urban Economics, Volume 19, Issue 2, pp. 190-217, 1986

No abstract is available for this item.
Testing Linear and Loglinear Regressions against Box-Cox AlternativesJournal articleRussell Davidson et James G. MacKinnon, Canadian Journal of Economics, Volume 18, Issue 3, pp. 499-517, 1985

No abstract is available for this item.
A Simplified Version of the Differencing TestJournal articleRussell Davidson, Leslie Godfrey et James G. MacKinnon, International Economic Review, Volume 26, Issue 3, pp. 639-47, 1985

No abstract is available for this item.
Model Specification Tests Based on Artificial Linear RegressionsJournal articleRussell Davidson et James G. MacKinnon, International Economic Review, Volume 25, Issue 2, pp. 485-502, 1984

This paper develops a general procedure for performing a wide variety of model specification tests by running artificial linear regressions and then using conventional significance tests. In particular, this procedure allows us to develop non-nested hypothesis tests for any set of models which attempt to explain the same dependent variable(s), even when the error specifications of the models differ. For example, it is straightforward to test linear regression models against loglinear ones. These procedures are illustrated with an application to estimate competing models of personal savings in Canada.
Unanticipated shocks and the maintenance and replacement of durable goodsJournal articleRussell Davidson, Richard Arnott et David Pines, Journal of Economic Dynamics and Control, Volume 8, Issue 1, pp. 99-115, 1984

We investigate how owners of durable goods respond to a once-for-all unanticipated shock in a housing market that was in a stationary state prior to, and after the shock. We determine the circumstances under which the landlord will: 1) abandon his building immediately; 2) run down his building optimally the abandon; 3) operate his building forever; 4) demolish immediately and reconstruct; 5) run down his building, demolish, and reconstruct.
Convenient specification tests for logit and probit modelsJournal articleRussell Davidson et James G. MacKinnon, Journal of Econometrics, Volume 25, Issue 3, pp. 241-262, 1984

We propose several Lagrange Multiplier tests of logit and probit models, which may be inexpensively computed by artificial linear regressions. These may be used to test for omitted variables and heteroskedasticity. We argue that one of these tests is likely to have better small-sample properties, supported by several sampling experiments. We also investigate the power of the tests against local alternatives. The analysis is novel because we do not require that the model which generated the data be the alternative against which the null is tested.
Distribution-Free Statistical Inference with Lorenz Curves and Income SharesJournal articleRussell Davidson et Charles M. Beach, Review of Economic Studies, Volume 50, Issue 4, pp. 723-735, 1983

The paper considers the problem of statistical inference with estimated Lorenz curves and income shares. The full variance-covariance structure of the (asymptotic) normal distribution of a vector of Lorenz curve ordinates is derived and shown to depend only on conditional first and second moments that can be estimated consistently without prior specification of the population density underlying the sample data. Lorenz curves and income shares can thus be used as tools for statistical inference instead of simply as descriptive statistics.