Davidson
Russell Davidson
Publications
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.
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
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.
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No abstract is available for this item.
No abstract is available for this item.
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.
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.
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.
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.
