This work was supported, in part, by a grantfrom the Social Sciences and Humanities Research Council of Canada. The paper was written mostly while the author was on sabbatical at the University of California, San Diego. I am grateful to everyone there for providing such a hospitable environment, and to Anil Bera, Russell Davidson, David Hendry, Timo Teriisvirta, Pravin Trivedi, three referees, and seminar participants at the University of -Indiana for helpful comments on earlier versions.

We develop a new specification test which can easily be applied to regression models that have been estimated by generalized least squares. The test is a variant of the F-test. It is derived for the general case, and also, in more detail, for the commonly encountered case of models with AR(1) errors. Two empirical examples are presented, one of them involving a well-known model of exchange rate determination.

This paper deals with the cost-benefit valuation of urban land in residential and road use, when there is flow congestion in transportation and congestion tolls are not imposed. Conventional procedures for determining the shadow value of land in road or residential use ignore certain general equilibrium effects, and always overstate the true values. To illustrate the correct procedures, an urban simulation model is used to calculate shadow rents of land as a function of location. The model is more realistic than most theoretical urban models, particularly in its treatment of congestion.

In this paper we discuss several statistical techniques which may be used to test the validity of a possibly non-linear and multivariate regression model, using the information provided by estimating one or more alternative models on the same set of data. We first exposit, from a different perspective, the tests proposed by us in Davidson and MacKinnon (1981a), and discuss modified versions of these tests and extensions of them to the multivariate case. We then prove that all these tests, and also the tests previously proposed by Pesaran (1974) and Pesaran and Deaton (1978), based on the work of Cox (1961, 1962), are asymptotically equivalent under certain conditions. Finally, we present the results of a sampling experiment which shows that different tests can behave quite differently in small samples.

A new form of the information matrix test is developed for a wide variety of statistical models. The test is constructed against an explicit alternative with random parameter variation. It is computed using a double-length artificial regression instead of the more conventional outer-product-of-the-gradient regression, which is known to have very poor finite-sample properties. In Monte Carlo experiments for the case of univariate linear regression models, the new form performs remarkably well. Some approximate finite-sample distributions are also calculated for this case and lend support to the use of the new form.

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.

Several procedures are proposed for testing the specification of an econometric model in the presence of one or more other models which purport to explain the same phenomenon.These procedures are shown to be closely related, but not identical, to the non-nested hypothesis tests recently proposed by Pesaran and Deaton [7], and to have similar asymptotic properties..They are remarkably simple both conceptually and computationally, and, unlike earlier techniques, they may be used to test against several alternative models simultaneously.Some empirical results are presented which suggest that the ability of the tests to reject false hypotheses is likely to be rather good in practice.

The widely used Cochrane-Orcutt and Hildreth-Lu procedures for estimating the parameters of a linear regression model with first-order autocorrelation typically ignore the first observation. An alternative maximum likelihood procedure which incorporates the first observation and the stationarity condition of the error process is proposed in this paper. It is similar to the Cochrane-Orcutt procedure, and appears to be at least as computationally efficient. This estimator is superior to the conventional ones on theoretical grounds, and sampling experiments suggest that it may yield substantially better estimates in some circumstances.