We develop simple procedures to test for omitted variables and perform other tests in regression directions, which are asymptotically valid in the presence of heteroskedasticity of unknown form. We examine the asymptotic behaviour of these tests, and use Edgeworth approximations to study their...

Associated with every popular nonlinear estimation method is at least one "artificial" linear regression. We define an artificial regression in terms of three conditions that it must satisfy. Then we show how artificial regressions can be useful for numerical optimization, testing hypotheses,...

In practice, bootstrap tests must use a finite number of bootstrap samples. This means that the outcome of the test will depend on the sequence of random numbers used to generate the bootstrap samples, and it necessarily results in some loss of power. We examine the extent of this power loss and...

Bootstrap tests are tests for which the significance level is calculated by some sort of bootstrap procedure, which may be parametric or nonparametric. We show that, in many circumstances, the size distortion of a bootstrap P value for a test will be one whole order of magnitude smaller than...

This paper discusses several statistical techniques which can be used to test the validity of a possibly nonlinear and multivariate regression model, using the information provided by estimating one or more alternative models on the same set of data. The techniques we propose can be regarded as...

This paper investigates the small-sample properties of several forms of the Lagrange Multiplier test. We find that alternative variants of the LM test, which can be easily computed from artificial linear regressions, perform very differently in small samples. One variant appears to be acceptably...

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...

Several procedures are proposed for testing the specification of an econometric model when one or more models purport to explain the same phenomenon. These procedures are closely related, although not identical, to non-nested hypothesis tests proposed by Pesaran and Deaton, and have similar...

This paper examines two explanations of the observed positive relationship between inflation rates and saving rates in Canada and the United States. Several models are estimated using quarterly time series data from both countries, and the best of these are subjected to a variety of tests. One...