Leslie Godfrey

Tests of non-nested regression models: Small sample adjustments and Monte Carlo evidence

Abstract It is known that the small sample significance levels of Cox-type tests of non-nested regression models can be much greater than the nominal level. Adjustments designed to overcome this problem are discussed and two tests are proposed. Monte Carlo evidence on the performance of the tests derived in this paper, the Davidson-MacKinnon J -test and the Fisher-McAleer test is presented. The F -test applied to the comprehensive model is also included in the simulation experiments.

Testing for multiplicative heteroskedasticity

Abstract The problem of testing for multiplicative heteroskedasticity is considered and a large sample test is proposed. The test statistic is based upon ordinary least squares results, so that only estimation under the null hypothesis of homoskedasticity is required. The test is, however, asymptotically equivalent to the likelihood ratio test and so has good asymptotic power properties. The finite sample behaviour of the test statistic is examined using Monte Carlo experiments which indicate that the test works well for quite small samples.

Variable Addition and LaGrange Multiplier Tests for Linear and Logarithmic Regression Models

The purpose of this paper is to examine the properties of various tests of linear and logarithmic (or log-linear) regression models. The test procedures may be categorized as follows: (1) tests that exploit the fact that the two models are intrinsically non-nested; (2) tests based on the Box-Cox data transformation; and (3) diagnostic tests of functional form misspecification against an unspecified alternative. The small-sample properties of several tests are investigated through a Monte Carlo experiment, as is their robustness to non-normality of the errors. Copyright 1988 by MIT Press.

Instrument Relevance in Multivariate Linear Models

Ameasure of the relevancy of instruments used to estimate the coefficients of a linear multiple regression model is discussed. A method for computing the measure using only standard results from ordinary least squares and two-stage least squares estimation is described. The method is illustrated using an empirical example.

Lectures on advanced econometric theory

Foundations of asymptotic theory simultaneous equation models (SEM) identification and the treatment of general linear restrictions estimation of single equation models 1 - OLS and GLS estimators estimation of single models 2 - the instrumental variable & 2SLS estimator the IV estimation of a set of simultaneous equations maximum likelihood estimation A - full information maximum likelihood (FIML) estimation B - limited information maximum likelihood (LIML) estimation testing equations for misspecification alternative significance tests methods of numerical optimization.

Tests of non-nested regression models some results on small sample behaviour and the bootstrap

The most popular procedures for testing a regression model against a single non-nested alternative can be substantially oversized in small samples. Also, when a regression model is to be tested in the presence of several non-nested alternatives, the null model is sometimes accepted only if testing against each alternative in turn produces no significant outcomes. This approach leads to an implicit overall test with a significance level that is not known, even asymptotically. It is shown that the bootstrap can be used to control significance levels in both types of situation. Power estimates for various tests using bootstrap critical values are also obtained and compared.

Discriminating between errors-in- variables/simultaneity and misspecification in linear regression models

Abstract A two-part test procedure is proposed to assist in discriminating between errors-in-variables/simultaneity and other misspecifications of a linear regression model. A result on the asymptotic independence of tests is established and a numerical example is provided.

Tests for regression models with heteroskedasticity of unknown form

Evidence is presented on the finite sample performance of tests that are robust to heteroskedasticity. In contrast to previous work, the focus is on testing several restrictions on the coefficients of a linear regression model, rather than on a quasi-t test of a single restriction. Tests based upon different forms of a heteroskedasticity-consistent covariance matrix estimator are examined, as are the relative merits of asymptotic and wild bootstrap critical values. As an alternative to such tests, procedures using the classical F statistic are investigated. These procedures use single and double wild bootstraps to assess the significance of the F statistic. The costs of using heteroskedasticity-robust tests when the errors are actually homoskedastic are discussed.

The wild bootstrap and heteroskedasticity-robust tests for serial correlation in dynamic regression models

Conditional heteroskedasticity is a common feature of financial and macroeconomic time series data. When such heteroskedasticity is present, standard checks for serial correlation in dynamic regression models are inappropriate. In such circumstances, it is obviously important to have asymptotically valid tests that are reliable in finite samples. Monte Carlo evidence reported in this paper indicates that asymptotic critical values fail to give good control of finite sample significance levels of heteroskedasticity-robust versions of the standard Lagrange multiplier test, a Hausman-type check, and a new procedure. The application of computer-intensive methods to removing size distortion is, therefore, examined. It is found that a particularly simple form of the wild bootstrap leads to well-behaved tests. Some simulation evidence on power is also given.

Some results on the Glejser and Koenker tests for heteroskedasticity

Abstract The Glejser and Koenker (Studentized Lagrange multiplier) tests for heteroskedasticity are considered. Asymptotic theory and Monte Carlo experiments are used to investigate the effects of nonnormality under null and alternative hypotheses, and also the consequences of using an incorrect alternative. A method for using test outcomes to select models of heteroskedasticity is critically examined. Glejsers test is not, in general, asymptotically valid under asymmetric disturbances. Koenkers test is asymptotically valid under asymmetric and other nonnormal disturbances, but has estimated finite-sample significance levels that are sometimes sensitive to skewness. An adjusted version of Koenkers statistic is discussed.