Abstract
This paper examines the asymptotic null distributions of the J and Cox non-nested tests in the framework of two linear regression models with nearly orthogonal non-nested regressors. The analysis is based on the concept of near population orthogonality (NPO), according to which the non-nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn. New distributional results emerge under NPO. The J and Cox tests tend to two different random variables asymptotically, each of which is expressible as a function of a nuisance parameter, c, a N(0, 1) variate and a χ 2( q) variate, where q is the number of non-nested regressors in the alternative model. The Monte Carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under NPO by plugging consistent estimates of c into the relevant asymptotic expressions. An empirical example illustrates the ‘plug in’ procedure.
Highlights
Most of the theoretical and empirical research on non-nested hypothesis testing in econometrics has been carried out in the context of two possibly nonlinear non-nested regression models and under the assumption of model non-orthogonality; that is when the sample or population covariance matrix among the non-nested regressors in the two models is a non-null matrix
The J and C tests tend to two di!erent random variables asymptotically each of which is expressible as a function of a nuisance parameter, denoted c, a N(0, 1) variate and a (q) variate, where q is the number of non-nested regressors in the alternative model
This paper investigated the asymptotic null distributions of the J and Cox non-nested tests under a speci"c assumption of model orthogonality
Summary
Most of the theoretical and empirical research on non-nested hypothesis testing in econometrics has been carried out in the context of two possibly nonlinear non-nested regression models and under the assumption of model non-orthogonality; that is when the sample or population covariance matrix among the non-nested regressors in the two models is a non-null matrix This restriction of model non-orthogonality introduces two related considerations regarding non-nested tests. Since Keynsian speci"cations have common regressors with the policy equations this procedure gives rise to rival empirical models with orthogonal regressors; see Pesaran (1982). Given these considerations, it is important to investigate the asymptotic distribution of non-nested tests under the assumption of model orthogonality
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