Journal of Econometrics
Опубликовано на портале: 13-04-2004Donald Wilfrid Kao Andrews Journal of Econometrics. 1988. Vol. 37. No. 1. P. 135-157.
The Pearson chi-square testing method is extended to nondynamic parametric econometric models, particularly models with covariates. A chi-square test is developed that is applicable in a variety of cross-sectional models including panel data methods. It can be employed to test the null hypothesis that the specified parametric model is correct, i.e., the classical goodness-of-fit hypothesis. It also can be employed to test more specific aspects of a parametric model. The tests are applicable in models with covariates that are discrete, continuous, or mixed. The cells may be chosen by using the data, may have flexible shapes, and may partition the product space of the response variable and covariate spaces. The estimator employed to calculate the conditionally expected number of outcomes in each cell can be chosen quite generally. Furthermore, any regular, asymptotically normal estimator can be used. Abstract2: This paper and its sequel, Andrews, extend the Pearson chi-square testing method to non-dynamic parametric econometric models, in particular, models with covariates. The present paper introduced the test and discusses a wide variety of applications. Andrews establishes the asymptotic properties of the test, by extending recent probabilistic results for the weak convergence of empirical processes indexed by sets. The chi-square test that is introduced can be used to test goodness-of-fit of a parametric model, as well as to test particular aspects of the parametric model that are of interest. In the event of rejection of the null hypothesis of correct specification, the test provides information concerning the direction of departure from the null. The results allow for estimation of the parameters of the model by quite general methods. The cells used to construct the test statistic my be random and can be specified in a general form.