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.