Econometrica: Nov, 1988, Volume 56, Issue 6

Chi-Square Diagnostic Tests for Econometric Models: Theory

https://doi.org/0012-9682(198811)56:6<1419:CDTFEM>2.0.CO;2-1
p. 1419-1453

Donald W. K. Andrews

This paper extends the Pearson chi-square testing method to nondynamic parametric econometric models, in particular, to models with covariates. The paper establishes the asymptotic distribution of the test statistic under the null and local alternatives when the test statistic is based on data-dependent random cells of a general form and on an arbitrary asymptotically normal estimator. These results are attained 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.