ON THE LIMIT BEHAVIOR OF A CHI-SQUARE TYPE TEST IF THE NUMBER OF CONDITIONAL MOMENTS TESTED APPROACHES INFINITY

In this paper, a consistent model specification test is proposed. Some consistent model specification tests have been discussed in econometr ics literature. Those tests are consistent by randomization, display a discontinuity in sample size, or have an asymptotic distribution that depends on the data-generating process and on the model, whereas our test does not have one of those disadvantages. Our test can be viewed upon as a conditional moment test as proposed by Newey but instead of a fixed number of conditional moments, an asymptotically infinite numb er of moment conditions is employed. The use of an asymptotically infi nite number of conditional moments will make it possible to obtain a c onsistent test. Computation of the test statistic is particularly simp le, since in finite samples our statistic is equivalent to a chi-squar e conditional moment test of a finite number of conditional moments.