A Consistent Test for Misspeciication in Polychotomous Response Models

We propose a test for misspeciication in polychotomous response models such as the conditional or the multinomial logit model. The test is based on comparing (a smoothed version of) the link functions of the parametric polychotomous model under consideration with a nonparametric estimate. If the parametric model is correct the nonparametric estimates should diier from (the smooth of) the hypothesized links only by random sampling error. If however the parametric model is misspeciied then systematic diierences should arise. We derive the asymptotic distribution of the test statistic under the null hypothesis, show that it is consistent against semiparametric alternatives and investigate its local power properties. A small Monte Carlo study investigates the nite sample performance of the test. I am greatly indebted to Joel Horowitz for many helpful suggestions and disussions. Helpful comments were also made