New goodness-of-fit diagnostics for dynamic discrete response models

Abstract

This paper proposes new specification tests for dynamic models with discrete responses. In particular, we test the specification of the conditional distribution of multinomial and count data, which is key to apply efficient maximum likelihood methods, to obtain consistent estimates of partial effects and to get appropriate predictions of the probability of future events. The traditional approach is based on a continuation random transformation of discrete data which leads to continuous uniform iid series under the true conditional distribution. Then standard specification testing techniques can be applied to the transformed series, but the extra random noise involved in the continuation may affect power properties of these methods. We investigate in this paper an alternative estimate of a cumulative distribution function based only on discrete data which can be compared directly to a continuous standard uniform cdf. We analyze the asymptotic properties of goodness-of-fit tests based on this new approach and explore the properties in finite samples of a bootstrap algorithm to approximate the critical values of test statistics which are model and parameter dependent. We find that in many relevant cases our new approach performs much better than random-continuation counterparts. (With Carlos Velasco - University of Carlos III - Madrid)