Model Adequacy Checks for Discrete Choice Dynamic Models

TL;DR

This paper introduces new parametric model adequacy tests for nonlinear, nonstationary, and noncontinuous time series models, enabling better specification checks of the true distribution in discrete choice models.

Contribution

It proposes a transformation-based testing method that assesses both uniformity and independence, extending integral transform tools for noncontinuous data in dynamic discrete choice models.

Findings

The tests are consistent and have power against local alternatives.

They do not require mixing conditions due to the iid nature of transformed series.

Performance comparisons show advantages over classical specification checks.

Abstract

This paper proposes new parametric model adequacy tests for possibly nonlinear and nonstationary time series models with noncontinuous data distribution, which is often the case in applied work. In particular, we consider the correct specification of parametric conditional distributions in dynamic discrete choice models, not only of some particular conditional characteristics such as moments or symmetry. Knowing the true distribution is important in many circumstances, in particular to apply efficient maximum likelihood methods, obtain consistent estimates of partial effects and appropriate predictions of the probability of future events. We propose a transformation of data which under the true conditional distribution leads to continuous uniform iid series. The uniformity and serial independence of the new series is then examined simultaneously. The transformation can be considered as an extension of the integral transform tool for noncontinuous data. We derive asymptotic properties of such tests taking into account the parameter estimation effect. Since transformed series are iid we do not require any mixing conditions and asymptotic results illustrate the double simultaneous checking nature of our test. The test statistics converges under the null with a parametric rate to the asymptotic distribution, which is case dependent, hence we justify a parametric bootstrap approximation. The test has power against local alternatives and is consistent. The performance of the new tests is compared with classical specification checks for discrete choice models.