An illustration of Cox's non-nested testing procedure for logit and probit models

We discuss some empirical and methodological issues arising when the Cox test statistic for non-nested models is used to test the probit vs. logit specifications. As an example, we consider the models in Bardasi and Monfardini (1997) for the occupational choice by Italian workers among the private, public and self-employed options. Different versions of the test are compared. The bootstrap technique is then used to control for the actual properties of the test. The results indicate the probit to be the more adequate model, providing evidence against the IIA assumption imposed by the logit formulation.