A Note on Additive Separability and Latent Index Models of Binary Choice: Representation Results

The standard binary choice model in econometrics has the choice determined by a latent index crossing a threshold. The latent index is almost always assumed to be additively separable in observable and unobservable regressors, and most commonly linear in all regressors. This note provides a class of non-separable latent index functions which will have equivalent representations as additively separable or linear index functions. These results demonstrate that assuming a linear or additively separable latent index function is less restrictive than previously recognized. Copyright 2006 Blackwell Publishing Ltd.