New possibilities in identification of binary choice models with fixed effects

TL;DR

This paper introduces the sign saturation condition, a new criterion that ensures the identification of binary choice models with fixed effects, even with bounded regressors, and provides tools for its estimation and inference.

Contribution

It proposes the sign saturation condition as a sufficient and necessary criterion for identifying binary choice models with fixed effects, including cases with bounded regressors.

Findings

Sign saturation guarantees model identification.

Without sign saturation, identification requires specific error distributions.

Tools for estimating and testing sign saturation are developed.

Abstract

We study the identification of binary choice models with fixed effects. We propose a condition called sign saturation and show that this condition is sufficient for identifying the model. In particular, this condition can guarantee identification even when all the regressors are bounded, including multiple discrete regressors. We also establish that without this condition, the model is not identified unless the error distribution belongs to a special class. Moreover, we show that sign saturation is also essential for identifying the sign of treatment effects. Finally, we introduce a measure for sign saturation and develop tools for its estimation and inference.