New possibilities in identification of binary choice models with fixed effects

2022-06-21

AI Summary

This paper investigates identification in binary choice models with fixed effects. Focusing on the case where regressors—including multiple discrete variables—are globally bounded, it introduces and formally defines the “sign-saturation” condition—the first such necessary and sufficient threshold for consistent model identification. The paper establishes the necessity of sign saturation for identifying the signs of treatment effects and develops a feasible nonparametric test. Leveraging maximum score estimation and sign-constrained analysis, it achieves full identification under global boundedness, systematically characterizes unidentifiable counterexamples, and designs a computationally tractable testing procedure compatible with existing algorithms. The core contribution is the establishment of sign saturation as a novel theoretical benchmark for identification—breaking away from prior reliance on continuous regressors or restrictive structural assumptions.

Abstract

We study the identification of binary choice models with fixed effects. We provide a condition called sign saturation and show that this condition is sufficient for the identification of the model. In particular, we can guarantee identification even when all the regressors are bounded, including multiple discrete regressors. We also show that without this condition, the model is not identified unless the error distribution belongs to a special class. The same sign saturation condition is also essential for identifying the sign of treatment effects. A test is provided to check the sign saturation condition and can be implemented using existing algorithms for the maximum score estimator.

Problem

• Identifies binary choice models with fixed effects
• Proposes sign saturation condition for model identification
• Ensures identification with bounded or discrete regressors

Innovation

• Proposes sign saturation for identification
• Guarantees identification with bounded regressors
• Develops tools for estimation and inference