Testing identifying assumptions in Tobit Models

TL;DR

This paper introduces new sharp tests for key assumptions in Tobit and IV-Tobit models, enabling detection of violations in error distribution, exogeneity, and relevance, with practical application demonstrated on labor supply data.

Contribution

It develops the first sharp, testable implications for Tobit model assumptions and proposes a practical testing procedure using existing inference methods.

Findings

Tests have adequate size and power in simulations.

The method detects violations of exogeneity and error structure.

Application to labor supply data demonstrates practical utility.

Abstract

We develop sharp, testable implications for the identifying assumptions of Tobit and IV-Tobit models: linear index, (joint) normality of errors, treatment (instrument) exogeneity, and relevance. The new sharp testable equalities can detect all possible observable violations of the identifying conditions. The proposed test procedure for the model's validity uses existing inference methods for intersection bounds. Simulations suggest adequate test size and power in detecting exogeneity and error structure violations. We review and propose alternatives to partially identify the parameters of interest under less restrictive assumptions. We revisit a study of married women's labor supply in Lee (1995) to demonstrate the test's practical implementation.