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A Simple and Powerful Diagnostic Test for Binary Choice Models

Ting Ji, Laura Liu, Yulong Wang, Jiahe Xing

Abstract

This paper proposes a specification test for the conventional distributional assumptions of error terms in binary choice models, focusing on its tail properties. Based on extreme value theory, we first establish that the tail index of the unobserved error can be recovered by that of the observed covariates. The null hypothesis of the index being zero essentially covers the widely used probit and logit models. We then construct a simple and powerful statistical test for both cross-sectional and panel data, requiring no model estimation and no parametric assumptions. Monte Carlo simulations demonstrate that our test performs well in size and power, and applications to three empirical examples on firm export and innovation decisions and female labor force participation illustrate its general applicability.

A Simple and Powerful Diagnostic Test for Binary Choice Models

Abstract

This paper proposes a specification test for the conventional distributional assumptions of error terms in binary choice models, focusing on its tail properties. Based on extreme value theory, we first establish that the tail index of the unobserved error can be recovered by that of the observed covariates. The null hypothesis of the index being zero essentially covers the widely used probit and logit models. We then construct a simple and powerful statistical test for both cross-sectional and panel data, requiring no model estimation and no parametric assumptions. Monte Carlo simulations demonstrate that our test performs well in size and power, and applications to three empirical examples on firm export and innovation decisions and female labor force participation illustrate its general applicability.

Paper Structure

This paper contains 22 sections, 7 theorems, 53 equations, 2 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related literature.
  3. Main Result
  4. Recover Tail Heaviness of Latent Error
  5. Test Statistic
  6. Extensions
  7. Multiple Covariates
  8. Panel Data
  9. Monte Carlo Simulations
  10. Cross-Sectional Model
  11. Panel Data Models
  12. Empirical Examples
  13. Export and Firm Size
  14. Innovation and Firm Size
  15. Female Labor Force Participation and Husband's Income
  16. ...and 7 more sections

Key Result

Proposition 1

Suppose Assumption ass:base holds. Then,

Figures (2)

  • Figure 1: Pareto fit of firm assets among non-exporters ($X_i\mid Y_i=0$): empirical (blue dashed) and fitted Pareto (black solid), top 0.1%.
  • Figure 2: Pareto fit of husband's income among non-participants ($X_{it}\mid Y_{it}=0$): empirical (blue dashed) and fitted Pareto (black solid), top 1%.

Theorems & Definitions (18)

  • Remark 1
  • Proposition 1
  • Remark 2
  • Theorem 1
  • Example 1: Firm export
  • Example 2: Female labor force participation
  • Proposition 2
  • Remark 3
  • Proposition 3
  • Proposition 4
  • ...and 8 more