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Event-Study Designs for Discrete Outcomes under Transition Independence

Young Ahn, Hiroyuki Kasahara

Abstract

We develop a new identification strategy for average treatment effects on the treated (ATT) in panel data with discrete outcomes. Standard difference-in-differences (DiD) relies on parallel trends, which is frequently violated in categorical settings due to mean reversion, out-of-bounds counterfactuals, and ill-defined trends for multi-category outcomes. We propose an alternative identification strategy with transition independence: absent treatment, transition dynamics conditional on pre-treatment outcomes are identical between control and treated groups. To capture unobserved heterogeneity, we introduce a latent-type Markov structure delivering type-specific and aggregate treatment effects from short panels. Three empirical applications yield ATT estimates substantially different from conventional DiD.

Event-Study Designs for Discrete Outcomes under Transition Independence

Abstract

We develop a new identification strategy for average treatment effects on the treated (ATT) in panel data with discrete outcomes. Standard difference-in-differences (DiD) relies on parallel trends, which is frequently violated in categorical settings due to mean reversion, out-of-bounds counterfactuals, and ill-defined trends for multi-category outcomes. We propose an alternative identification strategy with transition independence: absent treatment, transition dynamics conditional on pre-treatment outcomes are identical between control and treated groups. To capture unobserved heterogeneity, we introduce a latent-type Markov structure delivering type-specific and aggregate treatment effects from short panels. Three empirical applications yield ATT estimates substantially different from conventional DiD.
Paper Structure (33 sections, 12 theorems, 124 equations, 22 figures)

This paper contains 33 sections, 12 theorems, 124 equations, 22 figures.

Table of Contents

  1. Introduction
  2. Empirical illustration.
  3. Related literature.
  4. Discrete Outcome Models
  5. Potential Outcome Model with Transition Independence
  6. Comparison with the DiD Estimator
  7. The DiD Estimator and the Parallel Trends Assumption
  8. Conditional Parallel Trends with Pre-Treatment Outcomes
  9. An Issue in Conditioning on Pre-Treatment Outcomes
  10. Discrete Outcome Models with Latent Heterogeneity
  11. Estimation
  12. Applications
  13. Application to charoenwong2019does
  14. Application to hvide2018university
  15. Employment Effects of the Americans with Disabilities Act of 1990
  16. ...and 18 more sections

Key Result

Proposition 1

Suppose that Assumptions A-transition, A-anticipation, and A-overlap hold. Then, for $t=T_0+1,...,T$, ATTs are identified by

Figures (22)

  • Figure 1: Counterfactual Complaint Rates from the Dodd-Frank Act.
  • Figure 2: Patenting Rates Around the Norwegian Law Reform.
  • Figure 3: Decomposing the ADA's Effect on Employment by Transition Channels.
  • Figure 4: ATT Estimates of the ADA on Employment: DiD vs Our Method.
  • Figure 5: ADA's Effect on Employment Transitions.
  • ...and 17 more figures

Theorems & Definitions (23)

  • Proposition 1
  • Corollary 2
  • Remark 3: Relation to sequential exchangeability
  • Remark 4: Testing for transition independence in pre-treatment periods
  • Remark 5: Placebo test
  • Remark 6: Transition independence with covariates
  • Remark 7: Staggered treatment adoption
  • Remark 8: Decomposition by flows
  • Proposition 9
  • Proposition 10
  • ...and 13 more