Causal Duration Analysis with Diff-in-Diff

TL;DR

This paper develops new methods for causal analysis of duration data in economic evaluations, addressing limitations of traditional diff-in-diff when outcomes are absorbing states, and introduces hazard rate-based assumptions and estimators.

Contribution

It proposes hazard rate-based assumptions analogous to diff-in-diff for duration data, along with estimators and tests, extending causal inference tools to duration analysis.

Findings

New hazard rate assumptions for duration data

Proposed estimators and specification tests

Application to unemployment benefits policy impact

Abstract

In economic program evaluation, it is common to obtain panel data in which outcomes are indicators that an individual has reached an absorbing state. For example, they may indicate whether an individual has exited a period of unemployment, passed an exam, left a marriage, or had their parole revoked. The parallel trends assumption that underpins difference-in-differences generally fails in such settings. We suggest identifying conditions that are analogous to those of difference-in-differences but apply to hazard rates rather than mean outcomes. These alternative assumptions motivate estimators that retain the simplicity and transparency of standard diff-in-diff, and we suggest analogous specification tests. Our approach can be adapted to general linear restrictions between the hazard rates of different groups, motivating duration analogues of the triple differences and synthetic control methods. We apply our procedures to examine the impact of a policy that increased the generosity of unemployment benefits, using a cross-cohort comparison.