Was Javert right to be suspicious? Marginal Treatment Effects with Duration Outcomes

TL;DR

This paper develops semi-parametric methods to estimate marginal treatment effects with duration outcomes under censoring, revealing heterogeneity in recidivism effects based on punishment severity.

Contribution

It introduces consistent estimators and inference procedures for distributional and quantile treatment effects with censored duration data, applied to criminal recidivism analysis.

Findings

People most punished by judges take longer to recidivate.

Strict judges' punishments lead to earlier recidivism for less punished individuals.

Substantial heterogeneity in treatment effects based on punishment severity.

Abstract

We identify the distributional and quantile marginal treatment effect functions when the outcome is right-censored. Our method requires a conditionally exogenous instrument and random censoring. We propose asymptotically consistent semi-parametric estimators and valid inferential procedures for the target functions. To illustrate, we evaluate the effect of alternative sentences (fines and community service vs. no punishment) on recidivism in Brazil. Our results highlight substantial treatment effect heterogeneity: we find that people whom most judges would punish take longer to recidivate, while people who would be punished only by strict judges recidivate at an earlier date than if they were not punished.