Probability of Causation with Sample Selection: A Reanalysis of the Impacts of J\'ovenes en Acci\'on on Formality

TL;DR

This paper develops bounds for the probability of causation under sample selection and applies it to evaluate a Colombian job training program's impact on women's formal employment.

Contribution

It introduces a method to identify and bound the probability of causation with sample selection, incorporating various assumptions, and demonstrates its application with real experimental data.

Findings

At least 10.2% of women transitioned to formal employment due to the program.

Upper bound of causation probability is 13.4%.

Confidence interval includes zero, indicating statistical uncertainty.

Abstract

This paper identifies the probability of causation when there is sample selection. We show that the probability of causation is partially identified for individuals who are always observed regardless of treatment status and derive sharp bounds under three increasingly restrictive sets of assumptions. The first set imposes an exogenous treatment and a monotone sample selection mechanism. To tighten these bounds, the second set also imposes the monotone treatment response assumption, while the third set additionally imposes a stochastic dominance assumption. Finally, we use experimental data from the Colombian job training program J\'ovenes en Acci\'on to empirically illustrate our approach's usefulness. We find that, among always-employed women, at least 10.2% and at most 13.4% transitioned to the formal labor market because of the program. However, our 90%-confidence region does not reject the null hypothesis that the lower bound is equal to zero.