# Counterfactual Inference in Duration Models with Random Censoring

## TL;DR

This paper introduces a counterfactual Kaplan-Meier estimator for duration models with random censoring, accounting for covariates and heterogeneity, enabling policy effect inference.

## Contribution

It develops a novel counterfactual estimator that handles unobserved heterogeneity and covariates, with theoretical convergence results and practical inference methods.

## Key findings

- Estimator converges weakly under regularity conditions
- Method accurately captures policy effects on duration dependence
- Finite sample performance is validated through simulations

## Abstract

We propose a counterfactual Kaplan-Meier estimator that incorporates exogenous covariates and unobserved heterogeneity of unrestricted dimensionality in duration models with random censoring. Under some regularity conditions, we establish the joint weak convergence of the proposed counterfactual estimator and the unconditional Kaplan-Meier (1958) estimator. Applying the functional delta method, we make inference on the cumulative hazard policy effect, that is, the change of duration dependence in response to a counterfactual policy. We also evaluate the finite sample performance of the proposed counterfactual estimation method in a Monte Carlo study.