Estimating the Intensive Margin Effect in Panel Data Settings

TL;DR

This paper introduces a new method to estimate the effect of policies on the intensity of responses among participants using panel data, adapting existing bounds to improve identification and relax assumptions.

Contribution

It develops a novel identification strategy combining Changes-in-Changes and Horowitz-Manski-Lee bounds to estimate intensive margin effects, including quantile effects, with relaxed assumptions.

Findings

Partial identification of average and quantile intensive margin effects.

Method applied to analyze a Colombian job training program.

Enhanced estimation techniques with multiple sample sources.

Abstract

Many policies operate through two different channels: the extensive margin (e.g., the decision to participate) and the intensive margin (e.g., the intensity of the response among participants). This paper develops a novel identification strategy to estimate the intensive margin effect in panel data settings. I adapt the Horowitz-Manski-Lee bounds to the Changes-in-Changes framework to partially identify both the average and quantile intensive margin treatment effects. Additionally, I explore how to leverage multiple sources of sample selection to relax the monotonicity assumption in the original Horowitz-Manski-Lee bounds, which may be of independent interest. Alongside the identification strategy, I present estimators and inference results. I illustrate the relevance of the proposed methodology by analyzing a job training program in Colombia.