Extreme Changes in Changes

Abstract

Policy analysts are often interested in treating the units with extreme outcomes, such as infants with extremely low birth weights. Existing changes-in-changes (CIC) estimators are tailored to middle quantiles and do not work well for such subpopulations. This article proposes a new CIC estimator to accurately estimate treatment effects at extreme quantiles. With its asymptotic normality, we also propose a method of statistical inference, which is simple to implement. Based on simulation studies, we propose to use our extreme CIC estimator for extreme quantiles, while the conventional CIC estimator should be used for intermediate quantiles. Applying the proposed method, we study the effects of income gains from the 1993 EITC reform on infant birth weights for those in the most critical conditions. This article is accompanied by a Stata command.

Keywords:

• Extreme quantile
• Pareto exponent
• Quantile treatment effect

Supplementary Materials

The supplementary materials include files for our simulations and empirical application.

Acknowledgments

We thank the editor (Ivan Canay), associate editor, two anonymous referees, Alfonso Flores-Lagunes, Hilary Hoynes, Doug Miller, and David Simon for useful advice about our empirical application. We benefited from discussions with Jon Roth. All remaining errors are ours. A Stata command, ecic (extreme changes in changes), associated with this article can be installed from SSC archive with the following command line: ssc install ecic.

Disclosure Statement

The authors report there are no competing interests to declare.