Econometrica: Mar 2006, Volume 74, Issue 2

Identification and Inference in Nonlinear Difference‐in‐Differences Models

https://doi.org/10.1111/j.1468-0262.2006.00668.x
p. 431-497

Susan Athey, Guido W. Imbens

This paper develops a generalization of the widely used difference‐in‐differences method for evaluating the effects of policy changes. We propose a model that allows the control and treatment groups to have different average benefits from the treatment. The assumptions of the proposed model are invariant to the scaling of the outcome. We provide conditions under which the model is nonparametrically identified and propose an estimator that can be applied using either repeated cross section or panel data. Our approach provides an estimate of the entire counterfactual distribution of outcomes that would have been experienced by the treatment group in the absence of the treatment and likewise for the untreated group in the presence of the treatment. Thus, it enables the evaluation of policy interventions according to criteria such as a mean–variance trade‐off. We also propose methods for inference, showing that our estimator for the average treatment effect is root‐ consistent and asymptotically normal. We consider extensions to allow for covariates, discrete dependent variables, and multiple groups and time periods.

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Supplemental Material

Supplementary Materials for: "Identification and Inference in Nonlinear Difference-In-Differences Models"

In these supplementary materials we provide some details on the implementation of the methods developed in the paper. In addition we apply the different DID approaches using the data analyzed by Meyer, Viscusi, and Durbin (1995). These authors used DID methods to analyze the effects of an increase in disability benefits in the state of Kentucky, where the increase applied to high-earning but not low-earning workers. Next we do a small simulation study. Finally, we provide some additional proofs.

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