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Identification and Inference in Nonlinear Difference-In-Differences Models

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  • Susan Athey
  • Guido W. Imbens

Abstract

This paper develops an alternative approach to the widely used Difference-In-Difference (DID) method for evaluating the effects of policy changes. In contrast to the standard approach, we introduce a nonlinear model that permits changes over time in the effect of unobservables (e.g., there may be a time trend in the level of wages as well as the returns to skill in the labor market). Further, our assumptions are independent of the scaling of the outcome. 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 tradeoff. We provide conditions under which the model is nonparametrically identified and propose an estimator. We consider extensions to allow for covariates and discrete dependent variables. We also analyze inference, showing that our estimator is root-N consistent and asymptotically normal. Finally, we consider an application.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0280.

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Date of creation: Sep 2002
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Publication status: published as Athey, Susan and Guido W. Imbens. "Identification and Inference in Nonlinear Difference-in-Differences Models." Econometrica 74, 2 (2006): 431-497.
Handle: RePEc:nbr:nberte:0280

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