Identification and Inference in Nonlinear Difference-In-Differences Models

Susan Athey and Guido Imbens

No 280, NBER Technical Working Papers from National Bureau of Economic Research, Inc

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.

Date: 2002-09
New Economics Papers: this item is included in nep-ecm
Note: TWP
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Published as Athey, Susan and Guido W. Imbens. "Identification and Inference in Nonlinear Difference-in-Differences Models." Econometrica 74, 2 (2006): 431-497.

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Journal Article: Identification and Inference in Nonlinear Difference-in-Differences Models (2006)
Working Paper: Identification and Inference in Nonlinear Difference-in-Differences Models (2003)
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