SIEPR Policy
paper No. 01-025
Identification and Inference in Nonlinear
Difference-In-Differences Models
Susan Athey and Guido W. Imbens
May 2002
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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