Publication: Treatment effect identification using alternative parallel assumptions
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2012-12
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Abstract
The core assumption to identify the treatment effect in difference-in-differences estimators is the
so-called Parallel Paths assumption, namely that the average change in outcome for the treated in
the absence of treatment equals the average change in outcome for the non-treated. We define a
family of alternative Parallel assumptions and show for a number of frequently used empirical
specifications which parameters of the model identify the treatment effect under the alternative
Parallel assumptions. We further propose a fully flexible model which has two desirable features
not present in the usual econometric specifications implemented in applied research. First, it
allows for flexible dynamics and for testing restrictions on these dynamics. Second, it does not
impose equivalence between alternative Parallel assumptions. We illustrate the usefulness of our
approach by revising the results of several recent papers in which the difference-in-differences
technique has been applied.The core assumption to identify the treatment effect in difference-in-differences estimators is the
so-called Parallel Paths assumption, namely that the average change in outcome for the treated in
the absence of treatment equals the average change in outcome for the non-treated. We define a
family of alternative Parallel assumptions and show for a number of frequently used empirical
specifications which parameters of the model identify the treatment effect under the alternative
Parallel assumptions. We further propose a fully flexible model which has two desirable features
not present in the usual econometric specifications implemented in applied research. First, it
allows for flexible dynamics and for testing restrictions on these dynamics. Second, it does not
impose equivalence between alternative Parallel assumptions. We illustrate the usefulness of our
approach by revising the results of several recent papers in which the difference-in-differences
technique has been applied
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Difference-in-differences, Parallel paths, Treatment effect