Fuzzy Changes-in Changes

Clément de Chaisemartin and Xavier D'Haultfoeuille

CAGE Online Working Paper Series from Competitive Advantage in the Global Economy (CAGE)

Abstract: The changes-in-changes model extends the widely used difference-in-differences to situations where outcomes may evolve heterogeneously. Contrary to difference-in-differences, this model is invariant to the scaling of the outcome. This paper develops an instrumental variable changes-in-changes model, to allow for situations in which perfect control and treatment groups cannot be defined, so that some units may be treated in the "control group", while some units may remain untreated in the "treatment group". This is the case for instance with repeated cross sections, if the treatment is not tied to a strict rule. Under a mild strengthening of the changes-in-changes model, treatment effects in a population of compliers are point identified when the treatment rate does not change in the control group, and partially identified otherwise. Simple plug-in estimators of treatment effects are proposed. We show that they are asymptotically normal, and that the bootstrap is valid. Finally, we use our results to reanalyze findings in Field (2007) and Duo (2001).

Keywords: differences in differences; changes in changes; imperfect compliance; instrumental variables; quantile treatment effects; partial identication. (search for similar items in EconPapers)
Date: 2014
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (3)

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Working Paper: Fuzzy Changes-in-Changes (2014)
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