Fuzzy Differences-in-Differences
Fuzzy Differences-in-Differences （模糊倍分法）
de Chaisemartin, C., X. D'Haultfœuille, 2017, Fuzzy differences-in-differences, The Review of Economic Studies: forthcoming.
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Supplementary data (在上述原文下载页面中，数据和 Stata 实现程序, 部分使用 Matlab 实现)
Abstract:
Difference-in-differences (DID) is a method to evaluate the effect of a treatment. In its basic version, a\control group” is untreated at two dates, whereas a\treatment group” becomes fully treated at the second date.
However, in many applications of the DID method, the treatment rate only increases more in the treatment group. In such fuzzy designs, a popular estimator of the treatment effect is the DID of the outcome divided by the DID of the treatment.
We show that this ratio identifies a local average treatment effect only if the effect of the treatment is stable over time, and if the effect of the treatment is the same in the treatment and in the control group.
We then propose two alternative estimands that do not rely on any assumption on treatment effects, and that can be used when the treatment rate does not change over time in the control group.
We prove that the corresponding estimators are asymptotically normal. Finally, we use our results to revisit Duo (2001).
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