Fuzzy Differences-in-Differences
研究了当处理组和对照组处理率变化不同时，模糊双重差分估计量识别局部平均处理效应的条件，并提出了不依赖处理效应同质性假设的替代估计量。
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 treatment effects 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 two homogeneous treatment effect assumptions are satisfied. 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 Duflo (2001).