Institutional Affiliation: CEMFI
|Synthetic Difference In Differences|
with , , , : w25532
We present a new perspective on the Synthetic Control (SC) method as a weighted least squares regression estimator with time fixed effects and unit weights. This perspective suggests a generalization with two way (both unit and time) fixed effects, and both unit and time weights, which can be interpreted as a unit and time weighted version of the standard Difference In Differences (DID) estimator. We find that this new Synthetic Difference In Differences (SDID) estimator has attractive properties compared to the SC and DID estimators. Formally we show that our approach has double robustness properties: the SDID estimator is consistent under a wide variety of weighting schemes given a well-specified fixed effects model, and SDID is consistent with appropriately penalized SC weights when ...
|The Role of the Propensity Score in Fixed Effect Models|
with : w24814
We develop a new approach for estimating average treatment effects in the observational studies with unobserved cluster-level heterogeneity. The previous approach relied heavily on linear fixed effect specifications that severely limit the heterogeneity between clusters. These methods imply that linearly adjusting for differences between clusters in average covariate values addresses all concerns with cross-cluster comparisons. Instead, we consider an exponential family structure on the within-cluster distribution of covariates and treatments that implies that a low-dimensional sufficient statistic can summarize the empirical distribution, where this sufficient statistic may include functions of the data beyond average covariate values. Then we use modern causal inference methods to const...