When there are multiple outcome series of interest, Synthetic Control analyses typically proceed by estimating separate weights for each outcome. In this paper, we instead propose estimating a common set of weights across outcomes, by balancing either a vector of all outcomes or an index or...

I demonstrate that Ai and Norton's (2003) point about cross differences is not relevant for the estimation of the treatment effect in nonlinear difference-in-differences models such as probit, logit or tobit, because the cross difference is not equal to the treatment effect, which is the...

This paper re-examines inference for cluster samples. Sensitivity analysis is proposed as a new method to perform inference when the number of groups is small. Based on estimations using disaggregated data, the sensitivity of the standard errors with respect to the variance of the cluster...

Inference using difference-in-differences with clustered data requires care. Previous research has shown that t tests based on a cluster-robust variance estimator (CRVE) severely over-reject when there are few treated clusters, that different variants of the wild cluster bootstrap can...

Inference based on cluster-robust standard errors is known to fail when the number of clusters is small, and the wild cluster bootstrap fails dramatically when the number of treated clusters is very small. We propose a family of new procedures called the sub- cluster wild bootstrap. In the case...

We analyze the properties of the Synthetic Control (SC) and related estimators when the pre‐treatment fit is imperfect. In this framework, we show that these estimators are generally biased if treatment assignment is correlated with unobserved confounders, even when the number of...

This paper suggests a causal framework for disentangling individual level treatment effects and interference effects, i.e., general equilibrium, spillover, or interaction effects related to treatment distribution. Thus, the framework allows for a relaxation of the Stable Unit Treatment Value...

In many fields of economics, and also in other disciplines, it is hard to justify the assumption that the random error terms in regression models are uncorrelated. It seems more plausible to assume that they are correlated within clusters, such as geographical areas or time periods, but...