Supplement to Fuzzy Differences-in-Differences

This paper gathers the supplementary material to de Chaisemartin & D'Haultfoeuille (2015). First, we show that two commonly used IV and OLS regressions with time and group fixed effects estimate weighted averages of Wald-DIDs. It then follows from Theorem 3.1 in de Chaisemartin & D'Haultfoeuille (2015) that these regressions estimate weighted sums of LATEs, with potentially many negative weights as we illustrate through two applications. We review all papers published in the American Economic Review between 2010 and 2012 and find that 10.1% of these papers estimate one or the other regression. Second, we consider estimators of the bounds on average and quantile treatment effects derived in Theorems 3.2 and 3.3 in de Chaisemartin & D'Haultfoeuille (2015) and we study their asymptotic behavior. Third, we revisit Gentzkow et al. (2011) and Field (2007) using our estimators. Finally, we present all the remaining proofs not included in the main paper.