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Causal Panel Models with Sequential Exogeneity: a Balancing Approach

19th National Competition for Economic Research Grants

Economic analysis

Senior Researcher : Dmitry Arkhangelskiy

Research Centre or Institution : Fundación Centro de Estudios Monetarios y Financieros (CEMFI)

Abstract

The first one is called “Linear Estimators for Causal Panel Models with Sequential Exogeneity.” This paper focuses on the linear two-way fixed effects model with a staggered adoption design. This setting has been extensively analyzed in the last five years; however, this analysis has focused on the strictly exogenous case. I start by showing both negative and positive identification results. First, I demonstrate that linear estimators that have been overwhelmingly used in the recent literature on causal panel models fail to identify a meaningful effect in a model with unrestricted heterogeneity in treatment effects. This result is in stark contrast to strictly exogenous linear models. Second, I show that this negative result can be mitigated by making an additional design assumption: the presence of a control group that does not receive treatment for ex-ante known reasons. Once such a group is available, one can use a particular linear estimator to identify treatment effects. I am scheduled to present this work in the causal inference seminar at Stanford in the Spring quarter, and I am currently working on the first draft, which should be available in the next couple of months.

In the second project, joint with David Hirshberg and called “Randomization-based inference for Synthetic Control estimators,” we analyze the properties of the Synthetic Difference-in-Differences (SDID) estimator in the models with sequential exogeneity. We provide two sets of results. First, using the connection between Synthetic Control methods and balancing estimators, we demonstrate that in the models without unobserved heterogeneity, SDID is consistent and asymptotically normal under weak design assumptions. Second, we show that in the presence of unobserved heterogeneity, the estimator is in general inconsistent, even in the regime with a large number of periods. We provide a simple remedy that guarantees good statistical properties. This work has already been presented twice: at the 43 Meeting of the Brazilian Econometric Society (December 9, 2021) and at the joint PSE-CREST seminar (January 31, 2022). I am invited to present this work at the Synthetic Control conference at Princeton in the coming June. We expect to have a first draft available by the end of the Spring quarter.

 

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