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Advances in Difference-in-Differences

Paper Session

Sunday, Jan. 9, 2022 12:15 PM - 2:15 PM (EST)

Hosted By: Econometric Society
  • Chair: Xavier D'Haultfoeuille, Center for Research in Economics and Statistics

Inference in Differences-in-Differences with Few Treated Units and Spatial Correlation

Bruno Ferman
,
Sao Paulo School of Economics-FGV

Abstract

We consider the problem of inference in Difference-in-Differences (DID) models when there are few treated units and errors are spatially correlated. We first show that, when there is a single treated unit, existing inference methods designed for settings with few treated and many control units remain asymptotically valid when errors are weakly dependent. However, these methods may be invalid with more than one treated unit. We propose asymptotically valid, though generally conservative, inference methods for settings with more than one treated unit. These alternatives are valid even when the relevant distance metric across units is unavailable. We also present an empirical application that highlights some common misunderstandings in the use of randomization inference in DID applications, and illustrates how our results can be used to provide proper inference.

An Honest Approach to Parallel Trends

Ashesh Rambachan
,
Harvard University
Jonathan Roth
,
Brown University

Abstract

This paper proposes tools for robust inference for difference-in-differences and event-study designs. Instead of requiring that the parallel trends assumption holds exactly, we impose that pre-treatment violations of parallel trends ("pre-trends") are informative about the possible post-treatment violations of parallel trends. Such restrictions allow us to formalize the intuition behind the common practice of testing for pre-existing trends while avoiding issues related to pre-testing. The causal effect of interest is partially identified under such restrictions. We introduce two approaches that guarantee uniformly valid ("honest") inference under the imposed restrictions, and we derive novel results showing that they have good power properties in our context. We recommend that researchers conduct sensitivity analyses to show what conclusions can be drawn under various restrictions on the possible differences in trends.

Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey

Clement de Chaisemartin
,
Sciences Po
Xavier D'Haultfoeuille
,
Center for Research in Economics and Statistics

Abstract

Linear regressions with period and group fixed effects are widely used to estimate policies' effects: 26 of the 100 most cited papers published by the American Economic Review from 2015 to 2019 estimate such regressions. It has recently been show that those regressions may produce misleading estimates, if the policy's effect is heterogeneous between groups or over time, as is often the case. This survey reviews a fast-growing literature that documents this issue, and that proposes alternative estimators robust to heterogeneous effects.

Discussant(s)
Jonathan Roth
,
Brown University
Clement de Chaisemartin
,
University of California-Santa Barbara
Bruno Ferman
,
Sao Paulo School of Economics-FGV
JEL Classifications
  • C2 - Single Equation Models; Single Variables