@article{Borusyak_Jaravel_Spiess_2021,
  title        = {Revisiting Event Study Designs: Robust and Efficient Estimation},
  abstractnote = {A broad empirical literature uses “event study,” or “diﬀerence-in-diﬀerences with staggered rollout,” research designs for treatment eﬀect estimation: settings in which units in the panel receive treatment at diﬀerent times. We show a series of problems with conventional regression-based two-way ﬁxed eﬀects estimators, both static and dynamic. These problems arise when researchers conﬂate the identifying assumptions of parallel trends and no anticipatory eﬀects, implicit assumptions that restrict treatment eﬀect heterogeneity, and the speciﬁcation of the estimand as a weighted average of treatment eﬀects. We then derive the eﬃcient estimator robust to treatment eﬀect heterogeneity for this setting, show that it has a particularly intuitive “imputation” form when treatment-eﬀect heterogeneity is unrestricted, characterize its asymptotic behavior, provide tools for inference, and illustrate its attractive properties in simulations. We further discuss appropriate tests for parallel trends, and show how our estimation approach extends to many settings beyond standard event studies.},
  author       = {Borusyak, Kirill and Jaravel, Xavier and Spiess, Jann},
  year         = {2021},
  pages        = {48},
}

@article{Callaway_SantAnna_2018,
  title        = {Difference-in-Differences with Multiple Time Periods and an Application on the Minimum Wage and Employment},
  url          = {http://arxiv.org/abs/1803.09015},
  abstractnote = {In this article, we consider identiﬁcation and estimation of treatment eﬀect parameters using Diﬀerence-in-Diﬀerences (DID) with (i) multiple time periods, (ii) variation in treatment timing, and (iii) when the “parallel trends assumption” holds potentially only after conditioning on observed covariates. We propose a simple two-step estimation strategy, establish the asymptotic properties of the proposed estimators, and prove the validity of a computationally convenient bootstrap procedure to conduct asymptotically valid simultaneous (instead of pointwise) inference. Our proposed inference procedure naturally adjusts for autocorrelation and other forms of clustering in the data. We also propose a semiparametric data-driven testing procedure to assess the credibility of the DID design in our context. Finally, we illustrate the relevance of our proposed tools by analyzing the eﬀect of the minimum wage on teen employment from 2001-2007. Open-source software is available for implementing the proposed methods.},
  note         = {arXiv: 1803.09015},
  journal      = {arXiv:1803.09015},
  author       = {Callaway, Brantly and Sant'Anna, Pedro H. C.},
  year         = {2018},
  month        = {Aug},
}
@book{deChaisemartin_DHaultfoeuille_2019,
  place        = {Cambridge, MA},
  title        = {Two-way Fixed Effects Estimators with Heterogeneous Treatment Effects},
  url          = {http://www.nber.org/papers/w25904.pdf},
  doi          = {10.3386/w25904},
  abstractnote = {Linear regressions with period and group ﬁxed eﬀects are widely used to estimate treatment eﬀects. We show that they estimate weighted sums of the average treatment eﬀects (ATE) in each group and period, with weights that may be negative. Due to the negative weights, the linear regression coeﬃcient may for instance be negative while all the ATEs are positive. We propose another estimator that solves this issue. In the two applications we revisit, it is signiﬁcantly diﬀerent from the linear regression estimator.},
  number       = {w25904},
  institution  = {National Bureau of Economic Research},
  author       = {de Chaisemartin, Clement and D'Haultfoeuille, Xavier},
  year         = {2019},
  month        = {May},
  pages        = {w25904},
}
@unpublished{Gardner_2021,
  author = {Gardner, John},
  series = {Working Paper},
  title  = {{Two-Stage Difference-in-Differences}},
  url    = {https://jrgcmu.github.io/2sdd_current.pdf},
  year   = {2021},
}
@book{Goodman-Bacon_2018,
  place        = {Cambridge, MA},
  title        = {Difference-in-Differences with Variation in Treatment Timing},
  url          = {http://www.nber.org/papers/w25018.pdf},
  doi          = {10.3386/w25018},
  abstractnote = {The canonical difference-in-differences (DD) estimator contains two time periods, “pre” and “post”, and two groups, “treatment” and “control”. Most DD applications, however, exploit variation across groups of units that receive treatment at different times. This paper shows that the general estimator equals a weighted average of all possible two-group/two-period DD estimators in the data. This defines the DD estimand and identifying assumption, a generalization of common trends. I discuss how to interpret DD estimates and propose a new balance test. I show how to decompose the difference between two specifications, and provide a new analysis of models that include time-varying controls.},
  number       = {w25018},
  institution  = {National Bureau of Economic Research},
  author       = {Goodman-Bacon, Andrew},
  year         = {2018},
  month        = {Sep},
  pages        = {w25018},
}
@article{Sun_Abraham_2020,
  title        = {Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects},
  abstractnote = {To estimate the dynamic effects of an absorbing treatment, researchers often use two-way ﬁxed effects regressions that include leads and lags of the treatment. We show that in settings with variation in treatment timing across units, the coefﬁcient on a given lead or lag can be contaminated by effects from other periods, and apparent pretrends can arise solely from treatment effects heterogeneity. We propose an alternative estimator that is free of contamination, and illustrate the relative shortcomings of two-way ﬁxed effects regressions with leads and lags through an empirical application.},
  author       = {Sun, Liyang and Abraham, Sarah},
  year         = {2020},
  pages        = {53},
}
