Synthetic Controls with Imperfect Pre-Treatment Fit

Ferman, Bruno; Pinto, Cristine Campos de Xavier

doi:10.48550/arxiv.1911.08521

Cited by 4 publications

(4 citation statements)

References 24 publications

(97 reference statements)

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“…Given we were in the middle of a large expansionary economic period through the end of 2019, we also might be concerned that the common trends assumption a difference-indifference design would be violated. We construct our synthetic comparison with this critical assumption in mind by matching on the lagged values of the dependent variable and using both level and demeaned data to confirm the robustness of our results (Botosaru & Ferman, 2019;Ferman & Pinto, 2019). We find early evidence female earnings have increased relative to male earnings in states passing SHBs.…”

Section: Introductionmentioning

confidence: 62%

Information and the Persistence of the Gender Wage Gap; Early Evidence from California's Salary History Ban

Hansen

McNichols

2018

SSRN Journal

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Section: Introductionmentioning

confidence: 62%

Information and the Persistence of the Gender Wage Gap; Early Evidence from California's Salary History Ban

Hansen

McNichols

2018

SSRN Journal

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“…Different choices for these weights have been suggested by a variety of authors in the literature. Section 2 of Cattaneo et al (2019) provides a succinct summary of proposals by Abadie et al (2010), Hsiao et al (2012), Doudchenko and Imbens (2016), Chernozhukov et al (2018), Ferman and Pinto (2019), and Arkhangelsky et al (2019). For further discussion of and contributions to the synthetic control literature, see Abadie and LHour (2017), Amjad et al (2018), and Ben-Michael et al (2019).…”

Section: Resultsmentioning

confidence: 99%

Randomization Tests in Observational Studies with Staggered Adoption of Treatment

Shaikh¹,

Toulis²

2019

Preprint

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This paper considers the problem of inference in observational studies with time-varying adoption of treatment. In addition to an unconfoundedness assumption that the potential outcomes are independent of the times at which units adopt treatment conditional on the units' observed characteristics, the main restriction underlying our analysis is that the time at which each unit adopts treatment follows a Cox proportional hazards model. This assumption permits the time at which each unit adopts treatment to depend on the observed characteristics of the unit, but imposes the restriction that the probability of multiple units adopting treatment at the same time is zero. In this context, we study Fisher-style randomization tests of a "sharp" null hypothesis that there is no treatment effect for all units and all time periods. We first show that an infeasible test that treats the parameters of the Cox model as known has rejection probability no greater than the nominal level in finite samples. We then establish that the feasible test that replaces these parameters with consistent estimators has limiting rejection probability no greater than the nominal level. These tests rely upon an important implication of the Cox model that provides a parametric expression for the probability that a particular unit is the first to adopt treatment conditional on both the observed characteristics and the time of first treatment. If these probabilities are equal across all units, then our testing procedure reduces to the randomization test proposed by Abadie et al. (2010). In a simulation study, we examine the practical relevance of our theoretical results, including robustness to misspecification of the model for the time at which each unit adopts treatment. Finally, we provide an empirical application of our methodology using the synthetic control-based test statistic and tobacco legislation data found in Abadie et al. (2010)

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“…The modification introduced in Doudchenko and Imbens (2016) and Ferman and Pinto (2019), allows for an intercept by dropping the restriction M i0t = 0, leading to the Modified Synthetic Control (MSC) estimator:…”

Section: Feasible Weightsmentioning

confidence: 99%

A Design-Based Perspective on Synthetic Control Methods

Bottmer¹,

Imbens²,

Spiess³

et al. 2021

Preprint

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Since their introduction in Abadie and Gardeazabal (2003), Synthetic Control (SC) methods have quickly become one of the leading methods for estimating causal effects in observational studies with panel data. Formal discussions often motivate SC methods by the assumption that the potential outcomes were generated by a factor model. Here we study SC methods from a design-based perspective, assuming a model for the selection of the treated unit(s), e.g., random selection as guaranteed in a randomized experiment. We show that SC methods offer benefits even in settings with randomized assignment, and that the design perspective offers new insights into SC methods for observational data. A first insight is that the standard SC estimator is not unbiased under random assignment. We propose a simple modification of the SC estimator that guarantees unbiasedness in this setting and derive its exact, randomization-based, finite sample variance. We also propose an unbiased estimator for this variance. We show in settings with real data that under random assignment this Modified Unbiased Synthetic Control (MUSC) estimator can have a root mean-squared error (RMSE) that is substantially lower than that of the difference-in-means estimator. We show that such an improvement is weakly guaranteed if the treated period is similar to the other periods, for example, if the treated period was randomly selected. The improvement is most likely to be substantial if the number of pre-treatment periods is large relative to the number of control units.

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Synthetic Controls with Imperfect Pre-Treatment Fit

Cited by 4 publications

References 24 publications

Information and the Persistence of the Gender Wage Gap; Early Evidence from California's Salary History Ban

Information and the Persistence of the Gender Wage Gap; Early Evidence from California's Salary History Ban

Randomization Tests in Observational Studies with Staggered Adoption of Treatment

A Design-Based Perspective on Synthetic Control Methods

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