Virtual Room 2: Causal Inference


Thursday, July 16, 2020, 2:30pm to 4:00pm


Chair: Justin Esarey (Wake Forest University)


Co-Host: Md Mujahedul Islam (University of Toronto)

Retrospective causal inference via elapsed time-weighted matrix completion, with an evaluation on the effect of the Schengen Area on the labour market of border regions

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Author(s): Jason Poulos, Andrea Albanese, Andrea Mercatanti and Fan Li

Discussant: James Bisbee (Princeton University)


We propose a strategy of retrospective causal inference in panel data settings where (1) there is a continuous outcome measured before and after a single binary treatment; (2) there exists a group of units exposed to treatment during a subset of periods (switch-treated) and group of units always exposed to treatment (always-treated), but no group that is never exposed to treatment; and (3) the elapsed treatment duration, z, differs across groups. The potential outcomes under treatment for the switch-treated in the pre-treatment period are missing and we impute these values via nuclear-norm regularized least squares using the observed (i.e, factual) outcomes. The imputed values can be interpreted as the counterfactual outcomes of the switch-treated had they been always-treated. Differencing the counterfactual outcomes from the factual outcomes can be interpreted as the effect of not having assigned treatment to the switch-treated in the pre-treatment period. A possible complication for our strategy arises when the evolution of the potential outcomes under treatment for the two groups might not be only influenced by calendar time, but also by z. The latter is particularly important if the treatment effect takes time before stabilizing in a new “steady state” equilibrium. We address this problem by weighting the loss function of the matrix completion estimator so that more weight is placed on the loss for factual outcomes with higher values of z. We apply the proposed strategy to study the impact of the visa policy of the Schengen Area on the labour market of border regions. We first aggregate over 2.2 million individual labour market decisions from the Eurostat Labour Force Survey to the region-level for regions always-treated and switch-treated by the policy during the period of 2004 to 2018. We then estimate the effect of not implementing the policy on the probability of working in any bordering region for switch-treated regions. Preliminary results indicate the share of the labour market working in bordering regions would have been about 0.5% larger had the switch-treated regions adopted the policy prior to 2008.

A Negative Correlation Strategy for Bracketing in Difference-in-Differences with Application to the Effect of Voter Identification Laws on Voter Turnout

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Author(s): Ting Ye, Luke Keele, Raiden Hasegawa and Dylan S. Small

Discussant: Fredrik Sävje (Yale University)


The method of difference-in-differences (DID) is widely used to study the causal effect of policy interventions in observational studies. DID exploits a before and after comparison of the treated and control units to remove the bias due to time-invariant unmeasured confounders under the parallel trends assumption. Estimates from DID, however, will be biased if the outcomes for the treated and control units evolve differently if counterfactually in the absence of treatment, namely the parallel trends assumption is violated due to history interacting with groups. We propose a new identification strategy that leverages two groups of control units whose outcome dynamics bound the outcome dynamics for the treated group if in the absence of treatment, and achieves partial identification of the average treatment effect for treated. The identified set is of a union bounds form that previously developed partial identification inference methods do not apply to. We develop a novel bootstrap method to construct uniformly valid confidence intervals for the identified set and the treatment effect of interest, and we establish the theoretical properties. We develop a simple falsification test and sensitivity analysis for the assumption. We apply the proposed methods to an application on the effect of voter identification laws on turnout, and we find evidence that the voter identification laws in Georgia and Indiana increased turnout.

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