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Difference in Differences with Time-Varying Covariates

Carolina Caetano, Brantly Callaway, Stroud Payne, Hugo Sant'Anna Rodrigues

arXiv 7 Feb 2022 · Econometrics · 17 citations (OpenAlex)

arXiv:2202.02903 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper considers identification and estimation of causal effect parameters from participating in a binary treatment in a difference in differences (DID) setup when the parallel trends assumption holds after conditioning on observed covariates. Relative to existing work in the econometrics literature, we consider the case where the value of covariates can change over time and, potentially, where participating in the treatment can affect the covariates themselves. We propose new empirical strategies in both cases. We also consider two-way fixed effects (TWFE) regressions that include time-varying regressors, which is the most common way that DID identification strategies are implemented under conditional parallel trends. We show that, even in the case with only two time periods, these TWFE regressions are not generally robust to (i) time-varying covariates being affected by the treatment, (ii) treatment effects and/or paths of untreated potential outcomes depending on the level of time-varying covariates in addition to only the change in the covariates over time, (iii) treatment effects and/or paths of untreated potential outcomes depending on time-invariant covariates, (iv) treatment effect heterogeneity with respect to observed covariates, and (v) violations of strong functional form assumptions, both for outcomes over time and the propensity score, that are unlikely to be plausible in most DID applications. Thus, TWFE regressions can deliver misleading estimates of causal effect parameters in a number of empirically relevant cases. We propose both doubly robust estimands and regression adjustment/imputation strategies that are robust to these issues while not being substantially more challenging to implement.

Citation extraction

53
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Sant’Anna, Pedro HC, Zhao, Jun (2020) Doubly robust difference-in-differences estimators0.9416583%
2(2020) Interpreting OLS estimands when treatment effects are heterogeneous: Smaller groups get larger weights0.9285380%
3Goodman-Bacon, Andrew (2021) Difference-in-differences with variation in treatment timing0.87462100%
4(2020) Two-way fixed effects estimators with heterogeneous treatment effects0.87452100%
5Ishimaru, Shoya (2022) What Do We Get From A Two-Way Fixed Effects Estimator? Implications From A General Numerical Equivalence0.87452100%
6Chang, Neng-Chieh (2020) Double/debiased machine learning for difference-in-differences models0.8434475%
7Imai, Kosuke, Kim, In Song, Wang, Erik (2018) Matching Methods for Causal Inference with Time-Series Cross-Section Data0.84333100%
8Borusyak, Kirill, Jaravel, Xavier, Spiess, Jann (2021) Revisiting event study designs: Robust and efficient estimation0.81142100%
9Zeldow, Bret, Hatfield, Laura A (2021) Confounding and regression adjustment in difference-in-differences studies0.7373367%
10Gardner, John (2021) Two-stage difference in differences0.73732100%

Showing the top 10 of 53 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Good Controls Gone Bad: Difference-in-Differences with Covariates1.00094
2Causal Graphs for Conditional Parallel Trends1.00093
3Robust difference-in-differences models0.64422
4Difference-in-Differences with Unpoolable Data0.58531
5Dynamic covariate balancing: estimating treatment effects over time with potential local projections0.40511
6What Do We Get from Two-Way Fixed Effects Regressions? Implications from Numerical Equivalence0.40511
7Policy Evaluation during a Pandemic0.40511
8What's Trending in Difference-in-Differences? A Synthesis of the Recent Econometrics Literature0.40511
9Selection and parallel trends0.40511
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