Simple approaches to nonlinear difference-in-differences with panel data

Summary I derive simple, flexible strategies for difference-in-differences settings where the nature of the response variable may warrant a nonlinear model. I allow for general staggered interventions, with and without covariates. Under an index version of parallel trends, I show that average treatm...

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Vydáno v:The econometrics journal Ročník 26; číslo 3; s. C31 - C66
Hlavní autor: Wooldridge, Jeffrey M
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford University Press 01.09.2023
Témata:
nonlinear model
logit model
Difference-in-differences
staggered intervention
Poisson regression
ISSN:1368-4221, 1368-423X
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Shrnutí:Summary I derive simple, flexible strategies for difference-in-differences settings where the nature of the response variable may warrant a nonlinear model. I allow for general staggered interventions, with and without covariates. Under an index version of parallel trends, I show that average treatment effects on the treated (ATTs) are identified for each cohort and calendar time period in which a cohort was subjected to the intervention. The pooled quasi-maximum likelihood estimators in the linear exponential family extend pooled ordinary least squares estimation of linear models. By using the conditional mean associated with the canonical link function, imputation and pooling across the entire sample produce identical estimates. Generally, pooled estimation results in very simple computation of the ATTs and their standard errors. The leading cases are a logit functional form for binary and fractional outcomes—combined with the Bernoulli quasi-log likelihood (QLL)—and an exponential mean combined with the Poisson QLL.
ISSN:1368-4221
1368-423X
DOI:10.1093/ectj/utad016