{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T05:15:02Z","timestamp":1791954902712,"version":"4.3.4"},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T00:00:00Z","timestamp":1692921600000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,9,20]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>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\u2014combined with the Bernoulli quasi-log likelihood (QLL)\u2014and an exponential mean combined with the Poisson QLL.<\/jats:p>","DOI":"10.1093\/ectj\/utad016","type":"journal-article","created":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T05:00:59Z","timestamp":1692939659000},"page":"C31-C66","source":"Crossref","is-referenced-by-count":246,"title":["Simple approaches to nonlinear difference-in-differences with panel\u00a0data"],"prefix":"10.1093","volume":"26","author":[{"given":"Jeffrey M","family":"Wooldridge","sequence":"first","affiliation":[{"name":"Department of Economics Michigan State University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,8,24]]},"reference":[{"key":"2024011907224905700_bib1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/0034-6527.00321","article-title":"Semiparametric difference-in-differences estimators","volume":"72","author":"Abadie","year":"2005","journal-title":"Review of Economic Studies"},{"key":"2024011907224905700_bib2","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1111\/1468-0262.00456","article-title":"The nonparametric identification of treatment effects in duration models","volume":"71","author":"Abbring","year":"2003","journal-title":"Econometrica"},{"key":"2024011907224905700_bib3","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0165-1765(03)00032-6","article-title":"Interaction terms in logit and probit models","volume":"80","author":"Ai","year":"2003","journal-title":"Economics Letters"},{"key":"2024011907224905700_bib4","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1111\/j.1468-0262.2006.00668.x","article-title":"Identification and inference in nonlinear difference-in-differences models","volume":"74","author":"Athey","year":"2006","journal-title":"Econometrica"},{"key":"2024011907224905700_bib5","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.jeconom.2020.10.012","article-title":"Design-based analysis in difference-in-differences settings with staggered adoption","volume":"226","author":"Athey","year":"2022","journal-title":"Journal of Econometrics"},{"key":"2024011907224905700_bib6","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1023\/A:1008787013977","article-title":"Getting the unemployed back to work: The role of targeted wage subsidies","volume":"6","author":"Bell","year":"1999","journal-title":"International Tax and Public Finance"},{"key":"2024011907224905700_bib7","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1353\/jhr.2009.0009","article-title":"Alternative approaches to evaluation in empirical microeconomics","volume":"44","author":"Blundell","year":"2009","journal-title":"Journal of Human Resources"},{"key":"2024011907224905700_bib8","article-title":"Revisiting event study designs: robust and efficient estimation","author":"Borusyak","year":"2022"},{"key":"2024011907224905700_bib9","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.jeconom.2020.12.001","article-title":"Difference-in-differences with multiple time periods","volume":"225","author":"Callaway","year":"2021","journal-title":"Journal of Econometrics"},{"key":"2024011907224905700_bib11","doi-asserted-by":"crossref","first-page":"2964","DOI":"10.1257\/aer.20181169","article-title":"Two-way fixed effects estimators with heterogeneous treatment effects","volume":"110","author":"de\u00a0Chaisemartin","year":"2020","journal-title":"American Economic Review"},{"key":"2024011907224905700_bib12","first-page":"C1","article-title":"Two-way fixed effects and differences-in-differences with heterogeneous treatment effects: a survey","volume-title":"Econometrics Journal","author":"de\u00a0Chaisemartin","year":"2023"},{"key":"2024011907224905700_bib13","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1257\/000282804322970733","article-title":"Do police reduce crime? 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