{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:06:35Z","timestamp":1787313995513,"version":"build-2736575974"},"reference-count":36,"publisher":"The Econometric Society","issue":"6","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>One dominant approach to evaluate the causal effect of a treatment is through panel data analysis, whereby the behaviors of multiple units are observed over time. The information across time and units motivates two general approaches: (i) horizontal regression (i.e., unconfoundedness), which exploits time series patterns, and (ii) vertical regression (e.g., synthetic controls), which exploits cross\u2010sectional patterns. Conventional wisdom often considers the two approaches to be different. We establish this position to be partly false for estimation but generally true for inference. In the absence of any assumptions, we show that both approaches yield algebraically equivalent point estimates for several standard estimators. However, the source of randomness assumed by each approach leads to a distinct estimand and quantification of uncertainty even for the same point estimate. This emphasizes that researchers should carefully consider where the randomness stems from in their data, as it has direct implications for the accuracy of inference.<\/jats:p>","DOI":"10.3982\/ecta21248","type":"journal-article","created":{"date-parts":[[2023,12,6]],"date-time":"2023-12-06T07:55:13Z","timestamp":1701849313000},"page":"2125-2154","source":"Crossref","is-referenced-by-count":9,"title":["Same Root Different Leaves: Time Series and Cross\u2010Sectional Methods in Panel Data"],"prefix":"10.3982","volume":"91","author":[{"given":"Dennis","family":"Shen","sequence":"first","affiliation":[{"name":"Department of Data Sciences & Operations, University of Southern California"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peng","family":"Ding","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California, Berkeley"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jasjeet","family":"Sekhon","sequence":"additional","affiliation":[{"name":"Departments of Statistics & Data Science and Political Science, Yale University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bin","family":"Yu","sequence":"additional","affiliation":[{"name":"Departments of Statistics and EECS, University of California, Berkeley"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2023]]},"reference":[{"issue":"1","key":"ecta200628-bib-0001","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1257\/000282803321455188","volume":"93","author":"Abadie","year":"2003","journal-title":"American Economic Review"},{"issue":"2","key":"ecta200628-bib-0002","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1257\/jel.20191450","volume":"59","author":"Abadie","year":"2021","journal-title":"Journal of Economic Literature"},{"issue":"536","key":"ecta200628-bib-0003","doi-asserted-by":"crossref","first-page":"1817","DOI":"10.1080\/01621459.2021.1971535","volume":"116","author":"Abadie","year":"2021","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"ecta200628-bib-0004","doi-asserted-by":"crossref","first-page":"265","DOI":"10.3982\/ECTA12675","volume":"88","author":"Abadie","year":"2020","journal-title":"Econometrica"},{"issue":"490","key":"ecta200628-bib-0005","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1198\/jasa.2009.ap08746","volume":"105","author":"Abadie","year":"2010","journal-title":"Journal of the American Statistical Association"},{"issue":"2","key":"ecta200628-bib-0006","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1111\/ajps.12116","volume":"59","author":"Abadie","year":"2015","journal-title":"American Journal of Political Science"},{"key":"ecta200628-bib-0007","unstructured":"Agarwal, Anish, Devavrat Shah, and Dennis Shen (2021): \u201cSynthetic Interventions,\u201d. arXiv preprint arXiv:2006.07691."},{"issue":"2","key":"ecta200628-bib-0008","doi-asserted-by":"crossref","DOI":"10.1145\/3341617.3326152","volume":"3","author":"Amjad","year":"2019","journal-title":"Proc. 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