Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Nov, 2023, Volume 91, Issue 6

Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data

https://doi.org/10.3982/ECTA21248
p. 2125-2154

Dennis Shen, Peng Ding, Jasjeet Sekhon, Bin Yu

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‐sectional 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.


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Supplemental Material

Supplement to "Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data"

Dennis Shen, Peng Ding, Jasjeet Sekhon, and Bin Yu

This online appendix contains material not found within the manuscript.

Supplement to "Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data"

Dennis Shen, Peng Ding, Jasjeet Sekhon, and Bin Yu

The replication package for this paper is available at https://doi.org/10.5281/zenodo.8423395. The Journal checked the data and codes included in the package for their ability to reproduce the results in the paper and approved online appendices.