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.
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.
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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.
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