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

Abstract: 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.

Bio:
Dennis Shen is an assistant professor in the Data Sciences and Operations Department at the USC Marshall School of Business. Before joining USC, he was a FODSI postdoctoral fellow at the Simons Institute at UC Berkeley. He also served as a technical consultant for Uber Technologies and TauRx Therapeutics. He has received several recognition for his work, including the INFORMS George B. Dantzig Dissertation Award (2nd to his esteemed colleague, Somya) and MIT George Sprowls PhD Thesis Award in Artificial Intelligence & Decision-making.