B0794
Title: Horizontal and vertical regressions: From duels to duals
Authors: Dennis Shen - University of California, Berkeley (United States) [presenting]
Peng Ding - University of California, Berkeley (United States)
Jasjeet Sekhon - Yale University (United States)
Bin Yu - UC Berkeley (United States)
Abstract: A central goal in social science is to evaluate the causal effect of a policy. In this pursuit, researchers often organize their observations in a panel data format where a subset of units are exposed to a policy for some time periods while the other units are unaffected. The information across time and space motivates two general approaches: (i) horizontal regression (i.e., unconfounedness), which exploits time series patterns, and (ii) vertical regression (e.g., synthetic controls), which exploits cross-sectional patterns. Although conventional wisdom states that the two are fundamentally different, we prove that they yield numerically identical estimates under several standard settings. Within this regime, we study properties of the estimator from three model-based perspectives---horizontal, vertical, and their mixture---and construct corresponding confidence intervals that offer new approaches to inference. Our results highlight how the choice of randomness relates to the choice of estimand. We show that these insights carry over to the design-based framework as well.
