  A central goal in social science is to evaluate the causal effect of a
policy. One dominant approach is through panel data analysis in which the
behaviors of multiple units are observed over time. The information across time
and space 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 states that the two approaches are fundamentally different.
We establish this position to be partly false for estimation but generally true
for inference. In particular, we prove that both approaches yield identical
point estimates under several standard settings. For the same point estimate,
however, each approach quantifies uncertainty with respect to a distinct
estimand. In turn, the confidence interval developed for one estimand may have
incorrect coverage for another. This emphasizes that the source of randomness
that researchers assume has direct implications for the accuracy of inference.
