vertical regression

TL;DR This paper proves that horizontal regression (time series methods like unconfoundedness) and vertical regression (cross-sectional methods like synthetic controls) can produce algebraically identical point estimates for several common estimators including OLS, PCR, and ridge regression.

Here are my study notes on the matrix completion method for causal panel data models proposed by Athey et al. (2021). 1. Setup and Notation $Y(0),Y(1)$ are potential outcome matrices