matrix completion

Generalized Synthetic Control, Seen Through PCA

Xu (2017) in three PCA steps: learn factors from controls, fit loadings on the treated pre-period, reconstruct the missing block. Then how it relates to matrix completion, and when to use which.

Oct 4, 2026 9 min read Causal Inference

Triply Robust Panel Estimators 🛡: When You Don't Know Which Assumptions Hold

TL;DR Athey, Imbens, Qu, and Viviano introduce the Triply RObust Panel (TROP) estimator, which combines unit weights, time weights, and a flexible low-rank factor model to estimate causal effects in panel data.

Oct 20, 2025 7 min read Causal Inference

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

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.

Oct 5, 2025 4 min read Causal Inference

Notes on Matrix Completion Methods for Causal Panel Data Models

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

Jul 8, 2025 11 min read Causal Inference