Large Dimensional Latent Factor Modeling with Missing Observations and Applications to Causal Inference

47 Pages Posted: 28 Oct 2019 Last revised: 10 Nov 2021

See all articles by Ruoxuan Xiong

Ruoxuan Xiong

Stanford University

Markus Pelger

Stanford University - Department of Management Science & Engineering

Date Written: November 8, 2020

Abstract

This paper develops the inferential theory for latent factor models estimated from large dimensional panel data with missing observations. We propose an easy-to-use all-purpose estimator for a latent factor model by applying principal component analysis to an adjusted covariance matrix estimated from partially observed panel data. We derive the asymptotic distribution for the estimated factors, loadings and the imputed values under an approximate factor model and general missing patterns. The key application is to estimate counterfactual outcomes in causal inference from panel data. The unobserved control group is modeled as missing values, which are inferred from the latent factor model. The inferential theory for the imputed values allows us to test for individual treatment effects at any time under general adoption patterns where the units can be affected by unobserved factors.

Keywords: Factor Analysis, Principal Components, Synthetic Control, Causal Inference, Treatment Effect, Missing Entry, Large-Dimensional Panel Data, Large N and T, Matrix Completion

JEL Classification: C14, C38, C55, G12

Suggested Citation

Xiong, Ruoxuan and Pelger, Markus, Large Dimensional Latent Factor Modeling with Missing Observations and Applications to Causal Inference (November 8, 2020). Available at SSRN: https://ssrn.com/abstract=3465357 or http://dx.doi.org/10.2139/ssrn.3465357

Ruoxuan Xiong (Contact Author)

Stanford University ( email )

655 Knight Way
Stanford, CA 94305-9025
United States

Markus Pelger

Stanford University - Department of Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

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