Estimation of Semiparametric Factor Models with Missing Data

TL;DR

This paper introduces a projected principal component analysis method for semiparametric factor models that effectively handles missing data, ensuring consistent estimation and robust inference in high-dimensional panel settings.

Contribution

It develops a novel PPCA approach with inverse-probability weighting for missing data, providing theoretical guarantees and practical robustness for factor and loading estimation.

Findings

PPCA achieves consistent factor estimation with fixed T.

The method accounts for missing-at-random data mechanisms.

Simulations and empirical analysis validate the approach.

Abstract

We study semiparametric factor models in high-dimensional panels where the factor loadings consist of a nonparametric component explained by observed covariates and an idiosyncratic component capturing unobserved heterogeneity. A key challenge in empirical applications is the presence of missing observations, which can distort both factor recovery and loading estimation. To address this issue, we develop a projected principal component analysis (PPCA) procedure that accommodates general missing-at-random mechanisms through inverse-probability weighting. We establish consistency and derive the asymptotic distributions of the estimated factors and loading functions, allowing the sieve dimension to diverge and permitting the time dimension to be either fixed or growing. Unlike classical PCA, PPCA achieves consistent factor estimation even when T is fixed, and the limiting distributions under missing data exhibit mixture normality with enlarged asymptotic variances. Theoretical results are supported by simulations and an empirical application. Our findings demonstrate that PPCA provides an effective and robust framework for estimating semiparametric factor models in the presence of missing data.