Statistical analysis of factor models of high dimension

TL;DR

This paper develops a comprehensive inferential theory for maximum likelihood estimation of high-dimensional factor models, addressing consistency, convergence rates, and the impact of identification conditions, while allowing for heteroskedasticity.

Contribution

It introduces a new inferential framework for high-dimensional factor models using MLE, considering various identification conditions and heteroskedasticity.

Findings

MLE estimators are consistent and have known convergence rates.

Distribution of estimators depends on identification restrictions.

MLE explicitly models heteroskedasticity, unlike PCA.

Abstract

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We establish not only consistency but also the rate of convergence and the limiting distributions. Five different sets of identification conditions are considered. We show that the distributions of the MLE estimators depend on the identification restrictions. Unlike the principal components approach, the maximum likelihood estimator explicitly allows heteroskedasticities, which are jointly estimated with other parameters. Efficiency of MLE relative to the principal components method is also considered.