Limit Theorems for Factor Models

TL;DR

This paper develops central limit theorems and inference methods for factor models involving cross-sectional and time series data, providing tools for valid statistical inference without requiring structural cross-sectional dependence.

Contribution

It establishes new CLTs for factor models with heterogeneous micro-parameters and proposes bootstrap methods for variance estimation under minimal assumptions.

Findings

CLTs applicable to cross-sectional and time series aggregation

A bootstrap scheme for variance estimation when asymptotic variance is unknown

Simulation results demonstrate the effectiveness of the proposed inference procedures

Abstract

The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global parameter includes aggregation of a cross-section of heterogeneous micro-parameters estimated separately for each entity. The central limit theorem applies for quantities involving both cross-sectional and time series aggregation, as well as for quadratic forms in time-aggregated errors. The paper studies the conditions when one can consistently estimate the asymptotic variance, and proposes a bootstrap scheme for cases when one cannot. A small simulation study illustrates performance of the asymptotic and bootstrap procedures. The results are useful for making inferences in two-step estimation procedures related to factor models, as well as in other related contexts. Our treatment avoids structural modeling of cross-sectional dependence but imposes time-series independence.