Approximate Factor Models with Weaker Loadings

2021/09/08 by Jushan Bai, Bai, Jushan, Serena Ng +1 · 3 citations
Economics, Econometrics and Finance · #Econometrics (econ.EM) #Economic theories and models #FOS: Computer and information sciences #FOS: Economics and business #Firm Innovation and Growth #Methodology (stat.ME) #Monetary Policy and Economic Impact

paper · pdf · doi:10.48550/arxiv.2109.03773

openalex publication_date 2021/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where \Lop\Lo/N^α is positive definite in the limit when α=1, early work established convergence of the principal component estimates of the factors and loadings up to a rotation matrix. This paper shows that the estimates are still consistent and asymptotically normal when α∈(0,1] albeit at slower rates and under additional assumptions on the sample size. The results hold whether α is constant or varies across factor loadings. The framework developed for heterogeneous loadings and the simplified proofs that can be also used in strong factor analysis are of independent interest.

Cited by

• An alternative bootstrap procedure for factor-augmented regression models
• Bias Correction in Factor-Augmented Regression Models with Weak Factors
• High-Dimensional Matrix-Variate Diffusion Index Models for Time Series Forecasting

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