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Approximate Factor Models with Weaker Loadings

Jushan Bai, Serena Ng

arXiv 8 Sep 2021 · Econometrics · publishedJournal of Econometrics (2023) · 84 citations (OpenAlex)

arXiv:2109.03773 · PDF · DOI · OpenAlex · Extracted main text

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 $\Lop\Lo/N^\alpha$ is positive definite in the limit when $\alpha=1$, 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 $\alpha\in(0,1]$ albeit at slower rates and under additional assumptions on the sample size. The results hold whether $\alpha$ 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.

Citation extraction

24
references
48
in-text mentions
24
distinct cited
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13,975
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appendix boundary found by appendix_titled_section at “Appendix” · 74% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Bai and Ng (2002) Determining the Number of Factors in Approximate Factor Models1.00054100%
2Onatski (2012) Asymptotics of the Principal Components Estimator of Large Factor Models with Weakly Influential Factors1.00053100%
3Bai (2003) Inferential Theory for Factor Models of Large Dimensions self0.92843100%
4Freyaldenhoven (2022) Factor Models with Local Factors: Determining the Number of Relevant Factors0.92843100%
5Uematsu and Yamagata (2022) Estimation of Sparsity Induced Weak Factor Models0.92843100%
6Bai and Ng (2019) Rank Regularized Estimation of Approximate Factor Models0.64422100%
7DeMol, Giannone, and Reichlin (2008) Forecasting Using a Large Number of Predictors: Is Bayesian Regression a Valid Alternative to Principal Components?0.64422100%
8Stock and Watson (1998) Diffusion Indexes0.64422100%
9Stock and Watson (2002) Forecasting Using Principle Components from a Large Number of Predictors0.64422100%
10Bai and Ng (2006) Confidence Intervals for Diffusion Index Forecasts and Inference with Factor-Augmented Regressions0.58531100%

Showing the top 10 of 24 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1When can weak latent factors be statistically inferred?1.000206
2Universal Factor Models1.000135
3Supervised Dynamic PCA: Linear Dynamic Forecasting with Many Predictors1.000103
4The Canonical Decomposition of Factor Models: Weak Factors are Everywhere1.00053
5High Dimensional Factor Analysis with Weak Factors0.950146
6Bias Correction in Factor-Augmented Regression Models with Weak Factors0.95074
7Diffusion Index Forecasting with Tensor Data0.94163
8Inference on Linear Regressions with Two-Way Unobserved Heterogeneity0.87463
9An alternative bootstrap procedure for factor-augmented regression models0.81142
10Diffusion index forecasts under weaker loadings: PCA, ridge regression, and random projections0.780195