The DOI matches its Crossref record.
Determining the Number of Factors in Approximate Factor Models
Open accessAbstract
In this paper we develop some econometric theory for factor models of large dimensions. The focus is the determination of the number of factors (r), which is an unresolved issue in the rapidly growing literature on multifactor models. We first establish the convergence rate for the factor estimates that will allow for consistent estimation of r. We then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria. The theory is developed under the framework of large cross-sections (N) and large time dimensions (T). No restriction is imposed on the relation between N and T. Simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
A simple panel unit root test in the presence of cross‐section dependence
Pesaran, M. H. (2007) · Journal of Applied Econometrics · doi:10.1002/jae.951 · Cited by 12,787
Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure
Pesaran, M. H. (2006) · Econometrica · doi:10.1111/j.1468-0262.2006.00692.x · Cited by 5,078
Panel Data Models With Interactive Fixed Effects
(2009) · Econometrica · doi:10.3982/ecta6135 · Cited by 1,690
Electricity price forecasting: A review of the state-of-the-art with a look into the future
Weron, R. (2014) · International Journal of Forecasting · doi:10.1016/j.ijforecast.2014.08.008 · Cited by 1,646
Challenges of Big Data analysis
Fan, J., Han, F., & Liu, H. (2014) · National Science Review · doi:10.1093/nsr/nwt032 · Cited by 1,482
Transition Modeling and Econometric Convergence Tests
Phillips, P. C. B., & Sul, D. (2007) · Econometrica · doi:10.1111/j.1468-0262.2007.00811.x · Cited by 1,451
Machine Learning Methods That Economists Should Know About
Athey, S., & Imbens, G. W. (2019) · Annual Review of Economics · doi:10.1146/annurev-economics-080217-053433 · Cited by 1,163
Matrix Completion Methods for Causal Panel Data Models
Athey, S., Bayati, M., Doudchenko, N., Imbens, G., & Khosravi, K. (2018) · doi:10.3386/w25132 · Cited by 497
Regional policy evaluation: interactive fixed effects and synthetic controls.
Gobillon, L., & Magnac, T. (2016) · Review of Economics and Statistics · doi:10.1162/rest_a_00537 · Cited by 424
Factor Models, Machine Learning, and Asset Pricing
Giglio, S., Kelly, B., & Xiu, D. (2022) · Annual Review of Financial Economics · doi:10.1146/annurev-financial-101521-104735 · Cited by 187
Empirical Asset Pricing via Machine Learning
Gu, S., Kelly, B. T., & Xiu, D. (2018) · The Review of Financial Studies · doi:10.2139/ssrn.3159577 · Cited by 52
Causal models for longitudinal and panel data: a survey
Arkhangelsky, D., & Imbens, G. (2024) · The Econometrics Journal · doi:10.1093/ectj/utae014 · Cited by 50
Powell, D. (2022) · Journal of Business & Economic Statistics · doi:10.1080/07350015.2021.1927743 · Cited by 43
Carbon pricing and the elasticity of CO2 emissions
Rafaty, R., Dolphin, G., & Pretis, F. (2025) · Energy Economics · doi:10.1016/j.eneco.2025.108298 · Cited by 26
Determining the Rank of the Beta Matrix in Linear Asset Pricing Models
Ahn, S. C., Horenstein, A. R., & Wang, N. (2011) · SSRN Electronic Journal · doi:10.2139/ssrn.1784566 · Cited by 2
The Limits of Query Monitoring against Distributed Model Extraction
Khilar, S. C. (2026) · arXiv
“We tried four repairs that pool topic cells across accounts—robust per-cell statistics, per-cell lagged scoring with shrinkage, a factor model of cell drift (Bai & Ng, 2002; Ahn & Horenstein, 2013), and gating behind the two-scale test.”
Metadata
- Authors
- Bai, J., & Ng, S.
- Venue
- Econometrica
- Publisher
- The Econometric Society
- Published
- 2002-01
- Volume
- 70
- Issue
- 1
- Pages
- 191-221
- ISSN
- 0012-9682 (ISSN-L)
- 1468-0262
- OpenAlex
- W1593748280
- Cited by
- 4,099
- References
- 0
- FWCI
- 105.30
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
