xtnumfac: A battery of estimators for the number of common factors in time series and panel-data models

Abstract

In this article, we introduce a new community-contributed command, xtnumfac, for estimating the number of common factors in time-series and panel datasets using the methods of Bai and Ng (2002, Econometrica 70: 191–221), Ahn and Horenstein (2013, Econometrica 81: 1203–1227), Onatski (2010, Review of Economics and Statistics 92: 1004–1016), and Gagliardini, Ossola, and Scaillet (2019, Journal of Econometrics 212: 503–521). Common factors are usually unobserved or unobservable. In time series, they influence all predictors, while in paneldata models, they influence all cross-sectional units at different degrees. Examples are shocks from oil prices, inflation, or demand or supply shocks. Knowledge about the number of factors is key for multiple econometric estimation methods, such as Pesaran (2006, Econometrica 74: 967–1012), Bai (2009, Econometrica 77: 1229–1279), Norkute et al. (2021, Journal of Econometrics 220: 416–446), and Kripfganz and Sarafidis (2021, Stata Journal 21: 659–686). This article discusses a total of 10 methods to estimate the number of common factors. Examples based on Kapetanios, Pesaran, and Reese (2021, Journal of Econometrics 221: 510–541) show that U.S. house prices are exposed to up to 10 common factors. Therefore, when one fits models with house prices as a dependent variable, the number of factors must be considered.

Keywords

st0715 xtnumfac common factors factor models cross-section dependence panel-data models time-series models

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References

Ahn

S. C.

Horenstein

A. R.

2013. Eigenvalue ratio test for the number of factors. Econometrica 81: 1203–1227. https://doi.org/10.3982/ECTA8968.

Bai

2009. Panel data models with interactive fixed effects. Econometrica 77: 1229–1279. https://doi.org/10.3982/ECTA6135.

Bai

Liao

Yang

2015. Unbalanced panel data models with interactive effects. In The Oxford Handbook of Panel Data, ed. Baltagi

B. H.

, 149–170. Oxford: Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199940042.013.0005.

Bai

2002. Determining the number of factors in approximate factor models. Econometrica 70: 191–221. https://doi.org/10.1111/1468-0262.00273.

Bailey

Holly

Pesaran

M. H.

2016a. A two-stage approach to spatio-temporal analysis with strong and weak cross-sectional dependence. Journal of Applied Econometrics 31: 249–280. https://doi.org/10.1002/jae.2468.

Bailey

Kapetanios

Pesaran

M. H.

2016b. Exponent of cross-sectional dependence: Estimation and inference. Journal of Applied Econometrics 31: 929–960. https://doi.org/10.1002/jae.2476.

Bailey

Kapetanios

Pesaran

M. H.

2019. Exponent of cross-sectional dependence for residuals. Sankhyā 81: 46–102. https://doi.org/10.1007/s13571-019-00196-9.

Brownlees

Mesters

2021. Detecting granular time series in large panels. Journal of Econometrics 220: 544–561. https://doi.org/10.1016/j.jeconom.2020.04.013.

Chamberlain

Rothschild

1983. Arbitrage, factor structure, and meanvariance analysis on large asset markets. Econometrica 51: 1281–1304. https://doi.org/10.2307/1912275.

10.

Chudik

Mohaddes

Pesaran

M. H.

Raissi

2017. Is there a debt-threshold effect on output growth? Review of Economics and Statistics 99: 135–150. https://doi.org/10.1162/REST_a_00593.

11.

Chudik

Pesaran

M. H.

2015. Large panel data models with cross-sectional dependence: A survey. In The Oxford Handbook of Panel Data, ed. Baltagi

B. H.

, 3–45. Oxford: Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199940042. 013.0001.

12.

Ditzen

2018a. Estimating dynamic common-correlated effects in Stata. Stata Journal 18: 585–617. https://doi.org/10.1177/1536867X1801800306.

13.

Ditzen

2018b. Cross-country convergence in a general Lotka–Volterra model. Spatial Economic Analysis 2: 191–211. https://doi.org/10.1080/17421772.2018.1397285.

14.

Ditzen

2021. Estimating long run effects and the exponent of cross-sectional dependence: An update to xtdcce2. Stata Journal 21: 687–707. https://doi.org/10.1177/1536867X211045560.

15.

Duan

Bai

Han

2023. Quasi-maximum likelihood estimation of break point in high-dimensional factor models. Journal of Econometrics 233: 209–236. https://doi.org/10.1016/j.jeconom.2021.12.011.

16.

Eberhardt

Helmers

Strauss

2013. Do spillovers matter when estimating private returns to R&D? Review of Economics and Statistics 95: 436–448. https://doi.org/10.1162/REST_a_00272.

17.

El-Anshasy

Mohaddes

Nugent

J. B.

2017. Oil, volatility and institutions: Cross-country evidence from major oil producers. Federal Reserve Bank of Dallas, Globalization and Monetary Policy Institute Working Paper No. 310. https://doi.org/10.24149/gwp310.

18.

Forni

Lippi

1997. Aggregation and the Microfoundations of Dynamic Macroeconomics. Oxford: Oxford University Press.

19.

Forni

Reichlein

1998. Let’s get real: A factor-analytic approach to disaggregated business cycle dynamics. Review of Economic Studies 65: 453–473. https://doi.org/10.1111/1467-937X.00053.

20.

Gagliardini

Ossola

Scaillet

2019. A diagnostic criterion for approximate factor structure. Journal of Econometrics 212: 503–521. https://doi.org/10.1016/j.jeconom.2019.06.001.

21.

Gomez

2015 regife: Stata module to estimate linear models with interactive fixed effects. Statistical Software Components S458042, Department of Economics, Boston College. https://ideas.repec.org/c/boc/bocode/s458042.html.

22.

Holly

Pesaran

M. H.

Yamagata

2010. A spatio-temporal model of house prices in the USA. Journal of Econometrics 158: 160–173. https://doi.org/10.1016/j.jeconom.2010.03.040.

23.

Holly

Pesaran

M. H.

Yamagata

2011. The spatial and temporal diffusion of house prices in the UK. Journal of Urban Economics 69: 2–23. https://doi.org/10.1016/j.jue.2010.08.002.

24.

Kapetanios

Pesaran

M. H.

Reese

2021. Detection of units with pervasive effects in large panel data models. Journal of Econometrics 221: 510–541. https://doi.org/10.1016/j.jeconom.2020.05.001.

25.

Karabiyik

Reese

Westerlund

2017. On the role of the rank condition in CCE estimation of factor-augmented panel regressions. Journal of Econometrics 197: 60–64. https://doi.org/10.1016/j.jeconom.2016.10.006.

26.

Kripfganz

Sarafidis

2021. Instrumental-variable estimation of large-T paneldata models with common factors. Stata Journal 21: 659–686. https://doi.org/10.1177/1536867X211045558.

27.

Norkute

Sarafidis

Yamagata

Cui

2021. Instrumental variable estimation of dynamic linear panel data models with defactored regressors and a multifactor error structure. Journal of Econometrics 220: 416–446. https://doi.org/10.1016/j.jeconom.2020.04.008.

28.

Núñez

H. M.

Otero

2020. baing: Stata module to determine and estimate the number of common factors following Bai and Ng. Statistical Software Components S458851, Department of Economics, Boston College. https://ideas.repec.org/c/boc/bocode/s458851.html.

29.

Onatski

2010. Determining the number of factors from empirical distribution of eigenvalues. Review of Economics and Statistics 92: 1004–1016. https://doi.org/10.1162/REST_a_00043.

30.

Pesaran

M. H.

2006. Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74: 967–1012. https://doi.org/10.1111/j.1468-0262.2006.00692.x.

31.

Ross

S. A.

1976. The arbitrage theory of capital asset pricing. Journal of Economic Theory 13: 341–360. https://doi.org/10.1016/0022-0531(76)90046-6.

32.

Stock

J. H.

Watson

M. W.

1989. New indexes of coincident and leading economic indicators. NBER Macroeconomics Annual 4: 351–394. https://doi.org/10.1086/654119.

33.

Stock

J. H.

Watson

M. W.

1998. Diffusion indexes. NBER Working Paper No. 6702, The National Bureau of Economic Research. https://doi.org/10.3386/w6702.

34.

Stock

J. H.

Watson

M. W.

2002. Macroeconomic forecasting using diffusion indexes. Journal of Business and Economic Statistics 20: 147–162. https://doi.org/10.1198/073500102317351921.

35.

Sul

2019. Panel Data Econometrics: Common Factor Analysis for Empirical Researchers. Abingdon, U.K.: Routledge.

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