IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v224y2021i2p439-465.html
   My bibliography  Save this article

Recursive estimation in large panel data models: Theory and practice

Author

Listed:
  • Jiang, Bin
  • Yang, Yanrong
  • Gao, Jiti
  • Hsiao, Cheng

Abstract

Bai (2009) proposes recursive estimation for panel data models with interactive effects. We study the behaviours of this recursive estimator. The recursive formula is established that shows the behaviours of recursive estimators depend on the initial estimator, the population structure and the iterative steps. Under some general scenarios, we find that the recursive estimator becomes consistent after the first iteration from any initials. We also obtain the optimal number of iterative steps under some prescribed conditions. The central limit theorem of the recursive estimator is established when the initial estimator is OLS. Various simulations are conducted to support our theoretical findings.

Suggested Citation

  • Jiang, Bin & Yang, Yanrong & Gao, Jiti & Hsiao, Cheng, 2021. "Recursive estimation in large panel data models: Theory and practice," Journal of Econometrics, Elsevier, vol. 224(2), pages 439-465.
    • Handle: RePEc:eee:econom:v:224:y:2021:i:2:p:439-465
    DOI: 10.1016/j.jeconom.2020.07.055
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407620303870
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2020.07.055?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sabina Alkire, Maria Emma Santos, 2010. "Acute Multidimensional Poverty: A New Index for Developing Countries," OPHI Working Papers 38, Queen Elizabeth House, University of Oxford.
    2. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    3. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    4. Kapetanios, G. & Pesaran, M. Hashem & Yamagata, T., 2011. "Panels with non-stationary multifactor error structures," Journal of Econometrics, Elsevier, vol. 160(2), pages 326-348, February.
    5. Olivier Jean Blanchard & Stanley Fischer, 1989. "Editorial in "NBER Macroeconomics Annual 1989, Volume 4"," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 1-8, National Bureau of Economic Research, Inc.
    6. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    7. Dong, Chaohua & Gao, Jiti & Peng, Bin, 2015. "Semiparametric single-index panel data models with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 188(1), pages 301-312.
    8. Pastorello, Sergio & Patilea, Valentin & Renault, Eric, 2003. "Iterative and Recursive Estimation in Structural Nonadaptive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 449-482, October.
    9. Pesaran, M. Hashem & Tosetti, Elisa, 2011. "Large panels with common factors and spatial correlation," Journal of Econometrics, Elsevier, vol. 161(2), pages 182-202, April.
    10. Pastorello, Sergio & Patilea, Valentin & Renault, Eric, 2003. "Iterative and Recursive Estimation in Structural Nonadaptive Models: Rejoinder," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 503-509, October.
    11. Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2011. "Weak and strong cross‐section dependence and estimation of large panels," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 45-90, February.
    12. Xiao Huang, 2013. "Nonparametric Estimation in Large Panels with Cross-Sectional Dependence," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 754-777, August.
    13. Clifford Lam & Qiwei Yao & Neil Bathia, 2011. "Estimation of latent factors for high-dimensional time series," Biometrika, Biometrika Trust, vol. 98(4), pages 901-918.
    14. Lam, Clifford & Yao, Qiwei & Bathia, Neil, 2011. "Estimation of latent factors for high-dimensional time series," LSE Research Online Documents on Economics 31549, London School of Economics and Political Science, LSE Library.
    15. Harding, Matthew & Lamarche, Carlos, 2011. "Least squares estimation of a panel data model with multifactor error structure and endogenous covariates," Economics Letters, Elsevier, vol. 111(3), pages 197-199, June.
    16. Chen, Jia & Gao, Jiti & Li, Degui, 2012. "Semiparametric trending panel data models with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 171(1), pages 71-85.
    17. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    18. Rippin, Nicole, 2011. "A response to the weaknesses of the Multidimensional Poverty Index (MPI): the correlation Sensitive Poverty Index (CSPI)," Briefing Papers 19/2011, German Institute of Development and Sustainability (IDOS).
    19. Su, Liangjun & Jin, Sainan & Zhang, Yonghui, 2015. "Specification test for panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 186(1), pages 222-244.
    20. David I. Hastie & Peter J. Green, 2012. "Model choice using reversible jump Markov chain Monte Carlo," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(3), pages 309-338, August.
    21. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    22. Ban Kheng Tan & Anastasios Panagiotelis & George Athanasopoulos, 2017. "Bayesian Inference for a 1-Factor Copula Model," Monash Econometrics and Business Statistics Working Papers 6/17, Monash University, Department of Econometrics and Business Statistics.
    23. Frazier, David T., 2019. "A Simple Iterative Z-Estimator For Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 35(1), pages 111-141, February.
    24. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    25. Su, Liangjun & Jin, Sainan, 2012. "Sieve estimation of panel data models with cross section dependence," Journal of Econometrics, Elsevier, vol. 169(1), pages 34-47.
    26. Thomas J. Sargent & Christopher A. Sims, 1977. "Business cycle modeling without pretending to have too much a priori economic theory," Working Papers 55, Federal Reserve Bank of Minneapolis.
    27. Dominitz, Jeff & Sherman, Robert P., 2005. "Some Convergence Theory For Iterative Estimation Procedures With An Application To Semiparametric Estimation," Econometric Theory, Cambridge University Press, vol. 21(4), pages 838-863, August.
    28. Song, Peter X.K. & Fan, Yanqin & Kalbfleisch, John D., 2005. "Maximization by Parts in Likelihood Inference," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1145-1158, December.
    29. Aristidis Nikoloulopoulos & Harry Joe, 2015. "Factor Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 126-150, March.
    30. Kapoor, Mudit & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Panel data models with spatially correlated error components," Journal of Econometrics, Elsevier, vol. 140(1), pages 97-130, September.
    31. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    32. James H. Stock & Mark W. Watson, 1989. "New Indexes of Coincident and Leading Economic Indicators," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 351-409, National Bureau of Economic Research, Inc.
    33. repec:hal:journl:peer-00796743 is not listed on IDEAS
    34. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    35. Krupskii, Pavel & Joe, Harry, 2013. "Factor copula models for multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 85-101.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chen, Qiang & Yan, Guanpeng, 2023. "On the two algorithms for estimating interactive fixed effects models in Bai (2009)," Economics Letters, Elsevier, vol. 233(C).
    2. Bin Peng & Liangjun Su & Joakim Westerlund & Yanrong Yang, 2021. "Interactive Effects Panel Data Models with General Factors and Regressors," Monash Econometrics and Business Statistics Working Papers 23/21, Monash University, Department of Econometrics and Business Statistics.
    3. Fei Liu & Jiti Gao & Yanrong Yang, 2019. "Nonparametric Estimation in Panel Data Models with Heterogeneity and Time Varyingness," Monash Econometrics and Business Statistics Working Papers 24/19, Monash University, Department of Econometrics and Business Statistics.
    4. Jiti Gao & Bin Peng & Yayi Yan, 2022. "Nonparametric Estimation and Testing for Time-Varying VAR Models," Monash Econometrics and Business Statistics Working Papers 3/22, Monash University, Department of Econometrics and Business Statistics.
    5. Yu, Haijing & Shen, Shaowei & Han, Lei & Ouyang, Jian, 2024. "Spatiotemporal heterogeneities in the impact of the digital economy on carbon emission transfers in China," Technological Forecasting and Social Change, Elsevier, vol. 200(C).
    6. Gao, Jiti & Liu, Fei & Peng, Bin & Yan, Yayi, 2023. "Binary response models for heterogeneous panel data with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 1654-1679.
    7. Stauskas, Ovidijus & De Vos, Ignace, 2024. "Handling Distinct Correlated Effects with CCE," MPRA Paper 120194, University Library of Munich, Germany.
    8. Ruofan Xu & Jiti Gao & Tatsushi Oka & Yoon-Jae Whang, 2022. "Quantile Random-Coefficient Regression with Interactive Fixed Effects: Heterogeneous Group-Level Policy Evaluation," Papers 2208.03632, arXiv.org, revised Nov 2024.
    9. Jiti Gao & Fei Liu & Bin peng, 2020. "Binary Response Models for Heterogeneous Panel Data with Interactive Fixed Effects," Monash Econometrics and Business Statistics Working Papers 44/20, Monash University, Department of Econometrics and Business Statistics.
    10. Guohua Feng & Jiti Gao & Bin Peng, 2021. "Productivity Convergence in Manufacturing: A Hierarchical Panel Data Approach," Papers 2111.00449, arXiv.org.
    11. Feng, Guohua & Gao, Jiti & Peng, Bin, 2022. "An integrated panel data approach to modelling economic growth," Journal of Econometrics, Elsevier, vol. 228(2), pages 379-397.
    12. Guohua Feng & Jiti Gao & Bin Peng, 2022. "Multi-Level Panel Data Models: Estimation and Empirical Analysis," Monash Econometrics and Business Statistics Working Papers 4/22, Monash University, Department of Econometrics and Business Statistics.
    13. Guohua Feng & Jiti Gao & Bin Peng, 2019. "An Integrated Panel Data Approach to Modelling Economic Growth," Monash Econometrics and Business Statistics Working Papers 6/19, Monash University, Department of Econometrics and Business Statistics.
    14. Guowei Cui & Milda NorkutÄ— & Vasilis Sarafidis & Takashi Yamagata, 2022. "Two-stage instrumental variable estimation of linear panel data models with interactive effects [Eigenvalue ratio test for the number of factors]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 340-361.
    15. Chaohua Dong & Jiti Gao & Bin Peng, 2018. "Varying-coefficient panel data models with partially observed factor structure," Monash Econometrics and Business Statistics Working Papers 1/18, Monash University, Department of Econometrics and Business Statistics.
    16. Ruofan Xu & Jiti Gao & Tatsushi Oka & Yoon-Jae Whang, 2022. "Estimation of Heterogeneous Treatment Effects Using Quantile Regression with Interactive Fixed Effects," Papers 2208.03632, arXiv.org, revised Apr 2023.
    17. Feng, Guohua & Peng, Bin & Su, Liangjun & Yang, Thomas Tao, 2019. "Semi-parametric single-index panel data models with interactive fixed effects: Theory and practice," Journal of Econometrics, Elsevier, vol. 212(2), pages 607-622.
    18. Hong, Shengjie & Su, Liangjun & Jiang, Tao, 2023. "Profile GMM estimation of panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 927-948.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ban Kheng Tan & Anastasios Panagiotelis & George Athanasopoulos, 2017. "Bayesian Inference for a 1-Factor Copula Model," Monash Econometrics and Business Statistics Working Papers 6/17, Monash University, Department of Econometrics and Business Statistics.
    2. Vasilis Sarafidis & Tom Wansbeek, 2012. "Cross-Sectional Dependence in Panel Data Analysis," Econometric Reviews, Taylor & Francis Journals, vol. 31(5), pages 483-531, September.
    3. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    4. Hyungsik Roger Roger Moon & Martin Weidner, 2013. "Dynamic linear panel regression models with interactive fixed effects," CeMMAP working papers 63/13, Institute for Fiscal Studies.
    5. Hyungsik Roger Roger Moon & Martin Weidner, 2014. "Dynamic linear panel regression models with interactive fixed effects," CeMMAP working papers 47/14, Institute for Fiscal Studies.
    6. Baltagi, Badi H. & Feng, Qu & Kao, Chihwa, 2016. "Estimation of heterogeneous panels with structural breaks," Journal of Econometrics, Elsevier, vol. 191(1), pages 176-195.
    7. Bai, Jushan & Li, Kunpeng, 2021. "Dynamic spatial panel data models with common shocks," Journal of Econometrics, Elsevier, vol. 224(1), pages 134-160.
    8. Su, Liangjun & Ju, Gaosheng, 2018. "Identifying latent grouped patterns in panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 206(2), pages 554-573.
    9. Tomohiro Ando & Jushan Bai, 2016. "Panel Data Models with Grouped Factor Structure Under Unknown Group Membership," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(1), pages 163-191, January.
    10. Hugo Freeman & Martin Weidner, 2021. "Linear panel regressions with two-way unobserved heterogeneity," CeMMAP working papers CWP39/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Bai, Jushan & Liao, Yuan, 2017. "Inferences in panel data with interactive effects using large covariance matrices," Journal of Econometrics, Elsevier, vol. 200(1), pages 59-78.
    12. Michael Vogt & Christopher Walsh & Oliver Linton, 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Papers 2206.12152, arXiv.org.
    13. Freeman, Hugo & Weidner, Martin, 2023. "Linear panel regressions with two-way unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 237(1).
    14. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    15. Cai, Zongwu & Fang, Ying & Xu, Qiuhua, 2022. "Testing capital asset pricing models using functional-coefficient panel data models with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 227(1), pages 114-133.
    16. Vogt, M. & Walsh, C. & Linton, O., 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Janeway Institute Working Papers 2218, Faculty of Economics, University of Cambridge.
    17. Vogt, M. & Walsh, C. & Linton, O., 2022. "CCE Estimation of High-Dimensional Panel Data Models with Interactive Fixed Effects," Cambridge Working Papers in Economics 2242, Faculty of Economics, University of Cambridge.
    18. Li, Kunpeng & Cui, Guowei & Lu, Lina, 2020. "Efficient estimation of heterogeneous coefficients in panel data models with common shocks," Journal of Econometrics, Elsevier, vol. 216(2), pages 327-353.
    19. Zongwu Cai & Ying Fang & Qiuhua Xu, 2020. "Testing Capital Asset Pricing Models using Functional-Coefficient Panel Data Models with Cross-Sectional Dependence," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202009, University of Kansas, Department of Economics, revised Jul 2020.
    20. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2020. "Model uncertainty, nonlinearities and out-of-sample comparison: evidence from international technology diffusion," Working Papers hal-02790523, HAL.

    More about this item

    Keywords

    Factor model; Initial estimation; Multiplicative structure; Nonlinear optimization;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:224:y:2021:i:2:p:439-465. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.