IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v184y2015i1p111-123.html
   My bibliography  Save this article

Testing for time-invariant unobserved heterogeneity in generalized linear models for panel data

Author

Listed:
  • Bartolucci, Francesco
  • Belotti, Federico
  • Peracchi, Franco

Abstract

Recent literature on panel data emphasizes the importance of accounting for time-varying unobservable individual effects, which may stem from either omitted individual characteristics or macro-level shocks that affect each individual unit differently. In this paper, we propose a simple specification test of the null hypothesis that the individual effects are time-invariant against the alternative that they are time-varying. Our test is an application of Hausman (1978) testing procedure and can be used for any generalized linear model for panel data that admits a sufficient statistic for the individual effect. This is a wide class of models which includes the Gaussian linear model and a variety of nonlinear models typically employed for discrete or categorical outcomes. The basic idea of the test is to compare two alternative estimators of the model parameters based on two different formulations of the conditional maximum likelihood method. Our approach does not require assumptions on the distribution of unobserved heterogeneity, nor it requires the latter to be independent of the regressors in the model. We investigate the finite sample properties of the test through a set of Monte Carlo experiments. Our results show that the test performs well, with small size distortions and good power properties. We use a health economics example based on data from the Health and Retirement Study to illustrate the proposed test.

Suggested Citation

  • Bartolucci, Francesco & Belotti, Federico & Peracchi, Franco, 2015. "Testing for time-invariant unobserved heterogeneity in generalized linear models for panel data," Journal of Econometrics, Elsevier, vol. 184(1), pages 111-123.
  • Handle: RePEc:eee:econom:v:184:y:2015:i:1:p:111-123
    DOI: 10.1016/j.jeconom.2014.09.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407614001833
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jeconom.2014.09.002?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. Florian Heiss, 2008. "Sequential numerical integration in nonlinear state space models for microeconometric panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(3), pages 373-389.
    2. Till Stowasser & Florian Heiss & Daniel McFadden & Joachim Winter, 2011. ""Healthy, Wealthy and Wise?" Revisited: An Analysis of the Causal Pathways from Socioeconomic Status to Health," NBER Chapters, in: Investigations in the Economics of Aging, pages 267-317, National Bureau of Economic Research, Inc.
    3. Gregori Baetschmann & Kevin E. Staub & Rainer Winkelmann, 2015. "Consistent estimation of the fixed effects ordered logit model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 685-703, June.
    4. Stéphane Bonhomme & Elena Manresa, 2015. "Grouped Patterns of Heterogeneity in Panel Data," Econometrica, Econometric Society, vol. 83(3), pages 1147-1184, May.
    5. Verbeek, Marno & Nijman, Theo, 1992. "Testing for Selectivity Bias in Panel Data Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 681-703, August.
    6. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588.
    7. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1988. "Estimating Vector Autoregressions with Panel Data," Econometrica, Econometric Society, vol. 56(6), pages 1371-1395, November.
    8. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    9. Dean R. Hyslop, 1999. "State Dependence, Serial Correlation and Heterogeneity in Intertemporal Labor Force Participation of Married Women," Econometrica, Econometric Society, vol. 67(6), pages 1255-1294, November.
    10. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053, February.
    11. Kneip, Alois & Sickles, Robin C. & Song, Wonho, 2012. "A New Panel Data Treatment For Heterogeneity In Time Trends," Econometric Theory, Cambridge University Press, vol. 28(3), pages 590-628, June.
    12. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
    13. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    14. Bartolucci, Francesco & Farcomeni, Alessio, 2009. "A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 816-831.
    15. Ahn, Seung C. & Lee, Young H. & Schmidt, Peter, 2013. "Panel data models with multiple time-varying individual effects," Journal of Econometrics, Elsevier, vol. 174(1), pages 1-14.
    16. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    17. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    18. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    19. Ruud, Paul A., 1984. "Tests of Specification in Econometrics," Department of Economics, Working Paper Series qt4kq8m0hf, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    20. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 225-238.
    21. Nijman, T.E. & Verbeek, M.J.C.M., 1992. "Testing for selectivity in panel data models," Other publications TiSEM 7ec34a6c-1d84-4052-971c-d, Tilburg University, School of Economics and Management.
    22. Ahn, Seung Chan & Hoon Lee, Young & Schmidt, Peter, 2001. "GMM estimation of linear panel data models with time-varying individual effects," Journal of Econometrics, Elsevier, vol. 101(2), pages 219-255, April.
    23. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    24. Manuel Arellano & Stèphane Bonhomme, 2011. "Nonlinear Panel Data Analysis," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 395-424, September.
    25. J. Pfanzagl, 1993. "On the consistency of conditional maximum likelihood estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 703-719, December.
    26. Holly, Alberto & Monfort, Alain, 1986. "Some useful equivalence properties of Hausman's test," Economics Letters, Elsevier, vol. 20(1), pages 39-43.
    27. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
    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. Francesco, Bartolucci & Silvia, Bacci & Claudia, Pigini, 2015. "A misspecification test for finite-mixture logistic models for clustered binary and ordered responses," MPRA Paper 64220, University Library of Munich, Germany.
    2. González, Maximiliano & Guzmán, Alexander & Téllez, Diego Fernando & Trujillo, María Andrea, 2021. "What you say and how you say it: Information disclosure in Latin American firms," Journal of Business Research, Elsevier, vol. 127(C), pages 427-443.
    3. De Arcangelis, Giuseppe & Di Porto, Edoardo & Santoni, Gianluca, 2015. "Migration, labor tasks and production structure," Regional Science and Urban Economics, Elsevier, vol. 53(C), pages 156-169.
    4. Lukáš Čechura & Zdeňka Žáková Kroupová, 2021. "Technical Efficiency in the European Dairy Industry: Can We Observe Systematic Failures in the Efficiency of Input Use?," Sustainability, MDPI, Open Access Journal, vol. 13(4), pages 1-19, February.
    5. Atella, Vincenzo & Belotti, Federico & Depalo, Domenico & Piano Mortari, Andrea, 2014. "Measuring spatial effects in the presence of institutional constraints: The case of Italian Local Health Authority expenditure," Regional Science and Urban Economics, Elsevier, vol. 49(C), pages 232-241.
    6. Bartolucci, Francesco & Bacci, Silvia & Pigini, Claudia, 2017. "Misspecification test for random effects in generalized linear finite-mixture models for clustered binary and ordered data," Econometrics and Statistics, Elsevier, vol. 3(C), pages 112-131.
    7. Samer Hamidi & Fevzi Akinci, 2016. "Measuring Efficiency of Health Systems of the Middle East and North Africa (MENA) Region Using Stochastic Frontier Analysis," Applied Health Economics and Health Policy, Springer, vol. 14(3), pages 337-347, June.
    8. Jean-François Brun & Tiangboho Sanogo, 2017. "Effect of central transfers on municipalities' own revenue mobilization: Do conflict and local revenue management matter?," Working Papers halshs-01613108, HAL.
    9. Shun Yu & Xianzheng Huang, 2017. "Random-intercept misspecification in generalized linear mixed models for binary responses," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 333-359, August.
    10. Brown, Sarah & Ghosh, Pulak & Taylor, Karl, 2014. "The existence and persistence of household financial hardship: A Bayesian multivariate dynamic logit framework," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 285-298.
    11. Franco Peracchi & Claudio Rossetti, 2019. "A nonlinear dynamic factor model of health and medical treatment," EIEF Working Papers Series 1901, Einaudi Institute for Economics and Finance (EIEF), revised Feb 2019.
    12. Melik Ertugrul & Volkan Demir, 2018. "How Does Unobserved Heterogeneity Affect Value Relevance?," Australian Accounting Review, CPA Australia, vol. 28(2), pages 288-301, June.
    13. Sanogo, Tiangboho, 2019. "Does fiscal decentralization enhance citizens’ access to public services and reduce poverty? Evidence from Côte d’Ivoire municipalities in a conflict setting," World Development, Elsevier, vol. 113(C), pages 204-221.
    14. Tiangboho Sanogo, 2017. "Does fiscal decentralization enhance citizens’ access to public services and reduce poverty? Evidence from a conflict setting," Working Papers halshs-01582478, HAL.
    15. Tiangboho SANOGO, 2017. "Does fiscal decentralization enhance citizens’ access to public services and reduce poverty? Evidence from a conflict setting," Working Papers 201715, CERDI.

    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. Xin, Kai & Zhang, ZhengYu & Zhou, YaHong & Zhu, PingFang, 2021. "Time-varying individual effects in a panel data probit model with an application to female labor force participation," Economic Modelling, Elsevier, vol. 95(C), pages 181-191.
    2. Fernández-Val, Iván & Vella, Francis, 2011. "Bias corrections for two-step fixed effects panel data estimators," Journal of Econometrics, Elsevier, vol. 163(2), pages 144-162, August.
    3. Hübler, Olaf, 2005. "Panel Data Econometrics: Modelling and Estimation," Hannover Economic Papers (HEP) dp-319, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    4. Ahn, Seung C. & Lee, Young H. & Schmidt, Peter, 2013. "Panel data models with multiple time-varying individual effects," Journal of Econometrics, Elsevier, vol. 174(1), pages 1-14.
    5. Manuel Arellano & Olympia Bover, 1990. "La econometría de datos de panel," Investigaciones Economicas, Fundación SEPI, vol. 14(1), pages 3-45, January.
    6. Hayakawa, Kazuhiko, 2016. "Identification problem of GMM estimators for short panel data models with interactive fixed effects," Economics Letters, Elsevier, vol. 139(C), pages 22-26.
    7. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," Review of Economic Studies, Oxford University Press, vol. 82(3), pages 991-1030.
    8. Blazsek, Szabolcs & Escribano, Alvaro, 2016. "Score-driven dynamic patent count panel data models," Economics Letters, Elsevier, vol. 149(C), pages 116-119.
    9. Guido M. Kuersteiner & Ingmar R. Prucha, 2020. "Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity," Econometrica, Econometric Society, vol. 88(5), pages 2109-2146, September.
    10. 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.
    11. William H. Greene & David A. Hensher, 2008. "Modeling Ordered Choices: A Primer and Recent Developments," Working Papers 08-26, New York University, Leonard N. Stern School of Business, Department of Economics.
    12. Georges Bresson & Jean-Michel Etienne & Pierre Mohnen, 2011. "How important is innovation? A Bayesian factor-augmented productivity model on panel data," TEPP Working Paper 2011-06, TEPP.
    13. Geweke, J. & Joel Horowitz & Pesaran, M.H., 2006. "Econometrics: A Bird’s Eye View," Cambridge Working Papers in Economics 0655, Faculty of Economics, University of Cambridge.
    14. Manuel Arellano & Stéphane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 987-1020.
    15. Angrave, David & Charlwood, Andy & Wooden, Mark, 2014. "Working time and cigarette smoking: Evidence from Australia and the United Kingdom," Social Science & Medicine, Elsevier, vol. 112(C), pages 72-79.
    16. Wooldridge, Jeffrey M., 2014. "Quasi-maximum likelihood estimation and testing for nonlinear models with endogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 182(1), pages 226-234.
    17. Francesco BARTOLUCCI & Silvia BACCI & Claudia PIGINI, 2015. "A Misspecification Test for Finite-Mixture Logistic Models for Clustered Binary and Ordered Responses," Working Papers 410, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    18. repec:gnv:wpaper:unige:76321 is not listed on IDEAS
    19. Haan, Peter, 2010. "A Multi-state model of state dependence in labor supply: Intertemporal labor supply effects of a shift from joint to individual taxation," Labour Economics, Elsevier, vol. 17(2), pages 323-335, April.
    20. Robertson, Donald & Sarafidis, Vasilis, 2015. "IV estimation of panels with factor residuals," Journal of Econometrics, Elsevier, vol. 185(2), pages 526-541.
    21. Gabriele Fiorentini & Enrique Sentana, 2021. "Specification tests for non‐Gaussian maximum likelihood estimators," Quantitative Economics, Econometric Society, vol. 12(3), pages 683-742, July.

    More about this item

    Keywords

    Generalized linear models; Longitudinal data; Fixed-effects; Hausman-type tests; Self-reported health; Health and Retirement Study;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

    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:184:y:2015:i:1:p:111-123. See general information about how to correct material in RePEc.

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

    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 hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.