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Univariate versus multivariate modeling of panel data

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    Panel data can be arranged into a matrix in two ways, called 'long' and 'wide' formats (LF and WF). The two formats suggest two alternative model approaches for analyzing panel data: (i) univariate regression with varying intercept; and (ii) multivariate regression with latent variables (a particular case of structural equation model, SEM). The present paper compares the two approaches showing in which circumstances they yield equivalent—in some cases, even numerically equal—results. We show that the univariate approach gives results equivalent to the multivariate approach when restrictions of time invariance (in the paper, the TI assumption) are imposed on the parameters of the multivariate model. It is shown that the restrictions implicit in the univariate approach can be assessed by chi-square difference testing of two nested multivariate models. In addition, common tests encountered in the econometric analysis of panel data, such as the Hausman test, are shown to have an equivalent representation as chi-square difference tests. Commonalities and differences between the univariate and multivariate approaches are illustrated using an empirical panel data set of firms' profitability as well as a simulated panel data.

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    File URL: http://www.econ.upf.edu/docs/papers/downloads/1417.pdf
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    Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 1417.

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    Date of creation: Feb 2014
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    Handle: RePEc:upf:upfgen:1417
    Contact details of provider: Web page: http://www.econ.upf.edu/

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    1. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291, March.
    2. Trina Larsen Andras & Srini S. Srinivasan, 2003. "Advertising Intensity and R&D Intensity: Differences across Industries and Their Impact on Firm's Performance," International Journal of Business and Economics, College of Business, and College of Finance, Feng Chia University, Taichung, Taiwan, vol. 2(2), pages 167-176, August.
    3. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    4. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 38(2), pages 112-134.
    5. Schmalensee, Richard, 1985. "Do Markets Differ Much?," American Economic Review, American Economic Association, vol. 75(3), pages 341-51, June.
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    7. Anita M. McGahan & Michael E. Porter, 1999. "The Persistence of Shocks to Profitability," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 143-153, February.
    8. Thornhill, Stewart, 2006. "Knowledge, innovation and firm performance in high- and low-technology regimes," Journal of Business Venturing, Elsevier, vol. 21(5), pages 687-703, September.
    9. Jushan Bai, 2013. "Fixed‐Effects Dynamic Panel Models, a Factor Analytical Method," Econometrica, Econometric Society, vol. 81(1), pages 285-314, 01.
    10. Anderson, T. W. & Hsiao, Cheng, 1982. "Formulation and estimation of dynamic models using panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 47-82, January.
    11. Anderson, T. W., 1989. "Linear latent variable models and covariance structures," Journal of Econometrics, Elsevier, vol. 41(1), pages 91-119, May.
    12. Noel Capon & John U. Farley & Scott Hoenig, 1990. "Determinants of Financial Performance: A Meta-Analysis," Management Science, INFORMS, vol. 36(10), pages 1143-1159, October.
    13. Breusch, T S & Pagan, A R, 1980. "The Lagrange Multiplier Test and Its Applications to Model Specification in Econometrics," Review of Economic Studies, Wiley Blackwell, vol. 47(1), pages 239-53, January.
    14. Wallace, T D & Hussain, Ashiq, 1969. "The Use of Error Components Models in Combining Cross Section with Time Series Data," Econometrica, Econometric Society, vol. 37(1), pages 55-72, January.
    15. Kirner, Eva & Kinkel, Steffen & Jaeger, Angela, 2009. "Innovation paths and the innovation performance of low-technology firms--An empirical analysis of German industry," Research Policy, Elsevier, vol. 38(3), pages 447-458, April.
    16. Juan Carlos Bou & Albert Satorra, 2003. "The persistence of abnormal returns at industry and firm levels," Economics Working Papers 729, Department of Economics and Business, Universitat Pompeu Fabra.
    17. Satorra, Albert, 2002. "Asymptotic Robustness In Multiple Group Linear-Latent Variable Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 297-312, April.
    18. Satorra, Albert & Bentler, Peter M., 1990. "Model conditions for asymptotic robustness in the analysis of linear relations," Computational Statistics & Data Analysis, Elsevier, vol. 10(3), pages 235-249, December.
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