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A Penalized Spline Estimator for Fixed Effects Panel Data Models

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  • Peter Pütz
  • Thomas Kneib

Abstract

Estimating nonlinear effects of continuous covariates by penalized splines is well established for regressions with cross-sectional data as well as for panel data regressions with random effects. Penalized splines are particularly advantageous since they enable both the estimation of unknown nonlinear covariate effects and inferential statements about these effects. The latter are based, for example, on simultaneous confidence bands that provide a simultaneous uncertainty assessment for the whole estimated functions. In this paper, we consider fixed effects panel data models instead of random effects specifications and develop a first-difference approach for the inclusion of penalized splines in this case. We take the resulting dependence structure into account and adapt the construction of simultaneous confidence bands accordingly. In addition, the penalized spline estimates as well as the confidence bands are also made available for derivatives of the estimated effects which are of considerable interest in many application areas. As an empirical illustration, we analyze the dynamics of life satisfaction over the life span based on data from the German Socio-Economic Panel (SOEP). An open source software implementation of our methods is available in the R package pamfe.

Suggested Citation

  • Peter Pütz & Thomas Kneib, 2016. "A Penalized Spline Estimator for Fixed Effects Panel Data Models," SOEPpapers on Multidisciplinary Panel Data Research 827, DIW Berlin, The German Socio-Economic Panel (SOEP).
    • Handle: RePEc:diw:diwsop:diw_sp827
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    2. Badi H. Baltagi & Dong Li, 2002. "Series Estimation of Partially Linear Panel Data Models with Fixed Effects," Annals of Economics and Finance, Society for AEF, vol. 3(1), pages 103-116, May.
    3. Gholamreza Hajargasht, 2009. "Nonparametric Panel Data Models, A Penalized Spline Approach," CEPA Working Papers Series WP052009, School of Economics, University of Queensland, Australia.
    4. Frijters, Paul & Beatton, Tony, 2012. "The mystery of the U-shaped relationship between happiness and age," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 525-542.
    5. Manuel Wiesenfarth & Tatyana Krivobokova & Stephan Klasen & Stefan Sperlich, 2012. "Direct Simultaneous Inference in Additive Models and Its Application to Model Undernutrition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1286-1296, December.
    6. Li, Gaorong & Peng, Heng & Tong, Tiejun, 2013. "Simultaneous confidence band for nonparametric fixed effects panel data models," Economics Letters, Elsevier, vol. 119(3), pages 229-232.
    7. Ada Ferrer-i-Carbonell & Paul Frijters, 2004. "How Important is Methodology for the estimates of the determinants of Happiness?," Economic Journal, Royal Economic Society, vol. 114(497), pages 641-659, July.
    8. Henderson, Daniel J. & Carroll, Raymond J. & Li, Qi, 2008. "Nonparametric estimation and testing of fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 144(1), pages 257-275, May.
    9. Krivobokova, Tatyana & Kneib, Thomas & Claeskens, Gerda, 2010. "Simultaneous Confidence Bands for Penalized Spline Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 852-863.
    10. Laporte, Audrey & Windmeijer, Frank, 2005. "Estimation of panel data models with binary indicators when treatment effects are not constant over time," Economics Letters, Elsevier, vol. 88(3), pages 389-396, September.
    11. Mammen, Enno & Støve, Bård & Tjøstheim, Dag, 2009. "Nonparametric Additive Models For Panels Of Time Series," Econometric Theory, Cambridge University Press, vol. 25(2), pages 442-481, April.
    12. López Ulloa, Beatriz Fabiola & Møller, Valerie & Sousa-Poza, Alfonso, 2013. "How does subjective well-being evolve with age? A literature review," FZID Discussion Papers 72-2013, University of Hohenheim, Center for Research on Innovation and Services (FZID).
    13. Su, Liangjun & Ullah, Aman, 2006. "Profile likelihood estimation of partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 92(1), pages 75-81, July.
    14. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    15. Jia Chen & Degui Li & Jiti Gao, 2013. "Non- and Semi-Parametric Panel Data Models: A Selective Review," Monash Econometrics and Business Statistics Working Papers 18/13, Monash University, Department of Econometrics and Business Statistics.
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    Keywords

    First-difference estimator; life satisfaction; panel data; penalized splines; simultaneous confidence bands;
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