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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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    Cited by:

    1. Yashar Tarverdi, 2018. "Aspects of Governance and $$\hbox {CO}_2$$ CO 2 Emissions: A Non-linear Panel Data Analysis," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 69(1), pages 167-194, January.

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    Keywords

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