AStA Advances in Statistical Analysis

, Volume 102, Issue 2, pp 145–166 | Cite as

A penalized spline estimator for fixed effects panel data models

  • Peter Pütz
  • Thomas Kneib
Original Paper


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. An open-source software implementation of our methods is available in the R package pamfe.


First-difference estimator Life satisfaction Panel data Penalized splines Simultaneous confidence bands 

Supplementary material

10182_2017_296_MOESM1_ESM.pdf (183 kb)
Supplementary material 1 (pdf 183 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Centre for StatisticsUniversität GöttingenGöttingenGermany
  2. 2.Chair of Statistics, Faculty of Economic SciencesUniversität GöttingenGöttingenGermany

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