Estimating penalized spline regressions: theory and application to economics

Abstract

This article gives a brief survey of penalized spline smoothing. Penalized spline smoothing is a general nonparametric estimation technique which allows to fit smooth but else unspecified functions to empirical data. We depict the theory behind this estimation technique and we present an example demonstrating how this nonparametric estimation technique can help to gain insight into economics.

Acknowledgement

I thank Uwe Köller for providing me with the data.

Notes

¹ In Wood and Augustin (2002) an example is presented demonstrating how this matrix can be constructed.

² For a description of how to obtain the variance associated with the smooth term, see e.g. Wood and Augustin (2002) or Hastie and Tibshirani (1990).

³ Data source: OECD Economic Outlook, June 2003. The data are available upon request.

⁴ All estimations were performed using the mgcv package (version 1.2-3) in R (version 2.1.0), cf. Wood (2001).

Table 1. Estimates for the parametric part of model (10) with f(d_{t −1}) obtained by penalized spline estimation