Assessing parametric misspecification and heterogeneity in growth regression

Abstract

A fully nonparametric analysis is applied to address the problems of nonlinearity and heterogeneity in classical growth regression models using original data from seminal contributions in this field. Nonparametric specification tests and in-sample goodness-of-fit measures, as well as cross-validation based out-of-sample measures provide considerable evidence for parametric misspecification and a superior performance of a nonparametric model, despite the small sample size. In contrast to recent contributions identifying heterogeneity as the primal source of misspecification, a formal and graphical analysis does not reveal evidence for heterogeneity in a parametric and nonparametric quantile regression framework.

Acknowledgements

We thank the participants at the Annual Meeting of the German Statistical Society 2009 in Wuppertal. Special thanks go to Jeff Racine and Joachim Schnurbus for their valuable input on computational details. Any remaining errors are ofcourse ours.

Notes

¹ More specific, we estimate a local-linear model using the expected Kullback–Leibler cross validation proposed by Hurvich et al. (1998) and a second-order Gaussian kernel. The bandwidths for the covariates lpop and ligdp are 0.0934 (scale factor: 1.3497) and 1.1431 (scale factor: 5.2912), respectively. For all nonparametric computations in this article we use version 0.30-1 of the np-package for R from Hayfield and Racine (2008).

² We thank Jeff Racine for suggesting a formal test here.