A nonparametric approach to identify age, time, and cohort effects

Abstract

Empirical studies in the social sciences and biometrics often rely on data and models where a number of individuals born at different dates are observed at several points in time, and the relationship of interest centers on the effects of age a, cohort c, and time t. Because of t=a+c, the design is degenerate and one is automatically confronted with the associated (linear) identification problem studied intensively for parametric models (Mason and Fienberg 1985; MaCurdy and Mroz 1995; Kuang, Nielsen and Nielsen 2008a,b). Nonlinear time, age, and cohort effects can be identified in an additive model. The present study seeks to solve the identification problem employing a nonparametric estimation approach: We develop an additive model which is solved using a backfitting algorithm, in the spirit of Mammen et al. (1999). Our approach has the advantage that we do not have to worry about the parametric specification and its impact on the identification problem. The results can easily be interpreted, as the smooth backfitting algorithm is a projection of the data onto the space of additive models. We develop a complete asymptotic distribution theory for nonparametric estimators based on kernel smoothing and apply the method to a study on wage inequality in Germany between 1975 and 2004.