Introduction

In a seminal paper Rao (1945) introduced the concept of ‘Geodesic Distance’ (or ‘Rao Distance’) into statistics. This concept has important theoretical properties and is based on the demanding differential-geometrical approach to statistics. These mathematical requirements and difficulties in its application are responsible for the low level of familiarity by econometricians with this generalisation of the well-known Mahalanobis distance. Econometricians require some detailed knowledge of Riemannian geometry to gain a complete understanding of Rao distances. Section 2 provides a short introduction to the necessary theory on Rao distances, hyperbolic curvature, isocircles and Rao distance tests.

Since their original development in the paper by Aigner and Chu (1968), frontier functions have served almost exclusively for estimating production and cost functions consistently with an economic theory of optimising behaviour. In section 3 of this chapter, an extended human capital model is estimated as a stochastic earnings frontier with data from the German socio-economic panel. This provides a deeper interpretation of the deviations of observed income from estimated income. Distinguishing between ‘potential human capital’ and ‘active human capital’ accounts for the partial failure of human capital models when estimated as average functions.

There has been a tendency in Germany for the number of years of education attained to increase, in part owing to the combination of an apprenticeship with university studies. Büchel and Helberger (1995) call this combination an inefficient ‘insurance strategy’ pursued mainly by children from low-income and low-education families because of low efficiency or high risk-aversion.