A test for the convexity of human well-being over the life cycle: Longitudinal evidence from a 20-year panel

A huge cross-section literature, written by economists and others, argues that human well-being is U-shaped through the life cycle. In many cases this U-shape is robust (with a well-known exception the pattern evident in some U.S. data sets if few independent variables are included). However, a lively debate is currently ongoing about its true shape. This paper discusses the identification problem of age, time, and cohort effects. It suggests a simple way to interpret estimates of age variables in a first-difference framework. Building on McKenzie's (2006) methodology, the paper shows that no extra assumptions are needed in order to identify the second derivative of well-being to age, i.e. to estimate the changes in the actual age and well-being relationship. An empirical application, using a large German data set, finds that human well-being is convex in age until after midlife, which is approximately consistent with a U-shaped pattern through life, and not with the concave relationship sometimes found in U.S. studies.

► Human well-being is often found to be U-shaped over the life cycle.
► This paper illustrates the identification problem of age, time, and cohort effects.
► Second derivatives are identified following McKenzie's (2006).
► An application to German panel data finds convexity until after midlife.
► This is consistent with a U-shaped pattern of well-being through life.