A huge cross-section literature, written by economists and others, argues that human well-being is U-shaped through the life cycle. Although in many cases this U-shape is robust, an unusually vivid debate is going on about its true shape.
One issue discussed in the latest longitudinal literature is how to overcome the famous statistical problem of the linear dependency of age, time and birth cohort. This paper tries to suggest a new way to think about this, and to contribute to the debate by showing that what can be done is to test for the convexity of well-being through the life cycle. It uses a recently developed methodology to nationally representative longitudinal data to estimate the first derivative of well-being to age. The paper's approach has the advantage that identification is feasible under assumptions which are much weaker than in
previous work. The empirical analysis finds that well-being is convex in age (which would be in line with a U-shaped pattern through life). But eventually, late in life, there are signs that well-being becomes concave in age. The analysis also shows that well-being is nonlinear in time as well as year of birth.
 

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