People’s life satisfaction follows a U-shape through the life cycle, gradually falling from early adulthood, reaching a minimum at around the ages of 40 to 42 and then rising up to the age of 70. That is the central finding of research by academics including Andrew Oswald, Professor of Economics at the University of Warwick.

The study in the Economic Journal follows over 50,000 adults through their lives, is the first longitudinal and multi-country evidence for a midlife low in human happiness and wellbeing. The authors conclude that there really is a kind of midlife ‘crisis’ in people’s feelings of satisfaction with their lives.

The idea of U-shaped wellbeing over much of the human lifespan is not a new one. Indeed, this pattern has been documented for a large number of countries using cross-sectional data – that is, data covering different people at a point in time. But until now, researchers have not been able to replicate this pattern with genuinely longitudinal data – data on the same people observed over time.

In the new study, the researchers analyse four different data sets covering three countries – Australia, Britain and Germany. Collectively, these datasets track the lives of tens of thousands of individuals over time. The primary outcome of interest is their happiness and wellbeing, which is measured using a conventional life satisfaction questionnaire asking individuals to indicate how satisfied they are with their lives.

The authors propose a novel longitudinal test of a U-shape in wellbeing. The test is based on a simple mathematical fact from school calculus: that the derivative of a quadratic function is linear. This implies that it is possible to test for a U-shape in life satisfaction by examining the change in life satisfaction.

Applying the test to the data (rather than examining how levels of life satisfaction vary across different people, as it is usually done), the authors investigate the within-person changes in life satisfaction, and document how these changes evolve over time.

This emphasis on following the changes in life satisfaction in the same people is important as it implies that any results consistent with a U-shape in wellbeing cannot be due to a fluke or to differences from one individual to another. They must stem instead from changes through time in the quality of the lives of these individuals.