Multidimensionality of Longitudinal Data: Unlocking the Age-Happiness Puzzle

In social economic data analysis, sometimes the explanatory variables that are statistically significant in OLS regressions in cross-section or pooled data become insignificant after controlling for individual fixed effects. This phenomenon was observed in the study of the relationship between age and happiness. The discrepancy in estimates between regressions with and without controlling for individual fixed effects was known as the age-happiness mystery. This paper points out that OLS regressions based on cross-section data reflect the difference in average happiness across birth cohorts. In contrast, regressions controlling for individual fixed effects reflect the change in happiness over life cycle within individuals. For the first time in the literature, the co-existence of a cross-section U shape and a longitudinally declining pattern in the relationship between age and happiness is established. Using data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey, this paper explains the exact meaning of fixed-effects regressions of happiness on age, gives insight into the age-happiness puzzle, and raises the awareness of multidimensionality of longitudinal data.