Multidimensionality of Longitudinal Data: Unlocking the Age-Happiness Puzzle

Abstract

In social and economic analysis of longitudinal data, the socioeconomic variables that are statistically significant in pooled data regressions sometimes become insignificant after individual fixed effects are controlled for. This phenomenon has been observed in the analysis of the relationship between age and happiness. The discrepancy in results between regressions with and without controlling for individual fixed effects is sometimes known as a mystery in the research of age and happiness. This paper points out that cross-sectional information and longitudinal information reflect distinct aspects of the phenomenon under study. In age-happiness studies, cross-sectional information describes whether, in a particular year, people of a certain age are happier than people of other ages. Longitudinal information describes whether people become happier or less happy over the life cycle. The former compares happiness between different people, and the later compares happiness within the same person. Average happiness is U-shaped in age among different cohorts, and simultaneously decreases with age in the life cycle within individuals. Using data on happiness from the Household, Income and Labour Dynamics in Australia (HILDA) Survey, this paper explains what "individual fixed effects are controlled for" means in the context of FE regression, gives insight into the age-happiness puzzle and raises awareness of the multidimensionality of longitudinal data.

The U Shape of Happiness Across the Life Course: Expanding the Discussion

“…In a study using BHPS data, Grover and Helliwell (2019) found support for the U shape when earlier life satisfaction was not controlled (i.e., the effects of age and the age-squared terms were significantly negative and positive, respectively), but in models controlling for earlier life satisfaction (a methodologically rigorous approach), the age terms dropped to nonsignificance. Li (2016) conducted fixed-effects analyses to document decreasing life satisfaction across the life course in the HILDA sample, similar to the earlier report by Frijters and Beatton (2012). Such widely varying findings in more recent and earlier studies using the same data sources must give pause to the assumption of a single trajectory describing paths of happiness across the life span.…”

“…Cross-sectional studies confound age and cohort differences (people born in the same period of time share unique experiences that people born at different times do not), a limitation commonly acknowledged in the literature (Baird et al, 2010; Bell, 2014; Easterlin, 2006). Using Household, Income and Labour Dynamics of Australia (HILDA) survey data, Li (2016) demonstrated that the U shape in cross-sectional data is a result of averaging levels of life satisfaction of different birth cohorts and that life satisfaction actually declined across the life course when appropriate within-person (fixed-effects) longitudinal analyses were conducted. Li argues that the age-happiness connection is in fact a “cohort-happiness” (p. 317) connection, a point that has also been made by others (Bell, 2014; Frijters & Beatton, 2012).…”

“…That is, the shape (and associated nadirs and peaks) of the age-happiness connection varied depending on the country and region of the world (Bauer, Levin, Boudet, Nie, & Sousa-Poza, 2017; Laaksonen, 2018; Morgan, Robinson, & Thompson, 2015; Steptoe et al, 2015), whether control variables such as education and marital status were included in the analyses (Blanchflower & Oswald, 2019; Ferrante, 2017; Hellevik, 2017), year or period of time when the surveys were administered (Kolosnitsyna, Khorkina, & Dorzhiev, 2017; Olaroiu, Alexa, & van den Heuvel, 2017), and gender (Kolosnitsyna et al, 2017; Laaksonen, 2018). Some studies found a U shape, but the low point was outside of the typical range of midlife (defined as 40–60 years of age; Freund & Ritter, 2009), for example, in the 30s (Laaksonen, 2018; Li, 2016) or up to age 70 (Kolosnitsyna et al, 2017). One study found a wave shape with the lowest point at age 23 in a model without controls (Blanchflower & Oswald, 2019).…”

Ageing, Death and Life Satisfaction: Evidence from the Household, Income and Labour Dynamics in Australia Survey

“…This variable has been used in a large number of research studies into SWB in Australia, including a number of the previously cited studies on the relationship with age (Frijters and Beatton ; Cheng, Powdthavee and Oswald ; Li ).…”

“…This typically involves the estimation of panel data models where within‐person changes are isolated through the incorporation of individual‐specific fixed effects. Such models have been estimated by a number of recent studies employing household panel survey data (Gwodz and Sousa‐Poza ; Frijters and Beatton ; Kassenboehmer and Haisken‐DeNew ; Li ), all of which find that the U‐shape that is so prominent in cross‐sectional data largely disappears. Furthermore, in these models, self‐reported life satisfaction (the measure used in all of these studies) is found to be relatively stable over most of the life course, before declining quite markedly in older ages (beyond 70 years)…”