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Multidimensionality of Longitudinal Data: Unlocking the Age-Happiness Puzzle

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Abstract

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.

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Notes

  1. See the recent paper by López Ulloa et al. (2013) for a comprehensive review of the theoretical framework and empirical evidence on age-happiness research.

  2. These studies tried to control for individual fixed effects using methods different from the FE regression.

  3. An early version of the paper appeared in NCER Working Paper Series, Working Paper #26, 2008.

  4. See also López Ulloa et al (2013, p.239).

  5. Numerical results and graphs in the paper can be reproduced using the program codes in the Supplementary Material.

  6. See Summerfield et al. (2013) for detailed information about the HILDA data.

  7. Ferrer-i-Carbonell and Frijters (2004) have shown that ordinality or cardinality makes little difference to the final results in analysing happiness scores.

  8. For space constrain, the numerical results are not displayed in the paper. But they can be reproduced using the supplied programs.

  9. Lines between 391 and 440 in the Stata code show the calculation.

  10. This procedure is sometimes called regression under the matched data design.

  11. Why happiness is U-shaped in age across cohorts in a given year or negatively related to ageing over time is not the concern of this work.

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Acknowledgments

This paper uses unit record data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey. The HILDA Project was initiated and is funded by the Australian Government Department of Social Services (DSS) and is managed by the Melbourne Institute of Applied Economic and Social Research (Melbourne Institute). The findings and views reported in this paper, however, are those of the author and should not be attributed to either DSS or the Melbourne Institute. The author thanks Jongsay Yong for a suggestion that has improved the presentation of the first draft, and thanks Andrew Oswald and Nick Powdthavee for comments and discussions. The author is grateful for the challenging comments from the anonymous reviewers that have provided an opportunity to further clarify the work.

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  1. Melbourne Institute of Applied Economic and Social Research, University of Melbourne, Melbourne, Australia

    Ning Li

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Li, N. Multidimensionality of Longitudinal Data: Unlocking the Age-Happiness Puzzle. Soc Indic Res 128, 305–320 (2016). https://doi.org/10.1007/s11205-015-1032-4

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