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Life‐Cycle Happiness in a Discounted Utility Model

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  • Stephen Shmanske

Abstract

SUMMARY A discrete time, discounted utility model with a finite horizon is analyzed. Utility is separable and additive in the natural logarithms of the choice variables, consumption and leisure, and an exogenous ‘memory' series. Happiness is defined as the discounted value of the utility over the remaining lifespan. Simulations of the model show how happiness grows as the high consumption years get closer, peaks, then declines in later life as the remaining lifespan shortens, even though year by year utility may continue to rise. Simulations also show how the peak year for happiness depends on the subjective, personal discount rate, the rate of wage growth, the effect of a liquidity constraint, the effect of memories, and other parameters in the model. The model also illustrates those aspects of the life cycle characterized by the ‘slackers’, the ‘mid‐life crisis’, and the ‘golden years’. ZUSAMMENFASSUNG Ein diskretes, abdiskontiertes Nutzenmodell mit einem endlichen Zeithorizont wird analysiert. Nutzen wird als zerlegbar und additiv in den natürlichen Logarithmen der Wahlvanablen Konsum und Freizeit und in den exogenen Zeitreihen für ‘Erinnerungen’ angenommen. Gluck ist definiert als abdiskontierter Wert des Nutzens der verbleibenden Lebenszeit. Simulationen zeigen, wie das Glück bei der Annäherung an die Jahre erhöhten Konsums ansteigt, einen Hohepunkt erreicht, um dann in der verbleibenden Lebenszeit wieder abzunehmen, obwohl der Nutzen Jahr fur Jahr weiterhin zunehmen kann. Die Simulationen zeigen auch, wie der Höhepunkt des Glücks vom persönlichen Diskontsatz, der Zuwachsrate des Einkommens, Liquiditatsbeschrankungen, Erinnerungen und anderen Parametern abhangt. Das Modell veranschaulicht aber auch jene Aspekte der Lebenszeit, die üblicherweise als ‘Slackers’, ‘Mid‐life Crisis' und ‘Goldene Jahre’ bezeichnet werden RÉSUMÉ Analyse d'un modèle d'utilité d'escompte à temps discret et à horizon limité. L'utilité est séparable et additive dans les logarithmes naturels des variables de choix, la consomption et les loisirs, et une série exogène de ‘mémoire’. On définit le bonheur comme la valeur d'escompte de l'utilité pendant la durée de la vie qui reste. Des simulations du modèle montrent comment le bonheur s'augmente au fur et à mesure que les année de grande consomption s'approchent, atteint son comble, puis baisse dans la dernière partie de la vie pendant que la durée de la vie qui reste se réduit, quoique, année par année, l'utilité puisse continuer à s'augmenter. Les simulations montrent aussi comment l'année du point culminant de bonheur dépend du taux d'escompte subjectif et personnel, du taux d'augmentation de salaire, de l'effet d'une contrainte de liquidité, de l'effet des souvenirs, et d'autres paramètres du modèle. Le modèle illustre aussi les aspects du cycle de vie caractérisés par les fainéants, la crise de ‘mid‐life’ et les années ‘dorées’.

Suggested Citation

  • Stephen Shmanske, 1997. "Life‐Cycle Happiness in a Discounted Utility Model," Kyklos, Wiley Blackwell, vol. 50(3), pages 383-407, August.
  • Handle: RePEc:bla:kyklos:v:50:y:1997:i:3:p:383-407
    DOI: 10.1111/1467-6435.00022
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    Cited by:

    1. Jungeilges, Jochen & Kirchgassner, Gebhard, 2002. "Economic welfare, civil liberty, and suicide: an empirical investigation," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 31(3), pages 215-231.
    2. Van Landeghem, Bert, 2012. "A test for the convexity of human well-being over the life cycle: Longitudinal evidence from a 20-year panel," Journal of Economic Behavior & Organization, Elsevier, vol. 81(2), pages 571-582.

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