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Non-monotonicity in the longevity–income relationship

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Abstract

In this essay, I empirically analyze the relationship between income and life expectancy for pensioners in the public pension system in Germany and find that the relationship is non-monotonic for major sub-groups in the data. Due to the application of non-parametric methods, this cannot be explained as an artifact of the estimation technique or by anomalies of the data, and the finding is robust against the inclusion of control variables. Furthermore, I theoretically derive a non-monotonic relationship between income and longevity, based on heterogeneous elasticities of labor supply and otherwise standard assumptions.

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Notes

  1. See Section 2 and the references cited therein.

  2. To establish non-monotonicity empirically as well as theoretically, I rest on individuals with strictly positive labor supply and labor income.

  3. On the question of whether age at death in the Grossman model (as the planning horizon of the individual) is under direct control of the individual, see especially Ried (1998) and, in addition, Grossman (2000) for a short discussion.

  4. This counter argument is not valid in the present paper, as I use social insurance wealth as a measure for socio-economic status, which is not possible to bequeath.

  5. On the positive impact of education, see, e.g., Deaton and Paxson (2004) and Deaton (2006); on the positive impact of marriage or household composition in general, see, e.g., Martikainen et al. (2005) and Adams et al. (2003). A further factor is the type of occupation (see Hayward et al. 1989 and Moore and Hayward 1990 for its impact on mortality); unfortunately, the number of missing values (83%) in the occupation variable—which is usually not necessary to calculate the pension—is prohibitively high.

  6. On average and even without the restriction to at least 25 years of contribution, social security income adds to 80% of the household income if the household head is 65 or older, see Börsch-Supan and Schnabel (1999).

  7. Related to this is potential endogeneity of life expectancy with respect to benefit claims. Both might be driven by health status (a healthier individual might be more productive and live longer). Yet, the regressions control for health-status as potential common background variable via months in ill-health and existence of a disability pension. Direct reverse causality (longevity being the cause for benefit claims) is not plausible, since the income variable “benefit claims” is realized considerably before death occurs. Still, one potential endogeneity factor cannot be ruled out, which is education. See again Deaton and Paxson (2004) and Deaton (2006) on the importance of education as determinant of mortality and Adams et al. (2003), Meer et al. (2003), and Lindahl (2005) on the potential endogeneity of health and socio-economic variables.

  8. For international evidence, see, e.g., Oeppen and Vaupel (2002), for Germany; see p. 54 Statistisches Bundesamt (2007) and Human Mortality Database (2005), own calculations.

  9. See, e.g., Fan and Gijbels (1992), Fan (1992), pp. 105 Pagan and Ullah (1999), and pp. 60 Fan and Gijbels (2003) for a thorough discussion on this topic: The bias of m(x i ) from locally linear regression does not depend on the density of x; hence, it is not subject to the question of whether the local regression is performed at the boundaries or in the interior.

  10. See, e.g., the textbooks by pp. 47 Fan and Gijbels (2003) or pp. 14 Li and Racine (2007).

  11. See Table 2 for the size of the respective sub-populations and the corresponding optimal plug-in bandwidths.

  12. Statistisches Bundesamt (2007) shows that—conditional on reaching retirement age—life expectancy is only marginally higher in West Germany, whereas von Gaudecker and Scholz (2007) even find a slight and puzzling advantage for East Germans.

  13. Below, I utilize the result in the theoretical conjecture of Section 6.

  14. Furthermore, Ruhm (2000, 2007) provides an additional justification for this assumption: For aggregate variables, he finds that, in times of higher unemployment (hence, in times with less work), mortality declines. Yet, Johansson (2004) challenges this result and finds a negative effect of hours worked on mortality.

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Acknowledgements

This research was conducted during the course of my doctoral studies at the University of Konstanz, Germany. In November 2008, I joined the Boston Consulting Group GmbH as a management consultant. I gratefully acknowledge support by the German Research Foundation (DFG) under grant BR 740/15-2, “Heterogeneous Labor: Positive and Normative Aspects of the Skill Structure of Labor.” The former Federation of German Pension Insurance Institutes (VDR, now: Deutsche Rentenversicherung Bund) deserves thanks for producing and confiding the data set. I thank Friedrich Breyer, Ralf Brüggemann, Mathias Kifmann, Francois Laisney, Winfried Pohlmeier, Verena Utikal, and two anonymous referees appointed by the Journal of Population Economics for helpful discussions and suggestions. All errors are my own.

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    Stefan Hupfeld

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Hupfeld, S. Non-monotonicity in the longevity–income relationship . J Popul Econ 24, 191–211 (2011). https://doi.org/10.1007/s00148-009-0284-1

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