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Durable consumption, saving and retirement

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Abstract

Durables yield services through life but are also a store of value and both features may have important implications for savings and retirement decisions. Durables also affect bequests and thus induce intergenerational transfers. We show that allowing explicitly for durables has important implications for retirement decisions and responses to various changes in the environment. An improvement in the possibility of freeing housing capital makes the old retire earlier (income effect) while the young plan to retire later since they increase housing demand and reduce financial savings. Considering welfare in stationary equilibrium, we find that a reduction in wealth locking-in in durables is not necessarily welfare improving due to the effects on bequests. From a social welfare perspective, individuals tend to choose too much financial savings, too little durable acquisition and too early retirement.

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Notes

  1. The relationship between housing wealth and retirement has been considered by Doling and Horsewood (2003) using aggregate data for 19 countries (mostly EU member states) for the period 1990–1996. They find that the labour force participation rate for men aged 55–64 depends negatively on the home ownership rate. See also Farnham and Sevak (2007) and Blake (2004).

  2. Feinstein and McFadden (1989) and Venti and Wise (2002, 2004) find that the elderly in the USA do not, or only very slowly, decumulate housing equity. Significant reductions are mostly associated with the death of a spouse or deteriorating health. Yang (2009) shows that the lifecycle profile for housing stock is monotonically increasing in young ages and almost flat in old age. In a recent study, Chiuri and Jappelli (2010) estimate ownership trajectories for 15 OECD countries and they find small changes in ownership rates up to the age 65–70, but more substantial changes with considerable dispersion between countries for higher ages.

  3. A reverse mortgage allows the homeowner to receive part of the equity value in various ways (lump-sum payment, annuity, line of credit etc.), and all interest and repayment is made when the owner dies or voluntarily sells the house.

  4. Karatzas and Wang (2000) provide the mathematical tools for determining the optimal retirement time in the consumption-portfolio choice framework.

  5. Price variations introduce both risk and speculation. Moreover, price dynamics may arise due to changes in the demographic composition of the population, see e.g. Ċerný et al. (2010).

  6. That is, the survival probability to given ages may change, and thus longevity measured either by life expectancy at birth or longest achievable age may change, see Andersen and Gestsson (2010).

  7. For simplicity, we do not model the habit formation explicitly but impose the same choice of the durable good in young and old age. Habit formation could be implemented by specifying old age utility from durable consumption in deviation from the level chosen in young age. Infinite punishment for deviation from the amount of durable chosen in young age would then correspond to complete habit formation.

  8. It is assumed that the house does not depreciate, but this can easily be relaxed without changing the qualitative results by assuming that only a fraction of the house acquired as young is left when old.

  9. We could denote, \(f ph\), ‘consumable housing wealth’, cf. above.

  10. OECD (2006) also applies a healthy ageing assumption in projections of health and long-term care expenditures.

  11. Diamond (2003) assumes that disutility of work is a non-increasing function of the survival probability.

  12. To ensure that there is always some retirement period, we assume \( \lim _{R\rightarrow L}d'\left (\frac {R}{L}\right )=\infty \).

  13. Assuming an explicit bequest motive would make locking-in of wealth less costly for the representative agent. To change our results, however, the bequest motive has to be so strong that the desired amount of bequest exceeds the amount of wealth locked-in in the durable good as old.

  14. Assuming an interior solution for h.

  15. This is in line with the results of the deregulation of financial markets in the late 1970s and 1980s. The personal savings ratio dropped since households chose to spend some of their housing equity (Blake 2004).

  16. From Eq. 13 it can be shown that at least one of \(s^{\ast }\) and \(h^{\ast }\) has to be increasing in longevity.

  17. Note that the decisions made by the young are time consistent, and hence this situation arises only if unanticipated news arise. If the change in e.g. longevity is unanticipated but permanent, there will only be a difference between the planned and actual retirement for the generation for whom the shock is unanticipated.

  18. In the decentralized solution, the agent chooses a lower h than what is socially optimal. Therefore, an increase in f can only be welfare improving if it induces the agent to raise h sufficiently. In other words, bequests are not internalized, and they are too low socially. Raising f worsens the latter, but might help to reduce the negative consequences of the former, and therefore, the effect is ambiguous in the decentralized equilibrium.

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Acknowledgments

We gratefully acknowledge comments from two anonymous referees, Christian Bjørnskov, Svend E. Hougaard Jensen, Valdemar Smith and Øystein Thøgersen.

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  1. Department of Economics and Business, Aarhus University, Fuglesangs Allé 4, 8210, Aarhus V, Denmark

    Torben M. Andersen & Mikkel Nørlem Hermansen

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  1. Torben M. Andersen
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Correspondence to Mikkel Nørlem Hermansen.

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Andersen, T.M., Hermansen, M.N. Durable consumption, saving and retirement. J Popul Econ 27, 825–840 (2014). https://doi.org/10.1007/s00148-013-0490-8

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