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Aging society, health and the environment


In a general-equilibrium OLG model with endogenous longevity, a political economy and a social planner solution are contrasted mainly with respect to public supplies of health care and environment protection. The latter is relatively more supported by the young because its beneficial effect on longevity takes more time to occur but then lasts longer; while the old relatively prefer health spending. With population aging, political claims for health care expenditure are self-reinforcing. This framework is able to generate a quite rich set of results. In the political economy larger health care/consumption and health care/environmental quality ratios are implemented. Changes in risk aversion, production pollution, health inputs’ elasticity of substitution may have opposite impacts across regimes. More complete annuity markets improve welfare. Further comparative statics is analyzed.

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  1. Another difference is that in Jouvet et al. (2010) only the young do invest in health, whereas in our model health care expenditure is intended for the elderly people only. Both assumptions are extreme and made for analytical tractability as models work through simplifications; however, supporting health care provision is commonly one of the prior political items for retired and elderly voters.

  2. Differently from others in the existing literature (e.g. Finlay 2006; Chakraborty and Das 2005), we do not interpret p() as a mortality shock at the end of the first period. The dependence of p() on the second-period health status can be found also in Osang and Sarkar (2008).

  3. Most of the literature features similar assumptions, but usually considers only one determinant of health (Chakraborty and Das 2005; Osang and Sarkar 2008; Bhattacharya and Qiao 2007; Kalemli-Ozcan et al. 2000; Fioroni 2010). A two-input longevity function is considered by Finlay (2006) and Leroux et al. (2011) who, in addition to health spending, have respectively a health base-level and an amount of genes, which are however exogenous in either model. With respect to health-spending, the same conditions given in the text are assumed.

  4. See Chakraborty and Das (2005). In models with endogenous survival a cardinal assumption on the utility function is usually required since utility enters in level in the first order conditions with respect to the longevity inputs. As adding a positive constant to a utility function does not alter preference-ordering, this assumption does not seem restrictive.

  5. Looking at π as the probability of surviving throughout the whole second period, there is a probability (1 − π) of un-enjoying savings.

  6. A life annuity is an insurance product by which the insured person receives periodically a sum as long as she lives, in exchange for a premium charge. It allows agents to insure against the risk of outliving their savings, given the uncertainty of their remaining lifetime, by pooling the mortality risk across annuity purchasers. See Mitchell et al. (1999).

  7. This may occur for a number of reasons which are surveyed by Brown and Wharshawsky (2001). See also Chakraborty and Das (2005).

  8. Every variable is expressed per young agent and the young cohort size is assumed to be constant.

  9. Jouvet (1998) uses a natural decay rate. This avoids unit roots in environmental dynamics but, since it is not well-established that the environment deteriorates spontaneously, following Ono (2003) we do not introduce any natural decay rates.

  10. This approach is the same as in John and Pecchenino (1994).

  11. The lump-sum taxation scheme is preferred to a proportional tax rate for analytical tractability. With a proportional tax (shared between workers and capitalists according to their inputs’ shares) the dynamics of the model would become soon difficult to handle and the economic intuitions would be less clear, as expectations over future tax-rates would be involved. For the sake of simplicity, we abstract from the possibility that the government might run a deficit by issuing debt securities. The model’s taxation scheme keeps relatively simple the side of government’s revenues in order to focus on the expenditure side. Nevertheless, this scheme keeps nice properties: taxes are decided through voting, they can reflect intergenerational contrasts, they are more realistic than assuming only one tax as individuals’ contribution is usually different according to their age, they are consistent with the possibility of a negative lump-sum tax (i.e. an intergenerational transfer).

  12. Hence, with respect to majority voting, probabilistic voting allows for a smoother aggregation of preferences and can be applied irrespectively of whether preferences are single-peaked or not. Moreover, majority voting in our framework would imply the implausible outcome of a “dictatorship” of the young, as they are homogeneous and in a greater amount than the old. Nevertheless, our setting can be adapted to a majority voting scheme by assuming that the relative preference for health care expenditure over environmental maintenance is continuously distributed across the population and increasing in age.

  13. A parameter capturing exogenous political force for the old can be easily included in the model but it would complicate the storyline without adding substantial value or changing the qualitative results.

  14. The number 2 in the square brackets on the r.h.s. of Eq. 19 refers to this double effect. It is a consequence of the fact that, since each elector has the same weight for the government, the political importance of the old increases with population aging.

  15. Such a restriction is made in Chakraborty and Das (2005) as well. This has also the further implication that the savings function is increasing in the gross interest rate. However, in our framework, with no first-period consumption, this effect does not appear.

  16. With such a technology, a corner solution with no maintenance cannot be excluded a priori.

  17. See Brown (2001a) and Milevsky and Young (2007). The very low level of annuitised assets has been labeled as “annuity puzzle”. Possible explanations are the presence of bequest motives, adverse selection issues, risk pooling within family, high load factors by companies, presence of Social Security, inflation risk, ignorance and regulatory impediments (see Brown 2001a, b, Brown et al 2008). From a technical viewpoint, we could alternatively have obtained some simplifications by assuming the opposite case (γ = 1) which, however, would have been less realistic.

  18. A simple way of introducing dynastic bequests in the model can be through a negative shift in γ.

  19. This effect is partly contrasted by the one operating through α t and going in the opposite direction. In PE, indeed, the incentive to accumulate capital is reduced, as returns are decreasing and factors’ owners are remunerated according to the marginal productivity of their respective factor. This effect is taken into account by the government in the maximization problem.

  20. This is formally shown in Appendix A.2: see Eq. 57 and Eq. 60.

  21. Voluntary altruism can be introduced in the model either in the form of “joy-of-giving” (the old receive utility from intentionally giving the young part of their disposable income, which is thus available for capital accumulation) or in the form of care for next generation’s utility (the government at time t assigns a positive weight also to the generation which is old at time t + 2). In the former case, the optimization horizon of the political economy is substantially unaffected and there is no force leading toward the PL solution. In the latter case, the negative polluting effect of accumulating capital, and the long-lasting beneficial effect of improving environmental quality are taken into account like in PL (the PE first-order conditions are available from the authors upon request). However, the PE solution with intergenerational altruism still does not coincide with the PL outcome, as peculiar elements of PE are kept: e.g. the effect of population aging on generations’ political weight, the market constraints, the degree of completeness of annuity markets, etc. In particular, the result of Proposition 4 is confirmed.

  22. While in PE it is necessary to introduce Assumption 1.5 to isolate k and m from the other equations of the steady-state system, this is not the case in PL.

  23. More precisely, it is possible to rewrite Eq. 36 as: \(\nu'(m_{t})\; \pi'_{t+1,E}\left[\frac{u(c_{t+1})}{u'(c_{t+1})}-c_{t+1}- g_{t+1}\right] = \frac{1}{\rho} \frac{u'(c_{t})}{u'(c_{t+1})} - \frac{\nu'(m_{t})}{\nu'(m_{t+1})} \). Then, considering all variables in steady state yields Eq. 41.

  24. The results concerning σ in Propositions 2, 3, 4 and 5 admit a similar economic interpretation also intending σ as a measure of consumption-smoothing propensity. Basically, when the preference for consumption smoothing is high, agents wish to enlarge their lifetime at price of lower consumption (Proposition 3); in PE this is mainly pursued by increasing health expenditure (Proposition 2), whereas in PL by environmental quality (Proposition 5); in PL, absent the political channel, the g/c ratio is relatively more sensitive to consumption-smoothing propensity than in PE (Proposition 4).

  25. The specification in Eq. 45 implies that the mixed second derivative is positive, i.e.: h′′ g,E  ≥ 0.

  26. See Section 4.2 and footnote 17.

  27. See Auerbach et al. (1992). All changes are slightly magnified but not reversed for larger γ.

  28. Pestieau et al. (2006) based on a survey by Browning et al. (1999) set a parameter analogous to our σ to 0.8. We assess what happens for larger σ when we perturb parameters from the baseline calibration.

  29. When both k and m increase also the m − y ratio increases, because of more accentuated decreasing returns in production.

  30. A positive effect of the degree of annuity markets completeness on steady state capital is found also by Ludwig and Vogel (2010).

  31. See, for example, Schneider and Schneider (2006) who find empirical evidence that education is a central determinant of health relevant behavior.


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A preliminary version of this paper was written during authors’ staying at the Université catholique de Louvain (Louvain La Neuve, Belgium). Carlotta Balestra acknowledges financial support from Chair Lhoist Berghmans and University of Bergamo. Davide Dottori acknowledges financial support from the Belgian French speaking community (Grant ARC 03/ 08-235 “New macroeconomic approaches to the development problem”), and Polytechnic University of Marche. The authors wish to thank two anonymous referees, Thierry Bréchet, David de la Croix and Frédéric Docquier for valuable comments, participants in the European Economic Association Annual Conference held in Barcelona in August 2009, Conference “From GDP to Well-Being. Economics on the road to sustainability” held in Ancona (Italy) in December 2009, BEED 2008 meeting held in Brussels in February 2008, AFSE conference held in Toulouse in June 2008, EAERE 16th Conference held in Gothenburg in June 2008, “Journées Générations Imbriquées, Développement et Dynamique Economique” meeting held in Aix-en-Provence in October 2008. All remaining errors are of course of the authors. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Banca d’Italia. The scientific responsibility is assumed by the authors.

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Balestra, C., Dottori, D. Aging society, health and the environment. J Popul Econ 25, 1045–1076 (2012).

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  • Population aging
  • Environmental and health expenditure
  • Endogenous longevity

JEL Classification

  • Q58
  • H51
  • D70