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Optimal pensions in aging economies

  • Burkhard Heer EMAIL logo
Veröffentlicht/Copyright: 18. August 2017
The B.E. Journal of Macroeconomics
Aus der Zeitschrift The B.E. Journal of Macroeconomics Band 18 Heft 1

Abstract

We derive the optimal replacement ratio of the pay-as-you-go public pension system for the US economy in a life-cycle model that 1) replicates the empirical wage heterogeneity and 2) endogenizes the individual’s labor supply decision. The optimal net pension replacement ratio is found to be in the range of 0%–43% depending on demographic parameters and, in particular, the Frisch labor supply elasticity. Reducing the pensions from the present to the optimal pension policies implies considerable welfare gains amounting to approximately 0.1%–4.1% of total consumption. The welfare increase is particularly pronounced for the greyer US population that is projected for the time after the demographic transition.

Keywords: demographic transition; income and wealth distribution; optimal social security
JEL Classification: C68; D31; D91; H55; J11; J26

A Appendix

A.1 Properties of the Benchmark Equilibrium

In stationary equilibrium of the benchmark case, the average wealth a~s, working hours ls, and consumption c~s of the s-year-old cohort over the life cycle (or working life respectively) are graphed in Figure 5, Figure 6, and Figure 7. The solid (broken) lines of the graphs present the low (high) productivity type ϵ1 (ϵ2) and correspond to the lower (upper) curves in the figures.

Figure 5: Wealth-age profile.
Figure 5:

Wealth-age profile.

Figure 6: Labor-supply-age profile.
Figure 6:

Labor-supply-age profile.

Figure 7: Consumption over the life cycle.
Figure 7:

Consumption over the life cycle.

Households with high (low) productivity accumulate savings until the age of 59 (52) before they start to dissave. In their effort to smooth consumption over their lifetime, households start to consume part of their savings as their income drops. The drop in income from wages is caused by the decrease of age-dependent efficiency y¯s which peaks at age 50 (not illustrated). The decline in wealth is accelerated for the high-productivity households as soon as the households retire because pensions are below the former wage income.

The profile of working hours in Figure 6 also mirrors the age-productivity profile because the substitution effect of higher wages dominates the income effect. However, the peak of working hours (at age 30) takes place prior to the peak in age-dependent efficiency y¯s because of increasing wealth (prior to age 52) which reduces the labor supply.

Labor supply l and wealth a~ also depend on the permanent and temporary productivity types {ϵ, η}. Both variables increase with higher productivity ϵ = ϵ2 and η = η2. The household with ϵ = ϵ1 who experiences a negative productivity shock, η = η1, is also liquidity-constrained, a~=0, if he has not accumulated sufficient savings in former periods. In fact, the percentage of households without savings amounts to 34.5% in our benchmark calibration.

The heterogeneity with regard to individual productivity, ϵηy¯s, results in inequality of the household’s income and wealth distribution. The dsitributions of income and wealth are characterized by Gini coefficients of 0.362 (net income after taxes), 0.390 (gross income before taxes), and 0.664 (wealth). Notice that the OLG model is able to generate much more inequality in wealth than in income as observed empirically.[30] However, all our inequality measures fall short of values observed empirically. For example, Budría Rodriguez et al. (2002) report Gini coefficients of (gross) income and wealth equal to 0.553 and 0.803. Our model values fall short of the empirical ones for mainly three reasons: 1) We do not consider self-employed workers and entrepreneurs. Quadrini (2000) presents empirical evidence that the concentration of income and wealth is higher among entrepreneurs and that the introduction of an endogenous entrepreneurial choice in a dynamic general equilibrium model helps to reconcile the inequality in the model with that of the US economy. 2) We neglect the top income percentile of the wage earners in our model. 3) We omit bequests.[31]

Figure 7 displays the average consumption of the two productivity types over the life cycle. The profile is hump-shaped in both cases and declines after retirement. The profile accords with empirical observations in its qualitative features. For the US economy, Fernández-Villaverde and Krueger (2007) find that the empirical consumption-age profile display a significant hump over the life cycle even after correcting for the change of the family size. For the high-education households (that are roughly corresponding to the high-productivity households in our model), the peak occurs at age 55, while the low-education households attain their consumption maximum at an earlier age close to 50 and the hump is much smaller. Therefore, in our model, the hump occurs too late in the life cycle and the increase in consumption from age 20 to age 50 is too high for the low-productivity households. Since consumption and leisure are substitutes and leisure increases to 100% during retirement, consumption is only reduced at the beginning of retirement.[32] In addition, the consumption of the very old low-education households in the US economy drops to 70–80% of the consumption of the corresponding 20-year old, while this is not the case in the model.[33]

With regard to the cross-sectional distribution of consumption, our model is able to replicate the fact that consumption inequality is muss less than income inequality. Using US data from the Consumer Expenditure Survey, Krueger and Perri (2006) present evidence that the Gini coefficient of consumption amounts to 0.26 in 2003, while it is equal to 0.28 in the model.

A.2 Computation

The main computational problem is the numerical solution of the intertemporal household decision problem. We use value function iteration as described in Chapter 9.3 of Heer and Maußner (2009) .[34] We apply Golden Section Search in each step to find the optimal next-period assets a′ for each type {ι, η, ϵ, s} of the household. Our reason for this approach is that the Golden Section Search is a very robust method that can easily handle non-negativity constraints such as l ≥ 0 or a ≥ 0. Between gridpoints, we interpolate linearly.

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Published Online: 2017-8-18

©2018 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Advances
  2. Luxury consumption, precautionary savings and wealth inequality
  3. Unemployment insurance with limited commitment wage contracts and savings
  4. The marriage unemployment gap
  5. Fertility and labor supply of the old with pay-as-you-go pension and child allowances
  6. Optimal pensions in aging economies
  7. Estimating the New Keynesian Phillips Curve for the UK: evidence from the inflation-indexed bonds market
  8. An empirical note on the long-run relationship between education and religiosity in Christian countries
  9. Accounting for changing returns to experience
  10. Development accounting with intermediate goods
  11. The post-crisis slump in Europe: a business cycle accounting analysis
  12. Rational bubbles in a monetary economy
  13. Capital controls as a credit policy tool in a small open economy
  14. Labor income share and imperfectly competitive product market
  15. Macroeconomic costs of gender gaps in a model with entrepreneurship and household production
  16. Contributions
  17. Comparing the effects of discretionary tax changes between the US and the UK
  18. Erratum
  19. Erratum to: Life-cycle consumption, precautionary saving, and risk sharing: an integrated analysis using household panel data
https://doi.org/10.1515/bejm-2015-0166
Schlagwörter für diesen Artikel
demographic transition; income and wealth distribution; optimal social security

Artikel in diesem Heft

  1. Advances
  2. Luxury consumption, precautionary savings and wealth inequality
  3. Unemployment insurance with limited commitment wage contracts and savings
  4. The marriage unemployment gap
  5. Fertility and labor supply of the old with pay-as-you-go pension and child allowances
  6. Optimal pensions in aging economies
  7. Estimating the New Keynesian Phillips Curve for the UK: evidence from the inflation-indexed bonds market
  8. An empirical note on the long-run relationship between education and religiosity in Christian countries
  9. Accounting for changing returns to experience
  10. Development accounting with intermediate goods
  11. The post-crisis slump in Europe: a business cycle accounting analysis
  12. Rational bubbles in a monetary economy
  13. Capital controls as a credit policy tool in a small open economy
  14. Labor income share and imperfectly competitive product market
  15. Macroeconomic costs of gender gaps in a model with entrepreneurship and household production
  16. Contributions
  17. Comparing the effects of discretionary tax changes between the US and the UK
  18. Erratum
  19. Erratum to: Life-cycle consumption, precautionary saving, and risk sharing: an integrated analysis using household panel data
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