Svend E. Hougaard Jensen, Gylfi Zoega 21 December 2019

Government-run pay-as-you-go (PAYG) pension schemes discriminate between groups of people whose life expectancies vary by pooling them together: everyone contributes equally to the scheme while differing in the number of years they will spend in retirement. Those with a shorter life expectancy can anticipate a lower retirement income due to the longevity of other groups participating in the same scheme. Thus, individuals with shorter lives end up subsidising the many years of retirement enjoyed by those who will live longer. Model calibration in our recent paper (Jensen et al. 2019) shows the significant adverse effect that government pension schemes in Denmark had on the retirement income of men (who have shorter lives than women) and blue-collar workers (who have shorter lives than white-collar workers), to take just two examples. 

The adverse effect on the groups with shorter lives is magnified when the retirement age is explicitly linked to average life expectancy. That is the case in Denmark, where the official pension age increases in line with changes in average longevity (Andersen 2015). The unintended distributional effects may then jeopardise the otherwise egalitarian objectives pursued by the welfare state. For example, if longevity indexation reduces the lifetime utility of blue-collar workers with health issues due to a long and physically demanding working life, the broad political support behind longevity adjustment might gradually disappear. The new Danish government headed by Mette Frederiksen has made remedying these inequalities an important objective, and the issue is also drawing attention in other European countries.

In a related paper (Auerbach et al. 2017), we study the effects of Social Security and Medicare on intra-generational equity in the US and find that the difference in average lifetime benefits received by men in the highest and lowest income quintiles widened considerably between the 1930 and 1960 birth cohorts.1

Sizable differences in longevity

Differences in the life expectancy of men and women are well known and widely documented. The UN published data in 2015 showing that women have a longer life expectancy than men. Life expectancy for men is 80.9 years in Japan, 79.4 in Spain, 81.9 in Sweden, and 80.0 in Denmark; the corresponding numbers for women are 86.6 years in Japan, 85.1 in Spain, 83.7 in Sweden, and 81.9 in Denmark. According to the OECD in 2019, the life expectancy at age 65 for men is 19.6 years in Japan, 19.4 in Spain, 19.1 in Sweden, and 18.2 in Denmark; the corresponding numbers for women are 24.4 years in Japan, 23.6 in Spain, 21.5 in Sweden, and 20.8 in Denmark. A woman at age 65 can expect to live 4.8 more years than a man in Japan, 4.2 more years in Spain, 2.4 in Sweden, and 2.6 in Denmark. 

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There are also differences in life expectancy across income groups. Table 1 shows life expectancy in Denmark at age 60 by income quantiles. The difference between the life expectancy of men in the top and bottom income group at age 60 increased slightly from 5.9 years in 1996 to 6.0 years in 2016, while the gap between low-income and high-income women decreased, from 5.2 years in 1996 to 3.8 years in 2016.

Table 1 Life expectancy at age 60 by income quantiles, Denmark


Source: Danish Ministry of Finance.

In addition, there are differences between skill groups. Table 2 illustrates life expectancy at age 60 by skill group in Denmark.

Table 2 Life expectancy at age 60 by education, Denmark


Source: Danish Ministry of Finance.

The differences recorded in Table 2 are somewhat smaller. For men, the difference in life expectancy between those with higher education and those who are unskilled was 3.4 years in 2016 and 2.9 years in 2002. For women, the difference was 2.5 years in 2016 and 2.0 years in 2002. In this case, the gap between the two groups – those unskilled and those with higher education – is growing.

Not surprisingly, differences in life expectancy between high- and low-income workers are larger in the US. An early study found significant differences in mortality by education (Kitagawa and Hauser 1973). Waldron (2007) found differences in life expectancy between rich and poor in the US. More recently, Chetty et al. (2016) showed that the life expectancy of the richest 1% in the US is 14 years longer than that of the poorest 1%, while the top income quartile can expect to live about a decade longer than the bottom quartile. 

Furthermore, the difference in life expectancy between income groups is growing in the US. Case and Deaton (2017) find an increase in mortality and morbidity among white non-Hispanic Americans in midlife (35-59) from the beginning of the century until at least 2015 due to increases in drug overdoses, suicides, and alcohol-related mortality. Educational differences in mortality among whites are increasing to such an extent that mortality has risen for those without a college degree while decreasing for those with a college degree. The gap between income groups is evidently not as wide in Europe. The OECD (2017) reported an average gap in life expectancy between those with tertiary education and those below upper secondary education in Europe of 2.7 years. 

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Differences in longevity also exist for a wide array of other social groups, such as those defined on the basis of race, country of origin (in the case of immigrants), professions, etc. 

Intra-generational equity effects

We studied the effect of the Danish public pension system on intra-generational equities in an overlapping-generations model stated in continuous time with a heterogeneous population (based on Andersen and Gestsson 2016). Like that paper, ours departed from Blanchard (1985) by assuming that the probability of dying increases with age. Thus, the old differ from the young in facing a higher probability of death and there is a maximum possible age for every cohort.

We split the population into two heterogeneous groups and calculated the effect of pooling blue-collar and white-collar workers together in an unfunded public pension scheme. We assumed, initially, that the pension age is 66.5 years and that both groups earned the same level of wages but differed in life expectancy. We found that blue-collar workers suffered from a 10.4% drop in pension benefits from paying into the same scheme as white-collar workers, while white-collar workers enjoyed an increase in pension benefits by approximately the same amount. When we took into account differences in average income, we found that blue-collar workers suffered a 13.8% drop in pension benefits while white-collar workers’ benefits rose by 6.1%. Thus when the income of the long-lived goes up, those who suffer lower longevity are made worse off.

A proposed solution 

One solution to the problem of intra-generational inequities, and the one proposed in our paper (Jensen et al. 2019), is for the government to give each retiree a lump sum at a certain age that may coincide with formal retirement from the labour force. The recipient can either give that sum to her occupational pension fund or use it to buy an annuity. The pension fund then decides on the monthly benefits for its members depending on their average life expectancy. The heterogeneity of life expectancy within an occupational pension fund should be less than that found in the whole population, making the intra-member inequality within the pension system less than for the whole population. Alternatively, if there is too much heterogeneity in life expectancy within the pension fund or occupation, the retiree could go to an annuity company to assess his expected longevity. It should also be possible for him to start this arrangement some years before reaching the official retirement age. 

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In effect, the government would give the money used to fund retirement to an entity with more information about life expectancy, and discontinue pooling the resources of a heterogeneous group of workers. The government would issue a bond and give it to a pension fund in an amount depending on the number of members of that fund reaching a certain age and their income, providing the fund with a fixed income to finance the retirement benefits of its members. 

We calculate that in the public-private pension scheme, the drop in pension benefits received by blue-collar workers would diminish from 10.4% to 1.6%, suggesting that even without perfect information, governments can substantially mitigate intra-generational disparities by giving money to pension funds with more information on life expectancy and smaller within-group differences. The remaining intra-generational transfers are caused by the fact that members of the short-lived group are more likely to die before reaching retirement.


Andersen, T M (2015), Robustness of the Danish pension system, CESifo DICE Report 2/2015: 25-30

Andersen, T M and M H Gestsson (2016), “Longevity, growth and intergeneration equity – The deterministic case”, Macroeconomic Dynamics 20(4): 985-1021.

Auerbach, A J, K K Charles, C C Coile, W Gale, D Goldman, R Lee, C M Lucas, P R Orszag, L M Sheiner, B Tysinger, D N Weil, J Wolfers and R Wong (2017), “How the growing gap in life expectancy may affect retirement benefits and reforms”, The Geneva Papers on Risk and Insurance – Issues and Practice 42(3): 475-499.

Blanchard, O (1985), “Debt, deficits and finite horizons”, Journal of Political Economy 93(2): 223-247.

Case, A and A Deaton (2017), “Mortality and morbidity in the 21st century”, Brookings Papers on Economic Activity 397-476.

Chetty, R, M Stepner, S Abraham, S Lin, B Scuderi, N Turner, A Bergeron and D Cutler (2016), “The association between income and life expectancy in the United States, 2001-2014″, JAMA 315(16): 1750–66.

Jensen, S E H, T Sveinsson and G Zoega (2019), “Longevity, retirement and intra-generational equity”, CESifo Working Paper No. 7704.

Kitagawa, E M and P M Hauser (1973), Differential Mortality in the United States: A Study in Socioeconomic Epidemiology, Cambridge, MA: Harvard University Press.

OECD (2017), Understanding the Socio-Economic Divide in Europe.

Waldron, H (2007), “Trends in Mortality Differentials and Life Expectancy for Male Social Security-Covered Workers, by Socioeconomic Status”.

United Nations, Department of Economic and Social Affairs, Population Division (2015), “World Population Prospects: The 2015 Revision, Key Findings and Advance Tables”, Working Paper No. ESA/P/WP.241.


[1] The present value of lifetime benefits at age 50 is equal for those in the highest and lowest quintile of lifetime income for the 1930 cohort while the 1960 cohort experiences a $130,000 gap in benefits.