Chapter 6. Mortality differences across socioeconomic groups and their implications for pension outcomes
This chapter assesses the potential differences in pension outcomes across socioeconomic groups due to differences in mortality and given the rules of the pension system that are in place. The analysis uses four indicators to conclude that low socioeconomic groups may indeed face a disadvantage for their pension and retirement, but this disadvantage may be partially offset when considering public pension benefits and progressive taxation.
Differences in mortality and the fact that lower socioeconomic groups tend to have lower life expectancies may lead to differences in pension outcomes across socioeconomic groups because of the rules in place. This is largely because in many jurisdictions the rules governing access to pension assets for retirement use age as a reference. These rules include minimum age limits to access pensions, minimum and maximum withdrawal limits, and the rate at which accumulated assets can be converted into a lifetime stream of guaranteed income payments.
First, minimum age limits at which people can have full access to their pension savings may have an impact on pension outcomes across socioeconomic groups. For a given retirement age, lower socioeconomic groups will have to work longer relative to the time they can expect to spend in retirement given their lower life expectancy. Furthermore, if this age is linked to average increases in life expectancy, this disadvantage may grow over time to the extent that differences in life expectancy across socioeconomic groups continue to diverge.
Rules imposing maximum or minimum withdrawal limits may also reference average life expectancy measures. In this case, maximum limits may impede lower socioeconomic groups from having a higher level of income than they otherwise could have given their expected time in retirement. On the other hand, minimum limits could potentially lead higher socioeconomic groups to have a higher chance of exhausting their pension savings in retirement.
Finally, the annuitisation rate at which accumulated pension assets can be converted into a lifetime income stream will depend on some underlying mortality assumptions. Where annuitisation is mandatory, this could result in a poor value for money for lower socioeconomic groups having lower than average life expectancies. Where it is voluntary, this could result in an exclusion of lower socioeconomic groups from the annuity market as they could find that the annuities are too expensive relative to the time they expect to spend in retirement, thereby limiting their options for managing their longevity risk in retirement.
This chapter presents a framework to assess the differences in pension outcomes across socioeconomic groups due to differences in mortality given the rules of the pension system in place. The analysis demonstrates that low socioeconomic groups may indeed face a disadvantage for their funded pension and retirement, but this disadvantage may be partially offset when considering the entire pension system. The analysis shows that low socioeconomic groups work and contribute more time per year spent in retirement for a given retirement age. Low socioeconomic groups also ultimately receive less from their pension savings when they take it as regular income because they will spend less time in retirement. However, progressive rules for public pensions and marginal tax rates can offset some of these relative differences in pension wealth and income, raising the question as to whether this is the appropriate and/or sufficient way to address longevity inequalities in retirement.
The analysis in this chapter introduces metrics that assess the differences in gross pension outcomes for funded pension arrangements as well as account for the impact that public pensions and tax rules will have on the ultimate pension income that individuals of different socioeconomic groups will receive.1
Section 6.1 of the chapter presents the four indicators used to assess the pension outcomes across socioeconomic groups. Section 6.2 applies this framework to calculate the pension outcomes for six countries: Canada, Chile, Great Britain, Korea, Mexico, and the United States.2^{,}3 Section 6.3 concludes with a discussion of policy implications.
6.1. Indicators used to measure the impact of mortality differences on pension outcomes
This chapter uses four indicators to assess pension outcomes for each socioeconomic group. These indicators aim to capture the value of time spent in retirement, the return on the savings made for retirement, the potentially offsetting impact of public pensions and tax systems for the pensions received by individuals of lower socioeconomic groups, and finally the change in relative income pre and postretirement.
The first indicator, the “retirement ratio”, is the number of years spent working for each expected year in retirement given life expectancy at retirement. In other words, it is the number of years spent contributing to pensions divided by the life expectancy at the age of retirement. This is a measure of the time spent in retirement relative to years contributing.
The second indicator is the “asset payout ratio”, which measures the expected present value of pension income relative to the amount of retirement assets accumulated. This is calculated by taking the present value of gross pension income at retirement over the expected time spent in retirement (i.e. the life expectancy at retirement) divided by the assets accumulated at retirement. This is a way to measure the value, or return, that pensioners receive from their investment for retirement.
The third indicator is the “pension wealth ratio”, which measures the expected present value of pension income at retirement relative to annual earnings just before retirement. This measure has been introduced in order to be able to assess the impact that public pensions and tax policy can have in reducing the inequalities of pension outcomes. As such, it is calculated for gross pension income for funded pension arrangements, total gross pension income from both funded and public pension arrangements, and total netoftax pension income from both sources.4
The final indicator, referred to as the “income ratio”, focuses on the change in relative income in retirement compared to before retirement. This indicator shows the average combined net public and private pension income in real terms over the expected time spent in retirement for each group relative to the average real pension income for the average earner. While this measure does not provide an indication of how welloff individuals are in their retirement, it can show whether existing inequalities are exacerbated in retirement given the rules of the pension system in place.
6.2. Impact of mortality differences on pension outcomes
This section assesses the impact of mortality differences on pension outcomes using the indicators introduced in the previous section. In each case, the analysis takes the perspective of the individual at the time of retirement, assuming that the pension system and rules in place for defined contribution plans at the age of retirement have been unchanged over the lifetime of the individual. The calculations assume a full career with no breaks from age 20 to the statutory age of retirement, and do not consider differences due to unemployment, disability or maternity leave. Low and highincome groups earn 50% and 300% of the average wage, respectively.5
Retirement ratios
High socioeconomic groups can expect to spend a longer time in retirement and therefore work fewer years per year spent in retirement compared to low socioeconomic groups. The retirement ratio, calculated as the number of years spent contributing to pensions divided by the life expectancy at the age of retirement, captures this result that is common to all jurisdictions assessed. Table 6.1 shows the differences in life expectancies at retirement and the retirement ratios across socioeconomic groups for both males and females. It also shows the age at which each group could retire to spend a third of their adult life in retirement (i.e. a ratio equal to two years spent contributing per year spent in retirement).
Large differences in life expectancy translate into large differences in the retirement ratios and the ages needed to equalise the ratio across socioeconomic groups. Looking at the retirement ratios for the countries having the largest differences in life expectancy at retirement shows the potential magnitude of these impacts. The largest differences observed for the jurisdictions assessed are in Chile and Korea for males and in Mexico and Great Britain for females, where high socioeconomic groups can live around 4.1 years and 3.3 years longer, respectively, than low socioeconomic groups. Assuming an entry age into the labour force at 20 and retirement age 65, lowincome males in Chile work an additional 0.5 years per year spent in retirement than highincome males. For Mexican females, the gap in life expectancy at retirement results in low earners working 0.3 years longer per year in retirement.
Differences in the retirement ratios across socioeconomic groups increase when entry age varies. Assuming that lowincome workers begin to contribute at age 18, average earners at age 20, and high earners at age 24, lowincome workers need to work even more years per year spent in retirement. Lowincome males in Chile would need to work an additional 0.8 years and lowincome females in Mexico an additional 0.6 years per year spent in retirement compared to their highincome counterparts.
Lowincome groups would need to retire much earlier than highincome groups to spend an equivalent proportion of their adult lives in retirement, especially when entry age is assumed to vary. Lowincome males in Chile would need to retire six years earlier than highincome males to maintain a ratio of time spent working and contributing to time spent in retirement that implies that they will spend one third of their adult life in retirement. For most other countries, the difference in retirement age for males would be three to five years. For Mexican females, a fiveyear difference in retirement age would be needed to maintain a constant ratio of years spent working to years in retirement assuming that age of entry into the labour force varies across the income groups. For the other countries, the difference in retirement age for females would be two to four years.
Lowincome females will have to work longer than the average male to have an equivalent number of years in retirement and sufficient assets to generate an equivalent pension. This is because females in low socioeconomic groups still have a life expectancy higher than the average male, even though differences in life expectancy across socioeconomic groups tend to be smaller for females.
Asset payout ratios
The relative value that pensioners receive from their retirement assets is typically higher for highincome than lowincome pensioners because they receive their pension for a longer period. The asset payout ratio captures this notion. This ratio is calculated as the present value of gross pension income over the expected time spent in retirement divided by the assets accumulated at retirement.
Options involving some sort of annuitisation, either alone or combined with programmed withdrawals, result in the largest differences in asset payout ratios across socioeconomic groups. Table 6.2 shows that for the jurisdictions assessed here, programmed withdrawals never result in the largest differences in asset payout ratios between the low and high socioeconomic groups, despite the fact that the analysis assumes the same withdrawal limits across all groups.
Annuity options can result in the highest asset payout ratios for all socioeconomic groups despite the implicit premium that low socioeconomic groups pay due to their lower life expectancies. Table 6.3 shows that this is true for males in Canada, Chile, and Mexico. However, this result will also depend on the level of antiselection observed in the annuity market and the magnitude of the differences between the expected mortality of the low socioeconomic group and the difference in payments compared to those offered by programmed withdrawals. We could expect that lowincome males in Great Britain, for example, would pay a higher premium due to both antiselection and unisex pricing, so programmed withdrawals are more likely to be a better option. However, allowing for enhanced annuities eliminates the implicit premium and this option therefore results in the highest ratio for low earners.
In contrast to the result for males, programmed withdrawals tend to result in higher asset payout ratios for females than other options. The underlying reasons for this differ from one country to the next. In Canada, for example, limits on programmed withdrawals are the same for both genders whereas annuity pricing is gender distinct, which implies that programmed withdrawals will allow females to take a higher pension relative to their life expectancies. In Chile, the earlier retirement age of females drives this result.
Lump sums result in the highest ratios for Koreans and for males in low socioeconomic groups in the United States. In Korea, the mortality assumptions used for the pricing of the annuity drives this result, as they are based on a select group of insured individuals in Korea and therefore result in much higher life expectancies than those of the average population.
The remainder of this section looks at the actual asset payout ratios for each country specific payout options.6
Asset payout ratios for Canada
Depending on the type of plan, the payout of defined contribution plans in Canada can be subject to maximum or minimum withdrawal limits, and in most cases the option to use the accumulated assets to purchase a life annuity is also available. Some types of pension plans may also allow lump sums. Given the potential range of payout options, the analysis assesses the following options for Canada:

Withdrawal at the minimum limit

Withdrawal at the maximum limit

The purchase of an immediate life annuity at retirement

Withdrawal at the minimum limit until age 75 at which point an immediate life annuity is purchased with the remaining assets

Withdrawal at the maximum limit until age 75 at which point an immediate life annuity is purchased with the remaining assets

Withdrawing assets as a lumpsum at retirement7
The annuity option results in one of the smallest differences in outcomes across income groups. Table 6.4 shows that the payout option resulting in the largest difference in outcomes across income levels is the combination of taking minimum programmed withdrawals and deferring the purchase of an annuity to age 75.
For males, the purchase of an annuity results in the highest ratio for all income groups. For females, however, taking the maximum allowed programmed withdrawals results in the highest ratio. This result is reflective of the fact that the limits are the same for both genders, so would allow females to take a higher total level of income on average compared to males due to their longer lives.8
Pensioners taking programmed withdrawals at the minimum limit cannot expect to get back their assets in retirement with a return greater than the risk free rate, as indicated by ratios under 100. This is true even for the maximum withdrawal limit for low income males given that they have the shortest life expectancies.
Asset payout ratios for Chile
At retirement, individuals in Chile have the choice of using their assets accumulated within the mandatory defined contribution plan to take a programmed withdrawal, purchase an inflation indexed life annuity, purchase a deferred annuity combined with a programmed withdrawal, or take some combination of these options. The analysis therefore assesses the following payout options for Chile:

Programmed withdrawal9

Purchase of an inflation indexed annuity at retirement10

Purchase of a 10year deferred inflation indexed annuity at retirement, equal to 75% of the first temporary payment, combined with a programmed withdrawal for 10 years drawing the account to zero
For males, the purchase of an annuity at retirement results in a higher asset payout ratio than other options for all income groups (Table 6.5). Nevertheless, the difference in ratios across income groups is the largest for the annuity option. Programmed withdrawals result in the lowest ratio. For lowincome males, ratios are below 100% for all payout options, indicating that they cannot expect to get back their accumulated assets with a return greater than the risk free rate.
For females, programmed withdrawals result in the highest ratios for all income groups. This is driven again by the earlier retirement age of 60 (compared to 65 for males).11 Programmed withdrawals also result in the smallest dispersion of outcomes across income groups, while the deferred annuity option results in the largest difference in ratios across income groups.
Asset payout ratios for Great Britain
Since 2015, pensioners face no restrictions regarding how to withdraw their savings at retirement from their defined contribution pension plan. As such, the analysis assesses several options:

Programmed withdrawals based on an annuity factor calculated using gender distinct population mortality and the riskfree discount rate

The purchase of an immediate annuity at retirement with 75% of assets, and taking the rest as a taxfree lump sum12

The purchase of an immediate annuity at retirement

Programmed withdrawals based on an annuity factor calculated using gender distinct population mortality and the riskfree discount rate until the age of 75, at which point an immediate annuity is purchased with the remaining assets

The purchase of a 20 year deferred annuity at retirement with 10% of the accumulated assets, drawing down the remaining assets to zero over the twenty year period

The purchase of an inflation indexed annuity at retirement

The purchase of an enhanced annuity13

Withdrawing all assets as a lumpsum at retirement14
The purchase of an enhanced annuity results in the lowest difference in the asset payout ratios between the low and high income groups (Table 6.6). This option allows lowincome groups to purchase an annuity that provides higher payment given their lower life expectancy, and as such, it results in the highest overall asset payout ratio for the low income groups compared to other options.
Apart from the enhanced annuity option, options involving the purchase of an annuity generally result in a larger difference in the asset payout ratios across income groups for both genders, with the purchase of a 20year deferred annuity resulting in the largest differences. Low earners tend to benefit relatively more from taking programmed withdrawals. For lowincome males, no option involving regularly priced annuities results in a ratio over 100% due to a double penalty from their lower life expectancy and the unisex pricing of annuities. High earners benefit most from the option of combing programmed withdrawals with a deferred annuity, as they benefit more on average from the longevity risk protection that this option provides.
Asset payout ratios for Korea
Defined contribution plans in Korea allow only two options for withdrawing assets. Individuals must either purchase a life annuity with the accumulated assets or take them as a lump sum.15 This section assesses both of these options.
For both genders, lump sums result in a higher asset payout ratio than the purchase of an annuity at retirement for all income groups, with the difference between the two options for high income groups being smaller than that for low income groups. The mortality assumptions used for the pricing of the annuity drive this result because they imply much higher life expectancies than those of the average population and therefore lower incomes from the annuity. The difference in outcomes across socioeconomic groups for the annuity payout is particularly significant for males, with high income groups having a higher ratio than low income groups by 9.8 percentage points (Table 6.7).
Asset payout ratios for Mexico
Mexico has two mandatory defined contribution pension systems into which employees are required to contribute, one for private sector workers and one for public sector workers. At retirement, individuals have the option of either using the accumulated assets to purchase an inflationindexed life annuity or taking programmed withdrawals at a rate that changes with life expectancy. The analysis here assesses these two payout options for private sector workers.
Table 6.8. There is also little difference between the options of taking a programmed withdrawal or taking an inflationlinked annuity, though the ratio for the annuity is slightly higher.
The differences are larger for females, and in particular for the annuity, where the highly educated women can expect to receive 11.5 percentage points more from the retirement savings than the lower educated groups. However, for females the ratio for programmed withdrawals is higher than that for the annuity. Given the assumptions made for this analysis, the low and average income individuals would be required to take the programmed withdrawal option, as the income that an annuity would provide would be lower than the minimum guaranteed pension.16
Only highincome females can expect to receive a return on their accumulated assets of at least the riskfree rate in retirement, with ratios over 100% for both options. This result is largely due to low coverage of these types of pension plans, which results in a larger difference in mortality between the general population and the pensioner population. The mortality assumptions referenced for the payout amounts reflect the higher life expectancy of those covered by this pension system in Mexico.
Asset payout ratios for United States
The only constraint for withdrawing assets from a defined contribution plan in retirement is a required minimum distribution level from the age of 70 and a half. The analysis therefore considers a wide range of payout:

Programmed withdrawals based on an annuity factor calculated using gender distinct population mortality and the risk free discount rate

Programmed withdrawals at the required minimum distribution (RMD) level17

The purchase of an immediate annuity at retirement

Programmed withdrawals based on an annuity factor calculated using gender distinct population mortality and the risk free discount rate until the age of 75, at which point an immediate annuity is purchased with the remaining assets

The purchase of a 20 year deferred annuity at retirement with 10% of the accumulated assets, drawing down the remaining assets to zero over the twenty year period

The purchase of an inflation indexed annuity at retirement

Withdrawing all assets as a lumpsum at retirement18
The payout option resulting in the largest differences in the asset payout ratio across socioeconomic groups for both genders is the combination of a programmed withdrawal and a 20 year deferred annuity. This option is also the one that results in the highest ratio for both genders for the aerage and high socioeconomic groups (Table 6.9).
For low socioeconomic groups, programmed withdrawals result in higher ratios compared to options involving annuities, which result in much lower pension income in retirement compared to other options.19 However, the only option offering a ratio of at least 100% for lowincome males is taking a lump sum.
Pension wealth ratios20
The pension wealth ratio looks at the expected present value of pension income relative to gross salary at retirement rather than relative to accumulated assets. This measure allows the analysis to account for the impact that public pensions and taxes have on pension outcomes across socioeconomic groups. The difference in the wealth ratios between the high and low groups and how this difference changes for the indicators for private pensions, total pension and net pensions indicate the impact that public pensions and tax have on the differences in relative pension outcomes across socioeconomic groups.21
The pension wealth ratio for private pensions is greater for highincome groups than lowincome groups for all jurisdictions assessed except for Mexico. Table 6.10 shows in the first numerical column for each gender the difference in pension wealth ratios across socioeconomic groups for annuities and programmed withdrawals. In Mexico, lowincome groups can expect a higher pension wealth by around one times their annual salary. This is because the total contribution levels in Mexico vary depending on income, with the government providing higher matching contributions for lowincome workers into their defined contribution plan. This results in a higher pension for low earners relative to their preretirement income.
Public pensions offset the relative differences in total pension wealth from differences in life expectancy for all jurisdictions assessed here. Table 6.10 also shows how the inclusion of public pensions and taxes affects these differences. A negative figure in the second numerical column for each gender of Table 6.10 indicates a higher total wealth ratio for low earners than for high earners. Lowincome males in Canada, for example, can expect to receive a lower total pension by 0.4 times their annual preretirement income from purchasing an annuity relative to what highincome males can expect to receive. However, when public pensions are taken into account, they can expect to receive 6.4 times more their annual income relative to high earners. The difference between the pension wealth ratio based on total pension and that of the private pension ratio only is shown in the column labelled 'public pensions impact'. For the jurisdictions assessed here, the public pension in Korea has the largest offsetting impact for pension outcomes across socioeconomic groups when an annuity payout is selected. For programmed withdrawals, the public pension has the largest impact in Canada.
Tax rules can further offset the differences in pension outcomes across socioeconomic groups. The tax rules in all jurisdictions apart from Mexico further reduce the relative difference in pension income (Table 6.10). In Mexico, the high tax credits or exemptions that are in place result in little to no tax owed on pension income. Taxes generally have less of an offsetting impact than public pensions apart from Chile, where the impact of progressive taxation is equivalent or higher.
Income ratios22
The income ratios show whether the relative differences in preretirement income change during retirement. The calculations compare the expected average real income in retirement relative to that of the average earner. For all jurisdictions, progressive tax rules mean that the relative inequalities of preretirement salary between low and high earners are lower on a net basis than a gross basis.
Accounting for the progressivity of both public pensions and tax rules, reduces further the relative income differences across socioeconomic groups in retirement. Relative differences in total pension income in retirement are smaller than the relative difference preretirement in all jurisdictions examined. Table 6.11 shows the total net pension income ratios for someone receiving income from public pensions and an annuity purchased with retirement savings. Low earners can expect to receive at least 59% of the total net pension income of the average earner. The pension of high earners is also significantly reduced below 300%, primarily because they receive relatively lower public pension benefits.
6.3. Main results and policy implications
The objective of this analysis has been to assess the differences in pension outcomes across socioeconomic groups given differences in life expectancy observed in the general population. The indicators used attempt to highlight the differences in pension outcomes, as well as the potential for public pensions and tax rules to offset inequalities in pension outcomes across socioeconomic groups. This section first summarises the main results of the analysis, it then provides some qualifiers based on the assumptions made and finally presents some of the policy implications.
Main results

The four indicators used capture different aspects of the disadvantage of low socioeconomic groups with respect to pension outcomes, but none of these measures on their own fully captures this disadvantage. Together, however, they can provide an indication of the potential disadvantage that low socioeconomic groups can face with respect to the time spent in retirement and their relative financial position in retirement given the contributions that they have made and existing relative differences in income.

Retirement age would need to differ across socioeconomic groups in order to equalise the time spent working and contributing to pensions compared to the time spent in retirement. The retirement ratio shows this result by capturing the disadvantage that individuals in low socioeconomic groups may have due to a shorter expected time spent in retirement relative to their working lives. This is perhaps the most obvious disadvantage that those with shorter life expectancies will have for their retirement, but it cannot capture any financial disadvantage that these groups may experience in retirement.

For a given retirement age, lower socioeconomic groups have a financial disadvantage from funded pension sources. They will receive a pension for a shorter expected period, and therefore will receive a lower 'return' on the contributions they have made towards their pension over their working lives.

Taking an annuity at retirement often results in one of the highest asset payout ratios for all socioeconomic groups, but also the largest disparities across socioeconomic groups. Low earners pay an implicit tax on the price of the annuity to subsidise the longer lives and annuity payments for high earners because annuities are priced using average life expectancies. Low earners tend to benefit relatively more from taking programmed withdrawals, particularly lowincome women.

Higher public pension benefits for lowincome individuals can reduce or even reverse the financial disadvantage they have relative to high earners. Nevertheless, with these measures the more subjective question of whether these inequalities are reduced 'enough' cannot be answered. Even if the rules can reverse relative difference, absolute differences, of course, remain.
Caveats
The results presented in this report are bestcase scenarios in terms of the retirement assets accumulated and level of pension earned. First, contribution gaps are not considered, yet low socioeconomic groups are likely to have higher rates of disability and unemployment that could negatively affect the amount of pension income they can ultimately receive in retirement. Alternatively, the unemployment or disability benefits that these individuals receive could help to offset any negative impact on pensions. Second, the analysis assumes the same earnings patterns for all income groups, whereas lowincome groups are more likely to experience flatter income profiles. Considering this would also increase the inequalities in pension outcomes.
The analysis also relies on the differences in mortality observed for the general population, rather than using life expectancy estimations based only on individuals receiving pensions from funded sources.23 One advantage of this approach is that it provides a fuller picture of the potential for the entire pension system to ameliorate or exacerbate the disadvantage of lowincome groups in retirement since the analysis takes into account public pensions. Another advantage is that the analysis can more easily be expanded to more jurisdictions, as mortality by socioeconomic group for the general population is more widely available than mortality for the population receiving pensions from funded sources. However, this approach is less reflective of the reality that in many countries the population receiving pensions from funded sources tends to be skewed towards higher socioeconomic groups. Within this population, the differences in life expectancy across socioeconomic groups would therefore be smaller compared to the differences across the entire population, and the resulting impact on pension outcomes reduced. Furthermore, the approach assumes that the low earners are receiving the full potential pension from both public and funded sources, whereas low earners are likely not making full contributions to private pension systems throughout their working life, particularly where contributions are voluntary. The analysis here may therefore present on the one hand an overstatement of the differences in pension outcomes from funded sources, and on the other hand an overly optimistic view of the reduction of relative income differences when considering all pension sources.
In addition, the current analysis assumes deterministic market and mortality variables. The stochastic nature of these variables could significantly affect pension outcomes and determine the optimal strategy for drawing down pension income. Programmed withdrawals, for example, would be more attractive in highreturn environments, and traditional annuity products would be more beneficial in high volatility environments. Furthermore, as the analysis relies on average life expectancies, it does not capture the main advantage of annuity products to protect individuals from outliving their savings in retirement in the event that they live longer than expected.
The analysis also ignores considerations such as liquidity needs or the desire to leave a bequest to heirs. Both of these aspects could lead to a preference for less annuitisation of assets.
Finally, the assessment considers total life expectancy rather than healthy life expectancy. However, to the extent that differences in healthy life expectancy could be even larger across socioeconomic groups than total life expectancy, low socioeconomic groups could be at a particular disadvantage as they may not even be capable of working as long.
Nevertheless, the analysis does lead to several potential policy implications for reducing the inequalities in pension outcomes across socioeconomic groups.
Policy implications
First, annuities are a valuable option for pension payout for all socioeconomic groups, despite the implicit tax that lower socioeconomic groups pay. Allowing for segmentation of the annuity market and pricing based on variables that can be correlated with socioeconomic status (e.g. health, smoking) could reduce the implicit tax paid by low socioeconomic groups and improve further the benefit they can receive from an annuity.
However, some flexibility in the design of the payout phase and pension products is desirable. Annuities do not necessarily result in the best outcomes in all scenarios. Programmed withdrawals can be a valuable option particularly for lowincome individuals and those retiring early.
In considering the entire pension system, the progressivity of the public pension system and tax rules can do a lot for reducing financial disadvantages in retirement. Old age safety nets and lower marginal tax rates for low incomes can significantly reduce or eliminate relative inequalities in pension outcomes across socioeconomic groups. The Mexican case demonstrated that additional contributions provided for lowincome groups can also reduce differences in the relative total pension received.
Nevertheless reducing inequalities with respect to time spent working versus time spent in retirement will require some allowance for differences in retirement ages for different people. Having explicit rules that differ across socioeconomic groups, however, is not likely to be feasible or realistic in practice, but indirect ways to allow for differences could be considered. For example, linking the number of years spent contributing to the age at which full pension benefits can be received would allow lower educated individuals  who likely started working earlier than the highly educated  to also retire earlier. Such policies have been put in place, for example, in France, Germany and Portugal. Measures to encourage those who are able to continue working to do so could also be considered. For example, Sweden offers tax credits to individuals who decide to work beyond the statutory retirement age.
Differences in life expectancies between genders raise additional questions relating to fairness. The longer life expectancies of females imply that even those in low socioeconomic groups may need to work longer than males to maintain an equivalent proportion of time in retirement. Females are also more likely to have career interruptions relating to caretaking roles, which would reduce the level of assets they would have otherwise been able to accumulate at retirement. This implies that females are not only at a financial disadvantage when reaching retirement, but they are also more likely to outlive their male spouse. Joint and survivor pensions, discussed in more detail in Chapter 7, could help to mitigate this disadvantage by ensuring that the surviving female will continue to receive a portion of the pension of the deceased spouse. Pension legislation in Canada, for example, requires pension members with a spouse or commonlaw partner at the time of retirement to take a joint and survivor pension that pays at least 60% of the member’s pension to the surviving spouse at the expense of a lower initial income when the member retires.
In addition, the ability of females to work longer may be an issue, as females can also expect to spend a longer time disabled in old age. Pension policy will therefore need to consider ways to account for the length of time individuals can expect to spend in retirement in good health as opposed to total life expectancy alone.
Policies intending to improve the sustainability of pension systems in light of the increases in life expectancy will need to consider how those in different socioeconomic groups and different genders may be impacted. Working longer on average will be required, but not all groups will necessarily be able to work longer. Increased flexibility around the age at which individuals can retire will be key to improving pension outcomes for all groups and ensuring that lower socioeconomic groups are not penalised in retirement due to having shorter life expectancies.
References
[8] Baulch, B. and A. Quisumbing((n.d.)), Testing and adjusting for attrition in household panel data.
[7] Cairns, A. et al. (2016), Modelling SocioEconomic Differences in the Mortality of Danish Males Using a New Affluence Index, Pensions Institute.
[9] Dercon, S. and I. OutesLeon (2008), Survey Attrition and Attrition Bias in Young Lives.
[2] Luy, M. et al. (2015), “Life Expectancy by Education, Income and Occupation in Germany: Estimations Using the Longitudinal Survival Method”, Comparative Population Studies, Vol. 40/4, pp. 399436.
[1] Murtin, F. et al. (2017), “Inequalities in longevity by education in OECD countries: Insights from new OECD estimates”, OECD Statistics Working Papers, No. 2017/2, OECD Publishing, Paris, http://dx.doi.org/10.1787/6b64d9cfen.
[5] OECD (2017), Pensions at a Glance 2017: OECD and G20 Indicators, OECD Publishing, https://doi.org/10.1787/pension_glance2017en..
[10] OECD (2016), OECD Reviews of Pension Systems: Mexico, OECD Publishing, Paris, http://dx.doi.org/10.1787/9789264245938en.
[6] OECD (2015), The tax treatment of funded private pension plans, OECD Publishing, https://www.oecd.org/daf/fin/privatepensions/taxtreatmentpensionplanscountryprofiles.pdf.
[3] OECD (2014), Mortality Assumptions and Longevity Risk: Implications for pension funds and annuity providers, OECD Publishing, Paris, http://dx.doi.org/10.1787/9789264222748en.
[4] Superintendencia de Pensiones de Chile; Superintendencia Valores y Seguros de Chile; (2015), Norma de Carácter General SP/SVS No. 398.
This Annex details the methodologies and assumptions used for the analysis in this chapter. The first section describes the Longitudinal Survival Method (LSM), which was used to derive the mortality rates across socioeconomic groups for Korea and Mexico. The following section explains how OECD data was used to derive life expectancies by educational group for Canada, Great Britain and the United States and how these estimates differ from those detailed in (Murtin et al., 2017[1]). The final sections describe the general and countryspecific assumptions and results, including the specific details of the payout scenarios assessed, detailed results for the pension wealth ratios and income ratios, and the mortality assumptions used. The methodology used to derive mortality rates and life expectancy estimates for Chile, which relied directly from pensioners’ data, is explained in the section pertaining to Chile.
Longitudinal Survival Method (LSM)
The main challenge in deriving estimates of mortality for different socioeconomic groups is the lack of mortality data linked to socioeconomic variables. One potential source of data is longitudinal surveys, as they can track whether individuals are still alive and typically ask a number of questions that can indicate an individual's socioeconomic level. The number of respondents for such surveys, however, is usually not sufficiently large to derive robust mortality assumptions on their own.
The Longitudinal Survival Method developed by (Luy et al., 2015[2]) is a method inspired by indirect methods of mortality estimation which have been developed to estimate the mortality of populations with incorrect, incomplete or no data. However, methodological similarity enables LSM to estimate the mortality of the population of interest and its various subgroups based on the direct observation of mortality provided by longitudinal studies. It derives its estimations by adjusting the observed mortality of population subgroups from the known mortality of the entire population, as measured by life tables developed based on historical mortality data of the general population. As such, it overcomes the need for large amounts of data and has the potential to produce reasonable estimates for mortality and life expectancy based on a rather limited number of observations and a small number of inputs. The only inputs needed are the period of observation, the observed mortality of the general population over the period of observation (typically given by the life tables developed by national statistical bodies), the observed mortality of the respondents to the longitudinal survey, and basic demographic information for the respondents including birthday, gender and any socioeconomic variable that will be used for the analysis.
The accuracy of the methodology relies on the representativeness of the population sample of the longitudinal survey to that of the general population. That is, the total mortality of the sample is expected to be the same as that of the general population, and the improvements in life expectancy of the sample and all of its subpopulations over the period of observation mirror that of the general population.
Three main quantities are calculated to derive the estimated survival rates per age:

1. S_{R}  the observed probability of survival of respondents to the longitudinal survey between the first and last survey waves (the period of observation, z)

2. S_{L}  the expected probability of survival for a given cohort of the population over the period of observation, z (i.e. accounting for mortality improvements experienced over the period)

3. S_{P}  the expected probability of survival in the year corresponding to the central year of the period of observation, t (i.e. no mortality improvements accounted for)
For the calculation of S_{R}, respondents are grouped corresponding to their exact age, resulting in an average age of respondents of $\stackrel{}{x}$ over an average time between the first and last survey of $\stackrel{}{z}$. In practice, there are often not a sufficient number of observations to observe a death at every age in the longitudinal survey. S_{R} is therefore calculated based on a rolling weighted average of a larger age group, e.g. S_{R} for individuals aged 65 at their last birthday is estimated by summing the deaths and observations for the ages 60 to 70.
With these inputs, the estimated survival rate from age $\stackrel{}{x}$ to $\stackrel{}{x}+\stackrel{}{z}$ in year t becomes:
${}_{z}{p}_{x}={S}_{{R}_{x}}\bullet \raisebox{1ex}{${S}_{{P}_{x}}$}\!\left/ \!\raisebox{1ex}{${S}_{{L}_{x}}$}\right.$
The ratio ${S}_{{P}_{x}}/{S}_{{L}_{x}}$_{ }is thus used as an adjustment factor to convert the observed cohort survival (which would have experienced mortality improvements over time) to the period survival rate which would have been experienced in the central year of observation.
The zyear estimated survival rates for each age $\stackrel{}{x}$ are then converted into single year survival rates at each age x with these steps:

1. For each age x, the l_{x} given by the period life table (i.e. the number of expected survivors at age x) is interpolated between x and x+1 to calculate the l_{x} for the average exact age of the observations $\stackrel{}{x}$ and $\stackrel{}{x}+\stackrel{}{z}$.

2. An adjustment factor is calculated by dividing the z year survival for age x by the observed survival for $\stackrel{}{x}$ (based on the l_{x} calculated in Step 1) to adjust the survival rate from $\stackrel{}{x}$ to the exact age x at last birthday.

3. An adjustment factor is calculated by taking the difference of the logit of S_{R} and the logit S_{P}, taking into account the adjustment calculated in Step 2, to adjust the general population mortality to the mortality of the subgroup of interest.

4. The adjustment factor calculated in Step 3 is applied to the logit of the single year survival probabilities given by the period life table to obtain the estimated single year mortality rates for the subgroup of interest.
These steps are repeated for each $\stackrel{}{x}$, each resulting in an estimated set of mortality rates for year t. The final estimated mortality rates for the subgroup for each age x is obtained by taking a weighted average of these sets of rates. Additional smoothing can then be applied using the Brass methodology to change the shape of the survival curve, given a sufficient number of observations, to improve the fit of the estimated rates to the observed data, but is not necessary in all cases.
OECD mortality estimates by education
The data used to derive life expectancy estimates by educational attainment are described in (Murtin et al., 2017[1]). Low education refers to individuals having an educational attainment up to lower secondary level, average education refers to those having completed secondary education, and high education refers to those having completed tertiary education. This data was used as a basis for the estimations provided in this report for Canada, Great Britain and the United States, however there are some methodological differences to derive the mortality rates and life expectancies.
Life expectancy estimates in (Murtin et al., 2017[1]) use Chiang's method for abridged life tables based on smoothed mortality pooled into five year age groups and extrapolated to ages over 94 using the Gompartz methodology.
Estimates for this report use cubic splines with a smoothing parameter of 0.5 to interpolate the pooled mortality rates for individual ages through age 90, and use the Kannisto methodology fitted to ages 7690 to extrapolate beyond age 90 to age 120, unless otherwise stated in the country specific assumptions. In addition, cohort life expectancies for 2016 were used for this analysis assuming the mortality improvement scale indicated for the given country rather than the period life expectancies given in (Murtin et al., 2017[1]).
General assumptions used for the analysis
The baseline scenario presented assumes an entry age of 20 and the statutory retirement age specific to the jurisdiction assessed. The salary of the average worker is based on average worker earnings in 2016, with lowincome individuals earning 50% of the average income, and highincome individuals 300% of the average income.24 The calculation of total pension payments received (private pension + public pension) is based on the replacement rates for public pensions using these same income assumptions, and is assumed to be indexed to inflation unless otherwise noted.25 Net indicators are calculated based on the tax rules specific to each jurisdiction and assume that thresholds given for future years change in line with inflation.26 For all jurisdictions assessed, assumptions are that salary increases each year in line with inflation (2%) and productivity (1.25%), real investment returns are 3% and the real riskfree rate is 2%.27 All contributions and pension payments and withdrawals are assumed to occur at the end of the year.
Country specific results and assumptions
Canada
This analysis considers defined contribution pension plans in Canada. The two main types are Registered Pension Plans (RPPs) and Registered Retirement Savings Plans (RRSPs).
RPPs are established by employers. These plans are portable, and upon leaving their employer, employees may either transfer their accumulated assets into their new employer’s plan or into a lockedin retirement account. At retirement accumulated assets must be used to purchase either a Life Income Fund (LIF) or a life annuity from an insurer. If a LIF is chosen, annual withdrawals are allowed from age 55 and are subject to minimum and maximum withdrawal limits which increase with age. Some provinces require that funds remaining in the LIF at a certain age be used to purchase a life annuity.
RRSPs are taxdeferred voluntary personal retirement savings plans into which contributions may be made up until the age of 71. There is not an effective minimum age at which withdrawals can begin, however by age 71 the funds must be transferred into a Registered Retirement Income Fund (RRIF), used to purchase a life annuity from an insurer, or withdrawn as a lumpsum. If an RRIF is chosen, withdrawals are subject to an annual minimum percentage of assets which increase with age. No maximum withdrawal limit is imposed.
The analysis assumes that individuals contribute 8.5% of their annual salary to their pension plan.
Pension wealth ratios
The pension wealth ratios for Canada, shown in Annex Table 6.A.1 demonstrate that public pensions can significantly offset the financial disadvantage that lower income groups have with respect to the pension income they can receive in retirement. While low income groups can expect 2050% of their annual income less from private pensions compared to the high income groups, when public pensions are accounted for they can expect to receive six to seven times more their annual salary in total. Taxes further offset these differences at the income levels assumed. While low and average earners benefit from tax credits which offset most if not all of the tax owed on their pension, high earners still pay additional tax.
Income ratios
The rules around public pensions and taxation also mean that the relative differences in pension income across income groups is reduced in retirement compared to the relative differences over working lives. Annex Table 6.A.2 shows that low income individuals earning 53% of the net average salary can receive nearly 60% of the average pension in retirement.
Mortality assumptions
Canadian population mortality is based on the 20092011 life tables from Statistics Canada for males and females. The life expectancy of the average earner is based on this data.
Life expectancies for those with low and high education/income were based on the data used in (Murtin et al., 2017[1]) by educational attainment for a central year of 2009.
Mortality improvements for all socioeconomic levels are based on the mortality improvements developed in the Canadian Pensioners Mortality study (as described in (OECD, 2014[3])).
Factors used to price the annuity options were based on the GAM94 mortality table with the mortality improvement assumptions developed by the Canadian Institute of Actuaries (as described in (OECD, 2014[3])).
Chile
All formally employed individuals in Chile must contribute 10% of their salary to an individual defined contribution pension up to a limit of 73.2 UF.28 For lowincome individuals, the state makes additional contributions in the form of a subsidy for young workers with low incomes.29
The analysis assumes the statutory retirement ages of 65 for males and 60 for females. At retirement, individuals have the choice of using their accumulated assets to take a programmed withdrawal, purchase an inflation indexed life annuity, purchase a deferred annuity combined with a programmed withdrawal, or take some combination of these options.30 Programmed withdrawals are subject to maximum limits based on an actuarially neutral annuity factor calculated with the expected return on investment. For the deferred annuity option, the income received must be at least 50% but less than 100% of the first temporary payment withdrawn.
If accumulated assets are not sufficient to purchase an annuity providing the legal minimum pension,31 individuals must draw down their assets by taking a programmed withdrawal.
Pension wealth ratios
Annex Table 6.A.3 shows that lowincome individuals can expect to receive an overall lower pension relative to their level of income from private pensions compared to high income individuals.
The relative levels of the ratio for low and high earners equalise or reverse when accounting for public pension benefits to which lowincome individuals are entitled. Lowincome males receive nearly an additional year of their annual income when public benefits are accounted for, and females around 1.3 additional years of salary.
Taxes further offset the difference in pension outcomes between high and low income groups. The dispersion of net pension wealth between low and high earners is similar across all types of payouts, with low earning males receiving around 1.8 times their income more than high earners, and females around 2.3 times their income more.
Income ratios
Relative differences in pension income decrease in retirement when total pensions and taxes are accounted for Annex Table 6.A.4 shows that income taxation reduces income inequality for preretirement income compared to the 0.5 for lowincome earners and 3.0 for highincome earners gross of tax. The inclusion of public pensions and the specific tax treatment of retirement income results in more significantly reduced income inequalities in retirement for all types of payout.
Mortality assumptions
Programmed withdrawals are based on an actuarially neutral annuity factor derived using the 2016 Chilean pensioner mortality table and the expected real investment rate of return. Annuity conversion factors are based on this same mortality table and the risk free discount rate.
Mortality rates by socioeconomic group were derived from an analysis of the data of affiliates to the Chilean pension system. Low, average and high socioeconomic groups are defined as being in the first, third and fifth quintile of the first pension income received by pensioners. The analysis assumed mortality improvements from the 2014 Chilean mortality tables for the calculation of the indicators.
Derivation of mortality rates
Mortality rates were derived from 1.3 million observations of pension affiliates between 2008 and 2016. Death and exposure calculations relied on the methodology used to develop the 2014 Chilean mortality tables, as detailed in (Superintendencia de Pensiones de Chile; Superintendencia Valores y Seguros de Chile;, 2015[4]). The resulting mortality rates for a central year of 2012 were smoothed using the WhittakerHenderson method of graduation between the ages of 55 and 95. For older ages, mortality rates were extrapolated to 110 using the Kannisto method fitted to the graduated mortality rates for those aged 80 to 95.
Annex Table 6.A.5 shows the estimates of period life expectancy at age 60 for females and 65 for males by quintiles of first pension income calculated using the rates smoothed and extrapolated as described above. The difference in life expectancy between the 1^{st} and 5^{th} quintile is 3.3 years for females and 4.3 years for males.
Great Britain32
Since 2012, employers have been required to autoenrol employees into workplace pension schemes, with full rollout completed in 2018. These schemes are usually defined contribution schemes, and minimum contributions are building to 8% of earnings in 2019. The analysis therefore assumes that contributions are 8%.
Statutory retirement age is currently 65 for men and 62.5 for females, though the age will be 65 for both genders in 2018 and increase further to age 67 for both genders by 2028 (OECD, 2017[5]). The analysis assumes a retirement age of 65 for both genders.
Following the removal of an effective requirement to purchase a life annuity at retirement in 2015, pensioners face no restrictions regarding how to withdraw their savings at retirement.
Pension wealth ratios
In order to account for the impact that public pensions and tax rules can have on pension outcomes, Annex Table 6.A.6 shows the pension wealth ratios for DC pensions, total pensions, and total pensions net of tax.^{ }
The inclusion of public pensions largely offsets the relative differences in pension outcomes across socioeconomic groups.33 While for funded DC pensions, low earners could expect to receive around one to two thirds of their annual salary less in total pensions relative to high earners, with public pensions they can expect to receive on average around 6 to 7 times more their annual salary in total. Tax rules can further reverse these differences, but to a lesser extent.34
Income ratios
Annex Table 6.A.7 shows that relative differences in income are significantly reduced in retirement. Whereas the low earner could expect to earn a net salary 53% that of the average earner, in retirement they can expect a pension that is 7580% that of the average pension.
Mortality Assumptions
Population mortality was based on the 20132015 life tables for Great Britain from the Office of National Statistics. The mortality rates in the life tables were extrapolated from age 100 to age 120 with the Kannisto methodology. The rates assumed for programmed withdrawals is based these assumptions.
For low and high education/income groups, life expectancies were based on the data used in Murtin et al (2017) by educational attainment for a central year of 2011. Enhanced annuity rates rely on the mortality rates for those with low educational attainment.
Normal annuity rates are based on the LML08 and LFL08 tables developed for life annuitants. Unisex rates were derived by taking the average of the male and female rates.
All mortality assumptions are projected forward with improvements using the CMI model calibrated to data from England and Wales, and a long term improvement assumption of 1.25%.
Korea
This assessment assumes contributions go towards a defined contribution plan, and that pension payments can be taken either as a lump sum or an annuity at retirement. Private pensions in Korea are occupational, which are quasimandatory and take the form either of a defined benefit or defined contribution plan, or voluntary personal pension savings accounts. Payouts from either plan can be received as a lump sum or annuity. Other types of payouts are not allowed.
Total contributions are assumed to be 18.3%, with 8.3% assumed to be paid by the employer (the minimum allowed employer contribution) and the remaining 10% assumed to be paid by the employee (OECD, 2015[6]). Retirement age for both males and females is assumed to be 65.35
Pension wealth ratios
Public pensions and progressive taxation offset the relative differences in total pension wealth from differences in life expectancy. Annex Table 6.A.8 shows that while low income individuals can expect to receive an overall lower pension relative to their level of income from private pensions compared to high income individuals, the relative levels of the ratio reverse when accounting for public pensions. Low income individuals receive at least eight times their annual income in additional pension wealth when public pensions are accounted for, compared to around three times more for highincome people.
Taxes further offset the difference in pension outcomes between high and low income groups, shown in the 'Net' columns. When an annuity is taken, pension wealth decreases by a factor of nearly 1.5 annual income when accounting for taxes paid for low income compared to just under 2.5 for high income earners, so in other words low income earners pay relatively lower taxes. The result is that low income males can expect to receive 7.1 times their annual income more in pension net of tax from an annuity than high income males, and low income females expect to receive 10.1 times more.
Annuities remain an attractive option for all income groups compared to lump sums. Lump sums are taxed relatively more than the annuity option, so while pension wealth is higher for lump sums compared to annuities on a gross basis, the annuity option provides a higher pension wealth ratio on an after tax basis.
Income ratios
Annex Table 6.A.9 shows that while income taxation only slightly reduces relative income differences for preretirement income, the inclusion of public pensions and the specific tax treatment of retirement income results in more significantly reduced differences in retirement. This is true for both annuity and lump sum payouts.
Mortality assumptions
Annuity conversion factors are based on the 6^{th} EMT mortality table along with improvements projected using the LeeCarter model using Korean life tables from 19972011.36
Mortality rates for the different socioeconomic groups have been derived using the Longitudinal Survival Method (LSM) applied to the data obtained from the KLoSA longitudinal study carried out between 2006 and 2014 and based on selfevaluated economic status. This analysis produced mortality estimates for a central observation year of 2010. The same mortality improvements from the LeeCarter model were applied to these estimates. The following section details the results and caveats of the LSM applied to Korean data.
LSM applied to Korean data
The initial KLoSA is a total sample of 4 463 men and 5 791 women. 1 968 observations (811 men and 1 157 women) are dropped due to nonresponse to the final survey, resulting in total input data of 3 652 men and 4 634 women aged between 45 and 98.37 For the LSM, respondents over the age of 80 were also dropped.
The reported selfevaluation of economic status was used as the socioeconomic indicator to derive mortality rates by socioeconomic group.38 Respondents answered a question asking how satisfied they were on a scale of 0 to 10 with their economic situation relative to their peers. While this measure is subjective, it has the advantage of being able to capture more broadly the economic situation of the individual than is possible from using a single quantitative measure based on income or wealth, for example, which have not by themselves to be robust indicators of socioeconomic status (Cairns et al., 2016[7]). The responses were grouped as shown in the Annex Table 6.A.10 into low, medium and high socioeconomic groups.
The resulting life expectancies at age 65 calculated for the low, medium and high economic groups for males and females are shown in Annex Table 6.A.11.
Mexico
Mexico has two mandatory defined contribution pension system into which employees are required to contribute: one for private sector workers and one for public sector workers. For private sector workers, the system which is assessed for this analysis, total contributions of 6.5% of earnings are made up of 1.125% from workers, 5.15% from employers and 0.225% from the government. On top of these contributions, the government provides a supplementary contribution called the social quota which varies based on income level. This results in total contributions of 8.2%, 7.4% and 6.5% of annual salary for the low, average and high income workers that are assessed here, respectively.
At retirement, which is assumed to be the statutory retirement age of 65, individuals have the option of either using the accumulated assets to purchase an inflationindexed life annuity or taking programmed withdrawals at a rate which changes with life expectancy. If the accumulated assets are not sufficient to purchase an annuity providing an income at least as high as the minimum guaranteed pension, the individual must instead take the programmed withdrawal at this level until the account is depleted, after which the government will provide the minimum guaranteed pension.
These two payout options are therefore assessed here: the purchase of an immediate inflationindexed annuity at retirement and programmed withdrawals.
Pension wealth ratios
The pension wealth ratios, shown in Annex Table 6.A.12 are highest for lowincome individuals even before public pensions and taxes are accounted for due to the additional social quota contributions that vary by wage level. Low and average earners cannot take an annuity because the income provided would be lower than the minimum guaranteed pension. Public pension benefits significantly increase these ratios for lowincome groups in particular. These ratios do not change when taxes are taken into account, however, as pension benefits are taxexempt up to 15 times the annual minimum wage, which is higher than the benefits calculated for all income groups for this analysis.39
Income ratios
Annex Table 6.A.13 shows that relative differences in income are reduced in retirement for total pension income from programmed withdrawals, the only option available to all income groups. As both low and average income individuals receive the minimum guaranteed pension in most years, their income in retirement is very close.
Mortality assumptions
Average population mortality is based on 2009 figures from CONAPO, extrapolated to age 110 using the Kannisto methodology. Population mortality is assumed to follow the improvements used in the EMSSA 09 mortality table.
The maximum limits for programmed withdrawals are based on an actuarially neutral annuity factor derived using the EMSSA 09 mortality table and the riskfree rate of return. Annuity conversion factors are based on this same table and discount assumptions.
Mortality rates for the different socioeconomic have been derived using the Longitudinal Survival Method (LSM) applied to the data obtained from the Mexican Health and Aging Study (MHAS) longitudinal study carried out between 2001 and 2015.40 Socioeconomic groups are based on quartiles of the number of years of completed education for a central observation year of 2008, and subsequent mortality improvements are assumed to follow those used for the EMSSA 09 table.
The LSM is based on data collected by the MHAS in 2001, 2003, 2012, 2015 and panels for individuals born between 1895 and 1982. This resulted in a total sample of 6,504 men and 8,682 women, with 2,253 observations (937 men and 1,316 women) dropped from nonresponse to the final survey.41 The input data is therefore composed of 5,567 men and 7,366 women aged between 20 and 105. People aged below 33 and over 69 (1,263 men and 1,440 women) are excluded from the analysis. Final estimates used for the analysis were based on quartiles of the years of education. The resulting estimates for period life expectancy for both genders is found in Annex Table 6.A.14.
United States
Voluntary defined contribution pension plans in the United States can be either occupational or personal plans. Withdrawals from these types of plans are usually taxed at the marginal rate. Contributions are assumed to be 9%, and retirement at age 66, which is the statutory retirement age for a public pension for those reaching age 66 in years 2009 through 2020.42
Pension wealth ratios
Both public pensions and tax rules contribute to offsetting the relative differences in pension wealth for lowincome groups. Annex Table 6.A.15 shows that on average, public pension benefits result in low income males generally receiving at least 3.5 times their annual salary in total more than high income males, and around 5 times more for females. Tax rules result in around an additional 11.5 years more in total annual salary for lowincome groups compared to highincome groups.
Income ratios
Existing differences in income before retirement do not become relatively worse in retirement. Annex Table 6.A.16 shows that whereas lowincome individuals earn 53% less than average income individuals after tax, in retirement for most scenarios they can expect to receive around 60% of the average pension income.
Mortality assumptions
Population mortality was based on the 2014 life tables from the Human Mortality Database (HMD). Programmed withdrawals that are not based on the Required Minimum Distribution levels are based on this mortality.
For low and high education/income groups, life expectancies were based on the data used in Murtin et al (2017) by educational attainment for a central year of 2011. For females, these old age mortality rates were extrapolated from age 85 to centre the resulting estimated life expectancies around the observed population average. Nevertheless, the resulting mortality curves still demonstrate significant crossing of mortality rates at older ages due to the accelerating slope of mortality derived for the high income group beyond the age of 65. The average life expectancies at age 65, however, still follow the expected pattern that low educated groups also have lower life expectancies.
The base assumptions for the price of annuities are based on the IAMBasic rates for 2012.
Mortality improvement assumptions were based on the MP2017 improvement scale for all populations and annuity pricing.
Notes
← 1. The technical annex provides details regarding methodologies and mortality assumptions used for the analysis as well as more detailed results.
← 2. Data availability and the fact that DC plans are common guided the choice of countries.
← 3. The mortality assumptions used are those of Great Britain, not the United Kingdom.
← 4. This measure has the advantage of being able to reflect differences in absolute financial outcomes across socioeconomic groups independent of income inequalities existing before retirement. However, it falls short in capturing the differences in terms of individual effort towards their retirement income. For example, if we assume that low earners enter the labour force earlier yet retire at the same age (so work longer), this measure can result in a higher relative pension wealth for low earners than high earners. This is because the additional pension income that low earners receive from the earlier pension contributions accumulated over 45 years is greater than the present value of pension income lost at the end of retirement due to shorter life expectancies.
← 5. The general assumption is that low income and high income correspond with low and high socioeconomic groups regardless of the socioeconomic indicator used to derive life expectancy.
← 6. The specific results for each country are not comparable across countries as the assumptions used and scenarios assessed are countryspecific. For example, programmed withdrawals are not always calculated in the same manner, and the mortality assumptions on which annuity pricing is based may differ to varying degrees from the mortality of the general population in that jurisdiction. Countryspecific results and assumptions can be found in the Technical Annex.
← 7. This option will always result in a ratio of 101% rather than 100% as the analysis assumes that assets are withdrawn at the end of the year after retirement.
← 8. Note, however, that the maximum limits also quickly exhaust the account, with all assets withdrawn at age 89.
← 9. This is based on an annuity factor discounted at the expected real investment return of 3%.
← 10. The ability to take this option is conditional on being able to finance an annuity at the level of the Basic Solidarity Pension. For this analysis, this option is not available for lowincome females.
← 11. However, for females, lowincome workers will not have accumulated sufficient assets to opt for an annuity at retirement due to the earlier retirement age and higher life expectancies.
← 12. Since 2012 insurance companies in the EU are required to price on a unisex basis, so unisex rates are assumed here for annuities, except for the enhanced annuity, which is assumed to be specifically underwritten for the lowincome group based on gender distinct mortality.
← 13. This is equivalent to the purchase of an immediate annuity for average and highincome groups, with only lowincome groups receiving a higher annuity income from this option.
← 14. This option will always result in a ratio of 101% rather than 100% as the analysis assumes that assets are withdrawn at the end of the year after retirement.
← 15. The lump sum option will always result in a ratio of 101% rather than 100% as the analysis assumes that assets are withdrawn at the end of the year after retirement.
← 16. The minimum guaranteed pension (PMG) was equivalent to MXN 33 180.36 for private sector workers as of December 2016 (OECD, 2017[5]).
← 17. The RMD is defined in terms of a uniform lifetime table, and the RMD in amount is the account balance divided by the distribution period given in the table. This level is not defined before age 70, and is therefore assumed to be equivalent to 1.75 times the life expectancy of the male population, which is in the same order of magnitude as the limit at age 70.
← 18. This option will always result in a ratio of 101% rather than 100% as the analysis assumes that assets are withdrawn at the end of the year after retirement.
← 19. Excluding the option of taking the minimum required distributions, which results in a very low ratio indicating that it is not the optimal design for payout.
← 20. Detailed results of the actual pension wealth calculations by country and payout option can be found in the Technical Annex.
← 21. The assessment of the impact of public pensions relies on the replacement rate calculations presented in Pensions at a Glance 2017.
← 22. More detailed results of the income ratio calculations by country can be found in the Technical Annex.
← 23. Except for Chile, where the mortality assumptions are derived from those affiliated with the pension system, including pensioners with a pension amount lower than the PBS (Pensión Básica Solidaria).
← 24. Average wages as shown in Pension at a Glance 2017, Table 6.5.
← 25. Replacement rates assumed for public pensions are those calculated in Pensions at a Glance 2017. The case of Mexico is an exception, with the total replacement rate calculated directly.
← 26. Rules and thresholds provided typically correspond with the rules in place for 2015 (OECD, 2015[6]) but are applied for 2016.
← 27. These assumptions are those in Pensions at a Glance 2017.
← 28. All analysis assumes currency in Unidad de Fomento (UF), a unit of account indexed to prices.
← 29. Starting in July 2011, the worker directly receives a state subsidy in his/her individual pension savings account equivalent to 50% of the pension contribution, calculated on a minimum wage, for the first 24 contributions that he/she makes between the ages of 18 and 35, where his/her wage is equal to or lower than 1.5 times the minimum monthly wage.
← 30. An amount of 15 UF is taken from the account at retirement to cover funeral expenses.
← 31. This threshold is equal to the PBS, 3.5 UF in December 2016 (OECD, 2017[5]).
← 32. Great Britain is assessed rather than the United Kingdom because the mortality assumptions used are based on Great Britain only.
← 33. Public pensions are assumed to grow annually at the minimum rate of 2.5% rather than the assumed rate of inflation of 2%.
← 34. Tax calculations assume that 25% of withdrawals are taxfree (whenever they are withdrawn), and that income from annuities do not benefit from this tax exemption.
← 35. While currently the statutory retirement age for public pensions in Korea is 61, it is planned to be increased to 65 by 2033 (OECD, 2017[5]).
← 36. Korean life tables are issued by KOSIS and found here. Note that the 6^{th} EMT tables produce a life expectancy significantly higher than that of the Korean population, and the projections of mortality improvements based on the limited amount of historical data are relatively high. The price of an annuity used for this analysis is therefore quite conservative.
← 37. Sensitivity analysis to attrition based on health status and a probit regression on the KLoSA data indicate that the remaining sample is not health biased, though a Wald test indicates that there may be a bias in relation to other demographic characteristics.
← 38. The LSM was also tested based on educational attainment, but this resulted in less robust results for females.
← 39. The minimum wage for 2014 is MXN 21 609.
← 40. Estimates using the LSM were chosen over the data used by Murtin et al (2017) mainly because the former estimates were more in line with the observed life expectancy of the entire Mexican population. Estimates based on Murtin et al. (2017) for both genders result in figures for those with low education which are higher than estimates of life expectancy at age 65 for the general Mexican population.
← 41. Sensitivity analysis indicates that attrition was not health biased.
← 42. Contribution rate is consistent with that used in (OECD, 2017[5]).