Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

# Wealth and the effect of subjective survival probability

## Abstract

The life cycle hypothesis predicts that a longer life expectancy should, ceteris paribus, lead to the accumulation of more wealth during a working life to fund consumption in retirement. The prediction is tested by examining whether subjective survival probability (SSP)—a proxy measure of self-assessed life expectancy—affects retirement wealth among the pre-retirement older population in Ireland. The estimated relationship is complicated due to the correlation between SSP and life table estimates of life expectancy. SSP is instrumented to address measurement error and reverse causality. The findings suggest that a higher SSP increases retirement wealth.

This is a preview of subscription content, log in to check access.

## Notes

1. 1.

De Nardi et al. (2006, 2009) stratify aggregate life expectancy data by some observable characteristics (gender, health and income) to estimate heterogenous mortality rates.

2. 2.

The two populations were chosen because economists are assumed to have a better-than-average understanding of expectations and probabilities.

3. 3.

The optimism index methodology comes from Gan et al. (2005). O’Donnell et al. (2008) find that females are more pessimistic about their survival probabilities than men and that both genders on average overestimate their mortality risk when compared with life table information.

4. 4.

Salm (2010) measures consumption using two waves of the Consumption and Activities Mail Survey which was administered to a subset of the US Health and Retirement Study (HRS) respondents. He finds that a 1% increase in SSP leads to a 1.8% decrease in consumption of non-durables.

5. 5.

Each participant underwent a face-to-face computer-assisted personal interview (CAPI) in their home, was given a self-completion questionnaire and was invited to a health assessment. The overall response rate of the first wave was 62%. See Barrett et al. (2011) for a detailed description of the data, including sampling and the construction of survey weights (which are accounted for in this analysis).

6. 6.

See Dobrescu and Smith (2016) for more information about the HRS network of surveys in different countries.

7. 7.

Some TILDA respondents’ spouses are less than 50 years old. They are excluded from the analysis as their probability weights are set to zero in order to make the sample representative of the population aged 50 and over.

8. 8.

The spouse who is most knowledgeable about family finances and retirement planning is assigned the role of financial respondent.

9. 9.

Missing wealth data are imputed as described in Appendix C.

10. 10.

Current income has been equivalised by dividing total household income by 1.66 for two-person households.

11. 11.

The quality of TILDA wealth data is discussed in O’Sullivan et al. (2014).

12. 12.

For respondents who are older than 65, the “target” age is higher.

13. 13.

The STATA progamme “cqiv” (Chernozhukov et al. 2015, 2018) was used to estimate the models with 300 bootstrap replications to estimate the confidence intervals. Sensitivity analyses using 100 and 500 replications were carried out, without affecting the statistical significance of the main estimates presented.

14. 14.

The only information in wave 1 of TILDA on bequests is the value of “other assets” which includes due inheritances. There is no information about receipt of inheritances.

15. 15.

The estimates (available from author upon request) from the first-stage regressions suggest that parental longevity measures have positive and significant effects on SSP, with the father’s longevity having a stronger influence. The test statistic of the F-test of the joint significance of the instruments is consistently larger than 10, suggesting a high level of instrument strength. Interestingly, when the first-stage regressions are estimated separately for men and women, it is apparent that SSP is influenced more by the mortality experience of the parent of the same gender as the respondent. This finding is in contrast with Hurd et al. (1998) who report significant associations only between daughters and fathers.

16. 16.

Estimates of the characteristics of the different analysis sub-populations are available from the author upon request.

17. 17.

According to Banks et al. (2005), median real earnings in the UK for individuals aged between 50 and SPA and between 1978 and 2002 did not grow for men or for women. According to the Irish Central Statistics Office and inflation adjustment using CPI made by author, median real earnings for 50- to 59-year-olds show a growth rate of 0.2% for women and − 4.9% for men between 2011 and 2014.

18. 18.

According to Banks et al. (2005), median pension contribution rates among the under 60s in England are relatively invariant with age. Examining the TILDA data used in this analysis, the median contribution rate of the different types of supplementary pension schemes (described in Section B) is 8% among the 50–55-year-olds, 9% among the 56–60-year-olds and 8% among the 60–64-year-olds. Among these age groups, Banks et al. find median contribution rates of between 5 and 7%, with no noticeable age trend. The Irish rates are higher but similarly invariant with age. Therefore, it is a reasonable assumption that Irish pension savers aged 50 and over also have a constant contribution rate between the survey and retirement.

19. 19.

For the few individuals who do not know the number of years worked, a value is imputed using conditional hotdecking. The conditioning variables are gender, broad age group, marital status and education, following the methodology of Banks et al. (2005). See Appendix C for more information about the imputation methodology.

20. 20.

Except when calculating entitlements to the widow’s contributory state welfare pension. The entitlement is calculated only for those legally married.

21. 21.

Annuity rate is the average single life annuity rate of four Irish life insurance companies reported by the Department of Social Protection (2012), assuming a capital amount of EUR 500,000, with no escalation and no guarantee period.

22. 22.

Department of Public Expenditure and Reform (n.d.).

23. 23.

Department of Social and Family Affairs (2010), Department of Employment Affairs and Social Protection (2013, 2019).

24. 24.

However, increase for a qualified adult is a means-tested payment.

## References

1. Adda J, Gaudecker H-M, Banks J (2009) The impact of income shocks on health: evidence from cohort data. J Eur Econ Assoc 7(6):1361–1399

2. Alessie R, Kapteyn A (2001) New data for understanding saving. Oxf Rev Econ Policy 17(1):55–69

3. Attanasio OP, Hoynes HW (2000) Differential mortality and wealth accumulation. J Hum Resour 35(1): 1–29

4. Banks J, Emmerson C, Tetlow G (2005) Estimating pension wealth of ELSA respondents. IFS Working Papers Number WP05/09, Institute for Fiscal Studies (IFS)

5. Barrett A, Savva G, Timonen V, Kenny RA (2011) Fifty plus in Ireland 2011: first results from the Irish Longitudinal Study on Ageing (TILDA)

6. Bassett WF, Lumsdaine RL (2001) Probability limits: are subjective assessments adequately accurate? J Hum Resour 36(2):327–363

7. Benitez-Silva H, Ni H (2008) Health status and health dynamics in an empirical model of expected longevity. J Health Econ 27(3):564–584

8. Bíró A. (2013) Subjective mortality hazard shocks and the adjustment of consumption expenditures. J Popul Econ 26(4):1379–1408

9. Bissonnette L, Hurd MD, Michaud PC (2017) Individual survival curves comparing subjective and observed mortality risks. Health Econ 00:1–20

10. Bloom D, Canning D, Moore M (2004) Health, longevity, and optimal retirement. Available at SSRN: https://ssrn.com/abstract=594801 or https://doi.org/10.2139/ssrn.594801

11. Bloom DE, Canning D, Graham B (2003) Longevity and life-cycle savings. Scand J Econ 105(3):319–338

12. Bloom DE, Canning D, Moore M, Song Y (2006) The effect of subjective survival probabilities on retirement and wealth in the United States. NBER Working Paper 12688

13. Bloom DE, Canning D, Moore M, Song Y (2007) The effect of subjective survival probabilities on retirement and wealth in the United States. In: Clark RL, Ogawa N, Mason A (eds) Population aging, intergenerational transfers and the macroeconomy. Edward Elgar Publishing, Cheltenham

14. Central Statistics Office (2010) VSA30: period life expectancy at various ages by age, sex and year. Retreived from: http://www.cso.ie/px/pxeirestat/database/eirestat/Irish

15. Chernozhukov V, Fernández-Val I, Kowalski AE (2015) Quantile regression with censoring and endogeneity. J Econ 186(1):201–221

16. Chernozhukov V, Fernández-Val I, Han S, Kowalski A (2018) Censored quantile instrumental variable estimation with Stata (No. w24232). National Bureau of Economic Research

17. Cocco JF, Gomes FJ (2012) Longevity risk, retirement savings, and financial innovation. J Financ Econ 103(3):507–529

18. Crawford R, O’Dea C (2012) The adequacy of wealth among those approaching retirement. IFS Report No. R72, Institute for Fiscal Studies (IFS)

19. De Nardi M, French E, Jones JB (2006) Differential mortality, uncertain medical expenses, and the saving of elderly singles. NBER Working Paper No. 12554

20. De Nardi M, French E, Jones JB (2009) Life expectancy and old age savings. Am Econ Rev 99(2):110–115

21. Department of Employment Affairs and Social Protection (2013) State pension (Contributory): Internal guidelines used in processing claims. http://www.welfare.ie/en/Pages/860_State-Pension-Contributory.aspx

22. Department of Employment Affairs and Social Protection (2019) State Pension Non-Contributory. http://www.welfare.ie/en/Pages/State-Pension-Non-Contributory.aspx

23. Department of Public Expenditure and Reform (n.d.) Irish Civil Service Pensions Information Centre. http://www.cspensions.gov.ie

24. Department of Social Protection (2012) Report on pension charges in Ireland 2012. Stationery office, Dublin

25. Department of Social and Family Affairs (2010) Rates of Payment 2010. http://www.welfare.ie/en/downloads/sw19_10.pdf

26. Dobrescu LI, Smith JP (2016) The HRS around the world surveys. In: Piggott J, Woodland A (eds) Handbook of the economics of population aging, vol 1. Elsevier, pp 993–1018

27. Elder T (2007) Subjective survival probabilities in the health and retirement study: systematic biases and predictive validity. Michigan Retirement Research Center Research Paper No. 159

28. Fisher I (1930) The theory of interest. Macmillan, New York

29. Gan L, Gong G, Hurd M, McFadden D (2004) Subjective mortality risk and bequests. NBER working paper no. 10789

30. Gan L, Hurd M, McFadden D (2005) Individual subjective survival curves. In: Wise DA (ed) Analyses inthe economics of aging. University of Chicago Press, pp 377–412

31. Government of Ireland (2001) Pensions (Amendment) Bill, 2001. Stationery Office, Dublin

32. Government of Ireland (2011) Social Welfare and Pensions Act 2011. Stationery Office, Dublin

33. Hamermesh DS (1985) Expectations, life expectancy, and economic behavior. Q J Econ 100(2):389–408

34. Hurd M, Rohwedder S (2008) Adequacy of resources in retirement. In: 10th annual joint conference of the retirement research consortium, August, pp 8–9

35. Hurd MD (1989) Mortality risk and bequests. Econometrica 57(4):779–813

36. Hurd M, McFadden D, Gan L (1998) Subjective survival curves and life cycle behavior. In: Wise DA (ed) Inquiries in the economics of aging. University of Chicago Press, pp 259–309

37. Hurd MD, McGarry K (1995) Evaluation of the subjective probabilities of survival in the health and retirement study. J Hum Resour 30(4):268–292

38. Hurd MD, McGarry K (2002) The predictive validity of subjective probabilities of survival. Econ J 112(482):966–985

39. Levhari D, Mirman LJ (1977) Savings and consumption with an uncertain horizon. J Polit Econ 85(2): 265–281

40. Manski CF (2004) Measuring expectations. Econometrica 72(5):1329–1376

41. Meer J, Miller DL, Rosen HS (2003) Exploring the health-wealth nexus. J Health Econ 22(5):713–730

42. O’Donnell O, Teppa F, van Doorslaer E (2008) Can subjective survival expectations explain retirement behaviour? DNB working paper no 188

43. Oldfield Z (2012) Financial derived variables and imputation procedures, waves 1 to 4. mimeo

44. O’Sullivan V, Nolan B, Barrett A, Dooley C (2014) Income and wealth in the Irish longitudinal study on ageing. The Economic and Social Review 45(3):329–348

45. Post T, Hanewald K (2013) Longevity risk, subjective survival expectations, and individual saving behavior. J Econ Behav Organ 86:200–220

46. Salm M (2010) Subjective mortality expectations and consumption and saving behaviours among the elderly. Can J Econ 43(3):1040–1057

47. Scholz JK, Seshadri A, Khitatrakun S (2006) Are Americans saving ‘optimally’ for retirement? J Polit Econ 114(4):607–643

48. Siegel M, Bradley EH, Kasl SV (2003) Self-rated life expectancy as a predictor of mortality: evidence from the HRS and AHEAD surveys. Gerontology 49(4):265–271

49. Skinner J (1985) Variable lifespan and the intertemporal elasticity of consumption. Rev Econ Stat 67(4):616–23

50. Smith VK, Taylor DH, Sloan FA (2001) Longevity expectations and death: can people predict their own demise? The American Economic Review 91 (4):1126–1134

51. Yaari ME (1965) Uncertain lifetime, life insurance, and the theory of the consumer. Rev Econ Stud 32(2):137–150

## Acknowledegments

I would like to thank Alan Barrett, Gaia Narciso, Rob Alessie, Alessandro Cigno, Madeline Zavodny, seminar participants at TCD, TILDA, NERI, IEA, SMYE, the Geary Institute and the Royal Economic Society Postgraduate Meeting as well as the two anonymous referees for helpful comments and suggestions. I would like to thank TILDA study participants and research team. I am grateful to TILDA for access to the data used in the paper. TILDA is funded by the Department of Health, Irish Life and The Atlantic Philanthropies. TILDA data are available from the Irish Social Science Data Archive (www.ucd.ie/issda/), Gateway to Global Aging (www.g2aging.org/), and Interuniversity Consortium for Political and Social Research (www.icpsr.umich.edu/icpsrweb/). All errors are my own.

## Funding

This study was funded by a Government of Ireland Postgraduate Scholarship.

## Author information

Correspondence to Sanna Nivakoski.

## Ethics declarations

### Conflict of interest

The author declares that there is no conflict of interest.

### Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Responsible editor: Alessandro Cigno

## Appendices

### Appendix B: Wealth calculation

This appendix describes the methodology used in calculating the present value of different components of wealth.

General assumptions:

• The discount rate (d) and real interest rate (i) are assumed to be 2.5 %, as per the estimation of retirement wealth in England by Crawford and O’Dea (2012). Robustness of the findings to these assumptions is discussed in Appendix D.

• Variables that are assumed constant from now until the state pension age (SPA) in the wealth calculation:

• Employment status

• Marital status

• EarningsFootnote 17

• Future pension contributions (fraction of earnings)Footnote 18

• A person pays (and has paid in the past) full pay-related social insurance (PRSI) contributions while working

• A person has been in full-time employment for the number of years that they state they have worked since leaving full-time educationFootnote 19

• A couple is categorised as “married” if they are married of cohabiting as if marriedFootnote 20

• SPA is assumed to depend on the year of birth of the individual as outlined in the Social Welfare and Pensions Act of 2011 (Government of Ireland 2011):

• 66 if born before 1954

• 67 if born between 1954 and 1960

• 68 if born in or after 1961

### B.1 Net financial wealth

Financial wealth is calculated at the household level, and subsequently divided equally between the spouses in the case of a married or cohabiting couple. Net financial wealth includes saving and deposit accounts, stocks, bonds, life insurance, mutual funds, investment property, land, businesses, and due inheritance, less outstanding debt. If the asset value is not known, but the amount of interest earned on those assets is known, the value is estimated as the interest divided by an assumed interest rate. Financial wealth levels are imputed for households that provide bracketed values or who refuse or do not know the value of the asset. The imputation methodology is described in Appendix C.

Present discounted value of financial assets as follows:

$$W=\left( \frac{1}{1+d} \right)^{\text{SPA}-\text{age}}{(1+i)}^{\text{SPA}-\text{age}}A$$

where,

age =:

age at interview

SPA =:

state pension age (retirement age)

d =:

discount rate

i =:

real interest rate

A =:

current value of asset

### B.2 Supplementary pension wealth

Wealth held in occupational and private pensions (collectively known as supplementary pensions) is calculated at the individual level. The methodology follows that of Banks et al. (2005) and Crawford and O’Dea (2012) who estimate the pension wealth of ELSA respondents using data very similar to that of TILDA. The TILDA data contain detailed information about the length of work histories, the current value of pension plans, the pension contributions of both employees and employers, and the expected income from pensions. Estimating supplementary pension wealth requires assumptions to be made about past and future labour market participation, earnings and pension contributions. Supplementary pension wealth is calculated separately for private sector occupational DC schemes, private sector occupational DB schemes, public sector occupational schemes, PRSAs, private pension plans, and other plans.

Annual income from a supplementary pension (P) is calculated as follows:

$$P=\frac{r(\text{PV})}{1-{(1+r)}^{-\text{LE}}}$$

where,

r =:

annuity rate (assumed 5.367555 per annumFootnote 21)

LE =:

actuarial life expectancy at SPA

PV =:

value of supplementary pension at SPA

The present discounted value of wealth (W) held in a supplementary pension is calculated as follows:

$$W=\sum\limits_{n=\text{SPA}}^{\text{SPA}+\text{LE}} {\left( \frac{1}{1+d} \right)^{n-\text{age}}{(1+i)}^{n-\text{SPA}}P}$$

where,

age =:

age at interview

SPA =:

state pension age (retirement age)

LE =:

actuarial life expectancy at SPA

d =:

discount rate

i =:

real growth rate of pension payment

P =:

annual pension income at SPA

#### B.2.1 Private sector occupational pensions

If a private sector employee with an occupational pension does not know whether their pension scheme is of the defined benefit or defined contribution type, the TILDA questionnaire asks the respondent the questions related to a defined contribution scheme. Therefore, those who are unsure of their scheme type, the defined contribution is assumed.

#### B.2.2 Public sector pensions

Public sector (defined benefit) pensions are calculated by estimating the sum of all pension income for all years in retirement, and discounting this stream of income back to current year (year of interview). Following the calculation rulesFootnote 22 of the pension entitlements of public sector employees in Ireland (recruited before 2013), the pension income in first retirement year is estimated by multiplying the estimated plan participation years by estimated final salary and by a fraction of one eightieth.

#### B.2.3 Other pensions

PRSA (Personal Retirement Savings Account) (Government of Ireland 2001) wealth is calculated in the same way as private sector occupational pensions. PRSAs were introduced in 2002 with an aim to increase pension coverage among low-coverage employee groups.

Wealth in private pensions (up to 2 schemes) is calculated in the same way as private sector occupational pensions and PRSAs, and added together.

Those who refuse to say, or do not know if they have pension entitlements from previous employers are assumed to have wealth in these pensions. Other pensions from previous employers are calculated by estimating the present value of the stream of lump-sum payment and monthly payments that the individual expects to receive from these pensions (in total). The estimation technique differs from those of other pensions because the TILDA questionnaire does not include a question about the current value of, or contributions to, these additional pensions.

### B.3 Social welfare wealth

The rules and rates applied to the social welfare wealth estimation are obtained from the Department of Employment Affairs and Social Protection (formerly known as Department of Social and Family Affairs, and Department of Social Protection) documentation.Footnote 23 In the calculations, the payment rates and rules are assumed to remain at the 2010 levels in future years.

#### B.3.1 Contributory state welfare pension

State pension (contributory) is a social insurance payment made when an individual reaches the state pension age. It is based on social insurance (PRSI) contributions. The pension payment is not means-tested.Footnote 24 To qualify for state pension (contributory), an individual must have reached the SPA and fulfil the below conditions:

• Started paying social insurance before reaching age 56

• A yearly average of either:

• At least 10 appropriate contributions paid or credited from the year first entered insurance or from 1953, whichever is later to the end of the tax year before reaching SPA. This is called the normal average rule. A yearly average of 10 full rate contributions is needed for the minimum payment rate. A yearly average of 48 full rate contributions is needed for the maximum payment rate.

OR

• 48 class A, E, F, G, H, N or S contributions (paid or credited) for each contribution year from the 1979/80 tax year to the end of the tax year before reaching SPA. This average would entitle the individual to the maximum pension. There is no provision for a reduced pension when this alternative average rule is used.

• A minimum of total contributions:

• Born before April 1946

• No pension if < 5 years worked before SPA

• Full pension if 5 + years worked before SPA

• Born April 1946–January 1954

• No pension if 10 years worked before SPA

• Full pension if 10 + years worked before SPA

• Born after January 1954

• No pension if < 10 years worked before SPA

• 10 years worked by SPA= 10/30 of full pension

• 11 years worked by SPA= 10/30 + 1/30 of full pension

• 12 years worked by SPA= 10/30 + 2/30 of full pension

• ...

• 30 years worked by SPA= 10/30 + 20/30 of full pension

A person’s average contributions are assessed in two ways—the usual average and the alternative average. If an individual does not have an average of 48 contributions from 1979, then the normal method of assessing the average will be looked at and the individual may get a reduced pension.

The present discounted value of wealth (W) from future contributory state welfare pension income is calculated as follows:

$$W=\sum\limits_{n=\text{SPA}}^{\text{SPA}+\text{LE}} {\left( \frac{1}{1+d} \right)^{n-\text{age}}{(1+i)}^{n-\text{SPA}}P}$$

where,

age =:

age at interview

SPA =:

State Pension Age (retirement age)

LE =:

actuarial life expectancy at SPA

d =:

discount rate

i =:

real growth rate of pension payment

P =:

annual pension income at SPA

#### B.3.2 Widow’s contributory state welfare pension

Widow’s, widower’s or surviving civil partner’s (contributory) pension is paid to the husband, wife or civil partner of a deceased person. The payment is not means-tested. Weekly widow’s contributory state welfare pension payment rates in 2010:

• EUR 230.30 for 48 + contributions

• EUR 225.80 for 36–47 contributions

• EUR 220.40 for 24–35 contributions

In order to qualify for this pension, a person must have the following:

• Be widowed or a surviving civil partner OR divorced from late spouse prior to spouse’s death and not remarried OR have had their civil partnership dissolved and have not registered a new civil partnership

AND

• Not be cohabiting as a couple

AND

• Satisfy the following social insurance contribution conditions (before the death):

• Either the surviving or the deceased spouse (or civil partner) must have at least 260 weeks’ paid PRSI contributions.

• The surviving or the deceased spouse (or civil partner) must also have a yearly average of either:

• ∗ 39 paid or credited social insurance contributions in the 3 or 5 tax years before the death of the spouse/civil partner or before they reach SPA. This gives entitlement to a maximum rate pension

• OR

• ∗ At least 24 paid or credited social insurance contributions from the year of first entry into social insurance until either the year of death of the spouse/civil partner or the year they reached SPA, whichever is earlier. This gives entitlement to a minimum rate of pension. An average of 48 per year entitles the person to the maximum rate pension.

Present discounted value of wealth from future widow’s pension income is calculated using the formula as follows:

$$W = \sum\limits_{n=\text{SPA}}^{\text{SPA}+\text{LE}} {\left( \frac{1}{1 + d} \right)^{n-\text{age}}{(1 + i)}^{n-\text{SPA}}P} + I \left[ \sum\limits_{n=D^{s}}^{D^{s}+{\text{LE}}^{d}} {\left( \frac{1}{1+d} \right)^{D^{s}-\text{age}}{(1+i)}^{n-D^{s}}} \right]$$

where,

I =:

indicator that spouse is deceased

age =:

age at interview

Ds =:

age when spouse dies

LEd =:

actuarial life expectancy at spouse’s death

d =:

discount rate

i =:

real growth rate of pension payment

P =:

annual pension income at spouse’s death

#### B.3.3 Non-contributory state welfare pension wealth

In order to qualify for the non-contributory state welfare pension, a person must fulfil the below four conditions:

1. 1.

Aged 66 if born before 1955/aged 67 if born between 1955–1960/aged 68 if born in 1961 or later

2. 2.

Not eligible for the contributory state welfare pension

3. 3.

Pass a means test (see below)

4. 4.

Meet the habitual residence condition (all TILDA respondents are assumed to meet)

Different assets are added together and derived into weekly means income as per below table.

Means test for non-contributory state welfare pension

The first EUR 30 per week of means does not affect the rate of non-contributory state welfare pension payment. After that, the pension is reduced by EUR 2.50 per week for every EUR 2.50 of means.

When the means test is carried out for couples, income and capital are divided equally between the spouses.

The present discounted value of wealth (W) from future non-contributory state welfare pension income is calculated as follows:

$$W=\sum\limits_{n=\text{SPA}}^{\text{SPA}+\text{LE}} {\left( \frac{1}{1+d} \right)^{n-\text{age}}{(1+i)}^{n-\text{SPA}}P}$$

where,

age =:

age at interview

SPA =:

state pension age (retirement age)

LE =:

actuarial life expectancy at SPA

d =:

discount rate

i = :

real growth rate of pension payment

P =:

annual pension income at SPA

The maximum weekly payment of the non-contributory state pension was EUR 219 per week, with EUR 10 increase for those aged 80 or over.

If eligible for the non-contributory state welfare pension, a person may also be entitled to the following payments: supplementary welfare allowance, rent supplement, mortgage interest supplement, living alone increase, household benefits package, free travel pass, fuel allowance, island increase, centenarian’s payment, respite care grant. In the calculations in this paper, income from these additional payments is assumed to be zero.

### Appendix C: Unfolding brackets and data imputation

For observations with missing or bracketed data for a wealth item, conditional hotdeck imputation is used to predict a value for that wealth category. Specifically, this method is carried out by replacing the missing data point with a random draw from observations with similar characteristics who report a continuous value for the wealth item. Similar observations are defined as those with same values for categorical variables such as broad age group and household type. The wealth level category is also used as a defining characteristic for cases for whom the wealth range is known (reported via unfolding brackets).

The methodology adopted in this paper broadly follows the imputation procedure of Crawford and O’Dea (2012) and Oldfield (2012) for ELSA data. The conditioning variables used in the hotdeck imputation for wealth sub-categories are listed below:

• Financial wealth

• Deposit and savings accounts: broad age group (under/over 55) and household type (married/single female/single male)

• Other financial assets (life insurance, mutual funds, bonds or shares): broad age group (under/over 55), household type (married/single female/single male) and wealth bracket (if given)

• Investment property: broad age group (under/over 55), household type (married/single female/single male) and wealth bracket (if given)

• Other assets (land, a firm or business, an inheritance or money owed, etc.): broad age group (under/over 55), household type (married/single female/single male) and wealth bracket (if given)

• Debt (excluding mortgages): broad age group of the financial respondent (under/over 55) and household type (married/single female/single male)

• Supplementary pension wealth

• Private sector occupational pension contribution rate: gender and educational level (following Banks et al. (2005))

• Private sector occupational pension plan value: the quartile of current annual earnings multiplied by pension plan tenure (following Banks et al. (2005))

• Other pensions from previous employment, lump-sum and expected income amounts: unconditional hotdeck using values from individuals with non-missing data

• Equivalised household income

• Income bracket

### Exclusion of defined benefit and social welfare pensions

A possible issue with including annuity wealth (held in defined benefit pensions and social welfare pensions) in the wealth variable is that, by definition, the current value of an annuity payment is a function of life expectancy. This is because, as shown in Appendix Section B, LE (life expectancy as given by cohort life tables) enters the formula for calculating the present value of the future stream of payments from an annuity. Therefore, there exists a computational relationship between DB pension wealth and life expectancy. For example, the net present value of a social welfare payment is calculated as the sum of the income payments received by the individual over their estimated remaining lifetime, discounted to present time. The SSP measure is not equivalent to an actuarial cohort level life expectancy estimate, but the two are potentially highly correlated.

In order to test if the association between SSP and total wealth is caused or strengthened by this structural link, the models are re-estimated including only net financial wealth and defined contribution pensions in the wealth variable. Depending on specification, the estimated SSP coefficient is statistically significant at the 10% confidence level, and the coefficient estimate value is 2.4 in the specification mirroring model 2 in Table 6, and 3.15 in the specification mirroring model 3 in Table 6. Therefore, the findings appear not to be driven by the computational relationship between wealth and life expectancy. The estimates are available from the author upon request.

### Exclusion of early orphans

The exclusion restriction of the parental mortality instrument might be violated in the case of an early death of a parent influencing the child’s wealth directly through their choices when it comes to education and work. In order to mitigate this possibility, the models are re-estimated only using the observations on individuals whose parents died after the age of 50. The sample size falls to 1,182. In the case of financial wealth, the estimates are practically identical to the estimates presented in Table 5. In the case of total wealth, the magnitude of the coefficient estimate remains largely the same (point estimate of 3.60 for a specification mirroring model 3 in Table 6), but the significance falls to just below 90% level of confidence. The findings provide some evidence that the link between SSP and wealth is not driven by the correlation between parental mortality and the child’s later life wealth that might arise from losing a parent early in life. The estimates are available from the author upon request.

### Exclusion of focal responses

The main specifications are re-estimated excluding the focal responses, i.e. individuals whose SSP variable takes on value of 0, 50 or 100. This robustness analysis is carried out to establish whether the focal responses that are driving the results. The estimate of the coefficient on SSP in both financial and total wealth specifications is slightly larger in magnitude, and the statistical significance is broadly unchanged despite the reduction (to 642 individuals) in sample size. The findings suggest that the effect of SSP on wealth is heterogeneous across the focal and non-focal response groups, but the significant result is not driven by the focal respondents. The estimates are available from the author upon request.

### Assumptions underlying the estimates of wealth

Sensitivity analyses were carried out examining the responsiveness of the estimates to the choice of fixed values for discount rate (d) and the real interest rate (i). Both rates were varied between 1 and 3%, at intervals of 0.5 percentage points. As expected, the estimates of the level of retirement wealth (Table 4) change substantially because these rates are used directly in the wealth calculation. If (d) and (i) are set to be equal, the value of financial wealth does not change (and is equal to its present value). When (d) is higher than (i), financial wealth declines (to a minimum median value of EUR 15,500). When (d) is below (i), financial wealth increases (to a maximum median of EUR 22,060). The value of total wealth follows the same logic, with median values ranging from EUR 399,025 to EUR 670,883. The estimates of the coefficient of SSP of the subsequent multivariate models remain statistically significant and positive, with the coefficient of model 2 of Table 5 varying between 1.33 and 1.98. The SSP coefficient estimate of model 2 in Table 6 varies between 2.41 and 4.18. The values of (d) and (i) that increase the wealth estimate also increase the SSP coefficient estimate. The estimated proportional change to median wealth as a response to SSP increasing by one percentage point is remarkably invariant to the choice of (d) and (i): the estimated percentage change in financial wealth and total wealth varies between 8 and 9% and between 0.5 and 0.7%, respectively. This finding is to be expected because although the wealth estimates vary with (d) and (i) the estimates of the between-individual variation is less sensitive to the assumptions made about (d) and (i). The change in the coefficient estimates is proportional to the between-individual differences in portfolio allocation only. The estimates are available from the author upon request.

### Quantile regression

Because of the skewed nature of wealth distributions, and the presence of outliers, quantile regressions (estimated at the 25th, 50th and 75th percentiles of the distributions of net financial wealth and net total wealth) are estimated. They examine the differential impact that SSP has on wealth, depending on the wealth level. The estimates mirroring model 2 in Tables 5 and 6 show that in the case of net financial wealth, the coefficient estimate of SSP increases from 0.11 at the 25th percentile to 4.44 at the 75th percentile. Estimates that are similar in essence are obtained when total net wealth is used as the dependent variable. The coefficient estimate of the effect of SSP increases from 4.60 at the 25th percentile to 6.47 at the 75th percentile. The estimates are available from the author upon request.

## Rights and permissions

Reprints and Permissions

Nivakoski, S. Wealth and the effect of subjective survival probability. J Popul Econ 33, 633–670 (2020). https://doi.org/10.1007/s00148-019-00749-2

• Accepted:

• Published:

• Issue Date:

### Keywords

• Financial wealth
• Pension wealth
• Life cycle hypothesis
• Longevity
• Subjective survival probability
• Retirement savings

• D14
• D84
• D91