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Is there adverse selection in the U.S. social security system?
Journal Pre-proof Is there adverse selection in the U.S. social security system? Andrew Beauchamp, Mathis Wagner
PII: DOI: Reference:
S0165-1765(20)30031-8 https://doi.org/10.1016/j.econlet.2020.108995 ECOLET 108995
To appear in:
Economics Letters
Received date : 8 October 2019 Revised date : 14 January 2020 Accepted date : 26 January 2020 Please cite this article as: A. Beauchamp and M. Wagner, Is there adverse selection in the U.S. social security system?. Economics Letters (2020), doi: https://doi.org/10.1016/j.econlet.2020.108995. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier B.V.
Journal Pre-proof *Highlights (for review)
Unused observables tests for asymmetric information in US Social Security are presented.
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Individuals who live longer, and those who expect to live longer, systematically claim annuity benefits at higher levels. Instrumental Variables estimates help to confirm adverse selection.
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Higher wealth, and financially literate, individuals delay claiming more in response to higher longevity.
Journal Pre-proof *Title Page
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Is There Adverse Selection in the U.S. Social Security System? Andrew Beauchamp∗ Wright State University
Mathis Wagner† Bates White Economic Consulting
December 12, 2019
Abstract
Despite facing some of the same challenges as private insurance markets, little is known about the role of adverse selection in Old-Age Social Security. Using data from the Health and Retirement Study, we perform the unused observables version
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of the positive correlation test, and find robust evidence that people who expect to live shorter lives both choose smaller annuities - by claiming benefits early - and are less costly to insure, implying adverse selection in the system. Results are consistent when using either subjective expectations or observed longevity. Decomposing
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the sources of adverse selection we find that health, demographics, occupation and financial information together account for much of the positive correlation between mortality and claiming. IV estimates help to rule out moral hazard. Keywords: Adverse Selection, Social Security, Optimal Policy.
JEL Classification: H55; J26; D82
∗
Corresponding author, 3640 Col Gen Hwy Dayton OH 45435, [email protected]. 2001 K Street NW North Building, Suite 500 Washington, DC 20006, [email protected]. The views expressed in this paper are solely those of the authors and do not necessarily reflect the opinions of Bates White or its clients. †
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Introduction
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Recent reports indicate that the US Social Security Administration will only have enough resources to pay 75% of promised benefits as soon as 2035.1 In 2018, fully 20% of the federal budget in the US was spent on Old Age Social Security (OASS). Because OASS is an insurance against outliving assets, it is potentially subject to asymmetric information problems. We test for the presence of adverse selection in OASS using observed characteristics which are plausibly correlated with the underlying risk measure, and thus potentially with both insurance coverage and costs.2 Finkelstein and Poterba (2004, 2014) describe such variables as “unused observables.”3 Adverse selection in Social Security (hereafter SS) would arise if on average those with longer life expectancy (more risky individuals) systematically obtained more insurance (a larger annuity) by claiming their benefits later, conditional on the same earnings history. Establishing the presence of adverse selection is an important step in understanding the cost-structure the program faces today and in the future.
Testing for Adverse Selection
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We test whether individuals’ choice of annuity, as measured by the age at which they first claim (A), is correlated with underlying risk, as measured by longevity (θ) and the costs
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to SS (C). The estimating equations are:
Ai = µθi + εi ,
(1)
Ci = γθi + υi .
(2)
Chief Actuary Report, (2010) Adverse selection here is the choice of annuities with some foreknowledge of mortality likelihoods; moral hazard occurs when retiring earlier improves health and longevity. 3 The SSA is by law not allowed to use observables to price their annuity at any given age, though of course the level of benefits depends on a person’s earnings history. 2
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Statistically significant positive estimates of µ and γ imply the presence of adverse selection or moral hazard (opposite signs suggest advantageous selection). The set of condi-
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tioning variables are exclusively those observable characteristics that are used in pricing the insurance policy, but since SS charges a price equal to zero for claiming benefits, the simple regression is our starting point.4 It is worth emphasizing that the positive correlation test relies on identifying an equilibrium relationship between longevity and claiming, and costs. It does not require that longevity be exogenous.
The unused observables approach can provide information on the underlying source of asymmetric information. In particular, one can include a number of covariates in equation (1) that are predetermined before age 62. Equation (1) describes the selection of individuals into different SS annuities based on a measure of the underlying longevity risk. The degree to which this correlation is attenuated (or strengthened) by the inclusion of covariates is informative about how much of the selection can be unambiguously attributed to predetermined characteristics, ruling out moral hazard. The estimating equation is:
(3)
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Ai = µθi + Xi0 β + εi ,
where Xi is a set of predetermined individual characteristics. We apply order-invariant decomposition methods of Gelbach (2016), attributing to each group of covariates the percentage which they reduce (or increase) the raw correlation between claiming and
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longevity.
Our measures for the longevity are correlated with other factors that affect the OASS claiming age. The rich set of covariates included in the HRS enables us to control for many of these. One important covariate though is wealth, which is positively correlated with longevity and delayed claiming.5 By using detailed financial information we 4
Penalties for early claiming and the opportunity costs of waiting to retire make early claiming less attractive (all else equal), but they are not prices. Instead they shift both the demand for the annuity at any given age, as well as the cost of provision. 5 Shoven and Slavov (2014) calculate the financial gains to delayed claiming which are large for many individuals.
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present evidence below that wealth is unlikely to drive the bulk of the positive correlation, suggesting private information on longevity matters. Additionally, there will always
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be unobservables we are unable to control for (e.g. risk aversion, spousal labor market conditions, etc.). Using the unused observables approach it is possible to instrument the risk measure, providing evidence on whether the observed correlation can be considered causal, and therefore adverse selection and not moral hazard (which sees causation run the opposite direction).
We instrument for our proxies of longevity risk using parental death ages.6 This helps us identify a causal relationship between longevity risk and claiming age, as well as dealing with measurement error problems in the subjective measure. We use a spline in father’s death age as an instrument for longevity to ensure identification does not come from early paternal death, which is less likely to have biological causes.7
There are a number of legitimate concerns about parental longevity instrumenting for longevity which fall into three main categories: time use and income, health, and risk preferences. Firstly, it could have a direct impact on work status through the care needs
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of elderly parents. This is a greater concern for women than men, and our results are qualitatively robust for both sexes.8 Secondly, parental mortality could be correlated with the health status of individuals near retirement, and thereby claiming decisions. Our extensive health controls, and the fact that the IV-point estimates presented below are very similar with and without them, helps alleviate that concern. Thirdly, parental mortality
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may affect an individual’s human capital, occupation decisions and risk attitudes. To help deal with this we condition all our IV-estimates on occupation dummies, completed schooling, and risk attitude measures: smoking, drinking and the HRS elicited income 6 A sizable literature takes this approach. See Bloom et. al. (2006); Delavande, Perry and Willis (2006); and O’Donnell, Teppa and van Doorslaer (2008). Hurd and McGarry (1995, 2002) did early work on validating the use of the subjective life expectancy measure in the HRS. 7 Hurd and McGarry (1995), Gertler, Levine and Ames (2004), and Case and Ardington (2006). The spline leaves earlier paternal death ages in as an included instrument, but only identifies the effect of longevity expectations on retirement through individuals whose fathers died after age 65. 8 Skira (2015) shows that two-thirds of caregivers in the HRS are women.
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risk-preference rank.9 Finally, since earlier parental deaths are correlated with all three
after age sixty-five.
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concerns, we identify the effects of longevity off paternal deaths only from fathers passing
Finally, we use that fact that HRS asks an interest-rate calculation similar to that used in the “big three” financial literacy metrics popularized by Lusardi and Mitchel (2008). Specifically, it asks a respondent to calculate the principal on $200 after two years with 10% interest rate. This question has some ambiguities, namely it does not specify reinvestment of interest or clearly state if respondents should state principle and interest or interest.10 Given imperfections with this approach, we also examine selection patterns among respondents with high wealth levels who are more financially literate and more able to delay claiming.
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Data and Empirics
We use the Health and Retirement Study (HRS), a longitudinal study that has surveyed
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a representative sample of more than 26,000 Americans 51 years and older since 1992.11 The survey is representative of the cross-section of older Americans at any given point in time, but not of the longitudinal experience of particular cohorts. For this reason all analysis that follows uses cohort fixed-effects, and constrains attention to cohorts born between 1916 and 1938.
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The HRS’ comprehensive information is important for understanding the SS claiming decision including, health, demographics, wealth and spousal characteristics. They also contain observed mortality for respondents who died during the sampling period. We further construct a subjective longevity measure from questions on the probability of 9
Though not presented in the results below, all three are significantly correlated with both longevity and claiming. 10 We therefore, we categorize individuals as financially illiterate if they did not answer one of the following (242, 240, 42 or 40) 11 Data come from the RAND HRS Data file.
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living to various ages.12 One sample consists of 1807 individuals with observed mortality, another has 5772 individuals with subjective longevity measures, all of whom did not
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claim disability status prior to retirement.
Table 1 provides descriptive statistics for the two samples and lists the data used below. Around 50 percent of the sample claim benefits at age sixty-two, so we split the sample there. The first two rows show the simple positive correlation test (PCT): claiming age is positively correlated with costs and longevity.13 The descriptives tell the story: later claimants are healthier, especially on life-threatening conditions (e.g. cancer, heart and lung disease), despite being older. In financial terms later claimants can finance delayed claiming, they have substantially higher assets and incomes. In terms of spousal characteristics, later claimants’ spouses likely exacerbate the adverse selection problem: they have higher benefit levels and longer-life spans as well.
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Model Estimates
We present the results of the basic PCT in Table 2. The first three columns show results
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for different claiming decisions; Column 4’s dependent variable is the present discounted value of costs to the SSA; Column 5 shows the annual benefit payment the individual would have received if claiming at age 62. Panel A uses observed (objective) mortality and Panel B mean subjective mortality.
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The results show individuals with longer life expectancies claim benefits later.14 Objectively living one year longer is correlated with claiming three-quarters of a month later, a 1.3 percentage point lower likelihood of claiming at first eligibility, and a 1.5 percentage point higher likelihood of claiming at 65. It is also correlated with $10,958 in additional This mean was constructed as θisubj = .5∗(Awaveobs +75)∗P (θi < 75)+80∗(P (θi ∈ [75, 85])+90∗P (θi > 85), using different responses depending on the respondent’s age at survey. 13 Individuals who died before claiming had 40% lower SS benefit levels than those who claimed at age 62, meaning the adverse selection problem persists even if we expanded the sample to include those who died before claiming. 14 Consistent with Coile, Diamond, Gruber and Jousten (2002), Hurd, Smith and Zissimopoulos (2004). 12
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costs to the SSA and $390 in higher annual benefit payments. Taken together the re-
the timing of claims.
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sults provide clear evidence of asymmetric information being important in determining
Table 3 decomposes of the longevity-claiming correlation into observables. The lower panel reports how much of the correlation can be attributed to different covariate-groups. Including benefit levels increases the correlation, thus individuals with higher average lifetime earnings claimed earlier but died later (conditional on other covariates), reducing program costs (negative signs mean advantageous selection). Objective mortality shows spousal characteristics explain about one-third of the correlation. Subjective expectations show the explained portion of the correlation is driven by the health, occupation, and demographic information.
Table 4 presents IV estimates of Equation (1). The subjective measure shows the firststage is highly significant. The coefficient indicates subjective life expectancy increases by more than a month for every year ones’ father lives past age 65. The IV estimates in both panels are similar to the correlation using the objective measure (though no longer
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significant in the lower panel).15 In the upper panel, the magnitudes are remarkably similar between the objective and IV-subjective, suggesting measurement error in subjective longevity may be substantial. Nonetheless the IV-results suggest that the correlation is driven primarily by adverse selection, since with moral hazard the causation runs from annuity choice to longevity. In the US, Coe and Lindeboom (2008) find no negative effects
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of early retirement on health and Insler (2014) finds that the retirement effect on health is beneficial. Recent evidence from Australia (Atalay and Barret (2014)) point to very similar findings: health improves following retirement. The heterogeneity results are included in Table 5. At least with respect to objective longevity, the patterns are quite clear. Individuals with more wealth are much more likely to adversely select their social security claiming decisions (the PCT is much larger). 15
The first-stage correlation between the objective longevity and parental death age is insignificant, perhaps due to small sample sizes, and is therefore omitted.
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Similarly, individuals who had incorrectly answered the interest rate question had virtually no correlation between longevity and claiming age with all the effects concentrated among
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the rest of the sample. With respect to subjective longevity we see a less clear picture: mixed evidence that higher wealth individuals had a more attenuated correlation between claiming and mortality; no evidence that financial literacy matters. However, these results are also less robust since the inclusion of covariates eliminates their significance.
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Conclusions
Overall, we provide clear evidence that life expectancy is correlated with both claiming age and the cost to the insurer. Based on observed mortality, we find that living one year later is correlated with claiming three-quarters of a month later. Also, the costs to the Social Security trust fund are roughly $10,000 higher. Taken together the results provide evidence of asymmetric information being an important determinant in the timing and costs of OASS benefits. The correlations are robust to the inclusion of a large set of
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covariates, and hold up to instrumenting the subjective longevity measure, ruling out moral hazard. Thus we find convincing evidence that individuals’ private information about longevity significantly raises costs in an already struggling system.
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Acknowledgements
We are grateful to Susanto Basu for discussion and insightful suggestions in the early stages of this paper. We thank seminar participants at Boston College, Boston University, Northeastern University, the SOLE Annual Meetings 2013, University of Georgia, University of Rochester, Joe Altonji, David Autor, Laurent Bouton, David Dorn, Erzo F. P. Luttmer and James Poterba for helpful comments. Stacey Chan, Matthew Davis, Lauren Hoehn and Jinyong Jeong provided valuable research assistance. We gratefully acknowledge support from the Institute on Aging at Boston College. Remaining errors
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are our own.
References
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Atalay, Kadir and Garry F. Barrett, “The causal effect of retirement on health: New evidence from Australian pension reform,” Economics Letters, 2014, 125 (3), 392 – 395. Bloom, David E., David Canning, Michael Moore, and Younghwan Song, “The Effect of Subjective Survival Probabilities on Retirement and Wealth in the United States,” PGDA Working Papers 1706, Program on the Global Demography of Aging November 2006. Case, Anne and Cally Ardington, “The impact of parental death on school outcomes: Longitudinal evidence from South Africa,” Demography, August 2006, 43 (3), 401–420. Coe, Norma B. and Maarten Lindeboom, “Does Retirement Kill You? Evidence from Early Retirement Windows,” IZA Discussion Papers 3817, Institute for the Study of Labor (IZA) November 2008. Coile, Courtney, Peter Diamond, Jonathan Gruber, and Alain Jousten, “Delays in claiming social security benefits,” Journal of Public Economics, June 2002, 84 (3), 357–385. Finkelstein, Amy and James Poterba, “Adverse Selection in Insurance Markets: Policyholder Evidence from the U.K. Annuity Market,” Journal of Political Economy, February 2004, 112 (1), 183–208. and , “Testing for Asymmetric Information Using “Unused Observables” in Insurance Markets: Evidence from the U.K. Annuity Market,” Journal of Risk & Insurance, December 2014, 81 (4), 709–734. Gelbach, Jonah B., “When Do Covariates Matter? And Which Ones, and How Much?,” Journal of Labor Economics, 2016, 34 (2), 509–543. Gertler, Paul, David I. Levine, and Minnie Ames, “Schooling and Parental Death,” The Review of Economics and Statistics, February 2004, 86 (1), 211–225. Goss, Stephen C., “The Future Financial Status of Social Security,” Report, Social Security Office of Retirement and Disability Policy 2010. Hurd, Michael D and Kathleen McGarry, “Evaluation of the subjective probabilities of survival in the health and retirement study,” Journal of Human resources, 1995, pp. S268–S292. Hurd, Michael D. and Kathleen McGarry, “The Predictive Validity of Subjective Probabilities of Survival,” Economic Journal, October 2002, 112 (482), 966–985. , James P. Smith, and Julie M. Zissimopoulos, “The effects of subjective survival on retirement and Social Security claiming,” Journal of Applied Econometrics, 2004, 19 (6), 761–775. Insler, Michael, “The Health Consequences of Retirement,” Journal of Human Resources, 2014, 49 (1), 195–233. Lusardi, Annamaria and Olivia S. Mitchell, “Financial literacy around the world: an overview,” Journal of Pension Economics and Finance, 2011, 10 (4), 497?508. 9
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O’Donnell, Owen, Federica Teppa, and Eddy van Doorslaer, “Can subjective survival expectations explain retirement behaviour?,” DNB Working Papers 188, Netherlands Central Bank, Research Department November 2008. Shoven, John B. and Sita Nataraj Slavov, “Does it pay to delay social security?,” Journal of Pension Economics and Finance, 2014, 13 (2), 121?144. Skira, Meghan, “Dynamic Wage and Employment Effects of Elder Parent Care,” International Economic Review, Februaru 2015, 56 (1), 63–93.
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Table 1: Descriptive Means
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Longevity Cost of Retirement ($1000s)
Claiming Age 62 >62 62 >62 Objective Mortality Subjective Expectation 72.51 74.82** 79.57 80.24** 105.40 120.62**
0.11 0.06 0.09 0.04 0.13 0.46 0.75 11.65 0.97 0.17 1930
0.09 0.04** 0.05** 0.02 0.11 0.45 0.74 11.49 0.97 0.18 1928**
0.08 0.06 0.06 0.02 0.06 0.45 0.63 12.24 0.97 0.15 1934
0.06** 0.05** 0.05 0.02 0.05** 0.41 0.61 12.76** 0.97 0.16 1933**
Financials at Retirement (in $1000s) Social Security Age 62 Benefit ($) Capital Income ($) Housing Wealth ($) Non-housing Wealth ($) No Positive Wealth Private Pension Income ($) Missing Financials Zero Private Pension
11.50 10.93 87.47 150.01 0.05 5.35 0.59 0.35
11.74 14.53** 105.22** 176.69** 0.02** 5.38 0.66 0.29**
13.22 11.18 95.92 152.81 0.04 6.45 0.33 0.57
13.01 17.21** 119.14** 221.17** 0.03 6.59 0.32 0.56
Spouse: Subjective Longevity Longevity missing Death Age Alive SS Benefit SS Missing No SS Benefit Age Gap Age Gap Missing Age Gap X Female N
79.35 0.45 72.45 0.78 8.34 0.21 0.52 2.77 0.23 -0.10 891
79.77** 0.55** 72.76 0.77 9.12** 0.23 0.52 3.38** 0.25 0.30** 916
79.70 0.30 72.74 0.82 11.31 0.12 0.37 1.16 0.16 -0.89 2951
79.75 0.34** 72.67 0.84 11.20 0.14** 0.41** 2.40** 0.20** -0.23** 2821
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Health (Age 62) and Demographics Had Diabetes Had Cancer Had Heart Disease Had Stroke Had Lung Disease Had Arthritis Ever Smoke Education (years) Ever Married Minority Mean Birth Year
Note: Sample is restricted to men and women who did not claim SSDI Benefits prior to age 62, did claim OASS benefits. Sample includes those born after 1915 and before 1939. Objective sample size is 1807 claimants, subjective sample size is 5772 claimants. Dollar figures are inflated from the reporting year to 2010 using the CPI and are denoted in thousands. ** denotes significant difference claiming groups at the 5% level.
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Table 2: Correlation Test
Longevity Risk Correlated with: Annuity Choices Costs Claiming Claim at Age Age 62
N R2 /Pseudo R2
Death Age N R2 /Pseudo R2
0.062*** (0.012) 1807 0.133
0.019*** (0.004) 5772 0.074
Age-62 Benefit Level($)
Panel A:Objective Longevity Measure -0.013*** 0.015*** 10,958*** 390*** (0.004) (0.003) (382) (41.4) 1807 1807 1807 1807 0.051 0.087 0.467 0.069
Panel B: Subjective Longevity Measure -0.005*** 0.005*** 873** 72.44*** (0.001) (0.001) (370) (17.7) 5772 5772 1062 5772 0.020 0.044 0.257 0.014
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Death Age
Claim at Discounted Age ≥65 Costs($)
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Note: Objective longevity measure is observed death age; subjective measure is the mean of the individual distribution of subjective expectations of mortality. Costs are the discounted lifetime value of the observed retiree benefit. The first column is OLS of linear claiming age, column two and three are probit regressions, and column four is the linear regression of costs denominated in 2010 dollars. *,** and *** denote significance at the 10%, 5%, and 1% levels respectively. All regressions include cohort fixed-effects.
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Table 3: Correlation Decomposition
Linear Claiming Age Correlation Objective Subjective 0.062*** 0.0191*** (0.012) (0.006) 0.039** 0.008** (0.013) (0.004)
Longevity Coefficient: Model without Covariates Model with Covariates
% Raw Correlation Explained by: Annual Benefit Level Health History Demographics Occupation Financial Information I Financial Information II Spousal Characteristics Female Insurance N
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-0.130** 0.065 -0.030 0.071** 0.035 -0.021 0.351*** -0.072 0.018 1807
-0.058** 0.212*** 0.120** 0.155**** 0.095*** 0.038 0.061 -0.086*** 0.058 5772
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Note: Objective longevity measure is observed mortality; subjective measure is the mean of the individual distribution of subjective expectations of mortality. *,** and *** denote significance at the 10%, 5%, and 1% levels respectively. All Regressions include cohort fixed-effects.
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Table 4: Correlation Endogeneity
Objective Subjective IV-Subjective Without Covariates 0.062*** 0.019*** 0.069** (0.012) (0.004) (0.035)
Death Age
First-Stage Excluded Instrument Dad Death Age × 1{Dad Death Age > 62} N R2
1807 0.133
Death Age
0.039*** (0.013)
5772 0.074
With All Covariates 0.008** 0.049 (0.004) (0.037)
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First-Stage Excluded Instrument Dad Death Age × 1{ Dad Death Age > 62} N R2
1807 0.205
0.083*** (0.008) 5772 0.074
5772 0.141
0.076*** (0.009) 5772 0.162
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Note: Objective longevity measure is observed mortality; subjective measure is the mean of the individual distribution of subjective expectations of mortality. IV regressions without controls also include cohort fixed-effects, indicators for father still alive, and a linear paternal death age term for ages below 65, smoking, drinking, HRS elicited risk preferences, occupation indicators and completed schooling.. Regressions with controls include the same regressors and all variables listed in Table 1. *,** and *** denote significance at the 10%, 5%, and 1% levels respectively.
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Table 5: Adverse Selection, Wealth and Financial Literacy
Objective Subjective Without Covariates 0.0504*** 0.0628*** 0.0211*** 0.0192*** (0.012) (0.0129) (0.004) (0.004)
Mortality Mortality x 1(Wealth > $244) Mortality x Financially Illiterate
Mortality Mortality x 1(Wealth > $244)
N
-0.0250* (0.012)
-0.0668* (0.0320)
0.004 (0.0121)
0.0336* (0.013)
Without Covariates 0.0424** 0.0106* (0.0141) (0.004)
0.00768* (0.004)
0.124** (0.038)
-0.0191 (0.012)
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Mortality x Financially Illiterate
0.151*** (0.037)
-0.0553* (0.0317) 1807
1807
5772
-0.004 (0.0116) 5772
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Note: Dependent variable is claiming age. Objective longevity measure is observed mortality; subjective measure is the mean of the individual distribution of subjective expectations of mortality. Regressions without controls also include cohort fixed-effects. The mean wealth in the sample is $244. Financially Illiterate is an indicator equal to one if a respondent incorrectly answered the interest on savings question asked regularly in HRS beginning in 2002. Incorrect response was anything except $242, $240, $42, or $40. Regressions with controls include the same regressors and all variables listed in Table 1. *,** and *** denote significance at the 10%, 5%, and 1% levels respectively.
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PII: DOI: Reference:
S0165-1765(20)30031-8 https://doi.org/10.1016/j.econlet.2020.108995 ECOLET 108995
To appear in:
Economics Letters
Received date : 8 October 2019 Revised date : 14 January 2020 Accepted date : 26 January 2020 Please cite this article as: A. Beauchamp and M. Wagner, Is there adverse selection in the U.S. social security system?. Economics Letters (2020), doi: https://doi.org/10.1016/j.econlet.2020.108995. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier B.V.
Journal Pre-proof *Highlights (for review)
Unused observables tests for asymmetric information in US Social Security are presented.
lP repro of
Individuals who live longer, and those who expect to live longer, systematically claim annuity benefits at higher levels. Instrumental Variables estimates help to confirm adverse selection.
Jou
rna
Higher wealth, and financially literate, individuals delay claiming more in response to higher longevity.
Journal Pre-proof *Title Page
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Is There Adverse Selection in the U.S. Social Security System? Andrew Beauchamp∗ Wright State University
Mathis Wagner† Bates White Economic Consulting
December 12, 2019
Abstract
Despite facing some of the same challenges as private insurance markets, little is known about the role of adverse selection in Old-Age Social Security. Using data from the Health and Retirement Study, we perform the unused observables version
rna
of the positive correlation test, and find robust evidence that people who expect to live shorter lives both choose smaller annuities - by claiming benefits early - and are less costly to insure, implying adverse selection in the system. Results are consistent when using either subjective expectations or observed longevity. Decomposing
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the sources of adverse selection we find that health, demographics, occupation and financial information together account for much of the positive correlation between mortality and claiming. IV estimates help to rule out moral hazard. Keywords: Adverse Selection, Social Security, Optimal Policy.
JEL Classification: H55; J26; D82
∗
Corresponding author, 3640 Col Gen Hwy Dayton OH 45435, [email protected]. 2001 K Street NW North Building, Suite 500 Washington, DC 20006, [email protected]. The views expressed in this paper are solely those of the authors and do not necessarily reflect the opinions of Bates White or its clients. †
1
Journal Pre-proof *Manuscript Click here to view linked References
1
Introduction
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Recent reports indicate that the US Social Security Administration will only have enough resources to pay 75% of promised benefits as soon as 2035.1 In 2018, fully 20% of the federal budget in the US was spent on Old Age Social Security (OASS). Because OASS is an insurance against outliving assets, it is potentially subject to asymmetric information problems. We test for the presence of adverse selection in OASS using observed characteristics which are plausibly correlated with the underlying risk measure, and thus potentially with both insurance coverage and costs.2 Finkelstein and Poterba (2004, 2014) describe such variables as “unused observables.”3 Adverse selection in Social Security (hereafter SS) would arise if on average those with longer life expectancy (more risky individuals) systematically obtained more insurance (a larger annuity) by claiming their benefits later, conditional on the same earnings history. Establishing the presence of adverse selection is an important step in understanding the cost-structure the program faces today and in the future.
Testing for Adverse Selection
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2
We test whether individuals’ choice of annuity, as measured by the age at which they first claim (A), is correlated with underlying risk, as measured by longevity (θ) and the costs
1
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to SS (C). The estimating equations are:
Ai = µθi + εi ,
(1)
Ci = γθi + υi .
(2)
Chief Actuary Report, (2010) Adverse selection here is the choice of annuities with some foreknowledge of mortality likelihoods; moral hazard occurs when retiring earlier improves health and longevity. 3 The SSA is by law not allowed to use observables to price their annuity at any given age, though of course the level of benefits depends on a person’s earnings history. 2
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Statistically significant positive estimates of µ and γ imply the presence of adverse selection or moral hazard (opposite signs suggest advantageous selection). The set of condi-
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tioning variables are exclusively those observable characteristics that are used in pricing the insurance policy, but since SS charges a price equal to zero for claiming benefits, the simple regression is our starting point.4 It is worth emphasizing that the positive correlation test relies on identifying an equilibrium relationship between longevity and claiming, and costs. It does not require that longevity be exogenous.
The unused observables approach can provide information on the underlying source of asymmetric information. In particular, one can include a number of covariates in equation (1) that are predetermined before age 62. Equation (1) describes the selection of individuals into different SS annuities based on a measure of the underlying longevity risk. The degree to which this correlation is attenuated (or strengthened) by the inclusion of covariates is informative about how much of the selection can be unambiguously attributed to predetermined characteristics, ruling out moral hazard. The estimating equation is:
(3)
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Ai = µθi + Xi0 β + εi ,
where Xi is a set of predetermined individual characteristics. We apply order-invariant decomposition methods of Gelbach (2016), attributing to each group of covariates the percentage which they reduce (or increase) the raw correlation between claiming and
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longevity.
Our measures for the longevity are correlated with other factors that affect the OASS claiming age. The rich set of covariates included in the HRS enables us to control for many of these. One important covariate though is wealth, which is positively correlated with longevity and delayed claiming.5 By using detailed financial information we 4
Penalties for early claiming and the opportunity costs of waiting to retire make early claiming less attractive (all else equal), but they are not prices. Instead they shift both the demand for the annuity at any given age, as well as the cost of provision. 5 Shoven and Slavov (2014) calculate the financial gains to delayed claiming which are large for many individuals.
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present evidence below that wealth is unlikely to drive the bulk of the positive correlation, suggesting private information on longevity matters. Additionally, there will always
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be unobservables we are unable to control for (e.g. risk aversion, spousal labor market conditions, etc.). Using the unused observables approach it is possible to instrument the risk measure, providing evidence on whether the observed correlation can be considered causal, and therefore adverse selection and not moral hazard (which sees causation run the opposite direction).
We instrument for our proxies of longevity risk using parental death ages.6 This helps us identify a causal relationship between longevity risk and claiming age, as well as dealing with measurement error problems in the subjective measure. We use a spline in father’s death age as an instrument for longevity to ensure identification does not come from early paternal death, which is less likely to have biological causes.7
There are a number of legitimate concerns about parental longevity instrumenting for longevity which fall into three main categories: time use and income, health, and risk preferences. Firstly, it could have a direct impact on work status through the care needs
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of elderly parents. This is a greater concern for women than men, and our results are qualitatively robust for both sexes.8 Secondly, parental mortality could be correlated with the health status of individuals near retirement, and thereby claiming decisions. Our extensive health controls, and the fact that the IV-point estimates presented below are very similar with and without them, helps alleviate that concern. Thirdly, parental mortality
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may affect an individual’s human capital, occupation decisions and risk attitudes. To help deal with this we condition all our IV-estimates on occupation dummies, completed schooling, and risk attitude measures: smoking, drinking and the HRS elicited income 6 A sizable literature takes this approach. See Bloom et. al. (2006); Delavande, Perry and Willis (2006); and O’Donnell, Teppa and van Doorslaer (2008). Hurd and McGarry (1995, 2002) did early work on validating the use of the subjective life expectancy measure in the HRS. 7 Hurd and McGarry (1995), Gertler, Levine and Ames (2004), and Case and Ardington (2006). The spline leaves earlier paternal death ages in as an included instrument, but only identifies the effect of longevity expectations on retirement through individuals whose fathers died after age 65. 8 Skira (2015) shows that two-thirds of caregivers in the HRS are women.
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risk-preference rank.9 Finally, since earlier parental deaths are correlated with all three
after age sixty-five.
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concerns, we identify the effects of longevity off paternal deaths only from fathers passing
Finally, we use that fact that HRS asks an interest-rate calculation similar to that used in the “big three” financial literacy metrics popularized by Lusardi and Mitchel (2008). Specifically, it asks a respondent to calculate the principal on $200 after two years with 10% interest rate. This question has some ambiguities, namely it does not specify reinvestment of interest or clearly state if respondents should state principle and interest or interest.10 Given imperfections with this approach, we also examine selection patterns among respondents with high wealth levels who are more financially literate and more able to delay claiming.
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Data and Empirics
We use the Health and Retirement Study (HRS), a longitudinal study that has surveyed
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a representative sample of more than 26,000 Americans 51 years and older since 1992.11 The survey is representative of the cross-section of older Americans at any given point in time, but not of the longitudinal experience of particular cohorts. For this reason all analysis that follows uses cohort fixed-effects, and constrains attention to cohorts born between 1916 and 1938.
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The HRS’ comprehensive information is important for understanding the SS claiming decision including, health, demographics, wealth and spousal characteristics. They also contain observed mortality for respondents who died during the sampling period. We further construct a subjective longevity measure from questions on the probability of 9
Though not presented in the results below, all three are significantly correlated with both longevity and claiming. 10 We therefore, we categorize individuals as financially illiterate if they did not answer one of the following (242, 240, 42 or 40) 11 Data come from the RAND HRS Data file.
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living to various ages.12 One sample consists of 1807 individuals with observed mortality, another has 5772 individuals with subjective longevity measures, all of whom did not
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claim disability status prior to retirement.
Table 1 provides descriptive statistics for the two samples and lists the data used below. Around 50 percent of the sample claim benefits at age sixty-two, so we split the sample there. The first two rows show the simple positive correlation test (PCT): claiming age is positively correlated with costs and longevity.13 The descriptives tell the story: later claimants are healthier, especially on life-threatening conditions (e.g. cancer, heart and lung disease), despite being older. In financial terms later claimants can finance delayed claiming, they have substantially higher assets and incomes. In terms of spousal characteristics, later claimants’ spouses likely exacerbate the adverse selection problem: they have higher benefit levels and longer-life spans as well.
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Model Estimates
We present the results of the basic PCT in Table 2. The first three columns show results
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for different claiming decisions; Column 4’s dependent variable is the present discounted value of costs to the SSA; Column 5 shows the annual benefit payment the individual would have received if claiming at age 62. Panel A uses observed (objective) mortality and Panel B mean subjective mortality.
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The results show individuals with longer life expectancies claim benefits later.14 Objectively living one year longer is correlated with claiming three-quarters of a month later, a 1.3 percentage point lower likelihood of claiming at first eligibility, and a 1.5 percentage point higher likelihood of claiming at 65. It is also correlated with $10,958 in additional This mean was constructed as θisubj = .5∗(Awaveobs +75)∗P (θi < 75)+80∗(P (θi ∈ [75, 85])+90∗P (θi > 85), using different responses depending on the respondent’s age at survey. 13 Individuals who died before claiming had 40% lower SS benefit levels than those who claimed at age 62, meaning the adverse selection problem persists even if we expanded the sample to include those who died before claiming. 14 Consistent with Coile, Diamond, Gruber and Jousten (2002), Hurd, Smith and Zissimopoulos (2004). 12
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costs to the SSA and $390 in higher annual benefit payments. Taken together the re-
the timing of claims.
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sults provide clear evidence of asymmetric information being important in determining
Table 3 decomposes of the longevity-claiming correlation into observables. The lower panel reports how much of the correlation can be attributed to different covariate-groups. Including benefit levels increases the correlation, thus individuals with higher average lifetime earnings claimed earlier but died later (conditional on other covariates), reducing program costs (negative signs mean advantageous selection). Objective mortality shows spousal characteristics explain about one-third of the correlation. Subjective expectations show the explained portion of the correlation is driven by the health, occupation, and demographic information.
Table 4 presents IV estimates of Equation (1). The subjective measure shows the firststage is highly significant. The coefficient indicates subjective life expectancy increases by more than a month for every year ones’ father lives past age 65. The IV estimates in both panels are similar to the correlation using the objective measure (though no longer
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significant in the lower panel).15 In the upper panel, the magnitudes are remarkably similar between the objective and IV-subjective, suggesting measurement error in subjective longevity may be substantial. Nonetheless the IV-results suggest that the correlation is driven primarily by adverse selection, since with moral hazard the causation runs from annuity choice to longevity. In the US, Coe and Lindeboom (2008) find no negative effects
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of early retirement on health and Insler (2014) finds that the retirement effect on health is beneficial. Recent evidence from Australia (Atalay and Barret (2014)) point to very similar findings: health improves following retirement. The heterogeneity results are included in Table 5. At least with respect to objective longevity, the patterns are quite clear. Individuals with more wealth are much more likely to adversely select their social security claiming decisions (the PCT is much larger). 15
The first-stage correlation between the objective longevity and parental death age is insignificant, perhaps due to small sample sizes, and is therefore omitted.
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Similarly, individuals who had incorrectly answered the interest rate question had virtually no correlation between longevity and claiming age with all the effects concentrated among
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the rest of the sample. With respect to subjective longevity we see a less clear picture: mixed evidence that higher wealth individuals had a more attenuated correlation between claiming and mortality; no evidence that financial literacy matters. However, these results are also less robust since the inclusion of covariates eliminates their significance.
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Conclusions
Overall, we provide clear evidence that life expectancy is correlated with both claiming age and the cost to the insurer. Based on observed mortality, we find that living one year later is correlated with claiming three-quarters of a month later. Also, the costs to the Social Security trust fund are roughly $10,000 higher. Taken together the results provide evidence of asymmetric information being an important determinant in the timing and costs of OASS benefits. The correlations are robust to the inclusion of a large set of
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covariates, and hold up to instrumenting the subjective longevity measure, ruling out moral hazard. Thus we find convincing evidence that individuals’ private information about longevity significantly raises costs in an already struggling system.
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Acknowledgements
We are grateful to Susanto Basu for discussion and insightful suggestions in the early stages of this paper. We thank seminar participants at Boston College, Boston University, Northeastern University, the SOLE Annual Meetings 2013, University of Georgia, University of Rochester, Joe Altonji, David Autor, Laurent Bouton, David Dorn, Erzo F. P. Luttmer and James Poterba for helpful comments. Stacey Chan, Matthew Davis, Lauren Hoehn and Jinyong Jeong provided valuable research assistance. We gratefully acknowledge support from the Institute on Aging at Boston College. Remaining errors
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are our own.
References
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Atalay, Kadir and Garry F. Barrett, “The causal effect of retirement on health: New evidence from Australian pension reform,” Economics Letters, 2014, 125 (3), 392 – 395. Bloom, David E., David Canning, Michael Moore, and Younghwan Song, “The Effect of Subjective Survival Probabilities on Retirement and Wealth in the United States,” PGDA Working Papers 1706, Program on the Global Demography of Aging November 2006. Case, Anne and Cally Ardington, “The impact of parental death on school outcomes: Longitudinal evidence from South Africa,” Demography, August 2006, 43 (3), 401–420. Coe, Norma B. and Maarten Lindeboom, “Does Retirement Kill You? Evidence from Early Retirement Windows,” IZA Discussion Papers 3817, Institute for the Study of Labor (IZA) November 2008. Coile, Courtney, Peter Diamond, Jonathan Gruber, and Alain Jousten, “Delays in claiming social security benefits,” Journal of Public Economics, June 2002, 84 (3), 357–385. Finkelstein, Amy and James Poterba, “Adverse Selection in Insurance Markets: Policyholder Evidence from the U.K. Annuity Market,” Journal of Political Economy, February 2004, 112 (1), 183–208. and , “Testing for Asymmetric Information Using “Unused Observables” in Insurance Markets: Evidence from the U.K. Annuity Market,” Journal of Risk & Insurance, December 2014, 81 (4), 709–734. Gelbach, Jonah B., “When Do Covariates Matter? And Which Ones, and How Much?,” Journal of Labor Economics, 2016, 34 (2), 509–543. Gertler, Paul, David I. Levine, and Minnie Ames, “Schooling and Parental Death,” The Review of Economics and Statistics, February 2004, 86 (1), 211–225. Goss, Stephen C., “The Future Financial Status of Social Security,” Report, Social Security Office of Retirement and Disability Policy 2010. Hurd, Michael D and Kathleen McGarry, “Evaluation of the subjective probabilities of survival in the health and retirement study,” Journal of Human resources, 1995, pp. S268–S292. Hurd, Michael D. and Kathleen McGarry, “The Predictive Validity of Subjective Probabilities of Survival,” Economic Journal, October 2002, 112 (482), 966–985. , James P. Smith, and Julie M. Zissimopoulos, “The effects of subjective survival on retirement and Social Security claiming,” Journal of Applied Econometrics, 2004, 19 (6), 761–775. Insler, Michael, “The Health Consequences of Retirement,” Journal of Human Resources, 2014, 49 (1), 195–233. Lusardi, Annamaria and Olivia S. Mitchell, “Financial literacy around the world: an overview,” Journal of Pension Economics and Finance, 2011, 10 (4), 497?508. 9
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O’Donnell, Owen, Federica Teppa, and Eddy van Doorslaer, “Can subjective survival expectations explain retirement behaviour?,” DNB Working Papers 188, Netherlands Central Bank, Research Department November 2008. Shoven, John B. and Sita Nataraj Slavov, “Does it pay to delay social security?,” Journal of Pension Economics and Finance, 2014, 13 (2), 121?144. Skira, Meghan, “Dynamic Wage and Employment Effects of Elder Parent Care,” International Economic Review, Februaru 2015, 56 (1), 63–93.
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Table 1: Descriptive Means
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Longevity Cost of Retirement ($1000s)
Claiming Age 62 >62 62 >62 Objective Mortality Subjective Expectation 72.51 74.82** 79.57 80.24** 105.40 120.62**
0.11 0.06 0.09 0.04 0.13 0.46 0.75 11.65 0.97 0.17 1930
0.09 0.04** 0.05** 0.02 0.11 0.45 0.74 11.49 0.97 0.18 1928**
0.08 0.06 0.06 0.02 0.06 0.45 0.63 12.24 0.97 0.15 1934
0.06** 0.05** 0.05 0.02 0.05** 0.41 0.61 12.76** 0.97 0.16 1933**
Financials at Retirement (in $1000s) Social Security Age 62 Benefit ($) Capital Income ($) Housing Wealth ($) Non-housing Wealth ($) No Positive Wealth Private Pension Income ($) Missing Financials Zero Private Pension
11.50 10.93 87.47 150.01 0.05 5.35 0.59 0.35
11.74 14.53** 105.22** 176.69** 0.02** 5.38 0.66 0.29**
13.22 11.18 95.92 152.81 0.04 6.45 0.33 0.57
13.01 17.21** 119.14** 221.17** 0.03 6.59 0.32 0.56
Spouse: Subjective Longevity Longevity missing Death Age Alive SS Benefit SS Missing No SS Benefit Age Gap Age Gap Missing Age Gap X Female N
79.35 0.45 72.45 0.78 8.34 0.21 0.52 2.77 0.23 -0.10 891
79.77** 0.55** 72.76 0.77 9.12** 0.23 0.52 3.38** 0.25 0.30** 916
79.70 0.30 72.74 0.82 11.31 0.12 0.37 1.16 0.16 -0.89 2951
79.75 0.34** 72.67 0.84 11.20 0.14** 0.41** 2.40** 0.20** -0.23** 2821
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Health (Age 62) and Demographics Had Diabetes Had Cancer Had Heart Disease Had Stroke Had Lung Disease Had Arthritis Ever Smoke Education (years) Ever Married Minority Mean Birth Year
Note: Sample is restricted to men and women who did not claim SSDI Benefits prior to age 62, did claim OASS benefits. Sample includes those born after 1915 and before 1939. Objective sample size is 1807 claimants, subjective sample size is 5772 claimants. Dollar figures are inflated from the reporting year to 2010 using the CPI and are denoted in thousands. ** denotes significant difference claiming groups at the 5% level.
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Table 2: Correlation Test
Longevity Risk Correlated with: Annuity Choices Costs Claiming Claim at Age Age 62
N R2 /Pseudo R2
Death Age N R2 /Pseudo R2
0.062*** (0.012) 1807 0.133
0.019*** (0.004) 5772 0.074
Age-62 Benefit Level($)
Panel A:Objective Longevity Measure -0.013*** 0.015*** 10,958*** 390*** (0.004) (0.003) (382) (41.4) 1807 1807 1807 1807 0.051 0.087 0.467 0.069
Panel B: Subjective Longevity Measure -0.005*** 0.005*** 873** 72.44*** (0.001) (0.001) (370) (17.7) 5772 5772 1062 5772 0.020 0.044 0.257 0.014
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Death Age
Claim at Discounted Age ≥65 Costs($)
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Note: Objective longevity measure is observed death age; subjective measure is the mean of the individual distribution of subjective expectations of mortality. Costs are the discounted lifetime value of the observed retiree benefit. The first column is OLS of linear claiming age, column two and three are probit regressions, and column four is the linear regression of costs denominated in 2010 dollars. *,** and *** denote significance at the 10%, 5%, and 1% levels respectively. All regressions include cohort fixed-effects.
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Table 3: Correlation Decomposition
Linear Claiming Age Correlation Objective Subjective 0.062*** 0.0191*** (0.012) (0.006) 0.039** 0.008** (0.013) (0.004)
Longevity Coefficient: Model without Covariates Model with Covariates
% Raw Correlation Explained by: Annual Benefit Level Health History Demographics Occupation Financial Information I Financial Information II Spousal Characteristics Female Insurance N
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-0.130** 0.065 -0.030 0.071** 0.035 -0.021 0.351*** -0.072 0.018 1807
-0.058** 0.212*** 0.120** 0.155**** 0.095*** 0.038 0.061 -0.086*** 0.058 5772
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Note: Objective longevity measure is observed mortality; subjective measure is the mean of the individual distribution of subjective expectations of mortality. *,** and *** denote significance at the 10%, 5%, and 1% levels respectively. All Regressions include cohort fixed-effects.
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Table 4: Correlation Endogeneity
Objective Subjective IV-Subjective Without Covariates 0.062*** 0.019*** 0.069** (0.012) (0.004) (0.035)
Death Age
First-Stage Excluded Instrument Dad Death Age × 1{Dad Death Age > 62} N R2
1807 0.133
Death Age
0.039*** (0.013)
5772 0.074
With All Covariates 0.008** 0.049 (0.004) (0.037)
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First-Stage Excluded Instrument Dad Death Age × 1{ Dad Death Age > 62} N R2
1807 0.205
0.083*** (0.008) 5772 0.074
5772 0.141
0.076*** (0.009) 5772 0.162
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Note: Objective longevity measure is observed mortality; subjective measure is the mean of the individual distribution of subjective expectations of mortality. IV regressions without controls also include cohort fixed-effects, indicators for father still alive, and a linear paternal death age term for ages below 65, smoking, drinking, HRS elicited risk preferences, occupation indicators and completed schooling.. Regressions with controls include the same regressors and all variables listed in Table 1. *,** and *** denote significance at the 10%, 5%, and 1% levels respectively.
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Table 5: Adverse Selection, Wealth and Financial Literacy
Objective Subjective Without Covariates 0.0504*** 0.0628*** 0.0211*** 0.0192*** (0.012) (0.0129) (0.004) (0.004)
Mortality Mortality x 1(Wealth > $244) Mortality x Financially Illiterate
Mortality Mortality x 1(Wealth > $244)
N
-0.0250* (0.012)
-0.0668* (0.0320)
0.004 (0.0121)
0.0336* (0.013)
Without Covariates 0.0424** 0.0106* (0.0141) (0.004)
0.00768* (0.004)
0.124** (0.038)
-0.0191 (0.012)
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Mortality x Financially Illiterate
0.151*** (0.037)
-0.0553* (0.0317) 1807
1807
5772
-0.004 (0.0116) 5772
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Note: Dependent variable is claiming age. Objective longevity measure is observed mortality; subjective measure is the mean of the individual distribution of subjective expectations of mortality. Regressions without controls also include cohort fixed-effects. The mean wealth in the sample is $244. Financially Illiterate is an indicator equal to one if a respondent incorrectly answered the interest on savings question asked regularly in HRS beginning in 2002. Incorrect response was anything except $242, $240, $42, or $40. Regressions with controls include the same regressors and all variables listed in Table 1. *,** and *** denote significance at the 10%, 5%, and 1% levels respectively.
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