Social Security Claiming Decision Model

[alanlujan91]

Summary

Claiming Social Security a year early reduces benefits by roughly 7%, yet nearly 30% of men and 34% of women claim at 62, the earliest eligible age. HARK has lifecycle consumption-saving models and health-dependent mortality (BasicHealthConsumerType, MarkovConsumerType) but no model of this claiming decision. The agent must choose when to begin collecting benefits between ages 62 and 70, trading off smaller payments sooner against larger payments later, with early-claiming reductions of 5-6.7% per year and delayed retirement credits of 8% per year. Because claiming is irreversible, the decision interacts with longevity risk, health status, spousal benefits, portfolio withdrawal sequencing, and the retirement earnings test.

Connection to Financial Services Practice

The wealth-management plugin financial-plan skill (wealth-management/skills/financial-plan/SKILL.md) explicitly models Social Security timing as a "major lever" in retirement planning, requiring scenario analysis at claiming ages 62, 67, and 70. The skill computes retirement projections with Monte Carlo simulation, targeting an 85%+ probability of portfolio survival, and notes that Social Security start age is one of the largest determinants of that probability. A HARK model would replace the breakeven-age heuristic with an optimized policy function that accounts for health risk, tax interactions, and portfolio feedback.

Mathematical Model

Environment

Time is discrete, indexed by age $t \in {t_0, t_0+1, \ldots, T}$ with working life beginning at $t_0$ and maximum age $T$. The agent can claim Social Security at any integer age in the window $[\underline{t}, \bar{t}]$, where $\underline{t} = 62$ is the earliest eligibility age and $\bar{t} = 70$ is the age at which delayed retirement credits cease. The claiming decision is irreversible: once benefits begin, they continue (with cost-of-living adjustments) for life.

State Variables

The individual state is $(a_t, h_t, z_t, \chi_t, t)$, where we denote by $a_t$ financial wealth, by $h_t \in {1, 2, \ldots, H}$ a discrete health state (e.g., good, fair, poor), by $z_t$ a persistent income state governing earnings during the working years, and by $\chi_t \in {0, 1}$ the Social Security claiming indicator (0 = not yet claimed, 1 = claimed). Once $\chi_t = 1$, the claiming age $t^* \leq t$ is recorded and determines the permanent benefit level.

Social Security Benefit Formula

The Primary Insurance Amount (PIA) is determined by the agent's earnings history and is treated as a known constant at the time of the claiming decision. The actual monthly benefit depends on the claiming age $t^$ through the actuarial adjustment factor $\Lambda(t^)$:

$$b(t^_) = \text{PIA} \cdot \Lambda(t^_)$$

The adjustment factor follows the statutory formula:

$$\Lambda(t^_) = \begin{cases} 1 - \frac{5}{9} \cdot \frac{1}{100} \cdot \min(36, ; 12(t^{\text{FRA}} - t^_)) - \frac{5}{12} \cdot \frac{1}{100} \cdot \max(0, ; 12(t^{\text{FRA}} - t^_) - 36) & \text{if } t^_ < t^{\text{FRA}} \[6pt] 1 + 0.08 \cdot (t^* - t^{\text{FRA}}) & \text{if } t^* \geq t^{\text{FRA}} \end{cases}$$

where the Full Retirement Age $t^{\text{FRA}}$ is 67 for those born after 1960. This yields approximate values: $\Lambda(62) \approx 0.70$, $\Lambda(65) \approx 0.867$, $\Lambda(67) = 1.00$, $\Lambda(70) \approx 1.24$.

Health Dynamics and Mortality

Health evolves as a first-order Markov chain with age-dependent transition matrix:

$$\Pr(h_{t+1} = h' \mid h_t = h) = \Pi_t(h, h')$$

The survival probability depends on current health:

$$\varsigma_t(h) = \Pr(\text{alive at } t+1 \mid \text{alive at } t, ; h_t = h)$$

Poor health both increases mortality risk and shifts the optimal claiming age earlier (shorter expected collection period makes early claiming relatively more attractive).

Preferences

$$u(c) = \frac{c^{1-\rho}}{1-\rho}$$

with relative risk aversion $\rho$ and warm-glow bequest motive $\Phi(a) = \vartheta \frac{(a + \underline{a})^{1-\rho}}{1-\rho}$ upon death, where $\vartheta$ governs bequest intensity.

Recursive Formulation

Before claiming ($\chi_t = 0$, $t \in [\underline{t}, \bar{t}]$): The agent makes a joint consumption-claiming decision.

$$V_t(a, h, 0) = \max\bigl{V_t^{\text{wait}}(a, h),; V_t^{\text{claim}}(a, h, t)\bigr}$$

If the agent waits ($\chi_t$ remains 0):

$$V_t^{\text{wait}}(a, h) = \max_{c} ; u(c) + \beta, \varsigma_t(h) \sum_{h'} \Pi_t(h, h') , V_{t+1}(a', h', 0) + \beta\bigl(1 - \varsigma_t(h)\bigr) \Phi(a')$$

subject to

$$a' = R(a - c) + Y(z, t)$$

where $Y(z, t)$ is after-tax income (labor income if still working, zero if retired from labor but not yet claiming Social Security).

If the agent claims (sets $\chi_t = 1$ with claiming age $t^* = t$):

$$V_t^{\text{claim}}(a, h, t) = \max_{c} ; u(c) + \beta, \varsigma_t(h) \sum_{h'} \Pi_t(h, h') , V_{t+1}(a', h', b) + \beta\bigl(1 - \varsigma_t(h)\bigr) \Phi(a')$$

subject to

$$a' = R(a - c) + Y(z, t) + b(t)$$

where $b = b(t^*)$ is the permanent benefit level computed at the moment of claiming and carried forward as a scalar state.

At age $\bar{t} = 70$, claiming is forced: $V_{\bar{t}}(a, h, 0) = V_{\bar{t}}^{\text{claim}}(a, h, \bar{t})$.

After claiming ($\chi_t = 1$): The agent receives the fixed real benefit $b(t^*)$ each period.

$$V_t(a, h, b) = \max_{c} ; u(c) + \beta, \varsigma_t(h) \sum_{h'} \Pi_t(h, h') , V_{t+1}(a', h', b) + \beta\bigl(1 - \varsigma_t(h)\bigr) \Phi(a')$$

subject to

$$a' = R(a - c) + b(t^*)$$

For ages $t < \underline{t} = 62$, the claiming option is unavailable ($\chi_t = 0$ is forced), and the agent solves a standard consumption-saving problem with stochastic income and health transitions.

Extension: Couples and Spousal Benefits

For a married couple with PIA values $\text{PIA}_1$ and $\text{PIA}_2$, the state space expands to $(a_t, h_t^1, h_t^2, \chi_t^1, \chi_t^2)$. The spousal benefit follows the dual-entitlement rule: spouse $i$ receives the greater of their own retired-worker benefit and the spousal supplement. The total spousal benefit is:

$$b_i^{\text{spousal}} = \max\bigl(\text{PIA}_i \cdot \Lambda(t_i^*),; \tfrac{1}{2}\text{PIA}_j\bigr)$$

where the spousal supplement is reduced for early claiming by a different schedule than own-record benefits (maximum reduction of 35% at age 62 for FRA 67).

The survivor benefit upon the death of spouse $j$ gives the survivor the larger of their own benefit or the deceased's benefit, subject to a floor of 82.5% of the deceased's PIA if the deceased claimed before FRA:

$$b_i^{\text{surv}} = \max\bigl(b_i(t_i^_),; \max(b_j(t_j^_),; 0.825 \cdot \text{PIA}_j)\bigr)$$

The joint claiming decision $(t^_1, t^_2)$ is the key object of interest. Common heuristics (e.g., "the higher earner should delay to 70") emerge as approximate solutions.

Extension: Retirement Earnings Test

For claimants below the Full Retirement Age who continue to earn labor income $Y_t^{\text{labor}}$, Social Security benefits are reduced:

$$b^{\text{net}}_t = \max\bigl(0,; b(t^*) - \tfrac{1}{2}\max(Y_t^{\text{labor}} - \bar{Y}, 0)\bigr)$$

where the exempt amount is $\bar{Y}$ (approximately $22,320 in 2024). Withheld benefits are returned later through an actuarial adjustment, making the earnings test approximately actuarially fair; yet many retirees treat it as a tax, which distorts claiming and labor supply decisions.

Key References

• Coile, C., Diamond, P., Gruber, J., and Jousten, A. (2002). "Delays in Claiming Social Security Benefits." Journal of Public Economics, 84(3), pp. 357-385.
• Shoven, J. B. and Slavov, S. N. (2014). "Does It Pay to Delay Social Security?" Journal of Pension Economics and Finance, 13(2), pp. 121-144.
• Horneff, V., Maurer, R., Mitchell, O. S., and Rogalla, R. (2015). "Optimal Life Cycle Portfolio Choice with Variable Annuities Offering Liquidity and Investment Downside Protection." Insurance: Mathematics and Economics, 63, pp. 91-107.
• Sass, S. A., Sun, W., and Webb, A. (2013). "Social Security Claiming Decision of Married Men and Widow Poverty." Economics Letters, 119(1), pp. 20-23.
• Gustman, A. L. and Steinmeier, T. L. (2005). "The Social Security Early Entitlement Age in a Structural Model of Retirement and Wealth." Journal of Public Economics, 89(2-3), pp. 441-463.
• Kotlikoff, L. J., Moeller, P., and Solman, P. (2015). Get What's Yours: The Secrets to Maxing Out Your Social Security. Simon & Schuster.
• Iskhakov, F., Jørgensen, T. H., Rust, J., and Schjerning, B. (2017). "The Endogenous Grid Method for Discrete-Continuous Dynamic Choice Models with (or without) Taste Shocks." Quantitative Economics, 8(2), pp. 317-365.

Implementation Notes

• Claiming status $\chi_t$ is a Markov state with an absorbing state (once claimed, always claimed), fitting HARK's MarkovConsumerType architecture.
• Continuous state $(a, h)$ with discrete $\chi$ can be solved with EGM on the consumption choice, using the upper envelope method for the discrete claiming choice (DC-EGM, Iskhakov et al. 2017).
• Health transitions and heterogeneous mortality connect directly to BasicHealthConsumerType.
• For the couples extension, state space $(a, h^1, h^2, \chi^1, \chi^2)$ is 5-dimensional with some discrete components, tractable with HARK's grid-based approach.
• Natural calibration exercise: compare HARK's optimal claiming policy to the heuristic "delay to 70 if healthy and high-PIA" and quantify the welfare loss from suboptimal claiming.
• Connects to tax-differentiated accounts (Issue Tax-Differentiated Account Model (401k/IRA/Roth/Taxable) #1731), where withdrawal sequencing interacts with claiming timing through the tax bracket, and shares health transition structure with the insurance model (Issue Endogenous Insurance Purchase Model (Health/Life/LTC) #1734).