Summary
Lee and Tuljapurkar build the first fully stochastic (probabilistic) forecast of Social Security (Old-Age, Survivors, and Disability Insurance; OASDI) finances, combining the Lee-Carter stochastic mortality model with stochastic fertility and time-series models for productivity growth and interest rates. Running 750 simulated sample paths from 1995 to 2070, they find the trust fund exhausts on average three years earlier than the Social Security Administration (SSA) projects (2026 vs. 2029), the Long-Term Actuarial Balance is more negative (−3.3 percentage points (pp) vs. SSA's −2.2 pp), and fertility — not mortality — is the dominant source of 75-year uncertainty, reversing SSA's ranking exactly.
Key Claims
- Lee-Carter mortality projections: Mean life expectancy at birth (e0) rises from 76 to 86 by 2070 — twice SSA's projected gain. 95% confidence interval (CI): 81–90 years. SSA's intermediate projection falls near the lower bound of the Lee-Tuljapurkar interval.
- Stochastic components: Mortality via Lee-Carter (random walk with drift for k(t)); fertility with long-term mean constrained to SSA's 1.9 children/woman, 95% CI converging to 0.7–3.3; productivity growth and interest rates as undifferenced first-order autoregressive (AR(1)) processes with long-run means equal to SSA's middle assumptions (1% and 2.3%/year). Net immigration held fixed at SSA levels. 750 Monte Carlo sample paths, 1995–2070.
- Trust fund exhaustion: Mean fund crosses zero in 2026, three years before SSA's 2029 projection. 95% interval: 2014–2037, with some sample paths never reaching exhaustion. Reserve fund peaks at $1.3 trillion on average (1996 dollars); 95% CI includes $0.57T–$4.0T.
- Post-exhaustion debt: If unchecked, mean debt grows to $26T by 2070; 95% CI: $6–60T; median = 3× payroll; upper bound = 12× payroll. Authors note these figures are theoretical — policy would respond before this scale.
- Long-Term Actuarial Balance (LTAB): Lee-Tuljapurkar preferred mean = −3.3 pp (vs. SSA's −2.2 pp). When model is constrained to SSA's mortality assumptions, result is −2.3 pp — validating the calibration against SSA's own figures. SSA high-low range: +0.5 to −5.7 pp (width 6.1 pp). Lee-Tuljapurkar 95% CI: −0.2 to −6.5 pp (width 6.3 pp) — similar width but centered ~1.1 pp lower.
- Payroll tax to maintain year-ahead balance: Median rises from 12.4% (current) to ~21% by 2070 as the baby boom retires. P97.5 (the 97.5th percentile) reaches 34% by 2070 (SSA high-cost: 28%). P2.5 (2.5th percentile) rises modestly to ~16% by 2070 (SSA low-cost: 13%).
- Tax hike to reduce exhaustion risk: Immediate +2 pp (to 14.4%) → still 74% of sample paths exhaust by 2070. Immediate +4 pp → 22% exhaustion probability. Reducing exhaustion to 5% requires immediate +5 pp. The LTAB-implied 2.2 pp increase falls far short of eliminating exhaustion risk.
- Uncertainty decomposition (75-year horizon): fertility > productivity growth > interest rates > mortality. SSA's high/medium/low sensitivity ranking is the exact reverse: mortality first, fertility last. Rankings differ partly because SSA varies one factor at a time while holding others fixed, whereas the stochastic approach allows joint variation.
- Demographic share of total uncertainty: At 25 years, fertility+mortality alone generates a standard deviation (SD) = 1/5 of the fully stochastic model. At 75 years, it generates ~2/3 of the fully stochastic model. Economic uncertainty dominates short-run variance; demographic uncertainty dominates long-run variance.
Concepts Introduced or Extended
Entities Mentioned
Quotes
"Long-run decline of fertility and mortality will lead to secular aging of the U.S. population, punctuated by the retirement of the baby-boom generations in the early 21st century. These changes will severely stress our Social Security system."
"The main message, however, is uncertainty about this crossing point: the 95-percent interval includes fund exhaustion as early as 2014, as well as exhaustion as late as 2037, with some sample paths never reaching exhaustion."
"We find it more interesting and useful to ask different questions and forecast different quantities."
My Take
The paper's most important contribution is not the point forecast (mean exhaustion 2026 vs. SSA's 2029 — a modest three-year discrepancy) but the uncertainty decomposition and its policy implications. The finding that fertility dominates 75-year LTAB uncertainty while SSA ranks it last matters enormously for which policy levers deserve priority. The asymmetry between the two methods is starker than it appears: SSA's sensitivity analysis holds all other inputs fixed at middle values, while Lee-Tuljapurkar allows joint variation — a methodologically superior comparison. The paper also exposes a structural flaw in the LTAB as a communication tool: it implies a manageable 2.2 pp adjustment when the actual distribution of outcomes spans from near-zero need to a 5+ pp requirement. Figure 1 — showing the fan of payroll tax rates needed for year-ahead balance — is the more honest picture of the fiscal challenge.