Lee, Miller, and Anderson 2004 — Stochastic Infinite Horizon Forecasts for Social Security and Related Studies

Summary

Lee, Miller, and Anderson (2004) extend the Lee-Tuljapurkar stochastic Social Security forecasting framework in three directions: (I) stochastic immigration forecasts — which add negligible uncertainty to the old-age dependency ratio; (II) structural time series and parameter uncertainty for wage growth and fertility — which matter for individual inputs but little for integrated Social Security (SS) solvency; and (III) a 500-year stochastic infinite horizon actuarial balance estimate of −5.15% of payroll, substantially exceeding the 2004 Trustees Report's −3.5% primarily due to different (higher) mortality improvement assumptions. The paper demonstrates that the standard 75-year Actuarial Balance ($AB_{75}$ = 1.92%) is not a sustainability measure, and identifies the "Unstable measure" as a reliable 75-year-based approximation for the infinite horizon central estimate. NBER Working Paper No. 10917.

Key Claims

• Stochastic immigration makes negligible difference to solvency: Adding stochastic immigration to the stochastic population model has essentially no effect on the probability distribution of the old-age dependency ratio. Preferred immigration forecast: net flow drops from ~1.2M to ~1M by 2020, then slowly rises to 1.2M by 2100 (95% probability interval [PI]: 800K–1.8M). All major agencies (SSA, Census, UN) forecast a break with historical rising trend; Lee-Miller incorporate uncertainty by drawing trend from a uniform distribution between zero and the historical estimate.
• Parameter uncertainty in inputs matters little for the integrated projection: Adding parameter uncertainty, uncertain ultimate values, and structural (state-space) time series specifications to wage growth and fertility models sometimes substantially changes individual input probability intervals but makes relatively little difference to the full Old-Age, Survivors, and Disability Insurance (OASDI) solvency distribution. This confirms the robustness of the Lee-Tuljapurkar framework: offsetting uncertainties across four stochastic inputs (fertility, mortality, wages, interest rates) moderate the total SS forecast uncertainty.
• 75-year $AB_{75}$ is not a sustainability measure: Raising the payroll tax by the 2004 $AB_{75}$ (1.92%) leaves the median Trust Fund ratio going negative by 2074, declining to −82 times annual costs by 2200. The $AB_{75}$ achieves "balance" only within the 75-year window by construction — it does not indicate what is needed for long-run sustainability.
• 500-year stochastic median infinite horizon: −5.15% of payroll. The 2004 Trustees Report infinite horizon estimate is −3.5%; Lee et al. estimate −5.15% using their own mortality projections (based on the Lee-Carter / Lee-Miller 2001 implementation). The difference (~1.6 percentage points [pp]) is almost entirely attributable to different mortality assumptions, consistent with Lee and Yamagata (2003), who showed mortality accounts for ~1–2% of the infinite horizon gap vs. only ~0.5% over 75 years.
• 95% probability interval: −1.3% to −10.5% (range 9%), about 40% wider than the 75-year interval (6.5%). "Routine" uncertainty — conditional on structural continuity — understates true uncertainty because it excludes structural breaks, regime changes, and technological discontinuities.
• Flat Fund Ratio Tax (4.36%) underestimates; Unstable measure (5.21%) approximates well. The Flat Fund Ratio Tax (the immediate and permanent tax increase needed to keep Trust Fund/Costs constant at the 75-year horizon) underestimates the infinite horizon imbalance when costs grow faster than revenues. The Unstable measure — which extrapolates the end-of-projection growth rates of costs and revenues indefinitely — gives a median of 5.21%, very close to the 500-year result of 5.15%, and is thus the recommended approximation for central tendency. Flat Fund Ratio correlation with 500-year outcome is essentially zero.
• Cost of delay is exponential: At a residual discount rate of 1.4%/year (= 3% real interest − 1.1% wage growth − 0.5% population growth), a 1% payroll tax increase now is worth 2× as much as one in 50 years and ~70× as much as one in 300 years. Early adjustment has much greater expected fiscal impact than delayed adjustment.
• Immediate fix creates Trust Fund accumulation problem: Raising taxes by the full 5.15% now leads to Trust Fund accumulations approaching 150% of GDP by the 2070s (mean exceeds 170% by late 2070s, with 83rd percentile above 300%). These levels cannot be held as government bonds — it would require the rest of the federal government to go into equivalent debt. Adaptive policies that maintain a target Trust Fund ratio are preferred over immediate and permanent fixes.
• Mortality assumptions drive the Trustees gap: Using the Trustees' own mortality assumptions, Lee's infinite horizon calculation agrees with the −3.5% figure (consistent with Lee and Yamagata 2003). The gap to −5.15% is primarily a mortality disagreement: Lee et al. project faster mortality improvement using the Lee-Carter / Lee-Miller implementation, which implies more longevity, more benefit years, and a larger infinite horizon shortfall.

Concepts Introduced or Extended

• Long-Term Actuarial Balance
• Probabilistic Population Forecasting
• SSA Mortality Forecasting

Entities Mentioned

• Ronald Lee
• Timothy Miller
• Michael Anderson

Quotes

"The 75-year Actuarial Balance is not a Sustainability Measure."

"Based on our 500-year projection with our own mortality forecasts, we estimate [the infinite horizon imbalance] to be 5.15%, substantially larger [than the Trustees' 3.5%]."

"A 1% increase in the payroll tax rate implemented for the first year is worth twice as much as one implemented for the 50th year, and almost 70 times as much as a 1% increase implemented for the 300th year."

"We call these 'routine' or 'business as usual' stochastic forecasts, because their uncertainty does not reflect the possibility of structural shifts. They understate actual uncertainty."

My Take

This is a technically rigorous extension of the Lee-Tuljapurkar stochastic SS forecasting program. Its most durable contribution is the finding that the 75-year $AB_{75}$ is not a sustainability measure — a point that is obvious in retrospect but was not widely recognized at the time, and that the Trustees themselves acknowledged by separately reporting the infinite horizon figure starting in 2003. The −5.15% infinite horizon estimate is credible and well-reasoned; the key driver (mortality) is plausibly understated by SSA's assumptions, as documented repeatedly in the Lee-Carter-related literature. The "cost of delay" calculation is the most accessible pedagogical element. The limitation is the paper's own acknowledgment: 500-year projections, even stochastic ones, capture only "routine" uncertainty and cannot account for structural breaks, regime changes, or technological discontinuities that are likely to dominate over such horizons. The uncertainty bands (-1.3% to -10.5%) must be understood as conditional on a world that looks structurally like the past century — which is, at best, a useful lower bound on true uncertainty.