Key Equations in the Tuljapurkar-Lee Model of the Social Security System

Abstract

We present stochastic forecasts of the Social Security trust fund by modeling key demographic and economic variables as historical time series, and using the fitted models to generate computer simulations of future fund performance. We evaluate several plans for achieving long-term solvency by raising the normal retirement age (NRA), increasing taxes, or investing some portion of the fund in the stock market. Stochastic population trajectories by age and sex are generated using the Lee-Carter and Lee- Tuljapurkar mortality and fertility models. Interest rates, wage growth and equities returns are modeled as vector autoregressive processes. With the exception of mortality, central tendencies are constrained to the Intermediate assumptions of the 2002 Trustees Report. Combining population forecasts with forecasted per-capita tax and benefit profiles by age and sex, we obtain inflows to and outflows from the fund over time, resulting in stochastic fund trajectories and distributions. Under current legislation, we estimate the chance of insolvency by 2038 to be 50%, although the expected fund balance stays positive until 2041. An immediate 2% increase in the payroll tax rate from 12.4% to 14.4% sustains a positive expected fund balance until 2078, with a 50% chance of solvency through 2064. Investing 60% of the fund in the S&P 500 by 2015 keeps the expected fund balance positive until 2060, with a 50% chance of solvency through 2042. An increase in the NRA to age 69 by 2024 keeps the expected fund balance positive until 2047, with a 50% chance of solvency through 2041. A combination of raising the payroll tax to 13.4%, increasing the NRA to 69 by 2024, and investing 25% of the fund in equities by 2015 keeps the expected fund balance positive past 2101 with a 50% chance of solvency through 2077.