Stochastic Infinite Horizon Forecasts for Us Social Security Finances

Article excerpt

Even over a 75-year horizon, forecasts of PAYGO pension finances are misleadingly optimistic. Infinite horizon forecasts are necessary, but are they possible? We build on earlier stochastic forecasts of the US Social Security trust fund which model key demographic and economic variables as historical time series, and use the fitted models to generate Monte Carlo simulations of future fund performance. Using a 500-year stochastic projection, effectively infinite with discounting, we find a fund balance of -5.15 per cent of payroll, compared to the -3.5 per cent of the 2004 Trustees' Report, probably reflecting different mortality projections. Our 95 per cent probability bounds are -10.5 and -1.3 per cent. Such forecasts, which reflect only 'routine' uncertainty, have many problems but nonetheless seem worthwhile.

Keywords: Social security; sustainable; infinite horizon; stochastic; forecast. JEL classification: H55; JII; C15


Population ageing threatens the long-term finances of public pension programmes around the world. Many nations are discussing parametric adjustments or deeper reforms to address this problem. However, the design of effective pension policies requires a correct assessment of the magnitude of the problem. In the US, the recent debate about reform was accompanied by sharp controversy about the appropriate way to measure the imbalance. To measure the cost of keeping social security solvent, the Social Security Trustees and Office of the Actuary have traditionally relied primarily on the Summary Actuarial Balance calculated over a 75-year horizon. (1) Others, including the advocates of privatisation, argue for an assessment over the infinite horizon, since some of the advantages of privatisation accrue after 75 years, and are not reflected in the standard measure.

Whatever the merits of privatisation, we find that the 75-year horizon measure seriously understates the size of the true imbalance, and that some sort of infinite horizon measure or the equivalent is required. Many analysts agree that there are severe problems with the 75-year summary actuarial balance as a measure of the long-term fiscal soundness of the system, because it takes no account of what happens after the 75 year horizon, and therefore does not measure what it would cost to put the system on a sustainable footing. For closely related reasons, it is not time-consistent: given exactly the same underlying economic and demographic projections, it will nonetheless deteriorate from one year to the next due to the loss of a good year at the start of the evaluation period and the addition of a bad year at the end.

Lee and Yamagata (2003) developed analytic methods for making infinite horizon projections, and also discuss simpler measures which can be calculated from the standard 75-year projection under certain assumptions about stability, in which case they are equivalent to a certain kind of infinite horizon projection. One of these, which they call the Flat Fund Ratio Tax, is the immediate and permanent tax increase that would leave the ratio of the Trust Fund to Costs constant at the end of the projection horizon, a measure that has also been included in recent Trustees' Reports.

Before 1965 the Actuaries assessed solvency over an infinite horizon or "in perpetuity" (Myers, 1959). After 1965, they moved to a 75-year horizon on the recommendation of the Advisory Council. (2) This had a relatively small effect on the long-run cost projections at that time, because costs were projected to remain flat in any case, rather than rising exponentially as they do now (Goss, 1999). Starting in 1973, new legislation linked benefits to past earnings, so the projections began to assume a changing time path for earnings and benefits and consequently use of an infinite horizon might now make a considerable difference.

The 2003 Trustees' Report (TR) included an infinite horizon measure for the first time in many decades, which agreed with the Lee-Yamagata calculations in showing that the budget shortfall was about twice as great relative to payroll as for the 75-Year Summary Actuarial Balance. …