Frees et al 1997 — Forecasting Social Security Actuarial Assumptions

Summary

Frees et al. fit multivariate autoregressive moving average–generalized autoregressive conditional heteroscedasticity (ARMA-GARCH) time series models to the four economic "actuarial assumptions" used in U.S. Old-Age, Survivors, and Disability Insurance (OASDI) projections — inflation rate, 5-year Treasury returns, wage rate, and unemployment rate — using quarterly data from 1953:III to 1992:IV. The paper demonstrates that a multivariate model outperforms four independent univariate models when forecasting the Social Security trust fund balance, primarily because the series share strong contemporaneous correlations and lead/lag relationships. The key policy finding is that the Social Security Administration's (SSA) low/intermediate/high cost scenario range captures only the bottom ~50% of the stochastic forecast distribution, suggesting the official uncertainty range materially understates true risk.

Key Claims

• Investment returns are a statistically significant leading indicator of inflation; lagged inflation and unemployment are leading indicators of wages and unemployment (Table 13, multivariate AR(1)+ARCH(1) model).
• Conditional heteroscedasticity (GARCH effects) is significant in three of four series: inflation fits AR(3)+GARCH(1,1), investment returns ARMA(2,2)+GARCH(1,1), unemployment SARMA(1,0,0,0,0,2)+GARCH(1,1); the wage rate needs no GARCH component.
• Multivariate prediction intervals for the trust fund are wider than univariate ones — combining the four series in a consistent model increases rather than reduces uncertainty.
• Out-of-sample fund forecasts: the multivariate model tracks held-out 1993:I–1995:I experience well; univariate forecasts are too optimistic (coverage probabilities well below nominal levels, Table B-4).
• The SSA's three cost alternatives are tightly bunched; fewer than 20% of multivariate model draws fall between the low- and high-cost projections, suggesting expert-negotiated assumptions do not reflect historical variability.
• Important limitation (documented in published discussion by SSA Chief Actuary Foster): the model ignores the 1973:II real-wage level shift. Because it reverts to the full-period mean (+0.3%/qtr) rather than the post-1973 mean (~0%/qtr), point forecasts are systematically more optimistic than warranted.

Concepts Introduced or Extended

• Long-Term Actuarial Balance
• Stochastic Fertility Forecasting

Entities Mentioned

• Edward W. Frees
• Marjorie A. Rosenberg
• Virginia R. Young
• Social Security Administration

Quotes

"The authors' multivariate results argue persuasively that the true range of uncertainty, reflecting interactions among variables, is wider than that suggested by the univariate forecasts. In other words, combining the information from the four economic series in a consistent manner leads to less certainty, not more." — Richard S. Foster (published discussion)

My Take

A pioneering actuarial application of multivariate GARCH forecasting to OASDI, but its practical shelf life is limited by the regime-change problem Foster identifies: reverts-to-mean models fitted on pre- and post-1973 pooled data produce systematically optimistic fund projections. The stochastic prediction-interval methodology is the durable contribution — the finding that official SSA scenario ranges span only ~50% of historical variability is more informative than the point forecasts. The paper is squarely in the demographic/actuarial forecasting tradition (same North American Actuarial Journal venue as Lee 2000) but addresses economic assumptions rather than mortality or fertility.