Publication Date: July 2009
One measure of the health of the Social Security system is the diﬀerence between the market value of the trust fund and the present value of beneﬁts accrued to date. How should present values be computed for this calculation in light of future uncertainties? We think it is important to use market value. Since claims on accrued beneﬁts are not currently traded in ﬁnancial markets, we cannot directly observe a market value. In this paper, we use a model to estimate what the market price for these claims would be if they were traded.
In valuing such claims, the key issue is properly adjusting for risk. The traditional actuarial approach — the approach currently used by the Social Security Administration in generating its most widely cited numbers — ignores risk and instead simply discounts “expected” future flows back to the present using a risk-free rate. If beneﬁts are risky and this risk is priced by the market, then actuarial estimates will diﬀer from market value. Eﬀectively, market valuation uses a discount rate that incorporates a risk premium.
Developing the proper adjustment for risk requires a careful examination of the stream of future beneﬁts. The U.S. Social Security system is “wage-indexed”: future beneﬁts depend directly on future realizations of the economy-wide average wage index. We assume that there is a positive long-run correlation between average labor earnings and the stock market. We then use derivative pricing methods standard in the ﬁnance literature to compute the market price of individual claims on future beneﬁts, which depend on age and macro state variables. Finally, we aggregate the market value of beneﬁts across all cohorts to arrive at an overall value of accrued beneﬁts.
We ﬁnd that the diﬀerence between market valuation and “actuarial” valuation is large, especially when valuing the beneﬁts of younger cohorts. Overall, the market value of accrued beneﬁts is only 4/5 of that implied by the actuarial approach. Ignoring cohorts over age 60 (for whom the valuations are the same), market value is only 70% as large as that implied by the actuarial approach.
Social security, Market value, Risk adjustment, Actuarial value, Wage bonds, Unfunded obligations
JEL Classification Codes: E6, H55, D91, G1, G12