Saving the Surplus

Studies | Social Security

No. 241
Wednesday, January 31, 2001
by Dr. Liqun Liu, Dr. Andrew J. Rettenmaier, and Thomas R. Saving


Appendix Forumla

Social Security's Accrued Liability

The following equation identifies our estimate of Social Security's accrued liability at a point in time:

Accrued liabilities are equal to the present value of the benefits that all currently living taxpayers and retirees are expected to receive based on their earnings up to the year of the calculation. It is similar in concept to the method Kotlikoff (1995) suggested for crediting workers for their participation in Social Security. In the equation i identifies birth year, y0 is the starting year of the calculation, and r is the real rate at which future benefits are discounted. Nit represents the number of individuals born in year i who are alive in year t. Bit is the average benefit based on earnings up to year y0 received in year t by individuals born in year i. Because this calculation is based on accrued benefits it depends on earnings histories and is thus independent of earnings projections and future tax policy.

In practice the benefit calculation and the number of individuals are further separated into sex and education categories. Elsewhere we have presented our methodology for projecting Social Security taxable earnings by birth year, sex and education categories (Rettenmaier and Saving (2000)). For individuals born in 1933 and later, the benefits are derived from our earnings projections using the scheduled benefit formula. For individuals who retire in the future, zeros enter their earnings history between year y0 and their years of retirement. For older workers the benefits are taken from the average benefits reported Table 5.A1 in the 1997 Annual Statistical Supplement. The data include the average benefits for men and women by age and by type of benefit for retired workers, wives, and widows. Benefit amounts are converted to y0 using the Social Security Trustees intermediate estimate price level changes and are discounted to y0 using a real discount rate of 5.5 percent. Population is from the Census Bureaus middle series projection.

Extending the Budget Forecast to 2070

At the beginning of October the Congressional Budget Office released its long-term budget forecasts. The variant of the forecasts used here is referred to as the "Save the Off-Budget Surpluses" assumption. The CBO provides annual estimates out to 2049 of Gross Domestic Product (GDP) and federal tax receipts and the various expenditure categories as a percent of GDP. Federal debt held by the public and net interest payments also are provided. Beyond 2049 we assume that tax receipts, federal consumption expenditures and other expenditures retain the same share of GDP they had in 2049. GDP is estimated by letting GDP per worker grow at the rate of growth that existed over the last 20 years of the CBO forecast. The GDP estimates beyond 2049 are equal to the GDP per worker multiplied by the number of workers. The number of workers is obtained from the 2000 Trustees Report. Medicare and Social Security expenditures beyond 2049 are calculated by estimating expenditures per beneficiary by applying the growth rates in per beneficiary expenditures derived from the CBO's forecasts. Total Social Security or Medicare expenditures are obtained by multiplying the number of beneficiaries by the per-beneficiary estimates. Finally, total Medicaid expenditures are assumed to grow at the same rate as the Medicare expenditures.

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