Of all the interest groups in the U.S. economy, perhaps retired people living on money-fixed incomes from private pensions are the most vulnerable to the ravages of inflation. At an annual inflation rate of 12 percent, prices double about every six years. It is no wonder, therefore, that labor unions have started to demand cost-of-living escalators for retirement benefits in their contract negotiations.

Is this an unreasonable demand, or can private corporations find a way to satisfy it without bankrupting themselves in the process?

The answer hinges on the type of assets that private pension funds can invest in and what rate of return -- adjusted for inflation -- those assets will earn. Traditionally, pension funds have invested primarily in long-term bonds and have paid retirement benefits from the interest income the bonds provided. But at fixed interest rates, long-term bonds are a poor hedge against inflation. Any pension fund whose liabilities were linked to the cost of living would need to invest in some kind of asset that offers protection against unanticipated inflation.

The evidence of the past 25 years indicates that of the assets available to large institutional investors (such as pension funds), the one category offering the best long-run protection against inflation has been short-term, money-market instruments -- U.S. Treasury Bill, corporate commercial paper and bankers' acceptance and negotiable certificates of deposit, for example. This is because over this period, short-term interest rates have tended to follow rather closely movements in the rate of inflation.

Of course, this is not a coincidence. All market-determined interest rates contain an "inflation premium," which reflects expectations about the declining purchasing power of the money borrowed over the life of the loan. As the rate of inflation has increased in recent years, so too has the inflation premium built into interest rates.

While long-term as well as short-term interest rates contain such a premium, conventional long-term bonds lock the investor into the current interest rate for the life of the bond. If long-term interest rates on new bonds subsequently rise as a result of unexpected inflation, the funds already locked in can be released only by selling the bonds on the secondary market at a price well below their face value. But if an investor buys only short-term bonds with an average maturity of about 90 days, then the interest rate he earns will lag behind changes in the inflation rate by at most three months.

The problem with money-market instruments, however, is their low rate of return. Over the last 25 years, the average pre-tax, inflation-adjusted rate of return on money-market instruments has been barely half a percent per year. In the most recent five-year period, that return has actually been negative. Perhaps the most likely scenario for the future is that inflation-adjusted returns will hover around zero, i.e., the interest rate will be about equal to the rate of inflation.

So there we have it -- the asset that seems to offer the least variable, inflation-adjusted rate of return for pension funds also offers merely the possibility of maintaining the fund's purchasing power.

What size annuity benefit does this earning rate imply? Suppose that by the time a worker reaches retirement age, his firm has accumulated $100,000 to finance his monthly pension benefits. If the firm offers him an escalator clause and invests the $100,000 in money-market instruments, then, assuming a 15-year (180-month) life, his first monthly benefit would be $100,000 divided by 180 months, or $556. The benefit would, as promised, increase each month according to the cost of living; these increases would be financed by the return on the money-market instruments.

How would that compare with the amount he would receive under a conventional plan with no escalator clause? As in the case of the index-linked annuity, the amount of the monthly benefit under a conventional plan depends on the earnings rate assumed. Suppose that the firm invests the $100,000 at a guaranteed interest rate of 8 percent per year. Using standard compound interest tables and assuming 180 monthly payments, the monthly fixed benefit turns out to be $956.

In our simple yet realistic example, the pension fund could provide either a conventional retirement annuity of $956 per month or a "purchasing power annuity," which would start at $556 per month and rise each month in accordance with the cost of living. If offered a choice between the two, it is not clear which the average retiree would prefer. It would depend on a host of factors, especially his assessment of what the rate of inflation was going to be, how long he thought he would live and what other sources of retirement income he had.

Clearly, many of the proponents of the idea of indexed pension benefits see things differently. They would like to see the $956 monthly benefit plus a cost-of-living escalator. But that would be possible only if the $100,000 allocated to each worker were increased to $172,000, which could easily bankrupt the pension fund, or if the fund were able to earn 8 percent per year after adjusting for inflation. Realistically, there is no apparent way for an institutional investor to earn anywhere near that rate of return with an acceptable degree of risk.

These are the basic economic facts of pension funding. It is, however, worth pointing out that many private pension plans have voluntarily increased the amount of money they pay to retired employees in the past decade. They have been able to do so primarily because the benefit formulas they had originally used assumed an interest rate on invested funds of only 3 percent or 4 percent per year. Many pension funds have in fact earned much more than that and have been willing to share that "windfall" with their beneficiaries.

It seems clear, then, that private pension funds could offer a purchasing-power annuity option to retirees. However, it is quite possible that such an opinion might not be as attractive to the beneficiary as a conventional annuity costing the fund the same amount.