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Pension plans for state government employees today report they are underfunded by $450 billion, according to a recent report from the Pew Charitable Trusts. But this vastly underestimates the true shortfall, because public pension accounting wrongly assumes that plans can earn high investment returns without risk. My research indicates that overall underfunding tops $3 trillion.

The problem is fundamental: According to accounting rules adopted by the states, a public sector pension plan may call itself "fully funded" even if there is a better-than-even chance it will be unable to meet its obligations. When that happens, the taxpayer is on the hook. Yet public pension plans ignore market risk even as they shift into risky foreign investments, hedge funds and private equity.

A simple example illustrates the flaw. Imagine that you borrowed $100, which you absolutely, positively must repay in 20 years. How much money would you need today to consider that debt "fully funded?"

Here are two correct answers, followed by an incorrect one. All three rely on "discounting," a method of calculating the sum of money needed today to fund a given liability in the future.

First, discount $100 at the 4.5% yield on safe, 20-year Treasury notes. This produces a present value of $41.46, which you invest in Treasury securities. Barring federal government bankruptcy, you can repay your debt with certainty.

Second, discount $100 at the expected return on stocks--say 8%. This produces a present value of $21.45, which you invest in equities. Next, purchase a "put option" giving you the right to sell your portfolio 20 years hence for no less than $100. This option would cost $20.08, for a total cost today of $41.53. Barring the collapse of the options exchange, you also can be certain of repaying your debt.

But here is a third answer: discount $100 at an 8% interest rate. Invest $21.45 in stocks. Declare yourself "fully funded." This doesn't work because there's a very good chance your risky assets won't appreciate in value enough to cover the debt. Yet this is how public sector pension accounting operates.

Vested pension benefits are constitutionally guaranteed in eight states and protected by law in two dozen more. And in most every state politics makes accrued benefits impossible to cut. Orange County, Calif., in the 1980s and New York City in the 1970s effectively made pension obligations senior to government debt by paying full retirement benefits even as they inflicted losses on bondholders.

Yet public pensions discount ironclad liabilities at the high rates of return they project for risky investment portfolios. Consider New York state's Employees Retirement System (ERS), which assumes an 8% return on its assets. Discounted at this interest rate, ERS's liabilities had a present value of $141 billion as of 2008. ERS assets at that time were $152 billion, making the program overfunded by 7%.

But New York's portfolio is hardly likely to produce a steady 8% each year. Since 1990 its returns have varied widely, ranging from 30.4% in 1998 to -26.4% in 2009. A "Monte Carlo" computer simulation (a standard technique for modeling financial risks) incorporating fluctuating asset returns shows that New York's ERS has only around a 45% probability of meeting its liabilities. Instead of an $11 billion surplus, the ERS is almost $100 billion shy of funding its benefits with certainty.

In a recent AEI working paper I've shown that the typical state employee public pension plan has only a 16% chance of solvency. More public pensions have a zero probability of solvency than have a probability in excess of 50%. When public pension assets fall short, taxpayers are legally obligated to make up the difference. The market value of this contingent liability exceeds $3 trillion.

Public pension plans are hiding behind unrealistically low deficit figures. This allows policy makers to dodge difficult choices today at the cost of a much heavier burden on taxpayers in the future.

Andrew G. Biggs is a resident scholar at AEI.

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