SLOWLY but surely the cost of America’s public-sector pension promises is becoming clear. Last year the best estimate of the shortfall was more than $4 trillion. To deal with its deficit, a giant Californian pension fund, CalPERS, recently announced plans that will increase contributions by employers (in effect, taxpayers) by up to a half, starting in 2015-16.

Final-salary pension costs have risen for decades because workers are living longer and the retirement age has barely budged. The bill was disguised in the 1980s and 1990s by good asset returns. But dismal equity markets have since forced many private providers to close final-salary schemes to new members and switch to less lavish defined-contribution plans.

This shift has hardly happened in the public sector, in large part because the accounting treatment is so different. Devin Nunes, a Republican congressman, recently revived a bill to move to a more conservative accounting approach.

Failing to recognise the true cost of public pensions builds up all sorts of problems, as an academic paper last year made clear. As pension funds become more mature (ie, more of their members are retired) their asset allocation should, in theory, become more conservative. After all, the fund has to worry more about paying benefits immediately and has less scope to gamble that riskier assets will deliver long-term growth.

Sure enough, mature pension funds in Canada and Europe and in America’s private sector all follow this approach. But more mature American public plans have riskier portfolios than less mature equivalents. In its latest “Global Financial Stability Report” the IMF worried that American funds had increased the riskiness of their portfolios, “exposing them to greater volatility and liquidity risks”.

The explanation for such behaviour is not hard to find. American public-sector schemes discount their liabilities by the expected return on their assets. The riskier the asset mix, the higher the assumed return—and the lower the bill appears to be.

This is an odd way of thinking. Suppose a car company borrowed $10 billion in the form of a 20-year bond to build a manufacturing plant and planned to pay off the debt with the profits from running the plant. The car company will assume a higher return on capital than its financing cost (otherwise it should not build the plant). But it still has to recognise the $10 billion bond liability on its balance-sheet. It cannot say it owes only $2 billion because it expects a very high return.

The reason is clear. If the plant fails to earn a high return, the firm will still be liable to repay the bond. Similarly, if pension schemes fail to earn a high return on their assets, they still have to pay benefits. Final-salary pensions are a debt-like liability.

When private-sector companies account for their pension schemes, therefore, they discount liabilities with a corporate-bond yield. Lower yields have pushed up liabilities and led to big deficits. Moody’s, a ratings agency, will in future use a long-term bond yield to discount American public-pension schemes, resulting in much larger liabilities than before.

Even if you use the expected-return methodology, the discount rate used by public-sector pension funds should fall. That is because all pension funds tend to own some bonds, and low bond yields mean low future returns. But the paper finds no link at all between the discount rates used by public-sector funds and the level of bond yields. The motto seems to be: if reality is challenging, just ignore it.

The Governmental Accounting Standards Board (GASB) did change the rules for public pension funds last year. But the revised rules still throw up absurdities. In a paper for the Financial Analysts Journal, Robert Novy-Marx of the University of Rochester argues that by destroying assets invested in cash a scheme can reduce its deficit by increasing the expected return on remaining assets. “A plan can sometimes improve its funding status by literally burning money,” he remarks.

This seemed such a startling finding that The Economist asked GASB to comment. Instead of a detailed rebuttal, we received this response: “GASB gave serious consideration to the views of Professor Novy-Marx when developing its new pension standards.” Not serious enough, it seems. American taxpayers must not know whether to laugh or cry.

Economist.com/blogs/buttonwood