WALL STREET has been in buoyant mood in recent years. The S&P 500 equity index has reached repeated record highs. One might think that would be great news for America’s public-sector pension plans, which hold more than half their assets in equities.

Only up to a point. The latest report* from the Centre for Retirement Research (CRR) at Boston College estimates that the funding ratio of pension plans—the proportion of liabilities covered by assets—has risen from 72% in 2013 to (drum roll) 74% last year. A fifth of all schemes have a funding ratio of less than 60%—a group that includes not just the usual suspects in Illinois and New Jersey but some in Alaska, Arizona, Connecticut and Kentucky.

To make matters worse, this calculation makes a very generous assumption. Most liabilities of a pension plan fall well into the future—a stream of payments to current and future beneficiaries who may live into their 90s. These payments must be discounted to work out the sum in contemporary dollars needed to cover them, but at what rate? Private-sector pension plans are required to use long-dated AA-rated corporate-bond yields, currently around 4%. But public-sector plans are allowed to use the expected return on their investments, which they estimate to be 7.6% on average. The higher the discount rate, the smaller the liabilities seem.

This more generous approach means the aggregate deficit of public-sector plans is “just” $1.1 trillion. But if public plans used the same discount rate as private ones, the deficit would increase to $3.9 trillion and the funding ratio fall to 45%.

This is not an arcane matter of accounting. Deficits have eventually to be closed. That means lower benefits for the retired, bigger contributions from existing employees (a pay cut) or higher contributions from the employer—which means tax increases for state or city residents, or cuts to other services.

No wonder that no one is getting to grips with the problem. Unions do not like to draw attention to the deficits, for fear benefits will be cut. Politicians do not want to pick a fight with the unions, or increase taxes and annoy voters. Instead, states and cities tend to hope that rising markets will make the problem disappear.

The allure of pension promises is that the crunch point—when schemes run out of cash to pay their members—may be decades away. By the time that happens, the current group of politicians will be out of office. Nevertheless, the contribution rate required to meet even the generous funding standard has been rising rapidly this century—it is now almost treble its 2000 level (see chart). Worse, states only cough up seven-eighths of the required payments, so the hole is growing ever bigger.

The problem with relying on the markets is that high returns look unlikely. Neither cash nor government bonds are going to deliver 7.6% a year. That leaves equities. Investors tend to believe low interest rates help equities; certainly shares tend to rally when central banks cut.

But research by the London Business School, covering 20 countries over 113 years, shows that real (inflation-adjusted) returns on stockmarkets suffer when real interest rates are low. The average return when real rates were below average was 3%, compared to 7.6% when rates were above average. A real return of 3% when inflation is 2% would imply nominal equity returns of 5%—a far cry from the returns being counted on.

There is little sign that states will face reality soon. A recent rule change by the Governmental Accounting Standards Board was intended to bring the deficit calculations of public plans closer to those of the private sector. In practice, however, the CRR found that only seven of 150 plans had reduced their discount rate by more than half a percentage point.

All of this is an absurdity. It pretends that it is cheaper for the public sector to fund a pension promise than it is for the private sector. (If anything, it should be a little more expensive: public-sector workers seem to live slightly longer.) The private sector has tried to tackle the problem over the past 20 years by closing the most expensive schemes—those linked to a worker’s final salary—to new members.

Even so, Standard & Poor’s calculates that American companies have an aggregate pension deficit of $389 billion, or $585 billion if other post-retirement benefits (largely health care) are included. The problem is at least recognised on private-sector balance-sheets. The public-sector shortfall is still swept under the carpet.