IN A world of low investment returns, many a pension scheme is in trouble. In both Britain and America employers who have promised to pay workers a pension based on their final salary are struggling to cope with huge deficits.

But the problem is not confined to those with so-called defined-benefit (DB) pensions. It also affects those saving for retirement via a defined-contribution (DC) scheme, where both employer and employee contribute, and the worker takes charge of the pot when his career ends. In America the most popular form of DC savings are called 401(k) schemes after a section of the tax code.

In an article* in the Journal of Retirement, three authors from AQR Capital Management, an investment group, argue that workers in 401(k) schemes are simply not putting enough money aside.

What you get out of a pension depends on what you put into it. One would expect a DC pension to deliver a smaller income than a DB scheme because less money tends to be put in the pot. Total DC contributions average around 9% of payroll (6% from employees; 3% from employers). But figures from the Centre for Retirement Research at Boston College show that public-sector employers pay an average of 18.6% to fund DB pensions (with employee contributions of 6.5% on top).

So why don’t workers in DC schemes put more money aside? The paper suggests that savers may have been deceived by the robustness of past returns. The authors assume that workers would like to retire on 75% of their final salary and that 30 percentage points of that would come from other sources, including social security. Furthermore, they assume 2% annual real-wage growth during workers’ careers, and that, on retirement, savers buy a 25-year annuity with their pot.

Based on historical real returns of 7.5% from equities and 2.5% from Treasury bonds (before charges), it turns out that, in the past, workers could have hit the income-replacement ratio target with only an 8% contribution rate. That may explain why they are not saving more today.

But it is highly unlikely that future investment returns will be as high as they were in the past. Bond yields have fallen and equity valuations are high by historical standards. Investors have thus chalked up capital gains as bond and share prices have moved to these new, high levels. To replicate that performance, bond yields will have to fall even further and equities will have to be valued even more highly. This is not something that workers should be counting on. Real returns from equities are more likely to be 5% and from bonds 1%, the authors reckon.

Combine those real returns into a portfolio of 60% American equities and 40% Treasury bonds (a standard asset allocation) and you get an overall return of 3.5% a year. That is two percentage points lower than the 5.5% achieved from the same combination in the past. And it means that a worker would have to save 15% a year, not the current 9%, to reach the target.

Even that approach looks optimistic. With bond yields less than 2%, inflation will have to average under 1% to deliver the 1% real return assumed by the authors. And fund-management charges will eat into returns as well. On a 2.5% real-return assumption, contributions would need to hit 19% of payroll.

What about a different asset allocation? Many advisers suggest that workers start off with a high allocation to equities and then switch to bonds as they approach retirement. Even that scheme would still require a 15% payroll contribution to meet the target rate.

So why aren’t workers saving more? They may not be overestimating asset returns. Instead, they may be indulging in “hyperbolic discounting”—valuing the income they earn today far more highly than the income they will earn in old age. After all, employees in DC schemes tend to get lower retirement pay than those in DB plans (because employers are contributing less). Yet there is no evidence that workers in companies with DC plans demand more current pay to compensate.

But the main reason workers don’t put more aside is probably that they can’t afford to; since 1980, median pay in America has grown very sluggishly in real terms. That means they will face a stark choice as they approach retirement age: take a big cut in their incomes or keep working. Most will be forced to toil longer. Whatever the official retirement age may be, many Americans will be working at 70.