But such models, he said, don’t fully take into account changes in the retirement system, such as the shift away from pension plans and toward 401(k) accounts, or the potential for a catastrophic health event that would require a stay in a nursing home.

When those factors are accounted for, he said, the outlook is less optimistic, especially for lower-income workers. E.B.R.I.’s analytical model, he said, indicates that for those in the lowest quarter of incomes, workers would have to toil until age 84 before 90 percent of them would have at least a break-even chance for success.

That doesn’t mean, he said, that he is advocating that everyone work until their 80s, or that working that long is feasible. But it does suggest, he said, that it is a risky notion to think that you can work until you’re 65 and then simply work five more years if you don’t haven’t saved enough.

If a couple near retirement age has one member who become ill and requires a lengthy nursing home stay, he said, a good chunk of their savings may be exhausted. “How can you ignore that?” he said.

It’s much less of a gamble, he said, to save more while you’re working, if you can: “It’s much less risky than waiting until you’re 65 or 67 and seeing what happens.”

How long do you plan on working?