Headlines talk about a wave of money changing hands as the population ages and inheritances are passed on to the next generation.

But most of that money will be going to households that won’t have to depend on it for their retirement preparedness.

That’s the determination of a new study from the Center for Retirement Research at Boston College, which looked at data from the National Retirement Risk Index (NRRI), based on the Federal Reserve’s Survey of Consumer Finances (SCF). (The NRRI measures how well-prepared Americans are for retirement by comparing projections of how much money they’ll have in retirement with projections of how much money they’ll need.)

The study took that NRRI data and added additional data from the SCF about inheritances to see just how well inheritances do at reducing the percentage of households at risk of running out of money during retirement.

More than half of all households are currently at risk in retirement, even if they work to age 65 and annuitize all their financial assets, including receipts from reverse mortgages on their homes.

But the study found that “inheritances already received — and potential increased inheritances from unspent 401(k) balances — have only a modest effect on the overall percentage of households at risk. The reasons are that many households do not receive any inheritance at all and — among those that do — most inheritances are relatively small and the large inheritances go to households already prepared for retirement.”

The NRRI has risen over time, according to the study, because of “longer life expectancies, reduced Social Security replacement rates, and very low interest rates…. In 2013, the Index shows that 52 percent of today’s working-age households were at risk of being unable to maintain their preretirement levels of consumption once they stopped working.”

SCF data contributed the percentage of households that had received an inheritance, how much it was for, and when they received it.

The higher the income level of the household, the more likely it was to have received an inheritance, “rising from 14 percent for the households in the bottom third of the income distribution to 24 percent for those in the top third.”

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While within each income category, households that have received an inheritance are statistically significantly less likely to be at risk than those that have not, those at the bottom third and at the top third are least likely to have their retirement situation improved.

That’s because the ones at the bottom are least likely to receive an inheritance and are likely already at risk, while those at the top are already better prepared and don’t need the help of an inheritance.

Those in the middle third, however, were helped by receiving an inheritance, although the statistics didn’t change much.

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When inheritances were included in the 2013 NRRI, 51.6 percent were at risk. When inheritances were removed, that percentage rose to 52.4 percent — statistically significant, but small.