Michael Shreve, a teacher in Marysville, Wash., has watched helplessly as mortgage rates have fallen. Despite his stellar credit, no bank had been willing to let him trade in his 6.35 percent, 30-year mortgage because his house was worth less than when he bought it.

‘‘At some point,’’ he said, interest rates are going to go up again, ‘‘and I should have been able to get those low rates. It’s not fair.’’

Companies have been taking advantage of the cheap borrowing costs, but consumers have been largely left on the sidelines. Federal Reserve data show that in the first quarter of this year, US businesses were taking on new debt at the fastest rate since the 2008 financial crisis. Households, though, were shedding debt. Another recent Fed report shows that while more consumers are interested in buying homes or refinancing mortgages, banks remain hesitant to extend credit.

And consumers, wary of volatile financial markets, have been putting money into ordinary savings accounts. But those accounts pay an average of 0.1 percent, according to Bankrate.com.

‘‘There’s definitely winners and losers in this kind of extremely low interest rate environment,’’ said Ed Yardeni, president of Yardeni Research.

Of course, declining household debt is not necessarily bad. Many economists see it as a welcome shift from the borrowing binge that helped cause the financial crisis.

‘‘What Americans have learned is that they can live with the old house,’’ said Allen Sinai, chief executive of Decision Economics. ‘‘Why take on debt and obligate yourself?’’

But the new data underscore the polarizing impact of the central bank’s policy of pushing down interest rates. While low rates are supposed to encourage Americans to take more risks, ordinary Americans have been unwilling or unable to take advantage of them.

Not all types of consumer debt are in decline. As education costs rise, the amount of outstanding student loans rose in each of the first five months of the year, Equifax data analyzed by Moody’s Analytics showed. Lending to buy cars has also been heading upward.

The biggest category of household debt by far is residential real estate, and debt in that sector has continued to drop. Foreclosures and defaults have erased some obligations, and prospective home buyers are being held back, in part, by the banks’ restraint. A Fed survey indicated most banks had kept lending standards the same, or tightened them. About two-thirds of mortgage activity has been for refinancing loans, said Guy Cecala, publisher of Inside Mortgage Finance.

“The real problem is that relatively few borrowers meet the tougher standards of today even if they could benefit from refinancing, and that is the frustration,’’ he said.