Deleveraging means the size of our debt falls relative to the size of our income. The ideal way for a country to deleverage would be for incomes to rise faster than debts. The second-easiest (but far from ideal) way would be for practically every household to default on their debt, forcing the banks to lower credit standards, which might encourage people to borrow their next batch as the economy improved.
But what's happened in the U.S. has been a terrible, upside-down amalgam of the two. Rather than rising wages, we've got stagnant wages and low inflation, which makes it hard to pay down debt without cutting spending somewhere else. At the same time, we've seen households default in large numbers, but not so large that the banks have felt forced to lower credit requirements (in fact, they've raised them). The people who owe less than before can't borrow, and the people who can borrow don't owe less than before.
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