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Despite the enormous gains in the housing market, and the rapid surge in home prices in recent years, nearly 2 million people still owe more on their mortgage than their home is worth.

Throughout much of the housing downturn a decade ago, the plight of underwater borrowers sparked fierce debates. Many industry participants fretted about homeowners making “strategic defaults” — calculating that it would be smarter to cut their losses and walk away from the home, leaving an empty house and a broken promise to pay.

While there’s lots of evidence that most homeowners who defaulted did so because they had no other choice, the issue is still controversial.

Still, a survey published by the New York Fed this week sheds some light on how homeowners think about their mortgage payments when they’re underwater — or at least how they say they think about it.

The survey, the housing component of the massive Survey of Consumer Expectations, asked underwater owners: “Have you considered no longer making…