My spouse has occasionally asked whether we'd be better off having a mortgage in order to get a tax deduction.
I have explained that we'd get the deduction, and pay fewer taxes, but be worse off in the end.
In this blog post, Greg Mankiw (author of the most widely used economics textbook in the US) makes this same point in discussing the Obama's finances.
with some commentary by Tyler Cowen (author of competing economics textbooks) here:
The original source for this blogosphere activity appears to be this article, “Fixing the Obama’s Finances”, http://www.financial-planning.com/news/Financial-Planning-for-Barack-Obama-and-Michelle-Obama-2684504-1.html?zkPrintable=1&nopagination=1 by Allen S. Roth.
By selling some of those Treasuries and paying off the mortgage, they would effectively be getting five more percentage points on the amount; they would also be about $40,000 better off each year before taxes, not to mention being less exposed to notes that could take a hit from possible rising rates.
The Obamas would pay more in taxes but make much more after taxes -- especially since they aren’t getting the full deduction anyway, due to the AMT. That's more money going to the U.S. Treasury and more money for them; Northern Trust would be the loser.