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President Obama spent very little time on housing related policies in his State of the Union address Tuesday night. While disappointing, it’s not surprising as the problems are complex, extraordinarily difficult to tackle, and very costly. In his brief remarks, he focused on the right thing: facilitating more mortgage refinancings.

The president proposed to allow “every responsible homeowners” the chance to more easily refinance, a savings of about $3,000 annually. (Read: Full text of president’s speech.)

There is no better way to quickly buoy hard-pressed homeowners than helping them take advantage of the currently record low fixed mortgage rates and significantly reduce their monthly mortgage payments.

The administration has already been working to this end. Late last year they made a number of substantial changes to the HARP program – the program to refinance underwater homeowners with mortgages insured or owned by Fannie Mae and Freddie Mac – to make it more effective. Almost one million distressed homeowners have taken advantage of HARP since it was unveiled in 2009. While a clear plus, this is well short of the 4 to 5 million refinancings expected.

Among the changes to HARP are increasing the number of eligible homeowners and reducing mortgage rates to refinancing homeowners. Some 4 million Fannie and Freddie homeowners with little or no equity in their homes are good candidates for a refinancing under HARP 2.0 at current fixed mortgage rates. The new HARP is just kicking in and it is too early to judge whether it is working, but from what I’m hearing there are good reasons to be optimistic it will be more successful than its predecessor.

Given the encouraging signs, it is worthwhile to encourage even more refinancing activity as the president has proposed. Over 30 million homeowners are current on their mortgages and could profitably refinance at the current mortgage rate, which now average less than 4 percent for a 30-year fixed rate. The macroeconomic benefit could be significant. If, say, half refinance in the next six months, then this would save homeowners over $20 billion in mortgage payments this year and double that next year. Homeowners’ extra cash will quickly find its way into the economy.

It is important to note that while homeowners will have more cash to spend, investors in these mortgages will receive less interest income. This dilutes the economic benefit of facilitating more refinancing, but only modestly. The biggest mortgage investors include the Federal Reserve (through quantitative easing), Fannie and Freddie, and foreign investors. All mortgage investors are probably a bit surprised they haven’t already been refinanced out of their investments.

The president provided few details on his new refinancing plan, but he did say it would require legislation and a levy on financial institutions to pay for it. (He told Congress: “A small fee on the largest financial institutions will ensure that it won’t add to the deficit, and will give banks that were rescued by taxpayers a chance to repay a deficit of trust.”)

This significantly reduces the odds that whatever he does propose it won’t come to fruition. As last year’s debt ceiling drama highlights, getting anything through Congress is a very heavy lift, particularly in a presidential election year.

As such, it might be better for the president to expand HARP 2.0 even more broadly, say to all Fannie and Freddie loans. While not on the scale of what the President is currently proposing, an estimated 10 million homeowners would benefit. Not as big, but doable.

It also goes without saying that the administration should continue with other efforts to help support the housing market, including helping move more foreclosed property into rentals. The foreclosure crisis isn’t over and policymakers need to remain on high alert.

Related: Mark Zandi: Who’s really to blame for housing crash

Related: GOP candidates address how to fix housing market.

Mark Zandi is chief economist for Moody’s Analytics. He writes a regular column on the housing industry and housing policy for The Washington Post.