In the president’s electioneering lecture to Congress, Mr. Obama said, “To help responsible homeowners, we’re going to work with federal housing agencies to help more people refinance their mortgages at interest rates that are now near 4 percent… . I know you guys must be for this, because that’s a step that can put more than $2,000 a year in a family’s pocket, and give a lift to an economy still burdened by the drop in housing prices.”

Unfortunately, it is not quite that simple. Because using the leverage of Fannie Mae, Freddie Mac, or the Federal Housing Administration to promote riskier standards for refinancing would benefit only those homeowners who stay put in houses they already own, the unintended effect on sales of new or existing homes could be negative.  Moreover, gains to borrowers would be offset by potentially larger losses to investors in mortgage-backed securities (MBSs) – the “toxic assets” that provoked so much financial mischief in 2008.

As it happens, the Congressional Budget Office just released an “An Evaluation of Large-Scale Mortgage Refinancing Programs” by two CBO staffers and Deborah Lucas, a first-rate economist on loan from M.I.T.

Here are some key points:

We analyze a stylized large-scale mortgage refinancing program that would relax current income and loan-to-value restrictions for borrowers who wish to refinance and whose mortgages are currently insured by Fannie Mae, Freddie Mac, or the Federal Housing Administration. The analysis relies on an estimate of the volume of incremental refinancing that would occur and an estimate of how future default and prepayment behavior would be affected by such refinancing. Relative to the status quo, the specific program analyzed here is estimated to cause an additional 2.9 million mortgages to be refinanced, resulting in 111,000 fewer defaults on those loans and estimated savings for the GSEs and FHA of $3.9 billion on their credit guarantee exposure, measured on a fair-value basis. Offsetting those savings, federal investors in MBSs, including the Federal Reserve, the GSEs, and the Treasury, would experience an estimated fair-value loss of $4.5 billion… .

We also discuss the impact of this program on various stakeholders, including homeowners, non-federal mortgage investors, mortgage lenders, mortgage service providers, private mortgage insurers, and subordinated mortgage holders. For example, non-federal investors would experience an estimated fair-value loss of $13 to $15 billion; most of that wealth would be transferred to borrowers… .

In aggregate, the fair-value loss to both federal and non-federal investors is equivalent to the gain experienced by borrowers from the decline in their interest payments… Nevertheless, because a significant share of investors is composed of foreigners and the U.S. government, and because private investors would be expected to reduce spending in response their losses by less than the increase in spending by borrowers in response to their lower interest payments as well as their lower mortgage principal payments, the net effect would be an economic stimulus … but it is likely to be small relative to GDP.

With respect to the housing market, the overall impact of the program is also small; the 111,000 homeowners saved from foreclosure by virtue of lower monthly mortgage payments will have a minor impact on the path of future home prices. Because this program is directed toward current homeowners, it would do little to alleviate the tighter underwriting standards and increased credit pricing for purchase loans. In addition, it would not create much demand for homes, because all of its participants would already have at least one property.