In his State of the Union address President Obama called for Congress to send him legislation that would provide a solid foundation for housing finance in the future. Such legislation would protect homeowners, communities and taxpayers from another housing crisis. It would also enhance access to home loans for creditworthy borrowers and ensure the availability of consumer-friendly mortgages like the 30-year fixed-rate mortgage.In the run-up to the Great Recession, Fannie Mae and Freddie Mac took on large amounts of risky mortgage debt that resulted in large losses when housing prices collapsed and defaults rose. To stem the spillovers that their failure would have on the economy, the Treasury ultimately put nearly $190 billion into these two government-sponsored enterprises to keep them afloat. They are now in a conservatorship overseen by their regulator, the Federal Housing Finance Agency.Although these efforts helped foster a housing recovery, further progress will best be advanced by moving beyond what is, in effect, a government-supported duopoly. Today, Fannie and Freddie, supported by U.S. taxpayers, guarantee payments to investors in mortgage-backed securities covering approximately 60% of mortgages. The size of these two giants, and their uncertain future, deter private firms from making the large, long-term investments needed to promote a vibrant, competitive market.

The dominance of Fannie and Freddie in the secondary mortgage market also stifles innovation and puts homeowners, communities and taxpayers at risk for future housing downturns, and is not making transparent sustained contributions to affordable housing. Although there are indications of pent-up demand for homes, uncertainty, including regulatory uncertainty, is placing unnecessary restraints on lending by banks and other mortgage originators. Creditworthy borrowers are being limited in their ability to buy homes, thereby creating fewer jobs and slowing economic growth. To support the recovery and set a firm foundation for the future, now is the time for reform.

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Public discussion has highlighted a number of critical goals. The reformed housing-finance system should enable the dreams of middle-class and aspiring middle-class Americans to own homes by supporting consumer-friendly mortgage products such as the 30-year fixed-rate mortgage. It should provide help, through narrow and focused programs, to creditworthy first-time borrowers who might otherwise have trouble qualifying for a mortgage; and it should stimulate broad access to mortgages for historically underserved communities.

A reformed housing-finance system should support rental housing, which is vital to many Americans, especially younger and lower-income households. It should stimulate competition and innovation, for example in mortgage products and service delivery, while building in consumer protections to make sure that the innovations benefit the broad American public. And it should protect the taxpayer by placing substantial private capital in front of any government guarantee—and ensure that the taxpayer be properly compensated for that guarantee.

Less discussed, but also important for the future: Housing-finance reform presents an opportunity to enhance macroeconomic stability by making the housing sector more cyclically resilient. Housing has long been one of the most volatile sectors of the economy, and that volatility spills over into other sectors—with all Americans, but especially the most vulnerable and disadvantaged, bearing the brunt of housing-related or magnified recessions.

The basic idea of cyclical resilience is straightforward: Even if the economy is in a downturn, and even if there are disruptions to financial markets, reasonably priced mortgages should remain available to creditworthy borrowers. Financial-market failures can reduce liquidity in the mortgage market. This reduced liquidity was particularly evident during and after the most recent financial crisis, when even creditworthy borrowers had—and still have—difficulty getting a mortgage.

Fostering cyclical resilience means ensuring that the key securitization infrastructure on which the secondary mortgage market relies is not exposed to financial risk resulting from swings in housing prices or the economy. It also requires an institutional structure in which the government can quickly expand its normally remote position to one that temporarily, but flexibly, reduces the amount of risk borne by private capital so that funds continue to flow to qualified borrowers during a financial-market disruption or economic downturn. And that institutional structure needs to greatly minimize the chances of government bailouts, so that private participants do not have an incentive to take excessive risks.

Housing-finance reform is a key unfinished piece of business from the financial crisis, and putting all the parts together is a complex undertaking. But the current period of relative economic calm is exactly the right time to do so. The Senate Banking Committee is making promising bipartisan progress on this crucial task, and the administration looks forward to continuing to work with Congress to forge a new private housing-finance system that better serves current and future generations of Americans.

Mr. Furman is the chairman of the White House Council of Economic Advisers, of which Mr. Stock is a member.