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The Federal Housing Administration (FHA) administers single-family and multifamily mortgage insurance programs within the U.S. Department of Housing and Urban Development (HUD). It provides mortgage insurance for the purchase of single- and multifamily housing targeted to low and moderate-income families. FHA insures lenders against losses in case of mortgage default, enabling private industry to construct and rehabilitate multifamily housing, single-family homes, and assisted living facilities for low and moderate-income families and individuals. FHA plays an indispensable role in extending home financing to low-income homebuyers and other traditionally under-served populations.
HFAs and FHA Insurance
State HFAs use FHA single-family mortgage insurance in combination with Mortgage Revenue Bonds (MRBs) and other funding sources to finance modestly priced homes for first-time homebuyers. HFAs will often provide down payment assistance in connection with FHA-insured loans to help responsible homeowners who cannot afford a large down payment.
FHA Reform
During the recent economic crisis, FHA's lending increased substantially as it played a countercyclical role in helping to boost the weakened housing market. Partly as a result of this increased role, the FHA's single-family programs have recently experienced financial difficulties, causing some to push for strong returns to FHA's homeownership lending. 
NCSHA supports efforts to help FHA shore up its fiscal balance, but cautions policymakers to be careful not to overreach and price responsible low-and moderate income borrowers FHA traditionally serves out of the housing market. 
Helpful link: HUD's FHA Web Page