I saw this summary of a government report on Fannie Mae and Freddie Mac last week and thought it interesting. One third of all mortgages originated in 2005 and 2006 were subprime or Alt-A mortgages. Over 2005 and 2006, government agencies issued 45% and 44%, respectively, of mortgage backed securities. This compares to today, where agencies issue of 95% of mortgage backed securities.
Reading this report, it's clear that government agencies did not cause the housing market bubble. The market worked well, too well. People wanted any kind of mortgage to get into the housing market. When the agencies could not meet demand, or had standards that were too strict, the private market stepped in and created and originated mortgages, and then bought, packaged and sold these into non-government mortgage backed securities.
The housing market is still recovering from the excess of the mid-2000s. If the agencies eased their mortgage purchase standards it would help the housing market by increasing demand.