Trends in the agency mortgage-backed securities market suggest that private mortgage insurers may have gained some market share from government MI programs during the third quarter of 2016, according to a new Inside Mortgage Finance analysis. Fannie Mae and Freddie Mac securitized a total of $75.89 billion of insured single-family mortgages during the third quarter, an increase of 29.5 percent from the previous period. That was a tad below the 29.7 percent increase in overall MBS production by the two government-sponsored enterprises, but it kept the private MI share at 26.8 percent for the third quarter. Meanwhile, the booming Ginnie Mae market showed...[Includes two data tables]