What was the most profitable insurance company last year?

It wasn’t Berkshire Hathaway. It was a company that nearly collapsed in the 2008 financial crisis because of reckless housing bets and then required a colossal taxpayer bailout.

No, it was not American International Group.

It is Fannie Mae, the government-backed company that insures mortgages against default. Fannie made $17.2 billion last year, versus Berkshire Hathaway’s $14.8 billion. Fannie was the third-most profitable financial firm in 2012, after JPMorgan Chase and Wells Fargo. But this year, Fannie’s earnings could exceed even those of JPMorgan and Wells Fargo, if it decides to book a large tax-related gain.

The huge profits rolling in at Fannie, and at its corporate sibling Freddie Mac, reflect the enormous role the government is playing in the housing market nearly five years after the crisis. As a result, the earnings will intensify the debate over the amount of involvement that government should have in housing.

“This should change the dialogue of what we want to do with the companies,” said Guy Cecala, publisher of Inside Mortgage Finance, a trade publication.

Fannie and Freddie charge fees in return for a guarantee that they will pay back mortgages that default. In the first years after the crisis, that fee revenue was overwhelmed by losses. As those have abated, profits have returned for the two mortgage giants.

The big question looming over the housing market is how quickly to remove the support provided by Fannie and Freddie.

They shore up the market by purchasing mortgages from banks and selling them on, with the guarantee, to bond investors. Because the companies are government backed, they can borrow at a very low cost. They then effectively pass on some of that cost advantage to homeowners, making home loans cheaper for the average borrower. In addition, the sheer purchasing power of Fannie and Freddie in the mortgage market means there is always strong demand for home loans, which induces banks to keep making them.

As much as all that has helped the housing market, it has led to a situation where the government backed 86 percent of all mortgages last year, according to Inside Mortgage Finance. In 2000, the figure was 47 percent.

The concern in some quarters is that the government’s heavy involvement is distorting the housing market and the Treasury Department is moving too slowly to roll back the presence of Fannie Mae and Freddie Mac. “I’m glad Fannie Mae is showing an increase in income, but we have to remember that this is largely because we have crowded out private capital and made Fannie or Freddie the only viable execution option for new loans,” Senator Bob Corker, Republican of Tennessee, said in a statement.