Trick question: None, zero, zilch.  By law, Fannie and Freddie can’t originate loans–they can only buy or guarantee loans that have already been made by actors in the private sector.  This is no small point, but it’s a point that Zandi leaves blurry at best in his book Paying the Price which I reviewed for Barron’s here ($ probably).  Here’s a key graph from the first few pages of the book: 

If you read this, would you think government (presumably including Fannie and Freddie) was doing the rest of the mortgage originations?  I would. I

f mortgages aren’t originated “by nongovernment lenders” aren’t the rest originated “by government lenders?”  

Well, no. There might be some exceptions that slipped past my radar, but even VA and FHA loans are “originated by nongovernment [i.e., private] lenders.” In the coda, I speculate on what Zandi might mean–and I show that the Mortgage Bankers Association did an adequate job making (what I think is) Zandi’s point in their own report on the housing market.  
But in addition to being needlessly vague, the chart above dodges the whole question of what Fannie and Freddie have the power to do: They have the power to guarantee or purchase mortgages years after the original loan is made. 
This point gets lost in debates over which precise year F&F started buying up the worst mortgages: If mortgage lenders and buyers of mortgage-backed securities care about whether somebody will be around to pick up some bad mortgages if the market turns south, then the current activity of F&F matters a lot less than the expectation of future activity.  The commitment of F&F to maintain a liquid market changes the market.  Imagine the positive and negative side effects of central banks, apply them to the long-term debt market, lather rinse repeat.  Will somebody be there to take this hot potato off my hands? If so, I’m more willing to buy the potato today.  
Fannie and Freddie: In theory and sometimes in practice, buyers of last resort.  
Another element that gets lost when reporting market “%”: In dollar terms, Fannie and Freddie’s book (mortgages held outright + mortgages guaranteed) both grew throughout the bubble years.  
This matters: 
If I thought that Fannie and Freddie were solely responsible for igniting a private-sector housing bubble (I don’t, but play along), what would I expect to see in the data?  

I’d probably expect to see Fannie and Freddie’s total book growing, with the private sector growing even faster.  Fannie and Freddie light the fire, then the bubble-prone private sector takes it from there.  The result? Fannie and Freddie’s holdings of new mortgage backed securities (MBS) would grow in dollars, shrink in percentages. Just like in real life:

The fact that private-label MBS exploded in the bubble years isn’t great evidence against the theory that F&F spurred/prolonged/exacerbated a bubble.  And the more a person believes in the inherent bubbliness of the private sector the more they should worry about the risks of massive government programs to encourage long-term lending. 
Before the financial crisis, I would have expected a chart like the one above (from Barry Ritholz) to have little impact on normal economists’ views of Fannie and Freddie’s role in the crisis.  Expectations, liquidity provision, government backstops: All would be worthy topics of discussion, their side effects would be fretted over.  Back then intangible features of the economy like promises and beliefs and animal spirits got quite a bit of play.  I liked and still like that kind of economics.  
Coda: As I note in the review, Zandi used similarly opaque language in a coauthored policy paper, “The Future of the Mortgage Finance System,” with a chart entitled “% share of mortgage originations.”  So he wasn’t just writing informally for a popular audience. 
Here’s how you do Zandi’s kind of chart transparently: 
This is from the Mortgage Bankers Association; it’s about multifamily, but the point stands: Here you can tell that mortgages are originated for Fannie and Freddie, not by them.  Its gets readers looking in the right direction: Somebody originated loans for F&F, so maybe you should wonder about that party’s incentives.  Maybe this is what Zandi meant, maybe not, hard to say.