HICRC article estimates that over 20% of firearm acquisitions in the past 2 years had no background check 

Using data from a HICRC sponsored nationally representative survey of more than 1600 firearm owners, authors Matthew Miller, Lisa Hepburn and Deborah Azrael find that 22% of gun owners who reported obtaining their most recent firearm in the previous two years reported doing so without a background check.  For firearms purchased privately, 50% were obtained without a background check (with an even higher percentage for gun owners living in states that do not regulate private firearm sales).  The article appeared in Annals of Internal Medicine, with an accompanying editorial by Philip Cook of Duke University entitled “At last, a good estimate of the magnitude of the private-sale loophole for firearms.”