By "narrow keywords" do you mean long tail keywords or highly niche-specific keywords?
Long tail keywords are much more descriptive/qualified (think "shoes" versus "red satin dancing shoes for children") and as such may target leads further along the sales funnel. A study published in Search Engine Watch did find long tail keywords to be associated with higher conversion rates.
I suspect niche-specific keywords also hold similar benefits (highly targeted, possibly highly motivated leads) but I haven't personally come across any study citing these. In my own experience with PPC campaigns, the advantages of highly niche-specific keywords need to be balanced with the disadvantages of fewer queries, fewer impressions and less traffic in total.