Indeed. From Wikipedia: In the liner notes to 1975's The Best of Leonard Cohen, which includes the song, he mentions that the famous blue raincoat to which he

Indeed. From Wikipedia: In the liner notes to 1975's The Best of Leonard Cohen, which includes the song, he mentions that the famous blue raincoat to which he refers actually belonged to him, and not someone else: I had a good raincoat then, a Burberry I got in London in 1959. Elizabeth thought I looked like a spider in it. That was probably why she wouldn't go to Greece with me. It hung more heroically when I took out the lining, and achieved glory when the frayed sleeves were repaired with a little leather. Things were clear. I knew how to dress in those days. It was stolen from Marianne's loft in New York City sometime during the early seventies. I wasn't wearing it very much toward the end.