The yarn has a longer way to go on a purl stitch than a knit stitch and it can cause a gap. You can wrap the first purl stitch the "wrong way" which is under instead of over and it twists the stitch and makes it tighter. It will only show on the back so on a hat it makes no difference.
Here's my blog where I comment on this. It's about ribbing, but works on cables, too.
One other thought now...if you were knitting on a 16 inch circular needle have you switched to double points or another method so the stitches aren't stretched out? That may solve the problem entirely w/o changing the way you purl.