John Mueller from Google said in a Reddit thread that using a blank robots.txt file or just stating all is allowed in that file is the same thing, it doesn't matter which you use.
He said "Doesn't matter" when he was asked Is there a difference? I've always used Dissallow: (blank) as it seems more efficient. But the current client is using Allow: /.
He said "Doesn't matter. You can also just use a comment like:"
# there are not robots.txt directives here
I barely ever use robots.txt files on my sites but as you all know, I like to share as much as I can with others. :P
There are good reasons to block sections of your sites and URLs in a robots.txt but you do not have to, if you don't want to.
Forum discussion at Reddit.