Template dropdown missing from Page Attributes

I have set up WPMU and have installed Visual Composer. I'm going through their beginners tutorial but noticed that the templates dropdown section is missing from my page attributes, when I edit a page.

In the tutorial they select a 'full-width template'.
I'm on Theme twenty-sixteen. The same problem happened under Theme twenty-fifteen. Theme twenty-fourteen DID show the template dropdown in the page attributes, but it didn't change anything.

I feel that it may not be related to Visual Composer but could not find any pages that deal with this problem. All help very much appreciated!