Inconsistency in ability to use variables in nginx config

[miguel_hamster]

It seems like it's possible to use variables in some configuration
directives but not in others. This works:

root /usr/www/$sitename/httpdocs;

works, while these:

access_log /var/log/www/$sitename/access.log;
proxy_cache $sitename;

do not, instead generating errors when I try to restart nginx.

Is there any documentation that explains where I can and cannot use a
variable? Or is there some syntax I should be using to indicate variable
interpolation? It would be immensely helpful if they worked in all these
contexts, because then we wouldn't have to repeat so much across different
site configuration files, leading to the requirement for generating them
with clunky scripts. As it is, the variables are of very limited utility.

Posted at Nginx Forum: http://forum.nginx.org/read.php?2,244605,244605#msg-244605