Error_log doesn't accept a DRY variable

Here is my configuration file:

Let’s set some vars to be DRY

set $log_path /usr/local/nginx/logs;
set $rails_path /home/thomas/rails_apps;

access_log $log_path/traffic.log traffic;
access_log $log_path/access.video_on_demand.log main;
error_log /usr/local/nginx/logs/error.video_on_demand.log notice;

I can use $log_path with access_log but not with error_log. Anyone
else experienced this problem? I agree I won’t be changing the log
filename frequently but still, it would be cool to have to change it
in only one place.