Why do you single out the XIII century? In Western/Southern Europe and much of Asia, it was in many respects a golden age. The XIV century was worse, most notably due to the plague.
(I may have been echoing an old SF story where a XXX century displaced person was telling a friend about his punishment for trying a ruthless power grab, which was being dumped in Warsaw in September 1939. However, he had bounced back, remaking a good life. But the "friend" was an agent who then proceeded to continue the punishment by dumping him in Baghdad before Genghis hit it ...).
The Mongols are exactly why I didn't mention the space between Asia and Western Europe. To tie in the Crusades comment below, I also didn't mention Northern Africa or the Middle East. Anyway, once again it seems I've read too much into a random number, similarly to when I jumped all over someone on Reddit for saying nothing happened in 1789!
I wouldn't advise the XIII century. Or most of the XX. Or the 5th BC. Or ...
As a matter of fact, you probably just have "better" news of the world, not objectively worse conditions. There was a post about that recently ...