Hi,
My guess is 1910 to 1930. As Nicole said, the basic style stayed the same for many decades. Clues can be found in the lining, the height of the crown (which varied slightly over time), and type of crown ribbon used. The lining is an older style, and stores often had a choice of linings to be put in the hats, with their store name pre-stamped on the lining. The same quality hat would be made by Stetson, but the linings could be different in both look and quality, depending on the store which would sell them.
Yours is pretty badly beat up, but good for a costume.
Try the Fedora Lounge? It can be a good resource for info on men's hats, but be sure to get a variety of advice and make your own judgement too.
And Hollis is right, checking the store name is excellent advice too.
B