It does not provide any Damage Threshold, provides no bonuses, has no value, and is an undroppable/unsellable quest item from the quest Debt Collector. The hat looks very similar to Old Cowboy hats.
Caleb McCaffery's hat is possibly bugged; after you remove it from the Vegas Strip, you may experience crashes upon returning to the Strip in which the screen goes black and non-responsive, and music continues to play. This may be because it counts as a quest item that is surrendered upon completion. Getting an "old cowboy hat" from either the Crimson Caravan or Mick's store and wearing it upon entering seems to fix the problem, allowing you to return to the Vegas Strip. NOTE: This does seem to temporarily fix the bug, however short of keeping the 'old cowboy hat' in your inventory there seems to be a permanent risk of the problem reoccurring.
Fixed by downloading patch.
This bug can also corrupt your auto-save, so be sure when entering and exiting New Vegas locations to have a recent hard save.
Some reports of crashing while zoning from Mick & Ralph's to Freeside.
Caleb McCaffery's hat can be worn with many helmets. It is yet to be seen if it can be worn with a power armor helmet.
PlayStation 3Xbox 360 When trying to wear the hat upon immediately picking it up, the game will freeze. This probably occurs because when you pick it up it is considered a "broken" headgear but is still equippable.
When doing the quest Debt Collector he may appear in New Vegas before you are supposed to kill him, when it happenens you may be able to keep his hat because you were supposed to go and kill him, but instead it may cut to the end of the quest after you give 600 caps to Francine Garret she will say "Here take this room it was Caleb McCaffery's." and you may still have it in your inventory; however, this isn't a problem because it has 0 weight.