talk through one's hat vs feign

talk through one's hat and feign both are verbs.

Word	Noun	Adjective	Verb	Adverb
talk through one's hat	No	No	Yes	No
feign	No	No	Yes	No

As verbs, feign is a hypernym of talk through one's hat; that is, feign is a word with a broader meaning than talk through one's hat:

talk through one's hat: speak insincerely or without regard for facts or truths
feign: make believe with the intent to deceive

Other hypernyms of talk through one's hat include affect, dissemble, pretend, sham.

talk through one's hat (verb)	feign (verb)
speak insincerely or without regard for facts or truths	make believe with the intent to deceive
	make a pretence of