Please help me with understanding the meaning of the phrase

"I allowed as how I was"

In context

The stranger looked me over. "You're Private Hugh McNeal?" I allowed as how I was.

Thank you

I understand it to mean that the person answered the question of his identity.

allowed definition | Dictionary.com
Al·low (ə-lou') Pronunciation Key
v. al·lowed, al·low·ing, al·lows

Chiefly Southern & Midland U.S.

To admit; concede: I allowed he was right.
To think; suppose: "We allow he's straight" (American Speech).
To assert; declare: Mother allowed that we'd better come in for dinner.