What is the value of a 1963 US 1 dollar bill signed by Joseph Barr?

Unless it's uncirculated, face value only.

Even though Barr served as Treasury Secretary for only a month or so at the end of the Johnson administration, bills with his signature continued to be printed for a long time afterwards so they are not particularly rare. As of 05/2012 U.S. Currency Auctions lists a fair market value of an uncirculated Barr note at only $2.00. Many sellers on eBay are under the mistaken impression that these bills are rare - or are trying to play off others' lack of knowledge - and are attempting to charge highly inflated prices.