We survey the theories on why banks promise to pay par on demand and examine evidence on the conditions under which banks have promised to pay the par value of deposits and banknotes on demand when holding only fractional reserves. The theoretical literature is divided into four strands: liquidity provision; asymmetric information; legal restrictions; and a medium of exchange. We assume that it is not zero cost to make a promise to redeem a liability at par value on demand. If so, then the conditions in the theories that result in par redemption are possible explanations why banks promise to pay par on demand. If the explanation based on customers’ demand for liquidity is correct, payment of deposits at par will be promised when banks hold ...