Imperfect monitoring and the discounting of inside money

One of the fundamental questions concerning inside money is whether its issuers should be regulated and how. This paper evaluates the efficiency of one prevalent regulatory recommendation -- a requirement that private issuers redeem inside money on demand at par -- in a random-matching model of money where the issuers of inside money are only imperfectly monitored. I find that for sufficiently imperfect monitoring, a par redemption requirement leads to lower social welfare than if private money were redeemed at a discount. A central message of the paper is that if inside money and outside money are not perfect substitutes for one another, as is the case if there is sufficiently imperfect monitoring, a par redemption requirement may not be socially optimal because such a requirement effectively binds them to circulate as if they are. Such an outcome is a version of Gresham's law that bad money drives out good money.