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The authors study optimal monetary policy in a model in which fiat money and private debt coexist as a means of payment. The credit system is endogenous and allows buyers to relax their cash constraints. However, it is costly for agents to publicly report their trades, which is necessary for the enforcement of private liabilities. If it is too costly for the government to obtain information regarding private transactions, then it relies on the public information generated by the private credit system. If not all private transactions are publicly reported, the government has imperfect public information to implement monetary policy. In this case, they show that there is no incentive-feasible policy that can implement the socially efficient allocation.
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