Endogenous Monetary Policy: A Leviathan Central Bank in a Lagos-Wright Economy

This paper studies the nature of optimal monetary policy under a Leviathan monetary authority in a microfounded model of money based on ?. Such a monetary authority is a reality whenever and wherever fiscal policy is a primary driver of the monetary policy. Under no commitment, we characterize and solve for a Markov perfect equilibrium as well as for equilibrium with reputation concerns. For the Markov equilibrium, a generalized Euler equation is derived to characterize optimal policy that trades off the current benefit of increasing consumption against the reduced ability to do so in the future. Under reputation equilibrium, centralized market interaction is modeled as an infinitely repeated game of perfect monitoring, between a Leviathan monetary authority (a large player) and the economic agents (small players). Such a game has multiple equilibriums but the large-small player dynamics pins down the equilibrium set of payoffs and features less than maximum inflation tax. Depending on how we interpret the Leviathan central bank, the factors determining the realized equilibrium differ. Higher fiscal profligacy of the underlying political authority leads to a higher monetary growth rate and inflation tax, while existence of threat of competition in case of a private money supplier or threat of external aggression in case of a self interested sovereign leads to a lower one. The realized equilibrium monetary growth rate and the associated inflation tax is thus, affected by the intensity of context contingent factors. Concentrating only on Markov strategies in this repeated game shows that the Markov perfect equilibrium features maximum inflation tax.