On the Optimal Inflation Rate

How do financial frictions affect the optimal inflation rate? Can financial frictions alone annul the long-run super-neutrality of money? Should the inflation rate be higher in emerging market economies with less developed financial markets than in advanced economies, as is currently observed? To answer these questions we set up an incomplete markets model in which households choose portfolios consisting of risky (physical) capital and money. Physical capital holdings are encumbered with idiosyncratic risk. Financial frictions prevent the diversification of the idiosyncratic risk. Our analysis in this paper can be seen as a simplified discrete-time version of the “I Theory of Money” (Brunnermeier and Sannikov, 2015) – but without the “I”, the intermediaries and inside money, and with an exclusive focus on the long-run steady state. Like in Samuelson’s (1958) OLG and in Bewley’s (1980) uninsurable endowment risk model, money serves as store of value and can have positive value despite the fact that it never pays any dividends. Diamond (1965) introduces physical capital in Samuelson’s OLG model and Aiyagari (1994) in Bewley’s incomplete markets setting (but capital drives out money). In our setting, money and physical capital coexist and agents choose portfolios. Like in Diamond and Aiyagari, the market outcome is dynamically inefficient. In contrast, however, to Diamond and Aiyagari, in which