Hyperbolic Discounting and Positive Optimal Inflation

The Friedman rule states that steady-state welfare is maximized when there is deflation at the real rate of interest. Recent work by Khan, King, and Wolman [Review of Economic Studies 10 (4), 825–860] uses a richer model but still finds deflation optimal. In an otherwise standard New Keynesian model we show that, if households have hyperbolic discounting, small positive rates of inflation can be optimal. In our baseline calibration, the optimal rate of inflation is 2.1% and remains positive across a wide range of calibrations.