Inflation persistence and optimal positive long-run inflation

In this paper we prove that (I) inefficient natural level of output (Friedman (1968)), (II) central bank's desire to stabilize output around a level that is higher than the inefficient natural level of output, (III) long-run Phillips curve trade-off, and (IV) inflation persistence result in optimal positive long-run inflation. The combination of (I), (II), and (III) makes positive inflation forever in principles desirable as it would result in positive output gap forever. Optimal positive steady-state inflation obtains if and only if there is a long-run incentive for positive inflation. Inflation persistence, defined as costly, in terms of output, disinflation, generates a long-run incentive for positive inflation. Optimal positive steady-state inflation obtains in the basic neo-Wicksellian model (Woodford (2003)) with inflation persistence due to backward-looking rule-of-thumb behaviour by price setters. Optimal positive long-run inflation also obtains in what we refer to as the nonmicrofounded model. Prescinding from hyperinflation, the formula for steady-state inflation is capable of providing a positive theory of inflation.