Nonlinear unemployment effects of the inflation tax

Long-run inflation has nonlinear and state-dependent effects on unemployment, output, and welfare. We show this using a standard monetary search model with two shocks - productivity and monetary - and frictions in both labor and goods markets. Inflation lowers the surplus from a worker-firm match, in turn making it more sensitive to both productivity shocks and further increases in inflation. We calibrate the model to match key aspects of the US labor market and monetary data. The calibrated model is consistent with a number of empirical correlations, which we document using panel data from the OECD: (1) there is a positive long-run relationship between anticipated inflation and unemployment; (2) there is also a positive correlation between anticipated inflation and unemployment volatility; (3) the long -run inflation-unemployment relationship is stronger when unemployment is higher. The key mechanism through which the model generates these results is the negative effect of inflation on measured output per worker, which is likewise consistent with cross-country data. Finally, we show that the welfare cost of inflation is nonlinear in the level of inflation and is amplified by the presence of aggregate uncertainty.