The role of search frictions in the long-run relationships between inflation, unemployment and capital

This paper explores the long-run relationships between inflation, unemployment and capital accumulation by proposing a model with search frictions in both goods and labor markets. This framework allows us to identify a negative extensive margin effect of inflation on the number of firms demanding capital and a positive intensive margin effect of inflation on the capital demanded per firm. The two effects together generate a hump-shaped relationship between long-run inflation and aggregate capital. These results are consistent with our empirical evidence from a cross-section of 76 countries, which suggests a non-monotonic relationship between inflation and investment to GDP ratio in the long run. Our calibrated results are also consistent with empirical findings from the U.S. data on the effect of inflation on capital stock, unemployment and the real interest rates.