From beliefs to prices: Analyzing how inflation expectations affect the inflation distribution

This paper investigates how the distribution of inflation expectations influences realized inflation across its entire distribution. We find that shocks to median inflation expectations increase the median inflation rate for up to three years, and subsequently generate persistent upside risks in inflation that endure for more than six years. By analyzing higher-order moments; specifically, the standard deviation, skewness, and kurtosis of inflation expectations, we show that greater disagreement among agents has distinct impacts on the distribution of the inflation rate. While an increase in the standard deviation amplifies right-tail inflation risks and generates quantile-dependent effects at the 90th percentile of the inflation distribution, a negative skewness shock temporarily shifts the distribution without any quantile-dependent effects. In the long run, shocks to kurtosis have insignificant effects at lower quantiles, but significant effects at extremely upper quantiles. Furthermore, we show that the quantile dependence of the responses of inflation to shocks in the median and in the standard deviation of expectations is amplified when inflation is rising. Our results highlight the critical importance of the distributional properties of inflation expectations for understanding and managing inflation risks. The results also underscore the need for well-anchored expectations to promote macroeconomic price stability.