Does a Threshold Inflation Rate Exist? Quantile Inferences for Inflation and Its Variability

Using quantile regressions and cross-sectional data from 152 countries, we examine the relationship between inflation and its variability. We consider two measures of inflation -- the mean and median -- and three different measures of inflation variability -- the standard deviation, relative variation, and median deviation. All results from the mean and standard deviation, the mean and relative variation, or the median and the median deviation support both the hypothesis that higher inflation creates more inflation variability and that inflation variability raises inflation across quantiles. Moreover, higher quantiles in both cases lead to larger marginal effects of inflation (inflation variability) on inflation variability (inflation). We particularly consider whether thresholds for inflation rate or inflation variability exist before finding such positive correlations. We find evidence of thresholds for inflation rates below 3 percent, but mixed results for thresholds for inflation variability. Finally, a series of robustness checks, including a set of additional explanatory variables as well as controlling for potential endogeneity with instrumental variables, leaves our findings generally unchanged.