Effect of Moments on Aggregation and Long Memory in Inflation

There are two crucial conditions for cross-sectional aggregation of AR(1) parameters to produce long memory: 1) heterogeneity and 2) proximity to the unit root. We analyze role of moments, namely the mean and variance, of the distribution of the AR(1) coefficients in generating long memory. The positive relation between these moments and the order of integration suggests that the degree of fractional integration should decrease with a lower mean or variance. We investigate this result by first modeling long memory in inflation as a result of the aggregation of individual inflation expectations and then showing how the adoption of inflation targeting decreases the memory length in seven countries due to its moderating effect on individual inflation expectatio