How Well Does "Core" CPI Capture Permanent Price Changes?

We decompose core CPI and the food and energy CPI measures into permanent and transitory components using a correlated unobserved components model, to examine the behavior of core CPI when subject to shocks and to examine the claim that core CPI captures the persistent part of headline CPI. We find that the permanent component of core CPI is more volatile than core CPI, or that the permanent and transitory components are highly correlated. We find that the excluded food and energy components have important permanent components, and that core CPI has an important transitory component. We examine impulse response functions and find that headline CPI inflation responds more sharply to shocks than core CPI inflation, and after the first year the impact of shocks on headline inflation is less than the impact on core inflation.