The table indicates that for the entire sample inflation as measured by the CTPI or the PCELF are on average lower than either the CPI or MCPI and they both also have smaller standard deviations.
The results indicate that over the whole sample the CPILF has the highest correlation with the federal funds rate and the CTPI has the lowest correlation with the federal funds rate.
These results are interesting in that the CPILF and the PCELF have been touted as better measures of inflation that the CPI or the CTPI. The regression equation estimated with the MCPI as the measure of inflation has a highest adjusted R-squared value, the smallest standard error of regression, and the minimum AIC, indicating that the MCPI provides a better fit for the data.
The results indicate that the median consumer price index (MCPI) is a better measure of information on monetary inflation during the stable monetary regime from the early 1980s through the early 2000s, than either the consumer price index (CPI) or the GDP chain- type price index (CTPI), or several other measures of inflation including the CPI less food, the personal consumption expenditures index (PCE) and the PCE less food, based on estimated reaction functions.