"The chart shows that from 1969 to 2012, the PCE and my extended C-CPI-U series indicate that prices rose by a factor of 5, while the CPI-U-RS gives the ratio as 5.5 and the CPI-U as 6.3. These distinctions are important. If nominal income—income prior to taking the rising cost of living into account—rose by a factor of 7.2 over this period (as my own estimates suggest), using the CPI-U to adjust for inflation would give the conclusion that “real” income rose by 16 percent. Using the PCE or C-CPI-U, we would conclude that real income rose by 45 percent—nearly three times as much. For comparison, the CPI-U-RS would indicate a 31 percent increase—substantially lower than the estimate from indices that fully take substitution into account."