THIS ARTICLE DEMONSTRATES HOW ROUNDING A SERIES
before calculating its percent changes introduces an additional source of statistical error. Using an unrounded CPI data set as a benchmark reveals that the published values differ from an unrounded benchmark approximately a quarter of the time, and the errors can be large relative to the true underlying inflation rate.
Mathematical analysis and some simulation results demonstrate in more detail how the rounding-induced errors behave with respect to both the level of the CPI and the inflation rate over time. Three regimes emerge: (1) before 1970, both the frequency and magnitude of the errors were large; (2) the inflation of the mid-1970s and early 1980s cut the probability of a rounding error in half and led to moderation in the relative errors; and (3) during the present period, a high CPI value makes the reported inflation rate match the unrounded rate around 75 percent of the time, but the low underlying inflation rate has kept the probability of errors of a given relative size roughly constant and comparatively moderate. These findings certainly have implications for inflation research over the earlier periods.
Finally, the “take-home” message from the real-data experiments presented herein show that increasing the precision of