**Elliot Williams** (2006)
"The Effects of Rounding on the Consumer Price Index."

The Bureau of Labor Statistics rounds the Consumer Price Index (CPI) to a single decimal place before releasing it, and the published CPI inflation series is calculated from those rounded index values. While rounding has only a relatively small effect on the

levelof the CPI series at present, it can have a significant effct on CPI inflation, the monthlypercent changesin the CPI.This paper estimates the impact of rounding error on the published CPI inflation for both contemporaneous and historical data. Using an unrounded CPI series from January 1986 to July 2005 as a benchmark, I find that published CPI inflation differs from its full-precision counterpart approximately 25% of the time, and that reporting the CPI levels to three decimal places would reduce these discrepancies to under 0.5%. Further, the variance introduced by rounding error is large when compared to the sampling variation in CPI inflation. I find that the BLS could reduce total CPI inflation error variance by 42% by simply reporting more digits in the CPI index, resulting in a significantly more accurate reflection of monthly inflation.

In order to extend these results to the CPI historical series, I derive the distribution of the rounding error component of inflation. From this analysis, it is possible to estimate the probability of large rounding errors for a given CPI level and rounding precision. Three regimes emerge. Before the 1970's inflation, discrepancies due to rounding were both frequent and frequently large relative to the underlying inflation rate. During the inflationary period of the mid-1970's to mid-1980's, both the probability and relative magnitude of discrepancies decrease dramatically. Finally, the last twenty years are characterized by a slowly falling probability of any rounding-induced error, but a roughly constant probability of an error of a given size.

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