## Explanation of Benchmark Revisions for Quarterly Retail E-commerce Sales

The estimates of quarterly retail e-commerce sales are revised from fourth quarter 1999 through fourth quarter 2010 using the results of the Annual Retail Trade Survey (ARTS). First, we derive revised annual e-commerce sales estimates for the years 2000 through 2010 based on results from the current ARTS sample. For further information on the annual e-commerce sales estimates, please see http://www.census.gov/retail/arts/summary.html. We use these annual estimates as constraints to benchmark the estimates of quarterly retail e-commerce sales, as described below.

For select detailed NAICS codes, corrections are applied to the retail e-commerce sales estimates for third quarter 2006 through fourth quarter 2010. Then, for each detailed NAICS code, the retail e-commerce sales estimates for the fourth quarter 1999 (the beginning of the series) through second quarter 2006 from the prior sample are linked to the estimates derived from the current sample. The linkage is performed for each detailed NAICS level by multiplying the sample-based estimates, or unmodified estimates, from the prior sample by a ratio. The numerator of the ratio is the unmodified e-commerce sales estimate for the third quarter 2006 from the current sample, and the denominator is the unmodified e-commerce sales estimate for the third quarter 2006 from the prior sample.

After performing the above linkage, the resulting e-commerce sales estimates for fourth quarter 1999 through the fourth quarter 2010 are input to the benchmarking program. The estimates for a given detailed NAICS code are revised in a manner that-

• For 2000 through 2010, constrains the sum of the 4 quarterly e-commerce sales estimates to equal the corresponding annual e-commerce sales estimates from ARTS.
• Minimizes the sum of the squared differences between the quarter-to-quarter changes of the input and revised estimates for fourth quarter 1999 through fourth quarter 2010.

A mathematical result of the benchmarking methodology is that all revised estimates following the end of the last benchmark year (2010) are derived by multiplying the corresponding input estimates by the ratio of the benchmarked-to-input estimate for the last quarter of the last benchmark year. Therefore, for a given NAICS code, a ratio of the benchmarked-to-input estimate for the fourth quarter is computed. Quarterly e-commerce sales estimates after the fourth quarter 2010 are multiplied by this constant ratio, which is called a carry-forward factor, to derive published e-commerce sales estimates. The carry-forward factor remains the same until the next benchmarking operation.

Source: Retail Indicators Branch, U.S. Census Bureau
Last Revised:  August 16, 2012