Explanation of Benchmarking Revisions for E-commerce Estimates

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 2008 using the results of the Annual Retail Trade Survey (ARTS). We revised the estimates to:

After performing the above linkage, the resulting e-commerce sales estimates for fourth quarter 1999 through the fourth quarter 2007 are input to the benchmarking program. The estimates for a given detailed NAICS code are revised in a manner that-

Reflect corrections to data for the current Monthly Retail Trade Survey (MRTS) and ARTS samples.

Introduce results from the 2007 ARTS.

Link the previously published estimates from the prior sample to estimates from the current sample.

Incorporate updates to the seasonal adjustment models and parameters to reflect the newly benchmarked estimates.

First, we derive revised annual e-commerce sales estimates for reference years 2000 through 2007 based on results from the current ARTS sample. For further information on the annual e-commerce sales estimates, please see http://www.census.gov/svsd/www/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 levels, corrections are applied to the retail e-commerce sales estimates for third quarter 2006 through fourth quarter 2008. Then, for each detailed NAICS level, 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 2008 are input to the benchmarking program. The estimates for a given detailed NAICS level are revised in a manner that—

For reference years 2000 through 2007, 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 2008.

A mathematical result of the benchmarking methodology is that all revised estimates following the end of the last benchmark year (2007) 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 level, a ratio of the benchmarked-to-input estimate for the fourth quarter is computed. Quarterly e-commerce sales estimates after the fourth quarter 2007 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.

Revised estimates for aggregate industry levels are computed by summing the revised estimates for the appropriate detailed industries comprising the aggregate.

New seasonal factors are computed and used to adjust e-commerce sales estimates for the fourth quarter 1999 through fourth quarter 2008. The new seasonal factors are computed using the benchmarked estimates as input to the seasonal adjustment program.

Source: Retail Indicators Branch, U.S. Census Bureau
Last Revised: May 15, 2009