Annual & Quarterly Services

Benchmarking to the 2007 Economic Census

Estimation Method

Total estimates are computed using the Horvitz-Thompson estimator (i.e., as the sum of weighted data (reported or imputed) for all selected sampling units that meet the sample canvass and tabulation criteria). The weight for a given sampling unit is the reciprocal of its probability of selection into the sample. Estimates for industries that are being published for the first time as a result of the Services Expansion Initiative are published with no further adjustment. Therefore, the estimates for these industries are Horvitz-Thompson estimates. All other estimates are input to a benchmarking procedure as described below. Variances are estimated using the method of random groups and are used to determine if measured changes are statistically significant.

Benchmarking

Final results of the 2007 Economic Census are used to benchmark the SAS estimates. Benchmarking of total receipts estimates is described first, followed by benchmarking of total expenses. Next, the procedure used to adjust the remaining detail data items to the benchmarked totals receipts and total expenses estimates is described.

Prior to benchmarking, three operations are performed:

For industries affected by the change from 1997 to 2002 NAICS, published revenue estimates for 1998 through 2004 from the prior sample are restated on a 2002 NAICS basis, using revenue distributions from the 2002 Economic Census that link the two sets of classification codes. Of particular note, the estimates for Sector 51 (Information) are revised due to the creation of new industries for Internet publishing and broadcasting and Web search portals. For industries not affected by the change from 1997 to 2002 NAICS, there is no need to restate the published census-adjusted revenue estimates from the prior sample.

Historical corrections are made to current sample data back to 2004.

Receipts estimates from the current sample for 2005 and subsequent years are linked to the published estimates from the prior sample. For a given detailed industry based on 2002 NAICS, the linking is performed by multiplying the Horvitz-Thompson receipts estimate from the current sample by a ratio. (Call this the, “receipts ratio.”) The numerator and denominator of the ratio are as follows:

The numerator is the 2004 published receipts estimate for the industry on a 2002 NAICS basis from the prior sample.

The denominator is the 2004 Horvitz-Thompson estimate of receipts for the industry on a 2002 NAICS basis from the current sample.

The resulting receipts estimates (call these “modified” receipts estimates) are input to the benchmarking program. Using this program, the modified receipts estimates for 2002 through 2009 are revised in a manner that:

Uses the 2002 and 2007 Economic Census receipts totals as constraints.

Minimizes the sum of squared differences between the year-to-year changes of the input and revised estimates for 2002 through 2009.

Refer to the revised total receipts estimates output from the benchmarking operation as “benchmarked.” Note that total receipts estimates for 2002 and prior years are not revised, except for estimates for NAICS 54161. These estimates are revised because of changes between 1997 and 2002 NAICS codes that were not previously reflected in the estimates.

A mathematical result of the benchmarking methodology is that all 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 benchmark year. Therefore, for a given detailed NAICS level, a ratio of the benchmarked-to-modified receipts estimates for 2007 is computed. Mathematically, this ratio is equivalent to the 2007 Economic Census receipts divided by the 2007 Horvitz-Thompson receipts estimate from the current sample. Horvitz-Thompson receipts estimates for years after 2007 are multiplied by this constant ratio, which is called a carry-forward factor (or census adjustment factor), to derive published total receipts estimates for 2008 and subsequent years. The carry-forward factor remains the same until the next benchmarking operation.

A method similar to the one for benchmarking total receipts is used to benchmark total expenses. First, the receipts ratio described above is applied to the Horvitz-Thompson total expense estimates for each detailed industry for 2004 and subsequent years, resulting in modified total expense estimates for these years. Then, the difference between the 2004 modified total expenses estimate from the current sample and the 2004 published total expenses estimate from the prior sample is taken into account by applying a second ratio to the published total expenses estimates for 1998 through 2003 from the prior sample. The numerator and denominator of the second ratio are as follows:

The numerator is the 2004 modified total expenses estimate for the industry on a 2002 NAICS basis from the current sample.
The denominator is the 2004 published total expenses estimate for the industry on a 2002 NAICS basis from the prior sample.

The resulting total expenses estimates (call these “modified” total expenses estimates) are input to the benchmarking program. Using this program, the modified total expenses estimates for 1998 through 2009 are revised in a manner that:

Uses the derived 2002 (or the first year in the series if the series started after 2002) and 2007 total expenses estimates as constraints, where the constraints are derived by multiplying the modified total expenses estimates by the ratio of the benchmarked-to-modified total receipts estimates for each year. (Note that we do not benchmark using the total expenses estimates from the economic census.)
Minimizes the sum of squared differences between the year-to-year changes of the input and revised total expenses estimates for 1998 (or the first year the series started) through 2009.

The same mathematical result of the benchmarking methodology described above for total receipts estimates also applies to total expenses. That is, Horvitz-Thompson total expenses estimates for 2007 and subsequent years are multiplied by the same carry-forward factor described above (i.e., the 2007 Economic Census receipts divided by the 2007 Horvitz-Thompson receipts estimate from the current sample), to derive published total expenses estimates for 2007 and subsequent years.

Estimates for data items that sum to total receipts or total expenses are indirectly benchmarked using the following procedure. First, the same method for producing modified total expenses estimates is used to produce modified estimates for these items. Then, the modified detail receipts or expenses are raked to modified total receipts or total expenses. Finally, the raked modified estimates are raked to the benchmarked total receipts or total expenses estimates to obtain the “benchmarked” estimates for these data items.

For all other receipts data items (i.e., those that do not make up sums to total receipts, such as e-commerce), modified estimates for these data items are computed using the same method for producing modified total expenses estimates. Then, modified estimates for these data items are multiplied by the benchmarked-to-modified total receipts ratios for each year to produce “benchmarked” estimates for these data items.

The same procedure is used to produce “benchmarked” estimates for other expense data items (i.e., those that do not make up sums to total expenses, such as interest expense), except the benchmarked-to-modified total expenses ratios are used instead of the benchmarked-to-modified total receipts ratios to produce “benchmarked” estimates for these items.

Benchmarked estimates for any other sums of data items are obtained by adding the benchmarked estimates of the data items that comprise the sum.

Benchmarked estimates at aggregate industry levels are computed by summing the benchmarked estimates for the appropriate detailed industries comprising the aggregate.

Nonemployers:

Estimates for employers plus nonemployers are only published for total receipts. All other estimates are based only on employer firms. Because of the industry levels at which we benchmark nonemployer totals, the benchmarked nonemployer totals published in SAS may not sum to the nonemployer totals published by Nonemployer Statistics, except for years 2002 and 2007.