SAS estimates are computed using the Horvitz-Thompson estimator (see https://www.census.gov/programs-surveys/sas/technical-documentation/methodology.html for a complete description of the SAS estimation methodology). These SAS estimates are then benchmarked to the final results of the 2017 Economic Census.

Prior to benchmarking, two operations are performed:

• Historical corrections are made to current sample data back to 2015.
• Total Revenue estimates from the current sample for 2015 and subsequent years are linked to the published estimates from the prior sample. For a given detailed industry based on 2012 NAICS, the linking is performed by multiplying the Horvitz-Thompson total revenue estimate from the current sample by a ratio (the "revenue ratio"). The numerator and denominator of the ratio are as follows:
• The numerator is the 2015 published total revenue estimate for the industry on a 2012 NAICS basis from the prior sample.
• The denominator is the 2015 Horvitz-Thompson estimate of total revenue for the industry on a 2012 NAICS basis from the current sample.

The resulting total revenue estimates from these pre-benchmarking operations will be referred to as "modified" revenue estimates for the remainder of this paper.

Once the aforementioned operations are complete, benchmarking of total revenue estimates is executed first, followed by benchmarking of total expenses. Next, detail data items that sum to the benchmarked total revenue or total expense estimates are benchmarked. Finally, remaining data items that do not sum to benchmarked total revenue or total expenses are benchmarked. The details of each step are outlined below.

Total Revenue

The “modified" revenue estimates are input to the benchmarking program. Using this program, the modified revenue estimates for survey years 2013 and later are revised in a manner that:

• Uses the 2012 and 2017 Economic Census revenue totals as fixed constraints, and
• Minimizes the sum of squared differences between the year-to-year changes of the input and revised estimates for 2012 through the end of the time series.

Refer to the revised total revenue estimates output from the benchmarking operation as "benchmarked" estimates.

Exceptions to performing benchmarking operations occurred in industries that did not use any Economic Census revenue constraints: NAICS 485111, 485112, 485113, 485119, 488510, 521110 and 541840. For NAICS 48511x and 488510, this was due to there being too much difference in instructions of what to count as revenue between SAS and the Economic Census. For NAICS 521110, SAS estimates incorporated revised industry values which were not reflected in the Economic Census publication. For NAICS 541840, the Economic Census assigned/divided revenue to multiple product classifications (i.e. kinds of business) for an establishment while SAS only assigned revenue to one primary kind of business for an establishment. This distinction created too much difference for what is counted as revenue in NAICS 54184 between SAS and the Economic Census. For all of these industries, the benchmarked estimates were set equal to the modified estimates; and subsequently, their associated aggregate estimates do not match the 2012 and 2017 Economic Census results.

Note that total revenue estimates for 2012 and prior years are not generally revised. However, exceptions occurred in industries where updated prior Economic Census levels were believed to be more reflective of industry activity. In those cases, survey data prior to 2012 was recalculated. In addition, Economic Census revenue totals from 2012 or prior were updated and used in the benchmarking process as fixed constraints.

A mathematical result of the benchmarking methodology is that all benchmarked estimates following the end of the last benchmark year (2017) can be calculated simply by multiplying the corresponding input estimates by the ratio of the benchmarked-to-modified estimate for the last benchmark year. Modified revenue estimates for years after 2017 are multiplied by this ratio, called a carry-forward factor (or census adjustment factor), to derive published total revenue estimates for 2018 and subsequent years. The carry-forward factor can change during the life of the sample if historical corrections change the modified estimate for 2017. At the end of the current sample, the carry-forward factor remains the same until the next benchmarking operation.

Total Expenses

A method similar to the one for benchmarking total revenue is used to benchmark total expenses. First, to link to the previous sample, the revenue ratio described above is applied to the Horvitz-Thompson total expense estimates for each detailed industry for 2015 and subsequent years, resulting in modified total expense estimates for these years. Note that the revenue ratio was designed to make the modified estimate of revenue for 2015 equal to the published estimate from the prior sample. Since total expenses still uses the revenue ratio to create modified total expense estimates, for each detailed industry, the modified total expense estimates will not be equal to the published total expense estimates from the prior sample for 2015. This could lead to a potentially overstated change in the estimate between 2014 and 2015. To address this, the benchmarking operation is employed, using the published 2012 estimate from the prior sample and the 2015 modified estimate from the current sample as fixed constraints to adjust 2013 and 2014 estimates.

The resulting total expense estimates (call these "modified" total expense estimates) are input to the benchmarking program. Using this program, the modified total expense estimates for 2012 through the end of the time series are revised in a manner that:

• Uses as constraints the modified 2012 and 2017 total expense estimates multiplied by the benchmarked-to-modified ratio of total revenue for that year (note that we do not benchmark using the total expense estimates from the Economic Census). For 2017, this ratio is equal to the revenue carry-forward factor, for 2012, this ratio is usually equal to one.
• Minimizes the sum of squared differences between the year-to-year changes of the modified and revised total expense estimates for 2012 through the end of the time series.

The same mathematical result of the benchmarking methodology described above for total revenue estimates also applies to total expenses. That is, modified total expense estimates for 2017 and subsequent years can be multiplied by the same carry-forward factor described above to calculate published total expense estimates for 2017 and subsequent years.

For industries with updated 2012 (or 2007) Economic Census revenue, the 2012 (or 2007) benchmarked-to-modified revenue ratio(s) will not be one, respectively, so an additional constraint(s) is added: the modified 2007 (or 2002) total expense estimate (multiplied by the 2007 (or 2002) benchmarked-to-modified revenue ratio, which will always be equal to one).

All exceptions mentioned for benchmarking total revenue also apply for total expenses.

An additional exception to performing benchmarking operations for total expenses occurred in NAICS 521. During survey year 2020 processing, corrections were applied to total expense estimates for 2015 and subsequent years. Corrected Horvitz-Thompson total expense estimates were used as the revised modified total expense estimates. The “new” modified total expense estimates for 2017 and subsequent years were then multiplied by the 2017 benchmarked-to-modified revenue ratio (i.e., the carry-forward factor) to calculate benchmarked total expense estimates for 2017 and subsequent years. The same carry-forward factor was also applied to the “new” modified total expense estimates for 2015 and 2016, as a carry-backward factor, to calculate benchmarked total expense estimates for 2015 and 2016. For subsector 521, total expense estimates for years prior to 2015 will not be published.

Detail Revenue Items

Estimates for data items that sum to total revenue are indirectly benchmarked using the following procedure. First, the Horvitz-Thompson detail revenue estimates are modified by the same revenue ratio described above for each detailed industry for 2015 and subsequent years. Then, the modified detail revenue estimates are benchmarked by raking them to the benchmarked total revenue estimate.

Detail Expense Items

Estimates for data items that sum to total expenses are indirectly benchmarked using the following procedure. First, modified detail expense estimates are produced by multiplying the Horvitz-Thompson detail expense estimates by the same revenue ratio described above for each detailed industry for 2020 and subsequent years. Then, for each year, the modified detail expense estimates are benchmarked by raking them to the benchmarked total expense estimates, keeping the ratio of each benchmarked expense item to the benchmarked total expenses equal to the ratio of the corresponding modified expense item to the modified total expenses.

Other Items

Revenue-based items have their modified estimates multiplied by the benchmarked-to-modified total revenue ratios for each year and expense-based items have their modified estimates multiplied by the benchmarked-to-modified total expenses ratios for each year to produce benchmarked estimates for these data items.

With the release of the 2017 Service Annual Survey in November 2018, E-commerce data series for service industries was discontinued. New data series for Revenue from Electronic Sources were introduced. The revenue ratio described above is applied to the Horvitz-Thompson estimate for Revenue from Electronic Sources for 2017 and subsequent years, resulting in a modified Revenue from Electronic Sources estimate for these years. Subsequently, Revenue from Electronic Sources modified estimates for 2017 and subsequent years are multiplied by the benchmarked-to-modified total revenue ratio (i.e., the revenue carry-forward factor) to produce benchmarked estimates for this data item.  

For all items, benchmarked estimates at aggregate levels are computed by summing the benchmarked estimates for the appropriate detailed series comprising the aggregate.

Nonemployers

Nonemployer total revenue estimates are based on data from the Nonemployer Statistics program and are not benchmarked to the 2017 Economic Census.