1

EXPLANATION OF REVISIONS

Not adjusted estimates of monthly sales are revised for January 2013 through 

February or March 2022

1

(if an advance sales estimate is computed), as well as 

end-of-month inventory estimates for January 2011 through February 2022. Not 

adjusted estimates of quarterly retail e-commerce sales are revised for first quarter 

2011 through fourth quarter 2021.

Revisions to not adjusted estimates were made in two parts:

First, revisions were made to prior Monthly Retail Trade and Food Services

(MRTS) estimates to reflect historical corrections. Then, revisions were made 

when benchmarking the Monthly Retail Trade and Food Services estimates to the 

2020 Annual Retail Trade Survey (ARTS) and Service Annual Survey (SAS) 

estimates. 

Revisions to seasonally adjusted estimates were made based on the revised not 

adjusted estimates and revised seasonal adjustment factors. Adjusted estimates of 

monthly sales are revised for January 2010 through February or March 2022

1

(if 

an advance sales estimate is computed), as well as end-of-month inventory 

estimates for January 2008 through February 2022. Adjusted estimates of 

quarterly retail e-commerce sales are revised for first quarter 2008 through fourth

quarter 2021.

Reasons for Revisions

We revised the not adjusted estimates to: 

• Reflect corrections to data for the MRTS and ARTS samples. 

Corrections are made to replace previously reported data with more 

accurate data received at a later date or to replace imputed data with 

reported data obtained from the company. 

• Introduce the results from the 2020 ARTS and SAS. 

• Link the previously published estimates from the prior MRTS sample 

to estimates from the current MRTS sample. 

We revise the seasonally adjusted estimates to: 

• Reflect revisions to the not adjusted estimates. 

• Incorporate changes to the seasonal adjustment factors based on the 

annual review of the seasonal adjustment models. 
2

Benchmarking to 2020 ARTS and SAS estimates

There are several reasons for benchmarking estimates from the Monthly Retail 

Trade Survey to the Annual Retail Trade Survey and Service Annual Survey:

• Timing. The respondents have more time to prepare their annual and 

census reports than they do for their monthly reports. The annual and 

census responses are requested at a time when many firms have 

already compiled audited book figures for their own use. The timing of 

the annual survey is such that we are also able to obtain independent 

verification of the reported data from such sources as a company’s 

annual report. On the other hand, respondents to the monthly survey 

have just a few weeks to provide reports of their sales and end-ofmonth inventories. Sometimes these reports are based on incomplete 

or unaudited records and may include estimates made by respondents 

to represent their understanding of their business.

• Sampling. As described in more detail in the Technical 

Documentation, the estimates derived from the annual survey are 

based on a sample that is much larger than the samples used to 

produce the monthly sales and inventory estimates. MRTS estimates 

are benchmarked to the results from the 2020 ARTS and the 2020

SAS. See ARTS and SAS methodology pages for more information: 

<https://www.census.gov/programs-surveys/arts/technicaldocumentation/methodology.html>.

<https://www.census.gov/programs-surveys/sas/technicaldocumentation/methodology.html>

• Response. The annual estimates are based on more reported data than 

are the monthly estimates. The responses to the ARTS and SAS are

required by law, while the MRTS is voluntary. This requirement 

results in a total quantity response rate (TQRR) of approximately 90.4

percent for retail sales and 87.5 percent for inventories in ARTS and 

approximately 76.9 percent for food services and drinking places sales 

in SAS, and a rate of approximately 66.9 percent for sales and 66.6

percent for inventories for MRTS. An imputation process accounts for 

the sales and inventories data that fail edits or are missing because of 

nonresponse. For MRTS, this process assumes that non-responding 

firms have similar month-to-month changes to the responding firms of 

a similar size in the same industry. However, the ARTS and SAS 

imputation processes rely heavily on administrative data and 

relationships of these data for each individual firm, which could result 

in different data being tabulated for the MRTS and ARTS/SAS for 

non-responding firms.

Estimates of Monthly Sales

For detailed NAICS codes, corrections are applied to the monthly retail and 
3

food service sales estimates for February 2018 through February 2022. Then, 

for each detailed NAICS code, the monthly retail and food service sales 

estimates are linked to the estimates derived from the prior sample. The 

linkage is performed at each detailed NAICS level by multiplying the samplebased estimates prior to March 2018 by a geometric mean. The geometric 

mean is computed as the square root of the product of two ratios. The 

numerators of the ratios are the Horvitz-Thompson sales estimates for 

February and March 2018 from the current sample. The denominators of the 

ratios are the Horvitz-Thompson estimates for February and March 2018 from 

the prior sample.

After performing the above linkage, the resulting sales estimates for 

December 2012 through February 2022 are input to the benchmarking 

program. The estimates for a given detailed NAICS code are revised in a 

manner that—

• For 2013 through 2020, constrains the sum of the 12 monthly sales 

estimates to equal the corresponding annual sales estimate from the 2020

ARTS or SAS, 

• Minimizes the sum of the squared differences between the month-tomonth changes of the input and revised estimates for December 2012

through February 2022.

• Uses the previously published December 2012 sales estimate as a 

constraint, linking the revised estimates to the previously published sales 

estimates and resulting in no revision to the December 2012 estimate.

A mathematical result of the benchmarking methodology is that, for a given 

NAICS code, all published monthly sales estimates after December 2020 are 

derived by multiplying the Horvitz-Thompson estimates by the ratio of the 

benchmarked-to-input estimate for December 2020. This ratio, which is called 

a carry-forward factor, remains the same and is used to derive published 

monthly sales estimates 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.

Estimates of End-of-Month Inventories

For detailed NAICS codes, corrections are applied to the end-of-month 

inventory estimates for February 2018 through February 2022. Then, for each 

detailed NAICS code, the end-of-month inventory estimates are linked to the 

estimates derived from the prior sample. The linkage is performed using a 

procedure similar to the one used for sales, except the geometric mean is 

based on end-of-month inventory.

After performing the above linkage, the resulting end-of-month inventory 
4

estimates for December 2010 through February 2022 are input to the 

benchmarking program. The estimates for a given detailed NAICS code are 

revised in a manner that—

• For 2010 through 2020, constrains the December end-of-month inventory 

estimates to equal the corresponding end-of-year inventory estimate from 

the 2020 ARTS

• Minimizes the sum of the squared differences between the month-tomonth changes of the input and revised estimates for December 2010 

through February 2022. 

• Uses the previously published December 2010 end-of-month inventory 

estimate as a constraint, linking the revised estimates to the previously 

published end-of-month inventory estimates and resulting in no revision to 

the December 2010 estimate.

For a given detailed NAICS code, end-of-month inventory estimates 

subsequent to December 2020 are derived by multiplying the input estimates 

by the ratio of the benchmarked-to-input estimate for December 2020. This 

ratio is the carry-forward factor for inventory, and it 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.

Estimates of Quarterly E-commerce Sales

For select detailed NAICS codes, corrections are applied to the quarterly ecommerce sales estimates for first quarter 2018 through fourth quarter 2021. 

Then, for select detail NAICS codes (usually at the 3-digit NAICS level), 

these quarterly retail e-commerce sales estimates are linked to the estimates 

derived from the prior sample. The linkage is performed at these select detail 

levels by multiplying the sample-based estimates prior to first quarter 2018 by 

a ratio. The numerators of the ratios are the Horvitz-Thompson e-commerce 

sales estimates for first quarter 2018 from the current sample. The 

denominators of the ratios are the Horvitz-Thompson e-commerce sales 

estimates for first quarter 2018 from the prior sample. Monthly e-commerce 

estimates are also linked at these select detail levels using a procedure similar 

to the one used for sales, except the geometric mean is based on monthly ecommerce sales estimates.

After performing the above linkage, the resulting e-commerce sales estimates 

for fourth quarter 2010 through fourth quarter 2021 are input to the 

benchmarking program. The estimates for the select detailed NAICS code are 

revised in a manner that—

• For 2011 through 2020, constrains the sum of the 4 quarterly e-commerce 
5

sales estimates to equal the corresponding annual e-commerce sales 

estimate from the 2020 ARTS.

• Minimizes the sum of squared differences between the quarter-to-quarter 

changes of the input and revised estimates for fourth quarter 2010 through 

fourth quarter 2021.

• Uses the previously published fourth quarter 2010 e-commerce estimate as 

a constraint, linking the revised estimates to the previously published sales 

estimates and resulting in no revision to the fourth quarter 2010 estimate.

For a given detailed NAICS code, e-commerce estimates subsequent to fourth 

quarter 2020 are derived by multiplying the input estimates by the ratio of the 

benchmarked-to-input estimate for fourth quarter 2020. This ratio is the carryforward factor for e-commerce, and it remains the same until the next 

benchmarking operation.

Similarly, the monthly e-commerce sales estimates at these select detail levels for 

December 2010 through December 2021 are input into the benchmarking 

program. These estimates for the select detail levels are revised in a manner 

that—

• For first quarter 2011 through fourth quarter 2021, constrains the sum of 

the 3 months in a given quarter to equal the corresponding quarterly ecommerce sales estimate which has been benchmarked to the 2020 ARTS.

• Minimizes the sum of squared differences between the month-to-month 

changes of the input and revised estimates for December 2010 through 

December 2021.

• Uses the previously published December 2010 e-commerce estimate as a 

constraint, linking the revised estimates to the previously published ecommerce sales estimates and resulting in no revision to the December 

2010 estimate.

For a given detailed NAICS code, e-commerce estimates subsequent to 

December 2020 are derived by multiplying the input estimates by the carryforward factor for e-commerce described above, which remains the same until 

the next benchmarking operation.

The revised estimates for the total retail quarterly e-commerce sales are 

computed by summing the revised estimates for the appropriate detailed 

industries comprising the aggregate.

Seasonally Adjusted Estimates 
6

New seasonal, trading-day, and holiday factors are computed and used to adjust sales for 

January 2010 through February or March 2022 (if an advance sales estimate is 

computed). For inventories, new seasonal factors are computed and used to adjust 

inventories for January 2008 through February 2022. For quarterly e-commerce sales, 

new seasonal factors are computed and used to adjust e-commerce sales for first quarter 

2008 through fourth quarter 2021. For sales, inventories, and e-commerce sales, the new 

seasonal factors are computed using the revised unadjusted estimates as input to the 

Census Bureau’s X-13ARIMA-SEATS software, version 1.1 build 59, and using the X11 filter-based adjustment procedure.

A different seasonal adjustment model specification exists for select NAICS detail levels 

for sales, inventory, and quarterly e-commerce. Part of that specification defines a model 

span, which is the span of time used to calculate trading-day and holiday factors for the 

given time series. In general, the model span should not be too long since trading-day 

and holiday patterns can change over time. All model spans for sales, inventory, and ecommerce begin no earlier than January 2001 (or first quarter 2001). For end-of-month 

inventories series that exhibit significant trading day effects based on research, a trading 

day regressor was added to the model. The trading day regressor for end-of-month 

inventories estimates the day of the week effects based on the last day of the month. Sales 

series also use trading day regressors for MRTS. All model specifications are available 

upon request.

REVISIONS OF SALES AND INVENTORIES

The following table shows a comparison of the revised sales and inventories to 

the previously published estimates for 2021:

<https://www.census.gov/retail/mrts/www/benchmark/2022/excel/introtable.xls>

ADDITIONAL INFORMATION

Survey Questionnaires

The ARTS questionnaires can be found on the Census Bureau Web site at 

<https://www.census.gov/retail/arts/get_forms.html>. The MRTS 

questionnaires can be found on the Census Bureau's Web site at 

<http://www.census.gov/retail/mrts/get_forms.html>.

1 Advance sales estimates are computed for selected kinds of business and are based on a small subsample 

selected from the larger MRTS sample.

Related Links:

<https://www.census.gov/retail/>

<https://www.census.gov/programs-surveys/arts.html> 

<https://www.census.gov/programs-surveys/e-stats.html> 

Source: Retail Indicators Branch, U.S. Census Bureau

Last Revised: April 25, 2022