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EXPLANATION OF REVISIONS

Not adjusted estimates of monthly sales are revised for January 2003 through 

February or March 20151(if an advance sales estimate is computed), as well as 

end-of-month inventory estimates for January 1998 through February 2015. Not 

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

quarter 1999 through fourth quarter 2014.

Revised quarterly retail e-commerce sales estimates will be available in the 1st Quarter 

2015 Quarterly E-commerce Sales Report scheduled to be released on May 15, 2015.

Revisions to not adjusted estimates were made in two parts:

First, revisions were made to prior Monthly Retail Trade (MRTS) estimates to 

reflect historical corrections. Then, revisions were made when benchmarking the 

Monthly Retail Trade estimates to the 2013 Annual Retail Trade (ARTS)

estimates. Revisions to seasonally adjusted estimates were made based on the 

revised not adjusted estimates and revised seasonal adjustment factors

Reasons for Revisions

We revised the not adjusted estimates to: 

 Reflect corrections to data for the current 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 2013 ARTS, which has been 

benchmarked using the preliminary results of the 2012 Economic 

Census. ARTS estimates also reflect a revision to the 2007 Economic 

Census affecting NAICS 443112 (Radio, Television, and Other 

Electronics Stores).

 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. 
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Benchmarking to 2013 ARTS estimates

There are several reasons for benchmarking estimates from the Monthly Retail 

Trade Survey to the Annual Retail Trade 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 2013 ARTS, which have been 

indirectly benchmarked using the preliminary results of the 2012 

Economic Census and reflect a revision to the 2007 Economic Census 

affecting NAICS 443112 (Radio, Television, and Other Electronics 

Stores).. See ARTS methodology page for more information: 

http://www.census.gov/retail/arts/how_surveys_are_collected.html.

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

are the monthly estimates. The response to the ARTS is required by 

law, while the MRTS is voluntary. This requirement results in a total 

quantity response rate (TQRR) of 92.4 percent for sales and 92.8 

percent for inventories in ARTS and a rate of approximately 75.3 

percent for sales and 70.0 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 imputation process relies 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 for non-responding firms.

Estimates of Monthly Sales

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

estimates for January 1992 (the beginning of the series) through February 

2013 are linked to the estimates derived from the current sample. The linkage 
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is performed at each detailed NAICS level by multiplying the sample-based 

estimates prior to March 2013 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 

2013 from the current sample. The denominators of the ratios are the HorvitzThompson estimates for February and March 2013 from the prior sample.

After performing the above linkage, the resulting sales estimates for 

December 2007 through February 2015 are input to the benchmarking 

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

manner that—

 For 2008 through 2013, constrains the sum of the 12 monthly sales 

estimates to equal the corresponding annual sales estimate from ARTS.

 Minimizes the sum of the squared differences between the month-tomonth changes of the input and revised estimates for December 2007 

through February 2015.

 Uses the previously published December 2007 sales estimate as a 

constraint, linking the revised estimates to the previously published sales 

estimates and resulting in no revision to the December 2007 estimate.

Additionally for NAICS 443112, after performing the above linkage, the 

resulting sales estimates for December 2002 through February 2015 are input 

to the benchmarking program. The estimates are revised in a manner that—

 For 2003 through 2013, constrains the sum of the 12 monthly sales 

estimates to equal the corresponding annual sales estimate from ARTS.

 Minimizes the sum of the squared differences between the month-tomonth changes of the input and revised estimates for December 2002 

through February 2015.

 Uses the previously published December 2002 sales estimate as a 

constraint, linking the revised estimates to the previously published sales 

estimates and resulting in no revision to the December 2002 estimate.

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

NAICS code, all published monthly sales estimates after December 2013 are 

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

benchmarked-to-input estimate for December 2013. 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.
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If a March 2015 advance sales estimate is computed for an industry, the 

estimate may also be revised based on historical corrections made to data for 

February or March 2015. For more information on how advance estimates are 

computed, see the Census Bureau Web site at 

http://www.census.gov/retail/marts/how_surveys_are_collected.html.

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 each detailed NAICS code, the end-of-month inventory estimates for 

January 1992 (the beginning of the series) through February 2013 are linked 

to the estimates derived from the current 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 

estimates for December 2004 through February 2015 are input to the 

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

revised in a manner that—

 For 2004 through 2013, constrains the December end-of-month inventory 

estimates from MRTS to equal the end-of-year inventory estimates 

derived from ARTS.

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

changes of the input and revised estimates for December 2004 through 

February 2015.

 Uses the previously published December 2004 estimate as a constraint, 

linking the revised estimates to the previously published estimates and 

resulting in no revision to the December 2004 estimate.

Additionally for NAICS 443112, after performing the above linkage, the 

resulting sales estimates for December 1997 through February 2015 are input 

to the benchmarking program. The estimates are revised in a manner that—

 For 1997 through 2013, constrains the December end-of-month inventory 

estimates from MRTS to equal the end-of-year inventory estimates 

derived from ARTS.

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

changes of the input and revised estimates for December 1997 through 

February 2015.
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 Uses the previously published December 1997 estimate as a constraint, 

linking the revised estimates to the previously published estimates and 

resulting in no revision to the December 1997 estimate.

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

subsequent to December 2013 are derived by multiplying the input estimates 

by the ratio of the benchmarked-to-input estimate for December 2013. 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 detail NAICS codes (usually at the 3-digit NAICS level), quarterly 

retail e-commerce sales estimates for fourth quarter 1999 through fourth 

quarter 2012 are linked to the estimates derived from the current sample. The 

linkage is performed at these select detail levels by multiplying the samplebased estimates prior to first quarter 2013 by a ratio. The numerators of the 

ratios are the Horvitz-Thompson e-commerce sales estimates for first quarter 

2013 from the current sample. The denominators of the ratios are the HorvitzThompson e-commerce sales estimates for first quarter 2013 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 e-commerce sales estimates.

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

for fourth quarter 1999 through fourth quarter 2014 are input to the 

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

revised in a manner that—

 For 2000 through 2013, constrains the sum of the 4 quarterly e-commerce 

sales estimates to equal the corresponding annual sales estimate from 

ARTS.

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

changes of the input and revised estimates for fourth quarter 1999 through 

fourth quarter 2014.

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

October 1999 through February 2013 are input into the benchmarking program. 

These estimates for the select detail levels are revised in a manner that—

 For fourth quarter 1999 through fourth quarter 2014, constrains the sum of 

the 3 months in a given quarter to equal the corresponding quarterly e-
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commerce sales estimate which has been benchmarked to ARTS.

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

changes of the input and revised estimates for October 1999 through 

February 2015.

For select detailed NAICS levels, monthly e-commerce sales estimates 

subsequent to February 2015 will be derived by multiplying the input 

estimates by the ratio of the benchmarked-to-input estimate for fourth quarter 

2013. This ratio is the carry-forward factor for e-commerce sales, and it 

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 

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

January 2005 through February or March 2015 (if an advance sales estimate is 

computed). For NAICS levels impacted by the not seasonally adjusted revision to NAICS 

443112, factors were computed and used to adjust sales for January 2000 through 

February 2015. For inventories, new seasonal factors are computed and used to adjust 

inventories for January 2002 through February 2015. For NAICS levels impacted by the 

not seasonally adjusted revision to NAICS 443112, factors were computed and used to 

adjust inventory for January 1995 through February 2015. For quarterly e-commerce 

sales, new seasonal factors are computed and used to adjust e-commerce sales for fourth 

quarter 1999 through fourth quarter 2014. 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 and using the X-11 filter-based 

adjustment procedure.

REVISIONS OF SALES AND INVENTORIES

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

to the previously published estimates for 2014:

2014 Retail and Food Services Sales and Retail Inventories Comparison of the 

Revised Estimates to the Previously Published Estimates
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ADDITIONAL INFORMATION

Survey Questionnaires

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

http://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:

Advance Monthly Retail Trade & Food Services

Monthly Retail Trade Survey

Annual Retail Trade Survey

E-Stats – Measuring the Electronic Economy

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

Last Revised: April 30, 2015