Monthly State Retail Sales Technical Documentation

1. Background

The Census Bureau is producing new monthly state retail sales as an experimental product.

1 This product includes statelevel year-to-year percent changes of monthly retail sales both for Total Retail Sales excluding Nonstore Retailers and for

11 North American Industry Classification System (NAICS) retail subsectors. These measures are composite estimates 

combining independently-obtained synthetic estimates and hybrid estimates comprising third-party and directlycollected establishment (point of sale) sales data and modeled establishment data. Retail subsector NAICS 454 is not 

included in the experimental release. Consequently, the aggregated industry by state estimates will not equal the 

published MRTS total but will sum to the published retail sales total of this subset of the MRTS three-digit NAICS 

subsectors.

The MRTS is a mail-out/mail-back survey of about 13,000 retail and food services businesses with paid employees, 

whose sampling unit is the firm. The one-stage stratified sampling design is designed to produce reliable industry-level 

estimates. A new sample is selected from the Business Register approximately every five years, and the sample is 

updated quarterly to reflect employer business "births" and "deaths" by adding new employer businesses identified in 

the Business and Professional Classification Survey and dropping firms and EINs when it is determined they are no longer 

active. Sampled firms report for all their retail establishments. For more details on the MRTS sampling design and data 

collection, see https://www.census.gov/retail/mrts/how_surveys_are_collected.html.

Because the MRTS sampling unit is the firm, there is no geographic component to design. Sampling weights represent a 

firm’s contribution to the industry and do not reflect industry-state share in total sales. With MRTS, the geographic 

information is only available from the single-unit (SU)2firms and for the multi-unit (MU) firms that operate within a 

single state.

Throughout the remainder of the document, we use the following definitions:

Estimation Industry: 3-, 4-, or 5-digit NAICS code assigned to a study unit (establishment or MRTS sample unit), using 

the most specific disaggregation level supported by the frame and the third-party data 

described in Section 2.

Tabulation Industry: 3-digit NAICS code (ALL = aggregated over all relevant MRTS industries)

Geography: FIPS state code (ALL = aggregated over all states)

Appendix One provides the cross-walk between tabulation industries and estimation industries. 

2. Data Sources

Monthly Sales:

• MRTS sample data at statistical period t from the sampling unit (firm)

o Sampling unit data may be split into separate reporting parts (tabulation units) to represent the different 

industries in which the firm operates. 

• Third-Party Data

1 The Census Bureau has reviewed this data product to ensure appropriate access, use, and disclosure avoidance protection of the 

confidential source data (Project No. P-7506880, Disclosure Review Board (DRB) approval number: CBDRB-FY24-0004).

2 A single-unit (SU) firm owns or operates a business at a single physical location (establishment), whereas multi-unit (MU) firms 

comprise two or more establishments that are owned or operated by the same firm.
Monthly State Retail Sales Technical Documentation Page 2

The Census Bureau utilizes the following third-party data sources in the production of the Monthly State Retail Sales 

data product. 

o Retailer point-of-sale data purchased from Circana, Inc. (formerly The NPD Group, Inc.)

▪ Monthly point-of-sales sales data for all establishments in twenty-two large companies identified by 

the Census Bureau.

▪ Aggregated 3-digit NAICS by state point-of-sale sales data for a designated set of multi-unit 

companies.

o Retailer point-of-sale data purchased from Nielsen.

▪ Aggregated 3-digit NAICS by state point-of-sale sales data for a designated set of multi-unit 

companies.

Prior to incorporating these sources, an evaluation is done to determine the comparability and the suitability for use 

in this data product. This evaluation is completed as part of the initial review, as well as monthly upon receipt of the 

latest data from these sources. Should the data not meet the quality required, the data will not be used for a given 

month. When this happens, there is potential for higher variances, additional suppressions, lower coverage, and 

year-to-year trends that may not align with the months that include the third-party sources. To resolve these 

situations, the Census Bureau works with the third-party provider(s) to resolve the problem going forward. Quality 

metrics, including standard errors and coverage, are available in csv files on the website to provide context to the 

quality of the estimates.

Frame (Annual) Data

• Business register (BR): complete list of businesses in the U.S. Used to provide

o Geography for all establishments in MRTS frame

o Activity status of all establishments in MRTS frame

o NAICS code for all establishments in the MRTS frame

o Gross payroll for 2018, 2019, 2020, and 2021 for all establishments in MRTS frame obtained from tax returns

• MRTS sampling frame: union of the original sampling frame based on the Business Register as of December 2015 

and subsequent birth sampling frames

3. State-Level Monthly Retail Sales Estimators

The composite estimate of monthly retail sales in tabulation industry i and state g at statistical period t is given by:

Ŷ

igt

C = fit[∅igt(Ŷ

igt

B

) + (1 − ∅igt)(Ŷ

igt

T

)]

where 

Ŷ

igt

T

= “Top Down” synthetic estimate of monthly retail sales in tabulation industry i and state g at statistical period t (See 

Section 3.1)

Ŷ

igt

B

= “Bottom Up” hybrid estimator of monthly sales in tabulation industry i and state g at statistical period t (See 

Section 3.2)

Due to the independent estimation procedure, Ŷ

igt

T ⊥ Ŷ

igt

B

. This is a conservative assumption that could lead to 

overestimation of the variance of Ŷ

igt

C

. 

The compositing factor in tabulation industry i and state g at statistical period t is given by
Monthly State Retail Sales Technical Documentation Page 3

∅igt =

v(Ŷ

igt

T

)

v(Ŷ

igt

T )+ v(Ŷ

igt

B )

 

This minimizes the variance of the composite estimate. Traditionally, composite estimates minimize the mean squared 

error of the estimate (variance plus squared bias). However, it is not possible to estimate the bias of these composite 

estimates or the component estimates presented in Sections 3.1 and 3.2 because “true” monthly state-level retail sales 

totals by 3-digit tabulation industry are not available and comparable state-level benchmarks are limited to a small 

number of states and industries.

A final ratio adjustment is applied to each composite estimate within tabulation industry to ensure additivity to the 

corresponding published MRTS retail sales total (Ŷ

it

MRTS,PUB), computed as fit = Ŷ

it

MRTS,PUB/ ∑ Ŷ

igt

51 C

g=1

. 

The variance of the composite monthly estimate of sales in 3-digit tabulation industry i and state g at statistical period t

is obtained as

v(Ŷ

igt

C

) ≈ fi

2 ∅igtv(Ŷ

igt

B

)

3.1 Top Down (Synthetic) Estimator

The “Top Down” (TD) monthly retail sales estimate for state g in tabulation industry i at statistical period t is given by

Ŷ

igt

T = ∑(

X

jg

Xj

) Ŷ

jt

MRTS

j∈i

where

X

jg is total BR gross annual payroll in state g in estimation industry j obtained from the frame;

X

j

is total BR gross annual payroll in estimation industry j; and

Ŷ

jt

MRTS is the MRTS Horvitz-Thompson retail sales estimate before benchmarking from estimation industry j, hereafter 

referred to as the unpublished MRTS retail sales estimate

This synthetic estimator provides computationally simple state level estimates of monthly retail sales within an industry 

that add exactly to the survey total. However, it has numerous disadvantages. Specifically, it

1. Requires very strong assumptions about the relationship between gross payroll (annual) and monthly sales for all 

states;

2. Ensures that month-to-month and year-to-year change estimates for each state are equivalent to the corresponding 

industry total estimates;

3. Fails to capture regional or state seasonal patterns; and

4. Cannot be “improved” as its reliability is a function of the MRTS sample design and response.

Furthermore, as mentioned in Section 2 above, it is impossible to estimate the bias of the synthetic estimates.

Consequently, it is a useful fallback estimator when third party or MRTS state-level data are not available but is not 

favored in the compositing procedure.

The TD estimator variance is given by
Monthly State Retail Sales Technical Documentation Page 4

v(Ŷ

igt

T

) ≈ {∑ [

X

jg

Xj

]

2

v̂(Ŷ

jt

MRTS

j∈i ) + [

Ŷ

jt

MRTS

Xi

]

2

v̂(X

jg)}

where

v̂(Ŷ

jt

MRTS) = variance estimator for MRTS estimation industry-level monthly retail sales that accounts for sampling error, 

nonresponse error, and imputation error using the methods outlined in Kim and Rao (2009); and

v̂(X

jg) = variance of state-level gross annual payroll, assuming that xjgk~(μjg, σjg

2

) in the superpopulation from which 

the frame data are drawn, where k is the establishment within estimation industry j and state g, estimated as

v̂(X

jg) ≈ njg

∑ (xjgk − x̅jg)

2

k∈jg

njg − 1

= (

njg

njg − 1

) ∑(xjgk − x̅jg)

2

k∈jg

The variance estimator is a linearization estimator, since the frame totals are random variables, not constants. Business 

populations are not static, and the frame represents a “point in time” snapshot (sample). Furthermore, the assembled 

frame used to produce these estimates is subject to linking errors. Treating the frame totals of gross annual payroll as 

fixed appeared to underestimate the variance substantively in comparison to the corresponding “Bottom Up” estimator 

variances presented in Section 3.2. More important, the additional variance component increased the variability of the 

state-level monthly retail sales estimates within industry, with the variability increase approximately inversely 

proportional to the number of establishments in the industry and state. Finally, the linearization estimator does not 

include a covariance term because the unpublished MRTS estimation industry monthly retail sales estimates are 

independent of the frame estimation industry and estimation industry by state gross annual payroll estimates.

3.2. Bottom Up Estimator

3.2.1. Estimation

The “Bottom Up” (BU) estimate of monthly retail sales for state g in tabulation industry i at statistical period t is given by

Ŷ

igt

B = ZMU

igt + YMU∗igt + YSUigt + [

Ŷ

it

MRTS − ∑ (ZMU

igt + YMU∗igt + YSUigt

g∈i )

∑ Y̌

MU

igt

g

] Y̌MU

igt

where

ZMU

igt

are the third-party data aggregate retail sales in state g from the preselected MU companies in tabulation industry i

at statistical period t;

YMU∗

igt are the aggregated unweighted retail sales in state g in tabulation industry i at statistical period t for MRTS MU 

companies that operate entirely within a single state;

YSU

igt

 are the aggregated unweighted retail sales in state g in tabulation industry i at statistical period t from MRTS SU 

establishments; and 

Y̌MU

igt is the aggregate value of the imputed MU retail sales in state g in tabulation industry i at statistical period t

The bracketed term is a tabulation industry-level ratio adjustment that enforces consistency with the unpublished MRTS 

monthly retail sales estimates in each tabulation industry and accounts for units that are not eligible for imputation such 

as single unit establishments, MRTS sampling units that did not match to the frame, and new retail firms (births) without 

business register payroll data.

The BU estimator has several advantages in terms of statistical properties over the TD estimator presented in Section 

3.1. Because it maximizes use of auxiliary and directly-collected data, it could yield theoretically unbiased estimates if all 

retail trade establishments in the industry and state were available. As additional auxiliary or directly collected data are 
Monthly State Retail Sales Technical Documentation Page 5

available and are incorporated, the accuracy and precision will improve. Variance can also be reduced by improving the 

imputation models discussed in Section 3.2.2. This estimator has the following disadvantages:

1. It assumes there is no measurement error from auxiliary and directly-collected data.

2. It is a poor estimator for the single unit component, as single unit “imputation” is accomplished via the national 

industry level ratio adjustment. The overall effect of this poor imputation is minimized when third-party data total is 

close to corresponding MRTS industry total.

3. It can be extremely variable (see Section 3.2.2.)

The BU estimator variance is given by

v(Ŷ

igt

B

)= v ([

Ŷ

it

MRTS−∑ (ZMU

igt +YMU∗igt +YSUigt

g∈i )

∑ Y̌MU

igt

g

] Y̌MU

igt)

≈ [

Ŷ

it

MRTS−∑ (ZMU

igt +YMU∗igt +YSUigt

g∈ ) i

∑ Y̌MU

igt

g

]

2

v(Y̌MU

igt)

where v(Y̌MU

igt) is the multiple-imputation variance estimate for each industry and state. Note that since the BU

estimator approximates a population instead of a sample, there is no within-imputation term in the multiple imputation 

variance estimate (Vink and van Buuren 2014).

3.2.2. Imputation

The imputation model is a Bayesian formulation of a linear mixed model that uses regression and random effects 

parameters to predict monthly retail sales given gross payroll, state, and NAICS code. Multiple imputations from the 

predictive posterior distribution estimate the missing MU establishment data. Model parameters are estimated using 

MU establishment data with non-missing sales data; MU establishments with missing monthly retail sales data are

imputed from the estimated model using frame data. SU establishments’ sales data are not imputed but are accounted 

for in the final ratio adjustment to the bottom up estimates (see Section 3.2.1). Models are estimated and imputations 

are produced independently for each month and imputation industry, which are generally defined at the 3-digit NAICS 

level (see Appendix Two for a cross-walk between tabulation and imputation industries). All model parameters are 

estimated using R (R Core Team 2017, https://www.R-project.org).

Establishment level sales (zi(dgk)) are either provided by third-party data or estimated from reported MRTS firm data3, 

where d indexes the most disaggregated NAICS code available for establishment k; the parenthesis in the subscripts 

indicates nesting within tabulation industry. The regression parameters for this model capture the national level

relationship between an establishment’s logged monthly sales and logged annual gross payroll within 3-digit tabulation 

industry for a given month. For the remainder of this section, the t subscript (indexing statistical period) is omitted,

gross annual payroll is referred to as payroll, monthly retail sales are referred to as sales, and the disaggregated NAICS 

codes indexed by d are referred to as detailed NAICS.

Geography variations are modeled with state-level random effects, which capture deviation from the national industry 

trend. An Intrinsic Conditional Auto-Regressive (ICAR) prior is used for the random state effects, which smooths

estimates by modeling correlation between adjacent states (Morris et al., 2019). Hawaii and Alaska are treated as 

“islands” and are modeled independently from other states, but with the same variance. An additional detailed NAICS 

3 Establishment-level estimates of monthly sales are obtained by pro-rating the reported value from the MRTS firm to firm’s 

establishments by each establishment’s proportion of gross payroll (to the total firm). This procedure essentially mimics the Top 

down estimation procedure at the firm level. Firms with imputed values of monthly sales are excluded. 
Monthly State Retail Sales Technical Documentation Page 6

random effect is included in the imputation model when sales data is observed in a majority of detailed industries 

included in the imputation industry. 

The general form of the imputation model is given by

zi(dgk) = αi + βixi(dgk) + τi(g) + δi(d) + εi(dgk)(1)

where

zi(dgk)log( sales + 1 ) for establishment k in state g for detailed NAICS d within imputation industry i

xi(dgk)log( payroll + 1 ) for establishment k in state g for detailed NAICS d within imputation industry i

αi National level intercept for imputation industry i

βi National level industry slope for imputation industry i

τi(g) State random effect for state g within imputation industry i

δi(d) Detailed NAICS random effect for NAICS d within imputation industry i

εi(dgk) Residual error term for establishment k in state g for detailed NAICS d within imputation industry i

Error terms are modeled as

εi(dgk)~ normal(0, σεi

2

)

δi(d) ~ normal(0 , σδi

2

)

τi(g)~ normal(0, στi

2

[D − A]

−1

)

where A is an G x G matrix that defines neighbors and D is a diagonal G x G matrix that defines the number of neighbors.

The regression parameter priors are estimated using restricted maximum likelihood via the “lme4” R package. All other 

priors are from a uniform distribution.

αi~ normal (αi

∗

, σαi

∗

2

)

βi~ normal (βi

∗

, σβi

∗

2

)

If the relationship between log sales and log payroll appears to be nonlinear, a piecewise regression -- with at most two 

breaking points (ci1, ci2) -- may be used to model curvature. 

zi(dgk) = {

αi2 + βi2xi(dgk) + τi(g) + δi(d) + εi(dgk)

αi2 + βi2(xi(dgk) − ci1) + τi(g) + δi(d) + εi(dgk)

αi3 + βi3(xi(dgk) − ci2) + τi(g) + δi(d) + εi(dgk)

xi(dgk) < ci1

ci1 ≤ xi(dgk) < ci2

ci2 ≤ xi(dgk)

(2)

where αi2 = αi1 + βi1ci1 and αi3 = αi2 + βi2

(ci2 − ci1). Priors are added to the breaking points and are estimated 

using the bootstrap restarting algorithm described in Wood (2001) and implemented in the “segmented” R package: 

ci1~ normal (ci1

∗

, σci1

∗

2

) and ci2~ normal (ci2

∗

, σci2

∗

2

).

The industry level imputation models are evaluated each month. Each month, the first step of the model development 

process is to examine the percentage of reported zero sales from the establishments within the imputation industry4. In 

4 This step is crucial for the April 2020 and May 2020 estimates to address the differing state-level responses to the COVID-19 

pandemic.
Monthly State Retail Sales Technical Documentation Page 7

most statistical periods, zero sales values are treated as outliers and are therefore excluded from parameter estimation 

to prevent overrepresentation of “closed” businesses in a state and tabulation industry. However, if the frequency of 

establishments that reported zero sales is greater than one percent, then a two-step imputation procedure is adopted 

for the imputation industry. First, a logistic regression is used to model the probability of observing an establishment 

with zero sales, with geography as the sole predictor:

log (

p(zi(dgk)=0)

1−p(zi(dgk)=0)

) = αi0 + γi(g)

γi(g)~ normal(0 , σγi

2

[D − A]

−1

)

Then, the predicted nonzero establishment values are modeled using (1) or (2), depending on model fit diagnostics for 

the tabulation industry given the observed nonzero establishment data.

zi(dgk) = {

αi + βixi(dgk) + τi(g) + δi(d) + εi(dgk) zi(dgk) > 0

0 zi(dgk) ≤ 0

(3)

Appendix Two provides the imputation models used for each imputation industry. Unless otherwise specified, the 

general model is used.

Model parameters are estimated using Bayesian inference with the open-source probabilistic programming language 

“Stan” in R. Stan (https://mc-stan.org) uses a No-U-Turn sampler (NUTS), which is a variation of Hamiltonian Monte 

Carlo (HMC). Imputations and variances are estimated from 1,000 multiple imputations drawn from the posterior 

distribution. Point estimates for each establishment are obtained as the mean of the 1,000 independent draws. The 

imputation variances are estimated from 1,000 totals calculated from each posterior draw.

4. Year-to-Year Change Estimates

The year-to-year change (trend ratio) estimate is given by

θ̂

igt

TR =

Ŷ

igt

C

Ŷ

ig,t−12

C

with the corresponding percentage change estimate given by

θ̂P =

Ŷ

igt

C − Ŷ

ig,t−12

C

Ŷ

ig,t−12

C

The variance estimate is equivalent for the trend ratio and percentage change estimate and is estimated by the Taylor 

linearization variance estimator

v̂(θ̂

igt

TR) ≈ [

Ŷ

igt

C

Ŷ

ig,t−12

C

]

2

[

v̂(Ŷ

igt

C

)

(Ŷ

igt

C

)

2

+

v̂(Ŷ

ig,t−12

C

)

(Ŷ

ig,t−12

C

)

2

− 2

Cov(Ŷ

igt

C

, Ŷ

ig,t−12

C

)

Ŷ

igt

C Ŷ

ig,t−12

C

]

With

Cov( Ŷ

git

C

, Ŷ

git−12

C

) = (∅git∅gi,t−12)Cov( Ŷ

git

B

, Ŷ

git−12

B

) + (1 − ∅git)(1 − ∅gi,t−12)Cov( Ŷ

git

T

, Ŷ

git−12

T

)

= 0 + (1 − ∅git)(1 − ∅gi,t−12)Cov( Ŷ

git

T

, Ŷ

git−12

T

)

≈ (1 − ∅git)(1 − ∅gi,t−12)√v(Ŷ

git,T)v(Ŷgi,t−12,T)γ12,i,T
Monthly State Retail Sales Technical Documentation Page 8

Where γ12,i,T is the lag-12 autocorrelation of the Top down estimator in industry i, estimated from MRTS sales data. The 

autocorrelation term for the synthetic (Top down) estimator is derived from the national MRTS estimates.

The Lag-12 autocorrelations (γ12) for a time-series are defined as 

γ12 =

∑ (Yt − Yt

̅)(Yt+12 − Y̅

t+12)

t=T−12

t=1

∑ (Yt − Y̅

t

)

T 2

t=1

=

∑ Cov ̂ (Yt

, Yt+12)

T−12

t=1

∑ v̂ (Yt)

T

t=1

given measurements Y1, Y2, ... , YT from times t = 1, 2, ..., T on the same units. 

4.1. Top Down Lag 12 Autocorrelations

The TD monthly autocorrelations use T = 24 (12 pairs of covariances, 24 variance estimates) and are calculated monthly 

from January 2020 onward. Previous statistical periods use the averaged values from January 2020 through March 2020; 

the component estimates are extremely stable over this period (as expected) and did not appear to be subject to the 

pandemic effects of April 2020 and May 2020.

The covariance term in the lag-12 TD autocorrelation estimate is obtained for tabulation industry i at statistical period t

as 

cov̂ (Ŷ

it

m, Ŷ

i,t+12

m ) =

1

2

(v(Ŷ

it

m) + v(Ŷ

i,t+12

m ) − v(Ŷ

i,t+12

m + Ŷ

it

m),

where Ŷ

it

m is the Horvitz-Thompson estimate of monthly retail sales at time t. All stratified simple random sample 

variances are obtained using PROC SURVEYMEANS (SAS Institute Inc. 2016), where m = the set of all active eligible MRTS 

tabulation units in all t=1, 2, ...,24 statistical periods (i.e., the intersection, not the union). Respondents and 

nonrespondents are included in all calculations with nonrespondent data set to missing. Tabulation industry is treated 

as a domain estimate to reflect the variability due to random sample sizes in respondents caused by the matching 

process and by the random response status. The variance and covariance estimates include a pseudo “finite population 

correction factor”: the numerator is computed from the sampled units that responded in all statistical periods and the 

denominator is computed as the sum of the sampling weights assigned to the units in the current statistical period.

5. Quality Metrics

5.1. Statistical Quality Metrics of Composite estimator (Total and Trend)

Four metrics are produced for each state-level estimate of monthly retail sales within tabulation industry i:

Phi (∅igt): compositing factor, representing the percentage of composite estimator obtained from the Bottom Up 

estimator (see Section 3)

Coefficient of variation (c.v.), also known as the relative standard error: The c.v. of an estimator θ̂ is given as

cv(θ̂) =

√v̂(θ̂)

θ̂

At the 10% significance level (the U.S. Census Bureau standard), there is no evidence that monthly retail sales totals and 

percentage change estimates whose c.v.’s are greater than 1/1.645 ( 0.67) are statistically different from zero.

90% Confidence Limits: The lower and upper (normal theory) confidence limits of an estimator θ̂ are given as
Monthly State Retail Sales Technical Documentation Page 9

(θ̂ − 1.645√v̂(θ̂), θ̂ + 1.645√v̂(θ̂))

At the 90% confidence level (= 10% significance level), if the confidence interval of a monthly retail sales total or of a 

percentage change estimate includes zero, then there is no evidence that these estimates are statistically different from 

zero. If the confidence interval of a trend ratio includes one, then there is no statistical evidence of a change in the yearto-year trend.

Margin of Error (MOE): 1.645√v̂(θ̂)

The MOE (also known as the confidence interval half width) provides a measure of the variability of the point estimate. 

5.2. Data Composition: Proportion of Estimate from Directly Collected Data

The proportion of the BU estimator obtained from directly collected data is computed as

Pigt,B = ZYigt/Ŷ

igt,B

where ZYigt = [Zigt + Yigt, MU + Yigt, SU] as defined earlier in Section 3.2.1. This metric is computed for industry by 

state estimates of monthly retail sales and is useful for providing information on the percentage of computed data as 

well as for evaluating the value of the compositing factor.

The proportion of the composite estimator obtained from directly collected data is for all monthly composite estimates, 

at the individual industry by state level and at aggregated levels as

Tabulation Industry by State: Pigt,C = ∅igt[ZYigt/Ŷ

igt,B] = φigtPigt,B 

Tabulation Industry (Aggregated Over States): Pit,C = ∑g ∅igt ZYigt/ ∑ Ŷ

igt

C

g 

State (Aggregated Over Tabulation Industries): Pgt,C = ∑i ∅igt ZYigt/ ∑ Ŷ

igt

C

i

Grand Total: Pt,C = ∑i ∑g ∅igt ZYigt/ ∑ ∑ Ŷ

igt

C

i g

The contribution of directly collected data is down-weighted by ∅igt; the top down estimator component does not 

include any directly-collected industry by state level monthly sales data.
Monthly State Retail Sales Technical Documentation Page 10

References

Kim, J.K. and Rao, J.N.K. (2009). A unified approach to linearization variance estimation from survey data after 

imputation for nonresponse. Biometrika, 96(4), pp. 917-932.

Morris, M., Wheeler-Martin, K., Simpson, D., Mooney, S.J., Gelman, A., and DiMaggio, C. (2019). Bayesian hierarchical 

spatial models: Implementing the Besag York Mollié model in stan. Spatial and Spatio-temporal Epidemiology

31, ISSN 1877-5845, https://doi.org/10.1016/j.sste.2019.100301.

R Core Team (2017). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, 

Austria. https://www.R-project.org/.

SAS Institute Inc. (2016). SAS/STAT® 14.2 User’s Guide. Cary, NC: SAS Institute Inc.

Vink, G., & van Buuren, S. (2014). Pooling Multiple Imputations when the Sample Happens to be the Population. arXiv 

preprint arXiv:1409.8542.

Wood, S. N. (2001). Minimizing Model Fitting Objectives That Contain Spurious Local Minima By Bootstrap Restarting.

Biometrics 57, 240–244.
Monthly State Retail Sales Technical Documentation Page 11

Appendix One: Crosswalk between MSRS tabulation industries and estimation industries

Tabulation 

Industry

Estimation 

Industry

Description

441 4411 Automobile Dealers

4412 Other Motor Vehicle Dealers

4413 Automotive Parts, Accessories, and Tire Stores

442 4421 Furniture Stores

4422 Home Furnishings Stores

443 4431 Electronics and Appliance Stores

444 44411 Home Centers

44412 Paint and Wallpaper Stores

44413 Hardware Stores

44419 Other Building Material Dealers

44421 Outdoor Power Equipment Stores

44422 Nursery, Garden Center, and Farm Supply Stores

445 4451 Grocery Stores

4452 Specialty Food Stores

4453 Beer, Wine, and Liquor Stores

446 44611 Pharmacies and Drug Stores

44612 Cosmetics, Beauty Supplies, and Perfume Stores

44613 Optical Goods Stores

44619 Other Health and Personal Care Stores

447 4471 Gasoline Stations

448 4481 Clothing Stores

4482 Shoe Stores

4483 Jewelry, Luggage, and Leather Goods Stores

451 45111 Sporting Goods Stores 

45112 Hobby, Toy, and Game Stores

45113 Sewing, Needlework, and Piece Goods Stores

45114 Musical Instrument and Supplies Stores

451211 Book Stores

451212 News Dealers and Newsstands

452 452111 Department Stores (except Discount Department Stores)

452112 Discount Department Stores

4529 Other General Merchandise Stores (incl. Warehouse Clubs and Supercenters)

453 4531 Florists

45321 Office Supplies and Stationery Stores

45322 Gift, Novelty, and Souvenir Stores

4533 Used Merchandise Stores

45391 Pet and Pet Supplies Stores

45392 Art Dealers

45393 Manufactured (Mobile) Home Dealers

45399 Other Miscellaneous Store Retailers
441 Yes No reg0 state naics

442 No No reg0 state naics zero reg0 state naics

443 No No reg0 state naics zero reg0 state naics zero reg0 state naics

444 No No reg0 state naics

445 Yes No reg0 state naics zero reg0 state naics zero reg0 state naics

44611 Yes No reg0 state

Not 44611 Yes No reg0 state naics zero reg0 state naics

447 No No reg0 state

448 Yes Yes reg1 state zero reg0 state zero reg0 state zero reg1 state reg0 state reg0 state reg0 state

451 45111 Yes Yes reg2 state zero reg0 state zero reg0 state reg1 state reg0 state reg0 state reg0 state reg0 state

452 Yes Yes reg1 state zero state zero reg0 state reg0 state reg0 state

453 Yes No reg0 state naics zero reg0 state naics zero reg0 state naics

Appendix Two: MSRS Model Specifications

August 2018, 

August 2019, 

September 2020-

November 2020

August 2023 - 

Present

446

NAICS3 Imputation NAICS Third Party Aggregate Data Third Party Establishment Data General Model April 2020 May 2020 June 2020

February 2021, 

March 2021, June 

2021, July 2021, 

September 2021-

May 2022, July 

2022 - May 2023, 

July 2023

August 2021

January 2021, 

June 2023

April 2021, 

May 2021

Unless specified, the General Model is used for all months. 

“Reg<breaking points>” indicates the number of breaking points included in the linear regression imputation 

component αi + βixi(dgk) + εi(dgk)from in equation (10).

“State” and “naics” indicate the addition of respective random effects in equation (9), τi(g) and δi(d)

respectively

“Zero” indicates usage of the two-stage imputation model described in equations (3) in Section 3.2.2.

Monthly State Retail Sales Technical Documentation Page 12
Monthly State Retail Sales Technical Documentation Page 13

Appendix Three: Explanation of Annual Revisions

June 12, 2023

The February 2023 MSRS publication reflects an annual update to the MSRS estimates to incorporate revisions of the Monthly Retail 

Trade Sales estimates and other improvements to methodology. 

MSRS year-over-year percentage change estimates were revised from January 2019 to January 2023 to: 

• Update the business frame and gross payroll from 2018 for imputation and estimation for 2019

• Update the business frame and gross payroll from 2019 for imputation and estimation for 2020

• Update the business frame and gross payroll from 2020 for imputation and estimation for 2021

• Use gross payroll from 2021 for imputation and estimation for 2022 and 2023

• Incorporate the most recent annual revision of the MRTS sales estimates. The MRTS estimates reflect historical corrections 

to company data and introduce the results from the 2021 Annual Retail Trade Survey and the 2021 Service Annual Survey, 

which have been benchmarked using the final results of the 2017 Economic Census.

• Incorporate additional third-party data from Nielson in estimation.

The changes noted above will also be applied to MSRS year-over-year percentage changes going forward, beginning with February 

2023.