Brave et al., Tracking U.S. Consumers in Real Time with a New Weekly Index of Retail Trade (2021-03-30)

Summary

In this Federal Reserve Bank of Chicago working paper (WP 2021-05, revised March 30, 2021), Scott A. Brave, Michael Fogarty, Daniel Aaronson, Ezra Karger and Spencer Krane build a weekly index of retail trade that predicts the Census Bureau's Monthly Retail Trade Survey. The index extracts the co-movement in weekly series on credit and debit card transactions, small business revenue, mobility and consumer sentiment, and a mixed-frequency dynamic factor model constrains it to match the monthly survey. The authors say the index would have predicted the survey more accurately in real time during the pandemic than consensus forecasts, monthly autoregressive models or other high-frequency data, with roughly 60 to 80 percent reductions in mean absolute forecast errors.

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“Brave et al., Tracking U.S. Consumers in Real Time with a New Weekly Index of Retail Trade (2021-03-30).” Original at web.archive.org. Archived at Pandemic Darlings, https://pandemicdarlings.com/source-documents/brave-et-al-tracking-u-s-consumers-in-real-time-with-a-new-weekly-inde-1beb0c1f40/, SHA-256 302770bcb36455bcba5b33691fc9eabf51c76eea15d0d1c78e9dab4706206491.

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Tracking U.S. Consumers in Real Time

Federal Reserve Bank of Chicago
with a New Weekly Index of Retail Trade
Scott A. Brave, Michael Fogarty, Daniel
Aaronson, Ezra Karger, and Spencer Krane

REVISED
March 30, 2021

WP 2021-05
https://doi.org/10.21033/wp-2021-05

*
Working papers are not edited, and all opinions and errors are the
responsibility of the author(s). The views expressed do not necessarily
reflect the views of the Federal Reserve Bank of Chicago or the Federal
Reserve System.
Tracking U.S. Consumers in Real Time with a
New Weekly Index of Retail Trade

Scott A. Brave, Michael Fogarty, Daniel Aaronson,
Ezra Karger, Spencer Krane

Federal Reserve Bank of Chicago

March 30, 2021

Abstract
We create a new weekly index of retail trade that accurately predicts the U.S.
Census Bureau’s Monthly Retail Trade Survey (MRTS). The index’s weekly frequency
provides an early snapshot of the MRTS and allows for a more granular analysis of the
aggregate consumer response to fast-moving events such as the Covid-19 pandemic. To
construct the index, we extract the co-movement in weekly data series capturing credit
and debit card transactions, small business revenue, mobility, and consumer sentiment.
To ensure that the index is representative of aggregate retail spending, we implement
a novel benchmarking method that uses a mixed-frequency dynamic factor model to
constrain the weekly index to match the monthly MRTS. We use the index to document
several interesting features of U.S. retail sales during the Covid-19 pandemic, many of
which are not visible in the MRTS. In addition, we show that our index would have
more accurately predicted the MRTS in real time during the pandemic when compared
to either consensus forecasts available at the time, monthly autoregressive models, or
other high-frequency data that attempts to track consumer spending. The gains are
substantial, with roughly 60 to 80 percent reductions in mean absolute forecast errors.

Keywords: mixed-frequency dynamic factor model, retail sales, consumer spending
JEL: C32, C38, C43, C53, D12

*The views expressed herein are solely those of the authors and do not necessarily reflect
the views of the Federal Reserve Bank of Chicago or the Federal Reserve System.

Corresponding author: Scott A. Brave, Federal Reserve Bank of Chicago, Economic Re-
search, 230 S. LaSalle St., Chicago, IL 60604, sbrave@frbchi.org

1
1 Introduction

With the onset of the Covid-19 pandemic, many researchers turned to new high-frequency
data sources to measure the impact of the virus on the U.S. economy. These alternative
data sources provided private sector analysts and policymakers with valuable real-time in-
formation about the effect of the spread of Covid-19 on economic activity. Researchers also
used these data to evaluate the impacts of federal, state, and local policies on households
and businesses.
Though useful, these data are not typically derived from samples designed to be repre-
sentative of the population at large. Notably, credit and debit card transactions or business
electronic payments reflect the subset of consumers or businesses that use the particular
service gathering the data. Accordingly, it can be problematic to draw inferences about
aggregate economic conditions from these non-representative high-frequency time series.1
This paper addresses these concerns in the context of high-frequency indicators of U.S.
retail sales. We create a new weekly index that accurately predicts the U.S. Census Bureau’s
Monthly Retail Trade Survey (MRTS), a carefully designed representative-sample survey
that produces the gold standard measure of aggregate U.S. retail spending. The MRTS is
released monthly with about a two-week lag. In contrast, our index can be produced weekly,
providing an early snapshot of consumer activity.2 Moreover, the weekly frequency of our
index allows for a more granular analysis than can be performed with monthly data of fast-
moving changes in consumer behavior such as the stockpiling of goods immediately preceding
the nationwide shutdowns in mid-March 2020 and consumer responses to the Covid-relief
package stimulus payments.
Our index uses alternative data from a number of private vendors: store revenue data
1
See, for example, the case studies in Brave et al. (2020). Other researchers have used carefully designed
surveys to produce more representative samples but at the cost of a lower frequency of observation, e.g.
Coibion et al. (2020), Bartik et al. (2020), and the U.S. Census Bureau Household and Small Business Pulse
surveys described at https://www.census.gov/newsroom/press-kits/2020/pulse-surveys.html.
2
For example, the March 2020 MRTS was released on April 15, 2020. This means that researchers and
policymakers had to wait over a month before understanding how the onset of Covid-19 in early March 2020
affected aggregate consumer spending.

2
from Womply; financial transactions from Facteus and Consumer Edge; consumer sentiment
from Morning Consult; and retail foot traffic from SafeGraph; as well as more traditional
publicly available data on motor fuel consumption from the U.S. Energy Information Admin-
istration (EIA). We construct the index using a mixed-frequency dynamic factor model that
extracts the co-movement in these six weekly series and monthly retail and food services sales
excluding automotive spending from the MRTS.3 The model constrains the latent factor in
a way that ensures that growth in the resulting Weekly Index of Retail Trade matches the
MRTS data at a monthly frequency.
We first use our weekly index to document several interesting features of U.S. consumer
spending during the Covid-19 pandemic, many of which are not visible in the MRTS:

• Retail sales in the U.S. plummeted at the same time as the rapid increase in Covid-19
cases and the closure of nonessential businesses in mid-to-late March 2020; they then
began to recover by mid-April 2020. There was also a “stockpiling” effect, where retail
sales increased substantially in the weeks leading up to the large declines in March.
These intra-month patterns are not apparent in the lower frequency MRTS.
• As state and local governments lifted stay-at-home orders and the federal government
disbursed the first round of economic impact payments, the pace of recovery accelerated
in April-June. However, progress over the summer of 2020 was uneven, with the
variation in weekly sales coinciding with developments during the second wave of Covid-
19 cases.
• Sales fell again in the fourth quarter of 2020 as the third wave of the virus hit but began
to recover in late December and early January, with the weekly pattern pointing to
the second round of economic impact payments playing an important role in boosting
spending.

We use the weekly index to “nowcast” the MRTS in real time.4 Based on out-of-sample
monthly predictions, we show that our index more accurately predicted retail and food
services sales ex. autos from the MRTS during the March 2020–February 2021 period than
either the consensus forecasts available at the time or monthly autoregressive models. The
3
We exclude automotive spending since consumer analysts often rely on MRTS excluding automotive
spending for analyses while separately analyzing the automobile sector using industry reports on vehicle
sales.
4
Our use of the word “nowcast” parallels that of Giannone et al. (2008) in referring to the contempo-
raneous forecasting of a macroeconomic time series that is published infrequently using information that is
available in real time.

3
gains are substantial, with approximately 60 to 80 percent reductions in mean absolute
forecast error.
Our results contribute to several related literatures. A number of recent papers have
used credit and debit card transactions data as an alternative high-frequency source to track
consumer spending (e.g., Aladangady et al. (2019), Dunn et al. (2020), Chetty et al. (2020),
and Carvalho et al. (2020)). Similarly, researchers have used cellphone mobility measures
(e.g., Atkinson et al. (2020) and Alexander and Karger (2020)) and daily consumer sentiment
to track consumer behavior during the Covid-19 pandemic. However, to the best of our
knowledge, we are the first to combine this information into a single measure in a way that
retains comparability to the U.S. Census Bureau’s MRTS data. We show that by using
multiple sources of data we more accurately track the underlying trend in aggregate retail
activity relative to any individual data series including those used by the BEA and Chetty
et al. (2020) to track consumer spending.
Other work has used similar high-frequency data in forecasting exercises. For example,
Galbraith and Tkacz (2018) use monthly payments system data to nowcast Canadian retail
sales and Gross Domestic Product (GDP), and Lewis et al. (2020) use a variety of weekly
data to nowcast U.S. GDP.5 Our work differs in that we combine the weekly frequency of
our data with a multivariate and mixed-frequency data structure akin to the dynamic factor
models of Giannone et al. (2008) and Aruoba et al. (2009). Furthermore, we modify a
traditional mixed-frequency dynamic factor model to exploit the representative sampling of
the MRTS in a way that is similar to what Aruoba et al. (2016) do for U.S. GDP.

2 High-Frequency Data Sources

Our Weekly Index of Retail Trade is targeted to match retail and food services sales excluding
automotive spending (ex. autos) from the U.S. Census Bureau’s Monthly Retail Trade Survey
5
Ludvigson (2004) and Croushore (2005) also use consumer confidence data to forecast consumer spending.
Unlike our high-frequency data results, they find little evidence that more traditional measures of consumer
confidence are useful in predicting current growth in aggregate consumer spending.

4
(MRTS). The MRTS is based on a mailed survey of about 13,000 retail businesses that sell
merchandise and related services to final customers. The data record sales over the entire
month and are published with about a two week lag. Sales include both online and in-store
purchases.6
The MRTS is a vital snapshot of consumer spending. As the Census Bureau notes:
“These data are widely used throughout government, academic, and business communities.
The Bureau of Economic Analysis uses the estimates to calculate Gross Domestic Product.
The Bureau of Labor Statistics uses the estimates to develop consumer price indexes and
productivity measurements. The Council of Economic Advisers uses the estimates to analyze
current economic activity. The Federal Reserve Board uses the estimates to assess recent
trends in consumer purchases. The media use the estimates to report news of recent consumer
activity. Financial and investment companies use the estimates to measure recent economic
trends.”7
To construct our weekly index, we complement the low-frequency MRTS data with several
high-frequency measures of retail activity that inform the index’s within-month dynamics:

• Revenues for more than 400 thousand small businesses, from Womply;

• Credit and debit card transactions from a sample of over 30 million unique cards,
collected by Consumer Edge;

• Transactions from a collection of over 90 million debit, general purpose, payroll, gov-
ernment cards, and single-issue gift cards from Facteus;

• Consumer sentiment from daily polls, conducted by Morning Consult;

• Retail foot traffic based on cell phone data, collected by SafeGraph; and

• Finished motor gasoline product supplied, from the U.S. Energy Information Admin-
istration.
6
The sample of firms is chosen approximately every five years (most recently in 2018) and is then updated
quarterly to reflect business “births” and “deaths.” Added firms are typically represented in the sample with
a nine month delay. Estimates are updated annually when the MRTS is benchmarked to the Annual Retail
Trade Survey.
7
See https://www.census.gov/retail/mrts/aboutthesurveys.html. Wilcox (1992) describes the process by
which the Bureau of Economic Analysis uses the MRTS.

5
2.1 Revenue and Transactions Data

Although they are correlated, the Womply, Consumer Edge, and Facteus datasets cover
different scopes of businesses, consumers, and transactions, and hence each independently
provides useful information for our index. To align ourselves as much as possible with the
MRTS, we only use data for firms that are classified with either North American Industry
Classification System (NAICS) codes or Merchant Category Codes (MCC) that are included
in the retail and food services ex. autos aggregate sales measure.8
Turning to the specifics of each data source:

• The Womply data are from payment processors used by more than 400,000 primarily
brick and mortar establishments in the United States.9 At about $400 billion, annual
sales at Womply firms amount to a little less than 10% of our MRTS benchmark. Wom-
ply filters the data by removing businesses that are inactive or that exceed the Small
Business Administration’s size threshold.10 Data are available at a daily frequency
with a five- to seven-day lag.

• Consumer Edge tracks consumer spending from more than 30 million unique credit and
debit cards. We use a version of the data in which the number of active cards is scaled
to be consistent over time; this means that changes in spending will reflect changes in
either the number of transactions per card or the size of transactions rather than the
size of the underlying sample. The data capture about $ 60-65 billion in annual sales,
or about 1.3% of our MRTS benchmark. Data are available at a daily frequency with
a five- to seven-day lag.11

• Facteus aggregates, anonymizes, and standardizes transaction-level data from a dozen
banks, covering a total of more than 90 million debit cards, payroll cards, government
benefit cards, and single-issue gift cards. The subset of Facteus transactions that we
use amounts to about 1.25% of our MRTS benchmark.12 The data are available at a
8
NAICS codes are available for Consumer Edge. Facteus and Womply are instead categorized by MCC,
which allows us to exclude transactions categorized as automotive.
9
Chetty et al. (2020) and Alexander and Karger (2020) also use the Womply data in their analysis of the
pandemic’s effects on economic activity.
10
See https://www.sba.gov/document/support\OT1\textendashtable-size-standards for the definition of
small business thresholds by industry.
11
Consumer Edge is geared toward providing real-time data for investors. For more information, see
https://www.consumer-edge.com/.
12
Facteus’ share of retail and food services sales ex. autos increased to over 2% in the first four to
five months after the onset of the pandemic. We view this as consistent with the stabilization of lower-
income households’ spending by various income support policies, including extended unemployment insurance
benefits, the Pandemic Unemployment Assistance program, and the $1200 economic impact payments that
were all part of the CARES Act passed in March. For more evidence on the impact of the stimulus payments
on spending behavior using the Facteus microdata, see Karger and Rajan (2020).

6
daily frequency with a five- to seven-day lag.

Two issues suggest that a simple aggregation of these data would have difficulty matching
the MRTS. First, sampling error could be large as, even together, the samples represent a
small fraction of the spending covered by the MRTS. Second, and likely more important,
systematic errors could arise because the alternative data reflect nonrandom slices of the
MRTS universe.
The MRTS’s sample design and construction methodology are aimed at producing a rep-
resentative sample of all U.S. retail and food services spending. In contrast, each of our alter-
native data providers record spending by whomever is covered by their service. For example,
Womply measures activity only at small businesses, the Facteus data are weighted towards
lower-income and younger consumers, and by construction, none of these data sources cap-
ture cash payments. These discrepancies cannot be eliminated by reweighting the alternative
data using the same type-of-store weights that the Census Bureau uses, as these selection
issues occur for every type-of-store category.
Instead, we construct a statistical index that treats the individual alternative data as
“noisy” high-frequency measures of broader spending to isolate the common factor across
datasets that is correlated with the MRTS. In this framework, the estimated factor loadings
on the component series will capture systematic differences between the spending covered
by the component sample and the MRTS universe, while the error term will reflect any
remaining random variation idiosyncratic to each data source.

2.2 Consumer Sentiment, Mobility, and Gasoline Data

To aid in identifying the common factor, our model includes two non-spending series that
have also been widely used to examine the impact of the pandemic on economic activity
– consumer sentiment from Morning Consult and retail foot traffic from SafeGraph13 – as
13
See, for example, the Mobility and Engagement Index described in Atkinson et al. (2020) produced by
the Federal Reserve Bank of Dallas that is based on the SafeGraph data.

7
well as a publicly available weekly indicator of gasoline consumption from the U.S. Energy
Information Administration (EIA). These three additional measures help align our high-
frequency transaction data with the MRTS universe by capturing drivers of spending related
to a broad base of U.S. households.
Morning Consult constructs consumer sentiment indices based on a nationally represen-
tative daily email survey of about 6,000 people across the United States. Their survey is
based on five questions that are identical to those used in the monthly University of Michigan
Survey of Consumers and is available daily, without a lag.14 It thus brings sample design
discipline and timely information on household conditions to our index. We use weekly
averages of their overall index of consumer sentiment.
SafeGraph uses cell phone data to measure visits to individual business establishments.
They record NAICS code identifiers for these locations, which allows us to measure total
visits (or foot traffic) to establishments defined to be in the MRTS universe.15 Since cell
phone usage is ubiquitous, this measure may provide a fairly representative measure of the
population’s visits to retail establishments. They also then would help capture retail sales
that are not covered by credit and debit card transactions, such as payments with cash or
check. They would not, however, capture online sales, which are included in the MRTS.
We also use EIA’s weekly data for finished motor gasoline supplied in our index.16 These
data serve two purposes. First, they complement the SafeGraph data in capturing broad-
based mobility. Second, the EIA data provide useful forecasting power for gasoline sales,
which are a large and volatile component of the MRTS series.
14
For additional details, see
https://morningconsult.com/2020/03/10/morning-consult-economic-intelligence-methodology/. More in-
formation on the University of Michigan Survey of Consumers can be found at https://data.sca.isr.umich.
edu/.
15
Over 99% of establishments in the SafeGraph data are categorized at the 4-digit NAICS code level. A
summary of the foot traffic data available from SafeGraph can be found at https://www.safegraph.com/
data-examples/covid19-commerce-patterns.
16
These data are measured in thousands of barrels per day and represent shipments from “primary” supply
chain facilities (refineries, bulk storage terminals, etc.) to retail outlets and other secondary suppliers. They
thus differ from retail sales of gasoline by changes in inventories at retail gasoline stations and the shipment to
the other secondary suppliers. These are generally small—indeed, the Bureau of Economic Analysis (BEA)
uses these data to help estimate personal consumption expenditures of gasoline in the national accounts.

8
Figure 1 shows the six high-frequency time series in our seasonally adjusted Weekly Index
of Retail Trade from January 2018-February 2021.17 The figure makes clear the extent of
heterogeneity across data sources, even during the onset of the recession in March 2020. Our
index aims to combine these different sources in a representative way to explain national
retail activity at a weekly frequency.

3 Modeling Weekly Retail Sales

The statistical framework underlying our Weekly Index of Retail Trade is a mixed-frequency
dynamic factor model with one latent factor.18 However, unlike a standard dynamic factor
model, we impose an additional constraint that forces the latent factor to temporally ag-
gregate to match the MRTS’s monthly retail and food services sales excluding autos data.
Below, we describe the model and its estimation.

3.1 Establishing a Regular Weekly Calendar

Weekly data pose a particular problem for mixed-frequency models. With standard methods
of defining the calendar, some weeks span two months, which is problematic for temporally
aggregating a weekly sales measure to a month.19 Accordingly, we instead define an alter-
native calendar. To begin, we partition each month into four weeks in the following way:
each of the first three seven-day periods within the month are categorized as a week and the
remaining seven to ten days are grouped into the fourth week of the month. This process
results in a regular calendar in which each week is identified with a unique month.
Within each of our weeks, we aggregate the daily high-frequency data by summing across
17
Several of these time series exhibit significant seasonal components that have been removed in the figure
using the methodology described in the Appendix.
18
For additional information on dynamic factor models, see Stock and Watson (2011). Similar mixed-
frequency models to ours include Aruoba et al. (2009) and Mariano and Murasawa (2003), who both estimate
a latent factor describing changes in U.S. economic activity, as well as Brave and Butters (2012), who estimate
a latent factor capturing U.S. financial conditions.
19
Three common standards for defining weeks are: the number of seven-day periods from the first day of
the year; a consistent Monday starting day; or a Sunday start day.

9
the days within the week for the transaction data and by averaging across the days of the
week for the consumer sentiment data.20 For the retail foot traffic and motor fuel data,
which are reported in calendar weeks, we take weeks that span two months and allocate the
visits or fuel supplied to each of the two months proportionally based on the number of days
the week has in each month. We then re-allocate visits or fuel supply within the month to
match the number of days in each of our four weeks.
Because the MRTS data are seasonally adjusted, we also seasonally adjust our weekly
inputs before estimating our factor model. This seasonal pre-filtering turned out to be
critical in extracting the signal from the volatile unadjusted input data. Our adjustment
methodology accounts for the regular intra-month patterns in the data and the fact that the
fourth week of each month contains a varying number of days. The full seasonal adjustment
procedure is described in detail in the Appendix.

3.2 Benchmarking to the MRTS

In our framework, growth in the weekly data (Wn,i,t ) are “noisy” measures of growth (in log
differences) in latent weekly MRTS spending (Fi,t ), with n denoting the indicator series and
i the week of month t. Each series loads onto the latent factor according to loadings γn with
average growth rates αn and measurement errors n,i,t that follow first-order autoregressive
processes. In terms of equations, with L being a weekly lag operator, we have

Wn,i,t = αn + γn Fi,t + n,i,t (1)

(1 − ψi L) n,i,t = υn,i,t . (2)

The factor follows a fourth-order autoregressive process with average growth rate αF ,
20
The Morning Consult data are a 5-day moving average. We back out daily values from the moving
average and then re-average them to our weekly values. For details, see https://stats.stackexchange.com/
questions/67907/extract-data-points-from-moving-average.

10
(1 − ρ1 L − ρ2 L − ρ3 L − ρ4 L) Fi,t = αF + ηi,t . (3)

The shocks υn,i,t and ηi,t are assumed to be jointly distributed N (0, Σ).
To maintain the link with the MRTS data, the factor’s weekly growth rates, Mi=4,t , are
constrained by the triangle average formula shown below,

1 2 3
Mi=4,t = Fi=4,t + Fi=3,t + Fi=2,t (4)
4 4 4
+ Fi=1,t
3 2 1
+ Fi=4,t−1 + Fi=3,t−1 + Fi=2,t−1 .
4 4 4

This temporal aggregation constraint ensures that the Fi,t generate a monthly series with
the same growth rate as the MRTS data for retail and food services sales ex. auto.
To implement the triangle average, we assume that the log difference in monthly MRTS
sales, Mi=4,t , is observed in the fourth week of the month. In calendar time, this occurs near
the middle of the following month with the release of the Advance Monthly Retail Trade
Survey, or MARTS. The above mixed-frequency dynamic factor model is then put into
state-space form using the Harvey (1990) accumulator to handle the temporal aggregation
constraint imposed on the latent factor. We estimate the model by maximum likelihood
using a Kalman filter.21
Unlike a standard mixed-frequency dynamic factor model, we do not include a measure-
ment error term for the MRTS data. By treating them as being measured without error, we
are in essence recursively benchmarking the latent factor to the representative MRTS data.
However, this also means that the model would be over-identified if we make the typical
21
We use the Matlab toolbox MFSS described in Brave et al. (2020) for this purpose, where we further
restrict ρ(L) and ψi L to be stationary processes.

11
assumption that Σ is a diagonal variance-covariance matrix. Instead, we estimate the ele-
ments of Σ associated with the covariances between ηi,t and each of the υn,i,t .22 This slight
modification leads to an exactly identified model as well as modest gains in our ability to
nowcast the MARTS data. This is because the additional covariances contain useful infor-
mation about the direction and magnitude of expected deviations of the MRTS data from
their historical dynamics and, thus, help to improve our high-frequency estimate of ρ(L).23
Once the model has been estimated, to arrive at a weekly level of spending that is bench-
marked to the MRTS data, we construct the weekly index Ik from the Kalman smoothed
estimate of the weekly latent factor as:

k
!
X
Ik = exp M0 + Fj , (5)
j=1

where k references the number of weekly observations for the index, k = 1, ..., K, and M0
is the level of Census sales in the base period. Given the triangle average restrictions, the
monthly average of the weekly index will approximately equal the monthly MRTS data, with
the small difference attributable to the log transformation and the use of a monthly value,
M0 , to initialize the index. Given data availability constraints, we are only able to produce
an index that begins in the first week of January 2018.24

3.3 The Estimated Index

Figure 2 shows our Weekly Index of Retail Trade as a seasonally adjusted monthly spending
rate in comparison to retail and food services sales ex. autos from the MRTS over our entire
22
The resulting near-diagonal Σ resembles the U.S. GDP measurement error model of Aruoba et al. (2016),
who create an alternative measure called GDPplus by combining information from the product and income
sides of the National Income and Product Accounts.
23
For another example of the use of dynamic factor model methods for the purpose of benchmarking to
official statistics, see Brave et al. (2021).
24
M0 corresponds to retail and food services sales ex. auto from the MRTS in December 2017. At the
moment, the SafeGraph series only begins in January 2019. An unbalanced panel for estimation is not a
concern for models of this type and just requires that a small modification be made to the Kalman filter as
described in Brave et al. (2020).

12
sample (upper left) and some selected sub-sampled time periods. The gray shading plots the
number of newly diagnosed Covid-19 cases in the U.S. Several interesting features appear
in the weekly index that are not readily apparent in the MRTS data. First, weekly sales in
March 2020 were very uneven, rising substantially in the first half of the month and then
plummeting in the second half (upper right). This is consistent with consumers’ increasing
awareness of the Covid-19 virus in mid-March (Keane and Neal, 2021) and anecdotal evidence
of “stockpiling” just prior to the closure of nonessential businesses across much of the U.S. in
the second half of March. These closures and the accompanying stay-at-home orders issued
by many states and locales then coincides precisely with the sharp decline in the index in
the latter half of March.
Subsequently, the weekly index begins to recover around mid-April 2020, as local com-
munities lifted stay-at-home orders and the federal government expanded unemployment
insurance and disbursed the first round of economic impact payments. In contrast, in the
MRTS the impact of these developments are not apparent until the May data. Note, too,
that the advance estimate of the May MRTS was published in mid-June, whereas the first
estimate of the index for the second half of April was produced at the beginning of May.
Accordingly, the weekly index identified the rebound in sales well in advance of the MRTS.
The recovery continued throughout the summer months of 2020, with the index returning
to pre-pandemic levels by July 2020. However, as the figure shows, the recovery was not
without some variation at the weekly frequency. In particular, when new cases of Covid-19
began to rise again during the summer, the index exhibited periods of decline in both July
and August (lower left). This drop-off is not apparent in the MRTS data, because they
average in the weeks of substantial positive growth both before and after the peak of the
summer wave of cases.
The index also highlights the uneven nature of sales during the fourth quarter of 2020 and
into the first quarter of 2021 (lower right). Sales fell sharply starting around Thanksgiving,
corresponding to the resurgence in Covid-19 cases. Sales remained at a low level through

13
much of December, but then improved markedly around the turn of the year during the
week when many Americans received their second round of Covid-19 stimulus payments.
But after that initial burst, sales fell sharply again, driven in part by severe winter weather
across much of the U.S. in February and then recovering by the first week of March.
As a policy-relevant application of our weekly index, figure 3 compares the week-to-
week movements in the index in 2020-21 against their similar 2018-19 averages. The vertical
dashed lines mark weeks when each of the initial disbursements of each of the three rounds of
economic impact payments over the past year took place—the CARES Act in April 2020, the
CRA in January 2021, and the ARP in March 2021. We can see a clear connection between
stimulus payments and retail spending, with sales jumping during all three episodes. While
the impact of the latter payments on retail sales are apparent in the MRTS as well (see figure
2), the CARES Act payments in April are not because the MRTS data is only available at
a monthly frequency.
Overall, our weekly index reveals patterns in retail sales that are of interest to those
studying the impacts of the pandemic and the policy responses to it that are not always
visible in the MRTS data. Moreover, we do so in a way that preserves the representative
structure of the MRTS.
Our model’s combination of time series and benchmarking to the MRTS also provides
a more stable reading of activity than two alternative measures of weekly retail sales, one
from the Bureau of Economic Analysis (BEA) and one from the Opportunity Insights (OI)
lab.25 These measures also use credit and debit card data, but both come from a single data
provider with different coverage and use different statistical methods than our index.
This is seen in figure 4, which plots the series as a percent deviation from a pre-pandemic
January 2020 baseline.26 All three indexes generally track one another, but ours is sub-
25
See Aladangady et al. (2019) and Dunn et al. (2020) for more detail on the underlying data and con-
struction of the BEA card spending estimates based on data from Fiserv First Data. Monthly and weekly
data are available at https://www.bea.gov/recovery/estimates-from-payment-card-transactions. The OI es-
timates are based on data from Affinity Solutions and are described in more detail in Chetty et al. (2020).
Daily and weekly data are available at https://www.tracktherecovery.org/.
26
In addition, the BEA and Opportunity Insights measures include spending on automobiles and car parts

14
stantially less volatile.27 This suggests that using information from a range of data sources
could do a better job at extracting the underlying trend in overall retail activity than any
individual data series. For example, the OI measure described in figure 1b of Chetty et al.
(2020) has a root mean-squared error of close to 5 percentage points in comparison to the
Advance Monthly Retail Trade Survey (MARTS), whereas our indicator’s RMSE is only
1.4 percentage points. As we show below, there is substantial variation over time in the
contributions of different indicators to explaining the common factor in overall retail sales,
which our multivariate structure exploits to produce superior forecasts of the MARTS.

3.4 Contributions of Components to the Weekly Index

Figure 5 plots the contribution of each individual indicator to our overall index for every
week in our sample. The variation in the index that cannot be explained by the weekly
series is attributed to the MRTS data; in turn, this contribution largely reflects the temporal
aggregation constraint imposed on the mixed-frequency dynamic factor model. The figure
highlights the wide and time-varying range of contributions from these different elements. For
example, while the dynamics generated by the MRTS (dark blue) often are quite important,
they fall short in accounting for the depth of decline of the index in March and contributed
little to the rebound in April. At these times, the EIA (purple), and Consumer Edge (orange)
data made substantial contributions to the index.
Table 1 decomposes the variance of the weekly growth rate of the index into the per-
centages explained by each of our six high-frequency data sources and the MRTS data over
the January 2018- February 2021 period. The first column presents the results for the index
depicted in figure 5, which is produced by the Kalman smoother. Almost 59 percent of
its variation is explained by the MRTS, leaving about 41 percent to be explained by the
(NAICS code 441) and exclude either gas station sales (BEA) or in some instances groceries (OI). Our
Weekly Index of Retail Trade excludes autos. Both the BEA and OI data also use weeks defined as seven-
day intervals starting from January 1 of each year. Our Weekly Index of Retail Trade instead uses the week
definitions laid out above in section 3.1
27
One caveat is that our index excludes auto sales, a component of retail sales known to be somewhat
more volatile than other components of retail spending. Both the BEA and OI index include auto sales.

15
high-frequency data. Of these data sources, the EIA data explain about 30 percent. While
important for a number of specific episodes, together on average the transaction data only
explain roughly 7 percent of the variation in the index, with the remaining roughly 4 percent
accounted for jointly by SafeGraph and Morning Consult.
To assess the degree of uncertainty around the values in table 1, we perform a leave-one-
out cross-validation exercise, re-estimating the model each time dropping one of the weekly
data series. This produces a range of values showing the impact of omitting each weekly
data source one-by-one. In this way, we can capture interdependencies in the estimation of
our model. The lower and upper bounds of these ranges are shown in table 1 in brackets.
Overall, this exercise suggests that the MRTS data explains no less than 59 and no more
than 80 percent of the variation in the growth rate of our weekly index.
The Kalman smoother uses data from the entire sample to inform the index in any given
period. Of course, in real-time analysis, data for (i, t) and beyond are unknown. To gauge
the influence of this future information, the second column of table 1 presents variance
decompositions for the Kalman (forward) filtered index, which is the expectation of the
index’s growth rate based on the data in hand prior to (i − 1, t).28 This decomposition is
substantially different from that for the smoothed index. Here, the Safegraph data explain
about 36 percent of the variation, and the EIA, Womply, and Morning Consult data also
make important contributions. In contrast, the MRTS data explain very little, suggesting
that much of their impact on the smoothed index comes from the constraint matching it to
the MRTS data at the monthly frequency.
The filtered decompositions also are useful because they give us a sense of how the
model may be expected to perform in forecasting the MRTS. The third column of table 1
shows a variance decomposition of nowcasts for the months of March 2020-February 2021
taken from an out-of-sample forecasting exercise with our model. Viewed through this lens,
the importance of each high-frequency data source is more balanced. At 27 percent, the
28
Data from after (i, t) are still used in estimation of the model parameters.

16
SafeGraph data still account for the largest share, but the contribution of the MRTS, EIA,
Consumer Edge and Womply indices are all in the range of 14 to 18.5 percent and Morning
Consult contributes nearly 9 percent. We now turn to describing this nowcasting exercise in
more detail.

4 Nowcasting the MARTS

Our results so far suggest that the mixed-frequency dynamic factor model could be a useful
tool for predicting retail sales. We examine this question in a nowcasting exercise that
iteratively re-estimates and forecasts in a fashion meant to mimic the real-time construction
of the index during the pandemic period. We then compare its predictions for the Advance
Monthly Retail Trade Survey (MARTS) against consensus forecasts available at the time
and real-time monthly autoregressive forecasts.

4.1 Constructing Out-of-Sample Predictions

To nowcast the MARTS measure of retail and food services sales excluding autos, we use
recursive estimates of the Kalman filter to project the weekly latent factor forward in time
and obtain the resulting nowcast for month T , Mi=4,T . Forecasts can be made h weeks ahead
of each MARTS release, where h = 0, 1, 2, 3, or 4.29
Our procedure needs to account for the fact that even when we observe all of the weekly
data for a month (h = 0), the MARTS data are not yet observed. This means that we cannot
fully infer the current month’s error structure, or ηi=1:4,t=T and Σ to be precise. To do so,
we use the simulation smoother of Durbin and Koopman (2012).30 This procedure allows
29
Technically, this is done within the Matlab toolbox MFSS by appending missing values for the Wn,i,t
to extend the estimation period by the number of weeks necessary to reach the end of the month being
forecast. Mi=4,T is then the end-of-month triangle average of the latent factor tracked in the state-space
with an accumulator variable. For further details, see Brave et al. (2020) and the documentation for the
Matlab toolbox MFSS.
30
We also account for the impact of data revisions by augmenting the errors in the draws of the estimated
end-of-sample variance of the model’s latent states to reflect historical differences between the advance and
final releases of the MRTS using data from the St. Louis Fed’s ALFRED database to calculate the variance

17
us to simulate multiple paths for the Weekly Index of Retail Trade by taking draws from
a multivariate normal distribution of the model’s shocks, and so produce coverage intervals
as well as point forecasts. To obtain the intervals, we take percentiles of the distribution of
Mi=4,T from 1.5 million simulated paths.

4.2 Out-of-sample Performance

We evaluate the out-of-sample forecasting performance of our nowcasts by comparing them
to consensus forecasts available at the time and to predictions from a monthly autoregressive
forecast of the MRTS data. The exercise could help reveal if our index suffers from overfitting,
which clearly is a risk given our short sample period and the number of parameters in the
model.
For our first out-of-sample exercise, we consider previous forecasts of MARTS when all
available weekly data through the end of the month are known, h = 0. We seasonally adjust
all data with the seasonal factors estimated at the time, iteratively re-estimate the model
with real-time values, and produce nowcasts for the MARTS releases between March and
February 2021.
Figure 7 decomposes our MARTS nowcasts into the contributions from each of the high-
frequency data sources and the lagged MRTS data. For ease of viewing, we present the data
only in terms of month-over-month percent (log) changes. The figure highlights the wide
and time-varying range of contributions from the different components that we also saw for
the smoothed index in figure 5. For example, the improvement in January 2021 retail sales
was principally driven by an increase in credit card spending and gasoline consumption. In
contrast, last March and April the mobility and consumer sentiment data made outsized
contributions to the forecast. In addition, notably, the lagged values of MRTS played a
substantial role only in the May and June 2020 and February 2021 nowcasts. This variation
over time in contributions to the index highlights the value of using a multi-variate model as
of revisions in our sample.

18
opposed to relying on a single indicator to gauge the evolution of aggregate retail activity.
Table 2 reports mean absolute error ratios comparing the h = 0 nowcasts (now ex-
pressed as simple month-over-month percent changes) against the median projections from
two weekly consensus surveys taken on the Fridays prior to the release of the MARTS data
during our sample period: Informa Global Markets (MCM Research) and Action Economics.
Values less than 1 (greater than 1) in the table denote that our models produced a lower
(higher) mean absolute error for the pandemic period.
We report two ratios for each comparison, with the first calculated based on the initial
release of the MARTS data being nowcast and the second based on the MRTS data published
as of February 17, 2021. The latter accounts for revisions to the MARTS data, which occur
in the two months following the initial release.31 To establish statistical significance for the
comparisons, we use the equal mean absolute error test proposed by Diebold and Mariano
(1995) with the small sample size correction of Harvey et al. (1997) and standard errors
computed with the Bartlett kernel with lag length set equal to sample size as suggested by
Kiefer and Vogelsang (2005).
As seen in table 2, the nowcasts of the month-over-month percent change in the MARTS
data outperform the consensus forecasts made during the pandemic by about 60 percent, for
both surveys and releases of the Census data. Moreover, even with only ten observations,
the Diebold-Mariano test indicates that these differences are significant at the 95 percent
confidence level.32 Thus, the nowcasts have a large and economically significant informational
advantage relative to the surveys. This is true even abstracting from March-June 2020, where
the informational gains are the largest.
We can also characterize the informational advantage provided by the high-frequency data
over and above the MRTS data. To do so, we compare the accuracy of our nowcasts against
one-month ahead forecasts from first-order autoregressive models for the MRTS. We consider
31
The data also undergo an annual revision that is published in April.
32
One caveat is that we do not account for possible revisions to the high-frequency data. Note too that
the results are slightly worse for a version of the model with a diagonal Σ.

19
two such specifications. The first estimates the model parameters using data from January
2006 through February 2020 and holds them fixed when producing forecasts for March 2020
through February 2021. The second instead recursively updates these parameters by adding
the previous month’s data to the estimation sample.
To capture the real-time data flow within each month, we produce five nowcasts based
on the number of weeks of the high-frequency data available. Given the mid-month calendar
release of the MARTS and the lags in the availability of the high-frequency data, there is
typically at most only one week of high-frequency data available for the current month at
the time of release for the previous month’s MARTS data. This situation corresponds to
either the h = 3 or h = 4 nowcast. Starting from this baseline, we can then track the relative
importance of each subsequent week’s worth of data.
Table 3 demonstrates that our dynamic factor model outperforms a monthly AR(1)
specification for the MRTS by about 10-30 percent when no weekly data are used in the
model (h=4) and an even greater 45-55 percent when only 1 week of high-frequency data is
used in the model (h = 3). The gains steadily increase from there, peaking at about 75-80
percent when all four weeks’ worth of high-frequency data are used (h = 0) in the model.

4.3 Sources of Forecast Error

While this forecasting performance is impressive, several potential sources of forecast error
in our model are worth noting.

1. Sampling error : The high-frequency spending data we use collectively account for
only a small fraction of the universe of retail sales covered by MRTS and the data are
not representative of the universe of retail transactions. Our methodology attempts to
address this issue by including more representative data from EIA and Morning Consult
in the model and forcing our index to match the MRTS at the monthly frequency.
Nonetheless, these corrections are not perfect, and a portion of our forecast errors will
be caused by these differences in coverage.

2. Parameter instability: The wide variation in the data during the first few months of
the pandemic mean that period will have an outsized effect on identification. This is
an issue for all forecast models estimated over this period. Indeed, between March

20
and June our parameter estimates jumped around considerably before settling down
to relatively consistent values in the months since then. This parameter instability is
another potential source of forecast error, especially for the relatively larger misses of
our model in the March-June period.
3. Census seasonal factors and revisions: The seasonal factors we use to adjust the weekly
spending series are directly proportional to the MRTS seasonal factors (see Appendix).
Since the MRTS seasonals are re-estimated concurrently, we must forecast them prior
to the MARTS release. Any error in this forecast can propagate into our nowcasts.
So, too, can large revisions to past values of the MRTS. And in fact, at times during
the pandemic both the errors in seasonal factor forecasts and revisions to past MRTS
data have been extremely large by historical standards.

Figure 8 decomposes our forecast errors (h = 0 nowcasts minus actual) during the pan-
demic into each of these three sources. To create this decomposition, we re-ran our nowcasts
under alternatives that altered the real-time exercise by using: 1) the model parameters
estimated at their latest values, and 2) the latest MRTS data and seasonal factors. Dif-
ferences between the resulting nowcasts and our original estimates are informative on the
roles of parameter instability and data revisions in explaining our errors; the residual is then
attributed to sampling error.33
Parameter instability played a large role in explaining forecast errors in the early months
of the pandemic. As our parameter estimates have settled down since July 2020, this par-
ticular source of error has become less impactful, with the exception of January 2021. In
contrast, revisions to the Census data and seasonal factors typically played a minor role,
with the notable exception of March 2020. The large error in our forecast for the monthly
seasonal factor, which is due to a large change in the Census seasonal factor, caused us to
underestimate the decline in retail sales in March. At the same time, several of the underly-
ing weekly data series overestimated the March decline and the two sources of forecast error
largely canceled each other out.
Overall, the errors in our nowcast are largely driven by sampling variability attributable
to differences in the coverage of our high-frequency data sources and the MRTS. This was
most evident in the early stages of the pandemic in March and June 2020, but was also true
33
At the time of writing, the January and February 2021 MRTS values were still subject to further revisions.

21
at the end of 2020 when retail sales declined more than our model expected in October and
November. Similarly, our largest misses in January and February 2021 were also primarily
attributable to sampling variability.
All together, the mean absolute error for our nowcasts during the pandemic is 1.2 per-
centage points. This is against an average absolute percent change in retail and food services
sales ex. autos of 4.9 percent over this period. June and November 2020 and January and
February 2021 are the only months in our sample where our absolute errors are greater than
1 percentage point; excluding those four months, the mean absolute error of the other eight
months was just 0.2 percentage point, versus an average absolute change in retail and food
services sales ex. autos of 4.8 percent.

5 Conclusion

We used weekly measures of revenue, credit and debit card transactions, consumer sen-
timent, mobility, and gasoline shipments to create a seasonally adjusted Weekly Index of
Retail Trade that is benchmarked to monthly retail and food services sales (excluding auto-
motive spending) from the Census Bureau’s Monthly Retail Trade Survey (MRTS). To do
so, we use a novel mixed-frequency dynamic factor model that combined the valuable real-
time information from alternative high-frequency data sources of consumer activity with the
representative sampling of the MRTS.
Using our weekly index, we showed that retail sales during the Covid-19 pandemic in the
U.S. were highly variable at the weekly frequency, with a considerable amount of interesting
variation masked at the monthly frequency by the MRTS. The weekly spending patterns
that we document align well with the timing of the waves of Covid-19 cases, restrictions
imposed on businesses and households, and economic impact payments that we have seen
during the course of the pandemic.
In addition, we found that the mixed-frequency dynamic factor model used to create our

22
weekly index could be reliably used to nowcast the Census Bureau’s Advance Monthly Retail
Trade Survey (MARTS) in real time, besting by about 70 percent both consensus forecasts
available at the time and forecasts from monthly autoregressive specifications for the MRTS
in terms of lower mean absolute error.
Going forward, our methodology can be extended to include finer levels of disaggregation,
both geographically and by sales categories. For example, the Census Bureau has recently
begun to release monthly state-level retail spending measures. Insofar as the high-frequency
data sources we used can be disaggregated to the U.S. state level, estimating similar models
for state retail sales would be a straightforward extension of our analysis.
Furthermore, we focused on the retail and food services sales ex. autos category of
spending, but other categories of consumer spending may also prove to be forecastable.
Tailoring our model to the sub-aggregates used by the BEA may be useful for forecasters
and others interested in mapping at a high frequency into GDP the effects of pandemics and
future business cycles on consumer spending.

23
References
Aladangady, A., S. Aron-Dine, W. Dunn, L. Feiveson, P. Lengermann, and C. Sahm (2019).
From transactions data to economic statistics: Constructing real-time, high-frequency,
geographic measures of consumer spending. NBER Working Paper Series (26253).

Alexander, D. and E. Karger (2020). Do stay-at-home orders cause people to stay at
home? effects of stay-at-home orders on consumer behavior. FRB of Chicago Working
Paper (WP-2020-12).

Aruoba, S. B., F. X. Diebold, J. Nalewaik, F. Schorfheide, and D. Song (2016). Improving
gdp measurement: A measurement-error perspective. Journal of Econometrics 191 (2),
384–397.

Aruoba, S. B., F. X. Diebold, and C. Scotti (2009). Real-time measurement of business
conditions. Journal of Business & Economic Statistics 27 (4), 417–427.

Atkinson, T., J. Dolmas, K. Christoffer, E. Koenig, K. Mertens, A. Murphy, and K.-M. Yi
(2020). Mobility and engagement following the sars-cov-2 outbreak. Federal Reserve Bank
of Dallas Working Paper (2014).

Bartik, A. W., M. Bertrand, Z. B. Cullen, E. Glaeser, M. Luca, and C. Stanton (2020). How
are small businesses adjusting to covid-19? early evidence from a survey. NBER Working
Paper Series (26989).

Brave, S. and R. A. Butters (2012). Diagnosing the financial system: Financial conditions
and financial stress. International Journal of Central Banking 8 (2), 191–239.

Brave, S. A., R. A. Butters, and M. Fogarty (2020). The perils of working with big data
and a small framework you can use to avoid them. FRB of Chicago Working Paper (WP-
2020-35).

Brave, S. A., R. A. Butters, and D. Kelley (2020). A practitioner’s guide and matlab toolbox
for mixed frequency state space models. Available at SSRN 3532455 .

Brave, S. A., W. Kluender, C. Gascon, and T. Walstrum (2021). Predicting benchmarked
u.s. state employment data in real time. International Journal of Forecasting. forthcoming.

Carvalho, V. M., S. Hansen, A. Ortiz, J. R. Garcia, T. Rodrigo, S. R. Mora, and J. Ruiz
(2020). Tracking the covid-19 crisis with high-resolution transaction data. CEPR Working
Paper Series (214642).

Chetty, R., J. N. Friedman, N. Hendren, and M. Stepner (2020). The economic impacts of
covid-19: Evidence from a new public database built using private sector data. NBER
Working Paper (27431).

Cleveland, W. and S. Scott (2007). Seasonal adjustment of weekly time series with ap-
plication to unemployment insurance claims and steel production. Journal of Official
Statistics 23 (2), 209 – 221.

24
Coibion, O., Y. Gorodnichenko, and M. Weber (2020). The cost of the covid-19 crisis:
Lockdowns, macroeconomic expectations, and consumer spending. NBER Working Paper
Series (27141).

Consolvo, V. and K. G. Lunsford (2019). Residual seasonality in gdp growth remains after
latest bea improvements. Economic Commentary (2019-05).

Croushore, D. (2005). Do consumer-confidence indexes help forecast consumer spending in
real time? The North American Journal of Economics and Finance 16 (3), 435–450.

Diebold, F. X. and R. S. Mariano (1995, July). Comparing predictive accuracy. Journal of
Business & Economic Statistics 13 (3), 253–63.

Dunn, A., K. Hood, and A. Driessen (2020). Measuring the effects of the covid-19 pandemic
on consumer spending using card transaction data. BEA Working Paper Series.

Durbin, J. and S. J. Koopman (2012). Time series analysis by state space methods. Oxford
university press.

Galbraith, J. W. and G. Tkacz (2018). Nowcasting with payments system data. International
Journal of Forecasting 34, 366–376.

Giannone, D., L. Reichlin, and D. Small (2008). Nowcasting: The real-time informational
content of macroeconomic data. Journal of Monetary Economics 55 (4), 665 – 676.

Harvey, A. C. (1990). Forecasting, structural time series models and the Kalman filter.
Cambridge university press.

Harvey, D. I., S. J. Leybourne, and P. Newbold (1997). Testing the equality of prediction
mean squared errors. International Journal of Forecasting 13 (2), 281–291.

Karger, E. and A. Rajan (2020). Heterogeneity in the marginal propensity to consume:
Evidence from covid-19 stimulus payments. FRB of Chicago Working Paper (WP-2020-
15).

Keane, M. and T. Neal (2021, January). Consumer panic in the covid-19 pandemic. Journal
of Econometrics 220 (1), 86–105.

Kiefer, N. M. and T. J. Vogelsang (2005). A new asymptotic theory for heteroskedasticity-
autocorrelation robust tests. Econometric Theory 21 (6), 1130–1164.

Lewis, D. J., K. Mertens, J. H. Stock, and M. Trivedi (2020). Measuring real activity using
a weekly economic index. Federal Reserve Bank of New York Staff Reports (920).

Ludvigson, S. C. (2004). Consumer confidence and consumer spending. Journal of Economic
Perspectives (2), 29–50.

Mariano, R. S. and Y. Murasawa (2003). A new coincident index of business cycles based
on monthly and quarterly series. Journal of Applied Econometrics 18 (4), 427–443.

25
Stock, J. H. and M. W. Watson (2011). Dynamic Factor Models. Oxford Handbook of
Forecasting.

U.S. Census Bureau (2017). X-13 arima-seats reference manual. Technical report, Washing-
ton DC.

Wilcox, D. W. (1992). The construction of u.s. consumption data: Some facts and their
implications for empirical work. American Economic Review (4), 922–941.

26
6 Tables and Figures

Table 1: Variances Explained by Data Source

Series Smoothed Filtered Nowcast
Census 59.2 1.8 18.5
(59.2, 79.6) (1.8, 8.8)
Consumer Edge 6.7 5.5 14.0
(6.7, 16.9) (5.5,26.3)
Facteus 0.0 0.5 0.6
(0.0, 0.2) (0.4, 0.7)
EIA 29.8 27.8 16.4
(8.8, 29.8) (27.8, 47.5)
Womply 0.4 17.5 14.6
(0.4, 8.8) (11.5, 22.1)
Morning Consult 0.3 10.9 8.7
(0.3, 2.7) (10.3, 18.8)
SafeGraph 3.5 35.9 27.2
(1.8, 3.5) (13.7, 35.9)

Note: This table contains a variance decomposition of the smoothed, filtered, and out-of-sample nowcast
for the growth rate of our Weekly Index of Retail Trade by data source. The percentage values in the table
sum to 100 (within rounding error) by construction. The values in brackets for the smoothed and filtered
variance decompositions are the lower and upper bounds from a leave-one-out cross-validation exercise of the
weekly data sources. The smoothed and filtered growth rates cover the period from January 2018-February
2021. The out-of-sample nowcasts are for March 2020-February 2021.

27
Table 2: Mean Absolute Errors Relative to Consensus Forecasts

Release
Forecaster First Current
MCM Research 0.40∗ 0.42∗
Action Economics 0.37∗ 0.40∗

Note: This table shows mean absolute error (MAE) ratios for nowcasts from our mixed-frequency dynamic
factor model. The ratios are expressed relative to the MCM Research and Action Economics survey median
nowcasts of the month-over-month percent change in retail & food services sales ex. auto for both the
First and Current releases of the Census Bureau’s Monthly Retail Trade Survey from March 2020 through
February 2021. The marker * denotes statistical significance from a Diebold-Mariano test of equal mean
absolute error (i.e. ratios equal to 1) at the 95% confidence level using the Bartlett kernel with lag length
equal to sample size and a small sample size correction. Both survey forecasts were obtained through a
subscription to Haver Analytics. The MCM Research survey is maintained by Informa Global Markets.

28
Table 3: Mean Absolute Errors Relative to Monthly Autoregressive Models

AR Type
Weeks of Data (h Steps Ahead) Fixed Recursive
0 (h = 4) 0.93 0.73
∗∗
1 (h = 3) 0.59 0.46∗∗
2 (h = 2) 0.48∗∗ 0.37∗∗
3 (h = 1) 0.25∗∗ 0.20∗∗
4 (h = 0) 0.24∗∗ 0.19∗∗

Note: This table shows mean absolute errors (MAEs) for nowcasts of retail & food services sales ex. auto
from our mixed-frequency dynamic factor model relative to monthly autoregressive specifications estimated
over a fixed and recursive window each with 1 lag. The fixed-window model was estimated over a sample
period from January 2006 through February 2020 and its coefficients held fixed to produce one-month ahead
forecasts over the period from March 2020 through December 2020. The recursive-window model adds one
month of data to the estimation sample iteratively from March 2020 through January 2021 and uses the
updated model coefficients to produce one-month ahead forecasts. To produce similar forecasts from our
mixed-frequency dynamic factor model we estimate the model separately including from zero to four weeks
of available weekly data for the month being nowcasted. The markers */** denotes statistical significance
from a Diebold-Mariano test of equal mean absolute error (i.e. ratios equal to 1) at the 95% confidence level
using the Bartlett kernel with lag length equal to sample size and a small sample size correction. Retail &
food services sales ex. auto data used to construct mean absolute errors were obtained from Haver Analytics.

29
Figure 1: Weekly Data Series, by Source

Source: Authors’ calculations based on data from the U.S. Census Bureau and Energy Information
Administration, Consumer Edge, Womply, Facteus, Morning Consult, and SafeGraph.

Note: Daily data are aggregated to weekly and seasonally adjusted with the procedure described in
the appendix. All of the data series as shown in the figure are set equal to 100 in January 2020.

30
Figure 2: Retail and Food Services Sales ex. Auto

Source: Authors’ calculations based on data from the U.S. Census Bureau and Energy Information
Administration, Consumer Edge, Womply, Facteus, Morning Consult, and SafeGraph.

Note: We align the monthly MRTS data to the second week of each month to emphasize the tem-
poral aggregation constraint that requires the monthly average of our Weekly Index of Retail Trade to
approximately equal the MRTS data. The gray shaded area represents the weekly average of new Covid-19
cases in the United States for various time periods.

31
Figure 3: Weekly Retail Sales and the Timing of Economic Impact Payments

Source: Authors’ calculations based on data from the U.S. Census Bureau, Energy Information Admin-
istration, and Department of the Treasury; Consumer Edge, Womply, Facteus, Morning Consult, and
SafeGraph.

Note: The figure compares week-over-week percent changes in our Weekly Index of Retail Trade
over the 2020-21 period relative to the average of the same weeks of 2018 and 2019 in order to highlight the
impact of the various rounds of Economic Impact Payments on retail and food services sales ex. auto. The
first vertical line corresponds to April 10, 2020, when the CARES Act funds were initially disbursed; the
second to January 6, 2021, when the second round of payments authorized in the 2020 year-end omnibus
federal spending bill were deposited; and the third line to March 17, 2021, the date when the payments
authorized in the American Rescue Plan were initially disbursed. All initial payment disbursement dates
were determined from the U.S. Treasury’s Daily Treasury Statement using data from Haver Analytics.

32
Figure 4: Weekly Measures of Retail and Food Services Sales

Source: Author’s calculations. Bureau of Economic Analysis and Opportunity Insights were obtained via
Haver Analytics.

Note: The figure compares relative to a pre-pandemic baseline three weekly measures of retail and
food services sales: our Weekly Index of Retail Trade and two different measures of credit and debit card
spending from the U.S. Bureau of Economic Analysis (BEA) and the Opportunity Insights (OI) lab.

33
Figure 5: Contributions to Growth for the Weekly Index of Retail Trade

Source: Authors’ calculations based on data from the U.S. Census Bureau and Energy Information
Administration, Consumer Edge, Womply, Facteus, Morning Consult, and SafeGraph.

Note: The contributions sum to the Kalman smoothed estimate in each week of the percent (log)
change of the Weekly Index of Retail Trade. The method of calculation for these contributions is described
in detail in Brave, Butters, and Kelley (2020).

34
Figure 6: February 2021 Nowcast for Retail and Food Services Sales ex. Auto

Source: Authors’ calculations based on data from the U.S. Census Bureau and Energy Information
Administration, Consumer Edge, Womply, Facteus, Morning Consult, and SafeGraph.

Note: The figure shows our February 2021 nowcast using weekly data available through the first
week of the month. The shaded regions represent 70% (dark gray) and 90% (light gray) coverage intervals.

35
Figure 7: Contributions to Growth for our MARTS Nowcasts

Source: Authors’ calculations based on data from the U.S. Census Bureau and Energy Information
Administration, Consumer Edge, Womply, Facteus, Morning Consult, and SafeGraph.

Note: The figure displays contributions to our MARTS nowcasts for March 2020 through January
2021 using the weekly data available through the end of each month and previously released MRTS data.
The contributions in the figure sum to the nowcast value by construction.

36
Figure 8: Nowcast Error Decomposition

Source: Authors’ calculations based on data from the U.S. Census Bureau and Energy Information
Administration, Consumer Edge, Womply, Facteus, Morning Consult, and SafeGraph.

Note: The total nowcast error is defined as the (revised) MRTS value minus our model’s nowcast.
The portion of the forecast error attributed to parameter instability is defined as the difference between
the nowcast and the value from an alternative nowcast where our model parameters have been fixed
at their current estimates. The error due to Census revisions is defined as the difference between the
alternative nowcast with the fixed model parameters and another alternative nowcast that uses both the
fixed parameters and the revised, rather than real-time, MRTS data. We attribute the remaining nowcast
error to sampling variation, such that all three sources of error sum to the total nowcast error.

37
7 Appendix

7.1 Seasonal Adjustment of Weekly Data

Seasonal variation is large in retail sales, yet none of the high-frequency data are available
on a seasonally adjusted basis. Standard seasonal adjustment procedures, such as the X13
ARIMA-SEATS program published by the Census Bureau (U.S. Census Bureau, 2017), are
not well suited to the seasonal adjustment of high-frequency data series. In our case, we
are also handicapped by the very short history of our time series. For instance, the method
described in Cleveland and Scott (2007) that is commonly used to seasonally adjust weekly
time series like unemployment insurance claims requires much more than the roughly two
years of data that we have available to us.
However, we are still able to seasonally adjust our weekly data by making. First, we
assume that the seasonal factors for our weekly data when temporally aggregated to the
monthly frequency are the same as the MRTS seasonal factors. Second, we assume that the
weekly seasonal factors are a specific function of the monthly seasonal factor, the number of
days in the week, and a week-of-the-month effect.
Below we describe how the MRTS seasonal factors can be used to seasonally adjust the
high-frequency data sources at a first pass. This procedure reliably removes the majority of
seasonal patterns in our transaction and foot traffic data (the EIA data are already seasonally
adjusted using the Cleveland and Scott (2007) method by Haver Analytics and the Morning
Consult data do not exhibit seasonality). To then account for any residual seasonality in the
data, we remove prominent week-of-year effects.

Derivation of the Weekly Seasonal Factors

To account for seasonality in the high-frequency data, we incorporate the monthly seasonal
factors from the Census Bureau’s retail and food services sales ex. autos series.34 We assume
34
The seasonal factor for month is defined as , where is the seasonally adjusted Census series and is the
unadjusted Census series.

38
that the observed monthly Census seasonally adjusted (SA) and non-seasonally adjusted
(NSA) time series are the sum of latent (unobserved) weekly series:

4
X
N SA
Ci,t = CtN SA
i=1
X 4
SA
Ci,t = CtSA
i=1

N SA SA
where Ci,t and Ci,t are NSA and SA weekly Census retail sales, CtN SA and CtSA are NSA
and SA monthly Census retail sales, and the subscripts t and i index months and weeks,
respectively.
The seasonal factors are multiplicative in levels (additive in logs) at both the weekly and
monthly levels

SA N SA C
Ci,t = Ci,t · SFi,t

CtSA = CtN SA · SFtC

C
where SFi,t is the latent weekly Census seasonal factor and SFtC is the monthly Census
seasonal factor. Together with our assumption that monthly Census retail sales are the sum
of latent weekly sales, this yields the following relationship between the monthly and weekly
data and seasonal factors:

4
X
CtN SA · SFtC = N SA
Ci,t C
· SFi,t
i=1
4
N SA
Ci,t
X
⇒ SFtC = N SA
C
· SFi,t
i=1
Ct
4 N SA

C
X Ci,t /Di,t Di,t C
⇒ SFt = N SA
· SFi,t
i=1
(Ct /Dt ) Dt

39
where Di,t is the number of days in week i of month t and Dt is the number of days in month
t . The first term in the sum of the last expression is the ratio of sales per day in week i to
sales per day in the month. This will reflect week fixed effects. For example, weeks 2 and 4
may have greater sales because they coincide with pay periods. The second term is the ratio
of days in the week to days in the month – in our week dating scheme, the last week of the
month has a variable number of days, and this adjusts for the fact that weeks can make up
a different share of the total days in the month across months of different length.
C
The goal of the weekly Census seasonal factor, SFi,t , is to offset these two calendar
sources of weekly sales variation. This suggests setting the weekly seasonal adjustment
factors according to the formula:

1 1
C
SFi,t = · SFtC
4 (Ci,t
N SA /D
i,t ) Di,t
avgi,t
(CtN SA /Dt ) Dt

Here, avgi,t refers to the average of the ratio of sales per day in week i to sales per day in
the month (averaging over some window of months).
We can perform a related exercise to seasonally adjust the high-frequency data. We
exploit this structure and the Census monthly seasonal factors to set weekly seasonal factors
N SA
for HFi,t , the NSA high frequency weekly retail sales data, in order to create a SA series,
SA
HFi,t :

HF 1 1
SFi,t = · SFtC
4 (HFi,t
N SA /D
i,t ) Di,t
avgi,t
(HFt /Dt )
N SA Dt

SA N SA HF
HFi,t = HFi,t · SFi,t
4
X
HFtSA = SA
HFi,t
i=1

40
HF
where SFi,t and SFtHF are weekly and monthly seasonal factors and avgi,t is taken over all
of the week i ’s of month t in the data sample (for which we have a complete month of data).
Averaging the weekly sales share ratios at the week-by-month level allows us to control for
varying distributions of sales within the month, which are most noticeable during specific
times such as the end-of-year holiday period.
Our approach still has several implementation issues, for example whether or not to
include holidays in the Di,t and Dt variables. Through testing, we found that the more
parsimonious approach - including the holidays - produced better results than only including
non-holiday days in the formulas. In addition, SFtC , the monthly Census seasonal factor, is
not available until the MARTS is published, and so we must estimate it for our nowcasting
work. The Census Bureau seasonally adjusts retail sales on a concurrent basis; that is, every
month they re-rerun their programs and estimate new factors with all the available data.
These programs produce forecasts for future seasonal factors, which the Census Bureau
publishes for the closely related retail and food services sales category. Accordingly, we
forecast SFtC with a regression using this seasonal factor and 12 lags of the seasonal factor for
our sub-aggregate. In practice, this produces accurate forecasts of SFtC with one exception,
when Census substantially revised their seasonal factors in March 2020 at the onset of the
pandemic. To illustrate, over the nine-month period from January 2020 through September
2020, the mean absolute percent error for our forecasts of the monthly Census seasonal factor
was 2.6% . However, excluding the month of March reduces this to just 0.6% .

Residual Seasonality

Even after implementing the seasonal adjustment procedure described above, several of our
weekly data series still contain a degree of residual seasonality. Residual seasonality is a
phenomenon where there is a predictable seasonal pattern left over in a data series that
has already been seasonally adjusted by some standard procedure (Consolvo and Lunsford,
2019). The residual seasonality in the various weekly data series that we use are most

41
noticeable during the end-of-year holiday period, where there is often a predictable pattern
in the weekly growth rates around the first week of the year. This could arise, for example,
because the seasonal spending patterns for credit and debit card transactions do not exactly
mirror the seasonal pattern in the Census retail sales measure as assumed above.
To account for residual seasonality, we regress each of the spending and foot traffic series,
in log growth rates, on a constant and regressors for important retail holidays that move
within the year, such as Easter and Thanksgiving, as well as individual week dummies for a
small set of important weeks that we identified for each individual series. To get the series
back to levels, we take the residuals from these regressions, add back in the mean growth
rate taken out by the constant in the regression, and cumulate them forward from the series’
initial log-level. We then exponentiate the series to get it back into natural units. We do
not find evidence of any seasonality in the consumer sentiment data and, therefore, do not
seasonally adjust it.

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