**Retail Statistics During a Time of Disaster**

Ruth E. Detlefsen

Assistant Division Chief for Research and Methodology

Services Sector Statistics Division

Census Advisory Committee of Professional Associations Meetings

October 26-27, 2006

Abstract

The U.S. Census Bureau surveys approximately 12,000 firms across the
United States each month to produce national estimates of sales and
inventories for retail industries. After the widespread destruction
caused by Hurricane Katrina, the Census Bureau took steps to assess the
validity of its yet-to-be published retail estimates. This paper briefly
describes those steps and the modifications we made to data collection
and post-data collection processes such as response analysis,
imputation, estimation, and seasonal adjustment.

In the end, we needed to make no adjustments to the imputation and
estimation methods used to produce the retail estimates following the
hurricane. We did use this as an occasion to explore what we might do
should such an adjustment be necessary. This paper proposes a model for
estimating retail statistics in the event of future catastrophic events
that are confined to some well-defined geographic area.

Questions:

1.  Are the proposed methods sound and reasonable?

2.  Are there other issues we should be considering?

3.  We propose a method for handling disasters that are confined to
    well-defined geographic areas. Are there suggestions for how one
    would handle situations when there are no well-defined geographic
    areas?

This report is released to inform interested parties of research and to
encourage discussion. The views expressed on statistical,
methodological, technical, or operational issues are those of the
authors and not necessarily those of the U.S. Census Bureau.

This paper summarizes the Census Bureau's efforts to collect and analyze
monthly retail sales and inventory data following Hurricane Katrina.
Additionally, it offers a model for evaluating sample coverage and
estimating retail data for similar future events.

**Data Collection and Analysis of Retail Data Following Hurricane
Katrina**

The widespread destruction caused by the August 29, 2005 landfall of
Hurricane Katrina gave the Census Bureau many concerns about data
collection and evaluation for its retail estimates. Would the
infrastructure for contacting respondents be available? Would the
respondents be available? Would physical records still exist? How would
inventory be valued? Would we be able to correctly analyze the data
since evacuees would shift consumption to other areas? What would the
net effect of the hurricane be on the estimates? These concerns needed
to be addressed quickly since estimates for the August data month were
scheduled for release on Sept. 14.

We needed to ensure that the effects of Katrina would not be missed in
our national level estimates. Subnational geography is not used in the
sample design, so there was the potential that the sample did not
include units from the hurricane area. We took the steps below to decide
whether to develop alternative imputation and estimation techniques.

**1. Determined the Affected Areas** - We used maps and information
available from the Federal Emergency Management Agency and the United
States Postal Service.

**2. Gauged the Potential Impact on National Sales Totals** - About 1.2%
of 2002 total retail sales, as measured by the 2002 Economic Census,
were from the metropolitan areas affected by Katrina. Because the
destruction from Katrina did not include all of the land area in those
areas, we concluded that the impact to total retail sales would probably
be less than a percentage point of total U.S. retail sales.

**3. Analyzed the Sample Coverage** - We tabulated administrative annual
sales and estimated monthly sales from the sample for the U.S. and
affected geographic areas by industry. The percents of total U.S. sales
from the affected area as computed from the two tabulations were
compared. We concluded that the sample representation was adequate given
the standard errors achieved by our national estimates.

**4. Assessed the Impact on Collection Units** - Our sample has single
store firms (singleunits) and multiple store firms (multiunits).
Locations of singleunits were known, but special follow-ups were
necessary to determine if multiunits had stores in the affected area. If
so, we also asked about number of stores, store closings, length of
closings, and accounting for inventories and when and how much inventory
might be written off. Most collection units could report data for stores
in the affected areas. The hurricane had both positive and negative
effects on sales. Some firms had reduced sales but others had increases
as needs were met from open stores.

**5. Analyzed Response Rates for the Affected Period** -- Response rates
for the affected period were comparable to those achieved during the
prior six months.

**6. Reviewed Inventory Data** - We contacted over 1000 firms and found
that less than 2% had inventory damage or loss. None reported write-offs
to end-of-month inventories for August, but most expected to have
write-offs sometime in the future.

**7. Reviewed Seasonal Adjustment Output and Diagnostics** -- We made no
adjustments to the options.

We concluded that no changes were needed to imputation or estimation
procedures.

**Evaluating Sample Coverage and Estimating Retail Data in Future
Events**

Though we made no changes to imputation or estimation, we considered
what to do if some event, restricted to a well-defined geographic area,
were to affect the ability of businesses to operate or report data.
Damage could vary from none to complete infrastructure destruction.
Thus, some units might still be active and some might even be able to
report. The first issue is that we do not know whether a nonrespondent
is still in business, so we do not know whether to impute or adjust for
the nonresponse.

The illustration in the attachment represents the catastrophic
situation. Box A is the affected area. Sampling units for our retail
surveys are either singleunits (circles) or clusters of multiunit stores
(squares connected by lines). A black square designates the unit which
reports for all stores belonging to a particular multiunit cluster.

A singleunit is either in A or not. A multiunit may have all, none, or
some of its stores in A. If some stores are in A, the reporting unit may
either be in A or not. Four possible multiunit types are shown in the
attachment.

Suppose we have a simple random sample. The estimated total of interest
can be written as shown below. This expression separates the multiunits
into the four types shown in the attachment and the singleunits into
those inside and outside of A.

$\overset{}{Y}\  = \ \frac{N}{n}\ \left( \sum_{\text{Type}\ I}^{}{\ y_{I_{i}\ }\  + \ \sum_{\text{Type}\ \text{II}}^{}{\ y_{\text{II}_{i}\ }\  + \ \sum_{\text{Type}\ \text{III}}^{}{\ y_{\text{III}_{i}\ }\  + \ \sum_{\text{Type}\ \text{IV}}^{}{\ y_{\text{IV}_{i}\ }\  + \ \sum_{\text{SU}\  \in \ A}^{}{\ y_{i}\  + \ \sum_{\text{SU}\ \text{not}\ \text{in}\ A}^{}{\ y_{i}}}}}}} \right)$
,

\(1\) (2) (3) (4) (5) (6)

where N is the number of units in the frame, n is the number of units in
the sample, MU refers to multiunits, SU refers to singleunits, Type
refers to the four MU situations, and y is the variable of interest.

Based on the Katrina experience, we assume that reports contributing to
terms (1), (2), and (6) are of the same quality as before the event.
These terms account for units with either no stores in A; or if they
have stores in A, the reporting unit is outside of A. Reporting units
outside of A are expected to provide estimates for their stores inside
of A.

We are left with estimating terms (3), (4), and (5). We would first
exhaust follow-up strategies, then evaluate the magnitude of these
terms, and only apply the models below if the components are
substantial.

**Term (5) -** This term estimates for singleunits in A. An estimate for
term (5) is:

$\underset{\text{SU}\ i\ \text{in}\ A}{\overset{}{\sum_{}^{}y_{{}_{i}}}}\ $$= \ (1\  - \ p_{1})\ p_{2}\ {\overset{}{Y}}_{A}^{\text{before}},$

${\overset{}{Y}}_{A}^{\text{before}}$

where is the estimate for the period just prior to the event for all
singleunits in A, p~1~ is the percent of inactive units in A after the
event, and p~2~ is the percent of prior average activity that stores in
A realize after the event.

We estimate p~1~ as shown here:

$\overset{}{p}\ _{1}\  = \ \frac{R_{\text{???}}^{\text{before}}\  - \ R_{\text{???}}^{\text{after}}}{R_{\text{???}}^{\text{before}}}$
, where R is the unit response rate before or after the event.

By using this expression we assume that stores still active after the
event will respond at the same rate as before the event. That assumption
may not hold. We know the number of nonresponses after the event, but do
not know if they did not respond because they were inactive or for some
other reason. The decision to use this value or another should be
justified through follow-ups with respondents, news reports, or other
sources.

The ??? in the subscript indicates that the industry and geographic
levels at which to compute response rates is difficult to address. It is
unknown whether the same level should be used to compute before and
after response rates. Finer levels may be desirable but the estimates
may be unstable if sample sizes are too small. On the other hand,
broader levels may incorporate responses from areas that are not
affected by the event.

Consider p~2~. The level of activity for stores in A that are still
active after the event will likely change from what it was before the
event. We assume that data for units still active after the event
changes to p~2~ percent of the prior average level. We use this
expression:

$\overset{}{p}\ _{2}\  = \ \frac{\sum_{\text{Re}\text{spondents}\ \text{in}\ A\ \text{after}}^{}y^{\text{after}}}{\sum_{\text{Re}\text{spondents}\ \text{in}\ A\ \text{after}}^{}y^{\text{before}}}$

${\overset{}{Y}}_{A}^{\text{before}}$p~2~ is estimated as the ratio of
the after event data for respondents in A to the before event data for
the same units. It is used to create a link-relative estimate of the
current level assuming no change in active units. Multiplying 1- p~1~,
p~2~, and gives an adjusted link-relative estimator for the singleunits
in A as shown in (a) above.

**Term (4)** -- While term (5) estimates for [all singleunits in
A]{.underline}, term (4) estimates for [multiunits with all stores in
A]{.underline}. The model used for term (5) can be used to estimate term
(4) as shown below:

${\overset{}{Y}}_{A}^{\text{before}}$$\underset{\text{TypeIV}}{\overset{}{\sum_{}^{}y_{\text{IV}_{i}}}}$$= \ (1\  - \ p_{1})\ p_{2}\ {\overset{}{Y}}_{A}^{\text{before}},$where
is the estimate for the period just prior to the event for all
multiunits in A.

We could compute separate estimates of p~1~ and p~2~ for multiunits and
singleunits or combined estimates without regard to the distinction.
Which one is appropriate will depend on there being enough units to
create stable estimates, the magnitude of the two components, and
whether the underlying parameters differ significantly.

**Term (3)** -- Terms (4) and (5) address situations when the entire
unit is in A. Term (3) addresses multiunits that have stores outside of
A but the reporting unit is in A. With these units there is most likely
some retail activity that is not well represented by the activity
reported from units in A. An estimate for term (3) can be expressed as
shown below, where the first term estimates for the stores outside of A
and the second for those inside of A.

$\underset{\text{TypeIII}}{\overset{}{\sum_{}^{}y_{\text{III}_{i}}}}$
![](media/image1.wmf)

${\overset{}{Y}}^{\text{TypeIafter}}$

$x_{j}^{\text{frame}}$where is the value of a frame variable for store j
in multiunit i and is the

estimate of the variable for multiunit reporting units entirely outside
of A.

The first term consists of: 1) the reported or imputed total prior to
the event, 2) a ratio that prorates the reported amount to units not in
A, and 3) a link-relative ratio that adjusts the value to an after-event
basis. This estimate assumes that the contribution for units not in A is
in the same proportion as some frame information and imputes their level
assuming they behave like multiunits having no stores in A. The second
term, which estimates for stores outside of A, is an adjusted
link-relative estimator prorated to the establishments in A.

A simple model has been developed, but work still remains before the
model could be applied. We need to consider the complex sample design
actually used for the retail survey. We need to determine the levels for
the different adjustments. The six components should be analyzed for
both the frame and the sample. Standard errors should be computed for
performing statistical tests. Estimates from this approach should be
compared to those using the usual methods for periods not affected by
the event.

Attachment

![](media/image2.wmf){width="5.0in" height="4.875in"}**Catastrophic
Situation**

Multiunit Types

I -- No stores in A

II -- Some store in A, reporting unit not in A

III -- Some stores not in A, reporting unit in A

IV -- All stores in A