Sales and the (Mis)Measurement of
Price Level Fluctuations
Philip J. Glandon, Jr.
∗
Vanderbilt University
October 25, 2011
Please do not circulate or quote without the author's permission
Abstract
Using a large set of scanner data from grocery and drug stores located in the US, I
show that temporary price reductions (sales) have a large impact on the level of average price paid. Although sales account for about 17 percent of price quotes, roughly 40
percent of revenue occurs at sale prices. Sales also signicantly inuence the dynamics
of average price paid. The growth rate of monthly unit price is four times as volatile
as that of the regular price. This implies that the quantity response to sales and the
frequency and depth of sales varies over time. Following the recession of 2001, average unit price fell by two to three percentage points more than average regular price.
Panel regressions suggest a positive relationship between unemployment and the average amount saved from sales. These results imply that the use of CPI item indexes to
deate nominal consumption expenditure results in errors that are correlated with the
business cycle. This paper adds to the literature that recommends the use of scanner
data in price index calculations.
Contact: [email protected]
Web Page: https://my.vanderbilt.edu/pglandon
∗
This research was generously supported by a grant from the Vanderbilt University Council of Economic
Graduate Students. I would like to thank Mario Crucini, Jacob Sagi, Caleb Stroup, and Matt Jaremski for
helpful conversations on this topic. I am especially thankful for comments and advice from Ben Eden.
1
Introduction
For certain product categories, temporary price reductions (sales hereafter) account for
about 17% of price quotes and up to 40% of revenue. Sales are an important source of price
variation for 40 percent of non-shelter consumption spending (Nakamura and Steinsson,
2008) so they have a large eect on the level of average price paid. Several recent articles
analyze the macroeconomic relevance of sales in the context of state dependent (Eichenbaum,
Jaimovich and Rebelo, 2011; Kehoe and Midrigan, 2010) and time dependent (Guimaraes
and Sheedy, 2011) sticky price models. These studies uniformly conclude that sales are of
little interest to macroeconomists and that they have nothing to do with price adjustment
to nominal shocks.
The fact that sales have a large impact on the average price paid and yet have nothing
to do with aggregate price adjustment in New Keynesian models raises an important empirical question. Do sales have much inuence on the dynamics of average price paid? One
possibility is that the eect of sales on unit price is static. Another possibility is that the effect of sales uctuates orthogonally to macroeconomic conditions. A third possibility is that
stores have more sales or deeper discounts during economic downturns and that households
mitigate the eect of a drop in income on consumption by exploiting temporary discounts.
Using a large set of scanner data from grocery and drug stores, I nd that sales have a large
inuence on average price paid over time that is related to macroeconomic conditions.
The eect of rms' decisions about sales and shopper response to sales can be summarized by looking at the dierence between average unit price and average regular price.
1
Using scanner data, I construct an index of the average price paid and compare it to an
index of average regular price. These two indexes are parallel when the size, frequency, and
quantity response to sales are constant. In the data, unit price is much more volatile than
regular price, even when prices are aggregated over long periods.
The most important result in this paper can be seen in Figure 1, which plots the two
1 Regular price is the price that is charged in non-sale weeks and is discussed in detail in Section 3.
2
indexes described above along with the comparable components of the CPI. Following the
recession of 2001, average unit price fell earlier and more substantially than either of the
other two price indexes. This is primarily because the fraction of items on sale increased by
about ve percentage points (25 percent). The impact of sales falls considerably by the end
of the sample period.
[Figure 1 about here.]
Frequent variation in the price of an item over time poses challenges for both the
measurement of the price level and for modeling price setting behavior.
I submit that a
useful way for macroeconomists to think about sales is in terms of price dispersion that
arises out of imperfect information and search (or transaction) costs.
2
From this point of
view, the frequency and size of sales, as well as search intensity are all important factors
aecting the price level.
One practical implication of my results is that price indexes used to deate nominal
magnitudes into real magnitudes should incorporate information on quantity sold to the
extent possible. This is important because, as demonstrated above, indexes of unit price and
posted price do not move in parallel, particularly during an episode of downward pressure
on prices.
My results and conclusions are similar to those in Stigler and Kindahl (1970), which
emphasizes the importance of identifying prices paid rather than the menu price, in the
context of producer prices. The analysis in Chevalier and Kashyap (2011) is closely related
to this work and reaches similar conclusions. Chevalier and Kashyap (2011) focus on average
unit price and the best price within very narrow product categories.
In this paper, I
summarize the aggregate eect of sales on the price level across 29 categories. We reach the
same conclusion that sales (best prices) have an important eect on the average price paid
over time.
2 This is as opposed to modeling sales as a response to transient cost shocks.
3
A related line of research explores cost of living measurement issues created by high
frequency price changes. Feenstra and Shapiro (2003) develop the theoretically correct cost
of living index using a model that allows consumers to buy for storage. The model presumes
that households have perfect foresight of prices during a xed planning period over which
they optimize purchases and consumption. Using scanner data on canned tuna, it is shown
that a xed base Törnqvist index is the best approximation of the theoretically correct index.
The data also support the hypothesis that a substantial amount of items purchased at sale
prices is stored for future consumption.
Grith et al. (2008) use household purchasing data from the UK to show that an
average of 29.5% of consumption expenditure is on items that are on sale. This results in
an average amount saved of 6.5% of total expenditure. These measures vary substantially
across households with some saving as much as 21% of annual expenditure from buying
on sale.
The contribution of the present study to the empirical research on cost of living
measurement is to get a sense of the magnitude of the measurement error caused by high frequency price changes and the associated shopper behavior. I conclude that this measurement
error is potentially large correlated with macroeconomic conditions.
The rest of this paper is organized as follows. In Section 2, I present a model in which
a rm selects the frequency and depth of sales to maximize prot. Section 3 describes the
data I use and discusses how I identify sale prices and regular prices.
Section 4 contains
the empirical analysis in which I show that changes in the regular price and seasonal sales
account for less than half of the monthly volatility in average unit price.
I also provide
evidence that the eect of sales on unit price is positively correlated with the unemployment
rate. In Section 5, I discuss the implications of these results and conclude.
4
2
A Model of Sale Frequency and Size
The purpose of the following model is to sketch a plausible way in which sales could vary
with macroeconomic conditions under the presumption that the primary reason sales exist
is to price discriminate between dierent types of consumers. In this model, sales are used
to attract a particular type of consumer (a shopper) to visit the rm. I assume that a rm
can attract more shoppers to the store (who will buy a basket of goods) by increasing the
fraction of items on sale and/or by increasing the depth of sales. The idea that sales are
used to attract shoppers is supported by a number of empirical studies (Chevalier, Kashyap
and Rossi, 2003; DeGraba, 2006; Hosken and Reien, 2004). The trade o to having a sale
is that a rm's loyal customers, who are perfectly willing to pay the regular price, end up
paying the sale price some of the time. Firms choose the frequency and the depth of sales
to maximize prots.
I do not explicitly model consumer optimizing behavior. Instead, I assume that some
consumers do not react to sale prices, while others do.
This assumption is motivated by
the theoretical literature on price dispersion which focuses on consumer heterogeneity and
3
search costs as key ingredients.
In the model below, as in other models of price dispersion,
sales are a way for stores to imperfectly price discriminate.
2.1
Model Setup
A representative rm sells a continuum of items with measure one. For simplicity, I assume
that a unit of each item has the same marginal cost
C.
Consumers wish to purchase one unit
of each item during the shopping period as long as its price is not more than their maximum
willingness to pay,
R.
There are two types of consumers: buyers and shoppers. There is one buyer per store
and a total of
S
shoppers (who may visit any store). Firms cannot distinguish buyers from
3 For some examples of this literature, see Burdett and Judd (1983); Conlisk, Gerstner and Sobel (1984);
Lal (1990); Reinganum (1979); Sobel (1984); Varian (1980)
5
shoppers. Buyers visit a predetermined store and purchase one unit of each item as long as
its price is no larger than
R.
Therefore, rms set the regular price equal to
to attract shoppers, rms must put some fraction of items
R(1 − d).
Note that
d
f ∈ [0, 1]
R .4
In order
on sale at a price of
is the discount versus regular price and will always be between 0
and 1. For tractability, I assume that the discount is the same for all items.
The eect of shopper behavior on a rm's revenue is summarized by two functions.
First, the fraction of shoppers who visit the representative store is given by the function
Φ(f, d) ∈ [0, 1],
which maps the fraction of items on sale,
f
and the discount,
d
onto some
number between zero and one. I also assume that more items on sale and deeper discounts
attracts a larger share of the shoppers (Φ1 ,
Φ2 ≥ 0).5
purchase a larger fraction of items at the sale price than
Second, I assume that shoppers
f,
the fraction of items on sale.
This assumption captures the idea that shoppers are more attentive to sale prices and may
substitute across similar items or make multiple trips to obtain a larger share of items at a
sale price. This behavior is summarized by
at the sale price. By assumption,
µ(f ),
the fraction of items that shoppers obtain
1 ≥ µ(f ) ≥ f > 0, and µ0 (f ) ≥ 0.
and buy one unit of everything, they get a fraction
f
Since buyers are passive
of their items at the sale price.
Stores select the fraction of items to put on sale,
f,
and the discount
d
to maximize
prots.
max (Rf (1 − d) + R(1 − f ) − C) + Φ(f, d)S (Rµ(f )(1 − d) + R (1 − µ(f )) − C)
f,d
which can be written:
max R [(1 − f d − c) + Φ(f, d)S (1 − µ(f )d − c)]
f,d
where
c≡
C
is the marginal cost expressed as a fraction of the regular price,
R
4 I choose not to model how
R
is determined in order to focus on sales. Any price above
R.
R
Also, for
would result
in zero purchases and anything less would result in no additional units sold, so the regular price is
5 Φ is the partial derivative of
1
Φ
with respect to the rst argument,
6
f.
R.
notational convenience, I drop the arguments of
Φ
and
µ.
The rst order condition (for an interior solution) to the prot maximization problem
with respect to
f
is:
Φ1 S(1 − µd − c) = d (1 + ΦSµ0 )
This says that the marginal prot from additional shoppers must be equal to the marginal
cost of putting more items on sale. The marginal cost of putting more items on sale (increasing
and
f)
is due to the reduction in average price paid, which occurs at a rate of
dΦSµ0
for shoppers. The term
µ0
d
for buyers
is the rate at which shoppers increase the proportion
of units purchased on sale.
The rst order condition (for an interior solution) with respect to
d
is:
Φ2 S(1 − µd − c) = f + SΦµ
The interpretation of this condition is similar. The marginal prot of increasing
d
is
equal to the additional shoppers times the prot per unit from shoppers. The marginal cost
of increasing
d
is the reduction in revenue from buyers,
f,
and from shoppers
SΦµ.
The point of this model is to illustrate that multiproduct retailers might adjust
d
f
and
in response to changes in the number of shoppers. Without making specic assumptions
about the functional forms of
Φ and µ, little can be said about the optimal choice of d and f .
An increase in the proportion of shoppers,
sales, but changing
f
S,
would seem to increase the benet to having
aects the marginal benet
d and vice versa.
Intuitively, it seems that
stores would be more willing to cut average price if the number of shoppers increases. This
is one of the empirical questions I address in Section 4.3.
7
2.2
The Behavior of Average Unit Price
To get some idea of how
f
and
d
are related to
S,
I analyze a numerical example. Before
doing so, it will be useful to describe a measure of sales activity that summarizes the eects
of
f , d,
and the average response to sales. First, note that the average price paid is:
U≡
R ((1 − f d) + ΦS (1 − µd))
1 + ΦS
Rearranging terms yields the following expression:
U
µ
1 − = f d wb + ws
R
f
where
wb =
1
and
1+ΦS
ws =
(1)
ΦS
indicate the fraction of the rm's customers that are buyers
1+ΦS
and shoppers respectively. I refer to the LHS of equation 1 as the realized discount. The
last term on the RHS of 1 can be thought of as the average quantity response to a sale. It is
the quantity sold at a sale price relative to the average quantity sold (at any price). Buyers
buy the same quantity of a sale item as a non-sale item. Shoppers buy proportionately more
items on sale, as indicated by the ratio
µ
f
> 1.
In Section 4, I derive this relationship using
a dierent approach that may make it more intuitive.
The model predicts that the realized discount will depend on the number of shoppers
S,
and the marginal cost divided by the regular price,
selecting the following functional forms:
c.
I explore the model further by
Φ(f, d) = f α1 dα2 ,
and
µ(f ) = f β .
With these
functional forms, the optimization problem must be solved numerically, which I do using a
grid search over the domain of
f
and
d.
I selected the parameters
that yield results similar to those found in the data (d
Figure 2 plots the optimal
f
and
≈ .20
(α1 = .25, α2 = .5, β = .38)
and
f ≈ .15).
d as well as the realized discount (RD) against S , the
fraction of consumers that are shoppers. From this chart we can see that as the proportion of
shoppers increases, the fraction of items on sale increases; but the average discount actually
falls. The net eect of an increase in the number of shoppers is an increase in the realized
8
discount. As we will see in Section 4.1, these predictions are qualitatively consistent with
the data. The correlation between
UR
f
and
d
is negative and the correlation between
f
and
is positive.
[Figure 2 about here.]
3
Data
In the analysis that follows, I use the Symphony IRI Scanner Data research database (Bronnenberg, Kruger and Mela, 2008). Scanner data is highly disaggregated and has three ad-
6
vantages over Bureau of Labor Statistics survey data for studying pricing behavior.
quantity sold is available which indicates how important a particular price is.
First,
Second,
scanner data contain weekly observations which allows researchers to observe almost all
movements in prices since intra-week price movements are rare. BLS survey data are sampled monthly or bimonthly. Finally, with scanner data we observe the price and quantity
sold of all products available within a category-store. The main disadvantage of this particular scanner data set is that it covers a small subset of the universe of consumption goods
contained in the CPI.
The IRI data cover 31 categories in 50 dierent markets and contain both grocery
7
stores and drug stores from several dierent chains.
The data have detailed information
about product attributes and also contain information about other marketing activity such
as feature and display. The primary disadvantage to this data is that we cannot determine
the exact location of the stores or the demographics of the shoppers who typically visit them.
The data contains weekly observations for the calendar years 2001 through 2007.
This is
important because it spans the relatively mild recession of 2001.
6 Scanner data contains an observation for each store-UPC-week. Each observation contains the quantity
sold and total dollar sales as well as information about feature and display for the store selling the item.
7 I use only the data generated by stores that provided data for all seven years (2001-2007) so that all of
the analysis is done with a balanced panel of stores and categories.
9
3.1
Identifying a Sale and the Regular Price
To proceed, I need to construct two variables: 1) a binary variable,
whether item
i
was on sale during week
t
saleit ,
that indicates
and 2) the non-sale or regular price (which is
dierent from the observed price when an item is on sale). Ideally these variables would come
straight from the store, but unfortunately they do not. Instead, I construct them using an
8
algorithm discussed in detail below.
There are several operational denitions of sale and regular prices used in the literature.
I nd that they are not well suited for this study because they tend to miss sales that are
more complicated than a one or two week drop in price followed by a return to the previous
price.
Part of the diculty in choosing an operational denition of a sale is that there is no
widely accepted theoretically based denition.
My starting point for settling this issue is
the fact that an item's price is usually one of two frequently observed prices (Eichenbaum,
Jaimovich and Rebelo, 2011). In Glandon (2011), I present a simple model in which stores
select randomly between two prices, the higher of which is the regular price and the lower
of which is the sale price. Thus, I use the following algorithm to create a series of regular
prices for each product.
I start by setting the regular price equal to the observed price whenever one of the
following two conditions holds:
1. The observed price is larger than or equal to its 13 week centered moving average.
2. The observed price does not change for six weeks or more.
Next, if the the regular price is identied for week
t
and week
t
is part of a price spell
(consecutive weeks of identical prices), I set the regular price for the entire spell to the
8 The IRI data contain a price reduction indicator that is computed using IRI's proprietary algorithm for
identifying sale prices. For the sake of transparency I chose to create my own sale indicator. I use the IRI
sale ag as a benchmark for evaluating the algorithm.
10
9
observed price.
I also do not allow the regular price to drop for one week and return to the
previous price. Instead, I set the regular price in all three periods to be equal to each other.
Following Kehoe and Midrigan (2010), I set the remaining unspecied regular prices equal
to the previous period's regular price.
10
I now have an observed price series and a regular
price series. An item is considered to be on sale if the observed price is at least ve percent
below the regular price.
11
[Figure 3 about here.]
Figure 3 shows an example of the regular price series that I constructed using the
algorithm described above. The thin lines connect the observed price series. This particular
example is Pepsi 2 Liter Bottles from a store in New York City. It happens to be the number
one revenue generating store-UPC in the sample of carbonated beverages sold in New York
City. Notice that there are several instances in which the price drops in one week and then
drops further the next week before returning to the regular price.
A sale is often more
complicated than a simple price drop followed by a return to the previous price.
3.2
Summary Statistics
There are three characteristics of sales that deserve our attention:
1. Frequency:
2. Size:
d
f
(measured by the fraction of items on sale per week)
(percentage discount o of the regular price)
3. Quantity Ratio:
z
(quantity sold per sale week relative to average quantity sold)
Frequency and size are often referred to in the marketing literature as the breadth and
depth of price promotions and are determined by the store's managers in order to maximize
9 The purpose of this is to ensure that regular price changes in the week that we observe the change. It
is needed when regular price falls because the moving average is slower to fall.
10 In these instances the observed price is likely to be a sale price.
11 Chevalier and Kashyap use a similar tolerance to allow for the fact that there are occasional small price
measurement errors. These errors result from the fact that price is calculated from total dollar sales and
total unit sales.
11
prot given expectations about shopper behavior (Blattberg, Briesch and Fox, 1995). The
quantity ratio,
z is the quantity sold per sale relative to the average quantity sold.
It measures
consumer response to sales.
[Table 1 about here.]
Table 1 contains summary statistics by category, including the following measures of
sales: fraction of weeks on sale, fraction of revenue from sales, fraction of units sold at a
sale price, the median discount, and the median quantity ratio. I also provide the number
of store-products and average annual revenue for the entire sample. There are several things
worth mentioning about these statistics.
First, although sales account for a small fraction of price quotes (16.7 percent), they
account for a relatively large fraction of revenue (34.2 percent). Two to three times as many
units are sold during a sale week compared to the average (as measured by the quantity
ratio).
Second, the larger categories tend to have sales more frequently. Figure 4 illustrates
this by plotting annual revenue against fraction of items on sale for each category in the
sample. There is a positive relationship between a category's share of expenditure and its
frequency of sales.
[Figure 4 about here.]
The relationship between expenditure and frequency of sale holds at the UPC level
as well. To show this, I calculate average weekly revenue for each UPC in the sample and
separate UPCs into deciles by store. I plot the average fraction of weeks on sale by revenue
decile in Figure 5. There is a strong positive relationship between an item's long run revenue
share and the frequency with which it is on sale. This relationship is consistent with the
idea that sales are often used to attract trips to the store (Chevalier, Kashyap and Rossi,
2003; Hosken and Reien, 2004; Lal and Matutes, 1994).
[Figure 5 about here.]
12
Third, the discount is often quite large. In the IRI data, the median discount versus
regular price is over 20 percent for 21 of the 29 categories and over 25 percent for six of them.
If shoppers are willing to search for deals, hold some inventory, and selectively substitute,
substantial savings are available from buying on sale. One study has found that households
in the UK save an average of 6.5 percent of annual expenditure by buying on sale (Grith
et al., 2008).
Finally, sales result in far more purchases than a regular price. In this sample, 2.6 times
as much revenue is generated per sale price than per regular price. The spike in quantity
sold during a sale is much higher than can be explained by a simple model of supply and
demand (Hendel and Nevo, 2006; Feenstra and Shapiro, 2003).
To summarize, sale prices occur most frequently on popular items, discounts are often
20% or more, and a disproportionate share of purchases occur at sales prices. These facts
indicate that sales are an important determinant of average price paid (unit price) and also
nominal consumption expenditure. Chevalier and Kashyap (2011) suggest that average unit
price (or more practically, an average of best price and regular price) provides a better picture
of the price consumers are paying over time than any individual price series. In the following
section I will quantify the eect of sales on the dynamics of average unit price.
4
Empirical Analysis
I wish to answer the following two empirical questions: 1) How much do sales contribute to
variation in the growth rate of average price paid? 2) Is the eect of sales on average unit
price related to macroeconomic conditions?
I address the rst question by looking at time variation in the unit price relative to
the regular price at the store-product level. The average (across store-products) standard
deviation of the realized discount is 7.1 percent.
About two thirds of this variation can
be attributed to variation in the frequency and discount of sales. Next, I aggregate across
13
products to show that product level variation in sale activity is not entirely idiosyncratic.
Finally, I construct indexes of average regular price and average unit price to see how much
of the change in unit price can be explained by changes in the regular price. Variation in
sale activity is at least as important as variation in the regular price in terms of explaining
variation in average unit price.
As for the second question, recall that the model presented in Section 2 predicts that
the realized discount depends on the proportion of consumers who respond to sales. I test
this hypothesis via panel regressions in which unemployment is a proxy for the proportion of
consumers who are shoppers. The idea is that as the unemployment rate rises, more people
will have the time and incentive to shop for better prices. I show that the unemployment
rate is positively related to the realized discount. Relatively high unemployment rates are
associated with more sales activity in this sample.
4.1
Regular Price and Unit Price
I begin by looking at the behavior of sales at the store-product level. Consider the following
expression of
Uit ,
the average price per unit sold of store-product
i
during quarter
t:
Uit = (1 − wit ) Rit + wit Sit
where
Uit , Rit ,
and
Sit
are, respectively, the average unit price, average regular price, and
average sale price during quarter
t.
The term
wit
is the quantity sold at a sale price divided
by the total quantity sold during the quarter. This equation simply says that average unit
price is the weighted average of regular price and sale price. We can rearrange this equation
the following way:
1−
Here,
dit ≡
Uit
= wit dit
Rit
(2)
Rit −Sit
is the average sale discount expressed as a percent of the regular
Rit
14
price. Just as we did in Section 2, let us call the LHS of equation 2 the realized discount.
This is the amount saved from buying on sale expressed as a percentage of regular price.
Note also that we can write
wit = zit fit ,
where
zit
is the quantity response to a sale (the
ratio of units sold per sale week to units sold per week) and
sale in quarter
t.
fit
is the fraction of weeks on
Thus, we have the following expression:
1−
Uit
= zit fit dit
Rit
(3)
This equation is analogous to equation 1 from the model. It states that the realized
discount,
RDit
the discount
is equal to the product of the quantity response
dit .
zit ,
the frequency
fit ,
and
To get an idea of which of these three components is most inuential, we
can decompose variance of the log of the realized discount into the variance of the logs of
zit , fit
, and
dit ,
plus a covariance term:
2
2
2
2
σln
RDi = σln zi + σln fi + σln di + covariances
(4)
This allows us to see whether variation in the realized discount is the result of rm decisions (variation in
fit
and
dit ) or shopper behavior (variation in zit ).
average (across products) variance expressed as a percent of
In Table 2, I report the
h 2
≡
V
ar
σln
t ln 1 −
RDi
Uit
Rit
i
|i .
About two thirds of the variation in the realized discount comes from changes in the frequency and depth of sales.
[Table 2 about here.]
It is possible that within product variation cancels out after aggregating across products. For instance, close substitutes may be on sale in alternating periods as they are in Lal
(1990). To see if this is the case, I calculate the mean of
1−
Uit
Rit
,
zit , fit ,
and
dit
(across
store-UPCs) for each quarter and plot the results in gure 6. The average realized discount
1−
Uit
Rit
increased rapidly over the course of 2002, after which it remained fairly high (with
15
seasonal uctuation) until about the end of 2004. By the end of 2007, the average realized
discount had fallen back to its initial level of about 9.3 percent.
The cause of the rapid rise in realized discount was evidently a large increase in the
frequency of sales that occurred during 2002. The frequency of sales continued its growth,
but at a much slower rate until the middle of 2006, after which it began to decline slowly.
The average quantity response (zt ) and average discount (dt ) fell sharply along with the
initial jump in the frequency of sales that occurred in the rst quarter of 2002. The rapid
rise in the realized discount that began in the third quarter of 2002 resulted from all three
components (frequency, discount, and quantity response) rising together. The eect of sales
on unit price shrinks (with some seasonal uctuations) for the rest of the sample period due
primarily to decreases in the average discount and quantity response.
[Figure 6 about here.]
4.2
Sales and Aggregate Price
In this section, we will analyze the impact of sales on the price level over time by comparing
an index of regular price to an index of average unit price. This allows us to see how the
dynamics of sales and regular price aect the average unit price over time.
Price Index Construction
In order to construct indexes of regular price and unit price, I employ the same approach
used by the BLS to calculate the consumer price index with one important dierence. The
BLS samples a single price quote each month. I have weekly price and quantity data and
wish to make use of this extra information. Rather than randomly selecting a single price
from each month (as the BLS does), I take an average of all prices within a month.
For
the index of regular price, I take a simple average of regular price for the month (usually
there are 4 and they are often all the same). For the index of unit price, I take total revenue
divided by units sold to get the average price paid.
16
I aggregate across store-UPC's the same way that the BLS aggregates sampled prices. I
calculate a price relative for each store-UPC-month (the ratio of current price to last month's
price) and then compute the geometric average of price relatives within each store-category
using xed weights.
12
Additional details can be found in the Appendix.
Explaining Unit Price Volatility
The rst thing to point out is that unit price is substantially more volatile than regular price.
The standard deviation of the log change of unit price is two to four times that of regular
price (see Table 5). Changes in regular price only explain a fraction of the variation in unit
price.
As a descriptive exercise, I project the log dierence of the unit price index,
the log change of the regular price index
rtr
and a vector of monthly dummies
mt
rtu ,
onto
to capture
seasonal variation in unit price:
rtu = mt λ + α1 rtr + et
(5)
The purpose of estimating equation 5 is to see how much of the variation in
explained by seasonal variation (captured by the term
mt λ)
and variation in
rtr .
rtu
is
Table 3
contains OLS estimates of Equation 5 for weekly, monthly, and quarterly frequencies. The
R-squared statistics indicate that only 15 to 36 percent of the week-to-week variation in
aggregate price can be explained by variation in regular price and seasonal variation in sales.
Aggregating to a monthly index increases the explanatory power of regular price, but still
leaves over half of the variation in unit price to be explained by non-seasonal variation in
(the frequency, size, and quantity ratio of ) sales.
[Table 3 about here.]
Finally, I construct the indexes described above taking quarterly averages of unit price
12 I use the store-UPC's average weekly revenue as the weight.
17
and regular price instead of monthly averages. The results are reported in the bottom panel
of Table 3.
Averaging across quarters smooths things out considerably, but non-seasonal
variation in sales still accounts for 35 to 50 percent of the quarter-to-quarter variation in
I conclude that non-seasonal variation in the aggregate behavior of sales is
unit price.
responsible for a signicant amount of variation the growth rate of average unit price.
4.3
Sales and Unemployment
To begin this section, I refer the reader back to Figure 1. This graph suggests that regular
price grows faster than average unit price when unemployment is relatively high. To take
a slightly dierent view of the data, in Figure 7, I provide a scatter plot of the realized
discount and the previous quarter's unemployment rate (for the full sample).
This gure
provides a basis for further investigation of the relationship between sales and macroeconomic
conditions.
[Figure 7 about here.]
The relatively short sample period limits my ability to draw strong conclusions about
the relationship between sales and unemployment over time. However, with over 500 individual stores located across 48 markets, we do have a fairly large cross section to work with.
Using panel regressions, I test the hypothesis that unemployment is related to the realized
discount.
In the model we found that the realized discount depended on the number of consumers
who respond to sales and the ratio of marginal cost to regular price. The baseline specication
that I test is the following:
RDijt = β1 U nempjt + β2 cijt + ui + eit
where
year
t,
RDijt
and
is the weighted average of the realized discount in store
cijt
i
in market
j,
during
is an average of the relevant Producer Price Indexes divided by the index of
18
store
i0 s
regular price. This variable controls for variation in the marginal cost relative to
the regular price. Using BLS data, I match each store to a city (MSA) and use the annual
average of the unemployment rate,
U nempjt , as the primary independent variable of interest.
The results of the baseline model along with several other specications are reported
in Table 4.
The point estimates suggest that the realized discount increases by 20 to 60
basis points for a one percentage point increase in the unemployment rate. I also estimate
the model after dierencing all of the variables, again using the xed eects estimator. This
allows for a unit specic trend in the realized discount. In this case, the point estimate for
β1
is much larger than in the model estimated in levels.
[Table 4 about here.]
To get a sense of whether these results are driven by a national trend or cross-sectional
variation, I compute a rank correlation coecient (Kendall's tau) between the realized discount and the unemployment rate for each quarter.
The idea is to test for a statistical
relationship between the realized discount and the unemployment rate without making any
assumptions about the structure of the relationship.
I plot Kendall's tau for each quar-
ter in Figure 8. Initially, when the national unemployment rate is relatively low, the rank
correlation coecient of realized discount and the local unemployment rate is statistically
indistinguishable from zero.
Once the average unemployment rate rises, we see a strong
positive relationship between the realized discount and local unemployment (Kendall's tau
of about .30). As the national unemployment rate falls back to pre-recession levels (during
2005), the cross-sectional relationship diminishes.
[Figure 8 about here.]
Figure 8 suggests that the relationship between the realized discount and unemployment is either time varying or non-linear. To see if this is the case, I add a vector of year
dummies to control for changes in sale activity that is common across cities, and
19
U nemp2jt
to capture possible non-linearity. The results are presented in Table 5. The rst thing to
note from these results is that there is indeed a signicant year eect that tracks the national pattern of unemployment. Secondly, the relationship between unemployment and the
realized discount does appear to be non-linear. The marginal eect of unemployment when
it is low (4% to 5%) is zero to negative. At unemployment rates above 6%, the marginal
eect on realized discount is positive.
[Table 5 about here.]
5
Conclusion
In the analysis above, I provided evidence that sales have a large inuence on the average
price paid and the rate at which it changes over time. In particular, indexes of unit price and
regular price diverged substantially (up to 3 index points) following the recession of 2001. I
presented a model of how a multiproduct rm might choose the frequency and depth of sales
when the primary objective is to attract price sensitive shoppers. Certain parameterizations
of the model predict that an increase in the number of consumers who respond to sales results
in a higher frequency of sales and a reduction in the average unit price. Panel regressions
support this prediction. Unit price falls relative to the regular price when the unemployment
rate rises.
I have also shown that the CPI is less volatile than an index of unit price. One task
often fullled by the CPI is to deate nominal magnitudes into real magnitudes. The intent
of this paper is not to recommend specic changes to CPI methodology, but my results
raise two important questions.
13
1) Does the CPI do a reasonable job of deating nominal
magnitudes into real magnitudes? 2) How accurately is ination measured over the course of
the business cycle? The characteristics of sales change over time and tend to aect average
unit price much more so than the CPI reects. Since it appears that uctuations in eect
13 For a lengthy discussion of scanner data and the CPI, see the book that contains the article by Feenstra
and Shapiro (2003).
20
of sales on unit price are correlated with macroeconomic conditions, the GDP deator is
subject to measurement error that is correlated with the business cycle. I leave attempts to
quantify the severity of this error for future research.
21
References
Blattberg, Robert C., Richard Briesch, and Edward J. Fox. 1995. How Promotions
Work. Marketing Science, 14(3): G12232.
Bronnenberg, Bart J., Michael W. Kruger, and Carl F. Mela.
2008. The IRI
Marketing Data Set. Marketing Science, 27(4): 745748.
Burdett, Kenneth, and Kenneth L. Judd. 1983. Equilibrium Price Dispersion. Econometrica, 51(4): 955969.
Chevalier, Judith A., and Anil K. Kashyap. 2011. Best Prices.
Chevalier, Judith A., Anil K. Kashyap, and Peter E. Rossi. 2003. Why Don't Prices
Rise during Periods of Peak Demand? Evidence from Scanner Data. American Economic
Review, 93(1): 1537.
Conlisk, John, Eitan Gerstner, and Joel Sobel.
1984. Cyclic Pricing by a Durable
Goods Monopolist. Quarterly Journal of Economics, 99(3): 489505.
DeGraba, Patrick. 2006. The Loss Leader Is a Turkey:
Targeted Discounts from Multi-
product Competitors. International Journal of Industrial Organization, 24(3): 613628.
Eichenbaum, Martin, Nir Jaimovich, and Sergio Rebelo.
2011. Reference Prices,
Costs, and Nominal Rigidities. American Economic Review, 101(1): 234262.
Feenstra, R. C, and M. D Shapiro. 2003. High-Frequency Substitution and the Measurement of Price Indexes. Scanner Data and Price Indexes, 64: 123146.
Glandon, Philip.
2011. The Economics of Sales.
PhD diss. Vanderbilt University,
Nashville, TN.
Grith, Rachel, Ephraim Leibtag, Andrew Leicester, and Aviv Nevo. 2008. Timing and Quantity of Consumer Purchases and the Consumer Price Index. SSRN eLibrary.
22
Guimaraes, Bernardo, and Kevin D. Sheedy. 2011. Sales and Monetary Policy. American Economic Review, 101(2): 844876.
Hendel, Igal, and Aviv Nevo. 2006. Measuring the Implications of Sales and Consumer
Inventory Behavior. Econometrica, 74(6): 16371673.
Hosken, Daniel, and David Reien.
2004. How Retailers Determine Which Prod-
ucts Should Go on Sale: Evidence from Store-Level Data. Journal of Consumer Policy,
27(2): 141177.
Kehoe, Patrick, and Virgiliu Midrigan.
2010. Prices Are Sticky After All. NBER
Working Paper No. w16364.
Lal, Rajiv. 1990. Price Promotions:
Limiting Competitive Encroachment. Marketing Sci-
ence, 9(3): 247262.
Lal, Rajiv, and Carmen Matutes.
1994. Retail Pricing and Advertising Strategies.
Journal of Business, 67(3): 345370.
Nakamura, Emi, and Jon Steinsson. 2008. Five Facts about Prices:
A Reevaluation of
Menu Cost Models. Quarterly Journal of Economics, 123(4): 14151464.
Reinganum, Jennifer F. 1979. A Simple Model of Equilibrium Price Dispersion. Journal
of Political Economy, 87(4): 851858.
Sobel, Joel. 1984. The Timing of Sales.
Review of Economic Studies, 51(3): 353368.
Stigler, G. J, and J. K Kindahl. 1970. The Behavior of Industrial Prices. NBER Books.
Varian, Hal R. 1980. A Model of Sales.
American Economic Review, 70(4): 651659.
23
Appendices
A
Regular Price versus Unit Price Calculations
Here I provide additional details of the unit price versus regular price calculations discussed
in Section 4.1:
I dene unit price of item
i
during quarter
Uit =
Where
qiw
and
piw
t
as
Uit .
1X
qiw piw
qt w∈t
are the quantity and price of item
i
during week
represent the set of weeks during which an item was not on sale in quarter
the set of weeks during which the item was on sale in quarter
quantity sold during weeks in
R(t)
dene the average regular price
Rit
and
S(t)
Let
qtr
respectively. Note that
and average sale price
Rit =
t.
and
qts
w.
t
Let
and
R(t)
S(t)
be
represent the
qit = qits + qitr .
Let us
Sit :
1 X
qiw piw
qtr
w∈R(t)
Sit =
1 X
qiw piw
qts
w∈S(t)
Let
wit =
s
qit
qit
⇒ 1 − wit =
r
qit
. Thus we can write unit price as the weighted average of sale
qit
price and regular price.
Uit = (1 − wit ) Rit + wit Sit
Rearranging, we have:
Uit
Sit
1−
= wit 1 −
Rit
Rit
24
We can decompose the term
wit
and the quantity response to a sale,
quarter
and
into the product of the fraction of weeks on sale,
zit .
s(t)
Let
and
r(t)
represent the number of weeks in
t that an item was on sale, and not on sale, respectively.
zit =
By denition,
s
q̄it
.
q̄it
wit =
s(t)
s(t) + r(t)
qits s(t) + r(t)
s(t)
qit
25
fit
= fit zit
fit =
s(t)
s(t)+r(t)
B
Calculation of Price Indexes
To analyze the importance of sales on the dynamics of prices, I calculate two dierent price
indexes using the scanner data. The only dierence between these two indexes occurs in the
aggregation across weeks within a store-product-month cell. The equations that follow show
how I construct the average price for each store-product-month. Denote the average price
of UPC
u
j
in month
t
as
Pj,t
with a superscript to denote the two dierent averages:
r
and
indicating regular, and unit respectively:
Average regular price:
1 X r
pj,w(t)
nj,t
(6)
1 X
qj,w(t) pj,w(t)
qj,t
(7)
r
Pj,t
=
w(t)
Average unit price:
u
Pj,t
=
w(t)
where
for UPC
j
w(t)
indexes the week of month
t, nj,t
is the total number of price observations
×
qj,w(t)
is the quantity sold. The average regular
in month
t
(stores
weeks), and
price is the simple average of regular price.
The average unit price is revenue divided by
quantity sold.
Since we have several thousand UPCs in our sample, we need to aggregate across
products into a single price index. To do so, I use the same technique as the BLS, which
is to take the geometric average of monthly price relatives (using the UPC's average share
of revenue as the weight). Importantly, I use the same aggregation procedure for both price
indexes. The month
t
price index with base period
I0,t−1 = exp
X
j
26
0
is:
Pj,t
wj ln
Pj,0
!
(8)
C
CPI Construction Details
I calculate a comparable index from the components of the CPI. Specically, I aggregate the
CPI item indexes that correspond to the product categories contained in the scanner data
sample. Table A.1 shows the CPI Item series used and the corresponding weights (which are
the same as those used to aggregate the scanner data). Table A.2 shows the weights I apply
to each of the markets contained in the IRI scanner data sample.
Table A.1: CPI Item Indexes Matched to IRI Categories
Series ID
Description
Weight
IRI Category(s)
CUUR0000SEFA02
Breakfast Cereal
0.11
coldcer
CUUR0000SS05011
Frankfurters
0.03
hotdogs
CUUR0000SEFN01
Carbonated Beverages
0.18
carbbev
CUUR0000SEFP01
Coee
0.04
coee
CUUR0000SEFR01
Sugar & Sweeteners
0.01
sugarsub
CUUR0000SEFS01
Butter & Margarine
0.02
margbutr
CUUR0000SS16014
Peanut Butter
0.01
peanbutr
CUUR0000SEFT01
Soups
0.05
soup
CUUR0000SEFT02
Frozen and Prepared Foods
0.11
fzdinent, fzpizza
CUUR0000SEFT03
Snacks
0.11
saltsnck
CUUR0000SEFT04
Spices Seasoning Condiments
0.06
spagsauc, mayo, mustket
CUUR0000SEFW01
Beer
0.14
beer
CUUR0000SS61021
Photo Supplies
0.00
photo
CUUR0000SEGB01
Hair Dental Shaving
0.06
toothpaste, shamp, deod, blades, toothbr
CUUR0000SSGE013
Infants Equipment
0.02
diapers
Other Dairy
0.06
yougurt
CUUR0000SEFJ04
Notes: This table contains the BLS item indexes used to construct the CPI-U comparable to the indexes I created
using the IRI data.
27
Table A.2: Market Weights Applied to IRI Scanner Data Market Indexes
IRI Market
BLS Weights
Notes
IRI Market
BLS Weights
Notes
(used Lincoln)
atlanta
1.37
omaha
0.88
birmingham
0.89
philadelphia
2.73
boston
2.52
phoenix
1.04
bualo
0.68
portland
0.83
raleigh
0.82
charlotte
1
cleveland
1.32
richmond
0.89
dallas
1.87
roanoke
0.2
(no match 25% size of Birmingham)
desmoines
0.8
sacramento
0.83
(no match - population ~ Portland)
detroit
2.4
saltlake
1.01
(no match used Provo)
grandrapids
0.2
No Match
sandiego
1.16
greenbay
0.2
No Match
sanfran
2.89
harrisburg
1
No Match
seattle
1.37
southcarolina
0.92
stlouis
1.15
washington
2.01
houston
indianapolis
No Match
No Match
1.73
1
kansascity
0.73
knoxville
0.81
la
(no match 1.7mm people)
(no match used Chattanooga)
westtex
1
4.1
syracuse
0.87
milwaukee
0.74
hartford
0.83
minneapolis
1.18
chicago
3.81
newengland
0.74
nyc
3.39
(no match - used Burlington)
Notes: These are the weights applied to each market in constructing the regular price index and unit price index
discussed in Section 4.
28
D
Sales and the CPI
The point of this appendix is to show how the CPI does not fully reect changes in unit
price due to changes in sales.
I begin with a brief description of how the BLS computes
the CPI. In the simplest terms, the BLS collects a sample of prices each month and then
aggregates them in two steps. The rst step takes sampled prices and aggregates them into
basic indexes which are specic to an item and a geographic area. An example of a basic
index is salad dressing in Chicago-Gary-Kenosha. The second step of aggregation is to take
averages of subsets of the basic indexes to form the various price indexes published by the
BLS (for example, the CPI-U).
I focus on how sampled prices are aggregated into a basic index (the stage at which
quantity sold could be incorporated). First, the BLS chooses several store-items whose prices
will be recorded on a monthly basis. A 20 oz. box of Cheerios from the Dominick's Finer
Foods on Lincoln Ave. is an example of a store-item. These prices are then aggregated into
a price relative for each area-item-month. An area-item price relative is (in most cases) the
expenditure share weighted geometric average of the ratio of adjacent period prices.
formula for a price relative of item
i
(9) below. A basic index for period
T
the base period and period
in area
a
between months
t
and
t−1
The
is presented in
is then formed by chaining the price relatives between
T.
a,i R[t,t−1]
Y Pj,t wj
=
Pj,t−1
(9)
j∈{a×i}
The point I wish to emphasize is that the weights
fraction of transactions that occurred at price
Pj,t .
wi
are not adjusted to reect the
This means that adjustments in average
unit price due to high frequency substitution are not reected in the CPI. Since a price index
is primarily used to measure the change in the price level, xing weights is not an issue if the
characteristics of sales are static. However, if the characteristics of sales change over time,
then it is unclear that a xed weight geometric average will accurately reect changes in the
29
price level due to sales.
The following numerical example will help to illustrate this point. Let us suppose that
instead of sampling a single price per month for a particular store-item, we are able to collect
price and quantity data for each of 4 weeks in the month. This additional data will require
another level of aggregation (assuming we wish to apply the same basic approach that the
BLS currently takes). There are many possible approaches to aggregating scanner data into
price indexes and this topic is addressed thoroughly in Feenstra and Shapiro (2003) and the
citations therein.
For this example, I simply wish to highlight the eect of changes in the characteristics
of sales on average price paid.
I compare the growth rates of average menu price and
average unit price under three dierent scenarios in which one of the characteristics of sales
changes while the other two are xed.
The results presented in Table A.3 show that an
index of average menu price and average unit price dier when any of the following three
characteristics of sales changes :
1. Frequency (measured by fraction of items on sale per week)
2. Size (percentage discount o of the regular price)
3. Quantity Ratio (quantity sold per sale relative to quantity sold per regular price).
The index of average menu price understates the change in average unit price. In practice,
an increase the average discount would likely correspond to an increase in the quantity ratio.
The eect of these two changes together would drive an even larger gap between unit price
and menu price. On the other hand, an increase in the frequency of sales may reduce the
quantity ratio and the eects would oset each other.
30
Table A.3: Numerical Example of Change in Simple Average vs. Weighted Average
Price
Panel A
Panel B
Panel C
Change in Frequency
Change in Size
Change in Quantity Response
Mo. 1
Mo. 2
Mo. 3
Mo. 1
Mo. 2
Mo. 3
Mo. 1
Mo. 2
Mo. 3
Week 1
.90
.90
1.00
.90
.80
.90
.90
.90
.90
Week 2
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
Week 3
1.00
.90
1.00
1.00
1.00
1.00
1.00
1.00
1.00
Week 4
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
Week 1
240
133
240
240
240
240
240
342
240
Week 2
120
67
120
120
120
120
120
86
120
Week 3
120
133
120
120
120
120
120
86
120
Week 4
120
67
120
120
120
120
120
86
120
Frequency of Sales
25%
50%
25%
25%
25%
25%
25%
25%
25%
Size of Sales
10%
10%
10%
10%
20%
10%
10%
10%
10%
2.0
2.0
2.0
2.0
2.0
2.0
2.0
4.0
2.0
0.98
0.95
0.98
0.98
0.95
0.98
0.98
0.98
0.98
0.0%
0.0%
0.94
0.96
Quantity Sold
Quantity Ratio
Average menu price
Ination (monthly)
Average unit price
-2.6% 2.6%
0.96
0.93
0.96
-2.6% 2.6%
0.96
0.92
0.96
0.96
Ination (monthly)
-2.8% 2.9%
-4.2% 4.3%
-1.8%
1.6%
Dierence
-0.2% 0.2%
-1.6% 1.7%
-1.8%
1.8%
31
Figure 1: Average Regular Price, Average Unit Price, and the CPI
Panel A: Regular Price, Unit Price, the CPI
Panel B: Regular Price Index minus Unit Price Index and Unemployment
Panel A plots quarterly indexes of unit price and regular price over the full sample. The CPI for comparable
items is also included. Panel B plots the dierence between the regular price index and the unit price index
(set to zero for the rst quarter).
32
Figure 2: Optimal Frequency and Discount of Sales
The gure above plots the optimal choice of f and d, as well as the resulting realized discount, RD
associated with various levels of S , the number of shoppers. I use the following functional forms
for this example: Φ(f, d) = f .50 d.25 and µ(f ) = f .38 .
33
Figure 3: Regular Price Filter Example from the Data
Notes: This is an example (Pepsi 2-Liter bottles at a store in New York City) from the IRI data set. The thin red line
represents the scanned price and the thick blue line is the regular price, as determined by the regular price algorithm
described in the text. All prices that are 5% or more below the regular price line are considered sale prices, which are
represented by green dots.
34
Figure 4: Annual Revenue versus Fraction of Items on Sale by Category
Notes: Each point represents a category. The vertical axis is fraction of item-weeks on sale and the horizontal axis is average
annual revenue (as reported in Table 1).
35
Figure 5: Fraction of Weeks on Sale by Average Weekly Revenue Decile
Notes: This gure plots average fraction of weeks on sale by (within store) average weekly revenue decile.
36
Figure 6: The Characteristics of Sales Over Time
Panel A:
1−
Panel C:
Uit
Rit
dit
Panel B:
fit
Panel D:
zit
Uit
Panel A: Revenue weighted mean of the realized discount: 1 − R
. Panel B: Revenue weighted mean of fit , the
it
it
fraction of weeks item i is on sale during quarter t. Panel C: Revenue weighted mean of dit = RitR−S
, the average
it
percent discount as a percent of regular price, conditional on at least one sale during quarter t. Panel D: Revenue
weighted mean of the quantity response, zit which is the average units sold per sale week relative to average units
sold in all weeks.
37
Figure 7: Realized Discount and One Quarter Lag of Unemployment
Notes: I take the average of realized discount 1 − U
across all products in all markets during
R
quarter t and plot it against the previous quarter's average US unemployment rate.
38
Figure 8: Cross Sectional Rank Correlation of Unemployment and Realized Discount
Notes: I compute the Kendall rank correlation coecient of realized discount and the unemployment
rate for each quarter in the data set. There are 48 observations (markets) in each quarter. The two
sided p-values for the test of statistical independence are plotted on the right axis.
39
Table 1: IRI Summary Statistics by Category
Annual
Store x
Category
Products
Median
Revenue
($Millions)
Sales Fraction of Total
Weeks
Revenue
Units
Median
Quantity
Discount
Ratio
Carbonated Beverages
225,408
180.0
21.9%
43.0%
44.5%
22.1%
1.9
Beer
125,690
136.0
16.6%
35.0%
30.1%
11.7%
1.8
Cold Cereal
160,894
107.3
16.1%
31.8%
41.5%
30.3%
2.9
Salty Snacks
317,814
104.5
17.6%
32.1%
35.8%
21.4%
2.0
Frozen Dinners
237,906
68.7
25.7%
42.5%
48.1%
28.3%
2.6
Yogurt
147,471
57.7
20.2%
28.0%
39.3%
23.9%
2.0
Toilet Tissue
35,925
49.7
17.5%
39.6%
35.3%
23.7%
3.2
Laundry Detergent
87,963
48.5
16.5%
35.7%
44.8%
24.1%
3.1
138,809
44.8
14.1%
29.6%
36.9%
27.1%
3.0
81,255
38.0
25.7%
42.7%
49.6%
24.1%
2.7
103,386
37.0
13.8%
32.2%
39.4%
19.3%
2.7
Soup
Frozen Pizza
Coee
Paper Towels
31,729
35.5
14.7%
36.4%
31.0%
22.6%
2.6
Hot dogs
28,152
26.7
22.2%
36.8%
48.3%
29.8%
2.4
Spaghetti Sauce
78,634
26.5
17.5%
33.5%
41.9%
22.7%
2.7
Diapers
80,693
23.2
14.5%
23.8%
27.3%
15.4%
2.5
Margarine and Butter
31,970
19.3
16.3%
22.6%
29.0%
22.7%
1.7
Mayonnaise
24,292
17.3
12.0%
26.7%
31.1%
21.6%
2.1
Facial Tissue
28,251
16.3
19.6%
31.7%
38.8%
23.6%
2.1
Toothpaste
122,630
16.0
13.0%
27.6%
34.3%
22.4%
2.7
Shampoos
223,410
14.1
11.4%
21.6%
29.0%
23.0%
3.0
Peanut Butter
21,693
13.6
14.0%
24.6%
34.0%
19.2%
2.2
Mustard and Ketchup
42,846
12.1
9.4%
23.2%
30.5%
19.1%
2.3
Deodorant
213,178
12.0
10.1%
21.3%
28.1%
25.1%
3.1
Blades
58,811
11.4
8.6%
13.3%
18.7%
20.2%
2.3
Household Cleaners
33,456
6.9
13.8%
22.4%
27.7%
19.5%
2.1
Toothbrushes
76,042
5.5
12.6%
25.8%
32.1%
25.1%
3.1
Sugar Substitutes
12,911
5.1
6.8%
9.9%
11.9%
13.1%
1.7
Photo Supplies
14,725
3.2
7.2%
20.0%
23.0%
21.3%
2.7
Razors
16,179
1.5
9.5%
21.2%
22.9%
16.7%
2.6
All Categories
3,012,670
1,380.5
16.7%
34.2%
39.5%
Notes: Column 2 contains the number of store-UPC combinations in the data (larger than the number of UPCs
since most UPCs are sold at several stores).
40
Table 2: Sale Variance Decomposition
Source of Variation
Mean
2
σln
zi
σ2
ln2RDi σln fi
σ2
ln2RDi σln di
2
σln
RDi
Quantity Response:
Sale Frequency:
Discount:
Covariance Terms:
Standard Dev.
18.7%
44.3%
23.9%
13.1%
RDt
σRD
7.1%
Uit
2
Notes: I decompose σln
for each UPC-store with
RDi ≡ V ar ln 1 − Rit
data in all 24 quarters and at least one sale. I present each term as a percent
2
of σln
RDi . The sources of variation are: zit (average units sold per sale week
relative to all weeks), dit (average discount versus regular price), and fit (the
fraction of weeks on sale in quarter t). I present the mean (across the
UPC-stores).
h
41
i
Table 3:
OLS Projection:
Weekly Frequency (t indexes weeks)
rtu = mt λ + α1 rtr + et
α1
R-Squared
σU nit P rice
σReg P rice
New York
0.42
0.19
1.1%
0.2%
Los Angeles
0.39
0.20
1.1%
0.2%
San Francisco
0.58
0.36
1.8%
0.3%
Dallas
0.36
0.16
1.0%
0.3%
Houston
0.35
0.15
0.9%
0.2%
All Markets
0.54
0.33
0.7%
0.1%
σU nit P rice
σReg P rice
Monthly Frequency (t indexes months).
α1
R-Squared
New York
0.16
0.31
1.1%
0.3%
Los Angeles
0.33
0.39
1.2%
0.4%
San Francisco
0.36
0.51
1.7%
0.5%
Dallas
0.40
0.39
1.1%
0.6%
Houston
0.41
0.44
1.0%
0.4%
All Markets
0.51
0.44
0.8%
0.2%
Quarterly Frequency (t indexes quarters)
α1
R-Squared
σU nit P rice
σReg P rice
New York
0.31
0.71
1.2%
0.4%
Los Angeles
0.55
0.49
1.5%
0.7%
San Francisco
0.34
0.50
1.5%
0.6%
Dallas
0.80
0.66
1.2%
0.8%
Houston
0.87
0.73
1.4%
0.8%
All Markets
0.80
0.66
0.6%
0.4%
Notes: The top, middle, and bottom panels use respectively, weekly, monthly, and quarterly time
periods. For example, the top panel uses the log change of a weekly price index. Each row contains
the coecient estimates for the specied market from an OLS projection of the log dierence of
u
unit price (rt
)
r
on the log dierence of regular price (rt ) and a vector of month dummies (mt ).
Each market is estimated separately (listed in Column 1). Both
rtu and rtr
are standardized
(demeaned and divided by the standard deviation) prior to the estimation.
42
Table 4: Panel Regressions (Annual Observations)
Dependent Variable:
Realized Discount
U nempjt
Specication:
Coecient
P P Ijt /RegP riceijt
S.E.
Coecient
S.E.
Groups
Time
Periods
R-Squared
(Within)
(1) All Variables in Levels
0.187***
0.050 -0.068*** -0.010
538
7
0.040
(2) All Variables in Levels
0.280***
0.051
538
7
0.015
(3) All Variables in First Dierence
0.570***
0.055
-0.0565*
-0.029
538
6
0.054
(4) All Variables in First Dierence
0.584***
0.056
538
6
0.051
The table above presents the results from four dierent panel regressions where a store-year is the unit of observation.
The average realized discount is the dependent variable and is described in Section 4.1. U nempjt is the average
unemployment rate for the BLS MSA that corresponds to IRI market j during year t. The variable P P Ijt /RegP riceijt
is a proxy for c in the model. It is the average of the PPI across all of the relevant categories divided that by the index
of the regular price for store i. The top two specications are estimated in levels and the bottom two are estimated
in rst dierences, all with the xed eects estimator. The reported standard errors are robust to arbitrary serial
correlation. Clustered standard errors are generally smaller than those reported above and have no qualitative eect
on inference.
43
Table 5: Panel Regressions With Time Dummies
Dependent Variable
Realized Discount
Realized Discount
Coecient
se
Coecient
se
U nemp
U nemp2
P P Ijt /RegP riceijt
-1.67***
.284
-1.24***
.335
13.83***
2.44
10.62***
2.77
-0.18***
0.012
Year = 2002
0.013***
0.0015
0.011***
0.0015
Year = 2003
0.022***
0.0016
0.016***
0.0016
Year = 2004
0.026***
0.0015
0.016***
0.0014
Year = 2005
0.023***
0.0015
0.012***
0.0012
Year = 2006
0.023***
0.0013
0.012***
0.0012
Year = 2007
0.017***
0.0013
0.005***
0.0011
R-squared
0.23
0.11
The table above presents results from the same models estimated in Table 4 but includes a vector of
year dummies and a quadratic term to capture potential non-linearity in the eect of unemployment
on realized discount.
44