Sales and the Real Effects of Monetary Policy

Federal Reserve Bank of Minneapolis
Research Department
Sales and the
Real E?ects of Monetary Policy?
Patrick J. Kehoe and Virgiliu Midrigan
Working Paper 652
April 2007
ABSTRACT
In the data, a sizable fraction of price changes are temporary price reductions referred to as sales.
Existing models include no role for sales. Hence, when confronted with data in which a large fraction
of price changes are sales related, the models must either exclude sales from the data or leave them
in and implicitly treat sales like any other price change. When sales are included, prices change
frequently and standard sticky price models with this high frequency of price changes predict small
e?ects from money shocks. If sales are excluded, prices change much less frequently and a standard
sticky price model with this low frequency of price changes predict much larger e?ects of money
shocks. This paper adds a motive for sales in a parsimonious extension of existing sticky price
models. We show that the model can account for most of the patterns of sales in the data. Using
our model as the data generating process, we evaluate the existing approaches and ?nd that neither
well approximates the real e?ects of money in our economy in which sales are explicitly modeled.
?Kehoe, Federal Reserve Bank of Minneapolis, University of Minnesota, and NBER; Midrigan, Federal Reserve
Bank of Minneapolis and New York University. The views expressed herein are those of the authors and not
necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.

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At the heart of monetary policy analysis is the question, How large are the real e¤ects
of monetary shocks? The answer to this question has important implications for the optimal
conduct of monetary policy, the linking of ‡uctuations in monetary aggregates to those in
real activity, and debates regarding the relative potency of …scal and monetary policy.
Recently there has been a vast surge in work to study this question. The most popular
class of models used to quantify the real e¤ects of money assume that goods prices are sticky.
In these models, …rms typically leave their prices unchanged for a number of periods and,
hence, monetary shocks have real e¤ects. A key ingredient in these models that determines
the size of the real e¤ects of money is the frequency of price changes: if …rms change prices
frequently, then monetary shocks have small real e¤ects; if they change them infrequently,
monetary shocks have large real e¤ects.
How frequently do prices change in the data? The answer to this question crucially
depends on how sales are treated in the data. Bils and Klenow (2004) treat sales just like
any other price change and …nd that prices change frequently: the median consumer good
experiences a price change about every 4.3 months. This number suggests that prices change
about three times as frequently as was previously believed. For example, in a survey of
the empirical literature on the frequency of price changes, Taylor (1999) argues that the
average frequency of price changes is about one year. Bils and Klenow (2004) and others
have interpreted this high frequency of price changes as casting doubt on the relevance of
price stickiness in accounting for business cycle ‡uctuations.
A recent study by Nakamura and Steinsson (2007) shows that Bils and Klenow’s
conclusion that prices are fairly ‡exible is due in large part to the fact that a large number
of price changes in the data are sales. When Nakamura and Steinsson exclude sales from the

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de…nition of price changes, they …nd frequencies close to those cited by Taylor, namely that
the median frequency of price changes is about every 8 to 11 months.
In summary, then, if sales are included in the data, prices are fairly ‡exible; if they are
excluded, prices are fairly sticky. To date, there are two approaches to deal with sales. The
most popular approach is to exclude sales from the data, write down a model without sales,
and then match the frequency of price changes to the data with sales excluded. We refer to
this approach as the take-sales-out approach.
An alternative approach is to include sales in the data, write down a model without
sales, and then match the frequency of price changes to the data with sales included. We
refer to this approach as the leave-sales-in approach. The leave-sales-in approach obviously
generates much smaller e¤ects from monetary shocks than the take-sales-out approach. The
leave-sales-in approach implicitly assumes that, in terms of evaluating the real e¤ects of a
money shock, a sale is just like any other price change. The take-sales-out approach, in
contrast, implicitly assumes that, in terms of evaluating monetary shocks, a sale is similar to
no price change. To date there seems to be little guidance from theory as to which approach
is preferable.
This paper takes up the issue of how to deal with sales in the price data. In the data
we use, sales are de…ned by a simple AC Nielsen algorithm that looks at the pattern of price
changes and classi…es price reductions as sales if they are reversed su¢ ciently quickly and
classi…es the rest as regular price changes.
Our approach di¤ers from existing ones in that we explicitly include a motive for
temporary price reductions in a simple sticky price model and then directly study how large
are the real e¤ects of monetary policy shocks. We then treat the model as the data-generating
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process and apply the two common approaches to data generated from our model. We …nd
neither of the existing approaches provides a good approximation to the key question of
interest: the take-sales-out approach leads to much larger e¤ects of monetary shocks than
are in the model with sales, and the leave-sales-in approach leads to much smaller e¤ects of
monetary shocks than in the model with sales.
We then show that a simple rule of thumb approach of using a model without sales
but choosing parameters, not to match the frequency of price changes, but rather to match
the fraction of time a price stays at its annual model gives a much better approximation than
either of the existing approaches. We end with two proposals to advance the sticky price
literature: either explicitly include sales in the model or follow a version of our rule of thumb.
We argue that either will represent progress relative to the existing approaches.
Our model is purposefully chosen to be an exceptionally simple and parsimonious
extension of the existing sticky price literature: we add one parameter to existing menu cost
models, the cost of having a one-period markdown. We show that even though the model is
simple, it can capture many of the features in the data concerning sales.
In the model a key state variable of each …rm is its regular price (or reference price)
inherited from the previous period. This price is the price it can charge in the current period
with no extra costs. If it wants to charge a di¤erent price in the current period, it has two
options: change its regular price or have a one-period markdown (a “sale”). To change its
regular price, the …rm pays a …xed cost which gives it the right to charge this price both
today and in all future periods with no extra costs. We think of this option as akin to buying
a permanent price change. To have a one-period markdown, the …rm pays a smaller …xed
cost which gives it the right to charge a price lower than the existing regular price for the
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current period only and keep its regular price unchanged.
The costs of various actions in the future depend on the actions taken in the current
period. If in the current period the …rm chooses to change its regular price, then in the
next period it inherits this new regular price and decides whether to charge this regular price
again at no cost, pay a …xed cost and change this regular price, or pay the smaller …xed
cost and have a one-period markdown. If in the current period the …rm chooses to have a
one-period markdown, then in the next period it inherits the unchanged regular price and
decides whether to charge this existing regular price at no cost, pay a …xed cost and change
its regular price, or pay the smaller …xed cost and again have a one-period markdown. The
problem of the …rm then proceeds recursively.
In terms of our data analysis, we use data from two sources. We primarily focus
on scanner price data from grocery stores. An appealing feature of this data is that it is
weekly data and there is independent evidence that pricing decisions are made at a weekly
level. Hence, we are comfortable modeling these grocery stores as making weekly decisions
on prices. We also do some experiments with the data used by Bils and Klenow (2004) and
Steinsson and Nakamura (2007). That data is much more comprehensive than the grocery
store data, but it is only collected as point-in-time data at the monthly frequency. Hence,
it gives no direct evidence about what happens within a month, and one needs to make a
variety of assumptions to come up with the frequency of price changes.
We focus on seven features of prices and sales in our grocery store data. First, prices
change frequently. Second, during the year prices spend most of their time at their modal
value. Third, prices are much more likely to be below their annual mode than above it.
Fourth, most price changes are associated with sales. Fifth, after a sale, the price tends to
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return to the pre-sale price. Sixth, sales are very transitory. Finally, price changes tend to
be clustered in time for a given product.
We show that our simple model does a remarkably good job of generating these fea-
tures. We then use our model to evaluate existing approaches to dealing with sales. To do
so, we treat our model as the data-generating process. We can ask, Which of two alternative
practices more closely reproduces the real e¤ects of monetary policy in our model: leaving
the sales out of the data or leaving the sales in the data?
We begin by comparing our model to two menu costs models without markdowns.
In one version of the model, the leave-sales-in version, we set the parameters of the model
to match statistics in the data in which sales are included. In the other, the take-sales-out
version, we set parameters to match statistics in data in which sales are excluded. We …nd
that the leave-sales-in version signi…cantly understates the real e¤ects of monetary policy
relative to these e¤ects in the model with markdowns and that the take-sales-out version
somewhat overstates the real e¤ects of monetary policy.
We then perform a similar comparison using the more popular Calvo model of pricing,
which is the benchmark model in the sticky price literature. These Calvo models are typically
viewed as approximations to the underlying menu cost models. We consider a leave-sales-in
version and a take-sales-out version of a Calvo model and …nd the same qualitative results as
in our previous comparison: the leave-sales-in version understates the real e¤ects of money,
while the take-sales-out version overstates it. At a quantitative level, the approximation error
with these models is large. In the leave-sales-in version, the real e¤ects of money, as measured
by the standard deviation of consumption, is less than one-…fth of the level in the menu cost
model with markdowns. In the take-sales-out version, the real e¤ects of money are about
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twice the level in the menu cost model with markdowns.
We then propose an alternative procedure to set the parameters of a model without
markdowns in order to approximate the real e¤ects of money in a model with markdowns.
In this procedure we leave sales in the data, but instead of choosing parameters to match the
frequency of price changes (along with other statistics), we choose parameters to match the
fraction of prices at the annual mode (along with the same other statistics). We show that
for either a menu cost model without markdowns or the Calvo model, this procedure implies
real e¤ects of money similar to those in the menu cost model with markdowns.
1. Some Facts about Prices
We begin by documenting seven facts about price changes in the data that we will use
both to calibrate and evaluate our model.
The source of our data is a by-product of a randomized pricing experiment conducted
by the Dominick’s Finer Foods retail chain in cooperation with the Chicago GSB. The data
consists of nine years (1989 to 1997) of weekly store-level data from 86 stores in the Chicago
area on the prices of more than 4,500 individual products which are organized into 29 product
categories. The products available in this database range from non-perishable foodstu¤s
(some of which are represented by the categories frozen and canned food, cookies, crackers,
juices, sodas, beer), to various household supplies (some of which are represented by the
categories, detergents, softeners, and bathroom tissue), as well as pharmaceutical and hygienic
products. In addition to price data, the database maintained by the Chicago GSB provides
information about the number of units of the good sold each period, the average acquisition
cost of the goods in each store’s inventory, as well as an indicator variable that records sales.
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Because data are recorded by scanners, price series are frequently interrupted by gaps
(periods when information about the price is missing, either because no consumers have
purchased that good in that period or because the store has stocked out). To partly address
this issue, we study, for each product (identi…ed by its UPC code), the time series of prices
of the store at which the product was most frequently available. Given that Dominick’s sets
prices on a chain-wide basis, price changes across stores are highly correlated, especially those
in one of Dominick’s three pricing zones (high, low, medium), and little information is lost
by restricting our analysis to the price of a single store for each good.1 Further, we restrict
our attention to those goods for which at least 50 weekly price observations are available out
of the total maximum of 400 weeks of the sample.
We use an algorithm to identify sales that is a minor extension of the algorithm
described in the AC NIELSEN-ERIM database.2 Here we discuss the algorithm presuming
that no data are missing and discuss the general case in the appendix.
Sales are de…ned relative to an arti…cial series called a regular price series, denoted
fPRtg; which is used mainly to de…ne which periods are sales periods. A period is a sales
period if in that period the original price Pt is lower than the regular price P R. The regular
t
price series is constructed from the original price series according to the following recursive
algorithm. For each price cut, de…ned as a period t in which Pt < Pt 1; check if the price rises
above the lower price within 5 weeks; that is, check if Pt+j > Pt for j 6 5: If it does, then let
j be the …rst time the price rises above the lower price Pt and replace Pt; Pt+1;::; Pt+j 1 with
Pt 1. If the price never rises above Pt in the next 5 weeks, then leave Pt unchanged. Using
the new series, repeat this algorithm 4 more times. The resulting series is the regular price
series.
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The rationale for repeating the algorithm several times is to allow sales periods to
include a whole variety of patterns in which, in the middle of the sale, the price cut is
partially reversed or even drops more during a sale. For a …rst example, suppose the original
data are 200, 100, 101, 102, 103, 104, 105, 106. In the …rst round of the algorithm, the
candidate for the regular price series is 200, 200, 101, 102, 103, 104, 105, 106; in the second
round it is 200, 200, 200, 102, 103, 104, 105, 106, and so on. The regular price is de…ned to be
the result of this algorithm after 5 such rounds and is given by 200, 200, 200, 200, 200, 200,
200, 106. Comparing the original series to this regular price series, we see that all periods
but the …rst and the last are considered sales periods.
We emphasize that in our de…nition of sales, we do not require that the price drop by
at least some minimum amount or that prices return to at least the pre-sale price. Notice
also that we restrict our attention to temporary price cuts and thus exclude clearance sales
(price decreases that are never at least partially reversed). As Nakamura and Steinsson (2007)
report, clearance sales are uncommon in the processed food industry and constitute a sizable
fraction of sales only for apparel products, which are absent in the Dominick’s sample. Finally,
in addition to using a 5-week duration for sales, we experimented with other durations and
report statistics for a 3-week duration as well.
For illustration purposes, in Figure 1 we graph an example of a price series, namely the
cost of a six-pack of Diet A&W Cream Soda. The dashed lines are the original transaction
prices while the solid line gives the regular price series constructed with the AC Nielsen
algorithm. For this series all periods in which the dashed line does not equal the solid line
are de…ned to be sales. The …gure makes clear that excluding sales (by using the regular
price series rather than the original series) excludes most of the price changes in the original
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series. We also see that price changes are large and the price changes tend to spend a lot of
time at only a couple of values. As we shall see, these features are common for the prices in
our data set.
To that end consider Table 1 in which we report a variety of facts about prices. For
each of the 29 product categories we …rst compute category-level statistics by weighting each
good by its sales share in each category. In Table 1 we report a weighted average of these
category-level statistics, where the weights are each category’s share in total sales. (See the
data appendix for details.) In discussing the facts about sales, we focus on those computed
using the 5-week de…nition. Those computed using the 3-week de…nition are broadly similar.
Several features of the data stand out.
Fact 1. Prices change frequently.
In Table 1 we see that 33% of prices tend to change every week. (As the second column
shows, if sales-related price changes are excluded this number drops to 5.6%.)
Fact 2. Price changes are large and dispersed.
Table 1 shows that mean size of price changes is 17%. The smallest 25% of price
changes are less than 4% and the largest 25% of price changes are over 19%. (As the second
column shows, if sales-related price changes are excluded the mean size of price changes drops
to 10%. Likewise, with sales-related changes excluded price changes are still dispersed, but
somewhat less so: with sales-related changes excluded, the smallest 25% of price changes are
less than 3% and the largest 25% of price changes are over 12%.)
Fact 3. During a year, prices spend most of their time at their modal value.
Table 1 also shows that, on average during a 50-week period, prices tend to be at their
modal value 58% of the time. Prices tend to be at their two most widely used prices 76%
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