Five Facts About Prices:
A Reevaluation of Menu Cost Models
Emi Nakamura and J´on Steinsson
∗
Harvard University
May 5, 2007
Abstract
We establish five facts about prices in the U.S. economy: 1) The median frequency of non-
sale price change is 9-12% per month, roughly half of what it is including sales. This implies
an uncensored median duration of regular prices of 8-11 months. Product turnover plays an
important role in truncating price spells in durable goods. The median frequency of price change
for finished goods producer prices is roughly 11% per month. 2) One-third of regular price
changes are price decreases. 3) The frequency of price increases covaries strongly with inflation
while the frequency of price decreases and the size of price increases and price decreases do not.
4) The frequency of price change is highly seasonal: It is highest in the 1st quarter and lowest in
the 4th quarter. 5) The hazard function of price changes for individual consumer and producer
goods is downward sloping for the first few months and then flat (except for a large spike at 12
months in consumer services and all producer prices). These facts are based on CPI microdata
and a new comprehensive data set of microdata on producer prices that we construct from raw
production files underlying the PPI. We show that the 1st, 2nd and 3rd facts are consistent with
a benchmark menu-cost model, while the 4th and 5th facts are not.
Keywords: Price Rigidity, Hazard Functions, Menu Cost Models.
JEL Classification: E30
∗
We would like to thank Robert Barro for invaluable advice and encouragement. We would like to thank Daniel
Benjamin, David Berger, Leon Berkelmans, Craig Brown, Charles Carlstrom, Gary Chamberlain, Tim Erickson, Mark
Gertler, Mike Golosov, Gita Gopinath, Oleksiy Kryvtsov, Gregory Kurtzon, Robert McClelland, Greg Mankiw, Ariel
Pakes, Ricardo Reis, Roberto Rigobon, John Rogers, Ken Rogoff, Philippa Scott, Aleh Tsyvinsky, Randal Verbrugge,
Michael Woodford and seminar participants at Harvard, the Federal Reserve Board and the Federal Reserve Bank
of New York for helpful comments and discussions. We particularly want to thank Mark Bils and Pete Klenow for
thoughtful and inspiring conversations. We are grateful to Martin Feldstein for helping us obtain access to the data;
without his help this work would not have been possible. We are grateful to the Warburg Fund at Harvard University
for financial support.
1 Introduction
The nature of price setting has important implications for a range of issues in macroeconomics
including the welfare consequences of business cycles, the behavior of real exchange rates and
optimal monetary policy. For this reason, macroeconomists have had a persistent interest in micro-
level empirical evidence about the behavior of prices. We use BLS microdata underlying the
consumer and producer price indices to document five basic features of price adjustment. We
interpret this evidence through the lens of a benchmark menu cost model.
We begin by estimating the frequency of price change. Until recently, the best sources of infor-
mation on U.S. pricing behavior were studies of price adjustment for particular products (Cecchetti,
1986; Kashyap, 1995), broader surveys of firm managers (Blinder et al., 1998), and evidence on the
dynamics of industrial prices (Carlton, 1986). The conventional wisdom from this literature was
that prices adjusted on average once a year. Bils and Klenow (2004) dramatically altered this con-
ventional wisdom by showing that the median frequency of price change for non-shelter consumer
prices in 1995-1997 was 21%, implying a median duration of 4.3 months.
We use a substantially more detailed dataset than Bils and Klenow (2004) that contains the
micro-level price data underlying the non-shelter component of the consumer price index.
1
This
dataset has been used by Klenow and Kryvtsov (2005) to analyze price adjustment behavior. We
find that temporary sales play an important role in generating price flexibility for retail prices in
categories that account for about 40% of non-shelter consumer expenditures. While the median
frequency of price change including sales is 19-21% per month, we find that the median frequency
of non-sale price change is only 9-12% per month depending on the time period and how we treat
non-sale price changes over the course of sales and stockouts. These frequency estimates imply an
uncensored duration of regular prices of between 8 and 11 months. If we include price changes
associated with product substitutions, the frequency of price change increases by between 1 and 2
percentage points.
The importance of temporary sales in generating price flexibility draws attention to the ques-
tion of how sales should be viewed when thinking about the macroeconomic implications of price
1
Bils and Klenow (2004) used the BLS Commodities and Services Substitution Rate Table for 1995-1997. This
data set contains average frequencies of price changes and substitutions by disaggregated product categories over the
1995-1997 period. In contrast, the CPI research database contains the actual data series on prices underlying the
consumer price index for the 1988-2005 period. See section 2 for a more detailed discussion of the data.
1
rigidity.
2
Are the macroeconomic implications of sales the same as those of other price changes?
Or are they different? The theoretical literature on price adjustment clearly indicates that different
types of price adjustments can have very different macroeconomic implications. For example, the
Calvo (1983) model and the Caplin and Spulber (1987) model have very different macroeconomic
implications for the same frequency of price change.
We document several important empirical differences between sale price changes and other types
of price adjustments. The most important differences are: 1) Sale price changes appear to be much
more transient than other types of price changes. In most cases where a price is observed before and
after a sale, the price returns to its original level following the sale. 2) Sales price changes are more
than twice as large as other price changes on average. 3) The frequency and size of sales have a very
different relationship to aggregate variables than regular price changes. 4) The hazard function of
price change including sales is very different from that excluding sales. This last feature is a direct
consequence of the transient nature of sales—the hazard function of price change including sales
reflects the presence of a greater number of short price spells.
There are a number of reasons why it may be important to distinguish between sale and non-sale
price changes. First, the transience of price adjustment associated with sales implies that a given
number of price changes due to sales yield much less aggregate price adjustment than the same
number of regular price changes (Kehoe and Midrigan, 2007). Second, some types of sales may
be orthogonal to macroeconomic conditions. Third, transitory sales are a much more pervasive
phenomenon in retail prices than in wholesale prices.
Our frequency of price change measures are for identical items. Product turnover is another
source of price flexibility that plays an important role in truncating price spells, particularly in
durable goods categories such as automobiles and apparel. The median frequency of product
substitution over the period 1998-2005 in transportation goods and apparel was 10.2% and 9.9%
per month, respectively. As with sales, it is important to distinguish between price changes due
to product turnover and price changes for identical items. Many factors other than a firm’s desire
to change its price influence its decision to introduce a new product. The theoretical literature
suggests that it is crucial to distinguish between price adjustments that are motivated primarily by
a large difference between a firm’s current price and its desired price and those that are motivated
2
A number of recent theoretical studies base their analysis on statistics for data where sales have been excluded
(e.g., Golosov and Lucas, 2006; and Midrigan, 2005).
2
by other factors.
3
We also present the first broad-based evidence on U.S. price dynamics at the producer level.
Price rigidity at the producer level is potentially important because even if retail prices are per-
fectly flexible, price rigidity of producer prices could imply that shocks to production costs are not
immediately passed through to consumer prices. In order to study this issue, we created a new data
set on producer prices from the production files used by the BLS to construct the Producer Price
Index. The median frequency of price change for finished goods producer prices was 10.8% in 1998-
2005; it was 13.3% for intermediate goods producer prices; and it was 98.9% for crude materials.
Price rigidity in finished goods producer prices thus seems comparable to the rigidity of consumer
prices excluding sales but substantially more than the rigidity of consumer prices including sales.
There is a tremendous amount of heterogeneity across sectors in both the frequency of price
change and the importance of temporary sales. Different summary statistics on price flexibility
therefore give very different answers regarding the degree of price flexibility in the U.S. economy.
Following Bils and Klenow (2004), we focus on the weighted median frequency of price adjustment
across categories. Excluding sales lowers the median frequency of price change of consumer prices
by over 50%, while it lowers the mean frequency of price change by only about 20%. This is due
to the fact that sales are concentrated in sectors of the economy—such as food and apparel—that
have a frequency of price change close to the median frequency of price change across sectors.
There is no model-free way of selecting what is the appropriate summary statistic to describe the
degree of monetary non-neutrality in an economy with heterogeneous price rigidity. In Nakamura
and Steinsson (2006), we calibrate a multi-sector menu cost model to the sectoral distribution of the
frequency and absolute size of price changes excluding sales. The degree of monetary non-neutrality
implied by this multi-sector model is triple that implied by a single-sector model calibrated to the
mean frequency of price change of all firms but similar to that implied by a single-sector model
calibrated to the median frequency of price change. Bils and Klenow (2002) and Carvalho (2006)
study the effect of heterogeneous price rigidity in time-dependent models.
The second feature of price change that we investigate is the fraction of price changes that are
price decreases. We find this fraction to be roughly one-third in both consumer prices excluding
3
In Nakamura and Steinsson (2006), we analyze a menu cost model in which product introduction represents
a random opportunity to set a new price. We show that increasing the frequency of product introduction lowers
monetary non-neutrality by about 5 times less than an equal increase in the frequency of regular price changes.
3
sales and finished goods producer prices. We present a benchmark menu cost model along the lines
of Golosov and Lucas (2006) and show that the fraction of price changes that are decreases helps
pin down the key parameters of this model. Building on the insights in Golosov and Lucas (2006),
we find that the combination of the fact that 1/3 of price changes are price decreases and the fact
that the average absolute size of price changes is large favors a model in which large but relatively
transient idiosyncratic shocks to firms are an important driving force behind most price changes.
The third feature of price change that we investigate is how the frequency and size of price
changes covary with variations in the inflation rate. We find that the frequency of price increases
covaries quite strongly with the rate of inflation, while the frequency of price decreases and the
size of price increases and decreases do not. This fact provides a natural test for our calibrated
benchmark menu cost model. We find that the model matches the data well along this dimension.
The frequency of price increases covaries much more with inflation than the other three components
in the model as in the data.
The fourth feature of price change that we investigate is the extent of seasonal synchronization
of price changes. We find that price rigidity is highly seasonal both for consumer and producer
prices. Prices are substantially more likely to change in the first quarter than in other quarters—
the difference is particularly large for producer prices. For consumer prices, we furthermore find
a consistent pattern within quarter. The frequency of price change is highest in the first month
of each quarter and falls monotonically across months within the quarter. This feature of price
change does not arise in our benchmark menu cost model. It could arise in a menu cost model
in which firms face seasonal variation in marginal costs or demand; or it may be evidence of a
time-dependent element of the pricing decisions of firms.
The fifth and final issue that we investigate is the hazard function of price change. We are
primarily interested in the slope of the hazard function. Menu cost models can give rise to a wide
variety of hazard functions depending on the specification of marginal costs. The hazard function
implied by our calibrated benchmark menu cost model is sharply upward sloping for the first few
months. This implies that prices are unlikely to change again in the month immediately following
a price change.
The main empirical challenge in estimating the hazard function of price change is the fact
that heterogeneity in the level of the hazard function across products—if not properly accounted
4
