The Skewness of the Price Change Distribution: A New Touchstone for Sticky Price Models
| DOI | http://doi.org/10.1111/jmcb.12700 |
| Author | DANIEL VILLAR,SHAOWEN LUO |
| Published date | 01 February 2021 |
| Date | 01 February 2021 |
DOI: 10.1111/jmcb.12700
SHAOWEN LUO
DANIEL VILLAR
The Skewness of the Price Change Distribution: A
New Touchstone for Sticky Price Models
Wepresent a new way of empirically evaluating various sticky price models
that are used to assess the degree of monetary nonneutrality. While menu
cost models uniformly predict that price change skewnessand dispersion fall
with ination, in the Calvo model, both rise. However,the U.S. Consumer
Price Index (CPI) data from the late 1970s onward show that skewnessdoes
not fall with ination, while dispersion does. We present a random menu
cost model that, with a menu cost distribution that has a strong Calvo avor,
can match the empirical patterns. The model exhibits much more monetary
nonneutrality than existing menu cost models.
JEL codes: E31, E32, E47, E52
Keywords: nominal rigidity, state-dependent pricing, random menu cost,
monetary nonneutrality
T —that is, when, how,and
why rms change the prices of the goods and services that they sell—has been an area
of active research in monetary economics over the past few decades. It is well known
that monetary variables haveno inuence on real economic activityif all prices can be
freely reset at any point in time. Therefore, much effort has been devoted toward in-
corporating frictions in price-setting models and using detailed price data to measure
how sticky prices really are (Klenow and Kryvtsov 2008, Nakamura and Steinsson
2008, etc.). One important nding in this literature is that the degree of monetary
We would like to thank Emi Nakamura, Jón Steinsson, Ricardo Reis, and Michael Woodford for their
invaluable advice and support. Wealso thank the editor, two anonymous referees, Jennifer La’O, Martín
Uribe, Stéphane Dupraz, JorgeMejía-Licona, Savitar Sundaresan, Erick Sager, Timothy Erickson. The data
were made accessible to us by the Bureau of Labor Statistics under MOU 3594, and we thank Ted Toand
John Molino for their help as our BLS coordinators. All remaining errors are our own. The viewsexpressed
in this paper are those of the authors and do not necessarily reect those of the Board of Governors or the
Federal Reserve System.
S L is an Assistant Professor in the Department of Economics at Virginia Tech (E-mail:
sluo@vt.edu). D V is an Economist in the Division of Researchand Statistics at the Federal
Reserve Board of Governors (Email: daniel.villar@frb.gov).
Journal of Money, Credit and Banking, Vol. 53, No. 1 (February 2021)
© 2020 The Ohio State University
42 :MONEY,CREDIT AND BANKING
0
Desired price change
Density
Inflation < 0
Skewness > 0, low dispersion
0
Desired price change
Density
Inflation = 0
Skewness = 0, high dispersion
0
Desired price change
Density
Inflation > 0
Skewness < 0, low dispersion
Fig 1. Intuition for the Menu Cost Model.
N: In the rst three panels, the black curve represents the distribution of the desired price change. The dashed lines
represent the Ss band. The gray shaded area represents the distribution of realized price changes.
neutrality depends not only on how often prices change, but also, crucially, on the
extent to which the prices that change are selected based on their misalignment. This
mechanism has come to be known as the selection effect (following Caplin and Spul-
ber 1987, Golosov and Lucas 2007, etc.). Specically, if the prices that change are
those heavily misaligned from their optimal level (as would be the case if rms must
pay price adjustment, or menu costs), money will have a much smaller real effectthan
if they were randomly selected (as is the case in Calvo-type models).
This paper evaluates the strength of the selection effect based on an empirical pat-
tern that has not been previously considered—the correlation between ination and
price change skewness, and a new data set of prices coveringhigh ination periods—
the Consumer Price Index (CPI) microdata going back to 1977. Moreover,we present
a new random menu cost model of sticky prices (based on Dotsey, King, and Wol-
man 1999) to capture the patterns observed in the data and use the model to assess
the degree of monetary nonneutrality.
The strength of the selection effect can be inferred through the distribution of re-
alized price changes, although it is not directly observable in the data. We exploit
the fact that the selection in price changes has a strong impact on the behavior of the
distribution of realized price changes in response to aggregate shocks. In xed menu
cost models, the presence of a xed adjustment cost induces a selection effect: the
price adjustment occurs if and only if the prot gains from the adjustment outweigh
the adjustment cost. This leads to an inaction region of price changes and rules out
small price changes. Because adjusting rms change prices by large amounts, the
real effect of monetary shocks is small. In addition, this selection effect implies that
both dispersion and skewness of the nonzero price change distribution fall with in-
ation. As illustrated in Figure 1, an inationary shock will push some price changes
out of the inaction region to the positive side, and push some changes into the inac-
tion region from the negative side. Thus, the realized price change distribution is less
dispersed and more asymmetric with a negative skewness. The opposite is true for a
SHAOWENLUO AND DANIEL VILLAR :43
deationary shock. These implications appear in a broad class of menu cost models
and can be tested empirically.1
In the data, we nd that while the dispersion of nonzero price changes clearly falls
in high ination periods, the skewness does not. The latter is contrary to the predic-
tions of menu cost models, and is therefore inconsistent with a very strong selection
effect. Moreover, the negative ination–dispersion correlation and the positive corre-
lation between ination and the frequency of price change contradict the predictions
of the Calvo model. Overall, we nd that no existing model can match all the empir-
ical patterns that we observe.
We use the data set recently presented in Nakamura et al. (2018), that extends the
CPI microdata back to 1977, to evaluate whether the dispersion and skewnessof price
changes do indeed fall with ination. Since the newly recovered period includes the
highest ination episodes in the postwar United States, as well as the disination pe-
riod initiated by the Federal Reserve under Paul Volcker, our data set is particularly
well suited for the tests that we propose.2The extended data set thus overcomes an im-
portant limitation faced by the CPI data from 1988 onward (the main source of price
data in the sticky price literature) covering only periods of low and stable ination.3
To develop a model consistent with nonnegative ination–skewness and negative
ination–dispersion correlations, we modify the menu cost model in a way that weak-
ens the selection effect. We do this by introducing random menu costs that add ran-
domness to whether the rm will have an opportunity to change its price following
Dotsey, King, and Wolman (1999). The model therefore incorporates some Calvo
features, and can be thought of as a hybrid between state- and time-dependent sticky
price models. Random menu cost models have been proposed by previous studies.
We follow the example of Dotsey, King, and Wolman (1999) and Dotsey and Wol-
man (2018) and adjust the distribution of menu costs to t the new correlations that
we report.4Wend that in order to capture the nonnegative ination–skewness corre-
lation, the probability of price changes being free must be nonzero and the probability
of price changes being costly must be high. The tted model features low state depen-
dence and implies a high level of monetary nonneutrality, six times higher than that
in a xed menu cost model, and approximately 70% as large as that in a Calvo model.
Our paper contributes to a large literature devoted to studying the selection ef-
fect of price changes and monetary nonneutrality. Caplin and Spulber (1987) show
1. As discussed in Section 1, the ination–dispersion relation is negative in the ination region, and
positive in the deation region. In the data, we mostly observepositive ination episodes. Because of this,
and for convenience, we will mostly refer to the “negativeination-dispersion correlation,” instead of “the
negative ination-dispersion correlation in the positiveination region.”
2. Although some studies (such as Gagnon 2009, Alvarez et al. 2019) haveused price data from coun-
tries that experienced high ination, theystudy how the frequency of price change behaves at high ination,
without considering the higher moments of the price change distribution. Notably, Alvarez et al. (2019)
look at the dispersion of price levels (within narrow product categories), but not of price changes.
3. Other commonly used data sets go back even less far,such as Dominick’s and the Nielsen Homes-
can Dataset.
4. Dotseyand Wolman (2018), in particular, use price microdata to estimate a random menu cost model
in order to derive results on nonneutrality. However, they do not consider the informative correlations
moments that we show in this paper.
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