What We can Learn About the Behaviour of Firms from the Average Monthly Frequency of Price‐Changes: An Application to the UK CPI Data

Date01 December 2017
Publication Date01 December 2017
AuthorHuw David Dixon,Kun Tian
DOIhttp://doi.org/10.1111/obes.12173
907
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
doi: 10.1111/obes.12173
What We can Learn About the Behaviour of
Firms from theAverage Monthly Frequency of
Price-Changes:AnApplication to the UK CPI
Data*
Huw David Dixon† and Kun Tian‡,§
Cardiff Business School, Colum Drive, Cardiff CF10 3EU, UK
(e-mail: dixonh@cardiff.ac.uk)
University of Xiangtan, Xiangtan, China
§Centre for Price & Inflation, Cardiff University, Cardiff, UK (e-mail: ktian@hotmail.co.uk)
Abstract
The monthly frequency of price-changes is a prominent feature of many studies of the
CPI micro-data. In this paper, we see what the frequency implies for the behaviour of
price-setters in terms of the cross-sectional distribution average of price-spell durations
across firms. Wederive a lower bound for the mean duration of price-spells averagedacross
firms. We use the UK CPI data at the aggregate and sectoral level and find that the actual
mean is about twice the theoretical minimum consistent with the observed frequency. We
construct hypothetical Bernoulli–Calvo distributions from the frequency data which we
find can result in similar impulse responses to the estimated hazards when used in the
Smets–Wouters (2003) model.
I. Introduction
In recent years, there have been many studies using comprehensive micro-data on pricing.
For the US we have Bils and Klenow (2004), Klenow and Kryvtsov (2008) and Nakamura
and Steinsson (2008). In the Euro area, there has been the inflation persistence network
(IPN) consisting of national studies of the CPI and PPI microdata,1which are summarized
in Alvarez et al. (2006). There are other studies: for example Bunn and Ellis (2012) for the
UK and Baharad and Eden (2004) for Israel. One common focus of these studies has been
JEL Classification numbers: E50.
*We would like to thank the referees, whose insightful comments led to fruitful revisions in the paper. Thanks
are due also to Erwan Gautier, James Costain, Steven Millard, seminar participants at the Universities of Bath and
Manchester, theT2M conference at Nantes in 2012, the European Monetary Forum 2013, the Anglo-French workshop
(Marseilles) 2014. Huw Dixon would like to thank the Foundation Banque de Francefor financial suppor t and Kun
Tian the National Social Science Foundation China (Grant no. 11CJL017), and the Julian Hodge foundation. Faults
remain our own.
1See Baudry et al. (2007) and Alvarez and Hernando (2006) for France and Spain inter alia.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 79, 6 (2017) 0305–9049
908 Bulletin
the frequency statistic of the proportion of prices changing per month (this can either be
an average over several months, or a monthly statistic). This statistic can be presented in
several ways,depending on the level of disaggregation and the treatment of temporary sales
and so on.2In this paper, we seek to analyse what this frequency statistic implies for the
behaviour of ‘firms’(or more accurately price-setters) in the economy in terms of the mean
duration of prices set by firms. Each period firms set prices: they may either choose to leave
the price unchanged or to change it. The proportion of firms resetting price corresponds to
the proportion of prices changing (for simplicity we take a 1-1 correspondence between
firms and prices3). The prices of some product types change frequently (e.g. gasoline,
tomatoes) and some very infrequently (coin-operated laundromats).
We can think of the CPI data set as a panel of observations, each cross-section corre-
sponding to the prices set by the price-setters at that date. The cross-sectional distribution
and corresponding mean completed price spells can be seen as capturing the behaviour
of the firms, which represents the ‘structure’ of the economy in this respect: what pro-
portion of firms set prices of a particular duration, what is the average behaviour of the
firms in the economy. The purpose of this paper was to explore what we can learn about
the cross-sectional distribution from the frequency data. The cross-sectional distribution
is also required if we are to calibrate price-setting on the economy as a GeneralizedTaylor
economy (GT) where we consider the economy as made up of price-setters who set prices
for different durations which are known ex ante (Taylor, 2016, Dixon and Le Bihan, 2012).
What is the cost of losing information by summarizing the distribution of price changes
based on the frequency data? In fact, we show that the loss can be quite small: it turns out
that the behaviour of the economy using the hypothetical distributions can look quite sim-
ilar to those based on the estimated distribution. However, a wide variety of hypothetical
distributions are consistent with a given frequency and some can give rise to behaviour
that are quite different. We need to know which hypotheticalfrequency-based distributions
work best. In particular, Dixon and Kara (2010, 2011) assume that the frequencies
correspond to the Bernoulli–Calvo distribution – there is a fixed Bernoulli probability
each period that a firm’s price will change.
Our approach to interpreting the frequency data is twofold: first, we ask a purely the-
oretical question – what is the range of possible cross-sectional means consistent with a
given frequency; secondly, we compare the cross-sectional distribution estimated from the
micro data with two hypothetical distributions – (a) the ‘minimum distribution’generating
the lowest mean durations and (b) the Bernoulli–Calvo distribution which is implied by
the popular Calvo model of pricing. We use the UK CPI data for the period 1996–2007 and
consider frequency data at three different levelsof disagg regation:the 11 sector COICOP,4
the 67 sector COICOP and the highest possible level of disaggregation at 570 items, to
see how the actual data on price-spell durations compares to the hypothetical distribu-
tions consistent with the frequency data. We find that the cross-sectional mean duration
2See Kehoe and Midrigan (2015) for a discussion of the US data.
3See Alvarez and Lippi (2014) for the case of multi-product firms.
4COICOP stands for ‘Classification of Individual Consumption According to Purpose’ and is an inter-
national standard used for constructing consumer price indexes (see e.g. UN Statistics division http://unstats.
un.org/unsd/cr/registry/regcst.asp?Cl=5).
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd

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