Understanding price stickiness: firm-data evidence
on price adjustment lags and their asymmetries
Daniel A. Dias∗, Carlos Robalo Marques†, Fernando Martins‡,
and J.M.C. Santos Silva§
January 8, 2014
Abstract
We study the speed of price reactions to positive and negative demand and
costs shocks. In line with the predictions of optimal price setting models, we
find that price adjustment lags vary with firm’s characteristics that are related
to the importance of menu costs, the variability of the optimal price, and the
sensitivity of profits to sub-optimal prices. We also find that the majority of
firms react faster to positive than to negative cost shocks, and more quickly to
negative than to positive demand shocks. However, the direction and magnitude
of these asymmetries vary across firms and with the type of shock in a way that
cannot be fully explained by any single theoretical model of asymmetric price
adjustment. Overall, these results suggest that the reaction to monetary policy
shocks may depend on which firms or sectors are particularly affected by them
and, therefore, that richer models are needed to fully understand the effects of
monetary policy.
JEL classification codes: C41, D40, E31.
Key Words: Asymmetries in price rigidity, Firm heterogeneity, Ordered data, Survey
data.
∗
Department of Economics, University of Illinois at Urbana-Champaign and CEMAPRE. Email:
[email protected].
†
Banco de Portugal. E-mail: [email protected].
‡
Banco de Portugal, ISEG (Technical University of Lisbon) and Universidade Lusíada de Lisboa.
E-mail: [email protected].
§
Department of Economics, University of Essex and CEMAPRE. E-mail: [email protected]
1
1. INTRODUCTION
Price stickiness has a central role in macroeconomics and, besides a vast theoretical
literature, it has generated numerous empirical studies trying to explain its origins and
gauge its importance.
Most of the literature aimed at identifying the reasons of price stickiness has focused
on the frequency of price changes.1 However, an important issue that arises when
using observed price changes to measure price rigidity at the micro-level is that the
differences in the frequency of price changes across products are not expected to strictly
correspond to differences in firm behaviour. Rather, the frequency of price changes is
likely to also depend in a significant way on the frequency and magnitude of the shocks
that hit the firms in the period under consideration. This suggests that the frequency
of price changes is not the best variable to use in empirical studies on the nature and
origins of price rigidity. As Blinder (1991, p. 94) puts it: “From the point of view of
macroeconomic theory, frequency of price change may not be the right question to ask,
for it depends as much on the frequency of shocks as on the firms’ pricing strategies. We
are more interested to know how long price adjustments lag behind shocks to demand
and cost.”
Therefore, rather than looking into the reasons for infrequent price changes, in this
paper we use survey data to directly investigate the deeper and more meaningful question of the determinants of the speed of price reactions to demand and cost shocks.2
Furthermore, we study two important and intertwined forms of heterogeneity in the
speed with which firms respond to shocks.
1
See among others, Bils and Klenow (2004), Alvarez and Hernando (2005), Dhyne et al. (2006),
Munnick and Xu (2007), Klenow and Kryvtsov (2008), Gopinath and Itskhoki (2010), Klenow and
Malin (2011), Druant et al. (2012), and Vermeulen et al. (2012).
2
Other authors have studied similar survey data; see, e.g., Small and Yates (1999), Fabiani et
al. (2004), Loupias and Ricart (2004), Alvarez and Hernando (2005), Kwapil et al. (2005), and Martins
(2010). However, the main objective of these papers was to document and explain the existence of
price rigidity and not so much to study the determinants of the speed of price adjustments.
2
First, we study between-firm heterogeneity by identifying firm-, product-, and
market-level characteristics that explain why some firms react faster than others to
each of the four types of shock on which we have information. In line with theoretical
models on optimal price-setting rules (e.g., Barro, 1972, Caballero, 1989, and Alvarez
et al., 2011), we find evidence that the degree of price stickiness is influenced by variables that are related to the importance of menu costs, the variability of the optimal
price, and the sensitivity of profits to sub-optimal prices. These results, therefore, lend
support to the idea that firms optimally choose the degree of price stickiness.
Second, we study within-firm heterogeneity by checking whether firms react differently to demand and cost shocks, and asymmetrically to positive and negative shocks
(in a slight abuse of terminology we refer to all these differences as asymmetries). We
find that, in line with similar evidence reported in the literature, most firms in our
sample react faster to positive than to negative cost shocks, and more quickly to negative than to positive demand shocks. However, and more importantly, we also find
that the direction and magnitude of the asymmetries varies across firms and with the
type of shock in a way that cannot be fully explained by any single existing theoretical
model of asymmetric price adjustment.
The results we present are important because the forms of heterogeneity in the speed
of firms’ responses to shocks that we find have implications for macroeconomic models
and monetary policy. First, it has been shown that the between-firm heterogeneity in
price stickiness leads monetary shocks to have larger and more persistent real effects
(see, e.g., Carvalho, 2006, and Nakamura and Steinsson, 2009). Second, the existence
of within-firm heterogeneity has important consequences for the relationship between
inflation and aggregate demand. The literature suggests that whether the Phillips curve
is linear, concave, or convex depends on the existence and sign of the asymmetries in
price rigidity at the firm level (see, e.g., Buckle and Carlson, 1996, Laxton et al., 1999,
Dolado et al., 2004, and Dolado et al., 2005). Our results show that asymmetries of
different signs can coexist in the same economy and therefore the reaction to monetary
policy shocks may depend on which firms or sectors are particularly affected by them.
Overall, these results suggest that economic models should try to account for the
3
documented heterogeneity in firms’ responses to shocks, and that richer and more
eclectic models are needed to fully understand firms’ reactions to different types of
shocks and to better predict the effects of monetary policy.
The rest of the paper is organised as follows. Section 2 describes the novel dataset
used in the paper. Section 3 introduces the econometric model we use and describes its
links to the literature on price stickiness. Section 4 presents and analyses the estimation
results, and Section 5 summarizes and discusses our main findings. Finally, the appendices provide a detailed description of the econometric model used, and information on
how the different variables were constructed.
2. THE DATA
Most of the data used in this study come from a survey about price setting practices
carried out by the Banco de Portugal.3 The idea of using survey data to study price
setting behaviour was pioneered by Blinder et al. (1998), and is becoming increasingly
popular (see, e.g., Fabiani et al., 2004, Loupias and Ricart, 2004, Alvarez and Hernando, 2005, Kwapil et al., 2005, Lünnemann and Mathä, 2006, and Martins, 2010).
A potential disadvantage of this type of data is that it corresponds to reported, not actual, behaviour and it is impossible to know whether the answers provided are close to
reality. However, in our model we will use only the ordinal information in the answers
given by the firms, which significantly mitigates potential measurement errors.4
3
4
For further details on this survey, see Martins (2005, 2010).
Another potential disadvantage of the type of data we use is that it does not distinguish between
aggregate and idiosyncratic shocks. Indeed, the economic literature has stressed that the reaction of
firms to shocks may depend on whether these are aggregate or idiosyncratic (Lucas, 1973), and recently
Mackowiak and Wiederholt (2009) developed a model in which prices react quickly to idiosyncratic
shocks, but only slowly to aggregate shocks (see also Dhyne et al., 2011). The fact that our data
has no information on whether the firm sees the shock as aggregate or idiosyncratic is an important
limitation. In any case, we do not expect this fact to seriously limit the interpretation of our results
because, since we have four observations for each firm, our panel data model will to some extent
account for the heterogeneity resulting from firms interpreting the nature of the shock in different
ways.
4
In the particular survey for which we have data, firms were asked how long they
would take to react to significant cost and demand shocks. More specifically, they were
asked the following four questions: 1) “After a significant increase in demand how much
time on average elapses before you raise your prices?”; 2) “After a significant increase
in production costs how much time on average elapses before you raise your prices?”;
3) “After a significant fall in demand, how much time on average elapses before you
reduce your prices?”; and 4) “After a significant decline in production costs how much
time on average elapses before you reduce your prices?”.
The responses to these questions, which will be the dependent variable in our model,
are recorded as continuous interval data with six categories: 1 - less than one week; 2 from one week to one month; 3 - from one month to three months; 4 - from three to six
months; 5 - from six months to one year; 6 - the price remained unchanged. With the
expression “significant increase” or “significant decline” the authors of the survey had
in mind inducing respondents to interpret the shock as significant enough to lead firms
to react to it by changing their price. Therefore, we interpret option 6 as indicating
that the price will eventually change, but the adjustment lag is longer than one year.5
Table 1 displays the distribution of the observed price adjustment lags for each
type of shock. These distributions make it clear that there is a substantial degree
of heterogeneity in the way firms respond to shocks. Indeed, for each of the shocks
considered, the response lags vary between less than one week to more than a year.
Naturally, this heterogeneity reflects the fact that firms differ from one another in some
important characteristics; in the next section we present an econometric model that
partially explains this heterogeneity.
5
Some authors who have looked at similar surveys for other European countries have interpreted
option 6 literally as meaning that such firms do not react to shocks (see, for instance, Kwapil et al.,
2005, and Fabiani et al., 2004). This interpretation implies that the distribution of the lags is defective
(i.e., there is a positive probability that the lag is infinite). The model we use does not depend on the
particular interpretation that is given to option 6 because all we will assume is that firms choosing
option 6 do not have price adjustment lags of less that one year. As a robustness check we also
estimated models grouping categories 5 and 6 together and found that the results change very little.
5
Table 1: Distribution of the price responses to demand and cost shocks
Cost shocks
Demand shocks
Price adjustment lag
Positive Negative Positive Negative
1 - less than one week
47
35
28
48
2 - from one week to one month
168
152
122
168
3 - from one month to three months
250
257
193
234
4 - from three to six months
176
149
134
136
5 - from six months to one year
263
212
177
140
6 - more than one year
96
195
346
274
Total
1000
1000
1000
1000
The results in Table 1 also suggest that firms react differently to different shocks.
Specifically, firms in the sample are generally quicker to react to cost shocks, in particular when they are positive, than to demand shocks. For example, the share of the firms
that do not change their prices in the first year after a positive cost shock is around
10 percent, while for a positive demand shock the corresponding share is just below 35
percent. Interestingly, firms in the sample seem to react more quickly to positive than
to negative cost shocks, but to be slower to react to positive than to negative demand
shocks.6 Formal tests for the hypotheses that the reaction time is the same both for
positive and negative shocks and for demand and cost shocks, will be performed in
Section 4.
Besides the questions on price adjustments lags, the survey also contains information
on a large set of firms’ characteristics, some of which will be used as regressors in our
model. In addition, we supplemented the survey data with information from Central
de Balanços, a comprehensive dataset maintained by Banco de Portugal in which the
balance sheets and income statements of most Portuguese firms are registered. By
combining these datasets through the individual tax identification number of each firm,
we are able to obtain detailed information on 903 firms from different sectors. More
specifically, our sample includes firms with 20 or more employees, from which almost 90
percent belong to Manufacturing (NACE - classification of economic activities - 15 to
6
Similar results concerning the relative speed of price adjustment to cost and demand shocks using
survey data were obtained for Austria, Italy, France, Luxembourg, Spain and the US (see, respectively,
Kwapil et al., 2005, Fabiani et al., 2004, Loupias and Ricart, 2004, Lünnemann and Mathä, 2006,
Alvarez and Hernando, 2005, and Blinder et al., 1998).
6
37) and the remaining to Services (NACE 60 to 64, 80 and 85 - Transport, Storage and
Communication, Education and Healthcare). Sectors such as agriculture, construction,
or wholesale and retail trade are not included.
3. A MODEL FOR PRICE ADJUSTMENT LAGS
In this section we briefly present the model used to study the determinants of the
price adjustment lags. We start by explaining how the nature of the available data
shaped the particular type of econometric model used, and then we turn to the literature on optimal price setting to guide our choice of regressors. The section concludes
with a description of the regressors used and of the rationale for including them in the
model.
3.1. The econometric model
The econometric model we use to study the determinants of the price adjustment
lags takes into account both the interval nature of the data and the fact that each
firm contributes to the sample with four observations. Specifically, we model the latent
variable  , which represents the time firm  takes to react to a shock of type , as a
function of a set of firm characteristics and of a firm-specific random-effect. Because
 is not fully observable, and due to the potential existence of reporting errors, our
model uses only the ordinal information provided by the firms. That is, the dependent
variable in our model is e = 1     6, the indicator of one of the six possible response
categories. We therefore use a panel-ordered probit model that allows for the presence
of unobserved firm-specific effects.
Because the results in Table 1 suggest that the speed of price adjustment is shock
specific, we estimate a model which allows for the possibility of different coefficients
for each type of shock, including different cut-off parameters and different variances for
the non-observed stochastic components. This is almost equivalent to estimating four
different models, one for each type of shock, with the difference being that in our case
the models are linked by the unobserved heterogeneity component, which is assumed to
7
be common to the four shocks.7 A more detailed description of the model is provided
in Appendix A.
To complete the model specification it is necessary to define the set of regressors to
use; we next turn to the literature on price stickiness for guidance on this.
3.2. Theoretical background
There is now an extensive theoretical literature aiming at explaining why prices at
the micro level may remain unchanged for large periods of time. Here, we focus on
the recent contribution by Alvarez et al. (2011) because it combines both menu and
information costs, the leading explanations for the existence of price stickiness, and
thus may be seen as encompassing most of the previous literature.8
The model of Alvarez et al. (2011) describes how firms optimally choose the time between price reviews and price changes, and how they set the optimal price as a function
of the adjustment costs. This model can be used to identify firm’s characteristics that
may be related to their degree of price stickiness. Alvarez et al. (2011) assume that:
i) the out-of-equilibrium cost for a firm may be captured by the quadratic function,
 = [() − ∗ ()]2 , where  measures the sensitivity of profits to the price gap, i.e.,
the deviation of the actual (log) price, (), from the optimal (log) price, ∗ (); ii) the
optimal (log) price follows a random walk with Gaussian innovations with variance  2
per unit of time; iii) the firm incurs in a fixed information cost, , in order to determine
the optimal price and on a fixed menu cost, , in order to change the price; and iv)
the rate of inflation, or the drift of the stochastic process ruling ∗ (), is 0 or approximately 0.9 Under these hypotheses, Alvarez et al. (2011) showed that the expected
7
Qualitatively, the results do not change if the model is estimated without the random effects or
assuming that the random effects are independent across the four equations.
8
Other relevant contributions in this field include, for instance, Barro (1972), Caballero (1989),
Dixit (1991), Bonomo and Carvalho (2004), Reis (2006), Woodford (2009), Gopinath and Itskhoki
(2010), and Bonomo et al. (2010).
9
Note that  depends on the parameters of the demand and costs functions, and that, in particular,
it is increasing with the elasticity of demand faced by the firm. The parameter 2 may be seen as
measuring the volatility of demand and cost functions.
8
time between price reviews,  , can be approximated by
v ³
³
³
´´´
u
u  + 2 1 − Φ √
t
 
= 2
,
2

(1)
where  is some threshold such that the firm opts for not adjusting the price if − 
() − ∗ ()  , and Φ (·) denotes the CDF of the standard normal distribution.
Because  appears on both sides of (1), and also because  depends on some of
the parameters, obtaining comparative statics is not a straightforward task. However,
using some of the results and assumptions in Alvarez et al. (2011), it is possible to show
that: i)  increases with the information cost (   0); ii) for small ,  increases
with the menu costs (   0); iii) for small  2 , the more volatile the optimal price
is the smaller will  be (  2  0); and iv)  decreases with the sensitivity of profits
to the price gap (   0).
One may expect the price adjustment lags for a firm following this model to be
positively correlated with the average time between price reviews,10 and therefore the
results above also give us information about the possible determinants of price adjustment lags. In the absence of direct measures for , ,  2 , and , we use as regressors
sectoral, product, and firm-level characteristics which can be seen as indirect measures
of these parameters.
3.3. The covariates
In the remainder of this section we briefly present the covariates used as indirect
measures of , ,  2 , and , and discuss how they can be linked to these parameters.11
To make clear the connection between the regressors and the parameters in the optimal
price-setting model, we group the regressors into four categories.
10
This, of course, does not imply that looking at the frequency of price changes or at the speed
of price adjustment will deliver the same conclusions about the determinants of price rigidity. The
reason for this is that, as noted by Blinder (1991), the observed frequency of price changes depends
on non-observable shocks and it does not allow one to disentangle the effects of firm characteristics
from the effects of the shocks. We avoid this problem by looking at the lags of price adjustment after
a shock rather than at the frequency of price changes which may reflect the effect of multiple shocks.
11
Appendix B provides detailed descriptions of all the regressors, as well as basic summary statistics.
9
1) Menu and information costs
In the survey there are two questions about the importance of costs related to adjusting prices and of costs related to information gathering for the purpose of reviewing
prices. We use the answers to these two questions to construct the dummy variables
Importance of menu costs and Importance of information costs, which are equal to one
if the firm considers that the corresponding cost is a very important reason to postpone
price changes.
2) Variability of the optimal price
This group includes five regressors: three variables related to the cost structure of
the firm (Share of labour costs, Share of capital costs, and Share of intermediate input
costs), and two variables related to the relation between the firm and its customers
(Explicit contracts, i.e., the proportion of sales under written contracts, and Implicit
contracts, i.e., whether the relation with the customers is essentially of a long- or
short-term nature).
If prices of different inputs have different volatilities, it is expectable that the cost
structure of a firm will matter for the variability of the optimal price. For example, if
input costs are relatively stable, such as wages which are changed on average once a
year, the variability of the optimal price will be low. On the contrary, if input costs
are volatile, as it is the case of some raw materials, the variability of the optimal price
will also be high and therefore prices are likely to be reviewed and/or changed more
frequently leading on average to faster reactions to shocks.
Economic theory suggests that the existence of explicit and/or implicit contracts
may be an important source of price stickiness at the firm level (see, for instance,
Fisher, 1977, and Okun, 1981). With explicit contracts firms aim at building long-term
relationships with their customer in order to stabilise their future sales. Customers,
on the other hand, are attracted by a constant price because it makes their future
costs more predictable and helps to minimize transaction costs (e.g., shopping time).
In turn, the theory of implicit contracts is based on the idea that firms try to win
customer loyalty by changing prices as little as possible. Overall, the presence of
explicit and/or implicit contracts may be expected to reduce firm’s demand variability
10
and thus to reduce the frequency with which prices are reviewed and/or changed,
leading on average to slower reactions to shocks.
3) Sensitivity of profits to sub-optimal prices
This group includes a set of six covariates: Competition, Price competitiveness, Quality competitiveness, Delivery competitiveness, Intermediate goods and Services.
The variable Competition identifies firms with five or more competitors. It is known
that the more competitive a sector is, the more sensitive profits are to sub-optimal
prices, i.e., the higher is  (see, for instance, Martin, 1993). Thus, ceteris paribus,
stronger competition may be expected to translate into quicker responses to shocks.
The covariates Price competitiveness, Quality competitiveness, and Delivery competitiveness distinguish firms by their competitiveness source: price, quality, and time to
deliver; these are dummy variables that are equal to one if the firm considers price, quality, or the delivery period, respectively, as very important factors of competitiveness.
We may think of the regressors identifying the competitiveness factors as reflecting
different product characteristics which translate into different demand elasticities and
thus into different values for  (higher demand elasticity for firms for which price is an
important factor, and lower elasticity for firms that emphasize the other factors).12
The two remaining variables, Intermediate goods and Services, are, respectively, dummies indicating whether the firm produces mainly for other companies and the sector
in which the firm operates. These variables are expected to have a bearing on the sensitivity of profits to the price gap because final goods and services are typically more
differentiated than manufacturing and intermediate goods, respectively, and thus face
a less elastic demands.
4) Other controls
Finally, we include a set of covariates that we believe may be related to the speed of
price adjustments through more than one of the parameters in the optimal price-setting
12
Martin (1993) showed that the speed of price adjustment increases with the elasticity of demand,
that is, firms react faster to shocks when the demand schedule facing them is flatter. This same idea
was used by Gopinath and Itskhoki (2010) to show the link between the frequency of price adjustment
and exchange rate pass-through.
11
model. The first of these variables, Size, is a dummy indicating that the firm has more
than 250 employees. This variable may be seen as a measure of the firms’ market
power (which is expected to affect ), but can also be seen as an indirect measure
of . Indeed, Zbaracki et al. (2004) have argued that the importance of information
costs is likely to be higher in large firms (see, however, Buckle and Carlson, 2000).
The remaining variables in the group are directly related to price setting practices.
These covariates (Price discrimination, Quantity discount, Price set by customers, and
Price set by competitors) identify firms that discriminate prices either by deciding the
price on a case-by-case basis or by practising quantity discounts, and firms that do not
have price autonomy (the price is set or strongly influenced by its main customers or
competitors). These variables may be related to the information and menu costs faced
by the firm, but may also reflect the competitiveness of the market in which the firm
operates and therefore may also be related to the sensitivity of the firms’ profits to
sub-optimal prices.
4. EMPIRICAL RESULTS
4.1. Between-firm heterogeneity: what explains price stickiness?
Table 2 presents the estimates of the main parameters of the panel-ordered probit
model, as well as the corresponding standard errors. For ease of presentation, we
organize the discussion of the results around the groups of regressors described before
and that correspond to the four parameters of the theoretical model in (1).13
As could be expected, the results in Table 2 show that firms for which menu costs
are important tend to adjust prices more slowly than other firms, but this effect is
statistically significant only for demand shocks. Interestingly, we find that the information costs dummy does not emerge as a statistically significant factor in explaining
differences in the price adjustment lags across firms. Given the crucial role that information costs play in theoretical models of price rigidity, this result may seem somewhat
surprising. However, it is in line with the finding that very few firms in the sample
13
Table A1 in Appendix A presents the estimation results of the remaining parameters of the model.
12
ranked information costs as an important obstacle to adjusting prices (a similar pattern
is found for the Euro area, as documented by Fabiani et al., 2006). It is important to
emphasize that although we do not find direct evidence of the importance of the information costs, our results obviously do not imply that these are not a relevant source
of price rigidity. Indeed, it may just be that in our model the effect of the information
costs is being accounted for by the other regressors that we know can be related to
these costs (Price discrimination, Quantity discount, Price set by customers, Price set
by competitors, and Size), all of which are statistically significant for at least one type
of shock.
Turning now to the indirect measures of the variability of the optimal price, our
findings confirm that, ceteris paribus, the cost structure of the firm affects the speed
of price adjustment. In particular, we see that the firms with a share of labour costs
above the median are slower to adjust to all the four shocks considered.14 However, the
coefficients on the other variables that we assumed to be informative about the variability of the optimal price (Explicit contracts and Implicit contracts) are not statistically
different from zero for either of the four shocks.
The results in Table 2 show that all the regressors that we considered to be related
to the sensitivity of firms’ profits to non-optimal prices emerge as having a significant
impact on the speed of price adjustment. Firms operating in more competitive environments, or that consider price as an important factor of competitiveness, tend to
be faster to react to shocks, while firms that emphasize the quality of the product or
the delivery period as competitiveness factors tend to adjust their prices at a slower
pace (specially so, in face of demand shocks). Our results also show that the speed of
price adjustment varies with the type of market for the product and with the sector
where firms operate. Firms that operate in the services sector are substantially slower
to react to shocks than firms that operate in the manufacturing sector: for each of
the four shocks, Services shows up as having one of the largest coefficients. In turn,
14
This is a very robust result that has been extensively documented in the literature for the frequency
of price adjustments (see, among other, Altissimo et al. 2006, and the references therein). Our results
show that the same result is valid for the speed with which firms react to shocks.
13
firms that sell their products to other firms (Intermediate goods) tend to be quicker to
adjust their prices than firms whose products are mainly for final demand (whose main
destinations are wholesalers, retailers or consumers). These results are consistent with
previous evidence on the frequency of price changes which suggested a significantly
higher degree of price stickiness in the services sector and also that producer prices are
changed more frequently than consumer prices.
The remaining regressors also emerge as having significant impacts on price adjustment lags. In particular, our results indicate that whether or not firms follow a single
price policy has important consequences for the speed of price adjustment: firms that
decide the price on a case-by-case basis, or do quantity discounts, tend to be faster
to adjust to both cost and demand shocks. The speed of price adjustment also varies
with the differences in the price autonomy of the firm: Price set by customers has
a positive and significant impact in the case of positive cost shocks, suggesting that
for these firms customers have enough power to delay the firms’ reaction when costs
push prices up. Regarding Price set by competitors, our results show that firms that
have their prices significantly affected by the main competitors are faster to respond
to demand shocks than firms that set their own prices. This suggests that firms whose
prices are set by the main competitors may be acting as market followers in a market
where the presence of market leaders helps reducing potential coordination problems.
Finally, our results also suggest that size matters for the speed of price adjustment:
in the face of cost shocks, large firms tend to be slower at adjusting their prices than
small firms.
In summary, the results in Table 2 can be interpreted as confirming that optimal
price-setting models such as the one presented by Alvarez et al. (2011) provide an
adequate description of the forces determining how firms choose the degree of price
stickiness. Perhaps more importantly, our results also suggest that the degree of price
stickiness varies substantially across firms and depends on firm’s characteristics such
as the menu costs, the cost structure, the type of good, and the degree of competition.
The implications of these results will be further explored below.
14
Table 2: Panel-ordered probit estimates for the price adjustment lags (main results)
Cost shocks
Demand shocks
Covariates
Positive
Negative
Positive
Negative
∗∗∗
∗∗∗
∗∗∗
Constant
3091
4184
3192
3485∗∗∗
(0298)
(0412)
(0294)
(0350)
Importance of menu costs
0198
0274
0547∗∗∗
0580∗∗
Importance of information costs
0389
0036
0069
0038
Labour costs
0370∗∗∗
0352∗∗
0407∗∗∗
0507∗∗∗
Intermediate input costs
−0234∗
−0268∗
−0029
(0121)
−0065
0026
0021
Menu and information costs:
(0198)
(0240)
(0287)
(0196)
(0349)
(0276)
(0227)
(0324)
Variability of the optimal price:
(0122)
(0127)
(0149)
(0154)
∗∗
(0117)
(0139)
(0142)
Capital costs
0145
Explicit contracts
0084
0018
0099
0151
Implicit contracts
−0145
−0129
0088
(0149)
(0183)
(0142)
−0211
−0423∗∗∗
−0446∗∗∗
−0311∗∗
−0380∗∗
0272
(0110)
(0135)
(0128)
(0155)
(0105)
(0123)
(0122)
(0143)
(0169)
Sensitivity of profits to the price gap:
Competition
(0132)
Price competitiveness
−0051
(0113)
∗∗
Quality competitiveness
0258
Delivery competitiveness
−0093
(0129)
(0111)
Intermediate goods
Services
∗∗
(0161)
∗
(0126)
∗∗
−0266
−0236
0204
0301
0450∗∗∗
−0104
0247
0260
−0366
(0139)
(0158)
(0135)
∗∗∗
(0109)
∗∗
(0123)
∗∗
(0106)
∗∗∗
−0262
−0430
−0401
1057
1149
0584
(0123)
∗∗∗
(0204)
(0149)
∗∗∗
(0150)
∗∗∗
(0254)
(0117)
∗∗∗
(0196)
−0433
(0129)
(0147)
∗∗
(0125)
∗∗∗
(0139)
0982∗∗∗
(0233)
Other controls:
Price discrimination
−0444∗∗∗
(0160)
−0444∗∗
(0195)
−0586∗∗∗
(0155)
−0694∗∗∗
Quantity discount
−0464∗∗∗
−0357∗∗
−0382∗∗∗
−0424∗∗
−0162
0139
(0222)
(0173)
−0121
Price set by customers
(0152)
∗∗∗
0471
(0183)
∗∗
(0185)
(0147)
(0183)
(0173)
(0205)
Price set by competitors
0325
−0074
−0381∗∗
−0635∗∗∗
Size
0417
0599∗∗∗
−0101
0192
(0164)
∗∗∗
(0158)
(0199)
(0195)
(0155)
(0150)
(0184)
(0178)
Standard errors computed from analytical second derivatives are in parenthesis; ***marks
significance at 1% level, **marks significance at 5% and *marks significance at 10% level.
15
4.2. Within-firm heterogeneity: symmetric or asymmetric lags?
As discussed before, the results in Table 1 suggest that firms may react differently to
different types of shocks. Moreover, the results in Table 2 show that there are substantial differences between the parameters of the four equations,15 which also suggests the
existence of within-firm heterogeneity, that is, that a firm may have different reactions
to different types of shocks. The possible existence of firm-level asymmetric price rigidity is a relevant issue because it has consequences for the relationship between inflation
and aggregate demand, and thus may have important implications for monetary policy.
There is now a vast theoretical literature that focuses on the question of whether
prices are stickier in response to a shock that warrants a price decrease or to shocks
in the opposite direction, or whether prices react more quickly to cost or to demand
shocks. A survey of this literature tells us that there are many possible justifications
for the existence of differences between the speed of adjustment to different types of
shocks, but there seems to be no consensus about the sign and magnitudes of these
differences.16
Based on the argument that wages are flexible upwards but rigid downwards, some
literature favours the idea that prices are stickier downwards than upwards. If this is the
case, the relationship between inflation and aggregate demand (Phillips curve) must
be non-linear, calling for asymmetric monetary policy rules. In particular, negative
monetary policy shocks (interest rate increases) must be larger when inflation is above
target than positive shocks (interest rate cuts) when inflation is below target (see,
e.g., Laxton et al., 1994, Laxton et al., 1999, Dolado et al., 2004, Dolado et al., 2005,
and Dobrynskaya, 2008). However, if prices react faster to negative than to positive
15
16
See also Table A1 in Appendix A.
For models of aymmetric price reactions to positive and negative shocks, see, among many others,
Okun (1981), Maskin and Tirole (1988), Tsiddon (1993), Ball and Mankiw (1994), Hansen et al.
(1996), Kovenock and Widdows (1998), Bhaskar (2002), Rotemberg (2005), Ellingsen et al. (2006),
Devereux and Siu (2007), Chen et al. (2008), Yang and Ye (2008), Tappata (2009), Anderson and
Simester (2010), Lewis (2011), and Cabral and Fishman (2012).
16
demand shocks, things may be expected to work the other way around. The conclusions
in Buckle and Carlson (1996) and Fabiani et al. (2006) favour this alternative view.
In the context of our model, the existence of within-firm heterogeneity can be investigated formally by testing restricted models imposing symmetry, against the unrestricted model we have estimated. These tests can be easily implemented as tests of
the significance of the differences between the shock-specific parameters in the different
equations; we consider both differences within shocks (differences in the responses to
positive and negative cost shocks and positive and negative demand shocks) and the
difference between shocks (differences in the responses to positive shocks to costs and
demand and to negative shocks to costs and demand).
Table 3 presents the results of the four tests; in all cases the null of symmetry is
rejected at all usual significance levels. These results, therefore, strongly suggest that
firms react differently to negative and positive shocks, and to cost and demand shocks.
In order to investigate how price stickiness varies with the type of shock, we used
the estimated econometric model to compute, for each firm in the sample and for each
shock, the probability that it takes more than a year for the firm to adjust its price;17
then we computed the differences between these probabilities for each pair of shocks.
As before, we consider both the differences within shocks and the differences between
shocks.
Table 3 - Tests of symmetry
Symmetry within shocks
Symmetry between shocks
Positive and
Positive and
Positive cost
Negative cost
negative
negative
and demand
and demand
cost shocks
demand shocks
shocks
shocks
2
2
2
2
 (24) = 9029  (24) = 7718  (24) = 30064  (24) = 9449
( = 0000)
( = 0000)
( = 0000)
( = 0000)
2
 (24) stands for the Wald test statistic with 24 degrees of freedom and  for
the corresponding p-value.
17
We focus on the category e = 6 (i.e., price adjustment does not take place in the first year after
the shock) because it is more meaningful than the category e = 1 (see Table 1), and it is well known
that in models for ordered data only the results for the first and last categories can be unambiguously
interpreted; see, e.g., Winkelmann and Boes (2006).
17
9
9
8
Cost shock
8
7
5
4
4
3
3
2
2
1
1
0
‐0.5
‐0.4
Negative shock
6
5
‐0.6
Positive shock
7
Demand shock
6
Differences in the probabilities between shocks cost ‐ demand shocks
10
Differences in the probabilities within shocks positive ‐ negative shocks
10
‐0.3
‐0.2
‐0.1
0.0
0.1
0
0.2
‐0.6
Differences in probabilities
‐0.5
‐0.4
‐0.3
‐0.2
‐0.1
0.0
0.1
0.2
Differences in probabilities
Fig 1: Distribution of differences between probabilities for the category e = 6.
Figure 1 presents the distribution of these differences in our sample, revealing that,
for the majority of firms, prices adjust more quickly upwards than downwards following
cost shocks, but more slowly upwards than downwards in reaction to demand shocks
(differences in probabilities are mostly negative in the first case and mostly positive in
the second). Also, the majority of firms tend to be faster to respond to cost than to
demand shocks either positive or negative.18 In addition, Figure 1 also shows that there
is a high degree of heterogeneity in the size and even in the direction of the asymmetry.
In fact, a non negligible mass of firms adjust prices more quickly downwards than
upwards following cost shocks and more slowly downwards than upwards in reaction
to demand shocks.
The results regarding the asymmetry between positive and negative cost shocks for
the majority of firms in the sample are consistent with the predictions of a model with
18
Similar results concerning the relative speed of price adjustment to cost and demand shocks using
survey data were obtained for Austria, Italy, France, Luxembourg, Spain and the US (see, respectively,
Kwapil et al., 2005, Fabiani et al., 2004, Loupias and Ricart, 2004, Lünnemann and Mathä, 2006,
Alvarez and Hernando, 2005, and Blinder et al., 1998). Comparable results for positive and negative
cost shocks were obtained by Peltzman (2000), for the U.S., and by Loupias and Sevestre (2013), for
France.
18
menu costs and trend inflation (see Tsiddon, 1993, Ball and Mankiw, 1994, Ellingsen
et al., 2006), with a model that incorporates search costs or consumer inattentiveness (Chen et al., 2008, Yang and Ye, 2008, Tappata, 2009, Lewis, 2011, Cabral and
Fishman, 2012), and with the predictions of some models considering firms’ strategic
behaviour (e.g., Devereux and Siu, 2007). However, it is at odds with the predictions
of the oligopoly models with kinked demand curves of the type considered by Maskin
and Tirole (1988), which suggest that firms may react more quickly to negative than
to positive shocks, as is the case of a smaller share of firms in the sample.
In turn, the finding that the majority of firms in the sample react faster to negative
than to positive demand shocks is consistent with a model where customer anger is
taken into consideration (Okun, 1981, Anderson and Simester, 2010), but could have
not been anticipated, for instance, by menu-cost models with positive trend inflation.
However, the latter models will be able to explain the behaviour of the firms for which
the adjustment is faster after a positive than after a negative demand shock.
Finally, the results regarding the asymmetry between cost and demand shocks —
which show that most firms in the sample react faster to cost than to demand shocks
— are consistent with models of customer anger or fair pricing. These models predict
that consumers will more easily accept a price increase caused by a change in costs
than a price increase that is caused by an increase in demand.
Some important conclusions emerge from the analysis in this subsection. First, there
is evidence of significant asymmetries in the speed of price responses to positive and
negative demand and cost shocks. Second, for the majority of firms, prices adjust
more quickly upwards than downwards following cost shocks, but more slowly upwards
than downwards in reaction to demand shocks. However, there is a non negligible
mass of firms for which the asymmetry is the other way around. Third, there does
not seem to be a single theoretical model that can explain all the different results we
obtained. Finally, as regards the implications for monetary policy, our results show
that asymmetries with different signs can coexist in the same economy and, therefore,
the reaction to monetary policy shocks may depend on which firms or sectors are
particularly affected by them.
19
5. SUMMARY AND CONCLUDING REMARKS
This paper uses survey data to study the length of price adjustment lags in reaction
to positive and negative demand and cost shocks. Price adjustment lags are a direct
measure of price rigidity and therefore are a better measure of price stickiness than
the commonly used frequency of price changes, which is expected to also depend on
the number and magnitude of the shocks that affect the optimal price during the
observation period. Moreover, the survey data we use has the advantage of providing
information on the reaction time to different types of shock, and therefore allows us to
study both between- and within-firm heterogeneity.
We find evidence that the degree of price stickiness is influenced by variables that can
be construed as measuring the importance of menu costs, the variability of the optimal
price, and the sensitivity of profits to sub-optimal prices, which are key ingredients
in standard optimal price-setting models, such as the ones suggested in Barro (1972),
Caballero (1989), or Alvarez et al. (2011). More specifically, we find that the lags of
price adjustments vary with the firm, market and product, characteristics, such as the
menu costs, the cost structure of the firm, the competitive environment, or the type of
good.
We also find evidence of the existence of asymmetries in the speed with which firms
adjust their prices in response to positive and negative demand or cost shocks. In line
with similar evidence reported in the empirical literature, most firms in our sample
seem to react faster to positive than to negative cost shocks, and more quickly to
negative than to positive demand shocks. However, we also find that the direction
and magnitude of these asymmetries vary both across firms and with the type of
shock in a way that cannot be explained by any single existing theoretical model of
asymmetric price behaviour. This suggests that more eclectic models are needed to
better understand this phenomenon.
Our results on within- and between-firm heterogeneity in the speed of price reactions
to shocks have important implications for macroeconomic models and for the understanding of the effects of monetary policy. First, the evidence on price stickiness being
20
optimally set by firms in response to market conditions and the firms’ specific characteristics suggests that it may be important for monetary models to try to accommodate
the fact that price stickiness may change in response to changes in the economic structure as well as to monetary policy itself. Second, the fact that firms react differently
to different types of shocks has the implication that the relationship between inflation and aggregate demand (Phillips curve) must be non-linear, calling for asymmetric
monetary policy rules. However, in contrast to most of the theoretical literature which
tends to favour the idea that prices are stickier downwards than upwards, the evidence
obtained in this study suggests that the type of asymmetry prevailing at the aggregate
level may depend on the relative importance of different types of firms in the economy
and on how they are affected by the monetary policy shocks. Therefore, whether the
relation between inflation and aggregate demand is linear, concave, or convex is still
an open issue and thus more empirical evidence is required before definite conclusions
can be drawn on this matter.
ACKNOWLEDGEMENTS
We are most grateful to the Editor Christopher Bowdler and to an anonymous referee
for their many insightful and helpful suggestions. We also thank Nuno Alves, Mário
Centeno, Ana Cristina Leal, José Ferreira Machado, Stefan Niemann, and Pedro Portugal for helpful discussions and useful suggestions. The opinions expressed in this
paper are those of the authors and do not necessarily coincide with those of Banco de
Portugal or the Eurosystem. Daniel Dias and João Santos Silva gratefully acknowledge
the partial financial support from Fundação para a Ciência e Tecnologia, (Programme
PEst-OE/EGE/UI0491/2013). The usual disclaimer applies.
21
APPENDIX A
In this appendix we explain in detail the panel-ordered probit with random effects
introduced in Section 3.
We are interested in modelling the response of each firm to four different shocks.
These four responses are likely to depend on common unobserved firm characteristics, suggesting the use of a panel data set-up in which the four seemingly unrelated
equations are linked by a common random effect representing the unobserved firm
characteristics. However, because we let different covariates have different coefficients
in different equations, we allow the impact of the random effects to be shock-specific.
Besides providing potential efficiency gains, the inclusion of the random effects with
a flexible distribution makes the model more general and therefore less sensitive to
distributional assumptions.
The resulting model is very similar to a standard ordered probit with the only difference being the fact that we take into account the panel structure of the data. As
in the common ordered probit, we assume that there is a latent variable,  , which
represents the time firm  takes to react to a shock of type . Recall that the different
types of shocks are: 1) positive demand shock; 2) positive cost shock; 3) negative demand shock; and 4) negative cost shock. We also assume that  is related to a set of
firm characteristics by
¡
¢
 = Λ 0   +    +  
(A1)
where Λ (·) is a strictly increasing invertible function that is specific to shocks of type
;  is a set of firm characteristics whose impact, measured by vectors   , is shock
specific;  is a non-observed firm-effect whose impact, measured by   , is shock specific;
and  is a non-observed stochastic term that is firm and shock specific.
Equation (A1) implies that  = Λ−1
 ( ) is related to the firm characteristics by
the linear model
 = 0   +    +  
22
In our data,  is not fully observed and instead we observe e , which is related to
 as follows. For  = 1 2     6
e = 

−1     ,
(A2)
where the constants  are the limits of the intervals into which the domain of  is
partitioned due to the fact that  is observed as interval data.
At this point, two approaches can be followed. Because the price lags are reported
in the form of known time intervals, we could specify the form of Λ (·) and use this
information to determine the cut-off parameters  . Alternatively, we can estimate
the cut-off parameters, which avoids the need to specify Λ (·). This is the approach
we follow because by not specifying Λ (·) the model gains an interesting degree of
flexibility. Specifically, for identification purposes, we set 0 = −∞, 1 = 0, and
6 = +∞, estimating freely the remaining four cut-off parameters.
In order to be able to estimate the parameters of the model, we need to make distributional assumptions on the unobserved random components. We start by assuming
that  |   ∼  (0 1), where the normalization of the variance to 1 implies no loss
of generality. Then, based on (A2), the conditional probability of observing e = 
is given by
Pr (e
 = |   ) = Pr (−1 ≤    |   )
= Pr (   |   ) − Pr ( ≤ −1 |   )
¡
©
¢
ª
= Φ  − 0   +    |   −
¡
¢
ª
©
Φ −1 − 0   +    |  
=  (e
 |   ) 
where, as before, Φ (·) denotes the normal distribution function.
Assuming
that the disturbances  are conditionally independent (given  and  ) across
 and , we can write the probability that for a certain firm we observe
(e
1 = 1  e2 = 2  e3 = 3  e4 = 4 ) as
Pr (e
1 = 1  e2 = 2  e3 = 3  e4 = 4 |   ) =
23
4
Y
=1
 (e
 |   ) 
Since we also do not observe  , we need to integrate it out of  (e
 |   ) in order
to obtain an expression of the individual contribution to the likelihood that can be
used for estimation. This expression corresponds to
Z +∞ Y
4
 () =
 (e
 |   )  ( )  
−∞ =1
where  denotes the vector of parameters of the model and  (·) is the density function
of  .19 Following Dhaene and Santos Silva (2012), we assume that  ( ) is such that
sinh−1 ( )  has a standard normal distribution.20 That is, the shape-parameter 
introduces additional flexibility in the model by allowing the distribution of the random
effect component to have an unspecified degree of excess kurtosis.
Table A1 presents the estimates of 2      4 and   for  = 1     4, as well as
the estimate for , which indicates that the random-effects have a distribution with
substantial excess kurtosis.
Table A1: Additional estimation results
Cost shocks
Demand shocks
Parameters Positive Negative Positive Negative
2
1447∗∗∗ 1481∗∗∗ 1360∗∗∗ 1572∗∗∗
(0114)
(0169)
(0125)
(0129)
3
2613∗∗∗
3297∗∗∗
2408∗∗∗
2848∗∗∗
4
3396
4104
2983
3545
5
4996
5354
3664
4263∗∗∗

1054
1430
0936
1262
(0139)
∗∗∗
(0159)
∗∗∗
(0207)
∗∗∗
(0088)
(0226)
∗∗∗
(0262)
∗∗∗
(0316)
∗∗∗
(0133)
(0147)
∗∗
(0158)
∗∗∗
(0172)
∗∗∗
(0080)
∗∗∗
(0171)
∗∗∗
(0195)
(0222)
∗∗∗
(0108)
−0611

(0098)
Standard errors computed from analytical second derivatives
are in parenthesis; ***marks significance at 1% level, **marks
significance at 5% and *marks significance at 10% level.
APPENDIX B
In this Appendix we describe the covariates used in the ordered probit model whose
results are presented in Section 4, and provide the corresponding summary statistics.
All the covariates used in the model are dummy variables. The details are as follows:
19
20
In the application, the integration was performed using 50-point Gauss-Hermite integration.
The use of this sort of transformation was pioneered by Burbidge, Magee and Robb (1988).
24
Importance of menu costs - Equal to one if menu costs implied by price changes are
ranked by the firm as a very important factor to postpone price changes.
Importance of information costs - Equal to one if the costs involved in collecting
the relevant information for price decisions are ranked by the firm as a very important
factor to postpone price changes.
Labour costs — Equal to one if the labour cost share is above the median of the
sample.
Intermediate input costs — Equal to one if the other input costs share is above the
median of the sample.
Capital costs — Equal to one if the capital costs share is above the median of the
sample.
Explicit contracts — Equal to one if the percentage of sales under written contracts
is larger than 50 percent of total sales.
Implicit contracts — Equal to one if the relationship with customers is essentially a
long-term one (more than one year).
Competition — Equal to one if the number of firm’s competitors is equal to 5 or
larger.
Price competitiveness — Equal to one if the firm considers price as a very important
factor for competitiveness.
Quality competitiveness — Equal to one if the firm considers quality as a very important factor for competitiveness.
Delivery competitiveness — Equal to one if the firm considers delivery period as a
very important factor for competitiveness.
Intermediate goods — Equal to one if “other companies” is the main destination of
sales (as opposed to wholesalers, retailers, Government, consumers).
Services — Equal to one if the firm operates in the Services sector.
Price discrimination — Equal to one if the price of the firm’s product is decided on
a case-by-case basis.
Quantity discount — Equal to one if the price depends on the quantity sold but
according to a uniform price list.
25
Price set by customers — Equal to one if the price of the product is set by the firm’s
main customer(s).
Price set by competitors — Equal to one if the price of the product is set by the firm’s
main competitor(s).
Size — Equal to one if the number of employees is larger than 250.
Table B1 displays the share of firms in each category. For instance, from the Table
we see that around 83 percent of firms have implicit contracts, i.e., they have an
essentially long-term relationship with customers, and that the distribution of implicit
contracts is relatively homogeneous across sectors and does not vary much with the
size of firms. In contrast, only in about 25 percent of the firms do formal contracts
account for 50 percent or more of total sales (Explicit contracts), and its distribution
varies significantly across sectors and firms’ size.
Table B1: Share of firms in each category in percentage
Sectors
Firms’ size
Total Manufacturing Services Small Large
Importance of menu costs
8.0
8.1
6.7
8.3
6.0
Importance of information costs
4.2
4.3
3.3
4.5
2.3
Labour costs
50.1
48.6
63.3
51.2
43.6
Intermediate input costs
50.1
55.6
0.0
49.7
51.9
Capital costs
50.1
51.4
37.8
50.5
47.4
Explicit contracts
25.5
23.9
40.0
23.6
36.1
Implicit contracts
82.6
83.3
76.7
81.9
86.5
Competition
76.0
74.8
86.7
79.0
58.6
Price competitiveness
59.5
61.4
42.2
59.2
60.9
Quality competitiveness
77.0
76.4
82.2
76.1
82.0
Delivery competitiveness
51.1
51.7
45.6
50.0
57.1
Intermediate goods
30.9
30.6
33.3
31.8
25.6
Services
10.0
0.0
100.0
9.6
12.0
Price discrimination
37.4
38.3
30.0
37.8
35.3
Quantity discount
41.0
42.2
30.0
40.8
42.1
Price set by customers
11.8
11.9
11.1
11.0
16.5
Price set by competitors
12.4
13.0
6.7
13.8
4.5
Size
14.7
14.4
17.8
0.0
100.0
26
REFERENCES
Altissimo, F., Ehrmann, M., Smets, F., 2006. Inflation persistence and price-setting
behaviour in the euro area. A summary of the IPN evidence. European Central
Bank, Occasional paper series No. 46.
Alvarez, L.J., Hernando, I., 2005. The price setting behaviour of Spanish firms:
evidence from survey data. European Central Bank, Working Paper No. 538.
Alvarez, F., Lippi, F., Paciello, L., 2011. Optimal price setting with observation and
menu costs. Quarterly Journal of Economics, 126, 1909-1960.
Anderson, E.T., Simester, D. I., 2010. Price stickiness and customer antagonism.
Quarterly Journal of Economics, 125, 729-765.
Ball, L., Mankiw, N.G., 1994. Asymmetric price adjustment and economic fluctuations. Economic Journal, 104, 247-261.
Barro, R.J., 1972. A theory of monopolistic price adjustment. Review of Economic
Studies, 39, 17-26.
Bhaskar, V., 2002. Asymmetric price adjustment: Micro-foundations and macroeconomic implications. University of Essex, Discussion Paper No. 547.
Bils, M., Klenow, P.J., 2004. Some evidence on the importance of sticky prices.
Journal of Political Economy, 112, 947-985.
Blinder, A.S., 1991. Why are prices sticky? Preliminary results from an interview
study. American Economic Review, 81, 89-96.
Blinder, A.S., Canetti, D.E., Lebow, D.E., Rudd, J.B., 1998. Asking about prices: a
new approach to understanding price stickiness. Russel Sage Foundation, New
York.
Bonomo, M., Carvalho, C., 2004. Endogenous time-dependent rules and inflation
inertia. Journal of Money, Credit and Banking, 36, 1015-1041.
Bonomo, M., Carvalho, C., Garcia, R., 2010. State-dependent pricing under infrequent information: A unified framework. Federal Reserve Bank of New York,
Staff Report no. 455.
Buckle, R.A., Carlson, J.A., 1996. Inflation an Asymmetric Price Adjustment, Papers 96-013, Purdue University, Krannert School of Management - Center for
International Business Education and Research (CIBER).
27
Buckle, R.A., Carlson, J. A., 2000. Menu costs, firm size and price rigidity. Economics
Letters, 66, 59-63.
Burbidge, J.B., Magee, L., Robb, A.L., 1988. Alternative transformations to handle
extreme values of the dependent variable. Journal of the American Statistical
Association, 83, 123-127.
Caballero, R.J., 1989. Time dependent rules, aggregate stickiness and information
externalities. Columbia University Discussion Paper 60(11).
Cabral, L., Fishman, A., 2012. Business as usual: A consumer search theory of sticky
prices and asymmetric price adjustment. International Journal of Industrial Organization, (forthcoming).
Chen, H., Levy., D., Ray, S., Bergen, M., 2008. Asymmetric price adjustment in the
small. Journal of Monetary Economics, 55, 728-737.
Carvalho C., 2006. Heterogeneity in price stickiness and the real effects of monetary
shocks. The B. E. Journal of Macroeconomics, 6, 1-58.
Devereux, M.B., Siu, H.E., 2007. State dependent pricing and business cycle asymmetries. International Economic Review, 48, 281-310.
Dhaene G., Santos Silva, J.M.C., 2012. Specification and Testing of Models Estimated
by Quadrature. Journal of Applied Econometrics, 27, 322—332.
Dhyne, E., Alvarez, L., Le Bihan, H., Veronese, G., Dias, D., Hoffmann, J., Jonker,
N., Lunnemann, P., Rumler, F., Vilmunen, J., 2006. Price Changes in the Euro
Area and the United States: Some Facts from Individual Consumer Price Data.
Journal of Economic Perspectives, 20, 171-192.
Dhyne, E., Fuss, C., Pesaran, H., Sevestre, P., 2011. Lumpy price adjustments: a
microeconomic analysis. Journal of Business & Economics Statistics, 29, 529540.
Dixit, A., 1991. Irreversible investment with price ceilings. Journal of Political Economy, 99, 541-557.
Dobrynskaya, V.V., 2008. Asymmetric price rigidity and the optimal interest rate defence of the exchange rate: Some evidence for the US. Journal of Policy Modeling,
30, 713-724.
28
Dolado, J., Maria-Dolores, R., Naveira, M., 2005. Are monetary-policy reaction functions asymmetric? The role of nonlinearity in the Phillips curve. European Economic Review, 49, 485-503.
Dolado, J., Pedreiro, R. M-D., Ruge-Murcia, F. J., 2004. Nonlinear monetary policy rules: Some new evidence for the U.S. Studies in Nonlinear Dynamics &
Econometrics, Volume 8, Issue 3, Article 2.
Druant, M., Fabiani, S., Kezdi, G., Lamo, A., Martins, F. and Sabbatini, R., 2012.
Firms’ price and wage adjustment in Europe: Survey evidence on nominal stickiness. Labour Economics, 19, 772-782.
Ellingsen, T., Friberg, R., Hassler, J., 2006. Menu costs and asymmetric price adjustment. CEPR, Discussion Paper No. 5749.
Fabiani, S., Gatulli, A., Sabbatini, R., 2004. The pricing behaviour of Italian firms:
New survey evidence on price stickiness. European Central Bank, Working Paper,
No. 333.
Fabiani, S., Druant, M., Hernando, I., Kwapil, C., Landau, B., Loupias, C., Martins,
F., Mathä, T., Sabbatini, R., Stahl, H., and A. Stokman. 2006. What firms’
surveys tell us about price-setting behavior in the Euro Area. International
Journal of Central Banking, Vol. 2, Number 3, September.
Fisher, S., 1977. Long-term contracts, rational expectations and the optimal money
supply rule. Journal of Political Economy, 85, 191-205.
Gopinath, G., Itskhoki, O., 2010. Frequency of price adjustment and pass-through.
Quarterly Journal of Economics, 125, 675-727.
Hansen, R.S., Mollgaard, H.P., Overgaard, P.B., Sorensen, J. R., 1996. Asymmetric
adjustment in symmetric duopoly. Economics Letters, 53, 183-188.
Klenow, P. and Malin, B., 2011. Microeconomic Evidence on Price-Setting, in the
Handbook of Monetary Economics 3A, B. Friedman and M. Woodford ed.: Elsevier, 231-284.
Klenow, P.J., Kryvtsov, O., 2008. State-dependent or time-dependent pricing: Does
it matter for recent US inflation?. The Quarterly Journal of Economics, 123,
863-904.
29
Kovenock, D., Widdows, K., 1998. Price leadership and asymmetric price rigidity.
European Journal of Political Economy, 14, 167-187.
Kwapil, C., Baumgartner, J., Scharler, J., 2005. The price-setting behavior of Austrian firms: some survey evidence. European Central Bank, Working Paper No.
464.
Laxton, D., Meredith, G., Rose, D., 1994. Asymmetric effects of economic activity on
inflation - Evidence and policy implications. IMF Working Paper No. 139-EA.
Laxton, D., Rose, D., Tambakis, D., 1999. The U.S. Phillips curve: The case for
asymmetry. Journal of Economics Dynamics and Control, 23, 1459-1485.
Lewis, M., 2011. Asymmetric price adjustment and consumer search: An examination
of the retail gasoline market. Journal of Economics & Management, 20, 409-449.
Loupias, C., Ricart, R., 2004. Price setting in France: New evidence from survey
data. European Central Bank, Working Paper No. 423.
Loupias, C., Sevestre, P. 2013. Costs, Demand, and Producer Price Changes. The
Review of Economics and Statistics, 95, 315-327.
Lucas, R. E. Jr, 1973. Some international evidence on output-inflation tradeoffs. The
American Economic Review, 63, 326-334.
Lünnemann, P., Mathä, T., 2006. New survey evidence on the pricing behaviour of
Luxembourg firms. European Central Bank, Working Paper No. 617.
MacKinnon J.G., Magee, L. 1990. Transforming the dependent variable in regression
models. International Economic Review, 31, 315-339.
Mackowiak, B., Wiederholt, M., 2009. Optimal sticky prices under rational inattention. The American Economic Review, 99, 769-803.
Martin, C., 1993. Price adjustment and market structure. Economics Letters, 41,
139-143.
Martins, F., 2005. Pricing behaviour in Portugal: Evidence from survey data. Banco
de Portugal, Economic Bulletin, Summer, 49-68.
Martins, F., 2010. Price stickiness in Portugal: Evidence from survey data. Managerial and Decisions Economics, vol. 31, issue 2-3, 123-134.
Maskin, E., Tirole, J.,1988. A theory of dynamic oligopoly II: Price competition,
kinked demand curves, and Edgeworth cycles. Econometrica, 56, 571-599.
30
Munnick, D., Xu, K., 2007. Micro foundations of price-setting behaviour: Evidence
from Canadian firms. Bank of Canada, Working Paper 2007-31.
Nakamura, E., Steinsson, J. 2008. Five facts about prices: a reevaluation of menu
cost models. The Quarterly Journal of Economics, 123, 1415-1464.
Okun, A., 1981. Prices and Quantities: A macroeconomic Analysis. The Brookings
Institution, Washington D.C.
Peltzman, S., 2000. Prices rise faster than they fall. Journal of Political Economy,
108, 466-502.
Reis, R., 2006. Inattentive producers. Review of Economic Studies, 73, 793-821.
Rotemberg, J., 2005. Customer anger at price increases, changes in the frequency
of price adjustment and monetary policy. Journal of Monetary Economics, 52,
829-852.
Small, I., Yates, T., 1999. What makes prices sticky? Some survey evidence for the
United Kingdom. Bank of England Quarterly Review, 39, 262-271.
Tappata, M., 2009. Rockets and feathers: understanding asymmetric pricing. RAND
Journal of Economics, 40, 673-687.
Tsiddon, D., 1993. The (Mis)Behaviour of the aggregate price level. The Review of
Economic Studies, 60, 889-902.
Vermeulen, P., Dias, D., Dossche, M., Gautier, E., Hernando, I., Sabbatini, R., Stahl,
H., 2012. Price setting in the euro area: some stylised facts from individual
producer price data. Journal of Money Credit and Banking, 44, 1631-1650.
Winkelmann, R., and Boes, S. 2006. Analysis of microdata. Springer, Berlin.
Woodford, M., 2009. Information-constrained state-dependent pricing. Journal of
Monetary Economics, 56, Supplement: S100-S124.
Yang, H., Ye, L., 2008. Search with learning: Understanding asymmetric price adjustments. RAND Journal of Economics, 39, 547-564.
Zbaracki, M.J., Ritson, M., Levy, D., Dutta, S., and Bergen, M., 2004. Managerial
and customer costs of price adjustment: direct evidence from industrial markets,
The Review of Economics and Statistics, 86, 514-533.
31