Ination and price adjustments: micro evidence
from Norwegian consumer prices 19752004
∗
Fredrik Wulfsberg
†
Oslo and Akershus University College of Applied Sciences
May
29, 2015
Abstract
This is the rst paper documenting the frequency and size of price ad
justments using micro data from both the high-ination period in the 1970s
and 80s, and the period of low-ination since the early 1990s. This evidence
is highly relevant for the current discussion of optimal ination level. When
ination is high and volatile, prices change more frequently and in smaller mag
nitudes. When ination is low and stable, prices change less frequently but in
larger magnitudes. Decomposing the variation in ination into variation in the
frequency and magnitude of price changes, I nd that the frequency of price
changes is more important for the variation in ination when ination is high
and volatile and during the transition from high to low ination. When ina
tion is low and stable, however, the magnitude of the price changes is more
important than the frequency.
jel: E31, E32
Keywords: Consumer prices, price rigidity, ination
I wish to thank Statistics Norway for providing data and giving invaluable comments. I am
grateful to Alf Erik Ballangrud and Ingvil Benterud Gaarder for excellent research assistance, and
to the Federal Reserve Bank of Boston for their hospitality. I thank editor John Leahy, the refer
ees and in particular Steinar Holden for valuable comments. Carlos Carvalho, Huw Dixon, Etienne
Gagnon, Mike Golosov, Gisle Natvik, Roberto Rigobond, Julio Rotemberg, Asbjørn Rødseth, Kjetil
Storesletten, and Alexander Wolman gave useful comments to earlier drafts as did seminar partici
pants at the Federal Reserve Bank of Boston, ntnu, University of Oslo, and bi Norwegian Business
School.
†
School of Business, Oslo and Akershus University College of Applied Sciences, PO Box 4 St.
Olavs plass, 0130 Oslo, Norway. email: [email protected], url: https://sites.
google.com/site/fredrikwulfsberg/.
∗
This paper is a study of how price adjustments at the micro level vary with ination,
30
using an unprecedented data set spanning
period in the
1990s.
1970s
and
1980s,
years including both the high-ination
as well as the period of low ination since the early
Following Bils and Klenow (2004) many empirical studies have documented
prices adjustments using micro data for a large number of individual goods in several
1
countries.
Most of these studies use data from the recent period of relatively low and
stable ination. Klenow and Kryvtsov (2008) and Nakamura and Steinsson (2008)
investigated
us
data from
standard deviation was
from
19962001
deviation of
19882004
when annual ination rate was
and the
1.1%, and Dhyne et al. (2006) analyzed 10 euro area countries
where average annual ination rate was only
0.1%.
3.3%
1.7%
with a standard
The small amount of ination variability in these samples prevents
drawing strong conclusions regarding how price adjustments covary with ination. In
addition these studies yield dierent results regarding how price adjustments change
with ination.
The data used in this paper covers a much longer period than any other study,
allowing a more thorough analysis of the comovement between ination and the
frequency and size of prices adjustments. I document the frequency and size of price
adjustments using a high-quality dataset of more than
14 million monthly retail price
cpi) between 1975 and 2004.
quotes from the Norwegian consumer price index (
sample length is unrivaled and splits nicely into a high-ination period from
to
1989
and a low-ination period from
1990
to
2004.
As in other
oecd
The
1975
countries
cpi ination in Norway was high and volatile during the Great Ination years in the
1970s and 1980s with an average annual cpi ination rate of 8.4% and a standard
deviation of
2.7%.
Norway's ination rate peaked at
ination decreased during the
2.4%
1980s
and after
per year with a standard deviation of
1990
0.9%.
15.1%
in January
1981.
Its
the average ination rate was
The low-ination period is thus
quite similar in terms of the sample variation in ination in the U.S. and European
studies. Ination persistence during the sample period was .86 as measured by the
AR(1)
coecient for the growth in
cpi, compared to for example .80 for the United
States.
An important exception from the studies cited above is Gagnon (2009), who
analyzes micro
6.5%
in
1994
cpi data from Mexico during the period when ination soared from
to more than
90%
in
1995
The ination rate then declined below
1 See
due to the collapse of the Mexican peso.
10%
in
2000.
Gagnon (2009) thus explores
Klenow and Malin (2010) and Nakamura and Steinsson (2013) for surveys of this literature.
2
2
price adjustments in an emerging economy in the midst of hyperination.
Norwegian experience during the
1970s and 1980s represents a very dierent scenario
with moderately high and volatile ination over many years, as in the other
economies.
From around
1990
The
oecd
ination has been low and stable, also as in other
advanced economies. In addition, the shocks that hit the
oecd
economies leading
to the Great Ination period, were dierent from the shocks that hit the Mexican
economy in the
1990s.
This paper thus provides more relevant information on the
comovement between ination and price adjustments in advanced economies.
The evidence from this paper is also highly relevant for the current discussion of
optimal ination level. In the aftermath of the nancial crises some economists have
argued for raising the ination target to
4%
in order to reduce the risk of hitting the
zero lower bound (Blanchard et al. (2010) and Ball (2013)). Others oppose the idea,
referring to the experience of double-digit ination in the
1970s.
While
4%
ination
is well below the numbers from that period, price setting with moderate ination
may nevertheless be dierent from the current low ination regime.
The main result in this paper is that the variation in the frequency of price changes
is more important than the size of price changes when ination is high and volatile,
and for the transition from the high to the low ination regime. When ination is
low and stable, both the frequency and the size of price adjustments are important,
but the size is more important than the frequency. Prices thus changed more often
and in smaller steps when ination was high and volatile, and less often but by larger
steps when ination was low.
In section
1
I explain the data.
In section
2
I describe the variation in the
frequency of price adjustments over time. The frequency of price changes declined
from the high ination period to the low ination period and the frequency of price
changes is strongly correlated with ination. The long-term correlation in the trends
of ination and frequency of price increases is particularly strong.
In section
3
I
document that the absolute size of price changes is negatively correlated with the
ination rate: the average price change (in absolute value) increased by around
percentage points from the high-ination period, to around
period.
In section
4
I decompose the variation in the
12%
cpi
variation in the frequency and magnitude of price changes.
3
in the low-ination
ination rate into the
The variation in the
frequency of price changes is more important for the variation in the ination rate
when ination is high. However, the size of price changes is more important when
2 Alvarez
et. al (2013) is a recent study from the hyperination experience in Argentina.
3
Petrol, unleaded 95 oct., self−service
1998
1999
2000
2001
2002
2003
2004
300
7
400
8
Price
500
Price
9
600
10
11
700
Wash, clip and blow dry, ladies
1997
1998
1999
2000
2001
2002
2003
Figure 1: Examples of price trajectories.
ination is low and stable. In section
5 I document the properties of the distribution
of price changes at the micro level, which is quite symmetric and dominated by many
small price changes and fat tails. In section
Section
7
6
I compare my results to the literature.
concludes and briey discusses some theoretical challenges raised by my
ndings.
1 Data
Every month Statistics Norway collects data for price quotes on a wide range of con
sumer goods and services (henceforth products) to construct the
Norway (2001,
2006)
for details).
cpi (see Statistics
For example they record the price of a bag of
eight buns without raisins in a specic outlet or store once a month. On the basis
of these collected data I have constructed a panel database on prices for
ucts covering the
total
is
14,363,828
39,900.
360
months from January
1975
to December
2004,
1,124
prod
which together
price observations. The average number of observations per month
Price observations for a product from the same outlet constitute a price
trajectory (`quote line') of which there are
433,666.
On average there are
33.1
servations per trajectory. The average number of observations by product is
and the average number of trajectories for each product is
an product are on average sampled from
383
383,
12,678
i.e. the prices for
outlets. The sampled products change
over time as new goods are introduced while other goods disappear. There are
products in
Figure
1
1975
and
845
products in
ob
548
2004.
shows examples of typical price trajectories for two dierent products:
649 petrol, unleaded 95 octane, self-service
4
(left); and
599 wash, clip and blow dry,
ladies
(right). The trajectories show very dierent patterns of variation. Petrol prices
seem to change both upwards and downwards every month (and possibly more often)
while hairdressing salons seem to keep prices constant for some prolonged time, and
all price changes are increases.
649 petrol, un
599 wash, clip and
Products are dened with varying degrees of precision. Product
leaded 95 octane, self-service is precisely dened, while product
blow dry, ladies is less precisely dened as the quality and type of
clip is not neces
sarily identical across salons. However, the outlets report the price of the identical
product or service as the previous month. Sometimes the outlets report the price of
a new product compared to the previous month if the old product no longer exists, if
there is a change in the quality of the good since the last month, or if a new good has
been substituted for the old good. I drop observations agged with either of these
properties, as well as imputed prices.
Over such a long period new products enter the sample while others are removed
as they no longer play a role in household consumption. Nevertheless,
(36% of all products) are observed the entire period.
between
284
and
20
and
30
years,
223
When constructing the
uct
i
10
products
208 products (19%) are observed
products (20%) are observed between
products (25%) are observed less than
409
10
and
20
years,
years.
cpi, Statistics Norway applies weights, ωit , to each prod
reecting the product's importance in the average consumption basket. The
weights are computed as the average of the fraction of consumer expenditures over the
last three years, hence the weights change over time. The products in this database
represent on average
73.9%
of the
cpi.
The most important products that are not
included in the dataset are imputed housing rents, craftsmen services, and municipal
fees.
2 The Frequency of Price Changes
In this section I document the variation in the frequency of price changes over time.
I rst compute the average monthly frequency of price changes for each product in
each year
fit
as the fraction of the total number of non-zero price changes from one
month to the next to all price change observations (including zero price changes)
3
within each year.
and decreases
3 Price
of fit .
fit− .
I then decompose
fit
into the frequencies of price increases
Using product- and year-specic
cpi
weights,
ωit ,
fit+
I compute
changes from December in year t − 1 to January in year t are included in the estimates
5
25
Gcpi
Frequency of increases
Frequency of decreases
20
Frequencies, percent
20
15
10
15
10
5
5
0
0
1975
1980
1985
1990
1995
2000
5
10
2005
15
Inflation, percent
cpi
Figure 2: Left:
ination, π (solid line), the mean weighted frequency of price increases
(dashed line) and decreases (dotted line). Right: Mean weighted frequency of increases (red
dots) and decreases (green ×s) vs ination. Annual rates. Percent.
the weighted average monthly frequency of price changes
ft+
=
P
ft−
+
i ωit fit , and decreases
=
P
ft =
P
i
ωit fit ,
increases
−
i ωit fit for each year.
There is substantial temporal variation in the frequencies of price changes, and
there are systematically dierences between the high and low ination periods. The
left panel of Figure
2
shows
ft+ , ft− ,
and the
cpi
price increases declined markedly from around
12%
after
2000.
ination rate.
20%
negative eect on the frequency of price increases, and the
by these events. Figure
2
9%
had a temporary
devaluation of the
also shows that price decreases are frequently observed in
price decreases hovered around
is associated with a
1979
to around
The results of this paper are, however, not aected
the data even when ination was high in the
2001
1980s
in the early
Norway's price (and wage) freeze law in
nok explains the spike in 1986.
The frequency of
50%
1970s and early 1980s.
The frequency of
68%, but increased to 810% after 2000.
The hike in
decrease in the value-added tax on food. While about
one of four price changes were price decreases during the
were almost as frequent as increases after
1970s
and
1980s,
decreases
2000.4
To highlight the dierences between the high and low ination periods, the rst
two columns of Table
1
report statistics for the frequency of price changes when
splitting the sample in the two periods. The top panel reports the weighted mean,
4 The
temporal features of the frequency of price increases and decreases are not conned to
the means only. Figure B3 in the appendix shows the same tendency for dierent percentiles of
the year-specic distributions of the frequencies of price increases and decreases. However, it is the
upper tails of the distributions that show the biggest change. Hence, the dispersion in the frequency
of price increases is smaller when ination is low.
6
Table 1: The median and mean of the weighted frequency of price changes. Percent.
19751989
Median
Mean
Full sample
Excluding sales
12.8
17.9
Frequency of price increases, fi+ , (%)
8.3
9.4
9.2
12.1
14.8
14.6
3.5
5.8
Frequency of price decreases, fi− , (%)
4.5
4.3
3.8
7.5
7.1
6.7
15.6
23.7
Frequency of price changes, fi , (%)
12.8
14.3
13.0
19.6
21.9
21.3
Median
Mean
Median
Mean
19902004
median, and standard deviation of the frequency of price increases
ft+
across prod
ucts. The mean frequency of price increases dropped signicantly from an average of
17.9%
in the high-ination years to
12.1%
during the low-ination years. Similarly,
the median frequency of price increases fell from
In the second panel of Table
rose from an average of
12.8%
to
8.3%.
1 we see that the mean frequency of price decreases ft−
5.8% in the
high-ination period to
7.5% in the
low-ination
period. There was also a similar increase in the median frequency of price decreases.
The mean total frequency of price changes
ft
was
4.1
percentage points higher in
the high-ination period than in the low-ination period, as reported in the third
panel of Table
1.
The last column of Table
1 reports the frequencies of price changes
when sales related observations are removed from the dataset.
Only
3.3%
of the
observations are sales related. The impact of sales on the frequency of price changes
are small compared to the full sample statistics in column (3).
The frequency of price increases is highly correlated to the
seen from the scatter plot in the right panel of Figure
2,
cpi ination rate
as
which plots the frequency
of price increases and decreases versus the ination rate. The correlation coecient
is .80, illustrated by the regression line.
The frequency of price decreases is less
strongly correlated to the ination rate, with a negative correlation coecient of
0.49. However, the strong correlation between
ft+
and ination dominates so that
the correlation coecient between the average frequency of all price changes
ft
and
ination is as high as .70.
The left panel of Figure
2 shows that both the frequency of price increases and the
7
4
20
2
15
−2
0
10
−4
5
0
1975
1980
1985
1990
1995
2000
−4
−2
0
2
4
Figure 3: Trend components of the frequency of price increases ft+ and ination πt (left
panel) and a scatterplot of the cyclical components (right panel).
ination exhibit a strong downward trend. Thus, in order to assess the importance
of this common trend, I decompose the frequency of price increases
πt
into a trend and a deviation from trend using a
hp (10)-lter.
ft+
and ination
Figure
3
shows
the trend components as a time series plot in the left panel and the deviations from
trend as a scatter plot in the right panel. The long-term correlation between the trend
components is .88, while the short-term correlation is lower but still .50, illustrated by
5
a regression line.
The strong correlation between ination and the frequency of price
increases both in the long-term and short-term underscores the strong link between
these variables. Clearly, a correlations is not the same as a causal relationship, and in
particular the long-term correlation is probably aected by structural changes in the
economic environment over the decades.
For example, more information available
due to computers, the propagation of the Internet, and the type shocks hitting the
economy may have aected price setting. However, the correlation is present in the
short term as well as the long term, which makes it unlikely that the relationship
between the frequency and ination is spurious. In the event of a new period with
moderately high and volatile ination, one should thus expect a higher frequency of
price changes.
The duration of a price spell, which is the number of months between one price
change for a product and the next one, is inversely related to the frequency of price
changes.
I follow the standard approach in the literature by deriving the mean
implied duration for each product,
Di ,
from the weighted frequency estimates by
5 Another
measure of the short-term correlation is between the change in ination ∆π and the
change in the frequency of price increases ∆f + , which is .41.
8
Table 2: Implied duration. Months.
Median
Mean
19751989
19902004
Full sample
Excluding sales
5.9
6.7
7.3
12.3
6.5
8.1
7.2
8.4
Di = −1/ln(1 − fi ).6 From Table 2, we see that the mean implied
duration increased from an average of 6.7 months during the high-ination period to
12.3 months during the low-ination period.7 The last column of Table 2 reports the
using the formula
implied duration when sales related observations are removed from the dataset. The
mean duration increases by only
0.3
months to
8.4
months when excluding sales.
3 The Size of Price Increases and Decreases
To investigate the time variation in the magnitude of price changes, I rst compute
the average magnitude of non-zero monthly price increases and decreases in percent
dp−
it . Then I compute the yearly average
P
P
+
cpi-weighted price increase and decrease: dpt = i ωit dp+it and dp−t = i ωit dp−it .
The average magnitude of all the non-zero price changes for product i is often referred
∗
to as the intensive margin dpit . It is thus equal to the weighted-average of the size
+
−
of price increases dpit and decreases dpit weighted by their relative frequencies:
for each product and year, denoted
dp∗it
dp+
it
and
fit+ + fit− −
dp +
dp ,
=
fit it fit it
Note that a change in the relative frequency of price increases
will aect the intensive margin
(1)
f+
or decreases
dp∗it .
The aggregate intensive margin
dp∗t =
X
cpi-weighted average of the intensive margin for each product
ωit dp∗it .
dp∗t
f−
is the
(2)
i
6 Conditions
for this relationship to hold are that the products are homogeneous and that the
process is stationary. An advantage of using the frequencies to estimate the duration is that cen
sored price spells does not aect the estimates. Measuring the duration directly requires strong
assumption about censored spells. See Baudry et al. (2007) for a discussion on this method.
7 Note that because of the non-linear relationship between the frequency of price changes and
implied duration, applying the formula to the mean frequency yields a duration of −1/ ln(1 −
0.217) = 4.1 months which is dierent from the mean implied duration.
9
20
18
Mean increase
Mean intensive margin
Magnitude of price changes, percent
Gcpi
Mean decrease
15
10
5
Price increases
Price decreases
16
14
12
10
0
0
1975
1980
1985
1990
1995
2000
5
10
15
Inflation, percent
2005
cpi
Figure 4: Left: The
ination rate (blue solid line), the mean weighted magnitude of
+
price increases dpt (red dashed line), decreases dp−
t in absolute values (green dotted line),
and mean intensive margin dp∗t (orange dashed and dotted line). Right: The mean
weighted magnitude of price increases (red dots) and decreases in absolute values (green
×s) plotted against the ination rate with regression lines. Annual rates. Percent.
The left panel of Figure
−
∗
4 plots dp+
t , the absolute size of dpt , and dpt together with
the ination rate. The average size of price increases and decreases are substantial.
Interestingly, since the early
1990s, both the mean size of price increases and decreases
dp+
t rose from 11% in 1975
−
to 18% in 2004. Similarly, the mean size of price decreases dpt increased in absolute
value from about 10% to almost 14% by the end of the sample. The average size
have trended upwards. The mean size of price increases
of price increases are generally higher than the average size of price decreases in
absolute value.
As ination reduces the relative price between price adjustments,
one would expect price increases on average to be larger than the absolute size of
price decreases (see Ball and Mankiw,
1994).
The scatter plot in the right panel of Figure
tween the size of price changes and the
4
shows the negative correlation be
cpi ination rate.
The correlation coecient
between ination and the size of price increases is .52, and .60 between ination
and the size of price decreases. The upward trend in the magnitude of price changes
since early
1990s
documented above thus requires some scrutiny. How robust is this
nding? First, the trend increase in the magnitude of price changes is also present
in the data if I remove extreme observations. Second, the trend is also robust if we
look at the products which are included in the
cpi basket over the entire period (i.e.
I remove the products that enter or exit the sample over time). Hence, the trend is
not explained by changes in the composition of goods and services. Third, the trend
increase is signicant for most types of goods (see Figure B3 in the appendix).
10
Table 3: The weighted average price increase and decrease. Percent.
19751989
19902004
Full sample
dp+
i
Size of price increases
Median
Mean
Excluding sales
7.6
9.9
9.3
8.9
10.5
13.2
12.3
11.5
Size of price decreases
dp−
i
Median
7.8
10.2
9.7
9.0
Mean
9.1
11.2
10.5
9.7
Figure
4
also shows that the intensive margin
low ination period yielding a strong
positive
dp∗t
declined from the high to the
correlation with ination (correlation
coecient of .87). We see from (1) that the intensive margin depends on to what
extent
dp−
it
cancel out
and decreases.
Figure
2)
dp+
it
determined by the relative frequency of price increases
The increasing relative frequency of price decreases (as seen from
thus contributed to the fall in the average intensive margin
in the high-ination period to
In Table
3,
2.7%
dp∗t
from
4.9%
in the low-ination period.
columns (1) and (2) I report the weighted moments of the average
size of the price changes occurring in the high-ination period (19751989) and in
the low-ination period (19902004). The mean average size of price increases and
decreases were
13.2
and 11.2% in the low-ination period, about
23
percentage
points higher in absolute value than in the high-ination period. For completeness,
column (3) of Table
3
reports the weighted median and mean of the average magni
tudes of price increases and decreases over the whole sample. The median and mean
average price increases by product are
9.3
and
12.3%,
while the median and mean
average price decreases are 9.7 and 10.5%. The fourth column in Table
3
reports
the average size of price changes excluding sales-related observations. Because there
are relatively few sales-related price changes, the eect of sales on the average size
of price increases and decreases are a mere
1
percentage point.
One may expect that the size of a price change increases with the time elapsed
since the previous change. However, there is little indication of this in the data. I
have regressed the size of all price changes on the time since last price change for each
product. The median
ols
estimate on the time variable is .013 with a t-statistic
of .127. There is a signicant positive correlation for only
11
208
products (19%) (i.e.
the t-statistic is larger than
1.96).8
Figure B5 in the appendix shows a weak, albeit
signicant, tendency that products for which prices increase more often, adjust by a
smaller size, thus indicating that the size of price increases may be positively related
to duration.
Appendix B documents substantial variation in both the frequency and size of
price adjustments between products. The general upshot conrms that the temporal
variation in the average frequencies and sizes of price adjustments applies to most
categories of goods and services with few exceptions.
4 Decomposition of the Ination Rate
Sections
2 and 3 show that the average of both the frequency and magnitude of price
adjustments are correlated with ination.
In this section I illustrate their partial
contributions to the variation in the ination rate. To this end, I rst decompose
the ination rate into the frequencies and the magnitudes of price increases and
decreases.
I then construct counterfactual estimates of
cpi
ination by allowing
only one component to vary while holding the other constant at the means. Finally,
I compare the correlations between these conditional estimates with
cpi
ination.
A high correlation indicates that the conditioning variable may be an important
contributor to the variation in the ination rate.
To be able to decompose ination into frequencies and magnitudes, I rst derive
an estimate of
cpi
ination
π̂t
as the weighted average of product-specic price
changes,
π̂t =
X
(3)
ωit dpit ,
i
where
ωit
is the
cpi weight, and dpit
zero price changes) for product
i
is the average monthly price change (including
in year
t.
Figure
5
shows that
π̂t
tracks the ocial
cpi ination rate πt extremely well, with a correlation coecient of .91.
π̂
replicates the high and volatile ination period that from
the disination period that started in the latter half of the
period from
1990
until the end of the sample,
8 Using
π̂
1975
1980s.
also ts the
In particular
which ended with
In the low-ination
cpi history well.9
only price increases in the regression does not change this results. The median ols
estimate is .074 and the median t-statistic is .608. In this case, the number of products with
signicant positive estimates is 154.
9 The main reasons why π̂ is not identical to π is rst, that I do not have prices for the full set
of goods used to construct the cpi, second, that I do not include imputed prices which are used
to construct the cpi and third, the cpi adjusts individual prices for inter alia quality and regional
12
15
PIHAT
0
5
Percent
10
Gcpi
1975
1980
1985
1990
1995
2000
cpi
Figure 5:
Ination, πt , (solid line) and predicted
ination rate, π̂t (dashed line). Annual rates. Percent.
Using that the average price change for each product
fit times the size dp∗it , I substitute for
dpit
π̂t =
X
dpit is equal to the frequency
in (3) which yields
(4)
ωit fit dp∗it
i
Because the intensive margin
dp∗it
depends on the frequency of price changes cf.
equation (1) and the discussion above, I substitute for
π̂t =
X
dp∗it
using (1) which yields
(5)
−
−
ωit fit+ dp+
+
f
dp
it
it
it .
i
The decomposition shows that the frequencies and magnitudes enter multiplicatively
10
at the product level in (5).
I then construct two counterfactual estimates of
cpi
ination using the decom
position in (5) where I allow either the magnitudes or the frequencies to vary over
time while holding the other constant at its product-specic means. The conditional
estimate of
cpi ination allowing the frequencies of price changes to vary over time
but holding the size of price changes constant at
π̂t
−
fit+ , fit− dp+
i , dpi
=
X
dp+
i
and
dp−
i
is:
−
−
ωit fit+ dp+
i + fit dpi .
(6)
i
dierences (see Statistics Norway, 2001). π̂t is mean adjusted from 8.2 to 5.4%, which is the mean
of πt .
10 Note that ination is the weighted-average product of the frequencies and sizes for each product.
It is not possible to decompose ination into the aggregate frequencies and sizes.
13
15
15
Gcpi
PIHAT_m6
Percent
5
0
0
5
Percent
10
PIHAT_m5
10
Gcpi
1975
1980
1985
1990
1995
2000
1975
1980
1985
1990
1995
2000
cpi
Figure 6: Ination (solid line) and the conditional estimates of
ination π̂t (fit |dpi )
(left) and π̂t (dpit |fi ) (right). Annual rates, percent.
−
π̂t fit+ , fit− dp+
is thus from the time
i , dpi
+
−
variation in the frequency of price changes (fit and fit ). For notational simplicity I
denote this counterfactual estimate as π̂f,t .
The only contribution to variation in
Similarly, the conditional estimate of
cpi
ination allowing the magnitudes of
price changes to vary over time, but keeping the frequency of price changes constant
at
fi+
and
fi− :
X
−
− +
−
−
π̂t dp+
,
dp
f
,
f
=
ωit fi+ dp+
it + fi dpit .
it
it i
i
(7)
i
− +
−
π̂t dp+
is thus from the time
it , dpit fi , fi
+
−
variation in the size of price changes (dpit and dpit ). For notational simplicity I
denote this counterfactual estimate as π̂dp,t . Appendix C provides a more detailed
The only contribution to variation in
decomposition analyses.
Figure
6
shows
cpi ination πt
together with the frequency-related ination
in the left panel, and with the size-related ination
π̂dp,t
in the right panel. We see
that the frequency-related ination is strongly correlated with
a correlation coecient of
0.92).
cpi
ination (with
This is compelling evidence that the variation in
the frequency signicantly contributes to the variation in the ination rate.
size-related ination
the
cpi
π̂dp,t
π̂f,t
in the right panel of Figure
(with a correlation coecient of .24).
6,
is
negatively
The
correlated with
The variation in the size of price
changes has thus not been a major factor behind the overall variation in the ination
rate at least in the long term.
Over such a long period as thirty years the
14
cpi weights may have changed quite
a lot and aected the time variation in the weighted margins.
and
π̂dp,t
Recalculating
π̂f,t
using constant weights does, however, not aect the result. The correlation
π̂f,t
coecients between
and
π̂dp,t
using constant weights and
cpi
ination are .92
and .38.
The dominant contribution of the frequency of price changes is conrmed by a
simple unrestricted
ols regression of πt
on
π̂f,t
and
π̂dp,t :
(8)
πt = −3.52 + 0.69 π̂f,t + 0.31 π̂dp,t
(2.39)
(0.06)
(0.24)
where standard errors are reported in the parentheses and with
coecient on the frequency-related ination
π̂f,t
accounts for
69%
1.00,
The
is clearly signicant and twice the
size of the insignicant coecient of the size-related ination
unrestricted coecients sum to
R2 = 0.86.
π̂dp,t .
Note that the
so variation in the frequency of price changes
of the variation in ination, while variation in the size of price
changes accounts for
31%.11
The high correlation between the frequency-related ination rate and
cpi ination
is clearly dominated by a common long term trend. Decomposing each series into
a trend component and the deviation from trend using a
hp(10)
lter, shows that
the trend components have a correlation coecient of .99 while the deviations from
trend have a correlation of .58. For the size-related ination rate and
cpi ination,
the correlation coecient is .68 for the trend components and .27 for the deviation
component. Also the change in ination is more correlated with the change in the
frequency related ination as corr (∆π, ∆π̂f,t )
= .48
while corr (∆π, ∆π̂dp,t )
= .18.
Hence, the frequency is the dominating factor in both long and short term variability
in the ination rate.
Calculating the correlation coecients between
π̂dp,t
and the
cpi
ination rate
over the high- and low-ination periods separately, I nd correlation coecients of
.03 in the high-ination period and .52 in the low-ination period. Correspondingly
the correlation coecients between
π̂f,t
and .41 in the low-ination period. An
geneity, yields a coecient of .81 for
and
π
are .80 in the high-ination period
ols regression similar to (8) assuming homo
π̂dp,t
in the low-ination period and .33 in the
11 This
result is also robust to changes in the composition of products over time. Using only the
prices for the 409 products which are included in the whole sample period, an ols regression like
(8) yields πt = − 0.00 + 0.71 π̂f,t + 0.29 π̂dp,t . The results above are thus not a result of product
turnover.
(0.26)
(0.03)
(0.03)
15
.08
.06
.04
.02
0
−50
−40
−30
−20
−10
0
10
Price change, percent
20
30
40
50
cpi
Figure 7: Histogram of all
-weighted observations of non-zero price
changes truncated at 50 and 50 percent and with one percent bin width.
The solid line is a Laplace distribution.
high-ination period. Thus when ination is low, the size of price changes seems to
be more important for the variation in ination than the frequency, accounting for
81% vs 19% in the variation in ination.
of price changes accounts for only
the frequency accounts for
33%
When ination is high, variation in the size
of the variation in ination while variation in
67%.
5 The abundance of small price changes
Although this paper mainly focuses on the time variation of the
average
margins
of price adjustments, this section documents some important facts of the size of
individual price changes. The histogram in Figure
the size of
all
non-zero
7 shows the pooled distribution of
cpi-weighted price changes truncated at 50 and 50 percent.
The distribution of all price changes is single-peaked centered around zero and is very
similar to a Laplace distribution but with thicker tails. As many as
changes are less than
1%
in absolute value and
45%
13%
of the price
5%
in absolute
are less than
value.
Alvarez, Le Bihan, and Lippi (2013) argue that the real eect of monetary shocks
increases with the kurtosis (peakedness) in the price change distribution. Discarding
price changes larger than
ln(10/3)%
and smaller than .1% following Alvarez, Le
Bihan, and Lippi (2013), the kurtosis is
8.9
16
in the high ination period and
10.9
2−5 products
6−10 products
11−50 products
51−100 products
101−200 products
Density
0 .02 .04 .06 .08
0 .02 .04 .06 .08
0 .02 .04 .06 .08
1 product
−50
0
50
−50
0
50
Figure 8: Histograms of non-zero price changes by the number of
products per rm. Bin width 1% and truncated at 50 and 50%.
12
in the low ination period.
Based on the arguments of Alvarez, Le Bihan, and
Lippi (2013) , this indicates that monetary policy is somewhat more eective when
ination is low.
A distribution of non-zero price changes with a single mode around zero is not
consistent with state dependent models where rms face a xed cost of repricing. In a
menu cost model the distribution is bimodal with no mass around zero (Golosov and
Lucas (2007)). However, the histogram in Figure
7
is pooled over all products and
13
years and is not necessarily characteristic for distributions at the micro level.
is not appropriate to eyeball each histogram for
dip test (Hartigan and Hartigan,
1985)
86%
products, I apply Hartigan's
for each product level distribution. I reject
the null hypothesis of unimodality for only
signicance. Thus
1,124
14%
of all products at the
5%
239 893
level of
of the product distributions of price changes can be viewed
as unimodal. At the product-store level the test rejects unimodality for only
of
As it
product-store distributions with more than
20
observations, i.e.
420 out
0.2%.
Lach and Tsiddon (2007) and Midrigan (2011) argue that the many small price
12 The
kurtosis is 6 for a Laplace distribution and 3 for a normal distribution. The kurtosis of the
non-truncated data is 193.0 which is huge, because of the thick and long tails in the distribution.
13 Figure B2 in the appendix plots the distributions of the size of price changes for each coicop
division. It shows that all the distributions have a single mode with many small price changes,
but the degree of kurtosis dier. The coicop divisions clothing and footwear, communication, and
recreation and culture possess less peaked distributions than most notably alcoholic beverages and
tobacco, transport, and education.
17
changes in combination with a high average price change are, however, consistent
with a menu-cost model when rms sell many products, assuring there are economies
of scope in price adjustments.
To investigate this hypothesis I plot histograms of
non-zero price changes for categories of multi-product rms in Figure
8.
The his
togram in the top left panel shows the size of price changes for rms reporting the
price for only one product, the top right panel shows the size price changes for rms
reporting prices for
25
products, and so on. We see that the distribution for sin
gle-product rms is indeed bimodal with a minor mode below zero and a major mode
above as predicted by Golosov and Lucas (2007). However there are many small price
changes around zero in between the two modes. The distributions for multi-product
rms are clearly unimodal centered slightly above zero which is consistent with Lach
and Tsiddon (2007) and Midrigan (2011).
6 Empirical Comparisons
How do the ndings in this paper compare to previous studies? Klenow and Malin
(2010) survey the literature so I will be rather brief here.
First, for the overall
duration or frequency of price changes, the estimate of the mean implied duration
for the low-ination period in Norway is similar to the
(see Dhyne et al.,
2006).
13
months for the euro area
Nakamura and Steinsson (2008) report about
89 months for
the United States, and that temporary price changes due to sales have a big impact
on their duration estimates. In their data,
sales-related compared to
data (Dhyne et al.,
2006).
3.3%
21.5% of the price change observations are
in the present data, which is similar to the euro area
Sales thus seems to be less important for price adjustments
in Europe than in the United States.
Second, the Norwegian estimates of the size of price changes for the low-ination
period are similar to the European and
us
estimates.
For example, Klenow and
Kryvtsov (2008) nd that the mean average price increase is
12.7%
and the mean
average price decrease is 14.1% in the United States. Excluding sales, Nakamura
and Steinsson (2008) report a median average size of price increases and decreases
of
7.5
and 9.2% for the United States. Dhyne et al. (2006) report that the average
price increase in the euro area is
8.2%
and the average price decrease is 10.0%.
Third, there is diverging evidence on the comovement between ination and the
frequency and size of price changes.
Nakamura and Steinsson (2008) and Goette,
Minsch, and Tyran (2005) also nd a positive correlation between ination and the
18
frequency of price increases. Gagnon (2009) nds that ination and the frequency
of price changes correlates strongly when ination is high (above
relation when ination is low (less than
14
10%).
15%),
but no cor
Gagnon (2009, Figure VII b))
shows a negative correlation between ination and the magnitude of price increases
and decreases as in this paper, while neither Nakamura and Steinsson (2008) nor
Dhyne et al. (2006) report any correlation between ination and the magnitude of
price changes.
Klenow and Kryvtsov (2008) nd no correlation between the frequency of price
changes and
than
90%
us ination, but that variation in the intensive margin accounts for more
of the variation in ination. To reach this conclusion they decompose the
15
ination rate according to
π̂t =
X
ωit dpit =
X
i
i
P
ωit dpit
i
= ft dp†t ,
ωit fit P
ω
f
i it it
(9)
They then propose to decompose the variation in ination according to
var(π̂t )
where
f
and
=f
dp†
2
†
var(dpt )
+ dp†
are averages, and
2
Ot2
var(ft )
2
+ 2 f dp† covar(ft , dp†t ) + Ot2
are higher order terms depending on
f.
(10)
Lastly,
they estimate the contribution of the variation in the intensive margin to the variation
2
†
†
in ination by the term f var(dpt ) relative to var(π̂t ). Note that while dpt is not
dp∗t as dened in (1), they are strongly
16
correlated with a correlation coecient of .95.
Applying the Klenow and Kryvtsov
decomposition (10) on the Norwegian data yields that variation in the size, i.e. in
dp†t , accounts for 76% in the low ination period and as much as 68% in the high
equal to the aggregate intensive margin
ination period.
The interpretation of the Klenow and Kryvtsov decomposition is, however, am
biguous. The intensive margin,
dp†t ,
is an average of the size of price increases and
price decreases weighted by the relative frequencies (as in equation (1)). Variation in
dp†t
may thus be caused by variation in the relative frequencies as well as variation in
14 Gagnon
(2009) does not report separate correlations between ination and the frequency of
price increases or decreases.
15 See Klenow and Kryvtsov (2008, equation (4)). I use my notation, however, to simplify com
P
parison. (Also, I have dropped the t operator from their equation which is a typo.)
16 While dp∗ is the average of a fraction P ω dp /f , dp† is the fraction of two averages dp and
it it
t
t
t
i it
ft . Appendix D gives more details of this aggregation wedge.
19
18
.8
dp positives
.55
10
.6
12
.65
14
.7
16
.75
dp negatives (abs val)
1
2
3
4
5
6
1
2
3
4
5
6
Figure 9: Left panel: Scatter plot with regression line of ft+ /ft versus dp†t .
−
Right panel: Scatter plot with regression lines of dp+
t (blue) and the absolute value of dpt
†
(pink) versus dpt .
the size. Figure
9 shows that the variation in dp†t
is in fact mainly driven by variation
in the relative frequency of price increases vs decreases and not by variation in the
size. The left panel of Figure
9 shows that the relative frequency of price increases to
the total frequency is positively correlated with
Figure
dp†t .
In contrast, the right panel of
9 shows that the absolute size of price increases and price decreases separately
dp†t . Using the Klenow and Kryvtsov decomposition
†
on the Mexican data, Gagnon (2009) nds that the variation in dp is more impor
tant than variation in the frequency (89 vs 11%) when ination is below 10%, while
†
variation in the frequency is more important than variation in dp (65 vs 35%) when
are negatively correlated with
ination is high.
Fourth, the prevalence of many small price changes is a common nding in many
17
countries, see Klenow and Malin (2010) and Cavallo and Rigobon (2011).
whole sample the kurtosis is
9.7
compared to
Le Bihan, and Lippi (2013, Table
1))
and
12.8
10.0
for French
for
us
For the
cpi data (see Alvarez,
data (see Klenow and Malin
(2010)).
7 Conclusions
There is substantial empirical evidence on price adjustments in advanced economies
with low and stable ination.
This paper adds to this evidence by investigating
monthly retail price data over three decades characterized by both high and low
17 Eichenbaum
error.
et al. (2014) argue that the vast majority of these changes are due to measurement
20
ination.
During the
1970s
and
1980s,
cpi
high and volatile, with a mean ination of
From
1990
onwards
ination in Norway was moderately
8.1%
and standard deviation of
2.7%.
cpi ination came down and varied around a mean of 2.4% and
standard deviation of .9% per year.
The main ndings are that (i) high and volatile ination is strongly related to
the variation in the frequency of price changes and unrelated to the variation in
the size of price changes. (ii) When ination is low and stable, both the frequency
and the size of price adjustments are important, but the size is more important
than the frequency.
(iii) The transition from the high to the low ination regime
is also strongly related to the variation in the frequency of price changes and less
related to the variation in the size of price changes. To reach these ndings I use
a novel decomposition of the ination rate. I also document some other interesting
regularities: (iv) The mean size of price increases and the mean absolute size of price
decreases are higher in the low ination period than when ination was high. (v)
While the average size of price changes is large,
are smaller than
1%
in absolute value.
13%
of the (non-zero) price changes
There are fewer small price changes when
ination is low than when ination is high.
This evidence strongly indicates that rms not only treat the size of price changes,
but also the timing of price changes as choice variables.
(Calvo,
1983,
and Taylor,
1980)
Time-dependent models
assume that the frequency of price adjustment is
exogenous, and thus they do not capture the most important component behind the
variation in ination when it is high.
Monetary policy analysis that assumes an
exogenous probability of price changes, are thus subject to the Lucas (1976) critique.
Furthermore, it follows that the frequency of price changes should not be interpreted
as a structural parameter of price rigidity as in e.g. Dhyne et al. (2006).
The probability of changing prices should rather be treated as an endogenous
variable, depending on the state of the economy like in Sheshinski and Weiss (1977)
and Caplin and Spulber (1987). With a xed cost of changing prices state-dependent
models may explain the positive correlation between the frequency of price increases
and ination.
Lucas,
2007)
In state-dependent models with idiosyncratic shocks (Golosov and
rms change prices either because of ination to maintain its relative
price, or because of the shocks to change its relative price. In a menu cost model
with trend ination and idiosyncratic shocks, Blanco (2014) shows that higher ina
tion increases the frequency while lower ination tends to be associated with larger
size adjustments.
Hence, when ination is low and stable price adjustments are
21
dominated by idiosyncratic shocks which tend to increase the size of adjustments.
Another possible explanation for the negative correlation between the size of price
adjustments and ination is that adjustment costs increase in the size of price changes
as in Rotemberg (2009). In this case higher ination may lead rms to reduce the
size of their price increases because postponing a price change requires a larger price
increase when ination is higher. This eect can be so large that a rise in ination
leads rms to reduce the size of their price increases.
The correlations between ination and the frequency and size of price adjust
ments may of course not necessarily represent causal relationships. The long-term
correlation is probably aected by structural changes in the economic environment
over the decades, and the type of shocks hitting the economy have changed and so
on. The strong correlation in trends may give rise to a spurious relationship between
the frequency and ination. Nevertheless, the correlation is also present in the shortterm variation in the frequency and ination, which makes a spurious relationship
less likely. All in all, there is conclusive evidence the frequency of price adjustments
is not a constant independent of the economic environment. The evidence gives a
clear indication that the frequency of price changes is related to ination.
References
Alvarez, F.H., H. Le Bihan and F. Lippi (2013). Small and Large Price Changes
and the Propagation of Monetary Shocks. CEPR Discussion Paper No.
9770.
Alvarez, F.H., A. Neumeyer, M. Gonzalez-Rozada and M. Beraja (2013).
Hyperination to Stable Prices:
Argentina's Evidence on Menu Cost Models.
Stanford Center for International Development Working Paper No.
Ball, L. (2013).
From
The Case for Four Percent Ination.
470.
Mimeo, Johns Hopkins
University.
Ball, L. and G. Mankiw (1994). Asymmetric Price Adjustment and Economic Fluc
tuations
The Economic Journal 104(423), 247261.
Barro, R.J. (1972). A Theory of Monopolistic Price Adjustment.
Review of Eco
nomic Studies, 39, 1726.
Baudry, L., H. Le Bihan, P. Sevestre and S. Tarrieu (2007). What do Thirteen Mil
22
lion Price Records have to Say about Consumer Price Rigidity?
Oxford Bulletin
of Economics and Statistics, 69(2), 139183.
Bils, M. and P.J. Klenow (2004). Some Evidence on the Importance of Sticky Prices.
Journal of Political Economy 112(5), 947985.
Blanchard, O., G. Dell'Ariccia, and P. Mauro (2010). Rethinking Macroeconomic
Policy.
Journal of Money, Credit, and Banking, 42
Blanco, J.A. (2014).
(Supplement), pp.
A Regime Contingent Phillips Curve.
199215.
Mimeo, New York
University.
Calvo, G.A. (1983). Staggered Prices in a Utility-Maximizing Framework.
Journal
of Monetary Economics 12, 383398.
Caplin, A.S. and D. Spulber (1987).
Menu Costs and the Neutrality of Money.
Quarterly Journal of Economics 102(4): 703-725.
Cavallo A., and R. Rigobon (2011). The Distribution of the Size of Price Changes.
NBER Working Paper No.
16760
Dhyne, E., L.J. Álvarez, H.L. Bihan, G. Veronese, D. Dias, J. Homann, N. Jonker,
P. Lunnemann, F. Rumler, and J. Vilmunen (2006). Price Changes in the Euro
Area and the United States: Some Facts From Individual Consumer Price Data
Journal of Economic Perspectives 20(2), 171192.
Eichenbaum, M.S., N. Jaimovich, S. Rebelo, and J. Smith (2014). How Frequent
Are Small Price Changes?
pp.
American Economic Journal: Macroeconomics, 6(2)
137155.
Gagnon, E. (2009). Price Setting During Low and High Ination: Evidence from
Mexico.
The Quarterly Journal of Economics, 124(3), 12211263.
Goette, L., R. Minsch and J-R. Tyran (2005). Micro evidence on the adjustment of
sticky-price goods: It's how often, not how much Mimeo.
Golosov, M. and R.E. Lucas Jr. (2007). Menu Costs and Phillips Curves.
Journal
of Political Economy, 115(2), 171199.
Hartigan, J.A. and P.M. Hartigan (1985). The Dip Test of Unimodality.
of Statistics, 13(1),
pp.
7084.
23
The Annals
Klenow, P.J. and O. Kryvtsov (2008). State-Dependent or Time-Dependent Pricing:
Does It Matter for Recent U.S. Ination?
The Quarterly Journal of Economics,
123(3), 863904.
Klenow, P.J. and B.A. Malin (2010).
Microeconomic Evidence on Price-Setting.
in the Handbook of Monetary Economics
Elsevier,
3A,
B. Friedman and M. Woodford ed.:
231284.
Lach, S. and D. Tsiddon (2007). Small Price Changes and Menu Costs.
Managerial
and Decision Economics 28, 649656.
Lucas, R.E. (1976).
Econometric Policy Evaluation:
a Critique.
Carnegie-
Rochester Conference Series on Public Policy, 1, 1946.
Midrigan, V. (2011).
tions.
Menu Costs, Multi-Product Firms, and Aggregate Fluctua
Econometrica, 79(4)
pp.
11391180.
Nakamura, E. and J. Steinsson (2008). Five Facts About Prices: A Reevaluation of
Menu Cost Models
The Quarterly Journal of Economics, 123, 14151464.
Nakamura, E. and J. Steinsson (2013). Price Rigidity: Microeconomic Evidence and
Macroeconomic Implications
Annual Review of Economics, 5, 133163.
Rotemberg, J. (2009). Altruistic Dynamic Pricing with Customer Regret.
Scandi
navian Journal of Economics, 112(4), 646672.
Sheshinski, E. and Y. Weiss (1977). Ination and cost of price adjustment
Review
of Economic Studies 44, 287303.
Statistics Norway (2001). Konsumprisindeksen
tikk (NOS C
680),
19952000,
Norges Osielle Statis
Statistics Norway, Oslo.
Statistics Norway (2006).
About the
cpi. http://www.ssb.no/kpi_en/about.
html
Taylor, J. (1980). Aggregate dynamics and staggered contracts.
Journal of Political
Economy 88, 124.
United Nations (2000). Classications of Expenditure According to Purpose. Sta
tistical Papers Series M No.
84,
United Nations, New York.
24
Online Appendix for
Ination and price adjustments: micro evidence
from Norwegian consumer prices 19752004
by Fredrik Wulfsberg
Oslo and Akershus University College of Applied Sciences
May
29, 2015
A Data
Today the Norwegian
cpi
is computed from monthly data for
goods and services from approximately
goods and services are revised.
2,200
900
representative
rms. Once a year the representative
The sample of rms is rotated so that a rm is
included for a maximum of six years (72 months).
The rms report price data monthly, either by completed forms or by providing
scanner data. The quality of the observations are evaluated and revised before being
used to construct the
cpi,
which takes account of the revision status meaning
whether or not the price observation is imputed or corrected, status of the product
itself, and whether the observation is used in the
cpi.
There are missing observations
50,000
1975
1980
1985
1990
1995
20,000
10,000
20,000
30,000
30,000
40,000
40,000
50,000
in the sample resulting in breaks in the trajectories.
2000
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Figure A1: The Variation in the Number of Observations by
Year (Left) and by Month (Right)
i
Sep
Oct
Nov
Dec
12
11
10
COICOP Division
9
8
7
6
5
4
3
2
1
1975
1980
1985
1990
1995
2000
Figure A2: The distribution of observations across
2005
coicop groups over time.
Products represented by an index are excluded from the data set used in this
paper.
I removed
174,900
observations when the product is not oered anymore, has
changed in quality from the previous month, or is a new product.
The number of monthly observations varies between
17,606
and
46,128.
Figure
A1, left panel, shows that the number of observations per month declines steadily,
from an average of
42,815 in 1975 to 25,762 in 1990, then increasing to 38,836 in 2004.
The right panel of Figure A1 shows that there is no systematic variation between
dierent months. Figure A2 illustrates the number of observations by
over time, with the number of observations in
2004
coicop groups
appearing on the right.
B Heterogeneity
Figure B1 shows the distribution of the frequency of price adjustments
distribution is skewed to the right with a mean and median frequency of
14.3%
(as reported in Table
1).
Table B1 reports average frequencies and duration
estimates for the high- and low-ination periods for twelve
mean duration varies between
ation period and
39.6
fi . The
21.9 and
3.8
months for
months for
coicop divisions.18
1 Food and beverages
The
in the high in
12 Miscellaneous goods and services
in the low
ination period.
The frequency of price changes is higher in the high-ination period than in the
low-ination period for all
Communication,
and
coicop
divisions except for
9 Recreation and culture.
3 Clothing and footwear, 8
For all categories the frequency of
18 coicop is an acronym for Classication of Individual Consumption According to Purpose. Each
product is classied at the ve-digit coicop level (see United Nations, 2000).
ii
Table B1: Mean frequency of price changes and mean price duration
in months by
divisions (two-digit level).
coicop Division
coicop
Period
n
Products
f+
f−
D
1 Food and non-alcoholic
beverages
19751989
19902004
4,229,361
3,031,220
264
267
22.6
13.4
11.9
10.2
3.8
5.8
2 Alcoholic beverages, tobacco
and narcotics
19751989
19902004
87,036
188,042
41
42
16.0
11.0
1.6
3.2
5.4
7.1
3 Clothing and footwear
19751989
19902004
558,401
530,975
104
133
7.5
5.7
4.5
8.3
8.6
7.8
4 Housing, water, electricity,
gas and other fuels
19751989
19902004
39,829
139,542
26
29
16.2
13.5
2.8
9.6
6.3
8.4
5 Furnishings, household
equipment and routine
household maintenance
19751989
19902004
774,272
693,303
130
137
10.3
7.3
3.2
5.0
8.0
9.1
6 Health
19751989
19902004
3,070
199,018
15
52
8.8
7.5
0.7
2.0
11.7
12.6
7 Transport
19751989
19902004
228,883
458,504
111
86
29.9
23.1
7.3
11.6
4.2
16.0
8 Communication
19751989
19902004
3,131
14,885
10
15
4.0
2.6
2.6
8.2
21.2
13.7
9 Recreation and culture
19751989
19902004
131,627
344,534
88
120
9.7
9.2
3.2
4.9
9.7
9.7
10 Education
19751989
19902004
1,476
990
7
7
8.4
6.7
0.4
0.4
11.6
13.9
11 Restaurants and hotels
19751989
19902004
7,914
184,723
15
44
23.5
5.9
1.7
1.7
4.6
14.7
12 Miscellaneous goods and
services
19751989
19902004
305,800
414,329
58
96
15.8
6.9
1.9
2.7
6.6
39.6
Non-durable goods
19751989
19902004
5,181,731
4,280,974
437
490
22.0
17.3
9.3
11.8
4.2
5.9
Durable goods
19751989
19902004
178,431
346,304
101
109
23.6
14.0
4.5
6.9
5.2
6.3
Semi-durable goods
19751989
19902004
889,757
1,046,342
184
230
7.5
5.7
3.5
6.2
9.7
9.4
Services
19751989
19902004
120,881
526,445
147
199
12.8
7.3
1.7
2.6
10.6
25.6
Main categories
n is the number of observations, f + is the rate of price increases, f − is the rate of price
decreases, and D is the mean implied duration.
Note:
iii
.2
.15
Fraction
.1
.05
0
0
10
20
30
40
50
60
70
80
90
Figure B1: The distribution of the frequency of price changes in percent across products.
price increases is higher in the high-ination period, in particular for
and hotels
and
1 Food.
11 Restaurants
In contrast the frequency of price decreases is higher in the
low-ination period for all categories but
1 Food, 10 Education,
and
11 Restaurants
and hotels. In particular the frequency of price decreases was thrice as high for 4
Housing and fuels and 8 Communication products, and almost twice as high in the
low-ination period for 3 Clothing and footwear.
The coicop system also classify the products as non-durable goods, semidurable
goods, durable goods, and services.19 The bottom panel of Table B1 shows that
the frequency of price increases are higher in the high-ination period and that the
frequency of price decreases is higher in the low-ination period for all types of
durables
duration is 25.6
goods. The net eect is that duration is more than one month higher for
and
non-durables
in the low-ination period. For
months in the low-ination period compared to
services the mean
10.6 months in the
high-ination
period.
There are substantial dierences between the
coicop divisions also regarding the
size of price changes, see Table B2. For example when ination is low, the mean sizes
of the price increases and decreases vary from
footwear
to
4.4
and 4.0% for
7 Transport.
44.2
and 29.5% for
For all
coicop
3 Clothing and
divisions the absolute
size of price decreases were higher in the low-ination, particularly for
and
11 Restaurants and hotels.
period for all
10 Education
Price increases were also higher in the low-ination
coicop divisions but for 7 Transport
19 The
and
10 Education.
distinction between non-durable goods and durable goods is based on whether the goods
can be used only once, or repeatedly over a period of considerably more than one year. Semi-durable
goods dier from durable goods in that their expected lifetime of use, though more than one year,
is often signicantly shorter and their purchasers price is substantially less.
iv
coicop divisions,
Table B2: The mean absolute size of price increases and decreases by
main categories and high and low ination periods. Percent.
Increases
coicop Division
1 Food and non-alcoholic
beverages
2 Alcoholic beverages, tobacco
and narcotics
3 Clothing and footwear
4 Housing, water, electricity,
gas and other fuels
5 Furnishings, household
equipment and routine
household maintenance
6 Health
7 Transport
8 Communication
9 Recreation and culture
10 Education
11 Restaurants and hotels
12 Miscellaneous goods and
services
Decreases
19751989
19902004
19751989
19902004
11.5
13.6
−10.6
−11.9
4.5
6.0
−3.6
−6.1
25.5
5.9
44.2
10.8
−22.0
−4.9
−29.5
−9.2
11.9
14.5
−10.3
−12.7
7.1
7.4
5.8
9.9
9.6
3.7
8.3
9.5
4.4
7.8
13.7
6.2
13.3
9.9
−5.7
−3.5
−4.7
−8.7
−2.8
−2.6
−8.7
−7.1
−4.0
−9.5
−11.6
−15.5
−12.4
−10.1
8.0
6.1
17.5
5.3
8.5
7.1
20.5
9.6
−9.6
−7.9
−23.7
−8.2
−10.6
−9.4
−33.8
−8.8
Main categories
Non-durable goods
Durable goods
Semi-durable goods
Services
In the bottom panel for the main categories we see that the absolute size of price
increases are larger in the low-ination period than in the high-ination period in
particular for
Services
and for the absolute size of price decreases for
Semi-durables.
The latter category change prices by the largest amounts.
There is also a lot of variation in the size of price changes within each category.
Figure B2 shows histograms of individual non-zero price changes for each
coicop
division. All histograms are single peaked, but the degree of kurtosis (peakedness)
diers.
v
2
3
4
5
6
7
8
9
10
11
12
.05
0
.05
.1
0
Density
.1
0
.05
.1
1
−40 −20
0
20
40
−40 −20
0
20
40
−40 −20
0
20
40
−40 −20
0
20
40
coicop division. The
Figure B2: Histogram of all non-zero price changes in percent by
distributions are truncated at 50 and 50 percent.
Table B3: Weighted mean frequency of price changes and duration by
hicp
Unprocessed food
Processed food
Energy
Non energy industrial goods
Services
Period
n
19751989
hicp sectors.
Products
f+
f−
1,941,510
139
30.4
16.9
19902004
1,229,353
128
18.7
15.8
19751989
2,374,887
166
15.2
5.7
19902004
1,989,909
181
9.6
5.1
19751989
39,954
13
27.4
10.4
19902004
74,561
12
28.9
22.5
19751989
1,666,925
366
16.0
4.0
19902004
2,097,145
465
10.9
6.4
19751989
347,524
185
12.8
1.8
19902004
809,097
242
7.3
2.6
vi
D
2.1
(2.1)
3.8
(4.9)
5.4
(3.0)
7.3
(4.1)
3.5
(3.3)
4.4
(7.1)
7.1
(4.6)
7.6
(5.0)
10.4
(12.3)
24.9
(74.5)
Table B4: The mean absolute size of price increases and decreases by
Increases
hicp
hicp types of goods.
Decreases
19751989
19902004
12.1
13.0
−14.5
−17.8
Energy
2.0
4.0
−7.0
−7.5
Processed food
8.1
8.8
−8.8
−9.2
11.2
12.6
−14.2
−18.5
5.6
9.6
−8.5
−9.0
Unprocessed food
Non energy industrial
19751989
19902004
goods
Services
Table B3 and B4 report estimates for the main components of the Harmonized
hicp): energy, unprocessed food, processed food, non-en
Index of Consumer Prices (
ergy industrial goods,
and
services.
Although there are big dierences between types
of products, they share the features that the frequency of price changes is higher in
the high-ination period than in the low-ination period and that the absolute size
of price changes is higher when ination is low.
Table B5 reports frequency and size statistics for the less aggregated
groups and classes for the whole period.
Vegetables, fruit
and
petrol
coicop
are examples of
products with frequent price changes, while various services experience less frequent
price changes.
Table B5: Mean frequency of price changes and mean price duration in months by
groups (three-digit level) and classes (four-digit level).
coicop
11
Group/Class
n
Food
f
f+
6,629,455
31.4
20.0
111
Bread and cereals
1,158,122
16.7
11.6
112
Meat
1,080,387
42.1
27.6
113
Fish and seafood
750,056
25.2
15.7
114
Milk, cheese and eggs
739,958
19.2
13.1
115
Oils and fats
213,994
25.5
16.3
116
Fruit
455,828
52.1
28.7
coicop
D
dp+
dp−
4.4
11.9
11.0
10.9
11.6
9.2
9.7
12.5
11.7
8.3
6.8
8.8
8.1
23.2
18.3
(4.2)
6.0
(1.8)
2.6
(5.0)
3.7
(1.1)
5.7
(2.1)
3.5
(0.9)
2.4
(2.9)
Table B5 continues on next page.
vii
Table B5 continued.
coicop
12
21
Group/Class
n
f
f+
117
Vegetables
902,300
53.8
31.8
118
Sugar, jam, honey, chocolate
and confectionery
695,046
13.6
8.6
119
Food products n.e.c.
633,764
15.0
10.1
631,126
26.7
16.3
Non-alcoholic beverages
121
Coee, tea and cocoa
246,527
38.7
22.1
122
Mineral waters, soft drinks,
fruit and vegetable juices
384,599
16.0
11.0
124,910
18.2
14.5
Alcoholic beverages
211
Spirits
2,546
20.5
16.5
212
Wine
2,034
16.3
13.4
213
Beer
120,330
17.2
13.4
22
Tobacco
150,168
11.1
9.8
31
Clothing
917,552
12.6
6.7
20,997
7.2
5.2
807,201
13.5
6.7
32
dp+
dp−
2.4
21.9
18.7
12.0
10.8
9.7
9.1
11.1
10.4
10.6
8.7
11.5
11.9
4.6
4.9
3.4
2.8
3.9
4.4
5.6
6.5
7.6
7.0
33.3
25.3
18.8
20.9
36.3
27.5
20.7
14.8
7.4
10.0
28.1
24.9
28.4
25.1
12.8
15.0
13.7
10.2
8.2
7.0
8.2
7.0
10.1
9.1
10.8
9.8
4.5
3.7
13.5
12.0
(2.5)
9.0
(5.2)
6.7
(2.1)
4.3
(2.6)
2.3
(1.3)
6.2
(2.0)
5.1
(1.0)
4.4
(0.3)
5.7
(0.7)
5.4
(1.1)
8.6
(1.4)
8.5
(3.6)
311
Clothing materials
312
Garments
313
Other articles of clothing and
clothing accessories
73,983
8.1
6.3
314
Cleaning, repair and hire of
clothing
15,371
18.7
15.8
171,824
11.8
6.2
163,261
11.9
6.2
8,563
7.0
5.4
14.1
49,926
7.4
5.1
13.0
103,072
20.2
15.2
103,072
20.2
15.2
26,373
31.8
17.5
9,967
29.9
15.5
13,726
53.2
34.2
2,473
8.5
6.1
Footwear
321
Shoes and other footwear
322
Repair and hire of footwear
41
Actual rentals for housing
43
Maintenance and repair of the dwelling
431
45
D
Materials for the maintenance
and repair of the dwelling
Electricity, gas and other fuels
451
Electricity
453
Liquid fuels
454
Solid fuels
13.8
(2.5)
7.6
(3.0)
12.6
(3.5)
7.7
(5.3)
8.5
(2.6)
8.4
(2.5)
(2.2)
(.)
5.9
(3.0)
5.9
(3.0)
6.7
(8.2)
7.3
(11.6)
1.3
(0.1)
12.3
(3.9)
Table B5 continues on next page.
viii
Table B5 continued.
coicop
455
51
52
Heat energy
511
Furniture and furnishings
512
Carpets and other oor
coverings
Household textiles
Household textiles
Household appliances
531
Major household appliances
whether electric or not
532
Small electric household
appliances
533
Repair of household
appliances
54
Glassware, tableware and
household utensils
55
Tools and equipment for house
and garden
56
61
n
Furniture and furnishings,
carpets and other oor coverings
520
53
Group/Class
D
dp+
dp−
2.4
8.2
6.0
13.1
12.4
13.1
12.2
13.2
13.8
27.6
18.4
27.6
18.4
8.1
8.0
7.6
8.1
12.8
11.4
4.4
0.6
16.0
16.4
13.0
12.3
12.7
12.1
12.7
12.1
13.0
12.4
13.0
12.4
10.2
9.1
10.4
9.9
9.8
6.6
11.2
8.2
6.2
4.9
11.8
9.0
22.8
16.0
f
f+
207
33.8
18.3
154,657
11.7
7.9
137,512
11.9
8.1
17,145
10.8
7.0
108,081
9.7
6.3
10.2
108,081
9.7
6.3
10.2
172,532
18.5
11.5
137,759
18.2
10.8
34,578
13.4
8.0
195
32.2
25.5
2.6
153,311
10.3
7.4
10.8
95,651
10.6
7.7
10.6
(0.0)
8.5
(2.5)
8.4
(2.6)
9.0
(1.7)
(2.3)
(2.3)
5.3
(1.6)
5.2
(1.3)
7.1
(1.2)
(.)
(7.0)
(5.1)
551
Major tools and equipment
8,095
10.7
6.3
551
Major tools and equipment
8,095
10.7
6.3
552
Small tools and miscellaneous
accessories
87,556
10.6
7.9
10.9
552
Small tools and miscellaneous
accessories
87,556
10.6
7.9
10.9
783,343
14.5
10.5
778,387
15.9
11.2
Goods and services for routine
household maintenance
561
Non-durable household goods
562
Domestic services and
household services
4,956
10.0
8.5
Medical products, appliances
and equipment
201,344
12.6
8.7
184,185
15.3
10.4
611
Pharmaceutical products
612
Other medical products
9,109
12.6
8.4
613
Therapeutic appliances and
equipment
8,050
6.3
4.6
8.9
(0.6)
8.9
(0.6)
(5.5)
(5.5)
8.1
(6.7)
7.6
(7.6)
9.5
(1.4)
9.2
(5.0)
6.3
(1.6)
7.8
(2.2)
16.2
(4.0)
Table B5 continues on next page.
ix
Table B5 continued.
coicop
62
71
72
73
81
Group/Class
n
Outpatient services
f
f+
D
dp+
dp−
744
6.9
6.8
14.7
8.1
1.8
10.0
1.6
(4.0)
621
Medical services
199
4.9
4.4
19.9
622
Dental services
185
8.0
8.0
12.0
623
Paramedical services
360
6.0
5.8
17.1
70,360
36.0
30.4
51,850
37.1
31.6
3,767
11.7
6.0
14,743
13.3
7.6
607,779
46.0
29.8
270,143
11.4
8.1
Purchase of vehicles
711
Motor cars
712
Motor cycles
713
Bicycles
Operation of personal transport
equipment
(.)
(0.0)
(4.2)
3.0
(1.7)
2.8
(1.4)
8.1
(0.9)
7.0
(0.3)
8.1
(30.6)
721
Spare parts and accessories
for personal transport
equipment
722
Fuels and lubricants for
personal transport equipment
88,142
61.3
39.1
723
Maintenance and repair of
personal transport equipment
234,542
10.9
8.8
724
Other services in respect of
personal transport equipment
14,952
35.1
22.8
9,248
8.1
7.7
12.7
Transport services
8.5
(1.6)
1.3
(1.5)
9.3
(3.3)
46.9
(90.7)
(3.8)
731
Passenger transport by
railway
2,537
6.9
6.7
14.6
732
Passenger transport by road
5,497
6.8
6.5
14.7
733
Passenger transport by air
203
11.0
10.4
734
Passenger transport by sea
and inland waterway
1,011
8.4
7.7
11.6
699
4.8
4.8
20.4
699
4.8
4.8
20.4
13,816
28.2
10.3
3,501
8.1
3.2
152,405
18.2
8.7
Postal services
810
Postal services
82
Telephone and telefax equipment
83
Telephone and telefax services
91
Audio-visual, photographic and
information processing
equipment
(4.6)
(3.0)
8.6
(0.0)
(1.4)
(3.0)
(3.0)
4.1
(3.1)
16.7
(25.6)
6.4
(3.5)
5.1
13.3
2.0
3.3
3.5
2.9
3.2
11.7
7.6
11.8
11.4
5.0
4.2
9.2
8.8
3.4
2.8
9.9
8.9
4.6
1.5
18.2
4.6
9.4
7.6
34.7
5.7
4.1
3.2
6.4
4.7
13.2
13.2
34.6
19.8
5.2
7.3
17.7
11.1
Table B5 continues on next page.
x
Table B5 continued.
coicop
92
93
94
95
96
Group/Class
n
f
f+
D
dp+
dp−
5.5
14.0
10.0
18.5
12.3
20.8
14.2
29.8
14.2
2.2
0.5
9.0
8.7
7.2
2.7
14.4
13.1
18.6
15.8
19.9
15.9
17.2
16.0
22.0
17.4
8.1
10.1
9.8
9.7
5.6
2.8
11.9
15.0
9.2
13.5
12.5
14.5
4.4
9.3
19.7
16.7
4.7
1.9
911
Equipment for the reception,
recording and reproduction of
sound and pictures
75,610
18.0
8.0
912
Photographic and
cinematographic equipment
and optical instruments
18,864
15.4
6.4
913
Information processing
equipment
12,483
26.2
9.4
914
Recording media
45,249
8.7
5.3
915
Repair of audio-visual,
photographic and information
processing equipment
199
32.6
25.0
8,895
7.8
7.0
12.6
Other major durables for
recreation and culture
(1.9)
7.4
(4.0)
4.1
(3.0)
11.4
(2.5)
2.5
(0.0)
(2.4)
921
Major durables for outdoor
recreation
1,216
7.9
7.8
12.2
922
Musical instruments and
major durables for indoor
recreation
7,679
7.5
4.4
14.0
168,794
13.9
7.5
10.4
12.5
Other recreational items and
equipment, gardens and pets
931
Games, toys and hobbies
18,438
8.2
4.8
932
Equipment for sport, camping
and open-air recreation
87,083
8.0
5.3
933
Gardens, plants and owers
47,300
24.2
11.6
934
Pets and related products
15,973
11.4
7.0
Recreational and cultural services
29,807
9.0
7.9
727
11.9
11.1
29,080
7.4
6.3
116,061
16.3
14.8
941
Recreational and sporting
services
942
Cultural services
Newspapers, books and stationery
(1.2)
(4.4)
(8.6)
(3.1)
16.2
(13.0)
4.8
(3.7)
8.4
(1.2)
12.7
(6.2)
9.4
(5.1)
14.4
(6.3)
9.3
(6.3)
951
Books
36,860
7.1
5.9
952
Newspapers and periodicals
42,015
24.5
22.9
954
Stationery and drawing
materials
37,186
6.5
4.8
16.0
199
10.3
7.7
9.2
Package holidays
14.3
(3.8)
4.4
(2.9)
(4.8)
(.)
Table B5 continues on next page.
xi
Table B5 continued.
coicop
Group/Class
n
f
f+
D
dp+
dp−
9.9
0.0
7.8
18.0
5.6
8.6
12.5
11.7
12.4
11.3
14.4
16.9
15.6
10.5
10.0
11.1
7.8
9.3
20.1
15.7
11.0
12.1
20.9
14.6
17.0
9.9
25.9
20.6
5.7
10.7
3.1
0.8
10.8
30.0
101
Pre-primary and primary education
235
7.2
6.7
13.3
102
Secondary education
777
7.4
7.1
13.0
104
Tertiary education
1,454
7.8
7.3
12.3
111
Catering services
154,295
6.8
5.5
15.2
1111
Restaurants, cafes and the
like
141,037
6.9
5.6
15.2
1112
Canteens
13,258
6.4
4.9
15.4
112
Accommodation services
38,342
13.5
9.5
121
Personal care
677,888
12.1
9.0
74,108
9.5
8.6
8,476
12.0
6.6
595,304
13.8
9.3
Personal eects n.e.c.
37,028
9.1
5.6
12.1
1231
Jewellery, clocks and watches
16,146
9.0
5.6
11.7
1232
Other personal eects
20,882
9.4
5.6
12.4
123
1211
Hairdressing salons and
personal grooming
establishments
1212
Electric appliances for
personal care
1213
Other appliances, articles and
products for personal care
(.)
(0.8)
(0.9)
(4.8)
(5.0)
(2.4)
8.2
(3.6)
8.6
(2.6)
10.2
(1.2)
8.0
(1.5)
7.6
(2.7)
(5.9)
(4.6)
(7.7)
124
Social protection
516
5.2
5.1
20.4
125
Insurance
188
22.3
20.0
4.0
126
Financial services n.e.c.
4,509
4.8
2.6
Notes:
(6.6)
(.)
48.2
(58.0)
n.e.c. is short for not elsewhere classied.
Figure B3 shows the cross-sectional variation in
fit+ , fit− , dp+
it
and
dp−
it
over time.
Figure B4 shows a strong positive correlation between the average size of price in
creases and decreases for each product, a relationship that was also detected in the
euro area (see Dhyne et al.,
2006,
Figure
2).
The correlation coecient between the
size of price increases and decreases is .65.
Figure B5 shows a weak, albeit signicant, tendency that products for which
prices increase more often, adjust by a smaller size, thus indicating that the size
of price increases may be positively related to duration. The correlation coecient
between the (log) frequency of price increases and the (log) size of price increases is
xii
40
50
30
40
20
30
10
20
0
10
0
1980
1985
1990
1995
2000
1975
1980
1985
1990
1995
2000
1975
1980
1985
1990
1995
2000
1975
1980
1985
1990
1995
2000
0
0
10
10
20
20
30
40
30
1975
1
1
The size of price increases
5
10
20
40
The frequency of price increases
10
20
80
40 60
Figure B3: The annual distributions of the monthly frequency of price increases (top left),
the frequency of price decreases (top right), the average price increase (bottom left), and
the average price decrease (bottom right). The upper and lower ends of the dashed lines
represent the 90th and 10th percentiles, the dots marking the upper and lower ends of the
solid lines represent the 75th and 25th percentiles, the horizontal lines represent the
median, and the solid lines represent the means. Percent.
5
10
20
The size of price decreases
30
50
1
10
20 30
The size of price increases
50
100 150
Figure B4: The size of price increases by Figure B5: The frequency of price increases
product, dp+
by product, fi+ plotted on the vertical axis
i , plotted on the vertical axis
against the absolute size of price decreases
against the size of price increases by
−
by product, dpi . Log scales.
product, dp+
i . Log scales.
xiii
Low inflation period
.2
.15
.05
.1
Fraction
.25
.3
.35
High inflation period
−50
−40
−30
−20
−10
0
10
20
30
40
50 −50
−40
−30
−20
−10
0
10
20
30
40
50
+
Figure B6: Histograms of average price decreases (dp−
i ) and increases (dpi ) by product
for the high ination period 19751989 (left) and low ination period 19902004 (right).
The distributions are truncated at 50 and 50 percent.
.36. There is not any similar relationship between the frequency and size of price
decreases.
To help understand the increase in the mean size of price changes over time
as shown in Figure
decreases
4,
Figure B6 plots the histograms of the average size of price
+
dp−
i and increases dpi for the high-ination and low-ination periods.
Note
that for each period there are two histograms, one for the mean price decreases
(in red) and one for the mean price increases
mean price changes (below
dp+
i
dp−
i
(in blue). The fraction of smaller
5% in absolute value) are about the same for both periods.
The fraction of price changes between
5
and
10%
(in absolute value) is smaller for
both decreases and increases in the low ination period, while the fraction of price
changes between
10
and
15%
is larger.
Also the far tails of the distributions are
fatter, especially for price increases.
C Detailed decomposition analyses
To further explore the eect of variation in the frequencies and sizes of price ad
justments I compute four conditional estimates of
cpi
ination allowing only one
component to vary over time while holding the other three components constant at
+
π̂t (fit+ |fi− , dp−
i , dpi ) is the predicted in
+
ation rate when only the frequency of price increases fit varies as observed, when
−
+
−
the other three components fi , dpi , and dpi are held constant at their means.
their product-specic means. For example,
+
π̂t (fit+ |fi− , dp−
i , dpi ) =
X
−
−
ωit fit+ dp+
i + fi dpi ,
i
xiv
15
15
PIHAT_m1
Gcpi
PIHAT_m2
Percent
0
0
5
5
Percent
10
10
Gcpi
1985
1990
1995
2000
1975
1980
1985
1990
1995
2000
15
1980
15
1975
Gcpi
PIHAT_m4
Percent
5
0
0
5
Percent
10
PIHAT_m3
10
Gcpi
1975
1980
1985
1990
1995
2000
1975
1980
1985
1990
1995
2000
Figure C1: Ination (solid line) and the contribution from the frequency of price increases
(top left), the frequency of price decreases (bottom left), the mean size of price increases,
(top right) and the mean size of price decreases (bottom right). Annual rates. Percent.
+
π̂t (fit− |fi+ , dp−
i , dpi ) =
X
−
+
−
π̂t (dp+
it |fi , fi , dpi )
=
X
=
X
−
−
ωit fi+ dp+
i + fit dpi ,
i
−
−
ωit fi+ dp+
it + fi dpi ,
and
i
−
+
+
π̂t (dp−
it |fi , fi , dpi )
−
−
ωit fi+ dp+
i + fi dpit .
i
+
π̂t (fit+ |fi− , dp−
i , dpi ) is the predicted ination rate when only the fre
+
quency of price increases fit varies as observed, when the other three components
+
fi− , dp−
i , and dpi are held constant at their means. Figure C1 displays these four
For example,
predicted series. We see that the decline in the frequency of price increases (depicted
in the top left panel), the increase in the frequency of price decreases (on the bottom
left), and the increased absolute magnitude of price decreases (in the bottom right)
all contributed to the downward trend in the ination rate. The correlation coe
cient between
πt
and
π̂t (fit+ |•) is the highest of .90, while corr(πt , π̂t (fit− |•) = 0.79 and
xv
15
15
PIHAT_m8_adj
Gcpi
PIHAT_m7_adj
Percent
0
0
5
5
Percent
10
10
Gcpi
1975
1980
1985
1990
1995
2000
1975
1980
1985
1990
1995
2000
Figure C2: Ination (Solid Line) and the Contribution From Price Decreases (Left), and
Price Increases (Right). Annual Rates. Percent.
−
corr(πt , π̂t (dpit |•)
= 0.73.
The variation in the size of the price increases contributes
positive trend in the
+
between πt and π̂t (dp |∗) of
signicantly to a counterfactual
ination rate (top right) with
a correlation coecient
.51.
The contribution to in
ation from the size of price increases is thus opposite to the contribution from the
size of price decreases.
The eect on ination from the size of price decreases is
thus canceled out by a stronger opposite eect from the size of price increases as
seen in the right panel of Figure
6.
The short-run variability in the frequency of
price increases is important for estimating the short-run variability in ination, as
corr(∆π, ∆π̂t |f + )
=.58.
Figure C2 compares how price decreases (depicted on the left hand panel) and
price increases (depicted on the right) contribute to ination. The graph shows Sim
ilarly, I compute the separate contributions from price increases and decreases, by
π̂t |P OS =
P
i
−
−
ωit fit+ dp+
it + fi dpi ,
and
π̂t |N EG =
P
i
−
−
ωit fi+ dp+
i + fit dpit .
Time
variation in price increases and decreases both contributed to the variation in ina
tion, as shown by correlation coecients of .62 (increases) and .70 (decreases). How
ever, short-run variability in price increases is more important for short-run variabil
ity in ination than short-run variability in price decreases, as corr(∆π, ∆π̂t |P OS )
.65, compared to corr(∆π, ∆π̂t |N EG )
=
.27.
xvi
=
D The aggregation wedge
P
dp∗t is the average of a fraction i ωit dpit /fit , dp†t is the fraction of two averages
dpt and ft . The dierence between dp∗t and dp†t is
While
∆t =
dp∗t
−
dp†t
=
X
i
Figure D1 shows
P
P
X
ω
f
ω
dp
dpit
jt
jt
it
it
j6
=
i
∗
ωit
− Pi
=
ωit dpit
fit
ft
i ωit fit
i
dp∗t and dp†t .
The variables are strongly correlated with a correlation
coecient of .95. Numerically,
∆t
varies between .4% and
2.5% with a mean of 1.1%
8
and is correlated with ination with a coecient of .37.
0
2
4
6
dp^*
dp^\dagger
1975
1980
(D1)
1985
1990
1995
Figure D1: dp∗t and dp†t .
xvii
2000