Inflation and price adjustments: micro evidence from

Inflation and price adjustments: micro evidence from Norwegian consumer prices 1975–2004 By Fredrik Wulfsberg∗ This is the first paper documenting the frequency and size of price adjustments using micro data from both the high-inflation period in the 1970s and 80s, and the period of low-inflation since the early 1990s. When inflation is high and volatile, prices change more frequently and in smaller magnitudes. When inflation is low and stable, prices change less frequently but in larger magnitudes. The frequency of price changes is more important for the variation in inflation when inflation is high and volatile. When inflation is low and stable, the magnitude of the price changes is more important than the frequency. JEL: E31, E32 Keywords: Consumer prices, price rigidity, inflation This paper is a study of how price adjustments at the micro level vary with inflation, using an unprecedented data set spanning 30 years including both the high-inflation period in the 1970s and 1980s, as well as the period of low inflation since the early 1990s. Following Bils and Klenow (2004) many empirical studies have documented prices adjustments using micro data for a large number of individual goods in several countries.1 Most of these studies use data from the recent period of relatively low and stable inflation. Klenow and Kryvtsov (2008) and Nakamura and Steinsson (2008) investigated us data from 1988–2004 when annual inflation rate was 3.3 percent and the standard deviation was 1.1 percent, and Dhyne et al. (2006) analyzed 10 euro area countries from 1996–2001 where average annual inflation rate was only 1.7 percent with a standard deviation of 0.1 percent. The small amount of inflation variability in these samples prevents drawing strong conclusions regarding how price adjustments covary with inflation. In addition these studies yield different results regarding how price adjustments change with inflation. The data used in this paper covers a much longer period than any other study, allowing a more thorough analysis of the comovement between inflation and the ∗ Oslo Business School, 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/. 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 the referees and 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 participants at the Federal Reserve Bank of Boston, ntnu, University of Oslo, and bi Norwegian School of Management. 1 See Klenow and Malin (2010) and Nakamura and Steinsson (2013) for surveys of this literature.

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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 quotes from the Norwegian consumer price index (cpi) between 1975 and 2004. The sample length is unrivaled and splits nicely into a high-inflation period from 1975 to 1989 and a low-inflation period from 1990 to 2004. As in other oecd countries cpi inflation in Norway was high and volatile during the Great Inflation years in the 1970s and 1980s with an average annual cpi inflation rate of 8.4 percent and a standard deviation of 2.7 percent. Norway’s inflation rate peaked at 15.1 percent in January 1981. Its inflation decreased during the 1980s and after 1990 the average inflation rate was 2.4 percent per year with a standard deviation of 0.9 percent. The low-inflation period is thus quite similar in terms of the sample variation in inflation in the U.S. and European studies. Inflation persistence during the sample period was .86 as measured by the AR(1) coefficient 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 cpi data from Mexico during the period when inflation soared from 6.5 percent in 1994 to more than 90 percent in 1995 due to the collapse of the Mexican peso. The inflation rate then declined below 10 percent in 2000. Gagnon (2009) thus explores price adjustments in an emerging economy in the midst of hyperinflation.2 This paper considers a developed economy and inflation experiences typical of developed economies. The Norwegian experience during the 1970s and 1980s represents a very different scenario with moderately high and volatile inflation over many years, as in the other oecd economies. From around 1990 inflation has been low and stable, also as in other advanced economies. In addition, the shocks that hit the oecd economies leading to the Great Inflation period, were different from those shocks that hit the Mexican economy in the 1990s. The evidence from this paper is also highly relevant for the current discussion of optimal inflation level. In the aftermath of the financial crises some economists have argued for raising the inflation target to 4 percent in order to reduce the risk of hitting the zero lower bound (Blanchard, Dell’Ariccia, and Mauro (2010) and Ball (2013)). Others oppose the idea, referring to the experience of double-digit inflation in the 1970s. While 4 percent inflation is well below the numbers from that period, price setting with moderate inflation may nevertheless be different from the current low inflation 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 inflation is high and volatile, and for the transition from the high to the low inflation regime. When inflation 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 inflation was high and volatile, and 2 Alvarez

et. al (2013) is a recent study from the hyperinflation experience in Argentina.

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less often but by larger steps when inflation was low. In section I I explain the data. In section II I describe the variation in the frequency of price adjustments over time. The frequency of price changes declined from the high inflation period to the low inflation period and the frequency of price changes is strongly correlated with inflation. The long-term correlation in the trends of inflation and frequency of price increases is particularly strong. In section III I document that the absolute size of price changes is negatively correlated with the inflation rate: the average price change (in absolute value) increased by around 3 percentage points from the high-inflation period, to around 12 percent in the low-inflation period. In section IV I decompose the variation in the cpi inflation rate into the variation in the frequency and magnitude of price changes. The variation in the frequency of price changes is more important for the variation in the inflation rate when inflation is high. However, the size of price changes is more important when inflation is low and stable. In section V 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 VI I compare my results to the literature. Section VII concludes and discuss briefly some theoretical challenges raised by my findings. I.

Data

Every month Statistics Norway collects data for price quotes on a wide range of consumer goods and services (henceforth products) to construct the cpi (see Statistics Norway (2001, 2006) for details). For example they record the price of a bag of eight buns without raisins in a specific outlet or store once a month. On the basis of these collected data I have constructed a panel database on prices for 1,124 products covering the 360 months from January 1975 to December 2004, which together total 14,363,828 price observations. The average number of observations per month is 39,900. 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 observations per trajectory. The average number of observations by product is 12,678 and the average number of trajectories for each product is 383, i.e. the prices for an product are on average sampled from 383 outlets. The sampled products change over time as new goods are introduced while other goods disappear. There are 548 products in 1975 and 845 products in 2004. Figure 1 shows examples of typical price trajectories for two different products: 649 petrol, unleaded 95 octane, self-service (left); and 599 wash, clip and blow dry, ladies (right). The trajectories show very different 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. Products are defined with varying degrees of precision. Product 649 petrol, unleaded 95 octane, self-service is precisely defined, while product 599 wash, clip

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AMERICAN ECONOMIC JOURNAL Petrol, unleaded 95 oct., self−service

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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.

and blow dry, ladies is less precisely defined as the quality and type of clip is not necessarily 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 flagged 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, 409 products (36 percent of all products) are observed the entire period. 208 products (19 percent) are observed between 20 and 30 years, 223 products (20 percent) are observed between 10 and 20 years, and 284 products (25 percent) are observed less than 10 years. When constructing the cpi, Statistics Norway applies weights, ωit , to each product i reflecting 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 percent of the cpi. The most important products that are not included in the dataset are imputed housing rents, craftsmen services, and municipal fees. II.

The Frequency of Price Changes

In this section I document the variation in the frequency of price changes over time. I first 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

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Gcpi


Frequency of increases

5

Frequency of decreases 20

Frequencies, percent

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15

10

15

10

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5 0

0 1975

1980

1985

1990

1995

2000

2005

5

10

15

Inflation, percent

Figure 2. Left: cpi inflation, 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 inflation. Annual rates. Percent.

zero price changes) within each year.3 I then decompose fit into the frequencies of price increases fit+ and decreases fit− . Using product- and year-specific cpi weights, average monthly frequency changes Pof price P ωit , I compute the+weighted P − + − ft = i ωit fit , increases ft = i ωit fit , and decreases ft = i ωit fit for each year. There is substantial temporal variation in the frequencies of price changes, and there are systematically differences between the high and low inflation periods. The left panel of Figure 2 shows ft+ , ft− , and the cpi inflation rate. The frequency of price increases declined markedly from around 20 percent in the early 1980s to around 12 percent after 2000. Norway’s price (and wage) freeze law in 1979 had a temporary negative effect on the frequency of price increases, and the 9 percent devaluation of the nok explains the spike in 1986. The results of this paper are, however, not affected by these events. Figure 2 also shows that price decreases are frequently observed in the data even when inflation was high in the 1970s and early 1980s. The frequency of price decreases hovered around 6–8 percent, but increased to 8–10 percent after 2000. The hike in 2001 is associated with a 50 percent decrease in the value-added tax on food. While about one of four price changes were price decreases during the 1970s and 1980s, decreases were almost as frequent as increases after 2000.4 To highlight the differences between the high and low inflation periods, the first two columns of Table 1 report statistics for the frequency of price changes 3 Price

changes from December in year t − 1 to January in year t are included in the estimates of fit . temporal features of the frequency of price increases and decreases are not confined to the means only. Figure B3 in the appendix shows the same tendency for different percentiles of the year-specific 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 inflation is low. 4 The

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Table 1—The median and mean of the weighted frequency of price changes. Percent.

1975–1989

1990–2004

Full sample

Excluding sales

12.8 17.9

Frequency of price increases, fi+ 8.3 9.4 12.1 14.8

9.2 14.6

Median Mean

3.5 5.8

Frequency of price decreases, fi− 4.5 4.3 7.5 7.1

3.8 6.7

Median Mean

15.6 23.7

Frequency of price changes, fi 12.8 14.3 19.6 21.9

13.0 21.3

Median Mean

when splitting the sample in the two periods. The top panel reports the weighted mean, median, and standard deviation of the frequency of price increases ft+ across products. The mean frequency of price increases dropped significantly from an average of 17.9 percent in the high-inflation years to 12.1 percent during the low-inflation years. Similarly, the median frequency of price increases fell from 12.8 percent to 8.3 percent. In the second panel of Table 1 we see that the mean frequency of price decreases ft− rose from an average of 5.8 percent in the high-inflation period to 7.5 percent in the low-inflation 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-inflation period than in the low-inflation 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 percent 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 cpi inflation rate as seen from the scatter plot in the right panel of Figure 2, which plots the frequency of price increases and decreases versus the inflation rate. The correlation coefficient is .80, illustrated by the regression line. The frequency of price decreases is less strongly correlated to the inflation rate, with a correlation coefficient of –0.49. While the right panel of Figure 2 shows a strong, positive correlation between inflation and the frequency of price increases, the left panel shows that both these variables exhibit a strong downward trend. Thus, in order to assess the importance of this common trend, I decompose the frequency of price increases ft+ and inflation πt into a trend and a deviation from trend using a hp(10)-


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1980

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4

Figure 3. Trend components of the frequency of price increases ft+ and inflation πt (left panel) and a scatterplot of the cyclical components (right panel).

filter. 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 a regression line.5 The strong correlation between inflation and the frequency of price increases both in the long-term and short-term underscores the strong link between these variables. However, the correlations may of course not represent any causal relationships. In particular the long-term correlation is probably affected 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 affected 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 inflation is spurious. In the event of a new period with moderately high and volatile inflation, 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 using the formula 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-inflation period to 12.3 months during the low-inflation period.7 The last 5 Another measure of the short-term correlation is between the change in inflation ∆π and change in the frequency of price increases ∆f + which is .41. 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 censored price spells does not affect 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

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Table 2—Implied duration. Months.

1975–1989

1990–2004

Full sample

Excluding sales

5.9 6.7

7.3 12.3

6.5 8.1

7.2 8.4

Median Mean

column of Table 2 reports the 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. III.

The Size of Price Increases and Decreases

To investigate the time variation in the magnitude of price changes, I first compute the average magnitude of non-zero monthly price increases and decreases − in percent for each product and year, denoted dp+ I compute the it and dpit . ThenP + + yearly average cpi-weighted price increase and decrease: dp = t i ωit dpit and P − − dpt = i ωit dpit . The average magnitude of all the non-zero price changes for product i is often referred to as the intensive margin dp∗it . It is thus equal to the − weighted-average of the size of price increases dp+ it and decreases dpit weighted by their relative frequencies: (1)

dp∗it =

fit+ + fit− − dp + dp , fit it fit it

Note that a change in the relative frequency of price increases f + or decreases f − will affect the intensive margin dp∗it . The aggregate intensive margin dp∗t is the cpi-weighted average of the intensive margin for each product (2)

dp∗t =

X

ωit dp∗it .

i − ∗ The left panel of Figure 4 plots dp+ t , the absolute size of dpt , and dpt together with the inflation 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 have trended upwards. The mean size of price increases dp+ t rose from 11 percent in 1975 to 18 percent in 2004. Similarly, the mean size of price decreases dp− t increased in absolute value from about –10 percent to almost –14 percent by the end of the sample. The average size of price increases are generally higher than the average size of price decreases in absolute value. As inflation reduration, applying the formula to the mean frequency yields a duration of −1/ ln(1−0.217) = 4.1 months which is different from the mean implied duration.

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Mean increase Mean intensive margin Magnitude of price changes, percent

Gcpi Mean decrease


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Price increases

Price decreases

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0 1975

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Inflation, percent

Figure 4. Left: The cpi inflation rate (blue solid line), the mean weighted magnitude of − price increases dp+ t (red dashed line), decreases dpt 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 inflation rate with regression lines. Annual rates. Percent.

duces the relative price between price adjustments, price increases are on average larger than the absolute size of price decreases (see Ball and Mankiw (1994)). The scatter plot in the right panel of Figure 4 shows the negative correlation between the size of price changes and the cpi inflation rate. The correlation coefficient between inflation and the size of price increases is –.52, and .60 between inflation 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 finding? 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 significant for most types of goods (see Figure B3 in the appendix). Figure 4 also shows that the intensive margin dp∗t declined from the high to the low inflation period yielding a strong positive correlation with inflation (correlation coefficient of .87). We see from (1) that the intensive margin depends on + to what extent dp− it cancel out dpit determined by the relative frequency of price increases and decreases. The increasing relative frequency of price decreases (as seen from Figure 2) thus contributed to the fall in the average intensive margin dp∗t from 4.9 percent in the high-inflation period to 2.7 percent in the low-inflation period. In Table 3, columns (1) and (2) I report the weighted moments of the average size of the price changes occurring in the high-inflation period (1975–1989) and in the low-inflation period (1990–2004). The mean average size of price increases

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Table 3—The weighted average price increase and decrease. Percent.

1975–1989 Median Mean Median Mean

1990–2004

Full sample

Excluding sales

dp+ i

7.6 10.5

Size of price increases 9.9 9.3 13.2 12.3

–7.8 –9.1

Size of price decreases dp− i –10.2 –9.7 –11.2 –10.5

8.9 11.5 –9.0 –9.7

and decreases were 13.2 and –11.2 percent in the low-inflation period, about 2–3 percentage points higher in absolute value than in the high-inflation period. For completeness, column (3) of Table 3 reports the weighted median and mean of the average magnitudes of price increases and decreases over the whole sample. The median and mean average price increases by product are 9.3 and 12.3 percent, while the median and mean average price decreases are –9.7 and –10.5 percent. 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 effect 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 tstatistic of –.127. There is a significant positive correlation for only 208 products (19 percent) (i.e. the t-statistic is larger than 1.96).8 Figure B5 in the appendix shows a weak, albeit significant, 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 confirms that the temporal variation in the average frequencies and sizes of price adjustments applies to most categories of goods and services with few exceptions. IV.

Decomposition of the Inflation Rate

Sections II and III show that the average of both the frequency and magnitude of price adjustments are correlated with inflation. In this section I illustrate 8 Using only price increases in the regression do 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 significant positive estimates are 154.


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0

5

Percent

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Gcpi

1975

1980

1985

1990

1995

2000

Figure 5. cpi Inflation, πt , (solid line) and predicted inflation rate, π ˆt (dashed line). Annual rates. Percent.

their partial contributions to the variation in the inflation rate. To this end, I first decompose the inflation rate into the frequencies and the magnitudes of price increases and decreases. I then construct counterfactual estimates of cpi inflation 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 inflation. A high correlation indicates that the conditioning variable may be an important contributor to the variation in the inflation rate. To be able to decompose inflation into frequencies and magnitudes, I first derive an estimate of cpi inflation π ˆt as the weighted average of product-specific price changes, (3)

π ˆt =

X

ωit dpit ,

i

where ωit is the cpi weight, and dpit is the average monthly price change (including zero price changes) for product i in year t. Figure 5 shows that π ˆt tracks the official cpi inflation rate πt extremely well, with a correlation coefficient of .91. In particular π ˆ replicates the high and volatile inflation period that from 1975 which ended with the disinflation period that started in the latter half of the 1980s. In the low-inflation period from 1990 until the end of the sample, π ˆ also 9 fits the cpi history well. Using that the average price change for each product dpit is equal to the fre9 The main reasons why π ˆ is not identical to π is first, 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 differences (see Statistics Norway (2001)). π ˆt is mean adjusted from 8.2 to 5.4 percent, which is the mean of πt .

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MONTH YEAR

quency fit times the size dp∗it , I substitute for dpit in (3) which yields (4)

π ˆt =

X

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 dp∗it using (1) which yields (5)

π ˆt =

X

− − ωit fit+ dp+ it + fit dpit .

i

The decomposition shows that the frequencies and magnitudes enter multiplicatively at the product level in (5).10 I then construct two counterfactual estimates of cpi inflation using the decomposition in (5) where I allow either the magnitudes or the frequencies to vary over time while holding the other constant at its product-specific means. The conditional estimate of cpi inflation allowing the frequencies of price changes to − vary over time but holding the size of price changes constant at dp+ i and dpi is: X − − − π ˆt fit+ , fit− dp+ , dp = ωit fit+ dp+ (6) i i i + fit dpi . i

− The only contribution to variation in π ˆt 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 π ˆf,t . Similarly, the conditional estimate of cpi inflation allowing the magnitudes of price changes to vary over time, but keeping the frequency of price changes constant at fi+ and fi− : X − + − − − (7) π ˆt dp+ f , f = , dp ωit fi+ dp+ i it it i it + fi dpit . i

− + − The only contribution to variation in π ˆt 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 π ˆdp,t . Figure 6 shows cpi inflation πt together with the frequency-related inflation π ˆf,t in the left panel, and with the size-related inflation π ˆdp,t in the right panel. We see that the frequency-related inflation is strongly correlated with cpi inflation (with a correlation coefficient of 0.92). This is compelling evidence that the variation in the frequency significantly contributes to the variation in the inflation rate. The size-related inflation π ˆdp,t in the right panel of Figure 6, is negatively correlated 10 Note that inflation is the weighted-average product of the frequencies and sizes for each product. It is not possible to decompose inflation into the aggregate frequencies and sizes.

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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

Figure 6. Inflation (solid line) and the conditional estimates of cpi inflation π ˆt (fit |dpi ) (left) and π ˆt (dpit |fi ) (right). Annual rates, percent.

with the cpi (with a correlation coefficient of –.24). The variation in the size of price changes has thus not been a major factor behind the overall variation in the inflation rate at least in the long term. Time variation in the weights are also a source of variation in the inflation rate. Recalculating π ˆf,t and π ˆdp,t using constant weights does not affect the result.11 The dominant contribution of the frequency of price changes is confirmed by a simple unrestricted ols regression of πt on π ˆf,t and π ˆdp,t : (8)

πt = − 3.52 + 0.69 π ˆf,t + 0.31 π ˆdp,t (2.39)

(0.06)

(0.24)

where standard errors are reported in the parentheses and with R2 = 0.86. The coefficient on the frequency-related inflation π ˆf,t is clearly significant and twice the size of the insignificant coefficient of the size-related inflation π ˆdp,t . Note that the unrestricted coefficients sum to 1.00, so variation in the frequency of price changes accounts for 69 percent of the variation in inflation.12 The high correlation between the frequency-related inflation rate and cpi inflation 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) filter, show that the trend components have a correlation coefficient of .993 while the deviations from trend have a correlation of .577. For the size-related inflation rate and cpi inflation the correlation coefficient is –.679 for the trend components and .266 for the deviation component. Also the change in inflation is more correlated 11 The correlation coefficients between π ˆf,t and π ˆdp,t using constant weights and cpi inflation are .92 and –.38. 12 Over such a long period as thirty years the cpi weights may have changed quite a lot and affected the time variation in the weighted margins. To test the robustness of the results above I recalculate the correlation coefficients using constant weights. The correlation coefficients are not much affected: for example, with fixed weights corr(π, π ˆt (fit |dpi )) =.92 and corr(π, π ˆdp,t ) =–.38.


MONTH YEAR

0

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.06

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−10 0 10 Price change, percent

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Figure 7. Histogram of all cpi-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.

with the change in the frequency related inflation as corr (∆π, ∆ˆ πf,t ) = .48 while corr (∆π, ∆ˆ πdp,t ) = .18. Hence, the frequency is the dominating factor in both long and short term variability in the inflation rate. Calculating the correlation coefficients between π ˆdp,t and the cpi inflation rate over the high- and low-inflation periods separately, I find correlation coefficients of –.03 in the high-inflation period and .52 in the low-inflation period. Correspondingly the correlation coefficients between π ˆf,t and π are .80 in the high-inflation period and .41 in the low-inflation period. An ols regression similar to (8) assuming homogeneity, yield a coefficient of .81 for π ˆdp,t in the low-inflation period compared to .33 in the high-inflation period. Thus when inflation is low, the size of price changes seems to be more important for the variation in inflation than the frequency. V.

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 7 shows the pooled distribution of the size of all non-zero 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 13 percent of the price changes are less than 1 percent in absolute value and 45 percent are less than 5 percent in absolute value. Alvarez, Le Bihan, and Lippi (2013) argue that the real effect of monetary shocks increases with the kurtosis (peakedness) in the price change distribution. Discarding price changes larger than ln(10/3) percent and smaller than .1 percent

VOL. VOL NO. ISSUE


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

15

−50

0

50

−50

0

50

Figure 8. Histograms of non-zero price changes by the number of products per firm. Bin width 1 percent and truncated at –50 and 50 percent.

following Alvarez, Le Bihan, and Lippi (2013), the kurtosis is 8.9 in the high inflation period and 10.9 in the low inflation period.13 This indicates that monetary policy is somewhat more effective when inflation is low. A distribution of non-zero price changes with a single mode around zero is not consistent with state dependent models where firms face a fixed 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 years and is not necessarily characteristic for distributions at the micro level.14 As it is not appropriate to eyeball each histogram for 1,124 products, I apply Hartigan’s dip test (Hartigan and Hartigan, 1985) for each product level distribution. I reject the null hypothesis of unimodality for only 14 percent of all products at the 5 percent level of significance. Thus 86 percent of the product distributions of price changes can be viewed as unimodal. At the product-store level the test rejects unimodality for only 420 out of 239 893 product-store distributions with more than 20 observations, i.e. 0.2 percent. Lach and Tsiddon (2007) and Midrigan (2011) argue that the many small price changes in combination with a high average price change are, however, consis13 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. 14 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 differ. 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.

16


MONTH YEAR

tent with a menu-cost model when firms 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 firms in Figure 8. The histogram in the top left panel shows the size of price changes for firms reporting the price for only one product, the top right panel shows the size price changes for firms reporting prices for 2–5 products, and so on. We see that the distribution for single-product firms 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 firms are clearly unimodal centered slightly above zero which is consistent with Lach and Tsiddon (2007) and Midrigan (2011). VI.

Empirical Comparisons

How do the findings 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-inflation period in Norway is similar to the 13 months for the euro area (see Dhyne et al. (2006)). Nakamura and Steinsson (2008) report about 8–9 months for the United States, and that temporary price changes due to sales have a big impact on their duration estimates. In their data, 21.5 percent of the price change observations are sales-related compared to 3.3 percent in the present data, which is similar to the euro area data (Dhyne et al., 2006). 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-inflation period are similar to the European and us estimates. For example, Klenow and Kryvtsov (2008) find that the mean average price increase is 12.7 percent and the mean average price decrease is –14.1 percent 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 percent for the United States. Dhyne et al. (2006) report that the average price increase in the euro area is 8.2 percent and the average price decrease is –10.0 percent. Third, there is diverging evidence on the comovement between inflation and the frequency and size of price changes. Goette, Minsch, and Tyran (2005) and Nakamura and Steinsson (2008) also find a positive correlation between inflation and the frequency of price increases. On the other side Gagnon (2009) finds no correlation between inflation and the frequency of all price changes when inflation is below 10–15 percent.15 However, he does find a negative correlation between inflation and the magnitude of price increases and decreases (see Gagnon (2009, Figure VII b)) as in this paper, while Neither Dhyne et al. (2006) nor Nakamura and Steinsson (2008) report any correlation between inflation and the magnitude 15 Gagnon (2009) does not report separate correlations between inflation and the frequency of price increases or decreases.

VOL. VOL NO. ISSUE


17

of price changes. Klenow and Kryvtsov (2008) find no correlation in the us data and report that the intensive margin is more important for the variation in us inflation. They decompose the variation in the inflation rate according to16

(9)

π ˆt =

X

ωit dpit =

i

X i

P ωit dpit = ft dp†t ωit fit Pi i ωit fit

and find that the variation in dp†t accounts for more than 90 percent of the variation in π ˆt . Note, however, that dp†t as defined by Klenow and Kryvtsov (2008) deviates systematically from the aggregate intensive margin dp∗t as defined P in (1) and (2). While dp∗t is the average of a fraction i ωit dpit /fit , dp†t is the fraction of two averages dpt /ft and depends on the frequency of price changes.17 Fourth, the prevalence of many small price changes is a common finding in many countries, see Klenow and Malin (2010) and Cavallo and Rigobon (2011).18 For the whole sample the kurtosis is 9.7 compared to 12.8 for French cpi data (see Alvarez, Le Bihan, and Lippi (2013, Table 1)) and 10.0 for us data (see Klenow and Malin (2010)). VII.

Conclusions

There is substantial empirical evidence on price adjustments in advanced economies with low and stable inflation. This paper adds to this evidence by investigating monthly retail price data over three decades characterized by both high and low inflation. During the 1970s and 1980s, cpi inflation in Norway was moderately high and volatile, peaking at 15.1 percent in 1981. Inflation then decreased during the 1980s, and from 1990 onwards cpi inflation has varied around 2.4 percent per year. The main findings are that high and volatile inflation is strongly related to the variation in the frequency of price changes and unrelated to the variation in the size of price changes. The same is true for the transition from the high to the low 16 See Klenow and Kryvtsov (2008, equation (4)). I use my notation, however, to simplify comparison. P (Also, I have dropped the t operator from their equation – which is a typo.) 17 The difference between dp∗ and dp† is t t ! P P X X ωit dpit dpit j6=i ωjt fjt (10) ∆t = dp∗t − dp†t = ωit − Pi = ωit dp∗it fit ft i ωit fit i i

Numerically, ∆t varies between 0.4 percent and 2.5 percent with a mean of 1.1 percent (see Figure C1 in the appendix) and is positively correlated with inflation with a coefficient of .38. (∆t is computed as ∆t = dp∗t − π ˆ /ft .) Also, ∆t depends on the frequency of price changes (as do both dp†t and dp∗t ): we see that prices which change frequently (high fi ) contribute to a smaller ∆t . 18 Eichenbaum et al. (2014) argue that the vast majority of these changes are due to measurement error.

18


MONTH YEAR

inflation regime. When inflation is low and stable, both the frequency and the size of price adjustments are important, but the size is more important than the frequency. To reach these findings I use a novel decomposition of the inflation rate. I also document some other interesting regularities: (i) The mean size of price increases and the mean absolute size of price decreases are higher in the low inflation period than when inflation was high. (ii) While the average size of price changes is large, 13 percent of the (non-zero) price changes are smaller than 1 percent in absolute value. There are fewer small price changes when inflation is low than when inflation is high. A caveat, however, is in order when we interpret the correlations between inflation and the frequency and size of price adjustments as they may of course not represent any causal relationships. In particular the long-term correlation is probably affected by structural changes in the economic environment over the decades. For example, more information available due to computers, and the propagation of the Internet may have affected price setting. Furthermore, the type of shocks hitting the economy have changed and so on. The correlations are thus not conclusive evidence that higher inflation trigger more frequent price adjustments. Furthermore, the strong correlation in trends may indicate a spurious relationship between the frequency and inflation. However, the correlation is also present in the short-term variation in the frequency and inflation, which makes a spurious relationship less likely. Thus, it seems unreasonable to assume that the frequency of price adjustments is a constant independent of the economic environment. The reported correlations between price adjustments and inflation is suggestive evidence in favor of state dependent models. In time-dependent models like the Calvo model, the firms receive an exogenous signal allowing them to change their price either up or down allowing ft+ and ft− to covary with inflation. However, the correlation coefficient between the average frequency of all price changes ft and inflation is as high as .70, which is not explained by the Calvo model. When inflation is high prices thus increase on average more frequently, but in smaller amounts. In contrast prices increase less frequently though in larger amounts when inflation is low. Price decreases, on the other hand, are more frequent and larger in size when inflation is low. One possible interpretation of what is going on is that firms change prices either because of inflation or because of idiosyncratic shocks. When inflation is higher, firms increase prices more often and by smaller amounts just to keep up with the inflation rate. In this regime inflation is a relatively more important incentive than idiosyncratic shocks to change prices. In a low inflation regime, the opposite holds: Firms do not have to change prices often to keep up with inflation, only when hit by idiosyncratic shocks. This evidence strongly indicates that firms not only treat the size of price changes, but also the timing of price changes as choice variables. The probability

VOL. VOL NO. ISSUE


19

of changing prices should thus be treated as an endogenous variable, depending on the state of the economy like in Caplin and Spulber (1987) and Golosov and Lucas (2007). Time-dependent models (Taylor (1980), and Calvo (1983)) assume that the frequency of price adjustment is exogenous, and thus it is not able to explain the variation in inflation. Monetary policy analysis that assumes an exogenous probability of price changes, are thus subject to the Lucas (1976) critique. Furthermore, many empirical studies interpret the frequency of price changes as a measure of price rigidity following the Calvo model. For example Dhyne et al. (2006) conclude that prices are more rigid in Europe than in the United States. Following the same logic, we should conclude that prices were more rigid in the 1990s and 2000s than in the 1970s and 80s. However, this conclusion is questionable as deregulation in most sectors (see e.g. Høj, Kato, and Pilat (1995), Conway, Janod, and Nicoletti (2005) and Alesina et. al (2005); Alesina, Ardagna, and Galasso (2010)) have made product markets more competitive and price setting probably more flexible over this period. Furthermore, Caballero and Engel (2007) show that there is no relationship between price stickiness and the frequency of price changes in Ss type state-models. The strong correlation between the frequency of price changes and inflation suggest that the frequency of price changes is not a structural parameter. For the same reason one should also be careful when interpreting results from using frequency data to calibrate macro models. While state-dependent models with a fixed cost of changing prices (see Barro (1972) and Sheshinski and Weiss (1977)) may explain the positive correlation between the frequency of price increases and inflation, they unambiguously predict a positive correlation between the size of prices increases and the rate of inflation, in contrast to the evidence here. However, Rotemberg (2010) shows that if adjustment costs are increasing in the size of price changes, higher inflation may lead firms to reduce the size of their price increases. In a menu cost model with trend inflation and idiosyncratic shocks, Blanco (2014) shows that the latter tends to be associated with larger adjustments while inflation increases the frequency. Hence, when inflation is low and stable price adjustments are dominated by idiosyncratic shocks which tend to increase the size of adjustments. References

Alesina, Alberto, Silvia Ardagna, and Vincenzo Galasso (2010). “The Euro and Structural Reforms.” in Europe and the Euro ed. by Alberto Alesina and Francesco Giavazzi, nber, pp. 57–93. Alesina, Alberto, Silvia Ardagna, Giuseppe Nicoletti, and Fabio Schiantarelli (2005). “Regulation and Investment.” Journal of the European Economic Association 3(4), pp. 791–825. Alvarez, Fernando, Herv Le Bihan, Francesco Lippi (2013). “Small and

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Large Price Changes and the Propagation of Monetary Shocks.” cepr Discussion Paper No. 9770. Alvarez, Fernando, Andy Neumeyer, Martin Gonzalez-Rozada and Martin Beraja. (2013). “From Hyperinflation to Stable Prices: Argentina’s Evidence on Menu Cost Models.” Stanford Center for International Development Working Paper No. 470. Ball, Laurence (2013). “The Case for Four Percent Inflation.” Central Bank Review, Vol. 13, pp.17-31. Ball, Laurence and N. Gregory Mankiw (1994). “Asymmetric Price Adjustment and Economic Fluctuations” The Economic Journal 104(423), 247–261. Barro, Robert J. (1972). “A Theory of Monopolistic Price Adjustment.” Review of Economic Studies, 39, 17–26. Baudry, Laurent, Herv Le Bihan, Patrick Sevestre, and Sylvie Tarrieu (2007). “What do Thirteen Million Price Records have to Say about Consumer Price Rigidity?” Oxford Bulletin of Economics and Statistics, 69(2), 139–183. Bils, Mark and Peter J. Klenow (2004). “Some Evidence on the Importance of Sticky Prices.” Journal of Political Economy 112(5), 947–985. Blanchard, Olivier, Giovanni Dell’Ariccia, and Paolo Mauro (2010). “Rethinking Macroeconomic Policy.” Journal of Money, Credit, and Banking, 42 (Supplement), pp. 199–215. Blanco, Julio A. (2014). “A Regime Contingent Phillips Curve.” Mimeo, New York University. Caballero, Ricardo J. and Eduardo M.R.A. Engel (2007). “Price Stickiness in Ss Models: New Interpretations of Old Results.” Journal of Monetary Economics 54, 100–121. Calvo, Guillermo A. (1983). “Staggered Prices in a Utility-Maximizing Framework.” Journal of Monetary Economics 12, 383–398. Caplin, Andrew S. and Daniel F. Spulber (1987). “Menu Costs and the Neutrality of Money.” Quarterly Journal of Economics 102(4): 703-725. Cavallo, Alberto (2010). “Scraped Data and Sticky Prices: Frequency Hazards, and Synchronization,” mit Sloan Working Paper No. 4976-12. Cavallo Alberto, and Roberto Rigobon (2011). “The Distribution of the Size of Price Changes.” nber Working Paper No. 16760 Conway, Paul, Vronique Janod, and Giuseppe Nicoletti (2005). “Product Market Regulation in OECD Countries: 1998 to 2003” oecd Economics Department Working Papers, No. 419, oecd Publishing.

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´ Dhyne, Emmanuel, Luis J. Alvarez, Herv´ e Le Bihan, Giovanni Veronese, Daniel Dias, Johannes Hoffmann, Nicole Jonker, Patrick Lunnemann, Fabio Rumler, and Jouko 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), 171–192. Eichenbaum, Martin, Nir Jaimovich, Sergio Rebelo, and Josephine Smith (2014). “How Frequent Are Small Price Changes?” American Economic Journal: Macroeconomics, 6(2) pp. 137–155. Gagnon, Etienne (2009). “Price Setting During Low and High Inflation: Evidence from Mexico.” The Quarterly Journal of Economics, 124(3), 1221–1263. Gtte, Lorenz, Rudolf Minsch, and Jean-Robert Tyran (2005). “Micro evidence on the adjustment of sticky-price goods: It’s how often, not how much.” cepr Discussion Papers No. 5364. Golosov, Mikhail and Robert E. Lucas Jr (2007). “Menu Costs and Phillips Curves.” Journal of Political Economy, 115(2), 171–199. Hartigan, J.A. and P.M. Hartigan (1985). “The Dip Test of Unimodality.” The Annals of Statistics, 13(1), pp. 70–84. Høj Jens, Toshiyasu Kato and Dirk Pilat (1995). “Deregulation and Privatisation in the Service Sector” oecd Economic Studies, No. 25, pp. 37–74. Klenow, Peter J. and Oleksiy Kryvtsov (2008). “State-Dependent or TimeDependent Pricing: Does It Matter for Recent U.S. Inflation?” The Quarterly Journal of Economics, 123(3), 863–904. Klenow, Peter J. and Benjamin A. Malin (2010). “Microeconomic Evidence on Price-Setting.” in the Handbook of Monetary Economics 3A, B. Friedman and M. Woodford ed.: Elsevier, 231–284. Lach, Saul and Daniel Tsiddon (2007). “Small Price Changes and Menu Costs.” Managerial and Decision Economics 28, 649–656. Robert E. Lucas Jr (1976). “Econometric Policy Evaluation: a Critique.” Carnegie- Rochester Conference Series on Public Policy, 1, 19–46. Midrigan, Virgiliu (2011). “Menu Costs, Multi-Product Firms, and Aggregate Fluctuations.” Econometrica, 79(4) pp. 1139–1180. Nakamura, Emi and J´ on Steinsson (2008). “Five Facts About Prices: A Reevaluation of Menu Cost Models.” The Quarterly Journal of Economics, 123(4), 1415–1464. Nakamura, Emi and J´ on Steinsson (2013). “Price Rigidity: Microeconomic Evidence and Macroeconomic Implications.” Annual Review of Economics, 5, 133–163.

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Rotemberg, Julio J. (2010). “Altruistic Dynamic Pricing with Customer Regret.” Scandinavian Journal of Economics, 112(4), 646–672. Sheshinski, Eytan and Yoram Weiss (1977). “Inflation and cost of price adjustment” Review of Economic Studies 44(2), 287–303. Statistics Norway (2001). “Konsumprisindeksen 1995–2000,” Norges Offisielle Statistikk (NOS C 680), Statistics Norway, Oslo. Statistics Norway (2006). “About the cpi.” http://www.ssb.no/kpi_en/ about.html Taylor, John B. (1980). “Aggregate dynamics and staggered contracts.” Journal of Political Economy 88, 1–24. United Nations (2000). “Classifications of Expenditure According to Purpose.” Statistical Papers Series M No. 84, United Nations, New York.

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I

Online Appendix for

Inflation and price adjustments: micro evidence from Norwegian consumer prices 1975–2004 by Fredrik Wulfsberg, Oslo Business School January 18, 2016 A.

Data

50,000 1975

1980

1985

1990

1995

2000

20,000

10,000

20,000

30,000

30,000

40,000

40,000

50,000

Today the Norwegian cpi is computed from monthly data for 900 representative goods and services from approximately 2,200 firms. Once a year the representative goods and services are revised. The sample of firms is rotated so that a firm is included for a maximum of six years (72 months). The firms 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 in the sample resulting in breaks in the trajectories. 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 offered 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 different months. Figure A2 illustrates the number of observations by coicop groups over time, with the number of observations in 2004 appearing on the right.

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Figure A1. The Variation in the Number of Observations by Year (Left) and by Month (Right)

II


MONTH YEAR

12 11 10 COICOP Division

9 8 7 6 5 4 3 2 1 1975

1980

1985

1990

1995

2000

2005

Figure A2. The distribution of observations across coicop groups over time.

B.

Heterogeneity

Figure B1 shows the distribution of the frequency of price adjustments fi . The distribution is skewed to the right with a mean and median frequency of 21.9 and 14.3 percent (as reported in Table 1). Table B1 reports average frequencies and duration estimates for the high- and low-inflation periods for twelve coicop divisions.19 The mean duration varies between 3.8 months for 1 Food and beverages in the high inflation period and 39.6 months for 12 Miscellaneous goods and services in the low inflation period. The frequency of price changes is higher in the high-inflation period than in the low-inflation period for all coicop divisions except for 3 Clothing and footwear, 8 Communication, and 9 Recreation and culture. For all categories the frequency of

0

.05

Fraction .1

.15

.2

19 coicop is an acronym for Classification of Individual Consumption According to Purpose. Each product is classified at the five-digit coicop level (see United Nations (2000)).

0

10

20

30

40

50

60

70

80

90

Figure B1. The distribution of the frequency of price changes in percent across products.

VOL. VOL NO. ISSUE


III

Table B1—Mean frequency of price changes and mean price duration in months by coicop divisions (two-digit level).

Products

f+

f−

D

4,229,361 3,031,220

264 267

22.6 13.4

11.9 10.2

3.8 5.8

1975–1989 1990–2004

87,036 188,042

41 42

16.0 11.0

1.6 3.2

5.4 7.1

3 Clothing and footwear

1975–1989 1990–2004

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

1975–1989 1990–2004

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

1975–1989 1990–2004

774,272 693,303

130 137

10.3 7.3

3.2 5.0

8.0 9.1

6 Health

1975–1989 1990–2004

3,070 199,018

15 52

8.8 7.5

0.7 2.0

11.7 12.6

7 Transport

1975–1989 1990–2004

228,883 458,504

111 86

29.9 23.1

7.3 11.6

4.2 16.0

8 Communication

1975–1989 1990–2004

3,131 14,885

10 15

4.0 2.6

2.6 8.2

21.2 13.7

9 Recreation and culture

1975–1989 1990–2004

131,627 344,534

88 120

9.7 9.2

3.2 4.9

9.7 9.7

10 Education

1975–1989 1990–2004

1,476 990

7 7

8.4 6.7

0.4 0.4

11.6 13.9

11 Restaurants and hotels

1975–1989 1990–2004

7,914 184,723

15 44

23.5 5.9

1.7 1.7

4.6 14.7

12 Miscellaneous goods and services

1975–1989 1990–2004

305,800 414,329

58 96

15.8 6.9

1.9 2.7

6.6 39.6

Non-durable goods

1975–1989 1990–2004

5,181,731 4,280,974

437 490

22.0 17.3

9.3 11.8

4.2 5.9

Durable goods

1975–1989 1990–2004

178,431 346,304

101 109

23.6 14.0

4.5 6.9

5.2 6.3

Semi-durable goods

1975–1989 1990–2004

889,757 1,046,342

184 230

7.5 5.7

3.5 6.2

9.7 9.4

Services

1975–1989 1990–2004

120,881 526,445

147 199

12.8 7.3

1.7 2.6

10.6 25.6

coicop Division

Period

n

1 Food and non-alcoholic beverages

1975–1989 1990–2004

2 Alcoholic beverages, tobacco and narcotics

Main categories

Note: 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.

price increases is higher in the high-inflation period, in particular for 11 Restaurants and hotels and 1 Food. In contrast the frequency of price decreases is higher in the low-inflation 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

IV


MONTH YEAR

as high in the low-inflation period for 3 Clothing and footwear. The coicop system also classify the products as non-durable goods, semidurable goods, durable goods, and services.20 The bottom panel of Table B1 shows that the frequency of price increases are higher in the high-inflation period and that the frequency of price decreases is higher in the low-inflation period for all types of goods. The net effect is that duration is more than one month higher for durables and non-durables in the low-inflation period. For services the mean duration is 25.6 months in the low-inflation period compared to 10.6 months in the high-inflation period. There are substantial differences between the coicop divisions also regarding the size of price changes, see Table B2. For example when inflation is low, the mean sizes of the price increases and decreases vary from 44.2 and –29.5 percent for 3 Clothing and footwear to 4.4 and –4.0 percent for 7 Transport. For all coicop divisions the absolute size of price decreases were higher in the low-inflation, particularly for 10 Education and 11 Restaurants and hotels. Price increases were also higher in the low-inflation period for all coicop divisions but for 7 Transport and 10 Education. In the bottom panel for the main categories we see that the absolute size of price increases are larger in the low-inflation period than in the high-inflation 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) differs. Table B3 and B4 report estimates for the main components of the Harmonized Index of Consumer Prices (hicp): energy, unprocessed food, processed food, nonenergy industrial goods, and services. Although there are big differences between types of products, they share the features that the frequency of price changes is higher in the high-inflation period than in the low-inflation period and that the absolute size of price changes is higher when inflation is low. Table B5 reports frequency and size statistics for the less aggregated coicop groups and classes for the whole period. Vegetables, fruit and petrol are examples of products with frequent price changes, while various services experience less frequent price changes.

20 The 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 differ from durable goods in that their expected lifetime of use, though more than one year, is often significantly shorter and their purchasers price is substantially less.

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Table B2—The mean absolute size of price increases and decreases by coicop divisions, main categories and high and low inflation periods. Percent. Increases coicop Division

1975–1989

1990–2004

11.5 4.5

13.6 6.0

−10.6 −3.6

−11.9 −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

9.5 4.4

−5.7 −3.5

−7.1 −4.0

5.8 9.9 9.6 3.7 8.3

7.8 13.7 6.2 13.3 9.9

−4.7 −8.7 −2.8 −2.6 −8.7

−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

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 9 10 11 12

Decreases

Communication Recreation and culture Education Restaurants and hotels Miscellaneous goods and services

1975–1989

1990–2004

Main categories Non-durable goods Durable goods Semi-durable goods Services

Table B3—Weighted mean frequency of price changes and duration by hicp sectors. hicp Unprocessed food

Period

n

1975–1989

1,941,510

Products

f+

f−

139

30.4

16.9

D 2.1 (2.1)

1990–2004

1,229,353

128

18.7

15.8

3.8 (4.9)

Processed food

1975–1989

2,374,887

166

15.2

5.7

5.4 (3.0)

1990–2004

1,989,909

181

9.6

5.1

7.3 (4.1)

Energy

1975–1989

39,954

13

27.4

10.4

3.5 (3.3)

1990–2004

74,561

12

28.9

22.5

4.4 (7.1)

Non energy industrial goods

1975–1989

1,666,925

366

16.0

4.0

7.1 (4.6)

1990–2004

2,097,145

465

10.9

6.4

7.6 (5.0)

Services

1975–1989

347,524

185

12.8

1.8

10.4 (12.3)

1990–2004

809,097

242

7.3

2.6

24.9 (74.5)

VI


MONTH YEAR

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

Figure B2. Histogram of all non-zero price changes in percent by coicop division. The distributions are truncated at –50 and 50 percent.

Table B4—The mean absolute size of price increases and decreases by hicp types of goods. Increases hicp

Decreases

1975–1989

1990–2004

1975–1989

1990–2004

12.1

13.0

−14.5

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 goods Services

−17.8

VOL. VOL NO. ISSUE


VII

Table B5—: Mean frequency of price changes and mean price duration in months by coicop groups (three-digit level) and classes (four-digit level). coicop Group/Class 11

Food

n 6,629,455

f

f+

31.4

20.0

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

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

(4.2)

111

Bread and cereals

1,158,122

16.7

11.6

6.0 (1.8)

112

Meat

1,080,387

42.1

27.6

2.6 (5.0)

113

Fish and seafood

750,056

25.2

15.7

3.7 (1.1)

114

Milk, cheese and eggs

739,958

19.2

13.1

5.7 (2.1)

115

Oils and fats

213,994

25.5

16.3

3.5 (0.9)

116

Fruit

455,828

52.1

28.7

2.4 (2.9)

117

Vegetables

902,300

53.8

31.8

2.4 (2.5)

118 119

Sugar, jam, honey, chocolate and confectionery Food products n.e.c.

695,046

13.6

8.6

9.0 (5.2)

633,764

15.0

10.1

6.7 (2.1)

12

Non-alcoholic beverages

631,126

26.7

16.3

4.3 (2.6)

121

Coffee, tea and cocoa

246,527

38.7

22.1

2.3 (1.3)

122

21

Mineral waters, soft drinks, fruit and vegetable juices Alcoholic beverages

384,599

16.0

11.0

6.2 (2.0)

124,910

18.2

14.5

5.1 (1.0)

211

Spirits

2,546

20.5

16.5

4.4 (0.3)

212

Wine

2,034

16.3

13.4

5.7 (0.7)

213

Beer

120,330

17.2

13.4

5.4 (1.1)

22

Tobacco

150,168

11.1

9.8

31

Clothing

917,552

12.6

6.7

20,997

7.2

5.2

8.6

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

(1.4)

8.5 (3.6)

311

Clothing materials

13.8 (2.5)

312

Garments

807,201

13.5

6.7

7.6 (3.0)

313

32

Other articles of clothing and clothing accessories 314 Cleaning, repair and hire of clothing Footwear

73,983

8.1

6.3

12.6 (3.5)

15,371

18.7

15.8

7.7 (5.3)

171,824

11.8

6.2

8.5 (2.6)

321

Shoes and other footwear

163,261

11.9

6.2

8.4 (2.5)

322

Repair and hire of footwear

8,563

7.0

5.4

14.1 (2.2)

41

Actual rentals for housing

49,926

7.4

5.1

13.0 (.)

43

Maintenance and repair of the dwelling

103,072

20.2

15.2

5.9 (3.0)

431

45

Materials for the maintenance and repair of the dwelling Electricity, gas and other fuels

103,072

20.2

15.2

5.9 (3.0)

26,373

31.8

17.5

6.7 (8.2)

Table B5 continues on next page.

VIII


MONTH YEAR

Table B5 continued. coicop Group/Class 451

Electricity

n 9,967

f

f+

29.9

15.5

D

dp+

dp−

7.3

10.8

–9.8

4.5

–3.7

13.5

–12.0

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

8.1

–1.8

10.0

–1.6

(11.6)

453

Liquid fuels

13,726

53.2

34.2

1.3 (0.1)

454

Solid fuels

2,473

8.5

6.1

12.3 (3.9)

455

Heat energy

207

33.8

18.3

2.4 (0.0)

51

Furniture and furnishings, carpets and other floor coverings 511 Furniture and furnishings

154,657

11.7

7.9

8.5 (2.5)

137,512

11.9

8.1

8.4 (2.6)

512

Carpets and other floor coverings

17,145

10.8

7.0

9.0 (1.7)

52

Household textiles

108,081

9.7

6.3

10.2 (2.3)

520

Household textiles

108,081

9.7

6.3

10.2 (2.3)

53

Household appliances

172,532

18.5

11.5

5.3 (1.6)

531 532

Major household appliances whether electric or not Small electric household appliances

137,759

18.2

10.8

5.2 (1.3)

34,578

13.4

8.0

7.1 (1.2)

533

Repair of household appliances

195

32.2

25.5

2.6 (.)

54 55

Glassware, tableware and household utensils Tools and equipment for house and garden 551 Major tools and equipment

153,311

10.3

7.4

10.8 (7.0)

95,651

10.6

7.7

10.6 (5.1)

8,095

10.7

6.3

8.9 (0.6)

551

Major tools and equipment

8,095

10.7

6.3

8.9 (0.6)

552

56

Small tools and miscellaneous accessories 552 Small tools and miscellaneous accessories Goods and services for routine household maintenance 561 Non-durable household goods

87,556

10.6

7.9

10.9 (5.5)

87,556

10.6

7.9

10.9 (5.5)

783,343

14.5

10.5

8.1 (6.7)

778,387

15.9

11.2

7.6 (7.6)

562

61

Domestic services and household services Medical products, appliances and equipment 611 Pharmaceutical products

4,956

10.0

8.5

9.5 (1.4)

201,344

12.6

8.7

9.2 (5.0)

184,185

15.3

10.4

6.3 (1.6)

612

Other medical products

9,109

12.6

8.4

7.8 (2.2)

613

62

Therapeutic appliances and equipment Outpatient services

8,050

6.3

4.6

16.2 (4.0)

744

6.9

6.8

14.7 (4.0)

621

Medical services

199

4.9

4.4

19.9 (.)

622

Dental services

185

8.0

8.0

12.0

5.1

(0.0)

623

Paramedical services

360

6.0

5.8

17.1

13.3

–2.0

(4.2)


VOL. VOL NO. ISSUE


IX


Purchase of vehicles

n 70,360

f

f+

36.0

30.4

D

dp+

dp−

3.0

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

(1.7)

711

Motor cars

51,850

37.1

31.6

2.8 (1.4)

712

Motor cycles

3,767

11.7

6.0

8.1 (0.9)

713

Bicycles

14,743

13.3

7.6

7.0 (0.3)

72

73

Operation of personal transport equipment 721 Spare parts and accessories for personal transport equipment 722 Fuels and lubricants for personal transport equipment 723 Maintenance and repair of personal transport equipment 724 Other services in respect of personal transport equipment Transport services

607,779

46.0

29.8

8.1 (30.6)

270,143

11.4

8.1

8.5 (1.6)

88,142

61.3

39.1

1.3 (1.5)

234,542

10.9

8.8

9.3 (3.3)

14,952

35.1

22.8

46.9 (90.7)

9,248

8.1

7.7

12.7 (3.8)

731

Passenger transport by railway

2,537

6.9

6.7

14.6 (4.6)

732

Passenger transport by road

5,497

6.8

6.5

14.7 (3.0)

733

Passenger transport by air

203

11.0

10.4

8.6 (0.0)

734

81

Passenger transport by sea and inland waterway Postal services

1,011

8.4

7.7

11.6 (1.4)

699

4.8

4.8

20.4

13.2

(3.0)

810

Postal services

699

4.8

4.8

20.4

13.2

(3.0)

82

Telephone and telefax equipment

13,816

28.2

10.3

4.1

34.6

–19.8

5.2

–7.3

17.7

–11.1

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

(3.1)

83

Telephone and telefax services

3,501

8.1

3.2

16.7 (25.6)

91

Audio-visual, photographic and information processing equipment 911 Equipment for the reception, recording and reproduction of sound and pictures 912 Photographic and cinematographic equipment and optical instruments 913 Information processing equipment

152,405

18.2

8.7

6.4 (3.5)

75,610

18.0

8.0

5.5 (1.9)

18,864

15.4

6.4

7.4 (4.0)

12,483

26.2

9.4

4.1 (3.0)

914

Recording media

45,249

8.7

5.3

11.4 (2.5)

915

92

93

Repair of audio-visual, photographic and information processing equipment Other major durables for recreation and culture 921 Major durables for outdoor recreation 922 Musical instruments and major durables for indoor recreation Other recreational items and equipment, gardens and pets

199

32.6

25.0

2.5 (0.0)

8,895

7.8

7.0

12.6 (2.4)

1,216

7.9

7.8

12.2 (1.2)

7,679

7.5

4.4

14.0 (4.4)

168,794

13.9

7.5

10.4 (8.6)


X


MONTH YEAR


Games, toys and hobbies

n 18,438

f

f+

8.2

4.8

D

dp+

dp−

12.5

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

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

(3.1)

932 933

Equipment for sport, camping and open-air recreation Gardens, plants and flowers

87,083

8.0

5.3

16.2 (13.0)

47,300

24.2

11.6

4.8 (3.7)

934

Pets and related products

15,973

11.4

7.0

8.4 (1.2)

94

Recreational and cultural services

29,807

9.0

7.9

12.7 (6.2)

941

Recreational and sporting services

727

11.9

11.1

9.4 (5.1)

942

Cultural services

29,080

7.4

6.3

14.4 (6.3)

95

Newspapers, books and stationery

116,061

16.3

14.8

9.3 (6.3)

951

Books

36,860

7.1

5.9

14.3 (3.8)

952

Newspapers and periodicals

42,015

24.5

22.9

4.4 (2.9)

954

Stationery and drawing materials

37,186

6.5

4.8

16.0 (4.8)

96

Package holidays

199

10.3

7.7

9.2 (.)

101

Pre-primary and primary education

235

7.2

6.7

13.3 (.)

102

Secondary education

777

7.4

7.1

13.0 (0.8)

104

Tertiary education

1,454

7.8

7.3

12.3 (0.9)

111

Catering services

154,295

6.8

5.5

15.2 (4.8)

1111

Restaurants, cafes and the like

141,037

6.9

5.6

15.2 (5.0)

1112

Canteens

13,258

6.4

4.9

15.4 (2.4)

112

Accommodation services

38,342

13.5

9.5

8.2 (3.6)

121

Personal care

677,888

12.1

9.0

8.6 (2.6)

1211

123

Hairdressing salons and personal grooming establishments 1212 Electric appliances for personal care 1213 Other appliances, articles and products for personal care Personal effects n.e.c.

74,108

9.5

8.6

10.2 (1.2)

8,476

12.0

6.6

8.0 (1.5)

595,304

13.8

9.3

7.6 (2.7)

37,028

9.1

5.6

12.1 (5.9)

1231

Jewellery, clocks and watches

16,146

9.0

5.6

11.7 (4.6)

1232

Other personal effects

20,882

9.4

5.6

12.4 (7.7)

124

Social protection

516

5.2

5.1

20.4 (6.6)

125

Insurance

188

22.3

20.0

4.0 (.)

126

Financial services n.e.c.

4,509

4.8

2.6

48.2 (58.0)

Note: n.e.c. is short for not elsewhere classified.

XI

0

0

10

10

20

20

30

30

40

40


50

VOL. VOL NO. ISSUE

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

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.

− Figure B3 shows the cross-sectional variation in fit+ , fit− , dp+ it and dpit over time. Figure B4 shows a strong positive correlation between the average size of price increases and decreases for each product, a relationship that was also detected in the euro area (see Dhyne et al. (2006, Figure 2)). The correlation coefficient between the size of price increases and decreases is .65. Figure B5 shows a weak, albeit significant, 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 coefficient between the (log) frequency of price increases and the (log) size of price increases is –.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 4, Figure B6 plots the histograms of the average size of price


MONTH YEAR

1

1

The size of price increases 5 10 20 40

The frequency of price increases 10 20

80

40 60

XII

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 prod- Figure B5. The frequency of price increases + uct, dp+ i , plotted on the vertical axis against by product, fi plotted on the vertical axis

the absolute size of price decreases by prod- against the size of price increases by product, uct, dp− i . Log scales.

dp+ i . Log scales.

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 inflation period 1975–1989 (left) and low inflation period 1990–2004 (right). The distributions are truncated at –50 and 50 percent.

+ decreases dp− i and increases dpi for the high-inflation and low-inflation periods. Note that for each period there are two histograms, one for the mean price de+ creases dp− i (in red) and one for the mean price increases dpi (in blue). The fraction of smaller mean price changes (below 5 percent in absolute value) are about the same for both periods. The fraction of price changes between 5 and 10 percent (in absolute value) is smaller for both decreases and increases in the low inflation period, while the fraction of price changes between 10 and 15 percent is larger. Also the far tails of the distributions are fatter, especially for price increases.

VOL. VOL NO. ISSUE


The aggregation wedge

15

C.

XIII

delta

0

5

Percent

10

Gcpi

1975

1980

1985

1990

1995

2000

Figure C1. The aggregation error ∆t and cpi inflation. Percent.

D.

Detailed decomposition analyses

To further explore the effect of variation in the frequencies and sizes of price adjustments I compute four conditional estimates of cpi inflation allowing only one component to vary over time while holding the other three components con+ stant at their product-specific means. For example, π ˆt (fit+ |fi− , dp− i , dpi ) is the predicted inflation rate when only the frequency of price increases fit+ varies as + observed, when the other three components fi− , dp− i , and dpi are held constant at their means. X + − − π ˆt (fit+ |fi− , dp− ωit fit+ dp+ i , dpi ) = i + fi dpi , i + π ˆt (fit− |fi+ , dp− i , dpi )

=

X

=

X

=

X

− − ωit fi+ dp+ i + fit dpi ,

i − + − π ˆt (dp+ it |fi , fi , dpi )

− − ωit fi+ dp+ it + fi dpi , and

i − + + π ˆt (dp− it |fi , fi , dpi )

− − ωit fi+ dp+ i + fi dpit .

i + For example, π ˆt (fit+ |fi− , dp− i , dpi ) is the predicted inflation rate when only the + frequency of price increases fit varies as observed, when the other three compo+ nents fi− , dp− i , and dpi are held constant at their means. Figure D1 displays these four 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

MONTH YEAR

15


15

XIV

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 D1. Inflation (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.

decreases (in the bottom right) all contributed to the downward trend in the inflation rate. The correlation coefficient between πt and π ˆt (fit+ |•) is the highest of .90, while corr(πt , π ˆt (fit− |•) = 0.79 and corr(πt , π ˆt (dp− it |•) = 0.73. The variation in the size of the price increases contributes significantly to a counterfactual positive trend in the inflation rate (top right) with a correlation coefficient between πt and π ˆt (dp+ |∗) of –.51. The contribution to inflation from the size of price increases is thus opposite to the contribution from the size of price decreases. The effect on inflation from the size of price decreases is thus canceled out by a stronger opposite effect 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 inflation, as corr(∆π, ∆ˆ πt |f + ) =.58. Figure D2 compares how price decreases (depicted on the left hand panel) and price increases (depicted on the right) contribute to inflation. The graph shows Similarly, I compute the separate contributions from price and decreases, P P increases − − + + − − by π ˆt |P OS = i ωit fit+ dp+ + f dp , and π ˆ | = ω f dp t it N EG i it i i i i + fit dpit . Time variation in price increases and decreases both contributed to the variation

XV

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15

VOL. VOL NO. ISSUE

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 D2. Inflation (Solid Line) and the Contribution From Price Decreases (Left), and Price Increases (Right). Annual Rates. Percent.

in inflation, as shown by correlation coefficients of .62 (increases) and .70 (decreases). However, short-run variability in price increases is more important for short-run variability in inflation than short-run variability in price decreases, as corr(∆π, ∆ˆ πt |P OS ) = .65, compared to corr(∆π, ∆ˆ πt |N EG ) = –.27.