Dynamics of the U.S. Price Distribution David Berger Yale University

Joseph Vavra Yale University

August 29, 2011

Abstract Using BLS CPI microdata, we document four new facts about the dynamics of the distribution of price changes in the United States: 1) The cross-sectional dispersion (second moment) of price changes is strongly countercyclical. This countercyclical dispersion holds both within and between sectors, as well as for both price increases and decreases. 2) Price dispersion is positively correlated with the frequency of adjustment. 3) There is a U-Shaped relationship between price dispersion and in‡ation. 4) The skewness of price changes is correlated with in‡ation but is acyclical. We argue that standard price-setting models are inconsistent with the majority of these facts. Keywords: Price dispersion, price rigidity, uncertainty, second moments, business cycles, in‡ation JEL Classi…cation: E30, E32, D8, L16

We would like to thank Eduardo Engel, Nick Bloom, Nir Jaimovich, and Emi Nakamura for helpful comments and Randal Verbrugge for support at the BLS. Correspondence: Joe Vavra, Department of Economics, Yale University, PO Box 208268, New Haven CT 06520-8268, [email protected]

1

1

Introduction

Beginning with the work of Bils and Klenow (2004) there has been a proliferation of research using con…dential BLS data on the individual prices underlying the CPI to study the average behavior of price-setting in the United States.

Despite this widespread attention to "…rst moments1 " of

the price change distribution, there has been little study of higher moments of the distribution and of their relationship to the broader business cycle2 .

While higher moments of the price change

distribution have been little studied using CPI micro data, they may shed important light on both the nature of business cycle shocks and on …rms’ price setting behavior. Recent work by Bloom (2009) and Bloom, Floetotto, and Jaimovich (2009) has argued that second moment "uncertainty shocks" may be an important source of business cycle ‡uctuations, and we argue that CPI micro data indeed supports the presence of such second moment shocks. Our empirical results can be summarized with four new facts about the distribution of price changes3 in the United States. 1) The cross-sectional dispersion (second moment) of price changes is strongly countercyclical.

We further decompose this countercyclical price dispersion and …nd

that both dispersion within and across sectors is also counteryclical. Countercyclicality also holds for both price increases and decreases, although the dispersion of price decreases is substantially more countercyclical than is the dispersion of price increases.

2) Price dispersion is positively

correlated with the frequency of adjustment. This holds for our benchmark dispersion measure, which excludes zeros (non-adjusters), and is even stronger when dispersion is calculated including zeros.

3) While there is a negative correlation between in‡ation and relative price dispersion,

which may initially appear to be a puzzle for most pricing models, this is driven by the fact that the largest absolute changes in in‡ation during our sample period were de‡ationary. In fact, the overall relationship between in‡ation and relative price dispersion is U-Shaped around zero in‡ation, as predicted by most pricing models. 4) The skewness of price changes is modestly correlated with in‡ation and is uncorrelated with output. 1 Studies

typically focus on e.g. the frequency and size of price changes and their relationship to in‡ation. Klenow and Malin (2010) look at the cross-sectional standard deviation of item-level price changes and its relationship to aggregate in‡ation, they do not compute cyclical relationships and do not relate dispersion to the frequency of adjustment. 3 Our benchmark results exclude zero price changes. Most results are similar when zeros are included. 2 While

2

We believe these facts are important for two separate reasons: 1) They complement the recent work documenting counter-cyclical dispersion of real variables and provide additional evidence on the nature of business cycle shocks. 2) They provide a new set of business cycle moments that should inform the recent literature on the price-setting behavior of individual …rms (c.f. Klenow and Kryvtsov (2008), Nakamura and Steinsson (2008), Midrigan (2011b), and Eichenbaum, Jaimovich, and Rebelo (2009)). In particular, we show that our facts are largely inconsistent with both time-dependent and statedependent models of …rm pricing with only …rst moment shocks.

However, Vavra (2011) shows

that the addition of second moment "uncertainty" shocks can improve the menu cost model’s …t dramatically.

Furthermore, the addition of second moment shocks changes the transmission

of aggregate nominal shocks to the real economy:

in times of high uncertainty, the price level

endogenously becomes more ‡exible and the real e¤ects of nominal shocks are reduced. The remainder of the paper proceeds as follows: Section 2 describes that data and our empirical procedure. Section 3 describes our four facts. Section 4 brie‡y relates these new facts to models of …rm pricing, and Section 5 concludes.

2

Data

The restricted access CPI research database collected by the Bureau of Labor Statistics (BLS) contains individual price observations for the thousands of non-shelter items underlying the CPI from January, 1988 through August, 2010.

Prices are collected monthly for all items only in

New York, Los Angeles and Chicago, and we restrict our analysis to these cities to ensure the representativeness of our sample4 .

The database contains thousands of individual "quote-lines"

with price observations for many months.

Quote-lines are the highest level of disaggregation

possible and correspond to an individual item at a particular outlet. An example of a quote-line collected in the research database is 2-liter Brand-X soda at a particular Chicago outlet. These 4 The most representative sample would be to use all bimonthly observations, but then many price changes are potentially missing. Some items are sampled monthly outside of NY, LA and Chicago, but these items are not representative, so we restrict our monthly analysis to these three cities. However, we have also performed our analysis on the entire bimonthly sample and …nd similar results.

3

quote-lines are then classi…ed into various product categories called "Entry Level Items" or ELIs. The ELIs can then be grouped into several levels of more aggregated product categories …nishing with eleven major expenditure groups: processed food, unprocessed food, household furnishings, apparel, transportation goods, recreation goods, other goods, utilities, vehicle fuel, travel, and services5 . For more details on the structure of the database see Nakamura and Steinsson (2008). Let dpi;t = log

pi;t pi;t 1

be the price change observed for quote-line i at time t.

Then, using

aggregation weights provided by the BLS6 , it is straightforward to calculate the cross-sectional distribution of log price changes7 for each month and investigate how it varies over the business cycle. Our benchmark measure of price dispersion is then the interquartile range8 of price changes after excluding zeros (non-adjusters). We choose to focus on moments of the price change distribution excluding zeros rather than including them simply because the theoretical implications of pricesetting models are stronger for this distribution. Nevertheless, we also report most results for the distribution of price changes including zeros, and they are largely similar. Much of the recent literature has discussed the di¤erence between sales, regular price changes and product substitutions. In our benchmark analysis, we focus on regular price changes, excluding sales and product substitutions.

We use the series excluding sales and product substitutions as

our benchmark for two reasons: 1) Eichenbaum, Jaimovich, and Rebelo (2009) and Kehoe and Midrigan (2008) argue that the behavior of sales is often signi…cantly di¤erent from that of regular or reference prices and that regular prices are likely to be the important object of interest for aggregate dynamics. Thus, we choose to exclude sales in our benchmark analysis. 2) Product substitutions require a judgement on what portion of a price change is due to quality adjustment and which component is a pure price change.

Thus, this introduces measurement error in the

5 The BLS only de…nes eight major groups, but we de…ne our eleven groups following Nakamura and Steinsson (2008). 6 These weights are used for aggregating individual price series to create the CPI. The weights describe how individual quote-lines are weighted within ELIs and how ELIs are aggregated into overall expenditure. The ELI aggregation step is based on the Consumer Expenditure Survey and is updated by the BLS periodically. 7 In addition to this measure of the size of a price change, we also computed the price change size as dp = (pt pt 1 ) 2 (p +p ; which has the advantage of being bounded and thus less sensitive to outliers. We also investigated t t 1) using residuals from a regression of the current price on the previous price as a measure of the size of price changes. Results with these two alternative measures are very similar to the results reported below and so are excluded for brevity. The results are available from authors upon request. 8 We also report results for the standard deviation, which is less robust to outliers.

4

calculation of price changes at the time of product substitution.

Bils (2009) shows that these

errors can be substantial. For this reason, we exclude product substitutions from our benchmark analysis. Nevertheless, we have also repeated the analysis including sales and product substitutions and found broadly similar results.

3

Empirical Results

3.1

Price Dispersion is Countercyclical

We begin with our …rst fact: price change dispersion is countercyclical and rises during NBER recessions.9 Figure 1 displays the raw data. Clearly, price dispersion peaks during NBER recessions. A regression of price dispersion on recession dummies shows that dispersion is 38% higher during recessions and that this increase is signi…cant at the 1% level. Furthermore, this increase in price dispersion during recessions remains signi…cant even when the outlier in 2008q4 is removed. Nevertheless, this procedure is highly sensitive to the precise data of NBER recessions.

We

thus look at the cyclicality of price dispersion more generally. Figure 2 displays the relationship between bandpass …ltered price dispersion10 and industrial production11 . Overall, there appears to be a strong negative relationship, so that price dispersion is countercyclical. Table 1 con…rms this and shows that there is a strong and signi…cant negative correlation between production and various measures of price dispersion. In principle, there could be various sources of this overall negative correlation between price dispersion and production, so we next decompose overall price dispersion into various components. Figure 3 plots percentiles of the price change distribution. In this …gure, there is clearly a strong relationship between the behavior of price decreases and recessions, while the relationship between price increases and recessions is much less dramatic.

Using a simple variance decomposition we

can more formally decompose the overall variance of prices into the variance of price increases, 9 See

Vavra (2011) for additional discussion. use the bandpass …lter rather than HP …ltering in order to remove high frequency noise from the series. Alternative …ltering did not signi…cantly a¤ect the results. 1 1 We used monthly industrial production so that monthly price dispersion data could be used. Nearly identical results were obtained when the price data was aggregated quarterly and compared to GDP. 1 0 We

5

the variance of price decreases and the variance of the di¤erence between the mean increase and decrease. Table 2 reports correlations of these components of the overall variance with output.

The

dispersion of price increases, the dispersion of price decreases, and the dispersion between the mean increase and mean decrease are all countercyclical. However, the relationship is less strong for price increases than it is for price decreases and the di¤erence in means. Thus, while the variance of all components of price dispersion rise during recessions, the bulk of the cyclical changes are driven by the behavior of price decreases. In addition to this directional decomposition of price changes, we can also decompose dispersion into a within and between sector component. That is,

2

(dp) = E

2

(dpjSector) +

2

[E (dpjSector)])

with all components weighted using CPI expenditure weights. The bottom half of Table 2 shows that the correlations between production and the dispersion of prices within and across groups are strongly negative. Similar results were obtained using ELIs rather than the more aggregated major groups. Finally, we investigated other sectoral decompositions: we broke prices into 1) core and non-core, 2) durables and non-durables 3) six groups by frequency of adjustment 4) four groups by inventory holdings12 . In all cases, we obtained similar results: countercyclical price dispersion appears to be a robust and pervasive relationship across most items in the U.S. economy. 1 2 Inventory

groups were constructed using BEA inventories data available at http://www.bea.gov/national/nipaweb/nipa_underlying /TableView.asp?SelectedTable=1&FirstYear=1995&LastYear=1996&Freq=Qtr&ViewSeries=N using a rough correspondence between ELIs and BEA industry groups. We were able to categorize only approximately 40% of CPI expenditures into inventory groups, so these groups are far from comprehensive.

6

3.2

Price Dispersion is Correlated with the Frequency of Adjustment

We next investigate the relationship between price dispersion and the frequency of adjustment13 . Figure 4 shows that there is a strong positive relationship between price dispersion (excluding zeros) and the average frequency of adjustment. Table 3 numerically con…rms the strong positive correlation between price dispersion and the frequency of adjustment.

Unsurprisingly, Figure 5

shows that there is an even stronger relationship between price dispersion (including zeros) and the frequency of adjustment. Given the relatively low frequency of adjustment in the data and the fact that, conditional on adjustment, the absolute size of price changes is large, the inclusion of zeros necessarily increases the correlation between price dispersion and frequency14 . In contrast, there is no mechanical reason that the frequency of adjustment and price dispersion (excluding zeros) should be positively correlated. This positive relationship between the frequency of adjustment and price dispersion is extremely robust. It holds both including and excluding product substitutions and sales, as well as under a variety of alternative detrending and …ltering methods15 . The positive relationship holds for both core and non-core items, and for price increases and price decreases16 . The positive relationship is particularly strong for non-durable goods while it is weakest for durable goods17 . Many recent papers have emphasized that heterogeneity across sectors leads the median frequency of adjustment to be substantially lower than the mean frequency of adjustment.

Given

these large level di¤erences between the median and mean frequency we also computed the relationship between the median frequency and price dispersion and found slightly stronger positive 1 3 We investigate the relationship with both the average and the median frequency of adjustment. The average frequency of adjustment is the sum of an indicator for adjustment weighted according to each quote-lines aggregation weight. For the median frequency, we …rst calculate mean frequencies within ELIs and then we take the weighted median across ELIs using ELI weights. 1 4 This is mechanically true for the standard deviation. This is less of a concern for the 95-5 range. 1 5 The frequency data exhibit a modest slow-moving trend, so we view detrended relationships as more reliable. We investigated di¤erent parameter values for the Baxter-King bandpass …lter, and it did not materially a¤ect the results. We also found similar results using the HP …lter, although the positive comovement is dampened mildly since the HP …lter does not remove high frequency noise from the data. Finally, Table 3 shows that the positive correlations remain even with no …ltering. 1 6 That is, there is a positive correlation between the dispersion of price changes within these subgroups and the frequency of adjustment within these subgroups. 1 7 This may re‡ect mismeasurement of both price changes and the size of price changes amonst durable goods since durable goods exhibit frequent product substitutions and are also made up in large part of automobiles where prices are likely to face large measurement problems.

7

relationships.

3.3

U-Shaped Relationship Between In‡ation and Price Dispersion

There is a substantial empirical literature on the relationship between in‡ation and relative price variability18 . Unfortunately,there is little consensus in this literature. Older studies19 generally found a positive relationship whereas the results from more recent studies are more ambiguous. Klenow and Malin (2010) and Reinsdorf (1994), both of which utilize US CPI data, …nd a negative relationship, whereas Konieczny and Skrzypacz (2005), using a Polish data set, argue that the relationship is positive20 . Consistent with the numbers in Klenow and Malin (2010), we …nd that the correlation between in‡ation and price dispersion is small and negative, however this negative correlation is driven almost entirely by outliers from the 2007 recession21 . Figure 6 provides a possible explanation for these con‡icting results. It is clear that there is a strong U-shaped relationship between in‡ation and price-dispersion and that this relationship is symmetric around zero in‡ation22 . Thus, perhaps the reason that the older literature mostly found a positive relationship between in‡ation and relative price dispersion is because these studies typically used lower frequency data, and in an environment of positive trend in‡ation, temporal aggregation will tend to smooth out observations with negative in‡ation realizations. Figure 6 also shows that relative price dispersion is increasing in the absolute value of in‡ation, suggesting that dispersion rises when either in‡ation or de‡ation becomes larger. 1 8 For example, Parks (1978), Van Hoomissen (1988), Lach and Tsiddon (1992), Reinsdorf (1994), Konieczny and Skrzypacz (2006), and Bils and Malin (2010). 1 9 For example, Parks (1978), Van Hoomissen (1988), and Lach and Tsiddon (1992) all …nd a positive relationship between in‡ation and dispersion. 2 0 Interestingly, Konieczny and Skrzypacz also …nd a U-shaped relationship between in‡ation and dispersion (see …gure 1 in their paper), however, they do not emphasize it. Most likely this is because the correlation between in‡ation and dispersion is positive in their data set (see table 2 in their paper). 2 1 When the two biggest outliers from the 2007-09 recession are excluded, 10/2008 and 11/2008, then the correlation becomes small and positive. 2 2 The quadratic relationship remains when the outliers from the most recent recession are excluded.

8

3.4

The Relationship Between Price Skewness, Output and In‡ation

Thus far, we have focused on the second moment of the price change distribution. A long line of literature beginning with Ball and Mankiw (1995) has emphasized the importance of price change skewness in menu cost models. They …nd that there is an empirically strong, positive relationship between in‡ation and skewness using sectoral PPI data. More recent work by Bryan and Cecchetti (1999) argues that this correlation might be due entirely spurious due to …nite sample bias. Since our analysis uses fully disaggregated data, we have vastly larger sample sizes so that this critique is not a concern23 . Table 4 investigates the relationship between the skewness of price changes, output and in‡ation. There is a moderate positive relationship between skewness and in‡ation24 and no relationship between skewness and output. Since skewness depends upon the third moment of price changes, it is particularly sensitive to the presence of measurement error and outliers.

Thus, while we only …nd a mild positive

relationship between skewness and in‡ation, we are concerned that the true relationship may be attenuated if skewness is mismeasured.

Toward this end, we also construct the 75-25 Quantile

Skewness suggested by Kim and White (2004). This measure of skewness is de…ned as Quantile ercentile25 2 P ercentile50 Skewness= P ercentile75+P : This is analogous to the standard measure of P ercentile75 P ercentile25

skewness, but it is substantially more robust to the presence of mismeasured outliers. Indeed, Table 4 con…rms that the relationship between the robust Quantile Skewness and in‡ation is substantially stronger than it is for the raw skewness. Finally, for completeness, we also include results for the skewness of price changes including zeros. When zeros are included, we …nd a strong relationship between both skewness and in‡ation and skewness and output.

This is because the mean price

change shifts much less through time when zeros are included than when zeros are excluded. This in turn implies that the skewness of price changes including zeros moves more across time than does the skewness of price changes excluding zeros as the distribution of price changes moves across time. Interestingly, the positive correlation between in‡ation and skewness remains even after we 2 3 We

have approximately 15,000 price observations each month. is consistent with Klenow and Malin (2010).

2 4 This

9

restrict the sample to items that make up core in‡ation or when we perform the analysis within major groups. Ball and Mankiw (1995) argue that the skewness of price changes can capture the presence of relative supply shocks. In practice, energy and food prices are often used as a proxy for these relative supply shocks. That our skewness-in‡ation relationship holds within most major groups suggests that the skewness of price changes may be capturing something other than relative supply shocks.

4

Implications for Price-Setting Models

In the previous section, we presented four dynamic facts about the distribution of price changes in the United States. In this section, we relate these facts to two prominent models of price-setting.

4.1

Time-Dependent Models and the Facts

In time-dependent pricing models, output tends to be high after a positive sequence of aggregate money shocks. price dispersion.

Simultaneously, positive money shocks also lead to greater in‡ation and relative Thus, time-dependent models have di¢ culty matching the empirical counter-

cyclicality of price dispersion. In addition, time-dependent models …x the frequency of adjustment exogenously, so by assumption, they cannot match the empirical relationship between frequency and price dispersion. The ability of time-dependent models to match the U-Shaped relationship between in‡ation and price change dispersion depends on the relative size of aggregate and idiosyncratic shocks. In an environment where price changes are driven largely by aggregate shocks, after periods of large (absolute) in‡ation, some …rms have had a chance to adjust while others have not. This leads to a period of "catching up" that causes an increase in price change dispersion. This same e¤ect occurs whether in‡ation is large and positive or large and negative, so that the model is able to generate a U-Shaped relationship between price dispersion and in‡ation. In contrast, if the distribution of price changes is driven largely by idiosyncratic shocks with only small aggregate shocks then an increase in in‡ation shifts the mean of …rms’desired prices but

10

it has little e¤ect on the variance of the distribution. Since large idiosyncratic shocks move …rms’ through the ergodic distribution of desired prices more rapidly so that changes in in‡ation do not have much e¤ect on the distribution of …rms’desired price changes. Thus, in the presence of large idiosyncratic shocks and small aggregate shocks, there is little relationship between in‡ation and price change dispersion. A simple time-dependent model with idiosyncratic shocks estimated for the period 1988-2010 appears to lie much closer to the second rather than the …rst case so that there is little relationship between in‡ation and price dispersion.

Thus, it appears that time-dependent models are not

consistent with the U-Shaped relationship between in‡ation and price dispersion observed in the data, but additional quantitative robustness checks are warranted.25 Finally, time-dependent models of price setting predict no relationship between the skewness of price changes excluding zeros and in‡ation, while they predict a strong positive correlation between the skewness of price changes including zeros and in‡ation. The intuition can be obtained most clearly in a partial equilibrium model: when there is an increase in in‡ation, the distribution of desired price changes is shifted to the right by the increase in in‡ation. Since the distribution of price changes excluding zeros is exactly equal to the distribution of desired price changes, skewness is unchanged while in‡ation increases.

In contrast, the distribution of price changes including

zeros is a mixture of the previous distribution and a large mass point at zero. Since the average desired price change is greater than zero, the distribution of desired price changes lies largely to the right of the large mass point at zero so that distribution of actual price changes (including zeros) is positively skewed. When there is an increase in in‡ation, the distribution of desired price changes shifts further to the right and skewness rises26 . Thus, there is a strong positive correlation between skewness including zeros and in‡ation in models of time-dependent pricing. 2 5 For example, it would be of interest to see how changes in the persistence of nominal shocks would a¤ect this conclusion. 2 6 This intuitive argument relies on the frequency of adjustment being relatively low, which is the relevant case empirically. While not strictly true, thinking about the relationship between the mean and median price change can provide intuition for skewness. One can think of a positively skewed distribution as having a mean greater than the median. Since the frequency of adjustment is well below …fty percent, the median price change (including zeros) is always zero while the mean price change is positive. An increase in the distribution of price changes conditional on adjustment increases the mean change, leaves the median unchanged and increases skewness. We have also con…rmed these results in a calibrated DSGE model.

11

4.2

Menu Cost Models and the Facts

Vavra (2011) investigates the implications of our dynamic price dispersion facts for menu cost models in great detail. He shows that menu cost models with only …rst moment shocks induce a negative correlation between the frequency of adjustment and price dispersion. Figure 7, reproduced from Vavra (2011), provides intuition with a simple continuous time menu cost model.

Firms adjust

when their desired price change (price gap) is greater than the threshold of 0.1. When in‡ation is low, the distribution of …rm’s price gaps is symmetrically distributed, as is the distribution of price changes. After a positive in‡ation shock, the distribution of price gaps becomes negatively skewed as more …rms are near the threshold of raising prices. In this case, the overall frequency of adjustment rises and the distribution of price changes becomes less symmetric. Since the variance of the price change distribution is a linear transformation of a Bernoulli, its variance is maximized when the distribution of price changes is symmetric. Thus, in response to the positive aggregate in‡ation shock, the frequency of adjustment rises and the variance of price changes falls, implying that frequency and price dispersion are negatively correlated. Vavra (2011) shows that this counterfactual negative correlation continues to hold in a quantitative equilibrium menu cost model. Furthermore, this quantitative menu cost model with only …rst moment shocks implies procyclical price dispersion, a strong negative relationship between skewness excluding zeros and in‡ation, and a strong positive relationship between skewness including zeros and in‡ation. Figure 7 can again provide intuition: after a positive in‡ation shock, there are more price increases, fewer price decreases and the skewness of the price change distribution (excluding zeros) becomes more negative27 . This is in contrast to the argument in Ball and Mankiw (1995), that a menu cost model should induce a positive correlation between in‡ation and skewness.

Critical to this distinction is the

inclusion and exclusion of zeros. Ball and Mankiw (1995) use aggregated data so that price changes equal to zero are not observed, while in our disaggregated data, more than eighty percent of prices remain constant each month. Thus, their analysis focuses on the skewness of price changes including zeros. However, while relative supply shocks imply a positive correlation between in‡ation and the 2 7 This

is con…rmed numerically in a more general environment.

12

skewness of price changes (including zeros), they imply a negative correlation between in‡ation and skewness (excluding zeros). In their model, an increase in the skewness of desired price changes with a …xed inaction region leads to an increase in in‡ation.

However, while the skewness of

desired price changes becomes more positive, the skewness of actual price changes (excluding zeros) becomes more negative.

This is because the mass of actual price changes becomes asymmetric,

with most of the mass concentrated around price increases.

Thus, relative supply shocks to the

skewness of …rms’ price gaps imply a negative correlation between the skewness of price changes (excluding zeros) and in‡ation, in a menu cost model. This is inconsistent with the modest positive relationship observed in our data. While a menu cost model is inconsistent with the observed positive relationship between the skewness of price changes excluding zeros and in‡ation, it is consistent with a positive relationship between the skewness of price changes including zeros and in‡ation.

The intuition is similar to

that in the time-dependent model. Furthermore, this is the relationship emphasized by Ball and Mankiw (1995). Menu cost models also struggle to match the U-Shaped relationship between in‡ation and price change dispersion for reasons that are again apparent in Figure 6. A large change in (absolute) in‡ation leads to a greater correlation of …rms price choices, which decreases the variance of price changes. If in‡ation rises, then most price changes are increases, the distribution is less symmetric and dispersion is reduced. For this reason, we …nd that a calibrated menu cost model predicts a strong inverted U-Shape relationship between in‡ation and price change dispersion. While a menu cost model with only …rst moment shocks cannot match three of our four facts, Vavra (2011), shows that the addition of second moment "uncertainty" shocks, improves the model’s …t dramatically. Greater uncertainty has two e¤ects on …rm pricing: 1) It increases the option value of waiting, which widens …rms’adjustment bands and decreases price adjustment. 2) There is a direct volatility e¤ect that makes …rms hit bands of a given width for frequently.

Vavra

(2011) …nds that the second e¤ect strongly dominates so that frequency and the variance of price changes are positively correlated. In addition, if the level of uncertainty is negatively correlated with aggregate productivity, as it appears to be in the data (c.f. Bachmann and Bayer (2009)),

13

then price dispersion also becomes countercyclical. Thus, the addition of second moment shocks allows the menu cost model to match many dynamic facts about the distribution of price changes that it would otherwise miss. Furthermore, Vavra (2011) shows that matching these facts can have important implications for monetary policy, as an increase in uncertainty increases price ‡exibility and reduces the real e¤ects of nominal shocks.

5

Conclusions

In this paper, we investigate dynamic features of the distribution of price changes for the U.S. economy using CPI micro data. This complements recent work that has focused largely on …rst moments28 of the distribution. We document four new facts that we believe are useful both for di¤erentiating models of …rm pricing, as well as for identifying features of the distribution of shocks faced by …rms in the economy. 1) The dispersion of price change is countercyclical.

2) The dispersion of price changes is

positively correlated with the frequency of adjustment.

3) There is a U-Shaped relationship

between in‡ation and price dispersion. 4) The skewness of price changes is mildly correlated with in‡ation but uncorrelated with output. In general, these facts are at odds with most standard models of …rm pricing.

Only the U-

Shaped relationship between in‡ation and price dispersion is consistent with both time-dependent and state-dependent models of …rm pricing, as increases in the absolute value of in‡ation lead to increases in dispersion as …rms try to "catch up" with in‡ation since their last adjustment. Both state-dependent and time-dependent models of pricing also miss the empirical correlation between frequency and price dispersion. In time-dependent models this correlation is zero, by assumption, while in models of state-dependent pricing, increases in the frequency of adjustment tend to occur when all prices move in the same direction so that there is a decrease in cross-sectional dispersion. In addition, these models quantitatively imply that price dispersion is procyclical: output is high after a sequence of positive in‡ation, which also increases price dispersion. 2 8 For

example, the average frequency of adjustment or the average size of price changes.

14

Finally, we show that our evidence on the relationship between the skewness of price changes and in‡ation, if anything, supports time-dependent rather than state-dependent models of pricing. This is in contrast to Ball and Mankiw (1995) who argue that a positive correlation between in‡ation and skewness is evidence for menu cost models. Critical to this distinction is the inclusion and exclusion of zeros. Ball and Mankiw (1995) use aggregated data so that price changes equal to zero are not observed. In contrast, zero price adjustments are a prominent feature of our disaggregated micro data.

When zeros are excluded, menu cost models imply a strong negative correlation between

skewness and in‡ation. This is in contrast to the modest positive correlation observed empirically. While a standard menu cost model appears to be inconsistent with our empirical facts, Vavra (2011) shows that the model’s empirical …t can be improved dramatically with the addition of uncertainty shocks and that these shocks have important implications for the transmission of monetary shocks.

Our new dynamic facts on the distribution of price changes thus have important

policy implications in otherwise standard models of …rm pricing.

15

References Bachmann, R., and C. Bayer (2009): “Firm-Speci…c Productivity Risk over the Business Cycle: Facts and Aggregate Implications,” CESifo Working Paper Series 2844. Ball, L., and N. G. Mankiw (1995): “Relative-Price Changes as Aggregate Supply Shocks,”The Quarterly Journal of Economics, 110(1), 161–193, ArticleType: research-article / Full publication , date: Feb., 1995 / Copyright Âl 1995 The MIT Press. Bils, M. (2009): “Do Higher Prices for New Goods Re‡ect Quality Growth or In‡ation?,”Quarterly Journal of Economics, 124(2). Bils, M., and P. Klenow (2004): “Some Evidence on the Importance of Sticky Prices,” Journal of Political Economy, 112(5). Blejer, M., and L. Leiderman (1980): “On the Real E¤ects of In‡ation and Relative-Price Variability: Some Empirical Evidence,” Review of Economics & Statistics, 62(4). Bloom, N. (2009): “The Impact of Uncertainty Shocks,” Econometrica, 77(3). Bloom, N., M. Floetotto, and N. Jaimovich (2009): “Really Uncertain Business Cycles,” Mimeo. Bryan, M. F., and S. G. Cecchetti (1999): “In‡ation and the Distribution of Price Changes,” Review of Economics & Statistics, 81(2). Eichenbaum, M., N. Jaimovich, and S. Rebelo (2009): “Reference Prices, Costs and Nominal Rigidities,” American Economic Review. Kehoe, P. J., and V. Midrigan (2008): “Temporary Price Changes and the Real E¤ects of Monetary Policy,” National Bureau of Economic Research Working Paper Series, No. 14392. Kim, T., and H. White (2004): “On more robust estimation of skewness and kurtosis,” Finance Research Letters, 1(1).

16

Klenow, P., and O. Kryvtsov (2008): “State-Dependent or Time-Dependent Pricing: Does It Matter for Recent U.S. In‡ation?,” The Quarterly Journal of Economics, 123(3). Klenow, P., and B. Malin (2010): “Microeconomic Evidence on Price-Setting,”National Bureau of Economic Research Working Paper Series, 15826. Konieczny, J. D., and A. Skrzypacz (2005): “In‡ation and price setting in a natural experiment,” Journal of Monetary Economics, 52(3). Lach, S. (2002): “Existence and Persistence of Price Dispersion: An Empirical Analysis,” Review of Economics & Statistics, 84(3). Lach, S., and D. Tsiddon (1992): “The behavior of prices and in‡ation: An empirical analysis of disaggregated price data.,” Journal of Political Economy, 100(2). Loungani, P. (1986): “Oil Prices and the Dispersion Hypothesis,” Review of Economics & Statistics, 68(3). Midrigan, V. (2011a): “Is Firm Pricing State or Time-Dependent? Evidence from US Manufacturing.,” Review of Economics & Statistics. (2011b): “Menu Costs, Multi-Product Firms and Aggregate Fluctuations,”Econometrica, 79(4). Nakamura, E., and J. Steinsson (2008): “Five Facts about Prices: A Reevaluation of Menu Cost Models,” The Quarterly Journal of Economics, 123(4). Parks, R. W. (1978): “In‡ation and Relative Price Variability.,” Journal of Political Economy, 86(1), 79. Reinsdorf, M. (1994): “New evidence on the relation between in‡ation and price dispersion.,” American Economic Review, 84(3). Van Hoomissen, T. (1988): “Price Dispersion and In‡ation: Evidence from Israel.,” Journal of Political Economy, 96(6). 17

Vavra, J. (2011): “In‡ation Dynamics and Time-Varying Uncertainty: New Evidence and an Ss Interpretation,” Mimeo.

18

Table 1: Correlations with Production

Bandpass Filtered: Bandpass Filtered Production 75-25 Range, Excluding Zeros

-0.39***

Standard Deviation, Excluding Zeros

-0.44***

95-5 Range, Including Zeros

-0.42***

Standard Deviation, Including Zeros

-0.37***

Un…ltered Dispersion: Production Growth 72-25 Range, Excluding Zeros

-0.29***

Standard Deviation, Excluding Zeros

-0.31***

95-5 Range, Including Zeros

-0.27***

Standard Deviation, Including Zeros

-0.33***

*** p <0.01, ** p <0.05, * p <0.1 Industrial production data can b e downloaded at http://research.stlouisfed.org/fred2/series/INDPRO?cid=3 Data is seasonally adjusted using m onthly dum m ies. Bandpass …ltered disp ersion numb ers are com pared to bandpass …ltered production, and raw disp ersion data is com pared to pro duction growth rates. Standard deviations are com puted after 1% trim m ing of outliers to reduce m easurem ent error.

19

Table 2: Decompositions

Bandpass Filtered Production Bandpass Filtered: Std. Dev. Increases

-0.20***

Std. Dev. Decreases

-0.53***

Di¤erence in Means

-0.43***

Std. Dev. Within Major Group

-0.40***

Std. Dev. Across Major Group

-0.38***

*** p <0.01, ** p <0.05, * p <0.1 Industrial production data can b e downloaded at http://research.stlouisfed.org/fred2/series/INDPRO?cid=3 Data is seasonally adjusted using m onthly dum m ies. Bandpass …ltered disp ersion numb ers are com pared to bandpass …ltered production

20

Table 3: Frequency and Dispersion

Bandpass Filtered: Bandpass Filtered Frequency 75-25 Range, Excluding Zeros

0.52***

Standard Deviation, Excluding Zeros

0.42***

95-5 Range, Including Zeros

0.79***

Standard Deviation, Including Zeros

0.65***

Un…ltered Dispersion: Frequency 72-25 Range, Excluding Zeros

0.23***

Standard Deviation, Excluding Zeros

0.17**

95-5 Range, Including Zeros

0.66***

Standard Deviation, Including Zeros

0.54***

*** p <0.01, ** p <0.05, * p <0.1 Data is seasonally adjusted using m onthly dum m ies. Standard deviations are com puted after 1% trim m ing of outliers to reduce m easurem ent error.

21

Table 4: Skewness Correlations With Output and In‡ation

Excluding Zeros:

Including Zeros:

Bandpass Filtered Production

Bandpass Filtered Skewness

0.04

0.25***

Bandpass Filtered Quantile Skewness

0.11*

0.49***

Production Growth

Skewness

-0.01

-0.06

Quantile Skewness

0.04

0.16**

In‡ation

Skewness

0.12*

0.32***

Quantile Skewness

0.47***

0.83***

*** p <0.01, ** p <0.05, * p <0.1 Data is seasonally adjusted using m onthly dum m ies. All skewness m easures com puted with zeros in second colum n and without zeros in third colum n. Quantile Skewness including zeros is de…ned as P ercentile95+P ercentile5 2 P ercentile50 : Quantile Skewness ex 0’s uses the 75-25 rather than 95-5 range. P ercentile95 P ercentile5 A wider range is used when zeros are included, as the interquartile range is always zero when zeros are included.

22

5

10

15

20

Interquartile rang1: e of price (excluding Figure Pricechanges Dispersion andzeros) Recessions

1990

1995

2000

2005

2010 ®

Data is seasonally adjusted by …rst calculating seasonal m onthly dum m ies and then calculating residuals from these m onthly dum m ies. These residuals were then average within quarter and added to the m ean across all quarter. Disp ersion m easure is the Interquartile Range after Excluding Zeros.

-4

-2

0

2

4

Figure 2: Countercyclical Price Dispersion

1990m1

1995m1

2000m1

Interquartile Range of Price Dispersion

2005m1

2010m1

Industrial Production ®

M onthly data is seasonally adjusted and bandpass …ltered using the Baxter-King bandpass …lter. Series are standardized with m ean zero and unit variance

23

-30

-15

0

15

Percentiles of the price change distribution (excluding Figure 3: Distribution of Pricezeros) Changes

1990

1995

2000

2005

2010

Percentiles 10,12. 5,15,25,75,85,87. 5, and 90 plotted ®

Data is seasonally adjusted by …rst calculating seasonal m onthly dum m ies and then calculating residuals from these m onthly dum m ies. These residuals were then average within quarter and added to the m ean across all quarter.

24

-4

-2

0

2

4

Figure 4: Frequency and Price Dispersion (Excluding Zeros)

1990m1

1995m1

2000m1

2005m1

Interquartile Range of Price Dispers ion

2010m1 Frequenc y ®

M onthly data is seasonally adjusted and bandpass …ltered using the Baxter-King bandpass …lter. Series are standardized with m ean zero and unit variance

-4

-2

0

2

4

Figure 5: Frequency and Price Dispersion (Including Zeros)

1990m1

1995m1

2000m1

95-5 Range of Price Dis pers ion

2005m1

2010m1

Frequenc y ®

M onthly data is seasonally adjusted and bandpass …ltered using the Baxter-King bandpass …lter. Series are standardized with m ean zero and unit variance

25

0

Interquartile range 10 20

30

40

Figure 6: U-Shaped In‡ation-Disperion Relationship

-3

-2

-1

0 Inflation rate

Actual values

1

2

3

Fitted quadratic ®

Figure 7: Continuous Time Menu Cost Model Price Change Distribution

Zero Inflation

Price Gap Distribution 10

0.025 0.02

Frequency

Density

8 6 4 2 0 -0.1

0.01 0.005

-0.05

0

0.05

0

0.1

10

0.05

8

0.04

Frequency

0.06

6 Lower Price

0

0.05

0.1

0.05

0.1

0.03 0.02

4

0 -0.1

-0.05

Price Change Distribution

12

2

-0.1

Positive Inflation

Price Gap Distribution

Density

0.015

Raise Price

0.01 0

-0.05

0

0.05

0.1

26

-0.1

-0.05

0