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«I. INTRODUCTION The nature of price setting has important implications for a range of issues in macroeconomics, including the welfare consequences of ...»

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FIVE FACTS ABOUT PRICES: A REEVALUATION

OF MENU COST MODELS∗

´

EMI NAKAMURA AND JON STEINSSON

We establish five facts about prices in the U.S. economy: (1) For consumer

prices, the median frequency of nonsale price change is roughly half of what it is

including sales (9–12% per month versus 19–20% per month for identical items;

11–13% per month versus 21–22% per month including product substitutions). The median frequency of price change for finished-goods producer prices is comparable to that of consumer prices excluding sales. (2) One-third of nonsale price changes are price decreases. (3) The frequency of price increases covaries strongly with inflation, whereas the frequency of price decreases and the size of price increases and price decreases do not. (4) The frequency of price change is highly seasonal: it is highest in the first quarter and then declines. (5) We find no evidence of upwardsloping hazard functions of price changes for individual products. We show that the first, second, and third facts are consistent with a benchmark menu-cost model, whereas the fourth and fifth facts are not.

I. INTRODUCTION

The nature of price setting has important implications for a range of issues in macroeconomics, including the welfare consequences of business cycles, the behavior of real exchange rates, and optimal monetary policy. We use Bureau of Labor Statistics (BLS) microdata underlying the consumer and producer price indices to document five basic features of price adjustment. We interpret this evidence through the lens of a benchmark menu cost model.

We begin by estimating the frequency of price change. Until recently, the best sources of information on U.S. pricing behavior were studies of price adjustment for particular products (Cecchetti 1986; Kashyap 1995), broader surveys of firm managers (Blinder et al. 1998), and evidence on the dynamics of industrial prices (Carlton 1986). The conventional wisdom from this literature was ∗ We would like to thank Robert Barro for invaluable advice and encouragement. We would like to thank Daniel Benjamin, David Berger, Leon Berkelmans, Craig Brown, Charles Carlstrom, Gary Chamberlain, Tim Erickson, Mark Gertler, Mike Golosov, Gita Gopinath, Teague Ruder, Oleksiy Kryvtsov, Gregory Kurtzon, Robert McClelland, Greg Mankiw, Ariel Pakes, Ricardo Reis, Roberto Rigobon, John Rogers, Ken Rogoff, Philippa Scott, Aleh Tsyvinsky, Randal Verbrugge, Michael Woodford, seminar participants at various institutions as well as our editor, Larry Katz, and anonymous referees for helpful comments and discussions. We particularly want to thank Mark Bils and Pete Klenow for thoughtful and inspiring conversations. We are grateful to Martin Feldstein for helping us obtain access to the data; without his helpthis work would not have been possible.

We are grateful to the Warburg Fund at Harvard University for financial support.

C 2008 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.

The Quarterly Journal of Economics, November 2008

–  –  –

that prices adjusted on average once a year. Bils and Klenow (2004) dramatically altered this conventional wisdom by showing that the median frequency of price change for nonshelter consumer prices in 1995–1997 was 21%, implying a median duration of 4.3 months.

We use a substantially more detailed data set than Bils and Klenow (2004) that contains the micro-level price data underlying the nonshelter component of the Consumer Price Index (CPI).1 This data set has been used by Hosken and Reiffen (2007, 2004) and Klenow and Kryvtsov (2008) to analyze price adjustment behavior. We find that temporary sales play an important role in generating price flexibility for retail prices in categories that account for about 40% of nonshelter consumer expenditures.

Whereas the median frequency of price change including sales is 19%–20% per month, we find that the median frequency of nonsale price change for identical items is only 9%–12% per month depending on the time period and how we treat nonsale price changes over the course of sales and stockouts.

Our estimates of the median frequency of price change for identical items may be inverted to obtain estimates of the median duration of regular prices. Excluding product substitutions, these frequency estimates imply uncensored durations of regular prices of between 8 and 11 months. Yet, substitutions often truncate regular price spells. If we include price changes associated with product substitutions, the median frequency of nonsale price change increases by between 1 and 2 percentage points. This implies median durations until either the regular price changes or the product disappears at between 7 and 9 months.

The importance of temporary sales—and to a lesser extent substitutions—in generating price changes in the U.S. data draws attention to the question of whether the relative frequency of different types of price changes is an important determinant of the macroeconomic implications of price rigidity. In other words: “Is a price change just a price change?” An important lesson from the theoretical literature on price adjustment is that different types of price adjustments can have strikingly different macroeconomic





1. Bils and Klenow (2004) used the BLS Commodities and Services Substitution Rate Table for 1995–1997. This data set contains average frequencies of price changes and substitutions by disaggregated product categories over the 1995– 1997 period. In contrast, the CPI research database contains the actual data series on prices underlying the Consumer Price Index for the 1988–2005 period. See Section II for a more detailed discussion of the data.

FIVE FACTS ABOUT PRICES

implications. For example, the Calvo (1983) model and the Caplin and Spulber (1987) model have very different macroeconomic implications for the same frequency of price change.

For this reason, an important focus of this paper is to document and contrast the empirical characteristics of the different types of price changes observed in U.S. consumer data. First, we document that sale price changes display markedly different empirical features than regular price changes. Sale price changes are much more transient than regular price changes; and in most cases where a price is observed before and after a sale, the price returns to its original level following the sale.

There are a number of reasons why it may be important to distinguish between sale and nonsale price changes. First, the transience of price adjustment associated with sales implies that a given number of price changes due to sales yield much less aggregate price adjustment than the same number of regular price changes (Kehoe and Midrigan 2007). Second, some types of sales may be orthogonal to macroeconomic conditions. Third, transitory sales are a much more pervasive phenomenon in retail prices than in wholesale prices, implying that temporary sales may be less responsive to shocks at the wholesale than at the retail level of production.

Price changes due to product substitutions are a second class of price changes that we argue is fundamentally different from the regular price changes typically emphasized by macroeconomists.

This source of price flexibility is particularly important for durable goods. For example, the spring and fall clothing seasons in apparel and the new model year for cars are associated with a large number of price changes due to the introduction of new products. Many factors other than a firm’s desire to change its price influence its decision to introduce a new product. The theoretical literature on price adjustment has shown that price changes that are motivated primarily by a large difference between a firm’s current price and its desired price yield much greater aggregate price flexibility than those that are motivated by other factors (Caplin and Spulber 1987; Golosov and Lucas 2007). In state-dependent pricing models, it is therefore crucial to treat product substitutions separately from other types of price changes (Nakamura and Steinsson 2007). In contrast, time-dependent pricing models should arguably be calibrated to the frequency of price change including substitutions because in these models the timing of all price changes is exogenous.

1418 QUARTERLY JOURNAL OF ECONOMICS

We also present the first broad-based evidence on U.S. price dynamics at the producer level. To study this issue, we created a new data set on producer prices from the production files used by the BLS to construct the Producer Price Index (PPI). The median frequency of price change for finished-goods producer prices was 10.8% in 1998–2005; it was 13.3% for intermediate-goods producer prices; and it was 98.9% for crude materials. Moreover, we document a high correlation between the frequency of nonsale consumer price changes and the frequency of producer price changes at a very disaggregated level. The price rigidity in finished-goods producer prices is comparable to the rigidity of consumer prices excluding sales but substantially greater than the rigidity of consumer prices including sales.

There is a tremendous amount of heterogeneity across sectors in both the frequency of price change and the importance of temporary sales. Different summary statistics on price flexibility therefore give very different answers regarding the degree of price flexibility in the U.S. economy. Following Bils and Klenow (2004), we focus on the weighted median frequency of price adjustment across categories. Excluding sales lowers the median frequency of price change of consumer prices by over 50%, while it lowers the mean frequency of price change by only about 20%. This is because sales are concentrated in sectors of the economy, such as food and apparel, that have a frequency of price change close to the median frequency of price change across sectors.

There is no model-free way of selecting what is the appropriate summary statistic to describe the amount of aggregate price flexibility in an economy in which the frequency of price change varies across sectors from over 90% per month to less than 5% per month. In Nakamura and Steinsson (2007), we calibrate a multisector menu cost model to the sectoral distribution of the frequency and absolute size of price changes excluding sales. We use this model to investigate which statistic about price rigidity is most informative about the degree of monetary nonneutrality in the economy. The degree of monetary nonneutrality implied by our multisector model is triple that implied by a single-sector model calibrated to the mean frequency of price change of all firms but similar to that implied by a single-sector model calibrated to the median frequency of price change.2

2. Carvalho (2006) studies the effect of heterogeneous price rigidity in timedependent models. For the Calvo model, he finds that a single-sector model

FIVE FACTS ABOUT PRICES

The second feature of price change that we investigate is the fraction of price changes that are price decreases. We find this fraction to be roughly one-third in both consumer prices excluding sales and finished-goods producer prices. We present a benchmark menu cost model along the lines of Golosov and Lucas (2007) and show that the fraction of price changes that are decreases helps pin down the key parameters of this model. The third feature of price change that we investigate is how the frequency and size of price change covaries with the inflation rate. We find that the frequency of price increases covaries quite strongly with the rate of inflation, whereas the frequency of price decreases and the size of price increases and decreases do not. This fact provides a natural test for our calibrated benchmark menu cost model. The fourth feature of price change that we investigate is the extent of seasonal synchronization. We find that price rigidity is highly seasonal both for consumer and producer prices. Prices are substantially more likely to change in the first quarter than in other quarters.

The fifth and final issue that we investigate is the hazard function of price change. The main empirical challenge in estimating the hazard function of price change is the fact that heterogeneity in the level of the hazard function across products—if not properly accounted for—leads to a downward bias in the slope of the hazard function. We use the empirical model of Meyer (1990) to account for heterogeneity. The hazard function of consumer prices including sales is steeply downward sloping for sectors with frequent sales. In contrast, the estimated hazard function of price change for both consumer prices excluding sales and producer prices is slightly downward sloping for the first few months and then mostly flat. The only substantial deviation from a flat hazard after the first few months is a large spike in the hazard at twelve months for services and producer prices.3 We show that menu cost models can give rise to a wide calibrated to the mean duration of price spells in the economy replicates the degree of monetary nonneutrality in a multisector model. We present estimates of the mean duration in Table I.

3. Earlier empirical work on the hazard function of price changes includes ´ Cecchetti (1986), Jonker, Folkertsma, and Blijenberg (2004), Alvarez, Burriel, and Hernando (2005), Baumgartner et al. (2005), Campbell and Eden (2005), Dias, Robalo Marques, and Santo Silva (2005), Foug´ re, Bihan, and Sevestre (2005), and e Goette, Minsch, and Tyran (2005). Empirical support for upward-sloping hazard functions appears to arise mostly in studies in which almost all price changes are increases. Several of these papers use the conditional logit specification to account for unobserved heterogeneity. Unfortunately, this specification yields inconsistent estimates of the shape of the hazard function (Willis 2006).

1420 QUARTERLY JOURNAL OF ECONOMICS

variety of hazard functions, depending on the relative importance of inflation and idiosyncratic shocks. The hazard function implied by our calibrated benchmark menu cost model is sharply upward sloping for the first few months.



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