PRICE SETTING DURING LOW AND HIGH INFLATION: EVIDENCE FROM MEXICO∗ Etienne Gagnon October 2008

Abstract This paper provides new insight into the relationship between inflation and the setting of individual prices by examining a large data set of Mexican consumer prices covering episodes of both low and high inflation. When the annual rate of inflation is low (below 10-15%), the frequency of price changes comoves weakly with inflation because movements in the frequency of price decreases and increases partly offset each other. By contrast, the average magnitude of price changes correlates strongly with inflation because it is sensitive to movements in the relative shares of price increases and decreases. When inflation rises beyond 10-15%, few price decreases are observed and both the frequency and average magnitude are important determinants of inflation. I show that a menu-cost model with idiosyncratic technology shocks predicts well the average frequency and magnitude of price changes over a range of inflation similar to that experienced by Mexico.

∗

I would like to thank the members of my dissertation committee, Lawrence J. Christiano, Alexander MongeNaranjo, Sergio Rebelo, and especially my chairperson Martin Eichenbaum, for their continuous guidance and support. I also am grateful to Martin Bodenstein, Jeff Campbell, Reinout DeBock, Rodrigo García Verdú, Nicolas Vincent, and three anonymous referees for their insightful comments and suggestions. Chris Ahlin and José Antonio Murillo Garza offered valuable help with the data while Martha Carillo, Matthew Denes and Guthrie Dundas offered excellent research assistance. Financial support for this research was provided in part by the Northwestern University Center for International Economics and Development and the Fonds québécois pour les chercheurs et l’aide à la recherche (FCAR). The views expressed in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System. Send comments and questions to [email protected].

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1

Introduction

This paper presents new evidence on the setting of consumer prices during low and high inflation and sheds light on the empirical plausibility of competing models of price rigidities. It uses a new store-level data set containing over three million individual price quotes that are representative of more than half of Mexican consumers’ expenditures. The data start in January 1994 and end in June 2002. Over that nine-year period, CPI inflation rose from 6.8% in 1994 to a peak of 41.8% in 1995, before falling to a low of 3.9% in 2001.1 Given these considerable fluctuations, this data set allows me to document how individual consumer prices are set at various levels of inflation. It also can be used to discriminate among competing models of nominal price rigidities, as these models’ predictions diverge most in the presence of large shocks. My data set captures considerably more variation in inflation than do other studies of consumer prices with comparable product coverage.2 As Figure I indicates, inflation was low and stable in the United States and euro area relative to Mexico throughout the periods covered by the related studies. In the case of high-inflation economies, the evidence is limited mainly to food products in Israel (Lach and Tsiddon 1992; Eden 2001; Baharad and Eden 2004) and Poland (Konieczny and Skrzypacz 2005), and to supermarket products in Argentina (Burstein, Eichenbaum, and Rebelo 2005). My paper differs from these studies because my data set is representative of a much larger set of goods and services in the CPI. The monthly frequency of price changes varied extensively over my sample period. It rose from an average of 22.1% in 1994 to a high of 61.9% at the peak of inflation in April 1995, before leveling off around 27.4% in the last year of the sample. I find some important differences in pricesetting behaviors across low- and high-inflation periods. When inflation is low (below 10-15%), the frequency of price changes is only mildly correlated with inflation, especially when I restrict the sample to goods, in which case the correlation almost entirely disappears. On the other hand, the average magnitude of price changes in such a low-inflation environment displays a tight and almost linear relationship with the level of inflation. As a result, movements in the frequency of price changes account for little of the inflation variance: at most 11% for the full sample and 6% 1

Unless otherwise indicated, all inflation figures are computed using the change in the logarithm of the price index and annualized. 2 For studies on the United States, see Bils and Klenow (2004), Klenow and Kryvtsov (2008), and Nakamura and Steinsson (2008). Dhyne et al. (2005) review the main findings for the euro area.

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for the subsample of goods, figures that are similar to that of Klenow and Kryvtsov (2008) for the United States (about 5%). By contrast, when inflation is high (above 10-15%), both the frequency and average magnitude of price changes are strongly correlated with inflation. Movements in the frequency of price changes then comprise an important component of inflation variance. When I decompose price changes between price increases and decreases, I find that the frequency of price increases rises steadily as inflation rises from 0 to 10-15%. This rise is partly offset by a simultaneous decline in the frequency of price decreases, thereby dampening movements in the overall frequency of price changes. This offsetting effect stems from goods, which have the largest proportion of price decreases. By comparison, relatively few price decreases are observed among services. As inflation rises from a low level, the decline in the occurrence of price decreases relative to price increases exacerbates movements in the average magnitude of price changes. In my data set, the change in the composition of price changes largely explains the strong correlation between inflation and the average magnitude of price changes when inflation is low. Once inflation moves beyond 10-15%, price decreases have largely disappeared from most sectors of the economy with the exception of some fresh produce. The frequency of price increases continues to rise steadily with inflation, however, and the frequency of price changes thus becomes highly correlated with inflation. Overall, my empirical results suggest that pricing models should endogenize the timing of price changes if they wish to make realistic predictions at both low and high inflation levels. They also present the challenge of finding a model offering empirically plausible predictions at all levels of inflation. To investigate whether menu-cost models are consistent with my findings, I calibrate a discrete-time version of the Golosov and Lucas (2007) model. The model features idiosyncratic technology shocks giving rise to a distribution of both positive and negative nominal price adjustments. I show that the model performs well in terms of predicting the average frequency and magnitude of price changes for levels of inflation similar to the ones experienced by Mexico over my sample period. The success of the model comes in part from the presence of offsetting movements in the frequency of price increases and decreases, and highlights the importance of idiosyncratic shocks in this class of models for delivering empirically plausible predictions. The paper is organized as follows. In the next section, I provide a brief overview of the Mexican macroeconomic context over the sample period. In Section 3, I describe the assemblage of my 3

data set and discuss features of the data that are important for interpreting my results. Section 4 defines the statistics computed in this paper. The main empirical findings are presented in Section 5 and are then compared to other studies of high-inflation environments in Section 6. In Section 7, I calibrate a discrete-time menu-cost model with idiosyncratic technology shocks and investigate its consistency with some key empirical features reported in the paper. The last section provides concluding remarks.

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Macroeconomic Context

The sample period was marked by a severe economic downturn in the wake of the December 1994 peso devaluation. To most observers of the Mexican economy, however, 1994 opened rather positively.3 Inflation had been stabilized successfully below 10%, a major achievement in light of the three-digit rates of the late 1980s, and real interest rates also had decreased. The excess return on the three-month, dollar-denominated Tesobonos was only two percentage points above the American T-Bill. The budget deficit, seen by many as the culprit of previous economic crises, had been eliminated in 1992. Moreover, the North American Free Trade Agreement had taken effect on January 1, 1994. Foreign capital entered abundantly with a net inflow over 8% of GDP in 1993. However, growth in real GDP per capita remained modest, averaging 2.5% from 1991 to 1993. Many observers saw this situation as part of a restructuring process that soon would bring strong growth to the country. The devaluation brought a radical change of mood. On December 22, 1994, the exchange rate collapsed and lost more than 40% of its value vis-à-vis the U.S. dollar in the week that followed.4 As depicted in Figure II, short-term interest rates were pushed upward substantially as Banco de México tightened the supply of money to prevent further erosion of the peso and a capital flight. The devaluation left a major stagflation in its wake. Inflation took off almost immediately, increasing from 6.4% in November 1994 to 44.3% in January 1995 before peaking at 92.0% in April 1995. Real output per capita contracted 9.5% in 1995, while private consumption per capita fell a solid 13.2%. Mexicans would have to wait until 1998 for real GDP per capita to surpass its 1994 3

See Edwards (1998) for a review of observers’ opinions in 1994. Mexico pegged its exchange rate to the dollar in May 1992. In February 1994, the country switched to preannounced crawling bands around the U.S. dollar. 4

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level and until 1999 for inflation to settle below 10%. The decline in aggregate income, coupled with a rise in fiscal evasion, brought a sharp decline in government revenues.5 To prevent further revenue erosion, the government raised the general rate of the value added tax rate from 10% to 15% on April 1, 1995. This change affected all Mexican regions, with the notable exceptions of Baja California and a corridor along the country’s southern and northern borders where the rate remained at 10%.

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Mexican Micro Data on Consumer Prices

3.1

Description of Sources

The data comprise price quotes collected by Banco de México for computing the Mexican CPI. Most price quotes correspond to narrowly defined items sold in specific outlets (e.g., corn flour, brand Maseca, bag of 1 kg, sold in outlet 1100 in Mexico City). A limited number of quotes are city-wide indexes, or the average price of a small sample of narrowly defined items belonging to the same category and outlet. Since January 1994, the official gazette of the Mexican government, the Diario Oficial de la Federación, has published price quotes every month. This publication releases each quote with a key linking the item to a specific outlet, city and product category; these keys allow me to track individual prices over time.6 In this paper, I refer to an item’s complete price history as its price trajectory. The raw data set contains a total of 4.7 million price quotes from January 1994 to June 2002. Banco de México is required to make individual prices available to the public up to six months after their publication, but it does not keep a historical data set of individual prices. The data set was assembled by merging the information released in the Diario. The data for the months of January 1994 to February 1995 could not be extracted electronically, so they were typed in from original hard paper copies of the Diario using double-entry keying, a process ensuring a character-wise accuracy in excess of 99.998%.7 About 430,000 price quotes were added to the database in this way. Precise item descriptions were published in March 1995. The Diario also includes lists of 5

See OECD economic surveys, 1999-2000: Mexico for a description of the taxation system. Items from the same outlet are attributed store keys independently to ensure confidentiality. 7 I thank Chris Ahlin for lending me original copies of the Diario. 6

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items that are periodically added, dropped or substituted from the CPI basket. Unlike additions, substitutions are not planned events. They occur when the characteristics of an item (weight, size, model, presentation, etc.) change, when an outlet stops carrying an item or, in rarer cases, when an outlet goes out of business. The weights used in the CPI are derived from the Survey of Households’ Income and Expenditures (ENIGH). The CPI product categories are representative of all ENIGH categories accounting for at least 0.02% of households’ expenditures. This ensures a coverage well above 95% of Mexican households’ expenditures. To facilitate comparisons with other studies, I classify each product category according to the euro-area Classification Of Individual COnsumption by Purpose (COICOP).

3.2

Sample coverage

In January 1994, the CPI contained 30,692 price quotes spread over 302 product categories. By June 2002, the last month in my sample, it had expanded to nearly 50,000 price quotes distributed over 313 product categories. A major revision of the basket occurred in March 1995 when the number of cities covered in the CPI grew from 35 to 46. At the same time, 29 new product categories were introduced into the basket, and 18 were abandoned. This revision had been planned long before the peso’s devaluation. In July 2002, Banco de México updated the basket again to reflect the structure of Mexican households’ consumption in 2000. I cannot link items before and after the 2002 basket revision because of a change to the item keys. To ensure the greatest comparability across time, I compute my results for a sample covering January 1994 to June 2002 using the expenditure weights implemented in March 1995.8 The sample is further restricted to the product categories comprising individual prices that were unaffected by the 1995 basket revision and I consider only items whose price was not regulated. In addition, most education services and clothing items were dropped for reasons detailed below. The final sample contains 3.2 million price quotes from over 44, 000 price trajectories and covers 54.1% of CPI expenditures. The main groups of products excluded are rents and homeowners’ imputed rents, clothing (except for a few product categories containing individual observations) and education services, whose weight in the CPI are respectively 14.0%, 6.0% and 3.5%. Food items represent just under half of expenditures in the final sample, a proportion higher 8

These weights are derived from the 1989 ENIGH survey. They were updated using relative prices to reflect consumer expenditures in 1993.

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than in most U.S. and euro-area studies. Summary statistics are presented in Table I.

3.3

Other Aspects of the Data

I now address features of the data that are important to consider when interpreting the results. The most significant issue is price averaging. Banco de México collects prices twice monthly for all items but food; food price collection occurs four times per month.9 The collected prices are then averaged to produce the monthly figures reported in the Diario. Observing the monthly average rather than the actual price of an item complicates the inference about price changes. For example, an average price of $2 for an item is consistent with an actual price of $2 throughout the month. It also is consistent with an actual price of $1.50 in the first half of the month and $2.50 in the second, or any combination of prices with $2 as their average. Moreover, changes to an average-price series are typically more frequent and smaller on average than changes to an actual-price series with the same publication frequency. For example, a price hike from $1.50 to $2.50 in the middle of the month results in an average price of $2, which is $0.50 short of the new actual price, so that another change to the average-price series will likely be recorded in the next month. To make my results as comparable as possible to other studies, which typically do not use averaged price quotes, I have constructed alternative price trajectories that filter out the effect of averaging observations whenever possible. These new series correspond to the end-of-month series which are both consistent with the published average prices and minimize the number of price changes. In the Appendix, I provide an extensive discussion of how averaging observations affect the inference about the timing and magnitude of price changes, and of how the filter was implemented. I was provided with unpublished semi-monthly data by Banco of México which allows me to directly assess the performance of the filter. Overall, the filtered series are much closer to the end-of-period price series that they aim to reproduce. More importantly, the filtered series capture the timing of price changes with great accuracy. All the main patterns described in this paper are found whether prices are filtered or not. Another data issue is that price collectors do not always directly observe prices. Sometimes an item is out of stock, out of season or, in rarer cases, the outlet is closed when the CPI agent 9

In the United States, the BLS collects prices monthly for food consumed at home, energy, and a few additional items with volatile prices. Other prices are collected monthly for the three largest metropolitan areas (New York, Los Angeles, and Chicago) and every other month for the remaining areas.

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visits. In such situations, the price from the previous period is carried forward. Although I cannot identify prices that were imputed in my sample, I do find clear indications that the number of imputations was larger at the beginning of the sample. Item substitutions represented less than 0.1% of all published price quotes in 1994, a proportion that rose to 1.2% in 2001. A more systematic treatment of substitutions was implemented in 2001. Prices can now be carried forward for at most a month and a half before a substitution is sought. If the scarcity is generalized, this allowance can be extended up to three months. This methodological change likely creates a slight downward bias in the estimated frequency of price changes at the beginning of the sample. Prices are inclusive of sales as long as they are conditional on the purchase of a single item. For example, in a 3-for-2 promotion, the regular price would be reported. In the United States, the Bureau of Labor Statistics reports prices net of sales and promotions whenever possible; the same 3-for-2 promotion would result in a temporary 33% price decrease. There is no variable in the Mexican data set signaling that an item is on sale or that a promotion is ongoing. Most price quotes for the product categories of textiles, clothing, shoes and their related accessories are an average of a small sample of item prices; all items within a sample pertain to the same outlet whenever possible. Banco de México uses store samples to alleviate the problems associated with rapidly appearing and disappearing items due to changes in fashion and the seasons. All such samples were dropped from my analysis to limit the discussion to individual price changes. The decision to include or exclude store samples has little impact on the main findings. All education services observations, which cover registration, activity and tuition fees, were also dropped from the sample. These services are typically not available for purchase or not sampled during most months of the year. Prices are mechanically carried forward until the start of the next registration period, semester or academic year. For this reason, one cannot directly interpret the absence of price changes in the monthly series as evidence of price stickiness. A final issue is that item substitutions often accompany changes in product characteristics, thereby raising the question of whether substitutions should be treated as price changes. The Inflation Persistence Network’s approach is to assume that all item substitutions not previously planned by CPI agencies involve a price change, a choice guided in part by the absence of substitution flags in some of the national data bases. In this paper, substitutions were instead excluded from the computation of price changes because their treatment varied over the sample period. The main 8

patterns found in the paper are not affected by this choice.

4

Inflation Accounting Principles

Whenever a price is reported for two consecutive months, I create an indicator that a price change has occurred:

⎧ ⎪ ⎨ 1 if pit = 6 pit−1 Iit = , ⎪ ⎩ 0 if pit = pit−1

where pit is the price of item i (in logs) during month t. Inflation is defined as π t =

X

i∈Υt

ω it ∆pit ,

where ∆pit = pit − pit−1 , ω it is the sample weight of item i, and Υt is the set of all items in the sample for which Iit is defined. For ω it , I use the sample share of spending on the product category to which item i belongs, divided by the number of items in that product category for which I can compute a price change at t. Inflation also can be expressed as

πt =

⎛X ⎞ ´ ωit ∆pit ⎠. ω it Iit ⎝ Xi∈Υt i∈Υt ω it Iit {z } i∈Υt {z } | f rt

³X

|

dpt

The term frt , henceforth referred to as the frequency of price changes, is the share of spending in the sample on items whose price changed at month t. The term dpt is the average magnitude of those price changes. In the popular Calvo (1983) and Taylor (1980) models with uniform staggering of price changes, dpt is the only possible source of variation in π t . It is convenient to decompose inflation further into a weighted sum of price increases and decreases:

πt =

⎛X ⎞ ⎛X ⎞ ´ ´ ³X ω it Iit+ ∆pit ω it Iit− ∆pit i∈Υt i∈Υt ⎠+ ⎠. ω it Iit+ ⎝ X ω it Iit− ⎝ X + − i∈Υt i∈Υ t ω I ω I {z } {z } | it it it it i∈Υt i∈Υt {z } {z } | | f rt+ f rt−

³X |

dp− t

dp+ t

This decomposition is informative about the relationship between inflation and the distribution of price changes. The computation of inflation statistics for subregions of Mexico or special aggregates, such as goods and services, also follows the approach outlined above. My methodology for computing inflation is similar to the approach taken in most euro-area and

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U.S. studies of individual price changes but differs from that of Banco de México at the time, which computed inflation as the percentage change in a Laspeyres index. Despite differences in sample coverage, methodology, and filtering of price trajectories, the inflation rate in my sample is highly correlated with the change in the official CPI: The coefficient of correlation is 0.96 over the full sample period and 0.85 over the last three years of the sample.

5

Main Empirical Results

This section presents the key empirical findings, focusing on the relationship between inflation and the frequency and average magnitude of price changes. I treat (nonregulated) goods and services separately throughout the discussion due to differences in the way prices are set between the two groups.10 I place a special emphasis on the results for goods given their predominance in my sample and their greater representativeness.

5.1

Setting of Consumer Goods Prices

My subsample of goods accounts for 74.9% of all expenditures in my basket and is representative of 77.5% of Mexican consumer expenditures on goods (excluding energy). Most goods left out of the sample pertain to product categories falling under the apparel and related accessories group. 5.1.1

Frequency of Goods Price Changes

As seen in the upper panel of Figure III, movements in the frequency of price changes and inflation were very large over the sample period. In April 1995, the rate of inflation in my sample of goods peaked at 86.0% (7.2% in monthly terms). This rate is much greater than the average in 1994 (7.5%) or during the last year of the sample (1.5%). The frequency of price changes also peaked in April 1995, when the price of 64.7% of goods, measured in CPI weights, changed during that month. This number is more than twice the average frequency of 26.8% in 1994. There were large variations in the composition of price changes over the sample period, as shown in the lower panel of Figure III. At the peak of inflation, only 8.9% of price changes were negative, a proportion that 10

For the products in my sample, the COICOP goods/services classification is almost identical to the Bank of Mexico’s tradeables/nontradeables classification. The results reported in the paper for goods and services thus have an alternative interpretation in terms of tradeables and nontradeables.

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rose to 46.0% in the last year of the sample. The corresponding proportion for the full sample of goods and services over the last year of the sample is 43.4%, a figure echoing those from U.S. and euro-area studies. Positive comovement between f rt and π t is clearly visible in Figure III. The correlation coefficient between the two series is 0.91 for the whole period.11 This correlation is largely driven by the high-inflation episode, however; it is about zero if I consider only the last three years of the sample. After mid-1996, it is difficult to spot any downward drift in the frequency of price changes even though inflation trends down. The reason behind this loose relationship is apparent in the lower panel of Figure III, where I break down f rt into f rt+ and frt− . As inflation declined, so did the frequency of price increases. At the same time, price decreases became more frequent, thereby dampening movements in the overall frequency of price changes. A look at the correlation between f rt+ , f rt− and π t provides further evidence of these offsetting movements. In the last three years of the sample, the correlation is 0.59 between frt+ and π t , and −0.74 between f rt− and π t . The net result is a relative absence of correlation between frt and π t for my sample of goods over that period. There are a few apparent large negative movements in the inflation series of goods over the low-inflation period, in particular in March 1999, February 2001, July 2001, and February 2002, which are associated with unusually large changes in fresh produce prices. Shocks to the supply of fruits and vegetables, such as unusual weather conditions, can have a notable impact on the price of these items because they are perishable in nature. Some evidence of opposite movements in the frequency of price increases and decreases is apparent for these months. The scatterplot in the upper-left panel of Figure IV offers a view from a different angle of the relationship between the monthly frequency of price changes and inflation. Similar scatterplots for price increases and decreases are shown in the middle-left and lower-left panels, respectively. All panels display linear regression lines that use linear, quadratic and cubic goods inflation terms as explanatory variables, as well as a full set of year dummies. The dummies are included to account for potential shifts in the relationships over time that are unrelated to inflation, such as fluctuation in aggregate demand, basket composition, and methodology. I present regression lines for two sets of observations. The dashed lines include all monthly observations in the sample. The thick lines 11

All correlation statistics presented in this section are computed using linearly-detrended series.

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exclude April 1995, which was marked by a five percentage-point increase in the value-added tax, as well as all periods with negative inflation, which effectively removes all large shocks to food produce mentioned earlier. Variations in the supply of fresh fruits and vegetables and value-added tax changes are shocks that differ in nature from a general rise in the price level. For this reason, my discussion of the scatterplots focuses on the regression results for the smaller sample as it likely better captures the overall relationship between inflation and its components. All regression statistics can be found in Table II. When inflation is zero, each percentage-point increase in the rate of nonregulated-goods inflation is associated with a 0.35 (0.13) percentage-point rise in the frequency of price increases, and an opposite 0.22 (0.06) percentage-point decline in the frequency of price decreases.12 These opposite movements have dampening effects on the frequency of price changes, whose corresponding slope is 0.14 (0.13). As inflation increases from a low level, the frequency of price increases becomes more responsive to changes in inflation while the frequency of price decreases becomes less so, resulting in greater sensitivity of the frequency of price changes to inflation. At an inflation rate of 15%, a one-percent change in inflation is associated with a 0.56 (0.04) percentage-point rise in the frequency of price increases, and a 0.13 (0.01) percentage-point decline in the frequency of price decreases. As inflation increases further, few price decreases are observed in the economy; the rise in the frequency of price changes is then mainly driven by the steady growth in the occurrence of price increases. At all levels of inflation, I find that the response of the frequency of price increases to a change in inflation is larger than that of price decreases. A similar asymmetry is found in U.S. data, as reported by Nakamura and Steinsson (2008). The year dummies appear to capture some key changes in methodology and the economic environment over time. In particular, they are the lowest at the beginning of the sample, when maintaining a fixed basket was seen as important, and highest for 2001 and 2002, which had systematic substitutions of unavailable items to keep the basket up-to-date. No major change in methodology occurs over the 1996 to 2000 period and I cannot reject the hypothesis that the year dummies for 1996 to 2000 are jointly identical at the 10% confidence level. Imposing such equalities 12 Standard deviations are shown in parentheses. They were computed using the Huber-White estimator of variance. As a check, I also computed standard errors using the autocorrelation-robust Newey-West estimator for the entire sample period (consecutive observations are required) with negligible impact on the estimates. Moreover, the fit of the linear model is virtually identical to that obtained using the nonlinear estimator of Papke and Wooldrige (1996), which directly accounts for the zero-one bounds on the frequency.

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results in slightly more sensitive responses of the frequency of price increases and decreases at low levels of inflation but the overall sensitivity of the frequency of goods price changes to inflation is largely unchanged. Interestingly, the year dummies for price increases and decreases have a tendency to rise over time. It is thus possible that factors not directly related to inflation, such as innovations in the technology used by outlets to change prices or changes in the composition of stores, moderated the fall in the frequency of price changes as inflation declined in the latter years of the sample. 5.1.2

Average Magnitude of Goods Price Changes

The average magnitude of goods price changes comoves strongly with goods inflation, regardless of whether the latter is low or high. As shown in the upper panel of Figure V, dpt and π t follow similar patterns over the sample period.13 Both series registered sharp increases during the Tequila crisis, followed by a protracted decline and ultimately a stabilization. The correlation between the two series is 0.95 over the full sample period. The high-inflation episode does not drive this strong correlation, as was the case with the frequency of price changes; indeed, the correlation actually rises over the last three years of the sample. As the upper-right panel of Figure IV indicates, dpt and π t have a tight, almost linear relationship when inflation is low. When inflation is elevated, this relationship is still strong and positive, although a bit noisier and somewhat concave. The figure also displays linear regression lines computed using the same set of observations and regressors employed for the frequency of price changes. The corresponding regression statistics are presented in Table II. The average size of price increases and decreases are much less sensitive to the level of inflation than dpt . Except for a short period around the peak of inflation, the two series show relatively small oscillations around their respective sample mean: 9.0% for price increases and 9.8% for price decreases.14 In the case of price decreases, I cannot reject the hypothesis that the coefficients associated with the three inflation terms in the regression are jointly equal to zero. The middleright panel is consistent with a mild rise in the size of price increases as inflation moves from a low to a high level. One cannot exclude, however, that this positive relationship partly reflects a rise in 13 14

The inflation series displayed is the nonannualized monthly inflation rate to facilitate visual comparisons. The few large spikes in dp− t correspond to large variations in the price of a some fresh produce.

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the occurrence of multiple price increases during the month. When this is the case, dp+ t overstates the size of individual price increases. The finding of a tight relationship between the average magnitude of price changes and inflation should come as no surprise given the behavior of the frequency of price changes documented earlier. By definition, π t = frt · dpt . When inflation is low, frt moves little with inflation, implying that dpt moves strongly and almost linearly with π t . By contrast, when inflation is high, frt comoves strongly and positively with π t . This second source of variation in π t introduces some curvature in the relationship between π t and dpt . To better understand what drives dpt , it is convenient to express it as ¯ ¯ −¯ ¯ ¯ ¯ ¯ dpt = st · ¯dp+ t − (1 − st ) · dpt ,

¡ ¢ where st = frt+ / frt+ + frt− is the share of price increases among price changes. As this equation

makes clear, fluctuations in dpt can originate from two sources: changes in the relative occurrence

of price increases and decreases (the composition effect) and variations in their respective size. To assess the importance of each margin, I compute two counterfactual series which are displayed in the lower panel of Figure V. I obtain the first by holding st at its sample mean to show how ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ and ¯dp− ¯ alone affect dpt . In the second series, ¯dp+ ¯ and ¯dp− ¯ are held movements in ¯dp+ t t t t at their respective sample mean so that the relative occurrence of price increases and decreases is the only source of variation in dpt . The exercise indicates that the composition effect drives almost entirely dpt when inflation is below 10-15%. Had st been constant, dpt would have shown a counterfactual gentle rise in the last three years of the sample because of a mild upward trend in dp+ t after 1999. By contrast, the series allowing only for the composition effect predicts remarkably well the level of dpt over that period. When inflation nears its peak, the composition effect alone is insufficient to closely match the level of dpt , but it is a better predictor than merely allowing for changes in the average absolute magnitude.

5.2

Setting of Consumer Services Prices

Services represent a smaller share of expenditures (25.1%) in my basket than in the entire CPI (41.4%). This difference primarily reflects the exclusion of rents, which accounts for a third of

14

Mexican spending on services, for which individual data are not available. It also stems from my decision to exclude all items that are not available for purchase every month of the year (education services), or whose whose price is regulated (such as taxi and public transportation), in order to focus on market prices that are free to respond to changes in the economic environment. Overall, my basket is representative of 32.8% of consumer expenditures on services, compared to about half for the sample used by Bils and Klenow (2004) for the United States.15 The upper panel of Figure VI displays the frequency of price changes and in inflation in the subsample of services over my sample period. As was the case with goods, services inflation peaked in April 1995, reaching 65.7% (5.5% in monthly terms), while the corresponding frequency of price changes rose to a sample high of 53.7%. However, there are several notable differences between the setting of goods and services prices. First, price changes are much less frequent among services than among goods at all level of inflation. Even in 1995, as services inflation averaged 29.7%, the frequency of services price changes was lower (21.6%) than that of goods over the last year of the sample (33.6%), when goods inflation averaged only 1.5%. Second, services price changes are much less uniformly distributed over the year than they are for goods; nominal adjustments tend to cluster in the first quarter of each year. Another strong seasonal pattern would also be apparent in August and September if education services were added to the sample. Third, the frequency of price changes is the key margin driving the adjustment in services inflation, as hinted by the strong correlation between the two series. A role for movements in the average magnitude of price changes (whose time series is not shown) can be seen by noting the divergence between inflation and frequency series around the peak of inflation and at the beginning of some years, when price changes tend to be relatively large. Fourth, as shown in the lower panel of Figure VI, services price decreases are much less frequent than price increases, especially when inflation is high. In 1995, as inflation was rampant, a meager 1.5% of services price changes were negative, compared to 14.8% for goods. Over the last year of the sample, about 15.3% of services price changes were negative, compared to 46.1% for goods. Finally, services prices exhibited substantially more inertia than goods prices over the sample period. In the year prior to the Tequila crisis, the average 15 I estimated this proportion based on the 1993-1995 CPI weights for all urban consumers. For consistency with the COICOP methodology used throughout this paper, I excluded energy categories and classified food consumed away from home under “services” (items such as restaurant meals are categorized as “goods” under the BLS methodology, but as “services” under the COICOP).

15

rate of goods and services inflation were similar, at 7.6% and 6.6%, respectively. In 1995, the goods price index rose 15.4 percentage points more than that of services. By the turn of 1997, the ratio of services to goods prices had fallen 22.2 percentage points relative to its average in 1994, and would not return to its pre-crisis level before early 2002. Even in the last year of the sample, services inflation was running substantially higher than goods inflation, at 7.6% and 1.5% on average, respectively, suggesting that the inflationary consequences of the Tequila crisis had yet to be fully passed-through to services prices.

5.3

Inflation Variance Decomposition

In order to gauge the relative importance of movements in the frequency and magnitude of price changes for the variance of inflation, Klenow and Kryvtsov (2008) proposed the following decomposition:

2

2

var (π t ) = f r · var (dpt ) + dp · var (f rt ) + 2f r · dp · cov (dpt , f rt ) + Ot2 , | {z } | {z } Intensive margin

Extensive margin

where Ot2 are high-order terms that are functions of frt . If price changes are perfectly staggered, as in the baseline Calvo or Taylor model, then the intensive margin accounts for all of the variance of inflation. Using monthly U.S. CPI data from 1988 to 2004, Klenow and Kryvtsov (2008) find that the intensive margin accounts for about 95% of the inflation variance, while the extensive margin terms, collectively or individually, are small. As shown in Table III, the Mexican data also points to a minor role for movements in the frequency of price changes when restricted to the low-inflation period after mid-1999. The intensive margin’s share of inflation variance is 89.2% over that period for the full sample, a proportion that reaches 93.9% among goods. Over the entire sample period, however, the intensive margin’s share is only 41.4% of the inflation variance, and falls further to 34.7% when limited to the January 1995 to June 1999 period. This finding clearly indicates that fluctuations in frt played an important role in the dynamics of inflation over the full sample period, and especially when inflation was high and volatile. ¡ − ¢ − + + + − − Alternatively, inflation can be decomposed as π t = π + t +π t , where π t = f rt ·dpt π t = f rt · dpt

is the inflation contribution of items whose price rose (fell) over the month. Following Klenow and

16

Kryvtsov (2008), the variance of inflation can then be expressed as ¡ + −¢ ¡ + −¢ ¡ ¢ ¡ −¢ var (π t ) = var π + t + cov π t , π t + var π t + cov π t , π t . | {z } | {z } pos

neg

Over the full sample period, I find that pos/var (π t ) = 0.82, a clear indication that most of the variance of inflation can be traced back to movements in the inflation contribution of price increases. When restricted to the last three years of the sample, a period of relatively low inflation, I find that pos/var (π t ) = 0.32, a value noticeably lower than that reported by Klenow and Kryvtsov (2008) for the United States (0.65). The difference seems attributable to the exceptionally large downward movements in the price of fresh produce at the beginning of 2001 and 2002.16

6

International Comparisons

My findings for the low-inflation portion of my sample are broadly consistent with the results reported in U.S. and euro-area studies.17 Evidence on the setting of consumer prices under high inflation is more limited, however. Table IV lists the main empirical studies in high-inflation environments and shows, for each one, the composition of the basket, the average inflation rate and the mean frequency of price changes. In comparison to my Mexican data set, the samples from these studies are relatively small and predominantly composed of food items. My sample represents a significant broadening of the sample of Mexican food prices CPI used by Ahlin and Shintani (2007) in their analysis of price dispersion. Moreover, the sample periods from previous studies are typically restricted to a few consecutive years, which limits the performance of time series analysis. The first study of individual consumer price setting in a high-inflation context was done by Lach and Tsiddon (1992). They considered a sample of 26 food products from the Israeli CPI (mainly meat and alcohol) during two time periods: 1978-1979 and 1981-1982. For the former period, they found that 46.5% of prices changed every month while inflation averaged 77%.18 The frequency of 16

To verify this hypothesis, I computed pos/var (πt ) based on a sample of Mexican CPI prices starting in July 2002 and ending in March 2007. The average inflation rate over that period (3.9%) is similar to the July 1999 to June 2002 period (5.0%) but fresh produce prices display few exceptionally large movements. The corresponding value of pos/var (πt ) for this sample is 0.60, a figure similar to Klenow and Kryvtsov (2008). 17 See Dhyne et al. (2006) for a review of the main U.S. and euro-area findings 18 To facilitate comparisons, all inflation figures in this section are computed in the standard way rather than using

17

price changes rose to 60.4% in 1981-1982 as inflation reached an impressive 116%.19 Their results clearly indicate that the frequency of food price changes can be responsive to the rate of inflation. Konieczny and Skrzypacz (2005) study the transition from a planned to a market economy in Poland. At the peak of inflation in 1990, the price of 59% of items in their basket composed mainly of food products changed every month, a proportion that halved as inflation fell to just under 20% in 1996. Like mine, their findings are consistent with a nonlinear relationship between the frequency and inflation; the frequency fell about 0.4 percentage point for each percentage point decline in inflation from 1991 to 1993, but then only 0.25 percentage point from 1993 to 1996. One must be very careful when making cross-country comparisons, even when inflation rates are similar, because of large variations in basket composition and methodology. For example, the frequency of price changes reported by Ahlin and Shintani (2007) for their sample of food prices in Mexico in 1995 exceeds by 27 percentage points the one I find in my broader sample of goods and services. Similarly, Burstein, Eichenbaum, and Rebelo (2005) report a frequency of price changes that is similar to that reported by Konieczny and Skrzypacz (2005) for Poland in 1990 (54.5% versus 59%, respectively), even though the rate of inflation in Poland was over six times that of Argentina.20 The studies of Eden (2001) and Baharad and Eden (2004) are possibly the closest in spirit to mine as they make comparisons between low- and high-inflation periods while controlling for basket composition. Using data from the Israeli CPI for 1991 and 1992, a period of relatively low inflation, they construct a basket matching up to 23 of the 26 food products in the Lach and Tsiddon (1992) study, to which they compare their findings. Even though the product coverage of their sample is much smaller than mine for Mexico, the findings are very similar. In particular, the frequency of price changes at the peak of inflation (60.4%) is nearly double that for the relatively low inflation sample (34.6%), indicating a major role for the frequency of price changes in the adjustment to a higher inflation rate. logarithmic differences. 19 The figures for the samples considered by Lach and Tsiddon (1992) are taken from Eden (2001). 20 This relatively higher frequency of price changes in Argentina may be related to the type of establishments surveyed (supermarkets). Baudry et al. (2007) report that the outlet size is positively correlated with the frequency of price changes in French CPI data.

18

7

Empirical Performance of Menu-Cost Models

In this section, I investigate whether a menu-cost model with idiosyncratic technology shocks can correctly predict the average magnitude and frequency of price changes at levels of inflation similar to the ones observed in Mexico over my sample period. This particular model was chosen because it has several desirable features. First, the menu costs produce infrequent, lumpy nominal price adjustments. Second, the model leaves the frequency of price changes free to vary with inflation, a feature not found in most time-dependent models and in state-dependent models in which nominal prices adjust every period. Third, the presence of idiosyncratic technology shocks ensures that individual price changes will be observed even when aggregate inflation is near or at zero. Moreover, these shocks give rise to both positive and negative price adjustments, which might help the model to generate empirically plausible offsetting movements in the frequency of price increases and decreases.

7.1

Economic Environment

The economic environment is very similar to the models of Danziger (1999) and Golosov and Lucas (2007). The economy consists of three types of agents. An infinitely-lived representative household supplies labor and consumes a basket of differentiated consumption items. These items are produced by a continuum of monopolistically competitive firms subject to idiosyncratic technology shocks. Finally, there is a monetary authority that exogenously sets the rate of money growth, gt , at each period t. For simplicity, I assume that gt follows a Markov-switching process. 7.1.1

Households

The problem of the representative household is to choose a sequence for consumption, {Ct }, and for hours worked, {Nt }, in order to maximize its present discounted utility, max

{Ct ,Nt }

E0

∞ X t=0

β t (log Ct − ψNt ) ,

subject to a budget constraint, Pt Ct = Wt Nt + Pt Πt , and a simple money demand, Pt Ct = Mt . The variable Pt is the price index, Wt is the wage rate and Mt is the household’s holding of money.

19

Real profits, Πt , are expressed in units of the consumption basket and remitted every period by intermediate firms. The budget constraint states that consumption spending equals the sum of a household’s labor income and profits received from firms. Following Golosov and Lucas (2007), I assume that utility is separable, logarithmic in consumption and linear in labor. Under these Wt t assumptions, the wage rate is proportional to the stock of money, ψ = PW = M . Consumption, t Ct t θ ³R ´ θ−1 θ−1 (cj,t ) θ dj , is a composite of individual consumption items aggregated using a DixitCt =

Stiglitz specification. The resulting demand for individual items must satisfy cj,t = (pj,t /Pt )−θ Ct . ³R ´ 1 1−θ 1−θ The effective price index in this economy is Pt = (pj,t ) dj . To ensure comparability

with my empirical results, all statistics of the model, including inflation, are computed using the methodology outlined in Section 4. 7.1.2

Intermediate Firms

There is a continuum of measure one of monopolistically competitive firms. At the beginning of each period, each firm independently draws an idiosyncratic productivity shock and observes the monetary injection and aggregate objects. It then decides whether to keep selling its item at the same nominal price as in the previous period, or to incur a menu cost (expressed in units of labor), ξ, in order to re-optimize its price. The firm must satisfy the demand once a price is set for the period. The production function of the j th firm is linear in labor, yj,t = φj,t nj,t . I assume that labor ¯ + ρ log φj,t + εj,t , where technological productivity, φj,t , evolves according to log φj,t = (1 − ρ) log φ ¡ ¢ innovations, εj,t , are drawn from a normal distribution N 0, σ 2ε . Firms maximize the present

discounted value of their real profits.

It is convenient to express the problem of the firm recursively in order to solve it using dynamic programming techniques. To ensure stationarity, all nominal variables are scaled by the money stock. Let V (φ, p, μ, g) be the Bellman equation of an optimally-behaving firm just before it decides whether to change or retain its nominal price from the previous period. The state of the firm comprises its price, p, its technological level, φ, the joint distribution of individual prices and technologies in the economy, μ = Φ × P, and the current rate of money growth, g. The value function is given by

V (φ, p, μ, g) = max

{Vnc (φ, p, μ, g) , Vc (φ, μ, g)} , 20

where Vnc (φ, p, μ, g) is the value function associated with the firm’s decision to make no change to its nominal price in the current period and behave optimally thereafter, and Vc (φ, μ, g) is the corresponding value function of a firm changing its price in the current period. These functions are expressed as

Vnc (φ, p, μ, g) = π (φ, p, μ, g) + β

Z

¡ ¢ ¢ ¡ ¡ ¢ ¢ ¡ ¡ ¢ q μ, g, μ0 μ, g 0 , g 0 V φ0 , p − g 0 , μ0 μ, g 0 , g 0 dλ φ0 , g 0 |φ, g ,

(1)

and Vc (φ, μ, g) = max p˜

½ ¾ W (μ, g) Vnc (φ, p˜, μ, g) − ξ , P (μ, g)

(2)

respectively. The period real gross profit function is expressed as

π (φ, p, μ, g) =

µ

p 1 W (μ, g) − P (μ, g) φ P (μ, g)

¶µ

p P (μ, g)

¶−θ

C (μ, g) .

The integral on the right-hand side of Vnc (φ, p, μ, g) gives the expected value function in the next period, weighted by the ratio of marginal utility of consumption across periods, q (μ, g, μ0 , g 0 ) = C (μ, g) /C (μ0 , g 0 ). The transition probabilities across exogenous states are represented by the ¡ ¢ measure dλ φ0 , g 0 |φ, g . The law of motion for the distribution of firms, μ0 (μ, g 0 ), is an object to

be determined in equilibrium.

7.2

Definition of Equilibrium

Conditional on the money growth and technology processes, I define a competitive recursive equilibrium as a pair of value functions {Vnc , Vc }, a collection of aggregate objects functions {P, C, W, N }, a pricing function p˜, and a law of motion μ0 such that (a) {Vnc , Vc } is a fixed point of the system formed by equations (1) and (2) given P , C, W , p˜ and μ0 , (b) p˜ is optimal given P , W and Vnc , (c) C and N solve the household’s problem given P and W (d) μ0 correctly represents the law of motion of the distribution of firms given Vnc , Vc and p˜, and (e) the labor, consumption, individual items and money markets clear. All equilibrium objects are functions of the joint distribution of individual prices and technologies, which is an infinite-dimensional object. In order to make the computation of an equilibrium amenable to standard solution techniques, I follow Krussel and Smith (1998) and approximate μ0 21

using a selection of its moments. A solution is then computed using value function iterations. Details of the solution method and model calibration are relegated to Appendix B.21

7.3

Main Predictions of the Model

I first investigate whether the model is able to correctly predict the level of the frequency and average magnitude of price changes over a range of inflation similar to that experienced by Mexico. For computational and expositional convenience, I focus initially on a version of the model with nonstochastic money growth, so that all aggregate objects and the joint distribution of individual prices and technologies are constant over time. The findings are robust to considering changes in trend money growth in the stochastic money-growth version of the model. The model is calibrated to match the average frequency and absolute magnitude of price changes over the last three years of the sample, a period when annual inflation averaged 5.0%. The model’s predictions are then recorded for steady-state inflation rates ranging from 0 to 50%, holding all other parameters constant. In addition to calibrating the model using the full sample of items, I also considered separate calibrations for the subsamples of goods and services. Turning first to the results for the full sample, the upper-left panel of Figure VII indicates that the model matches remarkably well the average frequency of price changes at various levels of inflation. The diamonds, squares and triangles represent the average monthly frequency of price changes, increases and decreases, respectively, for each calendar year in my sample. The lines indicate the corresponding predictions of the model. As steady-state inflation is increased from a low to a high level, the model produces an initially slow rise in the monthly frequency of price changes similar in magnitude to the data. The model also fares well at reproducing the underlying opposite movements in the frequency of price increases and decreases. The frequency of price increases rises steadily and almost linearly in the model over the range of steady-state inflation considered. The corresponding decline in the frequency of price decreases is fastest at low levels of inflation. Overall, my calibration predicts that the frequency of price increases is more sensitive to a change in steady-state inflation than the frequency of price decreases, consistent with the evidence presented in Section 5. 21

The C programs, detailed calibrations, and instructions to replicate the results are available as an on-line appendix on the author’s web site.

22

The model fits equally well the average magnitude of price changes, as shown in the upperright panel of Figure VII. When inflation is low, the average magnitude of price changes responds almost linearly to a change in steady-state inflation, a counterpart to the weak response of the frequency of price changes. By contrast, a change in inflation has little impact on the average absolute magnitude of price increases and decreases. The panel thus hints that in the model, as it is the case in the data, the high correlation between the average magnitude of price changes and the level of inflation is driven primarily by shifts in the relative occurrence of price increases and decreases, not by changes in the absolute size of nominal adjustments. The panels on the second and third rows of Figure VII present corresponding sample and model statistics for the goods and services subsamples, respectively. Given that goods account for a large proportion of price changes in the full sample, the model’s fit of the goods subsample is very similar to the model’s fit of the entire sample. Despite important differences between goods and services price-setting behavior, the model matches reasonably well the annual statistics in the subsample of services. The calibration for services entail a smaller variance of technological innovations (σ 2ε = 0.0011) and larger menu costs (ξ = 0.0075) than the calibration for goods (for which σ 2ε = 0.0032 and ξ = 0.0035). As a result, services price changes in the model are relatively infrequent and mainly positive whenever inflation exceeds a few percentage points. Moreover, the model is consistent with a greater sensitivity of the frequency of services price changes when steady-state inflation moves up from a low level. I next investigate whether the model is consistent with the dynamic properties of aggregate inflation, in particular with the respective roles of movements in the frequency and magnitude of price changes in accounting for variations in the monthly inflation series. In order to do so, I assume that money growth follows a Markov-switching process, as described in Appendix B, and conduct two experiments. In the first experiment, I calibrate the money growth process so that the model matches the mean, standard deviation and persistence of inflation in the full sample over the low-inflation period shown in Table III. I then compute the inflation variance decompositions proposed by Klenow and Kryvtsov (2008) and compare the model’s predictions to the data. The procedure is repeated for the relatively high-inflation period of January 1995 to June 1999. In the second experiment, I hold constant the variance and persistence of the money growth process at its calibrated values in the low-inflation episode. I then compute the inflation variance decompositions 23

for levels of trend inflation ranging from 0 to 50%. Although factors not captured by my simple one-sector monetary model surely had an influence on inflation in my sample, these experiments highlights key differences in the dynamic properties of low and high inflation found both in the model and the data. When calibrated to the low-inflation period in Table III, the model predicts that the share of variance accounted for by the intensive margin is 94.3%, a proportion very similar to that found in the data (89.2%). All components of the extensive margin are relatively small, which indicates that movements in the frequency of price changes account for little of the variance of inflation during the low-inflation period. The relative unresponsiveness of the frequency in the model when inflation is low is a clear indication that the high share of inflation variance accounted for by the intensive margin in the data cannot be taken as prima facie evidence in favor of models in which the frequency of price changes is exogenously constant. This result echoes the conclusions of Golosov and Lucas (2007), who calibrated their model to match the recent U.S. inflation experience. When calibrated to the January 1995 to June 1999 period, a period of relatively high and volatile inflation, the model’s predicted extensive margin share of inflation variance is 57.4%. This figure is subtantially lower than over the low-inflation period but higher than in the data (34.7%). The second experiment indicates that the importance of intensive margin in the model depends importantly on the level of trend inflation. Holding constant the variance and persistence of money growth innovations, the share of inflation variance attributed to the intensive margin is 99.7% when inflation is zero, a proportion that falls to 46.9% and 17.1% once trend inflation reaches 25% and 50%, respectively. The presence of idiosyncratic shocks is a key factor behind the model’s good empirical performance over a wide range of inflation. First, it ensures that nonzero price changes, both positive and negative, are observed when aggregate inflation is near zero. Second, the occurrence of price increases and decreases typically respond in opposite directions in the face of inflationary shocks. The resulting variation in the composition of nominal adjustments has dampening effects on the frequency of price changes while making the average magnitude of price changes relatively responsive to inflation. Third, the distribution of idiosyncratic shocks helps the model match the absolute size of price increases and decreases over a wide range of inflation. In the steady state of the Sheshinski and Weiss (1977) menu-cost model, which has no idiosyncratic shocks, all price changes are positive whenever inflation is positive. The average size of price changes is directly determined by the 24

width of the (one-sided) Ss band, which is a strictly increasing function of steady-state inflation. As shown by Rotemberg (2004), a change in steady-state inflation generates an implausibly large change in the width of the Ss band in this model under standard specifications of demand. When idiosyncratic shocks are added to the environment, however, the width of the Ss band is no longer the sole determinant of the average magnitude of price changes: Shifts in the relative occurrence of price increases and decreases also can have an impact. In my calibrations, these shifts play a central role while the width of the Ss band is relatively insensitive to the level of inflation. As a result, the model produces both a strong response of the average magnitude of price changes to inflation and a weak response of the average absolute size. Danziger (1999) provides an interesting example of a dynamic general-equilibrium model with menu costs and idiosyncratic shocks in which the Ss band is independent of the money growth process. As I have shown, a menu-cost model with idiosyncratic technology shocks is consistent with some key features of individual consumer price setting at both low and relatively high levels of inflation. Despite this success, the model suffers from several known inconsistencies with the data. As discussed by Golosov and Lucas (2007) and several others, the model generates too few small price changes and has an amount of intrinsic persistence that is too small compared to the empirical evidence on the transmission of monetary shocks. Nevertheless, my findings offer hope that versions of the model eventually addressing these short-comings, such as perhaps ones in which the hypotheses of constant and time-invariant menu costs are relaxed, might continue to provide a good fit of the average magnitude and frequency of price changes if they embed a distribution of positive and negative price changes. Midrigan (2006) offers an interesting exploration along those lines in an environment with multi-product firms.

8

Conclusion

In this paper, I provide new evidence on the setting of individual consumer prices under low and high inflation. To do so, I assembled a large data set of store-level prices that is representative of over half of Mexican consumer expenditures. The number of observations in my sample, over thirty thousand per month, is an order of magnitude larger than in other high-inflation studies currently available. Moreover, the data set covers periods of both low and high inflation as well as

25

the transition between the two. The sample starts in January 1994, one year before the Tequila crisis and the sharp increase in inflation that accompanied it, and ends in June 2002, a few years after inflation had been successfully stabilized at a low level. Throughout the discussion, I focus on a decomposition of inflation into the frequency and the average magnitude of nonzero price changes. I find some key differences between the low- and high-inflation periods in my sample. When inflation is low (below 10 − 15%), most of the adjustment to inflation occurs through changes in the average magnitude of price changes. The latter is connected to inflation by a tight and near-linear relationship. The frequency of price changes, on the other hand, is only weakly correlated with inflation. By contrast, when inflation is high (above 10 − 15%), both the frequency and magnitude of price changes comove strongly and positively with inflation. Breaking down price changes into positive and negative adjustments helps understand differences in the behavior of inflation over the low- and high-inflation portions of my sample. As inflation rises from a low level, positive nominal adjustments become increasingly common, while negative ones become less so. These opposite effects of inflation on the frequency of price increases and decreases dampen variations in the overall frequency of price changes. As inflation rises further to a high level, the frequency of price increases continues to rise steadily with inflation. The rate of decline in the frequency of price decreases moderates, however, as few price decreases are observed in the economy, and the frequency of price changes then comoves strongly with inflation. One important challenge is to design price-setting models that offer empirically plausible predictions at both low and high levels of inflation. The baseline Calvo (1983) and Taylor (1980) models, which are widely used in the literature, assume that the frequency of price changes is constant over time. This assumption is clearly problematic for an environment in which inflation is as volatile as in Mexico over my sample period because both the frequency and magnitude of price changes displayed large variations. I show that a menu-cost model with idiosyncratic technology shocks, on the other hand, predicts remarkably well the level of the average frequency and magnitude of price changes over a wide range of inflation. The joint presence of menu costs and idiosyncratic shocks is key to this good fit. Menu costs ensure that nominal adjustments are lumpy and infrequent, two characteristic of price changes shared by most goods and services in my sample. The addition of idiosyncratic shocks helps generate a distribution of both positive and negative price changes that is free to move with inflation. Consistent with the data, my calibration of the model predicts 26

that a large number of price increases and decreases are observed when inflation is close to zero. As inflation increases, the model generates a steady rise in the occurrence of price increases and a simultaneous decline in the occurrence price decreases, which moderates as negative price changes rapidly dissipate. The model is consistent with a modest role for the frequency of price changes when inflation is low and stable, and a relatively important role when inflation reaches high levels, even holding constant the variance of money shocks. Note that the baseline Calvo and Taylor models are not inconsistent with infrequent and lumpy nominal adjustments and the simultaneous presence of positive and negative price changes; one could simply augment these models with idiosyncratic shocks. Unless the assumption of a constant frequency of price changes is relaxed, however, these models will inexorably fail to capture an important margin by which individual prices adjust from a low- to a high-inflation environment. Board of Governors of the Federal Reserve System

27

References Ahlin, Christian and Mototsugu Shintani, "Menu Costs and Markov Inflation: A Theoretical Revision with New Evidence," Journal of Monetary Economics, 54 (2007), 753—784. Baharad, Eyal and Benjamin Eden, "Price Rigidity and Price Dispersion: Evidence from Micro Data," Review of Economic Dynamics, 7 (2004), 613—641. Baudry, Laurent, Hervé Le Bihan, Patrick Sevestre, and Sylvie Tarrieu, "What do Thirteen Million Price Records Have to Say about Consumer Price Rigidity?," Oxford Bulletin of Economics and Statistics, 69 (2007), 139—183. Bils, Mark and Peter J. Klenow, "Some Evidence on the Importance of Sticky Prices," Journal of Political Economy, 112 (2004), 947—985. Burstein, Ariel, Martin Eichenbaum, and Sergio Rebelo, "Large Devaluations and the Real Exchange Rate," Journal of Political Economy, 113 (2005), 742—784. Calvo, Guillermo A., "Staggered Prices in a Utility-Maximizing Framework," Journal of Monetary Economics, 12 (1983), 383—398. Danziger, Leif, "A Dynamic Economy with Costly Price Adjustments," American Economic Review, 89 (1999), 878—901. Dhyne, Emmanuel, Luis J. Álvarez, Hervé Le Bihan, Giovanni Veronese, Daniel Dias, Johannes Hoffmann, Nicole Jonker, Patrick Lünnemann, Fabio Rumler, and Jouko Vilmunen, "Price Setting in the Euro Area: Some Stylized Facts from Individual Consumer Price Data," European Central Bank Working Paper Series No. 524, 2005. , "Price Changes in the Euro Area and the United States: Some Facts from Individual Consumer Price Data," Journal of Economic Perspectives, 20 (2006), 171—192. Eden, Benjamin, "Inflation and Price Adjustment: An Analysis of Microdata," Review of Economic Dynamics, 4 (2001), 607—636. Edwards, Sebastian, "The Mexican Peso Crisis: How Much Did We Know? When Did We Know It?," World Economy, 21 (1998), 1—30. Golosov, Mikhail and Robert E. Lucas, "Menu Costs and Phillips Curves," Journal of Political Economy, 115 (2007), 171—199. Klenow, Peter J. and Oleksiy Kryvtsov, "State-Dependent or Time-Dependent Pricing: Does it Matter for Recent U.S. Inflation?" Quarterly Journal of Economics, 123 (2008), 863—904. Konieczny, Jerzy D. and Andrzej Skrzypacz, "Inflation and Price Setting in a Natural Experiment," Journal of Monetary Economics, 52 (2005), 621—632. Krusell, Per and Anthony A. Smith, "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, 106 (1998), 867—896. Lach, Saul and Daniel Tsiddon, "The Behavior of Prices and Inflation: An Empirical Analysis of Disaggregated Price Data," Journal of Political Economy, 100 (1993), 349—389.

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Midrigan, Virgilu, Menu Costs, "Multi-Product Firms, and Aggregate Fluctuations," unpublished paper, New York University, 2006. Nakamura, Emi and Jón Steinsson, "Five Facts About Prices: A Reevaluation of Menu Cost Models," Quarterly Journal of Economics, 123 (2008), 1415-1464. Organisation for Economic Co-operation and Development, OECD economic surveys, 1999-2000: Mexico, 2000 (Paris and Washington, D.C.) Rotemberg, Julio J., "Fair Pricing," unpublished manuscript, Harvard Business School, 2008. Sheshinski, Eytan and Yoram Weiss, "Inflation and Costs of Price Adjustment," Review of Economic Studies, 44 (1977), 287—303. Taylor, John B., "Aggregate Dynamics and Staggered Contracts," Journal of Political Economy, 88 (1980), 1—23.

29

A

Price Averaging

In Mexico, price collectors visit outlets four times every month to collect prices of food items, and they visit twice per month to collect prices for all other items. The prices published in the Diario are an average of the prices collected over the month. In this appendix, I first discuss how observing a price’s average rather than its actual value at a particular point in time impacts inference about the timing and magnitude of price changes. I then describe how I filtered the data to make the results in this paper more directly comparable to those from studies using prices collected once per month.

A.1

Effects of Averaging on Frequency and Magnitude

Suppose a price collector observes the price of an item twice every month and then computes two monthly time series. The first series is a simple average of the two prices collected over the month (the average-price series). The other series contains the actual price observed at the second visit (the point-in-time series). The average-price series corresponds to Banco de México’s current method, whereas point-in-time series are used in the United States and euro area. Changes to the monthly average-price series typically are more frequent and smaller on average than changes to the monthly point-in-time series. To illustrate this point, consider an item whose price is constant over the months t − 1 to t + 1, with the exception of a single adjustment at t. If the price change occurs before the price collector’s first visit at month t, then both prices collected over that month equal the new price. In that case, the average-price and the point-in-time series are identical and correctly reflect the timing and magnitude of the actual price adjustment. Similarly, if the price change occurs after the price collector’s second visit during month t, then both the averageprice and point-in-time series display a unique price change of the correct magnitude detected at month t + 1. Only when the price change takes place between the two price collections do the average-price and point-in-time series differ. When this is the case, the point-in-time series still accurately matches the timing and size of the actual change in the item’s price. The average-price series, on the other hand, displays two price changes: one at month t and one at t + 1. The second price change is recorded because the average price at t has increased by only half the change in the actual price.

30

If several price changes occur within a month, then both the average-price and the point-in time series provide an inaccurate description of individual price changes. The change in the end-ofperiod series corresponds to the cumulative change in the price over the period, while the change in the average-price series reflects the change in the average price over the previous period. Under both approaches, the change in the monthly series may be smaller, equal or larger than the price changes that would be recorded were prices collected continuously.

A.2

Filtration of Average Price Trajectories

In the above example, a price change occurring between two price collections created two consecutive price changes of equal magnitude in the average-price series. My filtering strategy entails finding such patterns and then constructing a series for the last price collected during the month that minimizes the number of price changes and is consistent with the observed average prices. More formally, let pit be the prices of a nonfood item recorded during the price collector’s i-th visit at ¢ ¡ month t. The published monthly average is p¯t = p1t + p2t /2. Consider the case of two consecutive changes in the published average-price series starting at month t. If both changes have the exact same magnitude, that is if p¯t =

p¯t+1− p¯t−1 , 2

then I construct a sequence of semi-monthly observations,

(3) ©¡

p1τ , p2τ

¢ªt+1

τ =t

, that is consistent with

the observed average-price sequence {¯ pτ }t+1 τ =t and features no price change at t + 1. I simply assume that a single nominal adjustment was detected at the collector’s second visit, so that p1t = p¯t−1 and p2t = p¯t+1 . Whenever the filter finds such pattern, it replaces p¯t by p¯t+1 , thus eliminating a potentially spurious price change. A similar approach is used when the published average-price series features up to four consecutive price changes. Considering longer sequences, which are very few, did not improve the fit. The filtering of individual food prices, which are collected four times per month, follows the same approach. Suppose the price of a food item is constant during month t − 1, changes once during month t, and then stays constant during month t + 1. If the actual price change is recorded

31

at the collector’s second, third, or fourth visit, then the published average price is

p¯t =

(5 − dt ) p¯t−1 + (dt − 1) p¯t+1 4

(4)

for some visit time dt ∈ {2, 3, 4}. The change in the published price at t is exactly 1/4, 1/2 or 3/4 the total change from t − 1 to t + 1. For such cases, the filter replaces p¯t by p¯t+1 in the same way as for nonfood items. When more than two consecutive price changes are observed, there may be more than one combination of detection times {dt+τ }t+N−1 and end-of-period prices that is consistent τ =t with the published average-price series and features no price change in the last period. Filtering these longer sequences of food prices did not appear to improve accuracy.22

A.3

Example of Individual Price Trajectory and Filtering

Figure A.1 illustrates how the filtering procedure is implemented. The upper-panel displays two years of monthly average prices, along with the corresponding price changes, for a copy of the book “The Universal History of Literature” sold in a Mexico City outlet. From January 1994 to December 1995, there were six changes to this unfiltered series. The first happened in August 1994 when the average price increased from $23 to $25. Because the average price remained at $25 in September, the filter leaves the series unchanged. The next two changes occurred in January and February 1995. The published price for January, $28.5, is the exact average of the published prices for December and February ($25 and $32, respectively), a fact consistent with the occurrence of a single change in the actual price from $25 to $32 during the second half of January. The last three price changes occurred in May, June and July of 1995; the published price increased from $32 to $36.5, then to $47 and finally to $53. This sequence is consistent with a change in the actual price from $32 to $41 after the first price collection in May and then from $41 to $53 after the first price collection in June. The filtered series corresponding to the last observation of each month is displayed at the bottom of Figure A.1. It contains only four nonzero price changes, and their magnitude is typically equal or greater than those in the unfiltered series. 22

In practice, the filter verifies that both sides of equations (3) and (4) are within 0.005 of each other to allow for possible price rounding.

32

A.4

Discussion of the Filter

Banco de México provided me with unpublished semi-monthly observations for the months of October and November 2006. These data allow me to compare directly filtered and unfiltered prices of nonfood items to a monthly series of actual end-of-period prices, which the filters aims to reproduce. They can also be used to assess whether individual prices change more than once per month. In order to perform these checks, I first extended the database to December 2006. I then created unfiltered and filtered series in the same way I do for the main sample.23 For nonfood items, published prices were identical to the end-of-period prices observed by price collectors in the vast majority of cases (92.3%, weighted by product categories). The filter correctly left all but a tiny fraction (0.02%) of these exact observations unchanged. For the remaining cases (7.7%), published prices differed from actual end-of-period prices. Of these observations, 54.6% were left unchanged, 44.6% were assigned values that correctly matched end-of-period prices, and 0.9% were replaced by values that still did not match actual end-of-period prices. In short, filtering brings nonfood average-price data closer to actual end-of-period prices while introducing very few mistakes. More importantly, the use of the filtered series offers a very good approximation of the frequency of price changes. In 98.4% of nonfood observations, the filtered series either indicated a price change when one was observed in the actual end-of-period series, or indicated no price change when none was observed. The majority of the diverging cases is related to within-month sales for which an end-of-period series, contrary to an average-price series, fails to signal the occurrence of a price change. The filtered series also offers a better description of nonzero price changes than the unfiltered series. The change in the unfiltered series matched the change in the end-of-period series of actual prices in about a third of all cases, a proportion that rises to 62.0% after filtering. About half of the remaining cases displayed two price changes within the month, in which case inference about the magnitude of individual price changes is problematic under any monthly series. This discussion illustrates the need to use data collected frequently, such as scanner data, in order to measure precisely the magnitude of individual price changes for items with a high frequency of price changes. 23

Semi-monthly data are not available for the sample period considered in the paper. Individual items cannot be linked before and after June 2002 due to a change in the nomenclature of item keys.

33

In the case of food prices, the unpublished semi-monthly data are an average of two weekly prices. A direct comparison with actual price observations is therefore impossible. Inference about the magnitude of individual price changes is likely to be less accurate than for nonfood observations because a much larger proportion of food items witness several price changes within the month. For example, Campbell and Eden (2007) report a probability of nearly 50% that a price will change in the week following a price change for a sample of food products sold in U.S. grocery stores. Filtering the data has almost no effect on the main patterns reported in the paper. The number of price changes filtered out in any given period is roughly proportional to the number price changes observed in the unfiltered series. Consequently, movements in the unfiltered and filtered average frequency of price changes are highly correlated. Similarly, filtering raises the average (absolute) magnitude of price increases and decreases rather uniformly.

B

Solution Method and Calibration of the Model

Solution method. All equilibrium objects are approximated using Chebyshev polynomials. The equilibrium solution is obtained in three steps. First, I guess the aggregate objects functions, o n ª © (0) (0) (0) (0) P , C , W (0) , N (0) , μ0(0) , and compute the associated Vnc , Vc , p˜(0) by value function itern o (0) (0) ation. Second, I generate a long Markov chain conditional Vnc , Vc , p˜(0) , randomly sampling in

every period a money growth shock and a distribution of technological innovations. I then compute © ª new approximations of the aggregate objects functions P (1) , C (1) , W (1) , N (1) , μ0(1) based on the

Markov chain and compare them to my initial functions. If they differ, I update my guess and repeat the procedure until numerical convergence.

Selection of moment(s). I use as an approximation of μt the average log-deviation of individual prices from their optimum, μ ˜t =

Z

log

Ã

p ¡ i,t−1 ¢ p∗ φi,t , μ, g

!

di.

˜ t−1 I find that approximating the law of motion of μ ˜ t and the aggregate objects as functions of μ and gt provides a high degree of accuracy. For example, the correlation between μ ˜ t and Ct in the Markov chain and their predicted value is 0.997 and 0.948, respectively, based on my calibration to the July 1999 to June 2002 period. Money growth process. I assumed that money growth can take two values, gl = g¯ − δ and 34

gh = g¯ + δ, with a constant probability 1 − a of switching between states every period. This simple Markov switching process has several appealing properties. First, key moments can be easily derived, in particular E [g] = g¯, V ar (g) = δ 2 and ρ (gt , gt−1 ) = 2a − 1. Each moment is controlled by a single parameter, thus facilitating the calibration of the model. Second, although money growth can take only two values, the distribution of inflation outcomes is somewhat richer because it also depends on the joint distribution of technology and prices. Finally, this simple specification keeps the problem computationally manageable. Calibration. Some parameters of the model are taken directly from the literature while others are chosen to match particular moments of the distribution of price changes. For the elasticity of substitution across items, I pick a value of 7, the same as Golosov and Lucas. The discount factor is set to (1.05)−1/12 . The persistence of technology shocks is set to 0.75, a value similar to that implied by Golosov and Lucas’ (2007) quarterly calibration (0.551/3 ≈ 0.82 per month) but higher than Midrigan’s (2006) (0.5 per month). The utility parameter ψ is chosen so that households work exactly 25% of the time absent menu costs. In the nonstochastic money growth version of the model, the variance of technological innovations, σ 2ε , the size of menu costs, ¯ξ, and money growth, g¯, are chosen to match the average frequency and absolute magnitude of nonzero price changes over the last three years of the sample, as well as average inflation. In the stochastic money growth version, σ 2ε , ¯ξ, δ and a are picked so that the model additionally matches the variance and persistence of inflation over the low- and high-inflation periods shown in Table III. All calibrated parameters and C programs are available as an on-line appendix.

35

Table I Main Sample Statistics Period

January 1994 - June 2002

Price quotes Total Average per month Trajectories Substitutions Product categories

3,209,947 31,470 44,272 10,457 227

CPI coverage (%)

54.1

Sample composition (%) Unprocessed food Processed food Energy Nonenergy industrial goods Services

26.4 21.7 0.4 26.4 25.1

36

Table II Linear Regression Results (Nonregulated Goods) fr All

Restricted

All

Constant

0.252 (0.005)

0.250 (0.008)

0.147 (0.004)

π

0.128 (0.040)

0.136 (0.126)

π2

0.983 (0.162)

π3

fr+ Restricted

fr-

dp Restricted

All

dp+ Restricted

All

dpRestricted

All

Restricted

All

0.140 (0.007)

0.106 (0.002)

0.110 (0.004)

0.006 (0.001)

0.003 (0.001)

0.082 (0.002)

0.079 (0.003)

0.106 (0.004)

0.098 (0.005)

0.265 (0.047)

0.354 (0.132)

-0.137 (0.020)

-0.218 (0.061)

0.242 (0.010)

0.301 (0.015)

0.075 (0.011)

0.127 (0.048)

-0.226 (0.047)

-0.081 (0.094)

1.293 (0.546)

0.888 (0.164)

0.943 (0.568)

0.095 (0.066)

0.350 (0.256)

-0.200 (0.034)

-0.419 (0.078)

0.011 (0.035)

-0.196 (0.185)

0.645 (0.116)

0.195 (0.361)

-0.739 (0.163)

-1.310 (0.589)

-0.740 (0.162)

-1.083 (0.616)

0.001 (0.059)

-0.227 (0.274)

0.065 (0.030)

0.280 (0.088)

-0.028 (0.033)

0.189 (0.195)

-0.462 (0.086)

-0.063 (0.398)

1995

0.012 (0.010)

0.007 (0.011)

0.013 (0.010)

0.005 (0.010)

0.000 (0.006)

0.002 (0.006)

0.003 (0.002)

0.003 (0.002)

-0.006 (0.004)

-0.007 (0.004)

-0.014 (0.006)

-0.019 (0.005)

1996

0.050 (0.009)

0.041 (0.009)

0.049 (0.008)

0.038 (0.008)

0.000 (0.003)

0.003 (0.004)

-0.001 (0.001)

-0.002 (0.001)

-0.010 (0.003)

-0.011 (0.003)

0.013 (0.006)

0.008 (0.005)

1997

0.050 (0.007)

0.047 (0.007)

0.044 (0.006)

0.041 (0.006)

0.005 (0.003)

0.007 (0.003)

-0.002 (0.001)

-0.003 (0.000)

-0.011 (0.003)

-0.012 (0.003)

0.004 (0.003)

0.001 (0.003)

1998

0.056 (0.010)

0.050 (0.009)

0.051 (0.008)

0.043 (0.008)

0.005 (0.003)

0.007 (0.004)

-0.002 (0.001)

-0.003 (0.001)

-0.008 (0.003)

-0.009 (0.003)

0.015 (0.005)

0.011 (0.005)

1999

0.047 (0.007)

0.046 (0.007)

0.039 (0.008)

0.035 (0.007)

0.009 (0.004)

0.011 (0.003)

-0.004 (0.001)

-0.003 (0.000)

-0.008 (0.002)

-0.008 (0.002)

0.010 (0.009)

0.005 (0.008)

2000

0.054 (0.008)

0.054 (0.008)

0.028 (0.005)

0.030 (0.005)

0.026 (0.005)

0.025 (0.005)

-0.004 (0.001)

-0.003 (0.000)

0.001 (0.003)

0.001 (0.003)

0.002 (0.003)

0.004 (0.003)

2001

0.076 (0.006)

0.078 (0.007)

0.033 (0.006)

0.036 (0.007)

0.043 (0.003)

0.041 (0.003)

-0.005 (0.001)

-0.004 (0.000)

0.011 (0.003)

0.011 (0.003)

0.006 (0.003)

0.010 (0.003)

2002

0.085 (0.006)

0.082 (0.005)

0.029 (0.005)

0.027 (0.004)

0.056 (0.003)

0.055 (0.004)

-0.004 (0.001)

-0.004 (0.000)

0.016 (0.002)

0.018 (0.002)

-0.001 (0.004)

0.003 (0.004)

R2

0.92

0.90

0.95

0.95

0.92

0.90

0.99

0.99

0.79

0.77

0.48

0.31

Year Dummies

Notes:

The numbers in parenthesis are t-statistics based on the Huber-White estimator of variance. The restricted sample excludes the value added tax change of April 1995 and all observations with negative inflation. All inflation statistics are computed using the sample of nonregulated goods.

37

Table III Inflation Variance Decompositions

Mean

Inflation Std. Dev. Auto Corr.

Intensive Margin Share of Inflation Variance (%)

Full Sample Period (January 1994 - June 2002) Full Sample 14.4 14.2 Nonregulated goods 14.3 16.1 Nonregulated services 14.5 10.0

0.81 0.81 0.69

41.4 48.3 10.6

January 1995 - June 1999 Full Sample Nonregulated goods Nonregulated services

21.7 22.6 19.1

15.3 17.2 11.0

0.82 0.84 0.66

34.7 41.8 9.9

July 1999 - June 2002 Full Sample Nonregulated goods Nonregulated services

5.0 3.5 9.2

4.4 5.6 4.1

0.06 0.08 0.39

89.2 93.9 18.0

38

Table IV Comparison of High-Inflation Studies Observations per montha

Sample periodb

Inflation (%, a.r.) c

Mean monthly frequency (%)

58 goods sold in 8 supermarkets in Buenos Aires and 10 services

563

Mar. to Dec. 2002

39.7

54.5

Lach and Tsiddon (1992)

26 food products (mostly meat and alcoholic beverages)

258

1978-1979

77.0

46.5

Israel

Lach and Tsiddon (1992)

26 food products (mostly meat and alcoholic beverages)

278

1981-1982

116.0

60.4

Israel

Eden (2001)

23 food products (mostly meat and alcoholic beverages)

254

1991-1992

13.6

34.6

Israel

Eden (2001), Baharad and Eden (2004)

up to 390 narrowly-defined products from the Israeli CPI

2,802

1991-1992

13.6

24

Mexico

Ahlin and Shintani (2006)

44 food products sold in Mexico City

573

1994-1995 (1994) (1995)

7.1 52.0

49.3 66.0

Mexico

Gagnon (2007)

227 product categories, representing 54.1 percent of Mexican consumption expenditures

31,500

1994-2002 (1995) (1996) (1997) (1999) (2001)

52.0 27.7 15.7 12.3 4.4

39.2 32.2 28.3 27.5 27.3

Poland

Konieczny and Skrzypacz (2005)

52 goods, including 37 grocery items, and 3 services

up to 2,400

1990-1996 (1990) (1992) (1994) (1996)

249.3 44.3 29.5 18.5

59 39 32 30

Country

Authors

Argentina

Burstein et al. (2005)

Israel

Sample product coverage

Notes: (a) Author's calculations for Poland based on Konieczny and Skrzypacz (2005). The figures for the Lach and Tsiddon samples are taken from Eden (2001). (b) Selected subsample periods are shown in parentheses. (c) Author's calculations based on the change in the official CPI for Argentina, Israel, and Mexico. The figures are not in logarithmic changes, as in the remainder of the paper.

39

45 Austria Belgium Finland France Luxemburg Portugal Spain United-States Mexico

40

Four-quarter change in official CPI (%)

35

30

25

20

15

10

5

0 1988

1989

1990

1991

1992

1993

1994

1995

1996 1997 1998 1999 Period covered by country studies

2000

2001

2002

2003

2004

2005

2006

Notes: The studies shown are representative of at least 50% of consumer expenditures. Data on inflation comes from the OECD Main Economic Indicators, Banco de México, and the BLS. The sample period for the United States corresponds to the study of Nakamura and Steinsson (2007). Full references to the Euro-area country studies can be found in Dhyne et al. (2005).

Figure I Inflation and Time Coverage of U.S., Euro-Area and Mexican CPI Studies

40

a) Pesos per USD (logs, end−of−month, 1994M1=0)

b) Inflation rate

140

100

120

80

100

60

%

%

80 40

60 20

40

0

20 0 94

95

96

97

98

99

00

01

02

03

−20 94

04

95

c) Interest rate on 91−day Cetes (annualized)

96

97

98

99

00

01

02

03

04

d) Money aggregates (logs, 1994M1=0)

80

200 M1 M4

150

60

%

%

100 40

50 20

0 94

0

95

96

97

98

99

00

01

02

03

−50 94

04

95

e) Real output (logs, 1994Q1=0)

96

97

98

99

00

01

02

03

04

f) Real consumption (logs, 1994Q1=0)

50

40

40

30

30

%

%

20 20

10 10 0

0 −10 94

95

96

97

98

99

00

01

02

03

−10 94

04

95

96

97

Source: Banco de México

Figure II Main macroeconomic indicators

41

98

99

00

01

02

03

04

a) Frequency of price changes and inflation frequency inflation

80

%

60 40 20 0 1994

1995

1996

1997

1998

1999

2000

2001

2002

b) Frequency of price increases and decreases 60 increases decreases

50

%

40 30 20 10 0 1994

1995

1996

1997

1998

1999

2000

2001

Note: All statistics in the above figure, including inflation, are computed using the sample of nonregulated goods.

Figure III Monthly Frequency of Price Changes (Nonregulated Goods)

42

2002

Frequency of price changes

Magnitude of price changes

70

15

10

50

Magnitude (%)

Frequency (%)

60

40 30 20

0

0

data all observations excluding π<0 and VAT change

10 0

20 40 Inflation (%)

60

5

−5

80

Frequency of price increases

0

20 40 Inflation (%)

60

80

Magnitude of price increases

70

20

15

50

Magnitude (%)

Frequency (%)

60

40 30 20

10

5

10 0

0

20 40 Inflation (%)

60

0

80

Frequency of price decreases

60

80

20

20

15

Magnitude (%)

Frequency (%)

20 40 Inflation (%)

Magnitude of price decreases

25

15 10

10

5

5 0

0

0

20 40 Inflation (%)

60

0

80

0

20 40 Inflation (%)

60

80

Notes: Each panel contains a scatter plot of the annualized monthly inflation rate, on the x−axis, and the associated monthly frequency or average magnitude statistics, on the y−axis. All statistics were computed using all nonregulated goods in the sample. The frequency and average magnitude were regressed on a linear, quadratic and cubic inflation terms, as well as a full set of year dummies. The dashed lines show the predicted relationships using all monthly observations in the regressions, conditional on the mean year dummy, and the thick lines show the same relationships when observations associated with negative monthly inflation outcomes and the April 1995 value−added tax change are excluded.

Figure IV Scatterplot of the Monthly Frequency and Average Magnitude of Price Changes and Inflation (Nonregulated Goods) 43

a) Magnitude of price changes vs inflation 15 average change monthly inflation

%

10 5 0 −5 94

95

96

97

98

99

00

01

02

b) Average magnitude of increases and decreases 25 increases decreases

20

%

15 10 5 0 −5 94

95

96

97

98

99

00

01

02

c) Predicted average change 15 actual fixed magnitude fixed share

%

10 5 0 −5 94

95

96

97

98

99

00

01

02

Note: All statistics in the above figure, including inflation, are computed using the sample of nonregulated goods. The monthly rate of inflation is not annualized.

Figure V Average Magnitude of Price Changes (Nonregulated Goods)

44

a) Frequency of price changes and inflation frequency inflation

80

%

60 40 20 0 1994

1995

1996

1997

1998

1999

2000

2001

2002

b) Frequency of price increases and decreases 60 increases decreases

50

%

40 30 20 10 0 1994

1995

1996

1997

1998

1999

2000

2001

Note: All statistics in the above figure, including inflation, are computed using the sample of nonregulated services.

Figure VI Monthly Frequency of Price Changes (Nonregulated Services)

45

2002

Frequency − all items

Magnitude − all items

50

15

40 10 %

%

30 20

5

10 0

0

10

20

30

40

0

50

0

10

annual inflation (%)

20

30

40

50

40

50

annual inflation (%)

Frequency − goods

Magnitude − goods

50

15

40 10 %

%

30 20

5

10 0

0

10

20

30

40

0

50

0

10

annual inflation (%)

20

30

annual inflation (%)

Frequency − services

Magnitude − services

50

15

40 10 %

%

30 20

5

10 0

0

10

20

30

40

0

50

0

annual inflation (%) changes (model) changes (data)

10

20

30

40

50

annual inflation (%) increases (model) increases (data)

decreases (model) decreases (data)

Notes: The lines in the panels display either the model’s predicted frequency (left panels) or average magnitude (right panels) of price changes, increases, and decreases, at various levels of annual inflation. The first, second, and third rows of panels show separate model calibrations using all items in the sample, all goods, and all services, respectively. For each calendar year in each subsample, the diamonds, squares, and triangles show the corresponding sample annual averages for price changes, increases, and decreases, respectively.

Figure VII Average Frequency and Magnitude of Price Changes, Increases and Decreases Predicted by the Model 46

Unfiltered series 60 Price Price change

50

$

40 30 20 10 0 Jan−94

Apr−94

Jul−94

Oct−94

Jan−95

Apr−95

Jul−95

Oct−95

Jan−96

Apr−95

Jul−95

Oct−95

Jan−96

Filtered series 60 50

$

40 30 20 10 0 Jan−94

Apr−94

Jul−94

Oct−94

Jan−95

Note: The upper and lower panels display, respectively, the unfiltered and filtered price trajectories of a single copy of the book "The Universal History of Litterature" sold in a Mexico City outlet.

Figure A.1 Illustration of a Price Trajectory Correction

47