PRICE SETTING DURING LOW AND HIGH INFLATION: EVIDENCE FROM MEXICO ETIENNE GAGNON

Transcription

1 PRICE SETTING DURING LOW AND HIGH INFLATION: EVIDENCE FROM MEXICO ETIENNE GAGNON 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 1% 15%), the frequency of price changes comoves weakly with inflation because movements in the frequency of price decreases and increases partly offset each other. In 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 1% 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 the average frequency and magnitude of price changes well over a range of inflation similar to that experienced by Mexico. I. 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 22. Over that nine-year period, the rate of increase in the official consumer price index (CPI) rose from 6.8% in 1994 to a peak of 41.8% in 1995, before falling to 4.9% in the last year of the sample. 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. I would like to thank the members of my dissertation committee, Lawrence J. Christiano, Alexander Monge-Naranjo, Sergio Rebelo, and especially my chairperson Martin Eichenbaum, for their continuous guidance and support. I am also 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, and Martha Carillo, Matthew Denes, and Guthrie Dundas provided 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. etienne.gagnon@frb.gov. 1. Unless otherwise indicated, all inflation figures are computed using the change in the logarithm of the price index and annualized. C 29 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. The Quarterly Journal of Economics, August

2 1222 QUARTERLY JOURNAL OF ECONOMICS ) Austria Belgium Finland France Luxembourg Portugal Spain United States Mexico Period covered by country studies FIGURE I Inflation and Time Coverage of U.S., Euro-Area, and Mexican CPI Studies The studies shown are representative of at least 5% of consumer expenditures. Data on inflation come from the OECD Main Economic Indicators, Banco de México, and the U.S. Bureau of Labor Statistics. The sample period for the United States corresponds to the study of Nakamura and Steinsson (28). Full references to the euro-area country studies can be found in Dhyne et al. (25). 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 the euro area relative to Mexico throughout the periods covered by the related studies. For high-inflation economies, the evidence is limited mainly to food products in Israel (Lach and Tsiddon 1992; Eden 21; Baharad and Eden 24) and Poland (Konieczny and Skrzypacz 25) and to supermarket products in Argentina (Burstein, Eichenbaum, and Rebelo 25). 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 For studies on the United States, see Bils and Klenow (24), Klenow and Kryvtsov (28), and Nakamura and Steinsson (28). Dhyne et al. (25) review the main findings for the euro area.

3 PRICE SETTING DURING LOW AND HIGH INFLATION 1223 toahighof61.9% 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 price-setting behaviors across low- and high-inflation periods. When inflation is low (below 1% 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% for the subsample of goods, figures that are similar to that of Klenow and Kryvtsov (28) for the United States (about 5%). By contrast, when inflation is high (above 1% 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 % to 1% 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 1% 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

4 1224 QUARTERLY JOURNAL OF ECONOMICS whether menu-cost models are consistent with my findings, I calibrate a discrete-time version of the Golosov and Lucas (27) 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 III, I describe the assemblage of my data set and discuss features of the data that are important for interpreting my results. Section IV defines the statistics computed in this paper. The main empirical findings are presented in Section V and are then compared to other studies of high-inflation environments in Section VI. In Section VII, I calibrate a discretetime 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. II. 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 1%, a major achievement in light of the three-digit rates of the late 198s, 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 Moreover, the North American Free Trade Agreement had taken effect on January 1, Foreign capital entered abundantly with a net inflow over 8% of GDP in However, growth in real GDP per capita remained modest, averaging 2.5% from 1991 to Many observers saw 3. See Edwards (1998) for a review of observers opinions in 1994.

5 PRICE SETTING DURING LOW AND HIGH INFLATION (b) Inflation rate % % % % (d) Money aggregates (logs, 1994M1=) M1 M (e) Real output (logs, 1994Q1=) 3 (f) Real consumption (logs, 1994Q1=) 3 2 % 2 1 % FIGURE II Main Macroeconomic Indicators Source: Banco de México. 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 4% 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 capital flight. 4. Mexico pegged its exchange rate to the dollar in May In February 1994, the country switched to pre-announced crawling bands around the U.S. dollar.

6 1226 QUARTERLY JOURNAL OF ECONOMICS The devaluation left 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.% in April Real output per capita contracted 9.5% in 1995, whereas 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 level and until 1999 for inflation to settle below 1%. 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 1% to 15% on April 1, 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 1%. III. MEXICAN MICRO DATA ON CONSUMER PRICES III.A. 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 11 in Mexico City). A limited number of quotes are citywide indices, or the average prices of small samples 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 22. 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, 5. See OECD (2) for a description of the taxation system. 6. Items from the same outlet are attributed store keys independently to ensure confidentiality.

7 PRICE SETTING DURING LOW AND HIGH INFLATION 1227 so they were typed in from original hard copies of the Diario using double-entry keying, a process ensuring a characterwise accuracy in excess of %. 7 About 43, price quotes were added to the database in this way. Precise item descriptions were published in March The Diario also includes lists of items that are periodically added to or 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.2% of households expenditures. This ensures a coverage of 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). III.B. Sample Coverage In January 1994, the CPI contained 3,692 price quotes spread over 32 product categories. By June 22, the last month in my sample, it had expanded to nearly 5, 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 22, Banco de México updated the basket again to reflect the structure of Mexican households consumption in 2. I cannot link items before and after the 22 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 22 using the expenditure weights implemented in March 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 7. I thank Chris Ahlin for lending me original copies of the Diario. 8. These weights are derived from the 1989 ENIGH survey. They were updated using relative prices to reflect consumer expenditures in 1993.

8 1228 QUARTERLY JOURNAL OF ECONOMICS TABLE I MAIN SAMPLE STATISTICS Period January 1994 June 22 Price quotes Total 3,29,947 Average per month 31,47 Trajectories 44,272 Substitutions 1,457 Product categories 227 CPI coverage (%) 54.1 Sample composition (%) Unprocessed food 26.4 Processed food 21.7 Energy.4 Nonenergy industrial goods 26.4 Services 25.1 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, 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 weights in the CPI are, respectively, 14.%, 6.%, and 3.5%. Food items represent just under half of the expenditures in the final sample, a proportion higher than in most U.S. and euro-area studies. Summary statistics are presented in Table I. III.C. Other Aspects of the Data I now address features of the data that are important to consider in 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 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.

9 PRICE SETTING DURING LOW AND HIGH INFLATION 1229 consistent with an actual price of $2 throughout the month. It also is consistent with an actual price of $1.5 in the first half of the month and $2.5 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 $1.5 to $2.5 in the middle of the month results in an average price of $2, which is $.5 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 both are consistent with the published average prices and minimize the number of price changes. Appendix I provides an extensive discussion of how averaging observations affects inferences about the timing and magnitude of price changes, and of how the filter was implemented. I was provided with unpublished semimonthly data by Banco de México, which allows me to directly assess the performance of the filter. Overall, the filtered series are much closer to the end-ofperiod 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 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.1% of all published price quotes in 1994, a proportion that rose to 1.2% in 21. A more systematic treatment of substitutions was implemented in 21. 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.

10 123 QUARTERLY JOURNAL OF ECONOMICS Prices are inclusive of sales as long as they are conditional on the purchase of a single item. For example, in a three-for-two 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 three-for-two 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 going on. Most price quotes for the product categories of textiles, clothing, shoes, and related accessories are averages of small samples 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 databases. In this paper, substitutions were instead excluded from the computation of price changes because their treatment varied over the sample period. The main patterns found in this paper are not affected by this choice. IV. 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 p it 1 I it = if p it = p it 1,

11 PRICE SETTING DURING LOW AND HIGH INFLATION 1231 where p it is the price of item i (in logs) during month t. Inflation is defined as π t = i ϒ t ω it p it, where p it = p it p it 1, ω it is the sample weight of item i,andϒ t is the set of all items in the sample for which I it 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 can also be expressed as ) ( π t = ω it I it ( i ϒt }{{} fr t i ϒ t ω it p it i ϒ t ω it I it ) } {{ } dp t The term fr t, 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 dp t is the average magnitude of those price changes. In the popular Taylor (198) and Calvo (1983) models with uniform staggering of price changes, dp t 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: ( ) ( π t = ω it I + i ϒ t ω it I + it p ) it i ϒ it }{{ t } i ϒ t ω it I + it }{{} fr + t ( ) ( + ω it I i ϒ it }{{ t } fr t dp + t i ϒ t ω it I it p it i ϒ t ω it I it. ) } {{ } dpt This decomposition is informative about the relationship between inflation and the distribution of price changes. The computation of inflation statistics for 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 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 strongly correlated with the change in the official CPI:.

12 1232 QUARTERLY JOURNAL OF ECONOMICS The coefficient of correlation is.96 over the full sample period and.85 over the last three years of the sample. V. 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. 1 I place a special emphasis on the results for goods, given their predominance in my sample and their greater representativeness. V.A. 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. 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.% (7.2% in monthly terms). This rate is much higher 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 the month. This number is more than twice the average frequency of 26.8% in 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 rose to 46.% 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. 1. For the products in my sample, the COICOP goods/services classification is almost identical to the Bank of Mexico s tradables/nontradables classification. The results reported in the paper for goods and services thus have an alternative interpretation in terms of tradables and nontradables.

13 PRICE SETTING DURING LOW AND HIGH INFLATION 1233 (a) Frequency of price changes and inflation 8 6 Frequency Inflation % % (b) Frequency of price increases and decreases Increases Decreases FIGURE III Monthly Frequency of Price Changes (Nonregulated Goods) All statistics in the figure, including inflation, are computed using the sample of nonregulated goods. Positive comovement between fr t and π t is clearly visible in Figure III. The correlation coefficient between the two series is.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 fr t into fr + t and fr t. 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 11. All correlation statistics presented in this section are computed using linearly detrended series.

14 1234 QUARTERLY JOURNAL OF ECONOMICS fr + t, fr t,andπ t provides further evidence of these offsetting movements. In the last three years of the sample, the correlation is.59 between fr + t and π t,and.74 between fr t and π t. The net result is a relative absence of correlation between fr t 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 21, July 21, and February 22, 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 solid lines exclude April 1995, which was marked by a 5-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 they likely capture the overall relationship between inflation and its components better. 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.35 (.13)-percentage-point rise in the frequency of price increases and an opposite.22 (.6)-percentage-point decline in the frequency

15 PRICE SETTING DURING LOW AND HIGH INFLATION (a) Frequency of price changes 15 (b) Magnitude of price changes 6 Frequency (%) Data All observations Excluding π< and VAT change Inflation (%) Magnitude (%) Inflation (%) 7 (c) Frequency of price increases 2 (d) Magnitude of price increases 6 Frequency (%) Magnitude (%) Inflation (%) Inflation (%) 25 (f) Frequency of price decreases 2 (f) Magnitude of price decreases 2 15 Frequency (%) 15 1 Magnitude (%) Inflation (%) Inflation (%) FIGURE IV Scatterplot of the Monthly Frequency and Average Magnitude of Price Changes and Inflation (Nonregulated Goods) 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 linear, quadratic, and cubic inflation terms, as well as a full set of year dummies. The dashed lines show the relationships predicted using all monthly observations in the regressions, conditional on the mean year dummy, and the solid lines show the same relationships when observations associated with negative monthly inflation outcomes and the April 1995 value-added tax change are excluded.

16 1236 QUARTERLY JOURNAL OF ECONOMICS TABLE II LINEAR REGRESSION RESULTS (NONREGULATED GOODS) fr fr+ fr dp dp+ dp All Restricted All Restricted All Restricted All Restricted All Restricted All Restricted Constant (.5) (.8) (.4) (.7) (.2) (.4) (.1) (.1) (.2) (.3) (.4) (.5) π (.4) (.126) (.47) (.132) (.2) (.61) (.1) (.15) (.11) (.48) (.47) (.94) π (.162) (.546) (.164) (.568) (.66) (.256) (.34) (.78) (.35) (.185) (.116) (.361) π (.163) (.589) (.162) (.616) (.59) (.274) (.3) (.88) (.33) (.195) (.86) (.398) Year dummies (.1) (.11) (.1) (.1) (.6) (.6) (.2) (.2) (.4) (.4) (.6) (.5) (.9) (.9) (.8) (.8) (.3) (.4) (.1) (.1) (.3) (.3) (.6) (.5) (.7) (.7) (.6) (.6) (.3) (.3) (.1) (.) (.3) (.3) (.3) (.3) (.1) (.9) (.8) (.8) (.3) (.4) (.1) (.1) (.3) (.3) (.5) (.5) (.7) (.7) (.8) (.7) (.4) (.3) (.1) (.) (.2) (.2) (.9) (.8) (.8) (.8) (.5) (.5) (.5) (.5) (.1) (.) (.3) (.3) (.3) (.3) (.6) (.7) (.6) (.7) (.3) (.3) (.1) (.) (.3) (.3) (.3) (.3) (.6) (.5) (.5) (.4) (.3) (.4) (.1) (.) (.2) (.2) (.4) (.4) R Notes: The numbers in parenthesis are standard errors based on the Huber White estimator of variance. The restricted sample (labeled restricted ) excludes monthly observations associated with negative inflation outcomes and the value-added tax change of April All inflation statistics displayed are computed using the sample of nonregulated goods.

17 PRICE SETTING DURING LOW AND HIGH INFLATION 1237 of price decreases. 12 These opposite movements have dampening effects on the frequency of price changes, whose corresponding slope is.14 (.13). As inflation increases from a low level, the frequency of price increases becomes more responsive to changes in inflation, whereas 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 1% change in inflation is associated with a.56 (.4)-percentage-point rise in the frequency of price increases and a.13 (.1)-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 (28). The year dummies appear to capture some key changes in methodology and the economic environment over time. In particular, they are lowest at the beginning of the sample, when maintaining a fixed basket was seen as important, and highest for 21 and 22, which had systematic substitutions of unavailable items to keep the basket up to date. No major change in methodology occurs over the 1996 to 2 period and I cannot reject the hypothesis that the year dummies for 1996 to 2 are jointly identical at the 1% confidence level. Imposing such equalities 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. 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 (26), which directly accounts for the zero one bounds on the frequency.

18 1238 QUARTERLY JOURNAL OF ECONOMICS 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, dp t and π t follow similar patterns over the sample period. 13 Both series registered sharp increases during the Mexican peso crisis, followed by a protracted decline and ultimately a stabilization. The correlation between the two series is.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, dp t 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 sizes of price increases and decreases are much less sensitive to the level of inflation than dp t. Except for a short period around the peak of inflation, the two series show relatively small oscillations around their respective sample means of 9.% 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 middle right 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, the possibility that this positive relationship partly reflects a rise in 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 = fr t dp t. When inflation is low, fr t moves little with inflation, implying that dp t moves strongly and almost linearly with π t. By contrast, when inflation is high, fr t comoves strongly and positively with π t. This second source of variation in 13. The inflation series displayed is the nonannualized monthly inflation rate to facilitate visual comparisons. 14. The few large spikes in dp t correspond to large variations in the price of some fresh produce.

19 PRICE SETTING DURING LOW AND HIGH INFLATION (a) Magnitude of price changes vs. inflation Average change Monthly inflation % (b) Average magnitude of increases and decreases Increases Decreases % (c) Predicted average change Actual Fixed magnitude Fixed share % FIGURE V Average Magnitude of Price Changes (Nonregulated Goods) All statistics in the figure, including inflation, are computed using the sample of nonregulated goods. The monthly rate of inflation is not annualized.

20 124 QUARTERLY JOURNAL OF ECONOMICS π t introduces some curvature in the relationship between π t and dp t. To better understand what drives dp t, it is convenient to express it as dp t = s t dp + t (1 s t) dp t, where s t = fr + t /(fr+ t + fr t ) is the share of price increases among price changes. As this equation makes clear, fluctuations in dp t can originate from two sources: changes in the relative occurrence of price increases and decreases (the composition effect) and variations in their respective sizes. 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 s t at its sample mean to show how movements in dp t + and dp t alone affect dp t. In the second series, dp t + and dp t are held at their respective sample means so that the relative occurrence of price increases and decreases is the only source of variation in dp t. The exercise indicates that the composition effect drives almost entirely dp t when inflation is below 1% 15%. Had s t been constant, dp t 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 By contrast, the series allowing only for the composition effect predicts the level of dp t remarkably well over that period. When inflation nears its peak, the composition effect alone is insufficient to match the level of dp t closely, but it is a better predictor than merely allowing for changes in the average absolute magnitude. V.B. 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 one-third of 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 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

21 PRICE SETTING DURING LOW AND HIGH INFLATION 1241 % (a) Frequency of price changes and inflation Frequency Inflation % (b) Frequency of price increases and decreases Increases Decreases FIGURE VI Monthly Frequency of Price Changes (Nonregulated Services) All statistics in the figure, including inflation, are computed using the sample of nonregulated services. services, compared to about half for the sample used by Bils and Klenow (24) for the United States. 15 The upper panel of Figure VI displays the frequency of price changes and 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), whereas 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 levels 15. I estimated this proportion based on the 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).

22 1242 QUARTERLY JOURNAL OF ECONOMICS 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 are those 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, service 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 Mexican peso crisis, the average rates 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 precrisis level before early 22. 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 Mexican peso crisis had yet to be fully passed through to services prices. V.C. Inflation Variance Decomposition To gauge the relative importance of movements in the frequency and magnitude of price changes for the variance of inflation, Klenow and Kryvtsov (28) proposed the following decomposition: var(π t ) = fr 2 var(dp t ) + dp 2 var(fr }{{} t ) + 2fr dp cov(dp t, fr t ) + Ot 2, }{{} Intensive margin Extensive margin

23 PRICE SETTING DURING LOW AND HIGH INFLATION 1243 TABLE III INFLATION VARIANCE DECOMPOSITIONS Inflation Intensive margin share of inflation Mean (%) Std. dev. (%) Auto corr. variance (%) Full sample period (January 1994 June 22) Full sample Nonregulated goods Nonregulated services January 1995 June 1999 Full sample Nonregulated goods Nonregulated services July 1999 June 22 Full sample Nonregulated goods Nonregulated services where Ot 2 are high-order terms that are functions of fr t. 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 24, Klenow and Kryvtsov (28) find that the intensive margin accounts for about 95% of the inflation variance, whereas the extensive margin terms, collectively or individually, are small. As shown in Table III, the Mexican data also point to a minor role for movements in the frequency of price changes when restricted to the low-inflation period after mid 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 period January 1995 to June This finding clearly indicates that fluctuations in fr t 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 + + πt, where π t + = fr + t dp t + (πt = fr t dpt ) is the inflation contribution of items whose price rose (fell) over the month. Following Klenow and Kryvtsov (28), the variance of inflation can then be expressed as var(π t ) = var(π t + ) + cov(π t +,π t }{{} ) + var(πt ) + cov(π t +,π t ). }{{} pos neg

24 1244 QUARTERLY JOURNAL OF ECONOMICS Over the full sample period, I find that pos/var(π t ) =.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 ) =.32, a value noticeably lower than that reported by Klenow and Kryvtsov (28) for the United States (.65). The difference seems attributable to the exceptionally large downward movements in the price of fresh produce at the beginning of 21 and VI. 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 (27) 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 highinflation 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: and For the former period, they found that 46.5% of prices changed every month, whereas inflation averaged 77%. 18 The frequency of price changes rose to 6.4% in as inflation reached an impressive 116%. 19 Their results clearly indicate that 16. To verify this hypothesis, I computed pos/var(π t ) based on a sample of Mexican CPI prices starting in July 22 and ending in March 27. The average inflation rate over that period (3.9%) is similar to the July 1999 to June 22 period (5.%), but fresh produce prices display few exceptionally large movements. The corresponding value of pos/var(π t ) for this sample is.6, a figure similar to that of Klenow and Kryvtsov (28). 17. See Dhyne et al. (26) 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 logarithmic differences. 19. The figures for the samples considered by Lach and Tsiddon (1992) are taken from Eden (21).