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Board of Governors of the Federal Reserve System
International Finance Discussion Papers
Number 896, May 2007--- Screen Reader Version*

Price Setting during Low and High Inflation:
Evidence from Mexico

Etienne Gagnon¹

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at http://www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at http://www.ssrn.com/.

Abstract:

This paper provides new insight into the relationship between inflation and consumer price setting by examining a large data set of Mexican consumer prices covering episodes of both low and high inflation, as well as the transition between the two. Overall, the economy shares several characteristics with time-dependent models when the annual inflation rate is low (below 10-15%), while displaying strong state dependence when inflation is high (above 10-15%). At low inflation levels, the aggregate frequency of price changes responds little to movements in inflation because movements in the frequency of price decreases partly offset movements in the frequency of price increases. When the annual inflation rate rises beyond 10-15 percent, however, there are no longer enough price decreases to counterbalance the rising occurrence of price increases, making the frequency of price changes more responsive to inflation. It is shown that a simple menu-cost model with idiosyncratic technology shocks predicts remarkably well the level of the average frequency and magnitude of price changes over a wide range of inflation.

Keywords: Price setting, consumer prices, frequency of price changes, time-dependent pricing, state-dependent pricing.

JEL classification: E31, D40, C23.

1.  Introduction

This paper presents new evidence on the setting of consumer prices during low and high inflation that sheds light on the empirical plausibility of competing models of price rigidities. It uses a new store-level data set containing more than six million individual price quotes that is representative of more than two-thirds of Mexican consumers' expenditures. The data starts in January 1994 and ends in December 2004. Over that 11-year period, CPI inflation rose from 6.8% in 1994 to a high of 41.8% in 1995 before falling to a low of 3.9% in 2001. Given these considerable fluctuations, this data set can potentially be used to discriminate among competing models of nominal price rigidities, as these models' predictions diverge most in the presence of large shocks.

Many macroeconomic models assume that price rigidities exist. There is, however, no consensus on how to model these rigidities. In time-dependent models, the set of firms optimizing their prices is fixed exogenously within the period.² In state-dependent models, on the other hand, the timing of price changes is an endogenous decision. In these models, price stickiness results from frictions like menu costs, imperfect or costly information and shifts in demand that accompany price changes.³ Recently, several authors have argued that variants of time-dependent models can deliver empirically plausible predictions despite their simplicity.⁴ Even advocates of time-dependent models would agree, however, that the performance of these models should decline as inflation becomes high or volatile. The inflation level at which time-dependent models break down remains an open question, as does the more general question of what price-setting models are empirically plausible at both low and high inflation levels.

My data set captures considerably more variation in inflation than do other studies of consumer prices with comparable product coverage.⁵ As Figure 1 indicates, inflation is low and stable in the United States and Euro area relative to Mexico over the periods covered by these studies. In the case of high-inflation economies, the evidence is limited mainly to food products in Israel (Lach and Tsiddon (1992); Baharad and Eden (2004)) and Poland (Konieczny and Skrzypacz (2005)) and supermarket products in Argentina (Burstein, Eichenbaum, and Rebelo (2005)). This paper differs from these studies because my data set is representative of most goods and services in the CPI with the exception of housing rents, and I provide evidence for both high and low levels of inflation.

Figure 1. Inflation and time coverage of U.S., Euro-area and Mexican CPI studies

I find sharp differences in the price-setting behaviors of low- and high-inflation economies: Whereas low-inflation economies exhibit several features of time-dependent pricing models, high-inflation economies show strong state dependence. More specifically, 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 nonregulated goods, in which case I find no correlation. On the other hand, the average magnitude of price changes in such low-inflation environments displays a tight and linear relationship with inflation. As a result, movements in the frequency of price changes account for little of the inflation variance: at most 17% for all nonregulated products and 5% for nonregulated goods, figures that fall in line with Klenow and Kryvtsov (2005) for the United States (5%).

In contrast, when inflation is high (above 10-15%), both the frequency and average magnitude of price changes are strongly correlated with inflation. In this case, a 1-percent increase in the annual inflation rate is associated with a rise of about 0.4 percentage-point in the monthly frequency of price changes for nonregulated consumer products. Movements in the frequency of price changes therefore comprise an important component of inflation variance. This central role of the frequency of price changes in inflation dynamics is best revealed by a rise of the value added tax from 10 to 15% in April 1995: The adjustment of prices occurs almost entirely through an increased frequency of price changes -- not an increased magnitude -- and is completed within a month of the tax change.

Price decreases are key to the dramatically different behaviors of low- and high-inflation economies. When I decompose the frequency of price changes into the sum of the frequencies of price increases and decreases, I find that the frequency of price decreases diminishes rapidly as inflation rises from 0 to 10-15%. This decline partly offsets a simultaneous rise in the frequency of price increases, thereby dampening movements in the overall frequency of price changes. Moreover, the decline in the occurrence of price decreases relative to price increases leads to a rise in the average magnitude of price changes. This change in the composition of price changes largely explains the strong correlation between inflation and the average magnitude of price changes in my data when inflation is low. Once inflation moves beyond 10-15%, however, there are no longer enough price decreases to offset price increases, so the frequency of price changes becomes highly correlated with inflation.

The important role of price decreases for inflation dynamics in Mexico is likely to be found in the United States and euro area. At similar levels of inflation, price decreases account for 42% of price changes in Mexico, a level comparable to the euro area (42%, Dhyne et al. (2005)) and the United States (45%, Klenow and Kryvtsov (2005)). For most groups of products, however, price changes are more frequent in the United States. I conjecture that the greater number of price decreases in the United States relative to Mexico likely will have similar dampening effects on the frequency of price changes at low levels of inflation.

The above empirical findings shed light on what types of pricing models deliver realistic predictions at various levels of inflation. Overall, my 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. Above a 10-15% inflation rate, the predictions of time-dependent models are clearly inconsistent with the strong state-dependence found in my data with respect to inflation. When inflation falls below 10-15%, the muted response of the frequency of price changes in the nonregulated good sector is more consistent, at least on the surface, with time-dependent models like Calvo's. These facts suggest that macroeconomists may need to resort to different price-setting models when focusing on either low or high inflation economies. They also present the challenge of finding a model offering empirically plausible predictions at all levels of inflation.

I calibrate a discrete-time version of the Golosov and Lucas (2003) menu-cost model. The model embeds idiosyncratic technology shocks giving rise to a distribution of both positive and negative nominal price changes. I show that the model performs remarkably well in terms of predicting the average frequency and magnitude of price changes over a wide range of inflation. In particular, the model generates a slow increase in the frequency of price changes as inflation takes off from a low level. 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 Section 2, I provide a brief overview of the Mexican macroeconomic context over the sample period. In Section 3, I describe the assemblage of my data set and discuss features of the data that are important for interpreting my results. Then, Section 4 defines the statistics computed in this paper. In Section 5, I explain how the average frequency and magnitude of individual price changes differ across low- and high-inflation episodes, and I investigate the inflation pass-through resulting from an April 1995 hike in the value added tax. Section 6 offers a comparison of consumer price stickiness between the Mexican economy and that of the United States and Euro area. In Section 7, I calibrate a discrete-time version of the Golosov-Lucas model and investigate its ability to match the main empirical features of consumer price setting when subject to levels of inflation similar to the ones experienced by Mexico over my sample period. The last section provides concluding remarks.

2.  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.⁶ Inflation had been stabilized successfully below 10 percent, a major achievement in light of the three-digit rates of the late 1980s.⁷ The real interest rate 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. This treaty was part of a broad set of Mexican government initiatives to deregulate the country's economy and open it to foreign trade and capital. 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.

Figure 2. Main macroeconomic indicators

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.⁸ As depicted in Figure 2, interest rates were pushed upward substantially as Banxico 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 6.5% in November 1994, to 44.3% in January 1995 before peaking at 92.0% in April 1995. Real output per capita contracted by 9.5% in 1995, while private consumption per capita fell by 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 10%.

The decline in aggregate income, coupled with a rise in fiscal evasion, brought a sharp decline in government revenues.⁹ To prevent further revenue erosion, the government raised the general rate of the value added tax rate (VAT) from 10 to 15 percent 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%.

3.  Mexican Micro Data on Consumer Prices

3.1  Description of Sources

The data comprise price quotes collected by Banco de México (Banxico) 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. This publication releases each quote with a key linking the item to a specific outlet, city and good category; these keys allow me to track individual prices over time.¹⁰ In this paper, I refer to an item's complete price history as its price trajectory. A price trajectory comprises one or several successive price spells, episodes when the price remained constant.

The data set contains 6.5 million price quotes from January 1994 to December 2004. Banxico makes individual prices available 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 from original hard paper copies of the Diario using double-entry keying, a process ensuring a character-wise accuracy in excess of 99.998%.¹¹ About 430,000 price quotes were added to the database in this way.

Precise item descriptions were published in March 1995 and August 2002. The Diario also includes lists of 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 categories are representative of all ENIGH categories accounting for at least 0.02 percent of households' expenditures. This ensures a coverage well above 95% of Mexican households' expenditures.

3.2  Sample coverage

In January 1994, the CPI contained 30,692 price quotes spread over 302 categories. By December 2004, it had expanded to more than 60,000 price quotes distributed over 315 categories. Two major revisions of the basket occurred over that period. The first occurred in March 1995, when the number of cities covered in the CPI grew from 35 to 46. At the same time, 29 new good categories were introduced into the basket, and 18 were abandoned. This revision had been planned long before the peso's devaluation. Secondly, in July 2002, Banxico updated the basket again to reflect the structure of Mexican households' consumption in 2000. In the process, 60 product categories merged into 27, another 36 were introduced into the basket and one was dropped. 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 core results for a sample covering January 1994 - June 2002 using the expenditure weights implemented in March 1995.¹² Unless otherwise indicated, the sample is restricted to the 266 product categories comprising nonregulated individual prices that were unaffected by the 1995 basket revision.¹³ This restricted sample covers 63.4% of CPI expenditures. The largest three excluded product categories are homeowners' imputed rents, gasoline and rents, whose weight in the CPI are respectively 11.6%, 3.2% and 2.4%. This more homogenous sample contains 3.8 million price quotes from over 51,000 price trajectories. Summary statistics of the data used in this paper are provided in Table 1.

Table 1. Summary statistics

Period	January 1994 - June 2002	July 2002 - December 2004
Price Quotes: Total	3,804,885	1,580,618
Price Quotes: Average per month	37,303	52,687
Trajectories	51,299	99,435
Substitutions	11,291	38,981
Unweighted frequency (%)a: Price changes	29.8	27.8
Unweighted frequency (%)a: Price increases	20.9	16.0
Unweighted frequency (%)a: Price decreases	8.9	11.7
Product categories: Dataset	266	289
Product categories: Full CPIbb	313	315
CPI weight (%)	63.4	65.9

Notes: (a) The unweighted frequencies are computed by dividing the number of positive or negative price changes by the total number of price quotes for which a price change can be computed. (b) The total number of product categories was expanded from 302 to 313 in March 1995.

3.3  Other Aspects of the Data

I now address features of the data that are important to consider when interpreting of the results. The most significant issue is price averaging. Banxico collects prices twice monthly for all items but food; food price collection occurs four times per month.¹⁴ 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 positive prices with $2 as their average. Moreover, changes to an average price series are typically more frequent and of smaller magnitude than changes to an actual price series. 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. Thus, if the actual price remains constant over the next month, another change to the average price series will be recorded.

To make my results as comparable as possible to other studies, which do not use averaged price quotes, I have constructed alternative price trajectories that filter the effect of averaging observations whenever possible. These new series correspond to the end-of-month series of actual prices, which are both consistent with the published averages and minimizes the number of price changes. In addition to being closer to the unobserved series of actual prices, the filtered series provide a lower bound on how frequently prices change. Appendix A discusses details of the filtering procedure.

Another issue in the data is that price collectors do not always directly observe prices. Indeed, 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 0.1% of all published price quotes in 1994, a proportion that rose to 1.2% in 2001 and 3.0% in 2004; this trend likely will create a downward bias in the estimated frequency of price changes at the beginning of the sample.¹⁵

Furthermore, 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 such cases, the unobserved effective price is lower than the observed reported price. There is no variable in the data set signaling that an item is on sale or that a promotion is ongoing. To assess the prevalence of sales in the sample, I define sales as a price spell that lasts three months or less, begins with a price decline and is ended by a price increase of the same magnitude. When goods are weighted by expenditure shares, sales amount to 4% of price changes over the sample period and 9% over the year prior before the 2002 basket revision. These figures are lower than the 20% reported by Klenow and Kryvtsov for the United States (cited by Bils and Klenow (2004)). This difference likely reflects a greater prevalence of sales and promotions in the United States than Mexico as well as methodological differences.¹⁶ All the results in my paper are inclusive of unconditional sales.

In interpreting the data, one must also consider that 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. Using the descriptions published in the Diario, I identified the exact number of items and brands within each store sample. A store sample typically contains two to four items (e.g., two cotton-based pants for men, brands Lee and Cimarron), with a mode of three for the number of both items and brands. Price changes generally are more frequent and of smaller magnitude for a sample than for its individual components, but the severity of this divergence depends on the price synchronization within the sample. For example, if an outlet runs a 30 sale on all jeans, then the average price of a sample of three pairs of jeans also decreases by 30%. I discard all store samples whenever a product category contains a large proportion of individual observations. For 34 categories encompassing all clothing and shoes categories except school uniforms, I retain only samples comprising three items and discard all other observations. I then treat those observations like other individual observations. Appendix B explores the extent of the bias this procedure introduces.

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 substitutions not previously planned by the CPI agency involve a price change. In this paper, I instead exclude all substitutions from the computation of price changes because their treatment varies over the sample period. The main conclusions are not affected by this decision.

3.4  Example of Individual Price Trajectory

The next figure shows an actual price trajectory and illustrates how the effect of averaging several price observations over the month is filtered out. It displays two years of monthly average prices for a copy of the book "The Universal History of Literature" sold in a Mexico City outlet. This series was computed by Banxico by averaging the two prices its CPI agent collected each month. From January 1994 to December 1995, there were six changes to the 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, I conclude that the two prices collected in August also equaled $25. 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). This figure is 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 series is consistent with a change in the actual price from $32 to $41 after the first price collection in May and then $41 to $53 after the first price collection in June. The filtered series, which contains only the last observation of each month, is displayed at the bottom of Figure 3. It contains only four price changes, and their magnitude is greater on average than those in the published average price series.

Figure 3. Illustration of a price trajectory correction

Note: The dashed line represents the actual monthly average price published in the Diario of a single copy of the book "The Universal History of Literature" sold in a Mexico City outlet. The solid represents the filtered point-in-time series.

Data for Figure 3

Month	Price: Unfiltered	Price: Filtered
Jan-94	23.00	23.00
Feb-94	23.00	23.00
Mar-94	23.00	23.00
Apr-94	23.00	23.00
May-94	23.00	23.00
Jun-94	23.00	23.00
Jul-94	23.00	23.00
Aug-94	25.00	25.00
Sep-94	25.00	25.00
Oct-94	25.00	25.00
Nov-94	25.00	25.00
Dec-94	25.00	25.00
Jan-95	28.50	32.00
Feb-95	32.00	32.00
Mar-95	32.00	32.00
Apr-95	36.50	41.00
May-95	47.00	53.00
Jun-95	53.00	53.00
Jul-95	53.00	53.00
Aug-95	53.00	53.00
Sep-95	53.00	53.00
Oct-95	53.00	53.00
Nov-95	53.00	53.00
Dec-95	53.00	53.00

4.  Inflation Accounting Principles

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

$$I_{it}=\left\{ \begin{array}[c]{cc} 1 & \text{if }p_{it}\neq p_{it-1}\ 0 & \text{if }p_{it}=p_{it-1} \end{array}\right.$$

where $p_{it}$ is the price of item $i$ (in logs) during month $t$. Inflation is defined as

$$\pi_{t}\triangleq {\displaystyle\sum\nolimits_{i\in\Upsilon_{t}}} \omega_{it}\pi_{it}$$

where $\pi_{it}=p_{it}-p_{it-1}$, $\omega_{it}$ is the weight of item $i$, and $\Upsilon_{t}$ is the set of all items for which $I_{it}$ is defined. For $\omega_{it}$, I use the weight of the CPI category to which item $i$ belongs, divided by the number of items in that category for which I can compute a price change at $t$. Inflation also can be expressed as

$$\pi_{t}\triangleq\underset{fr_{t}}{\underbrace{\left( {\displaystyle\sum\nolimits_{i\in\Upsilon_{t}}} \omega_{it}I_{it}\right) }}\underset{dp_{t}}{\underbrace{\left( \frac{ {\displaystyle\sum\nolimits_{i\in\Upsilon_{t}}} \omega_{it}I_{it}\Delta p_{it}}{ {\displaystyle\sum\nolimits_{i\in\Upsilon_{t}}} \omega_{it}I_{it}}\right) }}$$

The term $fr_{t}$, henceforth referred to as the frequency of price changes, is the total CPI weight of items whose price changes at $t$. The term $dp_{t}$ is the average magnitude of those price changes. In the popular Calvo and Taylor models with uniform staggering of price changes, $dp_{t}$ is the only possible source of variation in $\pi_{t}$.

It is convenient to decompose inflation further into a weighted sum of price increases and decreases:

$$\pi_{t}\triangleq\underset{fr_{t}^{+}}{\underbrace{\left( {\displaystyle\sum\nolimits_{i\in\Upsilon_{t}}} \omega_{it}I_{it}^{+}\right) }}\underset{dp_{t}^{+}}{\underbrace{\left( \frac{ {\displaystyle\sum\nolimits_{i\in\Upsilon_{t}}} \omega_{it}I_{it}^{+}\Delta p_{it}}{ {\displaystyle\sum\nolimits_{i\in\Upsilon_{t}}} \omega_{it}I_{it}^{+}}\right) }}+\underset{fr_{t}^{-}}{\underbrace{\left( {\displaystyle\sum\nolimits_{i\in\Upsilon_{t}}} \omega_{it}I_{it}^{-}\right) }}\underset{dp_{t}^{-}}{\underbrace{\left( \frac{ {\displaystyle\sum\nolimits_{i\in\Upsilon_{t}}} \omega_{it}I_{it}^{-}\Delta p_{it}}{ {\displaystyle\sum\nolimits_{i\in\Upsilon_{t}}} \omega_{it}I_{it}^{-}}\right) }}$$

This decomposition carries information about the relationship between the distribution of price changes and inflation. In the next section, the frequency of price increases and decreases, $fr_{t}^{+}$ and $fr_{t}^{-}$, will play a central role in the dynamics of inflation.

The statistic $fr_{t}$ yields information about the economy's degree of price stickiness; all else equal, the greater $fr_{t}$ is, the more flexible prices are. A closely related measure of price stickiness is the duration of price spells. Although price spells' length can be measured directly in the data, the literature generally has preferred duration measures derived from the frequency of price changes. Assuming price changes occur at a constant rate over the month, the average duration is given by $dur_{t}=-1/\ln\left( 1-fr_{t}\right)$. Aggregate measures of average or median durations are obtained by computing $fr_{t}$ and $dur_{t}$ at the category level and then aggregating them using the CPI product category weights.¹⁷

5.  Main Results

This section presents the main results regarding the frequency and magnitude of price changes and emphasizes their relationships to inflation. I leave aside all items whose price is regulated to focus on prices that are free to adjust. In addition, I treat separately non-regulated goods and non-regulated services as their behavior differ markedly.

5.1  Frequency

I first present the results for nonregulated goods which represents 73.1% of all expenditures in the main basket. For those items, movements in the frequency of price changes and inflation were very large over the sample period. In April 1995, the rate of inflation for nonregulated goods peaked at 82.9% (6.9% in monthly terms). This rate is much greater than the 7.2 percent average in 1994 and the 1.5 percent average in the last year of the sample. The frequency of price changes also peaked in April 1995, when the price of 64.3% of nonregulated goods, measured in CPI weight, changed over that month. This number is more than twice the average level of 24.2% in 1994 and 30.3% in the last year of the sample. In the case of services, inflation peaked at 54.3% in annual terms in April 1995 (4.5% in monthly terms).

Figure 4 presents the main time series statistics for non-regulated goods. Positive comovement between $fr_{t}$ and $\pi_{t}$ is clearly visible in the figure. The correlation coefficient between the two linearly detrended series equals 0.93 for the whole period. This correlation is largely driven by the high inflation episode, however; it falls to -0.02 if I consider only the last three years of the sample. After mid-1996, it is difficult to spot any downward trend in the frequency of price changes even though inflation trends down. The reason behind this loose relationship is apparent in the lower part of Figure 4, 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, however, price decreases became more frequent, thereby dampening movements in the frequency of price changes. A look at the correlation between $fr_{t}^{+},$ $fr_{t}^{-}$ and $\pi_{t}$ provides further evidence of this dampening effect. In the last three years of the sample, the correlation is 0.55 between $fr_{t}^{+}$ and $\pi_{t}$ and -0.72 between $fr_{t}^{-}$ and $\pi_{t}$. (All series are linearly detrended.) The net result is an absence of correlation between $fr_{t}$ and $\pi_{t}$ over that period.

Figure 4. Frequency of price changes (nonregulated goods)

The offsetting effect of price decreases operates mainly at low levels of inflation. Indeed, when inflation reaches above 10 to 15% in my sample, there are few price decreases left to offset movements in the frequency of price increases. At the peak of inflation, for example, only 8% of price changes were price decreases. In contrast, 45% of price changes were negative in the last year of the sample (42% if I include nonregulated services), a figure echoing those on the United States and the Euro area. This disappearance of price decreases creates the observed nonlinearity in the relationship of $fr_{t}$ to $\pi_{t}$.

Figure 5 shows evidence of the offsetting effect from a different angle by presenting scatterplots of $fr_{t}$, $fr_{t}^{+}$ and $fr_{t}^{-}$ against the inflation rate. The sample is divided into low- and high-inflation subsamples. The low-inflation subsample features a rapid fall in the frequency of price decreases as inflation takes off, thereby generating the offsetting effect. In comparison, in the high-inflation subsample, the frequency of price decreases is closer to its lower bound and responds less directly to movements in inflation. This change in behavior, seen as a "kink" in the relation, occurs for an inflation rate of 10 - 15%.¹⁸ The plots also show the predicted values from simple linear regressions on each subsample, using 12.5% as the cutoff inflation. The regression results are presented in Table 2.

Figure 5. Scatterplot of the frequency of price changes and inflation (nonregulated goods)

Note: Each graph displays linear regression lines using all observations below and above 12.5% annual inflation respectively. The regression statistics are presented in Table 2.

Table 2. Linear regression results for nonregulated goods (Panel 1: Frequency of Price Changes)

Observations	fr: Constant	fr: π	fr: R2	fr+: Constant	fr+: π	fr+: R2	fr-: Constant	fr-: π	fr-: R2
All	26.92, (0.42)	0.37, (0.02)	0.78	15.86, (0.31)	0.50, (0.01)	0.92	11.06, (0.25)	-0.13, (0.01)	0.56
π<=12.5%	29.16, (0.52)	-0.01, (0.07)	0.00	16.66, (0.42)	0.31, (0.05)	0.36	12.51, (0.32)	-0.32, (0.04)	0.51
π>12.5%	25.14, (0.79)	0.43, (0.02)	0.90	16.66, (0.67)	0.49, (0.02)	0.94	8.47, (0.27)	-0.05, (0.01)	0.55

Note: numbers in parentheses are standard errors

Table 2: Linear regression results for nonregulated goods (Panel 2: Magnitude of Price Changes)

Observations	dp: Constant	dp: π	dp: R2	dp+: Constant	dp+: π	dp+: R2	dp-: Constant	dp-: π	dp-: R2
All	0.91, (0.11)	2.02, (0.06)	0.92	8.58, (0.14)	0.54, (0.08)	0.34	11.06, (0.24)	-0.58, (0.14)	0.16
π<=12.5%	0.10, (0.04)	3.27, (0.06)	0.98	9.15, (0.21)	-0.42, (0.32)	0.03	11.99, (0.32)	-2.53, (0.50)	0.31
π>12.5%	2.44, (0.20)	1.50, (0.08)	0.91	7.67, (0.18)	0.86, (0.07)	0.82	10.41, (0.52)	-0.30, (0.20)	0.06

Note: numbers in parentheses are standard errors

When inflation is high, there is a clear positive relation between $fr_{t}$ and $\pi_{t}$: each percentage-point increase in the annual inflation rate is associated with a 0.37 (0.02) percentage-point increase in the frequency of price changes of nonregulated goods.¹⁹ In stark contrast, in the low-inflation subsample, the frequency of price changes shows no statistical relation to inflation in the low inflation subsample; the best point estimate for the slope of the regression line is actually negative at -0.01 (0.07) . The reason behind this very different behavior of $fr_{t}$ over the low- and high-inflation subsamples can be understood by taking a second look at $fr_{t}^{+}$ and $fr_{t}^{-}$. When inflation is low, a one percentage-point change in the inflation rate has a similar effect in magnitude on $fr_{t}^{+}$ and $fr_{t}^{-}$, 0.31 (0.05) versus -0.32 (0.04), but this effect takes opposite signs. The net effect renders unresponsive $fr_{t}$ to movements in inflation. As inflation moves toward high values, however, the rate at which $fr_{t}^{-}$ falls decreases as it approaches its lower bound of 0. The frequency of price increases still has room to respond, though, resulting in the significant, positive statistical relationship that surfaces between $fr_{t}$ and $\pi_{t}$. The offsetting effect of price decreases when inflation is low is robust to choosing any cutoff for the low- and high-inflation subsamples within the 10-15% range. Furthermore, the results are similar if I include nonregulated services, if I drop observations before the 1995 sample revision or around the inflation peak, and if I exclude all small-store samples.

Nonregulated services represent a much smaller share of expenditures than nonregulated goods in the basket at 26.9%. The upper part of Figure 6 displays the frequency of price changes and the inflation rate of nonregulated services over the sample period. There are several notable differences in price setting behaviors with respect to nonregulated goods. First, price changes are less frequent for nonregulated services than goods, a fact noted by several author (e.g. Bils and Klenow (2004) and Dhyne et al. (2005)). Second, the frequency of price changes is a much more important margin of adjustment for services inflation than for goods. Even at low levels of aggregate inflation, I observe large increases in the price index for nonregulated services associated with important movements in $fr_{t}$. These movements have a strong seasonal component, with the large adjustments of each year occurring almost inevitably in January and September. Second, the sample peak in inflation around April 1995 is associated with a smaller rise in the frequency of price changes. The frequency averaged 10.4% in the second half of 1994 and 24.7% in the first half of 1995 compared to 24.3% and 50.2% for nonregulated goods. Finally, most nonregulated services price changes are price increases. In the last year of the sample, less than 1 out of every 8 price changes was a price decrease. The strong movements in the frequency of price changes at low levels of inflation may be associated with this relative absence of price decreases. Movements in the frequency of price decreases are negligible for the dynamics of the frequency of price changes, in sharp contrast with nonregulated goods.

Figure 6. Frequency of price changes (nonregulated services)

Data for Figure 6

Month	Inflation	Frequency changes	Frequency increases	Frequency decreases
May-94	7.1	9.1	8.4	0.7
Jun-94	4.6	6.9	6.2	0.7
Jul-94	3.7	5.3	4.6	0.7
Aug-94	5.6	13.4	12.4	1.0
Sep-94	27.7	20.3	19.6	0.7
Oct-94	2.9	6.5	5.7	0.8
Nov-94	8.9	7.8	6.9	0.9
Dec-94	11.2	9.6	9.0	0.6
Jan-95	38.8	21.8	21.7	0.1
Feb-95	33.6	21.9	21.8	0.1
Mar-95	30.3	20.5	20.1	0.4
Apr-95	54.3	43.9	43.2	0.7
May-95	26.5	20.1	19.8	0.2
Jun-95	24.1	20.3	20.0	0.4
Jul-95	14.2	13.7	13.1	0.7
Aug-95	14.6	13.4	13.2	0.3
Sep-95	42.5	23.9	23.8	0.1
Oct-95	14.4	11.6	11.6	0.1
Nov-95	15.1	10.9	10.9	0.0
Dec-95	23.5	19.8	19.6	0.2
Jan-96	24.0	17.9	17.5	0.4
Feb-96	15.6	12.7	12.3	0.3
Mar-96	13.0	12.0	11.6	0.5
Apr-96	19.4	16.6	16.2	0.4
May-96	15.7	13.5	12.9	0.5
Jun-96	12.9	13.2	12.8	0.5
Jul-96	11.0	16.2	15.9	0.4
Aug-96	10.0	13.2	12.7	0.5
Sep-96	40.8	26.6	26.4	0.2
Oct-96	7.6	7.6	7.3	0.3
Nov-96	9.7	8.9	8.6	0.3
Dec-96	24.1	19.5	19.2	0.3
Jan-97	26.9	21.8	21.5	0.3
Feb-97	16.5	15.5	14.9	0.6
Mar-97	9.4	10.3	9.9	0.4
Apr-97	12.8	13.8	13.5	0.3
May-97	12.9	14.5	14.1	0.4
Jun-97	11.0	13.0	12.7	0.4
Jul-97	7.3	9.9	9.5	0.4
Aug-97	9.3	15.1	14.8	0.3
Sep-97	39.1	24.1	23.7	0.4
Oct-97	7.2	7.7	7.4	0.2
Nov-97	7.4	7.4	6.9	0.5
Dec-97	13.0	12.0	11.4	0.6
Jan-98	27.3	23.5	22.8	0.7
Feb-98	14.9	17.0	16.4	0.6
Mar-98	13.7	12.4	11.9	0.5
Apr-98	13.0	12.2	11.6	0.6
May-98	15.6	14.2	13.9	0.3
Jun-98	9.6	10.8	10.3	0.5
Jul-98	7.7	9.8	9.4	0.3
Aug-98	10.8	18.5	18.2	0.4
Sep-98	40.4	27.5	27.2	0.3
Oct-98	5.3	7.4	6.7	0.7
Nov-98	7.5	9.6	9.0	0.6
Dec-98	22.0	19.5	19.4	0.1
Jan-99	24.0	20.1	19.8	0.2
Feb-99	20.9	18.4	17.9	0.5
Mar-99	17.1	14.2	14.0	0.2
Apr-99	14.5	15.2	14.9	0.3
May-99	13.8	13.8	13.6	0.2
Jun-99	8.1	9.4	9.1	0.3
Jul-99	6.9	8.5	8.3	0.2
Aug-99	9.4	18.5	18.2	0.3
Sep-99	40.1	25.7	25.4	0.3
Oct-99	6.8	9.3	8.8	0.6
Nov-99	6.0	7.5	7.0	0.5
Dec-99	7.8	12.9	12.2	0.7
Jan-00	22.5	22.6	22.0	0.6
Feb-00	12.8	13.1	12.8	0.3
Mar-00	5.4	7.9	7.2	0.7
Apr-00	6.5	8.5	7.8	0.7
May-00	5.2	8.4	8.1	0.4
Jun-00	6.8	9.1	8.7	0.5
Jul-00	4.7	6.7	6.2	0.5
Aug-00	9.0	14.2	13.6	0.6
Sep-00	33.2	25.3	23.8	1.5
Oct-00	8.4	7.6	6.7	0.9
Nov-00	10.3	8.7	8.2	0.5
Dec-00	8.0	8.5	7.9	0.6
Jan-01	13.3	12.0	11.4	0.6
Feb-01	9.9	9.9	9.1	0.8
Mar-01	10.4	9.9	9.1	0.8
Apr-01	7.6	7.6	7.0	0.6
May-01	6.3	9.1	8.1	1.0
Jun-01	4.5	6.6	5.6	1.0
Jul-01	4.9	7.4	6.3	1.0
Aug-01	7.0	18.2	16.8	1.4
Sep-01	29.6	22.5	21.4	1.1
Oct-01	5.3	6.2	5.2	1.0
Nov-01	6.4	7.0	6.2	0.8
Dec-01	4.4	5.5	4.9	0.6
Jan-02	13.6	13.2	11.8	1.4
Feb-02	8.4	10.8	9.5	1.3
Mar-02	7.3	10.0	8.6	1.4
Apr-02	6.9	7.7	6.5	1.2
May-02	3.9	6.8	5.1	1.7
Jun-02	3.3	6.2	5.0	1.2

5.2  Magnitude of Price Changes

In the case of nonregulated goods, the average magnitude of price changes moves strongly with inflation, regardless of whether inflation is low or high. The series $dp_{t}$ and $\pi_{t}$, displayed in Figure 7, follow similar patterns over the sample period.²⁰ They register sharp increases during the Tequila crisis, followed by a protracted decline and ultimately a stabilization. The correlation between the two linearly detrended series is 0.94 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 to a solid 0.998 over the last three years of the sample. As the scatterplot of $dp_{t}$ against $\pi_{t}$ (Figure 8, with regression coefficients presented in Table 2) indicates, $dp_{t}$ and $\pi_{t}$ have a tight, almost linear relation when inflation is below 1% per month, or roughly 10-15 percent per year. When inflation is greater than 1% per month, the relation is still strongly positive, albeit noisier and slightly concave.

Figure 7. Average magnitude of price changes (nonregulated goods)

Data for Figure 7

Month	Inflation	Magnitude changes	Magnitude increases	Magnitude decreases	Predicted average change (fixed magnitude)	Predicted average change (fixed share)
May-94	0.4	1.9	9.0	10.3	2.0	3.2
Jun-94	0.7	2.7	9.9	10.2	2.1	3.9
Jul-94	0.5	2.2	9.5	10.2	2.0	3.6
Aug-94	0.4	1.9	8.1	9.2	2.3	2.9
Sep-94	0.5	2.2	8.6	9.5	2.2	3.2
Oct-94	0.4	1.6	8.6	10.8	2.2	2.8
Nov-94	0.9	3.4	10.2	10.3	2.7	4.1
Dec-94	1.0	3.6	9.2	9.4	3.3	3.7
Jan-95	4.8	10.2	13.0	10.9	6.9	5.9
Feb-95	4.7	9.9	12.2	10.4	7.2	5.4
Mar-95	4.5	8.8	11.6	9.5	6.6	5.3
Apr-95	6.9	10.7	12.5	9.0	7.7	6.0
May-95	5.1	10.1	11.9	7.1	7.3	6.2
Jun-95	3.2	7.8	10.9	7.1	5.8	5.5
Jul-95	1.8	5.8	10.0	7.5	4.5	4.8
Aug-95	1.8	5.7	9.6	7.3	4.6	4.5
Sep-95	1.9	6.0	9.3	8.4	5.5	4.0
Oct-95	2.2	6.9	9.8	7.7	6.0	4.6
Nov-95	3.1	7.4	10.1	6.6	6.1	5.1
Dec-95	3.8	8.4	10.2	9.2	7.4	4.4
Jan-96	3.2	7.3	10.2	12.3	6.7	3.4
Feb-96	2.0	5.3	9.7	13.6	5.5	2.7
Mar-96	2.5	6.4	10.1	9.2	5.5	4.3
Apr-96	2.9	7.9	11.4	9.0	5.9	5.3
May-96	2.3	6.6	10.2	9.1	5.5	4.4
Jun-96	1.3	4.3	9.0	9.1	4.2	3.6
Jul-96	1.1	3.6	8.2	8.7	3.9	3.1
Aug-96	1.3	4.0	8.6	10.7	4.5	2.8
Sep-96	1.3	4.0	8.6	10.1	4.4	3.0
Oct-96	1.3	4.0	8.6	10.6	4.5	2.9
Nov-96	1.7	5.0	8.8	11.0	5.4	2.9
Dec-96	2.0	5.5	8.5	9.8	6.0	3.0
Jan-97	2.4	6.4	9.3	9.2	6.1	3.8
Feb-97	1.3	3.7	8.3	10.2	4.3	2.7
Mar-97	1.0	3.3	8.7	10.2	3.7	3.0
Apr-97	1.0	3.2	7.6	9.6	4.3	2.4
May-97	1.0	3.3	7.9	9.6	4.1	2.7
Jun-97	0.6	2.0	7.1	9.1	3.1	2.3
Jul-97	0.7	2.6	9.5	10.7	2.5	3.5
Aug-97	1.0	3.4	9.1	9.2	3.2	3.6
Sep-97	0.9	3.0	7.6	10.1	4.1	2.3
Oct-97	0.5	1.8	7.7	10.5	2.8	2.3
Nov-97	0.9	2.9	7.9	9.6	3.6	2.6
Dec-97	1.3	4.4	8.4	8.6	4.6	3.3
Jan-98	2.2	5.6	9.8	10.9	5.2	3.6
Feb-98	1.2	3.6	9.5	13.6	4.3	2.6
Mar-98	0.9	3.0	8.2	11.1	4.0	2.4
Apr-98	1.0	3.3	8.1	8.6	3.6	3.1
May-98	1.6	5.0	9.5	9.5	4.6	3.8
Jun-98	1.1	3.7