Scraped Data and Sticky Prices: Frequency, Hazards, and Synchronization

Transcription

1 Scraped Data and Sticky Prices: Frequency, Hazards, and Synchronization Alberto Cavallo Harvard University This Version: September 10th, 2009 PRELIMINARY Abstract This paper introduces scraped online data to study price-stickiness in developing countries. Scraped data constitute a unique source of price information in terms of detail, sampling frequency, and country availability, allowing simultaneous cross-country analyses in a variety of macroeconomic settings. Using a dataset with more than 21 million prices in four Latin American countries during a time of high inflation, from October 2007 to October 2008, I present stylized sticky-price facts and provide four main empirical results. First, countries with higher inflation rates can also be stickier. Second, there is evidence of menu costs in the bimodal distribution of the size of price changes. Third, hazard functions can be upward sloping, consistent with statedependent pricing. Fourth, there is strong daily price synchronization within narrow categories, or aisles, which suggests that strategic complementarities can play an important role in price-setting decisions. acavallo@fas.harvard.edu I owe special thanks to Philippe Aghion, Robert Barro, and Roberto Rigobon for their help with this project. I also wish to thank Alberto Alesina, Michael Bordo, Gita Gopinath, Oleg Itskhoki, Pete Klenow, David Liabson, Julio Rotemberg, Greg Mankiw and seminar participants at Harvard for their helpful comments and suggestions. Surveys of offline prices were conducted with financial support from the Warburg Fund at Harvard University and excellent research assistance from Monica Almonacid, Enrique Escobar, Pedro Garcia, Andre Giudice de Oliveira, and Andrea Albagli Iruretagoyena. 1

2 1 Introduction Since the early 1970s, a large amount of theoretical research has focused on the microfoundations of sticky prices, a key element in modern explanations of the real effects of monetary policy. The empirical literature on price-stickiness, by contrast, has been relatively thin. Bils and Klenow (2004) made an important contribution by studying disaggregated US CPI data from the 1990s, and showing that the median retail price changed once every 4.3 months, more frequently than previously assumed. 1 Although other significant contributions followed, important empirical questions remain largely unanswered. 2 Are pricing decisions time-dependent or state-dependent? Is stickiness driven by menu costs, strategic complementarities, or imperfect information? What roles do competition and price synchronization play? Are there differences across countries or sectors, and what drives them? More generally, how do the macroeconomic environment, past inflation experiences, and institutional frameworks influence the way prices adjust? Insights into these questions are vital to constructing better models that can match the response of aggregate data to shocks, helping us understand how policy should react and what the impact will be on sectoral prices and output. The main problem in the current empirical research is that product-level data are limited in terms of the frequency, countries, and contexts in which they are collected. US and European CPI data have recently become available to some researchers on a limited basis. 3 Although these datasets are very detailed and cover a wide range of products, they are typically available only for a few developed countries 4, and were collected during times of stable macroeconomic environments where aggregate shocks are mild and micro price mechanisms harder to detect. 5 To determine which stylized facts are truly robust, the literature needs 1 The typical assumption in models was that retail prices changed once a year on average, following work by authors like Cecchetti (1986) and Kashyap (1995) on magazines and retail catalogs. 2 See Mackowiak and Smets (2008) for a review of the recent empirical literature. The main conclusion from early papers is that individual prices are more flexible than previously assumed. In fact, standard statedependent models calibrated with this observed firm-level flexibility cannot generate enough real effects of monetary policy to match aggregate data. Subsequent papers focused on improving the interpretation of the data. For example, Nakamura and Steinsson (2007) show that prices are stickier when sales are excluded (8-11 months), while Eichenbaum et al. (2008) show there is considerably stickiness in reference prices, measured as the most common price within a quarter. Other authors, like Burstein and Hellwig (2007) and Klenow and Willis (2006), have extended state-dependent models with strategic complementarities and real rigidities, which can potentially deliver more aggregate stickiness. 3 US CPI data are used by Bils et al. (2003), Nakamura and Steinsson (2007), Klenow and Kryvtsov (2008) and Klenow and Willis (2007). European CPI data are used by Dhyne et al. (2005), Boivin et al. (2007), Wulfsberg (2008), among others. 4 Even when data is available, cross-country comparisons are complicated by inconsistencies in the type of products and time periods used. 5 In a stable macroeconomic environment, many empirical results are driven by idiosyncratic shocks. That is why, in the words of Gopinath and Itskhoki (2008) P.1, there is little that empirically correlates with the 2

3 comparable data from different countries, under various inflation settings, macro volatilities, and institutional arrangements. This paper makes contributions on two fronts. First, I show that there is a unique and valid source of data in scraped online prices, which can be used to extend the empirical analysis into a much larger set of countries and economic conditions. 6 Second, I look for empirical evidence of sticky prices in four developing countries, with a focus on frequencies, hazard functions, and price synchronization, and present results that differ considerably from previous findings in the literature. 7 On the data front, I developed a methodology to efficiently scrape price information from online sources. For the purposes of this paper, I constructed a dataset with more than 21 million supermarket prices in Argentina, Chile, Brazil, and Colombia, between October 2007 and October The data are comparable across countries, with the same type of products and time periods. They are also available with daily frequency, which reduces measurement errors and makes it easier to study sales, hazards, and price synchronization. In addition, the data provide detailed information on each product, and were collected during a period of high inflation and volatility. I show that scraped prices are a valid source of information by comparing simultaneous surveys of online and offline prices in all supermarkets. Although price levels are seldom identical, price changes are similar in terms of timing and size of adjustment. In addition, daily price indexes generated with online data can closely match official statistics in nearly every country. The estimates for annual inflation are 22.5% in Argentina, 7.5% in Chile, 6.4% in Brazil and 7.7% in Colombia. The only country where this differs considerably from CPI figures is Argentina, where official price indexes have become widely discredited in recent years. 8 I use the data to present four main results: First, countries with more frequent price changes do not have higher inflation rates. I measure stickiness with the median frequency of price adjustment and its implied duration, as commonly done in the literature. Prices are stickier in Chile, with the median price changing every 166 days, followed by Argentina at 90 days, Colombia at 66 days, and Brazil at 52 days. In contrast to standard predictions, the stickiest countries have relatively high inflation rates. frequency of price adjustment. 6 Together with Roberto Rigobon at MIT Sloan, I started the Billion Prices Project that is extending the data collection and analysis to a sample of over 50 countries. See for details. 7 The study of stickiness in developing countries is rare because data are seldom disclosed at the product level, or they are very unreliable. A notable exception is Gagnon (2007), who provides a detailed analysis of sticky prices in Mexico using disaggregated CPI data. 8 In January 2007 the government intervened the national statistics institute (INDEC). See for more up-to-date inflation estimates in Argentina using some of the data in this paper. 3

4 The degree of stickiness seems more related to the recent history of price stability in each country than to current levels of inflation. 9 Second, there is evidence of bimodal distributions in the size of price changes, consistent with state-dependent menu cost models. In Argentina, Brazil and Chile, there are few changes close to zero, and in some cases the distribution has an asymmetry that is characteristic of a Golosov and Lucas (2007) model in the presence of strong positive aggregate shocks. These results differ from what Klenow and Kryvtsov (2008) found in the US CPI data, where very small price changes are common and distributions are symmetric. Third, I use duration analysis to find evidence of upward-sloping hazard functions in individual price adjustments. Hazards measure the probability of a price change conditional on the time passed since the previous adjustment. My results are consistent with statedependent models, where hazard functions tend to be upward sloping. 10 Finally, I find strong daily price synchronization within narrow categories, or aisles, in all four countries. Synchronization is independent of sales, and occurs both for price increases and decreases. In addition, aisles with more synchronization have less variability in the size of synchronized changes. This suggests that firms are acting like strategic complements, matching both the timing and size of their price changes. 11 Complementarities, however, are not linked to any real rigidities. The data shows that synchronization tends to increase the frequency of price adjustment at the aisle level. Overall, my results provide some empirical evidence in support of state-dependent pricing in developing economies. Some of these findings, like the bimodal distributions and upwardsloping hazard functions, differ considerably from previous results in the literature. 12 This highlights the importance of using scraped online data to study stickiness across countries and economic settings, in order to fully understand which facts are robust and how they should influence the design of theoretical models. The paper is organized as follows. In section 2, I describe the data, explain how it is collected, and explore how it relates to offline prices. In section 3, I provide stylized sticky price facts for all countries, with a focus on frequencies and magnitudes of price adjustments. In section 4, I estimate hazard functions of price changes. In section 5, I study 9 Chile has a long history of price stability. Official statistics show that the surge of inflation is a recent phenomenon, which could explain why frequencies are so low. Similarly, Argentina had a full decade of price stability in the 1990s, and price controls and fair pricing concerns could also be playing a role. I further explore the case of Argentina in the Appendix. 10 If pricing is state-dependent, prices are more likely to change as the duration increases. This is particularly true in high-inflation settings, where old prices move further away from their optimal price. By contrast, in time-dependent models (e.g. Calvo (1983)) hazards are constant because the probability of price change is fixed and exogenously determined. 11 Other likely causes of synchronization are common shocks and economies of scale in menu costs. 12 See Klenow and Kryvtsov (2008) and Nakamura and Steinsson (2007). 4

5 price synchronization. Section 6 concludes. 2 Scraped Data: a New Approach with Online Sources 2.1 Main Characteristics This paper uses a new and unique database of more than 21 million supermarket prices in four Latin American countries: Argentina, Brazil, Chile, and Colombia. The data comes from the online price tables of four different retailers, one in each country, and covers the period from October 2007 to October All the supermarkets included in this paper are major players in their respective countries, with hundreds of physical stores. They also sell their products online in large cities like Buenos Aires, Santiago, Sao Paulo, and Bogota. Buyers can enter these sites, select the products they want to purchase, and get them delivered in just a few hours. Since clients cannot physically see the products they are buying, retailers make an effort to collect and display very detailed information on each item, including the price, the product s name, an id, brand, package size, category, and whether it is on sale, under price control, or out of stock. Every day, during the course of a year, I connected to these online shopping platforms and recorded all available information for each good on display. I used an automated software, generically called a robot, that scans through the code of publicly available webpages and records all the relevant price information. This technique is commonly called web scraping, and hence I use the term Scraped Data. 13 Table 1 provides details on each country s data collected for this paper. There are roughly 18 thousand daily prices in each country for Argentina, Chile and Brazil, and about 5 thousand in Colombia. The initial date for each database differs by a few days, around October 2007, but they all end on October 12th In addition, the data include detailed descriptions for each product, including brand, size, sale and price control indicators. 13 All over the world, a large and growing share of retail prices are being posted online. Retailers show these prices either because they want to sell their products online or simply to advertise their prices with offline buyers. This source of data represents an huge opportunity for economists wanting to study prices, yet it has been largely untapped because the information is hard to collect, widely dispersed across sites, and needs to be collected on a regular basis. The technology to efficiently do so is only now becoming available. Together with Roberto Rigobon, we have started an academic initiative called the Billion Prices Project that is currently collecting data from retailers in over 50 countries. See for more details. 5

6 Table 1: Database Description Argentina Chile Brazil Colombia Total observations 6.8M 6.4M 6.2M 1.8M Products per day Initial date 10/7/ /24/ /10/ /13/2007 Final date 10/12/ /12/ /12/ /12/2008 Days Categories Aisles Product Description Yes Yes Yes Yes Sale indicator Yes - Yes Yes Price Controls Yes Brand Yes* Yes Yes* Yes Bulk Price Yes* Yes Yes* Yes* Size of Package Yes* Yes Yes* Yes Missing obs within spells 14.66% 19.69% 10.75% 22.62% Outliers (price change above 500%) Obs with sales (% of total) 5.78% % 6.26% Products with sales Products with price controls Life of goods (in days, Mean/Median) 267/ / / /334 Obs per good (Mean/Median) 230/ / / /243 Notes: *Constructed from product descriptions. To compare results for product categories across countries, I matched each supermarket s good classification into 95 standardized categories listed in Table 12. These categories include a wide variety of foods and household items. Products are further classified into aisles. These aisles are narrow product categories that include only close substitutes displayed next to each other. Before conducting the stickiness analysis, I treated the data following standard procedures in the literature. First, I completed missing values within price series using the last recorded value until another price is available. This is a natural approach given the daily frequency of the data and the fact that price gaps extend for only a few days. Second, in those cases where sale prices need to be excluded, I replaced them with the previous non-sale price available for that product. This means, for example, that if the price of a good drops in a sale but 6

7 later returns to exactly the same value (a v-shaped sale), the non-sale price series will show a constant price. Third, I excluded all price changes that exceed 500%. These represent a negligible number of observations, but can affect statistics related to the magnitude of price changes Comparison to other Data Sources Scraped data have important differences with CPI data and scanner data, the two sources commonly used for sticky price studies. These are summarized in Table 2. Table 2: Alternative Data Sources Scraped Data CPI Data Scanner Data Products Categories and Retailers Covered Few Many Few Quantities Sold No No Yes / Sometimes Data Frequency Daily Monthly - Bi-Monthly Weekly Countries Available for Research 50* 5-10 <5 Cross-Country Comparisons (categories and time) Yes Limited No Details - Sale, price control, other indicators Yes Limited Limited Eliminates Forced Substitutions Yes No Yes Few Time Gaps Yes Yes No Real-Time data availability (no lags) Yes No No *Data from over 50 countries are currently being collected by the Billion Prices Project ( Compared to other data sources, scraped data have two main disadvantages: First, they cover a much smaller subset of retailers and product categories than CPI data. In particular, in this paper I look at supermarket data, from one retailer in each country. However, this is not a major limitation in this paper because supermarket products represent over 40% of all CPI expenditure weights in Latin American countries. In general, scraped data can overcome this limitation in the future, as a growing number of companies start posting their prices online. Second, scraped data do not have information about quantities sold, which scanner datasets typically include. This prevents me from getting market shares or trying to estimate elasticities directly More treatment details are provided in the Appendix. 15 There are, however, other variables like the number of substitutes in an aisle, which can be used to estimate the degree of competition, as I do in section??. 7

8 Despite these limitations, scraped data have some key advantages that make them a unique source for sticky price analyses: First, they provide daily price information. This reduces measurement error biases in frequency calculations. It is also especially useful for the analysis of sales, price controls, hazards, and price synchronization. 16 Second, the information is available for a much larger set of countries. In this paper, I focus on four developing countries, where scanner data are scarce and disaggregated CPI prices are seldom disclosed or very unreliable, but scraped data can be obtained from any country where online prices are available. 17 Third, the data are comparable across countries, with information on the same categories of goods and the same time period, which makes it possible to perform simultaneous crosscountry analyses. Fourth, there is very detailed information on each product. In particular, the aisle indicator that identifies products displayed next to each other is unique to this type of data. Fifth, there are no forced item substitutions (which commonly occur in official statistics) or missing information if products are not purchased (as it happens with scanner data). 18 Finally, scraped data are available on a real-time basis, without any delays. This allowed me to collect prices during the recent period of aggregate volatility and inflation. The study of stickiness in this context is rare in the literature. In the future, this collection methodology can provide real-time estimates of stickiness in different sectors, allowing policymakers to better predict and monitor the impact of their policies. 2.3 Online vs. Offline Prices An important concern with scraped prices is that they may not be representative of any real transactions. Since online purchases are still a small share of transactions in most countries, can we assume scraped online prices are representative of a country s true pricing behavior? There are two parts to this question. First, do online and offline prices behave similarly? 16 See the Appendix for an analysis of how monthly data sampling can change the results in this paper. 17 See 18 Forced substitutions occur in official statistics when the agent surveying prices does not find the item she was looking for, and decides to replace it with another one, which becomes the surveyed item from then on. In practice, if the old item is offered again and/or the new item was being offered before, official statistics do not record these prices, effectively censoring the price series. In my data, prices are recorded from the first moment they enter the sample until the last day they have been offered to consumers, which solves substitutions for items that go temporarily out of stock. It is important to note, however, that I do not attempt to link price series of goods that may be discontinued and replaced by other goods permanently. In some cases, such substitution may be desired and could be attempted with this data. 8

9 Second, is one retailer representative of the pricing trends in the country as a whole? I explore both issues separately in this section Matching Offline Price Behaviors To answer the first question, I conducted simultaneous surveys of offline and online prices in each supermarket, and compared differences in price levels and the timing and size of price changes. Approximately 100 products in each supermarket were surveyed every 15 days, for a total of four times. 19 Table 3 shows the main results from this validation exercise. There is great overlap in the range of products sold through both channels. The percentage of products bought offline that were also available online ranges from 74% in Colombia to 100% in Argentina. Table 3: Offline vs. Online Prices Argentina Chile Brazil Colombia Matching IDs Yes No Yes Yes Available Online 100% 90% 80% 74% PRICE LEVELS online=offline 18% 93% 42% 29% online>offline 78% 4% 34% 32% Price Difference Online (Mean/SD) 0.05 / / / / 0.16 PRICE CHANGES Price change correlation % Changes matched 96% 95% 80% 68% Size of change offline (mean) Size of change online (mean) Notes: * Same timing of change. In terms of price levels, Chile is the only country where offline and online prices are practicably identical, with 93% of prices perfectly matched. In Argentina, online prices have a stable markup of 5%, while in Brazil and Colombia they can be either higher or lower depending on the product. These differences are not surprising if we consider that these websites are essentially just another branch, and that supermarkets tend to have different prices across branches More details on the surveying methodology are provided in the Appendix. 20 In fact, the perfect matching in Chile is surprising: either this supermarket has an undisclosed commonpricing policy in all branches, or we picked exactly the same branch that supplies all online sales. 9

10 More relevant for this paper is the comparison of price changes. For each product and sample, I constructed a binary price change series with value 1 if the price changed between supermarket visits, and 0 otherwise. Table 3 shows that, in all cases, price change series are similar, both in terms of timing and size of adjustments. In Chile and Argentina, over 90% of price changes occur at the same time, while in Brazil and Colombia these values are 80% and 68% respectively. Additionally, the mean size of price changes is nearly identical in all countries Tracking CPI Statistics Even if online prices can match offline price behaviors, are they representative of countrylevel trends? A way to test this is to compare scraped price indexes with official CPI statistics. Figure 1 plots a daily supermarket index -constructed with scraped data- and compares it to the official CPI index in each country, while Table 4 compares the annual inflation rate in both indexes More details provided in the Appendix 22 Details on the construction of the scraped indexes are provided in the Appendix. 10

11 oct jan apr jul oct2008 date oct jan apr jul oct2008 date Our Supermarket Index Official CPI Price Index Our Supermarket Index Official CPI Price Index (a) Argentina (b) Chile* oct jan apr jul oct2008 date oct jan apr jul oct2008 date Our Supermarket Index Official CPI Price Index Our Supermarket Index Official CPI Price Index (c) Brazil (d) Colombia Figure 1: Supermarket Index (daily) vs. the Official CPI (monthly) Table 4: Annual Inflation (%) Online Supermarket Index Official Consumer Prices (CPI) Oct 2008 Oct 2008 Argentina Chile 7.5* 9.8 Brazil Colombia *Includes sales As can be seen, daily online indexes can closely track the official CPI monthly series in most countries. 23 Official CPI inflation is nearly identical to the supermarket inflation in 23 This matching is aided by the fact that supermarket products were the main driver of inflation during 11

12 Brazil and Colombia, and only slightly higher in Chile. The only case in which scraped indexes are not consistent with official statistics is Argentina. I find that Argentina had the highest supermarket inflation rate, at 22.6%, even though officially only 8.4% was reported for this period. The difference is not surprising because official data has become widely discredited since January 2007, when the government intervened the national statistics institute (INDEC). 24 In conclusion, the analysis in section shows that the scraped dataset used in this paper is a valid source of price information; online prices are representative of offline transactions and can closely track the countries inflation trends. In the following sections I use the data to document sticky price facts in all countries and empirically evaluate of the predictions in standard theoretical models. 3 Evidence of Sticky Prices Many microeconomic mechanisms have been proposed to explain why prices do not adjust quickly to shocks and monetary policy. These mechanisms can be broadly classified into two types of models: time-dependent and state-dependent models. In time-dependent models, the timing of price adjustment is exogenously determined. A firm is able to set the optimal price after a given number of periods (as in Taylor (1980)), or randomly every period (as in Calvo (1983)). With random adjustments, price changes of any size are possible, and there is a stable fraction of firms adjusting every period, regardless of how much time has passed since their previous price change. This creates a tractable, exogenous staggering of individual price changes that can generate considerable aggregate stickiness. State-dependent models, starting with the menu cost models in Barro (1972) and Sheshinski and Weiss (1977), and more recently Dotsey et al. (1999) and Golosov and Lucas (2007), tend to have stronger micro-foundations. They are based upon the assumption that price setters are able to change their prices at any time, but must face adjustment costs to do so. These adjustments costs, which I will broadly refer to as menu costs in this paper, may include labor costs to change prices, information acquisition costs to make the decision, or even customer anger costs linked to the consumer s reaction after a price adjustment. 25 In this time period. Similar results, comparing a subset of food products, are provided in section?? in the Appendix. 24 For more up-to-date inflation estimates in Argentina, using some of the data in this paper, see 25 An example of models that include the latter are Fair Pricing models, like Rotemberg (2005) and Rotemberg (2008). These models build on the idea that prices are sticky because firms do not want to antagonize customers. Blinder et al. (1998) found in a survey of price setters that this was a major concern 12

13 state-dependent models, there are few small price changes (because it is not worth paying the menu cost) and adjustments tend to occur more frequently in older prices (where the deviation from the optimum is likely larger). As Klenow and Kryvtsov (2008) explain, the implications for real output and inflation can differ dramatically in time and state-dependent models, so it is important to empirically distinguish between them. Even though there is a large degree of heterogeneity in price changing behaviors, in this paper I find strong evidence in support of state-dependent pricing mechanisms. 3.1 General Price Change Statistics This section presents general price change statistics in each country. Table 5 shows that a large percentage of goods changed their prices twice or more within a year, ranging from 80% in Brazil to 56% in Chile. The median good changed its price 8.1 times a year in Brazil, and 4.2 times in Chile. Table 5: General Statistics on Price Changes by Country and Sale Treatment Including Sales Excluding Sales* Arg. Chile Brazil Col. Arg. Brazil Col. Supermarket Inflation (% per year) Goods with no price change 19% 27% 11% 16% 22% 11% 21% Goods with 2 or more price changes 66% 56% 80% 72% 59% 78% 66% Price changes per good (Mean/Median) 4.4/3 4.2/2 8.1/4 5/3 2.6/2 6.8/4 4/3 Price increases (% of price changes) 69% 57% 60% 55% 84% 63% 57% Price decreases (% of price changes) 31% 43% 40% 45% 16% 37% 43% Notes: *There is no sales information for Chile. Figure 2 shows that price changes occur every day, but the daily fraction of goods that change prices is highly volatile. 26 for firms setting prices in the US. I explore some evidence for this type of models in the Appendix, using data from Argentina. 26 This level of volatility could imply price synchronization. I explore this in detail in Section 5. 13

14 ratio of Price that changed per DAY TOTAL ratio of Price that changed per DAY TOTAL ratio of prices that changed ratio of prices that changed oct jan apr2008 date 01jul oct oct jan apr2008 date 01jul oct2008 (a) Argentina (b) Chile Ratio of prices that changed ratio of prices that changed ratio of Price that changed per DAY TOTAL 01oct jan apr2008 date 01jul oct nov feb may2008 date 01aug nov2008 (c) Brazil - Without December 15 and 19 (d) Colombia Figure 2: Fraction of prices that change each day Notes: The graph for Brazil excludes two exceptionally large ratios in December 15th and 29th, 2008, where over 90% of prices where adjusted by very small amounts, possibly in anticipation of the holidays. Price decreases represent a significant share of total price changes in each country. This is particularly surprising in Argentina, where inflation is three times higher than in other countries, and price decreases represent 31% of all price changes. Nakamura and Steinsson (2007) found a similar share in the US, with CPI data collected during a period of much lower inflation. What explains this large share of price decreases, even under high inflation? Sales play an important part in the answer for Argentina. This can seen in Table 5. When I remove sales, the share of price decreases in Argentina falls to only 16%. 27 Indeed, sales can have significant impact on sticky price facts, as Nakamura and Steinsson (2007) have shown with US CPI data. In Table 6, I present some basic sales statistics in all countries where sale data is available. 27 By contrast, the numbers for Brazil and Colombia are only slightly different when sales are excluded. 14

15 Table 6: Sales by Country Argentina Brazil Colombia Life of sales (in days, median) Sales as % of price changes 14% 8.8% 11% Sales as % of price decreases 45% 22% 25% Sales with no price change* 29% 13% 22% Sales with price increases* 3% 0% 3% Sales that end with old price (v-shaped) 89% 66% 52% Sales that end with higher price 6% 12% 20% Mean size of sale, given price decrease -13% -18% -22% Notes: *Price changes occurring within +/- one day from the date a sale indicator appears next to the product. In all countries, sale events tend to last only a few days. The median length is only 6 to 13 days. 28 Sales represent between 8.8% and 14% of all price changes, and between 22% and 45% of all price decreases. Typically, they lead to big discounts in price, with a mean drop of 13% to 22% when a sale is announced. Surprisingly, many sales are not associated with a reduction in prices at all. Consider the effect on prices within a one-day window of the announcement of a sale. 29 Between 13% and 29% of sales do not affect prices at all; and in Argentina and Colombia, 3% of the times when a sale is announced the price increases. A common trend is that, as inflation rises, sales become shorter, more v-shaped and increasingly unrelated to actual price changes. These facts suggest that sales play a role in pricing strategies that standard sticky price models do not explain. 30 Because sales can significantly alter stickiness calculations, in the following sections I provide results both including and excluding sale prices, and discuss any relevant differences. 28 This is an important cause of measurement error when using monthly prices, because many sales are either not be recorded at all, or assumed to last over a month. See the Appendix for more details. 29 Price changes occurring within +/- one day from the date a sale indicator first appears next to the product. I also ran these calculations allowing a 3-day window of price changes around each new sale, but the results do not change significantly. 30 One recent model consistent with the fact that sales remain frequent in a high-inflation setting, is Guimaraes and Sheedy (2008). It shows that if sales are strategic substitutes across retailers, they do not fall much after expansionary monetary shocks because retailers are using them to attract customers. Additionally, sales could potentially play a role in fair pricing models like Rotemberg (2008), as a way to reduce the negative impact that price increases are having on customer anger. I explore this in more detail in the Appendix, where I use data for Argentina to find evidence of anger concerns in pricing behaviors. 15

16 3.2 Frequency and Implied Durations To measure the degree of price stickiness in each country, I follow the frequency approach. This method, now standard in the empirical sticky price literature, 31 provides a single parameter to reflect the probability that a typical firm will change its price over a given period of time. To determine country-level frequencies, I first obtain the daily frequency per individual good by computing the number of daily price changes over the number of total valid observations for a particular product. Next, I calculate the median frequency per good category, and finally, the median frequency across all categories. 32 Given that CPI expenditure weights are different across countries, I use unweighed medians to facilitate cross country comparisons. 33 In addition to frequencies, I estimate implied durations by computing 1/frequency. 34 Implied durations provide an intuitive way to compare the degree of price stickiness across countries. Table 7 presents each country s frequency and durations results. On one extreme, Chile is the stickiest country, with the lowest median frequency and an implied duration of 166 days. On the other extreme, Brazil is the most flexible country, with the highest median frequency and an implied median duration of 52 days See Bils and Klenow (2004), Nakamura and Steinsson (2007) and Gopinath and Rigobon (2008) 32 I follow Gopinath and Rigobon (2008) (GR) and take the median frequency within each good category. For comparison, in the Appendix I also report the results of the Bils and Klenow (2004) (BK) approach used by most papers in this literature. This method computes the weighted mean frequency within good categories, before obtaining the weighted median frequency across all categories. The use of the two methods yield different results in the overall level of frequencies, but it does not significantly alter the cross-country comparisons included in this paper. In general, BK leads to higher frequencies (less duration or stickiness) in this sample because the distribution of frequencies within categories is right (or positively) skewed, so that the mean frequency is larger than the median. This is driven by those goods with no price changes, some of which are censored in the one-year sample period. In principle, with longer samples both methods would give similar results. 33 Since most papers in the literature conduct single-country analyses, the standard procedure is to use weighted medians. 34 This method makes the simplifying assumption of constant hazards, where the probability of a price change is independent from the amount of time elapsed since the previous adjustment. 35 Prices are stickier than what has previously been reported for similar products in more developed economies. Eichenbaum et al. (2008), for example, compute durations of only 2.5 weeks (18 days) for US supermarket prices collected between 2004 and 2006, even though inflation averaged only 3% annually during that period. The difference are surprising because daily data tends to increase durations considerably, as I show in the Appendix. The difference can partially be explained by different methodologies and different types of products surveyed. 16

17 Table 7: Frequency and Durations by Country and Sale Treatment Including Sales Excluding Sales Arg. Chile Brazil Col. Arg. Brazil Col. Median frequency (daily) Implied Durations (days) In contrast with standard predictions in sticky price models, countries with higher inflation rates do not tend to have more frequent price changes. 36 Argentina is probably the most curious example. The annual inflation rate is three times the level of any other country in the sample, but price changes are relatively sticky, with an implied median duration of 90 days (30% longer than Colombia and 70% longer than Brazil). Although frequencies are not increasing with current inflation levels, they seem positively related to the recent history of inflation in each country. Chile has a history of price stability that none of the other countries share, and official statistics show that the surge of inflation is a recent phenomenon; this could explain why frequencies are still so low. Brazil by contrast, experienced rising inflation levels in the 80s that culminated in a hyperinflation period that lasted until 1994; this is consistent with its current high levels of price flexibility. Finally, although Argentina also has a history of chronic inflation, it had a full decade of complete price stability in the 1990s, which may have influenced its current low frequencies of price adjustment In the Appendix, I show that the frequency of price increases and decreases also fails to correlate with inflation. However, the ratio of relative frequencies (increases over decreases) tends to increase with inflation. This result is also present in the cross-section of aisles within each country. 37 Note that Argentina s low frequency is not explained by a difference in the type of goods being sampled in each country. As can be seen in Table 12, Argentina has more stickiness than Brazil in 54 out of 60 common categories (or 90%). Additionally, the high frequency in Brazil is not the result of the two exceptional days in December 2007, where 90% prices were changed. When I exclude these days, Brazil s implied median duration rises from 52 to 61 days, still shorter than Argentina s. 38 Even though Argentina s government has been imposing price controls since 2002, Table 12 shows that Argentina is stickier than Brazil even in categories which are never under price controls. Also, in section?? I find that price controls are associated with higher frequencies at the individual good level. If price controls are playing a role, then they must be affecting pricing behaviors in unrelated goods categories. This is possible if firms are afraid of being selected by the government for future controls, or concerned about boycotts and other negative consequences associated with frequent price changes. I explore the case of Argentina in more detail in section??, where I find some evidence in support of fair pricing concerns. 17

18 3.3 Size of Adjustments: Bimodal Distributions Frequencies give only a partial view of pricing behavior. To understand the micromechanisms behind price changes, one also needs to study the magnitude of changes. Table 8 shows several basic statistics of the size of daily price changes, measured as the percentage change over the previous price. Table 8: Size of Price Changes by Country and Sale Treatment Including Sales Excluding Sales Arg. Chile Brazil Col. Arg. Brazil Col. Size of changes (Median*) 4.6% 3.4% 1.7% 1.8% 6.6% 1.6% 2% Share of price changes under 5% 22% 30% 37% 37% 31% 44% 45% Size of price increases (Median*) 11.4% 13.3% 10.5% % 8.6% 8.4% Size of price decreases (Median*) -13.6% -11.6% -12.5% -10.5% -11% -11.2% -7% Notes: *Calculated using the mean size of change per good, then mean per category, then the median across all categories. Results are similar with means across categories. The median size of changes varies considerably across countries. As expected, higher inflation countries have higher median sizes, and a smaller share of price changes with magnitudes below 5%. However, most of the difference in the median size is driven by the relative number of price increases over price decreases. Indeed, when considered separately, the median size of changes for increases and decreases are not so different across countries. 39 A better understanding can be achieved by looking at the distribution of the magnitude of price changes. The daily nature of the data allows me to plot detailed histograms in Figure 3, with bins that are only 0.1% wide. 39 This means that the size of increases and decreases is not sensitive to the level of inflation. This is consistent with customer regret costs that increase with the size of changes, as in Rotemberg (2009). 18

19 Distribution of Price Changes Distribution of Price Changes % of changes Size of price change (%) % of changes Size of price change (%) (a) Argentina (b) Chile % of changes Distribution of Price Changes Amount of price change in % % of changes Distribution of Price Changes Size of price change (%) (c) Brazil (d) Colombia Figure 3: Magnitude of Price Changes Notes: Bin size is 0.1%. Estimated kernel density shown. Brazil shown without changes on 15/12/07 and 29/12/07 (See Appendix). There are two important patterns emerging from these graphs. First, all countries have multiple spikes in their distributions. Argentina and Colombia have the largest spikes at -5% and +5%. In Chile, they occur at -10% and +10%, and in Brazil at approximately -2% and +2%. 40 One interpretation is that supermarkets, once they decide that they need to change prices, simply use integer numbers to implement them. In fact, these spikes tend to occur at integers like 5%, 10%, 20%, in all countries. 41 A second feature of these distributions is their bimodal shape. Argentina, Brazil, and Chile have distributions with a sharp dip in the density of changes close to zero. The lack of small price changes, both increases and decreases, is evidence in support of menu costs. 40 If we include the two days in December 2007, where nearly all prices in the supermarket changed by very small amounts, nearly 8% of all price changes are increases of 2%. 41 Another interpretation is that these spikes are the limits of S-s bands, typical of most state-dependent models. The fact that Argentina s bands are smaller than Chile s is consistent with the high level of inflation. 19

20 Furthermore, in Argentina and Brazil there is an asymmetry in the distribution, with less price decreases that price increases. This is predicted by menu cost models like Golosov and Lucas (04) in the presence of strong positive monetary shocks. The dip reflects the menu costs, while the asymmetry shows how positive aggregate shocks lead to a disproportionate amount of price increases. 42 This asymmetry is particularly strong in the case of Argentina, which explains why inflation is so high. The only country where the distribution of sizes is not bimodal is Colombia. It has a smooth shape, with a large number of tiny price changes. The distribution is similar to what Klenow and Kryvtsov (2008) found in the US CPI data. It does not necessarily imply that menu costs are not important, because Colombia has both small and large price changes, as evidenced by the fatter tails in Figure 3(d). This combination is possible in the presence of different menu costs for different types of goods, as in Dotsey et al. (1999), or with one menu cost for many goods, as in Midrigan (2005c). In summary, this section provides evidence of menu costs pricing in the sizes of changes. Distributions tend to be bimodal, and increasingly asymmetric in countries with more inflation. 4 Duration Analysis: Upward-Sloping Hazards The frequency approach in the previous section computes implied durations with the assumption that the daily probability of price change is independent from the time past since the previous adjustment, or in other words, that the hazard rate of price changes is constant over the whole sample period. 43 Although this method is a simple and effective way to compare the degree of stickiness across sectors and countries, one of the most contrasting predictions of time-dependent and state-dependent models lies precisely in the shape of the hazard function. The hazard is the instantaneous probability of price change at time t, conditional on the price not changing until that point in time. In time-dependent models like Calvo (1983), the hazard function is constant because the probability of price change is fixed and exogenously determined. In state-dependent models, by contrast, hazard functions tend to be upward sloping because non-stationary shocks increase deviations from the optimal price over time. 42 Another possible explanation for this, independent of any shocks that could be taking place, is that many of these drops are sales, and very small sales may be unattractive to customers and completely ineffective for the store to use. However, the dip in the distribution does not disappear once sales are excluded, as shown in Figure For example, consider a good that changes it price 3 times within a year. The frequency approach records 3/365 as the daily probability of price change, and assuming that this is constant over time, estimates an implied duration of approximately 365/3 = 121 days. 20

21 As the price moves away from the optimum, the conditional probability of a price change also rises. 44 In this section, I study the shape of hazard functions using Duration Analysis. This technique, also called Survival Analysis, is widely used in the life sciences to study the time elapsed from the onset of risk until the occurrence of a failure event (for example, from the time a decease is diagnosed until the time a patient dies). 45 In a price-setting context, we are interested in the time between the firm s optimal price adjustments. The onset of risk is the date when an optimal price is set, and the failure event occurs when the firm changes the price once again. The set of prices between these two dates is called a price spell, and the duration is the length of the spell, measured in days. The hazard function is the corner-stone of duration analysis. Formally, if T is a random variable measuring the duration of the price spell, with density function f(t) and cumulative density F(t), then the hazard h(t) is the limiting probability that a price change occurs at time t, conditional on the price not changing up to that point in time: 46 Pr(t < T < t + t t < T) h(t) = lim = f(t) t 0 t 1 F(t) This hazard function measures the instantaneous risk of a price change, conditional on survival. We can add all hazard rates over time, and obtain the total risk of price change accumulated up to time t. This is represented by the Cumulative Hazard Function: In fact, as Nakamura and Steinsson (2007) point out, state-dependent models can generate a variety of non-constant hazard functions. The shape can depend on the relative importance of temporary and permanent shocks. A series of permanent shocks, like those experienced in highly inflationary settings, will cause persistent deviations from the optimal price that accumulate over time, increasing the probability of price changes and leading to strictly upward-sloping hazards. If temporary shocks are relatively important, then most of the risk of price change can accumuluate within a short period of time, leading to hump-shaped or other type of non-constant hazards. 45 Economists mostly use duration analysis to study unemployment spells. Its use in the sticky price literature has been limited by the lack of suitable high-frequency data. 46 Note that Pr(t < T < t + t t < T) 1 Pr((t < T < t + t) (t < T)) h(t) = lim = lim t 0 t t 0 t P(t < T) 1 Pr(t < T < t + t) Pr(T < t + t) Pr(T < t) 1 = lim = lim t 0 t P(t < T) t 0 t P(t < T) F(t + t) F(t) 1 = lim t 0 t 1 F(t) = f(t) 1 F(t) 47 Note that h(u) = f(t) ln(1 F(t)) = 1 F(t) t 21