Nicoletta Berardi
email: nicoletta.berardi@banque-france.fr

Erwan Gautier
email: erwan.gautier@univ-nantes.fr

Herv É Le Bihan
email: herve.lebihan@banque-france.fr

Olympia Bover

Mikael Carlsson

Emmanuel Dhyne

Huw Dixon

Niels Gottfries

Roman Horvath

Francesco Lippi

Emi Nakamura

Julio Rotemberg

Patrick Sevestre

Anya Stockburger

Keywords: D40, E31, L11 price stickiness, inflation, consumer prices, sales, product substitution

More Facts about Prices: France Before and During the Great Recession

Using microprice data, we document new facts on price rigidity in France: (i) each month 20.1% of prices are changed, which compares to 24.1% in the United States-excluding sales, however, the fraction of prices modified each month is about the same in France and in the United States (around 17%); (ii) the distribution of price changes is quite dispersed; (iii) the frequencies of price increases and decreases contribute a lot to inflation variations, and price increases are more frequent in January (even when sales are excluded); (iv) sales contribute significantly to the volatility of inflation but play a minor role in the transmission of macroeconomic fluctuations to prices; and (v) during the Great Recession patterns of price adjustment were only slightly modified.

business cycles. Over the past decade, a number of empirical studies have provided evidence on microprice rigidity for more than 50 countries. Using price quotes collected for the Consumer Price Index (CPI) calculation, seminal studies by [START_REF] Bils | Some Evidence on the Importance of Sticky Prices[END_REF], [START_REF] Klenow | State-Dependent or Time-Dependent Pricing: Does It Matter for Recent US Inflation?[END_REF], and [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF] characterize price rigidity for the United States whereas [START_REF] Dhyne | Price Changes in the Euro Area and the United States: Some Facts from Individual Consumer Price Data[END_REF] summarize European evidence. 1 A recent strand of the U.S. literature has emphasized the relevance of a new set of patterns, such as the shape of the distribution of price changes (in particular its fat tails and the large proportion of small price changes) and the role played by sales and product substitutions in the United States. These patterns have important consequences for the real effects of monetary policy; see, for instance, [START_REF] Kehoe | Prices Are Sticky After All[END_REF] or Nakamura and Steinsson (2010a) for sales, and [START_REF] Costain | Price Adjustments in a General Model of State-Dependent Pricing[END_REF], [START_REF] Golosov | Menu Costs and Phillips Curves[END_REF], or [START_REF] Midrigan | Menu Costs, Multi-Product Firms, and Aggregate Fluctuations[END_REF] for the distribution of price changes. Our paper adds to the literature on price rigidity along three dimensions. First, we provide new facts on patterns of price rigidity that so far have been little documented for European countries, in particular, the impact of sales and product replacements on price rigidity indicators. Second, we provide a detailed comparison of the degree of price rigidity between France and the United States. Finally, we document the impact of the Great Recession on price-setting behavior.

For that purpose, we use a new release of CPI price quotes collected in France. Our data set consists of more than 11 million monthly price quotes collected by the national statistical office in order to compute the French CPI, spanning the period from April 2003 to April 2011. This sample allows to extend the evidence with respect to a study by [START_REF] Baudry | What Do Thirteen Million Price Records Have to Say about Consumer Price Rigidity?[END_REF] covering the period July 1994 to February 2003. Prices are collected for more than 700,000 individual products identified at the outlet level. The sample contains prices for more than 3,500 types of goods and services, allowing the construction of indicators of price rigidity that are representative of the nonfarm business economy.

Our first contribution is to provide new findings on price rigidity, with an emphasis on the influence of sales and product substitution-related price changes. Sales were shown to have strong implications for price rigidity in the United States-see, for instance, [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF]. Moreover, a growing recent literature examines the determinants of sales in the United States and their aggregate implications [START_REF] Kehoe | Prices Are Sticky After All[END_REF][START_REF] Guimaraes | Sales and Monetary Policy[END_REF][START_REF] Anderson | Informational Rigidities and the Stickiness of Temporary Sales[END_REF][START_REF] Kryvtsov | On the Importance of Sales for Aggregate Price Flexibility[END_REF][START_REF] Coibion | The Cyclicality of Sales, Regular, and Effective Prices: Business Cycle and Policy Implications[END_REF]. However, little evidence has been made available for European countries. 2 We find that the frequency of price changes when we exclude sales is 17.4%, versus 20.1% when they are included. We also find that aggregate inflation has a smaller impact on price changes associated with sales than on regular price changes; more generally sales play a minor role in the transmission of macroeconomic fluctuations to prices. Considering the distribution of price changes, excluding sales leads to smaller average absolute size; for example, the average price increase is 7.9% versus 12.8%. Following [START_REF] Klenow | State-Dependent or Time-Dependent Pricing: Does It Matter for Recent US Inflation?[END_REF], we also decompose the monthly fluctuations of inflation into an extensive margin (frequency of price changes) and an intensive margin (size of price changes); a substantial fraction of inflation volatility at the monthly frequency is due to sales. When sales are excluded, the frequencies of price increases and decreases are the most important contributions to inflation. In particular, when we exclude sales and promotional discounts, there is still a peak in inflation in January; this peak is mostly explained by an increase in the frequency of price increases (especially in services).

The importance of product substitutions has been stressed in a recent contribution by [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF], who argue that product replacements provide an opportunity for changing prices. Our baseline price rigidity indicators assume that price changes observed at the time of product substitutions are genuine price changes. Incorporating product substitution-related price changes contributes positively to the frequency and the average absolute size of price changes: the frequency, equal to 20.1% in the baseline data set, drops to 17.7% when disregarding substitutions. The average absolute size is 8.9% without substitutions versus 12.1% when including them. Overall, substitutions have a positive impact on average monthly inflation rate, and are needed to match the average inflation rate, although they only slightly contribute to the fluctuations of inflation.

Our second contribution is to run a detailed comparison of the degree of price rigidity between France and the United States. We construct a bridge table to match European and U.S. classifications of products, we identify products that are available in both French and U.S. microprice data sets, and we control for differences in CPI weight structures between France and the United States. On the common sample of products, when sales are included, the frequency of price changes is higher in the United States (24.1%) than in France (20.1%). However, when sales are excluded, the difference vanishes: 17.4% of prices change in France versus 17.1% in the United States. Similarly, the average size of price changes is larger in the United States than in France (14.9% versus 10.0% for price increases and -18.5% versus -13.4% for price decreases) but when sales are excluded the difference drops substantially: the average size of price increases (respectively decreases) is about 6% (respectively -9%) in France versus 9% (respectively -12%) in the United States.

Our last contribution is to document microprice setting behavior during the Great Recession. Most existing empirical results on price rigidity were obtained on data collected in the 90s or in this first years of 2000s, a period of stable GDP growth and inflation in Europe and in the United States. However, patterns of price rigidity may be different in a more unstable economic environment. 3 During the 2008-09 Great 3. [START_REF] Gagnon | Price Setting during Low and High Inflation: Evidence from Mexico[END_REF] on Mexican data during the peso devaluation or [START_REF] Wulfsberg | Inflation and Price Adjustment: Evidence from Norwegian Consumer Price Data 1975-2004[END_REF] on Norwegian data during the 70s provide evidence on price-setting features in unstable economic environments.

Recession, GDP growth dramatically decreased whereas inflation variations were mainly due to increasing then decreasing energy prices and core inflation remained rather stable (ECB 2012). To our knowledge, little is known about microprice setting features during that period especially in European countries. 4 We find that business cycle conditions affect price dynamics through variations in the probability of price increase and decrease rather than through variations in the size of price change. However, we also show that the specific effect of the Great Recession was small but positive on the frequency of price decreases and negative on the absolute size of price changes. We also find that the variance of price increases increased somewhat during the Great Recession, which may reflect the larger variance of economic shocks.

The paper is organized as follows. A description of the data is provided in Section 1. Section 2 provides cross-sectional evidence on the frequency and size of price changes. We also document the influence on price rigidity of removing sales, and of considering product substitutions as ends of price trajectories or not. We then analyze the patterns of the distribution of price changes. We compare our findings with U.S. results. Section 3 presents time-series evidence on the frequency and size of price changes and investigates the impact of the Great Recession on price rigidity indicators. We also explore the impact of sales and product substitution on the fluctuations of the monthly inflation rate. Finally, we provide detailed evidence on the seasonality of price changes and the contribution of sales to this seasonality. Section 4 concludes by summarizing our main results and discussing some of their macroeconomic implications.

DATA

The data consist of a longitudinal data set of monthly price quotes, and some additional information, collected by the Institut National de la Statistique et des Études Économiques (INSEE) in order to compute the French CPI. 5

Price Quotes

The sample contains monthly CPI records from April 2003 to April 2011 and each record is related to a precisely defined product sold in a particular outlet. The raw data set contains more than 11 million price quotes and covers about 65% of the CPI weights. 6 Those data contain prices for more than 3,500 goods and services, sold in more than 30,000 outlets in more than 100 locations. The large coverage of our data set allows us to calculate indicators of price rigidity that are representative of the 4. [START_REF] Berger | Dynamics of the U.S. Price Distribution[END_REF] and [START_REF] Dixon | The Impact of the 2008 Crisis on UK Prices: What We Can Learn from the CPI Microdata[END_REF] document some findings on price distributions during recessions in the United States and the United Kingdom, respectively.

5. The methodology of data collection is described in [START_REF] Caillaud | Pour comprendre l'indice des prix[END_REF], and also in [START_REF] Lequiller | L'indice des prix à la consommation surestime-t-il l'inflation?[END_REF]. 6. Some categories of goods and services are not available in our sample: centrally collected prices, among which car prices and administered prices (e.g., tobacco) or public utility prices (e.g., electricity), as well as other types of products such as fresh food or rents. nonfarm business economy. We aggregate product categories into four sectors: food, manufacturing goods (durables, clothing, and other manufacturing goods), energy, and services.

To extend the sample in our time-series exercises, and for comparison purposes, we also rely on results from an earlier data set, analyzed in [START_REF] Baudry | What Do Thirteen Million Price Records Have to Say about Consumer Price Rigidity?[END_REF], spanning from July 1994 to February 2003. However, because that earlier data set contains less information on product substitutions and the two data sets do not overlap, we are not able to pool the two data sets for our baseline microlevel analysis.

For each individual price quote (i.e., the exact price level of the product) the year and month of the record, as well as the type of price record (e.g., sale price), are reported. It is possible to track the price variation of an individual product (i.e., a particular product of a particular brand and quality, sold in a particular outlet) using a single identification number. The sequence of records corresponding to one individual product is called price trajectory. The individual products are characterized by the packaging quantity, 7 the category of product, the outlet where it is sold, and its type (e.g., supermarket, traditional store). In our basic analysis, price changes are computed as regular percentage changes, in order to better capture "psychological" price changes such as -50%. However, when time-series decompositions, econometric analysis, or comparison with other studies are involved, we compute price changes as log-difference in prices.

Outliers and imputed prices raise some concerns in the data set. We defined as outliers price change observations involving upward or downward changes by a factor larger than 5, and trimmed them from the data. In case of missing prices, the INSEE imputes prices, typically by carrying forward the last nonimputed price change. An important particular case is that of out-of-season items. We have removed those imputed observations from our baseline data set (details are available in the online appendix Table A).

To produce aggregate measures of the frequency or size of price changes, we compute all statistics using CPI weights. Products categories (five-digit COICOP level) are the lowest level for which these CPI weights are available to us. There are close to 300 product categories in the data set. Although available CPI weights are not defined at the store/product level, the statistical office designs the list of outlets present in the sample to be representative in terms of market shares. Moreover, weights of CPI categories change every year. To control for possible changes in the composition of the CPI over time, we use average weights of CPI categories over the sample period. Our benchmark procedure for computing aggregate statistics from individual observations is as follows. The weight of an individual observation is set equal to the average weight of the CPI category over the period 2003-11 (with weight set to zero at times when a product is not included in the CPI basket), divided by the number of observations in the category. This procedure gives the same importance in aggregation to all items belonging to the same category. For robustness purposes, 7. When relevant, we divide prices by the indicator of quantity sold in order to recover a consistent price per unit.

we have also replicated our analysis, using the actual time-varying CPI weights, and results were not significantly altered.

Sales and Promotional Discounts

Our data set contains a variable that identifies whether a price corresponds to a sale price, either in the form of seasonal sales or temporary promotional discounts. 8 These two kinds of sales are different in France and are regulated (contrary to the United States, United Kingdom, or Germany). Seasonal sales are limited to specific time periods and the timing of seasonal sales periods is administered. Before 2009, seasonal sales were allowed twice a year for a 6-week period each. With very small variations across years, the "winter sales" period covers from beginning of January to mid-February, and the "summer sales" period covers from end of June to end of July. From 2009 a new law, Loi de Modernisation de l' Économie (LME), slightly modified the regulation on sales. The durations of fixed periods of sales was reduced from 6 to 5 weeks and a flexible period of sales (2 weeks or two periods of 1 week), which can be freely set by stores, was introduced. During seasonal sales, outlets are allowed to sell below cost. Contrary to seasonal sales, temporary promotional discounts are allowed at any time during the year but the seller cannot sell its product below cost and must deliver the discounted product during all the promotion period. To compute our price rigidity indicators, we consider two alternative assumptions. First, we include sales-related price changes, using all price records. Second, following [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF], we exclude sales-related price changes: we consider that a price quote flagged by INSEE as "seasonal sales" or "promotional discounts" corresponds to a temporary price adjustment possibly irrelevant for macroanalysis purpose, so that we replace the price by the last nonsale price. Thus, to compute price rigidity statistics without sales, we exclude any price decrease implied by sales, as well as the subsequent price increase that generally follows. In the remaining of the paper, we denote by "regular price" any nonsale price observation. A potential concern is that the INSEE flag identifying sales might be subject to measurement error, for example, because sales were not sufficiently visible within the outlet. To address this, as a robustness check we implement several "sales filters" that automatically identify temporary price changes, in the vein of inter alia [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF]. The filters are described in the online appendix.

Product Substitutions

Product substitution is an important concern in the analysis of microprice data. The statistical agency may stop recording the price of a given product in a given outlet, either because the product is no longer sold by the outlet or, more rarely, because the outlet itself closes (attrition/forced replacement), or because the statistical office 8. Field agents are instructed to flag a price as a seasonal sale or a temporary promotional discount if this is indicated next to the price when it is collected. may decide to discard a product or an outlet in order to keep the sample of items representative of the structure of consumption (voluntary replacement). In our data set, when a given product in an outlet is permanently substituted by a similar one of another brand or of a different quality the substitution is tagged. When product substitution occurs, identifying price changes rely on assumptions. Three different possible assumptions on product replacements, differing in their consequence for price trajectories, can be made. 9 The first possibility is to consider that a new price trajectory starts with product substitution. Under this assumption, we simply discard from the sample the price change observation corresponding to product replacement. This simple approach has typically been followed in European empirical studies on price rigidity (e.g., [START_REF] Dhyne | Price Changes in the Euro Area and the United States: Some Facts from Individual Consumer Price Data[END_REF]. Alternative assumptions may however be relevant to characterize the implied price dynamics. In second and third cases, the price trajectory is assumed to continue at the time of product substitution, respectively, not taking and taking into account the potential quality adjustment. A key feature of our data is that we do know which product substitutes the old one and, when relevant, the coefficient of quality adjustment. 10 The implications of assuming that a price trajectory continues despite product replacement are particularly relevant in the analysis of some sectors where substitutions are frequent, such as clothing and durable goods. Following [START_REF] Klenow | State-Dependent or Time-Dependent Pricing: Does It Matter for Recent US Inflation?[END_REF], in our baseline analysis we consider that price trajectories continue after a product substitution, a case we refer to as "including product substitutions." Reasons for choosing this assumption as the baseline are twofold. First, forced substitution actually resembles pure and simple price changes. While we cannot distinguish between forced and voluntary substitutions, forced substitutions are likely much more common, as price collectors should diligently try to compare the same product and the consumption structure is slowly moving. Second, as will be documented below, including substitutionrelated price changes is necessary in order to match the aggregate inflation rate. For completeness purposes, we however report, as robustness checks, results assuming that price trajectories are stopped by a product substitution, a case we refer to as "excluding product substitutions." 11

Comparing France and the United States

One aim of this paper is to compare the average frequency and size of price changes in France to those in the United States, controlling for possible differences in the coverage of products between French and U.S. micro data sets and for differences in the weighting structure of both price indices. We here use the detailed results obtained by [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF] on the frequency of price changes, increases and decreases (including or not sales and including or not substitutions), 9. See Figure A in the online appendix for an illustration. 10. [START_REF] Baudry | What Do Thirteen Million Price Records Have to Say about Consumer Price Rigidity?[END_REF] consider product replacements as price changes, but they do not observe the new product that substitutes the old one. In particular, in the instance of product substitution they cannot infer whether the implicit price change is an increase or a decrease.

11. For further details on data treatment, see also the online appendix.

and on the average size of log-price increases and decreases calculated at the product level for the period 1998-2005. 12 The product classification used to compute the CPI used in Europe, the Classification of Individual Consumption According to Purpose (COICOP), differs from the one used in the United States, the Entry Level Item (ELI). 13 For France, we have information for products at level 5 of the COICOP (resulting in 304 products), while for the United States, [START_REF] Nakamura | More Facts about Prices Supplement to: Five Facts about Prices: A Reevaluation of Menu Cost Models[END_REF]

CROSS-SECTIONAL EVIDENCE ON PRICE ADJUSTMENT

Price rigidity is often approximated in macroeconomic models by the frequency of price changes. In this section, we present new results for France on the frequency and size of price changes, giving special attention to the sensitivity of results to assumptions regarding sales and product substitutions. Moreover, we provide new facts on the distribution of price changes. We compare our findings to recent U.S. results obtained on CPI price data.

Frequency of Price Changes

Table 1 provides the main statistics on the frequency of price changes and comparisons with findings from the United States, as reported by Nakamura and Steinsson 12. Tables 20 and 22 in [START_REF] Nakamura | More Facts about Prices Supplement to: Five Facts about Prices: A Reevaluation of Menu Cost Models[END_REF] supplementary material. 13. See, for instance, [START_REF] Lane | Comparing US and European Inflation: The CPI and the HICP[END_REF] for a discussion of the difference between U.S. and European CPI.

14. The bridge table is available upon request. 15. One main source of the discrepancy between French and U.S. coverage is shelter. Shelter is available neither in the U.S. data set used by [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF] nor in our French data set, but this has a lower impact on French CPI coverage, because the "owner-occupied" part of shelter is not included in scope of the French CPI. NOTES: Frequency of price changes is the weighted proportion of price changes on all price records; Median frequency of price changes is calculated as the weighted median of product average frequencies of price changes; % of seasonal sales is the weighted proportion of regulated sales among all observations; % of promotional discounts is the weighted proportion of promotional discounts (excluding seasonal sales) among all observations; % of product substitutions is the weighted proportion of product replacements among all price records; U.S. results are from Nakamura andSteinsson (2008, 2010b). In columns "U.S. weights," we compute aggregate frequencies of price changes using product-level frequencies for products available in United States and French data set and using the U.S. weight structure. (2008). We first focus on our baseline case, which is "including substitutions and sales" (i.e., when both price changes related to product replacements and those related to sales are included). The average monthly frequency of price changes in France is 20.1% over the period 2003-11, and the average implied price duration is about 9 months 16 while the median is close to 6 months. Consumer prices appear much more flexible in the United States since [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF] find that the frequency of price changes is 27.7% over the period 1998-2005. However, when restricting to the sample of products available in both data sets, and using the U.S. weight structure, the difference is smaller: each month, 20.1% of prices change in France versus 24.1% in the United States. Products whose prices are modified quite frequently like fresh food, cars, or electricity are not available in the French data set, which explains at least partly this smaller difference in the frequencies of price changes. The proportion of price increases among all price changes is close to 60% in France versus about 55% in the United States. 17

16. The mean implied duration is calculated averaging the inverse of price change frequency at product level. Note that the inverse mean frequency is not equal to the mean inverse frequency (i.e., average implied price duration) when there is heterogeneity in the frequency of price changes across products. 17. The U.S. figure here was computed in the "excluding substitutions" case, following information available in [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF]. NOTES: Frequency of price changes is the weighted proportion of price changes on all price records (including substitutions); % of seasonal sales is the weighted proportion of regulated sales among all observations; % of promotional discounts is the weighted proportion of promotional discounts (excluding seasonal sales) among all observations; % of product substitutions is the weighted proportion of product replacements among all price records.

One important pattern of price rigidity is the large degree of sectoral heterogeneity. 18 Table 2 shows the frequency of price changes for the four major sectors of products we consider. Prices in the energy sector are modified very often (77.1% on average each month) whereas the frequency of price changes for manufactured goods or food are close to 20%. The frequency of price changes is the lowest for services (8.2%). The proportion of price increases is close to 60% in food, other manufacturing goods, and energy sectors, whereas it is lower for durables and clothing (around 50%). In services, price decreases are rare: price increases amount to 77.6% of price changes. Similar findings were obtained for the United States [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF].

Many empirical studies emphasize that sales are common in the United States. A widespread conjecture is that the extent of sales is an important factor behind the differential in price flexibility between the United States and Europe. We now document some basic facts on the frequency of sales in France and their impact on the frequency of price changes. About 2.5% of price quotes are flagged by INSEE as sales or promotional discounts: the proportion of seasonal sales among price records is 0.7% and the proportion of temporary promotional discounts amounts to 1.7% (Table 1). Sales are much less frequent in France than in the United States: [START_REF] Klenow | State-Dependent or Time-Dependent Pricing: Does It Matter for Recent US Inflation?[END_REF] find that about 11% of price records are sales and [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF] find 7.4%. Sales concentrate in some sectors (Table 2): about 10% of price quotes in the clothing sector are promotional discounts or seasonal sales and 6% in durables whereas almost no price quotes are sales in energy or services. This sectoral heterogeneity is very similar to that found in the United States (even if the proportion of price quotes concerned by sales is much larger in the United States). If we disregard sales-related prices (i.e., when replacing any price flagged as 18. A recent macroeconomic literature shows the relevance of sectoral heterogeneity in the frequency of price changes for the real effects of monetary policy (see, e.g., [START_REF] Carvalho | Heterogeneity in Price Stickiness and the Real Effects of Monetary Shocks[END_REF]. sales or promotional discounts by the last previous "regular" price), the frequency of price changes is much lower than when sales are included (17.4% versus 20.1%), and the proportion of price increases is a little larger, from 60.2% to 62.3%. We investigated the robustness of these numbers to the procedure used to detect sales by using "V-shape" sales filters (results are available in the online appendix Table B). Results are broadly similar. 19 In the United States, [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF] find that excluding sales decreases the frequency of price changes by almost 5 percentage points from 26.5% to 21.1%, so that removing sales delivers closer figures for France and the United States. Moreover, when we restrict to products available in both data sets and use the U.S. weight structure, the difference between the United States and France vanishes: the frequency of price changes is 17.4% in France and 17.1% in the United States. 20 Nakamura and Steinsson ( 2012) recently illustrate the role played by product substitutions in price dynamics and their macroeconomic effects. 21 We now investigate the effect of product substitution on the measurement of the frequency of price changes, recalling that in our baseline analysis we include price changes related to product substitutions. In France, about 4.1% of nonimputed price quotes correspond to a product substitution (Table 1). A similar figure is obtained on U.S. CPI data: 3% and 3.4% of price quotes are product replacements according to, respectively, [START_REF] Klenow | State-Dependent or Time-Dependent Pricing: Does It Matter for Recent US Inflation?[END_REF] and [START_REF] Bils | Some Evidence on the Importance of Sticky Prices[END_REF]. Disregarding price adjustments associated with product substitutions significantly alters the characteristics of price dynamics. The frequency of price change drops by about 2.5 percentage points, from 20.1% to 17.7%. Whether or not we consider the INSEE correction for quality adjustment in the cases of substitution affects only marginally the frequency of price change. Our results are consistent with what is found on U.S. data: considering price changes at product substitution increases the frequency of price changes by 1 to 2.5 percentage points: from 26.5% to 27.7% for [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF] and from 23.6% to 26.1% for [START_REF] Bils | Some Evidence on the Importance of Sticky Prices[END_REF]. 22 The incidence of product substitution is strongly heterogeneous across products and especially widespread in the manufacturing industry (Table 2). In particular, about 10% of clothing and durables price records are product replacements. Comparable findings are obtained by 19. The frequency of price changes on sales-filtered data is smaller by 1 to 2 percentage points; the additional temporary price changes detected by the filters tend to be small (as reported in Figure B in the online appendix), pointing to measurement errors rather than genuine sales. 20. As robustness checks, we run the same comparison excluding observations between 2008 and 2011 for France (when inflation varies more) and also excluding energy prices for both countries. We also compute the frequency and size of price changes for France over the period 1998-2005 using numbers coming from [START_REF] Baudry | What Do Thirteen Million Price Records Have to Say about Consumer Price Rigidity?[END_REF] but excluding substitutions. We obtain similar results. See Table E in the online appendix.

21. Nakamura and Steinsson (2010a) suggest that the cost of price adjustment is low at product replacement; a firm may then wait for a predetermined product substitution to change its price.

22. [START_REF] Baudry | Price Rigidity Evidence from the French CPI Micro-Data[END_REF] find that when product replacements are included, the frequency of price changes increases from 16.2% to 18.9%; however, they consider that all product replacements are price changes (because the new product was not observable), whereas price changes are actually not systematic when products are replaced. [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF] on U.S. data. On the other hand, for food, services, or energy, the substitution rates are much lower (close to or less than 2% in our data).

The Distribution of Price Changes

The recent macroeconomic literature on price rigidity emphasizes some important features on the distribution of price changes: the average price changes are quite large; small price changes are frequent, as are large ones [START_REF] Klenow | Microeconomic Evidence on Price-Setting[END_REF]. Those empirical results have spurred some theoretical models of price rigidity-see, for instance, [START_REF] Costain | Price Adjustments in a General Model of State-Dependent Pricing[END_REF], [START_REF] Golosov | Menu Costs and Phillips Curves[END_REF], [START_REF] Klenow | State-Dependent or Time-Dependent Pricing: Does It Matter for Recent US Inflation?[END_REF], or [START_REF] Midrigan | Menu Costs, Multi-Product Firms, and Aggregate Fluctuations[END_REF]. We provide here new stylized facts on the distribution of price changes in France and compare them to U.S. results.

Table 3 reports our basic findings on the size of price changes. The average size of price changes is rather large: 12.8% for price increases and -11.5% for price decreases, while the median is much smaller: 4.3% for price increases and -6.1% for price decreases.

Table 4 provides a comparison of France and the United States. To enhance comparability, we restrict to the common sample of products and provide summary statistics following the same approach as [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF]: we compute the average size of log-price changes by product, then we compute (using product weights) the aggregate average price increase and decrease. We find that the average size of price changes in absolute value is lower in France than in the United States: a little more than 10% in France versus more than 15% in the United States. Overall, price changes are more frequent and larger in the United States compared to France. As stressed by earlier studies, the average size of price changes is large compared to the typical inflation rate, suggesting price changes do not simply correspond to indexation to inflation, but incorporate idiosyncratic shocks with large variance. Table 5 reports results on the sectoral heterogeneity of the size of price changes. The sectoral heterogeneity of the size of price changes is substantial. In the manufacturing sector, the average absolute size of price changes lies between 10% and more than 15%. On the contrary, in the energy and food sectors, the average absolute price change is much smaller (respectively, close to 4% and 6.5% in absolute values). For services, the size of price changes is about 10% in absolute values.

Two important and related facts are pointed out by the recent U.S. empirical literature on price rigidity, including [START_REF] Eichenbaum | How Frequent Are Small Price Changes?[END_REF], Klenow and Kryvtsov FIG. 1. Distribution of Nonzero Price Changes. NOTES: Individual sizes of price changes are here calculated in percentage, only nonzero price changes are considered, and product substitutions are considered as price changes; the distribution is weighted using CPI disaggregated weights on the period 2003-11. Gray histogram: price changes related to sales are included. Black solid line: price changes related to sales are excluded (using INSEE sales flag). ( 2008), or [START_REF] Midrigan | Menu Costs, Multi-Product Firms, and Aggregate Fluctuations[END_REF]: the distribution of price changes has fat tails (i.e., large price changes are quite frequent) and the proportion of small price changes is large. We now provide related results on the distribution of price changes for France. 23 Figure 1 plots the weighted (nonstandardized) distribution of all nonzero price changes. The distribution has a mode between 1% and 3%. The distribution has a "hole," with relatively few price changes between 0% and 1%, and a smaller mode 23. Focusing on the kurtosis of price changes, Alvarez, Le [START_REF] Alvarez | Sticky Prices, Menu Costs and the Effect of Monetary Shocks: Theory and Micro-Evidence[END_REF] document in detail these patterns on the same data set and investigate their macroeconomic consequences. at price changes around -1%. Therefore, there is a slight asymmetry in the central part of the distribution. Finally, the distribution of price changes has noticeable peaks at large price increases and decreases reflecting "attractive" price changes related to sales, such as -20%, -30%, -40%, -50%, and 25%, 33%, and 50%. These spikes to a large extent disappear when considering the distribution of nonsale price changes, also reported in Figure 1.

Tables 3 and5 also report statistics on the distribution of price changes. The proportion of small prices is quite large in France: 11.2% of price changes in absolute values are below 1% and around 23% of price changes are below 2%. By comparison, [START_REF] Klenow | State-Dependent or Time-Dependent Pricing: Does It Matter for Recent US Inflation?[END_REF] on U.S. price data find that 25% of price changes are below 2.5% in absolute values and [START_REF] Vermeulen | Price Setting in the Euro Area: Some Stylised Facts from Individual Producer Price Data[END_REF] find that a quarter of price increases and decreases in absolute values are smaller than 1.5% on producer prices. [START_REF] Eichenbaum | How Frequent Are Small Price Changes?[END_REF] recently challenge this result for the United States. They argue that for a number of specific products such as cigarettes, gas services, electricity, telephone services, or new cars, measurement errors occur because prices are computed as unit value indices, or include taxes, or pertain to a bundle of goods. They show that when these products are excluded the proportion of price changes lower than 1% is less than 5%. However, most of those problematic products are not available in the data set we use (in particular, telephone services, electricity, gas, new cars, or cigarettes). Furthermore, the items that remain in the data set are arguably all single-good transaction prices. We acknowledge however that some small price changes may be spurious, reflecting genuine measurement errors: evidence of this is given by the temporary small price changes detected by statistical filter (see Figure B in the online appendix). However, even excluding these statistically detected transitory price changes does not alter our conclusion on the pervasiveness of small price changes. The abundance of small price changes is at odds with the predictions of simple models of price rigidity, in which small price changes are predicted to be rare. However, small price changes are more frequent in some specific sectors (in particular, in energy,24 food, and other manufacturing goods).

Large price changes are also common: the upper quartile of the distribution is 10.9% for price increases and 16.1% in absolute value for price decreases (Table 3). [START_REF] Golosov | Menu Costs and Phillips Curves[END_REF] and [START_REF] Midrigan | Menu Costs, Multi-Product Firms, and Aggregate Fluctuations[END_REF] show that the extent of large price changes cannot be explained within a simple menu cost model, and suggest that this likely reflects the existence of large idiosyncratic shocks. Large price changes are more frequent in durables and the clothing sector whereas in energy, services, and other manufacturing goods the distribution of price changes is less dispersed (Table 5).

The size of price changes is typically larger, in absolute value, during sales. The average size of price decreases during sales is about -25% (versus -10% overall) (results on size of sales price change are available in the online appendix Table J). This is in line with [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF] who find a median size of price change of 29.5% in absolute value. Price decreases during "seasonal sales" are deeper than those during "promotional discounts" (about -35% versus -20% on average). Sales have a prominent contribution to the average size of price changes (Table 3). When we consider only nonsales prices, the average size of price changes in absolute value is about 8%, versus about 12% when including sales. 25 To compare French and U.S. results, we compute over the common sample of products the average size of log-price changes in both countries excluding sales (Table 4). The average size of price increases is 6.0% in France versus 9.2% in the United States, whereas for price decreases the average price change is -9.0% in France and -12.0% in the United States. As in the case of frequencies, sales contribute a lot to the difference in the average size of price changes between France and the United States. The dispersion of the price change distribution excluding sales is smaller than when sales are included since the number of large price increases and decreases drops substantially when excluding sales (the 75th percentile of price decreases is -10.0% versus -16.1% including sales). The exclusion of sales substantially reduces the sectoral heterogeneity in the size of price changes (Table 5).

We now briefly discuss the influence of including price changes related to product substitutions on the assessment of price change size. The average price increases and decreases are smaller in absolute value when substitution-related price changes are not considered. In particular, the average size of price increases is lower by around 4 percentage points (8.9% versus 12.8%) when replacements are excluded (the online appendix Table I provides detailed results). For retailers, product replacement seem to appear as an opportunity to increase prices. As a result, including substitutions is crucial for matching the aggregate inflation rate. These findings are qualitatively similar to those available for the United States.

TIME-SERIES EVIDENCE ON PRICE ADJUSTMENT

Inflation results from the aggregation of individual price adjustment behaviors: inflation may increase because more firms change their prices (the extensive margin) or because firms change their prices by a larger amount (the intensive margin). We here investigate how these two dimensions of individual behavior of price adjustment contribute to inflation dynamics over time. We also analyze how individual price changes themselves respond to aggregate inflation and business cycle conditions. In particular, we investigate the stability of price adjustment behavior during the 2008-09 Great Recession. Finally, we document the impact of sales and substitutions on inflation.

25. Results are robust to using V-shaped sales filters; see the online appendix Table C. we compute for all products, the average and the standard deviation of the monthly inflation rates and the coefficient of correlation between our recomposed inflation rate and the actual inflation rate at the product level. Finally, we compute the weighted median of average inflation, the weighted median of standard deviation, and the weighted median of correlation coefficient across all 134 products.

Decomposing Inflation Variations

Following [START_REF] Klenow | State-Dependent or Time-Dependent Pricing: Does It Matter for Recent US Inflation?[END_REF], we decompose the inflation rate into an extensive margin (the frequency of price changes) and an intensive margin (the mean size of price changes). The inflation rate can be written as the product of the frequency of price changes by the average size of price changes:

π t = F t • dp t , (1)
where π t is the approximation of the weighted monthly inflation rate using our microdata, F t is the weighted monthly frequency of price changes, and dp t is the weighted average size of all nonzero price changes (defined as the first differences of log-prices between months t and t -1). This approximation can be further decomposed by considering separately price increases and price decreases:

π t = F + t • dp + t + F - t • dp - t , (2)
where F + t and F - t are, respectively, the frequency of price increases and the frequency of price decreases, and dp + t and dp - t are the average size of price increases and the average size of price decreases.

We first check the quality of our approximation. Table 6 reports some summary statistics on the approximated inflation rates computed at the product level (including or not sales and substitutions) and it compares those statistics with moments of the actual inflation rates. 26 When sales and product replacements are included, the median correlation between our recomposed monthly inflation rates and the monthly inflation rates published by INSEE (excluding energy) is fairly large (0.826). The median correlation is lower when sales are excluded (0.70), reflecting that sales are included 26. Price indices at a disaggregated level are only available from INSEE at level 4 of the COICOP classification (134 products).

in INSEE price indices. When sales are included, the median of average monthly recomposed inflation rates is close to the median of average inflation rates (0.185 versus 0.170 in INSEE data), and the median standard deviation of inflation matches the one found in INSEE data (0.454 versus 0.460). When we remove sales-related price changes from the data, the average recomposed inflation rate is unchanged. Indeed sales-related price changes include price increases after the sales episodes, which tend to offset price decreases at the time of the sales (Table J in the online appendix provides detailed results). At the same time, the volatility of the inflation rate is much lower when excluding sales: 0.366 versus 0.454 (Table 6). When discarding substitutions, the average and the volatility of the approximate inflation rate are lower than the average and volatility of the actual inflation rate.

We then investigate the relative contribution of the frequencies and the sizes of price changes to the French aggregate monthly inflation rate. 27 For that, we consider deviations of inflation π t from its average over time π and we write the inflation rate as

π t = π t + π.
(3)

We then consider deviations of frequencies and sizes of price changes from their averages over time:

π t + π = F + + F + t • dp + + dp + t + F -+ F - t • dp -+ dp - t . (4)
Rearranging terms, it is possible to single out the contributions of the frequency and the size of price changes to the variations of the monthly inflation rate:

π t = F + t • dp + + F - t • dp - f requency contribution + F + • dp + t + F -• dp - t si ze contribution + F + t • dp + t + F - t • dp - t residual .
(5)

We compute the terms of this decomposition using our data set of individual price quotes excluding energy and including substitution-related price changes. We consider both the cases including and excluding sales.

Table 7 reports the correlations between monthly inflation and the frequency and size of price changes as well as the estimated parameters from OLS regressions of inflation on the frequency and size of price changes. The monthly inflation rate is positively associated with the average size of price increases and decreases: correlation coefficients are above 0.50 in each case. Correlation of aggregate inflation with 27. We here compute the approximation from aggregate time series of frequencies and sizes of price increases and decreases. This implies matching the volatility of aggregate inflation less accurately, but the correlation with headline aggregate inflation is still very high (about 0.8). We recompose monthly inflation rates using all individual price quotes (excluding energy) and under different hypotheses on sales (including substitutions). We compute the correlation coefficients between the recomposed monthly inflation rate and the frequency/size of price changes/increases/decreases (columns 1 and 3). We also report the results of two OLS regressions: (i) we regress recomposed monthly inflation on the frequency and size of price changes, and (ii) we regress recomposed monthly inflation on the frequency and size of price increases and decreases. Size of price changes are here calculated as the weighted average of log differences. The p-values are in parentheses.

the frequency of price increases is noticeably lower. Figure 2 shows the contributions of frequencies of price increases and decreases (black solid line) and those of the size of price increases and decreases (black dashed line) to monthly inflation deviations from its average (gray solid line). Inflation variations are mostly explained by the size contribution, while the contribution of the extensive margin is lower. The large contribution of the intensive margin to inflation variations at the monthly frequency seems mostly driven by large movements in the size of price changes due to seasonal sales. Indeed, considering inflation excluding sales results in a higher correlation with the frequency of price changes: 0.56. This correlation stems from a large positive correlation with the frequency of price increases (0.76) and to a lower extent from the negative correlation with the frequency of price decreases (-0.20). The larger correlation with the frequency of price increases can be explained by a positive inflation trend, which makes the distribution of relative prices asymmetric. When excluding sales, the correlation between inflation and size of price increases or decreases is smaller. Moving to our simple OLS regression estimates, we find that a one-standard-deviation shock on the frequency of price increases raises the monthly inflation rate by 0.13 percentage point whereas a similar shock on the size of price increases has a smaller impact (0.02 percentage point). [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF] obtain similar results on U.S. data. Figure 3 plots the contributions of the frequency and size of price changes when sales are excluded. Contrasting with Figure 2, the contribution of the frequency of price increases and decreases (black solid line) to inflation fluctuations is much larger than the contribution of sizes (black dashed line). Moreover, Figure 3 shows that the January effect is still present even when NOTES: Gray solid line: deviations of the monthly rate of inflation from its average over time (excluding energy), product replacements, and sales included. Black solid line: contribution of the frequencies of price increases and of price decreases to the deviations of monthly inflation over time. Black dashed line: contribution of the average sizes of price increases and of price decreases to the deviations of monthly inflation over time.

sales are excluded: in January, the peak in the frequency of price increases has a clear positive effect on the monthly inflation rate (gray solid line).

Finally, we find that, unlike sales, substitutions play a limited role to account for fluctuations in inflation over time (Figure C in the online appendix), although incorporating substitution-related price changes is crucial to match the average aggregate inflation rate. That last feature reflects the typical life cycle for some products: after NOTES: Gray solid line: deviations of the monthly rate of inflation from its average over time (excluding energy), product replacements are included and sales are excluded. Black solid line: contribution of the frequencies of price increases and of price decreases (excluding sales) to the deviations of monthly inflation over time. Black dashed line: contribution of the average sizes of price increases and of price decreases (excluding sales) to the deviations of monthly inflation over time.

being discontinued, a product is typically replaced by a new one with a price often larger than the previous "regular price" of the replaced item.

The Seasonality of Price Changes

The decomposition of inflation variations shows the relevance of seasonal movements in the monthly inflation rate. Olivei andTenreyro (2007, 2010) find that the seasonality of wage setting patterns may have an impact on the effects of the monetary policy. We now further document the seasonality of the frequency and size price of changes and assess the contribution of sales and substitutions to this seasonality.

Figure 4 plots the average frequency of price changes (black solid line), and increases (gray solid line) and decreases (gray dashed line) across months of the year. As in the United States, the frequency of price changes decreases slowly across the months within the year. The frequency of price changes has a significant peak in January (27%), two smaller peaks in July and September (about 21%), and a trough in December (16.2%). The seasonal pattern of the frequency of price changes mainly stems from the seasonality of price increases: the frequency of price increases is 16.8% in January and gradually decreases throughout the year to below 10% during the fourth quarter. The frequency of price decreases also exhibits two peaks at around 10% in January and July, reflecting seasonal sales especially in the clothing and durable sectors. 5 presents the frequency of price changes, increases, and decreases by of the six sectors. The frequency of price changes exhibits a peak in January all sectors (except energy and food). The peak is very marked in services: the frequency of price changes is above 15% in January versus less than 7% the rest of the year. In services there is also a peak in the frequency of price increases in September. In the manufacturing sector (in particular clothing), peaks in the frequency of price decreases are noticeable in January and July, while for price increases those peaks are in February and August.

Sales contribute significantly to the seasonal movements in the frequency of price changes. As discussed in Section 1, seasonal sales are regulated in France and by law take place mostly in January-February and June-July, while temporary discounts are less seasonal (Table K in the online appendix). The seasonality of sales is quite similar in the United States, although their frequency does not decrease as much after January and July there [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF]. Figure 6 plots the frequencies of price changes, increases, and decreases by month including or not sales. When FIG. 6. Seasonality of the Frequency of Price Changes-Impact of Sales. NOTES: Black line: frequency of price changes. Dark gray line: frequency of price increases. Light gray line: frequency of price decreases. Dashed lines: frequencies are calculated in the case including price changes related to sales and product replacements. Solid lines: frequencies are calculated in case excluding price changes related to sales but including product replacements.

excluding sales (solid lines), the frequency of price decreases becomes essentially flat, whereas the frequency of price increases still has a peak in January and is decreasing across the months of the year (Figure D in the online appendix documents sectoral heterogeneity). Overall, the noticeable peak in January in the frequency of price changes and the smaller one in September are mostly due to seasonal price increases, mainly in services.

Product substitutions are less seasonal than sales. They are somewhat more frequent in March and September-October, that is, after seasonal sales (e.g., for clothing, more than 30% of observations are replacements in March and in September; online appendix Table L). The seasonal patterns of the frequency of price changes are modified by considering product substitutions or not. Nakamura and Steinsson (2010a) report a similar pattern for the United States.

Similar to the frequency, the size of price changes has strong seasonal patterns. Figure 7 shows the average size of price increases and decreases by month of the year, including or not sales. Price decreases are larger in January and July: the average price decrease is around -16% versus -11.3% over the year (black dashed line). Price increases are larger in the February-March and August-September (black solid line): the average price increases is then above 15% versus 12.8% on average. These patterns are obviously related to large price variations during sales. 28 When we consider only nonsales prices, the seasonality of the size of price changes almost disappears (gray lines).

Explaining the seasonality of price changes is beyond the scope of this paper. While the administrative regulations on the timing of sales are an obvious factor, we may note that other motives for seasonal patterns include endogenous synchronization of price changes as well as the pattern of wages. Seasonality of wage changes in France is documented in particular in Avouyi-Dovi et al. ( 2013) and Le [START_REF] Bihan | Sticky Wages: Evidence from Quarterly Microeconomic Data[END_REF]. Another motive for seasonality is provided by [START_REF] Alvarez | Optimal Price Setting With Observation and Menu Costs[END_REF] based on a rational inattention-type argument: when there is a large "information cost" to observe or compute the optimal price, it is an optimal policy to reset prices at discrete pre-set intervals.

The Effect of Aggregate Fluctuations on Regular Prices Changes

We now examine to what extent macroeconomic fluctuations affect the probability and the size of regular price changes. 29 The 2008-11 period was characterized by relatively large shocks, such as the increase in the level and volatility of oil price and the Great Recession. Figure 8 displays headline inflation and inflation excluding energy over the period 2003-11. Inflation was relatively stable, except for between 2007 and 2008 when it increased to more than 3.5% and then quickly decreased in 2009 hitting negative values. While the fall of inflation corresponds to the recession (GDP growth was -1.5% in the first quarter of 2009), the episode of inflation volatility also reflects the volatility of energy prices and inflation excluding energy appears much more stable.

Investigating the determinants of the probability and the size of price changes at the micro level helps us to understand the dynamics of aggregate inflation. A simple Phillips curve would suggest that inflation may vary for three reasons: a change in inflation expectations, a variation in marginal costs, or a modification in the degree of price rigidity. Movements in the frequency of price changes over time can be related to a modification in the degree of price rigidity. Variations of the size of price changes may mirror fluctuations in the marginal costs.

Figure 9 shows the evolution of the frequencies of price changes, increases and decreases excluding sales. We plot the frequency of price changes from August 1994 to April 2011, using the frequency of price changes computed by [START_REF] Baudry | What Do Thirteen Million Price Records Have to Say about Consumer Price Rigidity?[END_REF] to extend the sample. Using a moving average to filter out the seasonal patterns, the frequency of price changes is broadly stable over the period 1994-2011, at levels between 12% and 17% (black line). Its main fluctuations reflect movements 28. The online appendix Table J documents the size of sales-related price changes. 29. We here disregard sales-related price changes, following a large fraction of the recent literature. Section 3.4 will be devoted to the analysis of determinants of price changes related to sales and substitutions. NOTES: Inflation rates are calculated as annual variations of CPI (overall) and CPI (overall excluding energy). Recession means that quarterly growth of GDP is negative during at least two quarters.

in commodity prices (in particular in the periods 1999-2000 and 2008-09), Value-Added Tax (VAT) changes in 1994 and in 2000, and the euro cash changeover in January 2002. The frequency of price changes seems to have slightly increased at the time of the Great Recession (about 17%) but it decreased to reach about 12% at the end of our sample period.

Figure 10 shows the average (solid lines) and the median (dashed lines) sizes of price changes over time for the period 1994-2011 excluding sales. The average and median sizes of price decreases and increases are rather stable until 2008. Over the period 2008 to 2011, measures of the output gap are typically negative, and both the average and the cross-sectional standard deviations of price increases are larger than previously. For instance, before 2008, the standard deviation of price increases was less than 6.5, while it was 8.6 between 2008 and 2011. Turning to price decreases, results are similar: the absolute size and standard deviation are larger after 2008. 30 30. Most of the changes in average size and standard deviations are statistically significant according to a formal test allowing for heteroskedasticity and autocorrelation correction and controlling for macroeconomic variables. Detailed results are presented in the online appendix Tables F andG. [START_REF] Berger | Dynamics of the U.S. Price Distribution[END_REF] provide similar evidence for the United States and argue that the increase in the volatility of price changes reflects an increase in the variance of shocks and macroeconomic uncertainty.

To formally investigate the effect of inflation and business cycle conditions on regular price changes at the microlevel, we estimate Tobit Type II models for price increases and price decreases. In these models, a first equation examines the determinants of the probability of price changes, while a second equation explains the size of price changes (details on the specification and estimation are presented in the online appendix). Our specification thus accommodates discreteness in price change and allows us to separate the extensive and intensive margins. In the first equation, we explain the probability of price increases (or decreases) by relating it to the cumulative inflation rate at the four-digit product level since the last price change of the outlet 31 and to a vector of variables capturing business conditions (the aggregate unemployment rate and a dummy for the Great Recession, as identified 31. Product-level inflation is calculated using our micro prices excluding sales to obtain a proxy for sectoral cost shocks. Our maintained assumption is that product-level inflation is exogenous for the price setter at the outlet level. We also underline that cumulative inflation varies between outlets and over time, which is an important source of identification in our exercise. by the CEPR). 32 Year, month, and product dummies are also included. When a price increases (or decreases), the second equation accounts for the size of the price change controlling for the selection effect, that is, the fact that the determinants of the first-stage regression did actually trigger a price change. This equation relates the size of price changes to the same determinants as in the first equation. Yet, for identification reasons, the monthly dummies included in the price change decision equation are excluded from the size equation: we here assume that the month of the year is relevant for outlets in the timing of their price decisions (because of, e.g., annual contracts or holidays), but that it has no specific effect on the size of price changes. Our exercise is similar in spirit to the regressions using aggregate frequency and size performed, for example, by [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF]. We expect however that using microdata and cumulative inflation enhances identification. We exclude price records from the energy sector from our estimation data set. Indeed, since the degree of price flexibility is much higher in this sector than in all others, it seems unlikely that the same model can fit energy and nonenergy price records. Moreover, this is a crude way to avoid confounding effects of the business cycle with those of commodity prices, since the recession is contemporaneous to large fluctuations in commodity prices.

Table 8 reports marginal effects of the Tobit models obtained separately for price decreases and price increases (excluding sales). First, as expected, cumulative productlevel inflation has a significant positive effect on the probability of price increases and a significant negative effect on the probability of price decreases. The marginal effects are however moderate: an additional 1 percentage point of inflation raises the probability of a price increase by 0.269 percentage point, and reduces that of a 32. As there is no benchmark business cycle dating for France and the euro area cycle is well correlated with that of the French economy, we use a dummy for euro area recession dates as identified by the CEPR. price decrease by 0.194. Inflation has also a small positive effect on the size of price increases and decreases: a shock of 1 percentage point on inflation raises similarly the size of increase and decrease by about 0.25 percentage point. Using related regressions, [START_REF] Nakamura | Five Facts about Prices: A Reevalutaion of Menu Cost Model[END_REF] find similar evidence for probability of price changes but do not find significant effects for the size of price changes.

Turning to the effect of the unemployment rate, it is found to be negative on the probability of price increase and positive on the probability of price decrease, consistent with intuition. 33 A higher unemployment rate by 1 percentage point raises the probability of a price decrease by 0.533 percentage point and reduces that of a price increase by 1.090 percentage point. The effect of unemployment on the sizes of price increase and price decrease are negative but small and nonsignificant. Thus, business cycle conditions seem to affect price dynamics more through variations in the probability of price increase and decrease (extensive margin) than through variations in the size of price change (intensive margin).

As expected, the impact of the Great Recession is positive on the probability of price decrease and negative on the probability of price increase. Moreover, the effect of the recession dummy on the size of price increase and decrease is negative. However, the effect of the Great Recession on the probability of both price increase and decrease is not very robust. For instance, we have considered an alternative specification of the model that includes the cumulative oil price change, to control for large commodity price fluctuations during the 2008-09 period. Results (presented in the online appendix Table M) remain similar except for an unexpected negative effect of the Great Recession on the probability of price decreases. 34 An additional robustness check is to restrict our sample to services prices, which are arguably less affected by oil prices. For this sector, the Great Recession dummy has significant and positive effect on the probability of price increases and whether or not including oil price variations has only minor effects on estimated parameters (Table N in the online appendix). Thus, the effect of the Great Recession should be regarded with some caution due to some possible identification difficulties. A positive effect would be however consistent with results suggesting that the Great Recession induced more volatility in prices, as obtained by [START_REF] Vavra | Inflation Dynamics and Time-Varying Volatility: New Evidence and an Ss Interpretation[END_REF] for the United States and [START_REF] Dixon | The Impact of the 2008 Crisis on UK Prices: What We Can Learn from the CPI Microdata[END_REF] for the United Kingdom. Finally the quantitative impact appears to be limited: the impact of the recession is -0.423 percentage point on the frequency of price increase and 0.266 percentage point on the frequency of price decrease in our baseline model.

Overall, fluctuations in the probability of price increase and decrease at the micro level, which play a substantial role in inflation dynamics, appear to respond to business cycle conditions and sectoral cost proxies. These results are qualitatively consistent with state-dependent models of price setting. At the same time, monthly 33. For a robustness check, we also ran the same regressions with output gap as an alternative business cycle indicator and found similar results.

34. The cumulative product-level inflation since the last price change may already account at least partly for changes in commodity or inputs prices, and the negative sign can reflect multicollinearity. dummies included in our model are still statistically significant and point to some time-dependent patterns in price setting. Another caveat in relating our model to standard models of price rigidity is that in a Calvo model, the overall frequency of price changes is constant, but the share of increase and decrease can respond to the business cycle.

The Effect of Aggregate Fluctuations on Sales and Substitutions

In this last section, we examine to what extent price changes associated with sales and product substitutions respond, beyond their seasonal variations, to inflation and business cycle conditions. One motivation is that a recent literature suggests that price changes associated with sales have different determinants from regular price changes, which justifies discarding sales-related price changes when computing indicators of price rigidity. To assess whether sales respond to macroeconomic variables, we estimate similar Tobit models as in the previous section, but now explain the occurrence and the size of the price drops that initiate a sales price spell. The exogenous variables included are as above the aggregate unemployment rate, a dummy variable for the Great Recession, and the cumulative inflation rate at the four-digit product level since the last price change in a given outlet, 35 and a set of year, month, and product dummies. Table 9 reports marginal effects obtained from the Tobit model for price drops at seasonal sales and temporary promotions. We find that the sensitivity of both the probability and size of sales price changes to cumulative inflation and 35. Product inflation rate is calculated from our micro data set excluding sales observations since due to regulation, sales are extremely synchronized across items, so the aggregate inflation rate (which is highly correlated to the dynamics of sales) will be mechanically correlated with the incidence and size of sales at the individual level.

unemployment is quite low. An additional 1 percentage point of inflation decreases the probability of a sale by 0.092 percentage points and an additional 1 percentage point of unemployment increases the probability of a sale by 0.208 percentage point (0.118 excluding seasonal sales). 36 By contrast, the marginal effects were, respectively, -0.194 and 0.533 for regular price decreases. Our conclusion is similar when we compare the results in terms of elasticities. For instance, the elasticity of the probability of sales to the unemployment rate is about 0.3 versus 0.7 for regular price decreases. 37 The effect of inflation and unemployment on the size of sales decreases is negative but small and nonsignificant. The impact of unemployment on the size of regular price decreases is not statistically different from the one on price decreases related to sales. 38 The impact of the Great Recession dummy on the probability of observing a sales price is positive but small (0.236 percentage point, which is consistent with the great stability of the frequency of sales over time [Figure E in the online appendix]). Its effect on the size of sales-related price decreases is barely significant. However, the effect of the crisis may be empirically difficult to disentangle from the impact of the change in competition regulation ("Loi de Modernisation de l' Économie"), which occurred in January 2009 and softened restrictions on sales. Moreover, the fact that seasonal sales are regulated in terms of their timing may blur the assessment about the effect of macroeconomic covariates. 39 Restricting to "temporary promotional discounts" (i.e., excluding seasonal sales) delivers even smaller and less significant effects of macroeconomic variables on temporary discounts (last two columns of Table 9).

Overall, we conclude that, adding to the fact that sales are a small fraction of price changes and are rather tightly regulated in France, the reaction of sales prices to activity is smaller than that of regular price change. [START_REF] Klenow | Sticky Information and Sticky Prices[END_REF] with U.S. data and [START_REF] Kryvtsov | On the Importance of Sales for Aggregate Price Flexibility[END_REF] with UK data find that reaction of sales prices to business cycle is important to understand the response of inflation to macroeconomic shocks whereas [START_REF] Anderson | Informational Rigidities and the Stickiness of Temporary Sales[END_REF] and [START_REF] Coibion | The Cyclicality of Sales, Regular, and Effective Prices: Business Cycle and Policy Implications[END_REF] reach the opposite conclusion. Our results are arguably more in line with the latter.

36. Using a linear probability model on UK data, [START_REF] Kryvtsov | On the Importance of Sales for Aggregate Price Flexibility[END_REF] report that a 1 percentage point shock on unemployment leads to an increase of 0.4 percentage point in the frequency of sales.

37. The frequency of sales in the sample that excludes services and energy is 6%. The average unemployment rate in the sample is 8.7%. The elasticity of the probability of sales is then 0.208 × 8.7 ÷ 6 ≈ 0.3. The frequency of price decreases in the sample is 6.6%, which leads to an elasticity for regular price decreases equal to 0.533 × 8.7 ÷ 6.6 ≈ 0.7.

38. We also compare results obtained with Tobit models excluding or including sales prices (reported in the online appendix Table O), marginal effects associated with macroeconomic variables are broadly similar, suggesting no strong difference in the reaction of sales or regular prices to macroeconomic shocks. This last result is also driven by the small proportion of sales in our data set.

39. For instance, when sales price are included in our baseline Tobit model (the online appendix Table O), we also incorporate a "sales period" seasonal dummy to control for the administrative dates of sales. The effect of "recession" turns out to become positive on the probability of price increases in all specifications. We also examine whether inflation or business cycle conditions affect product substitutions and the size of price changes related to product substitutions. Table 10 reports marginal effects obtained from Tobit regressions on product substitution-related price changes. The exogenous variables are the same as above (cumulative inflation at a disaggregated product level, unemployment, and a dummy variable for the Great Recession). Like for sales-related price changes, the effects of macroeconomic variables on both size and probability of price changes related to product replacements are small. This suggests that product substitutions are not driven by inflation developments, but more likely by other long-term firm decisions like product development cycle or seasonality of demand. This last result is consistent with those obtained by [START_REF] Klenow | Sticky Information and Sticky Prices[END_REF] on U.S. data.

CONCLUSION

To conclude, we summarize our main stylized facts and discuss some of their possible macroeconomic implications.

First, one-fifth of prices change each month in France. For the available common sample of products and using the U.S. weighting structure, the frequency of price changes is higher in the United States than in France (24.1% versus 20.1%). When sales are excluded however, the difference is very limited (around 17% both in the United States and in France). Our baseline estimates incorporate price changes related to product substitutions. This has rather similar consequences in France and in the United States: the estimated frequency of price changes in both countries is larger by about 2 percentage points than when disregarding substitution-related price 15384616, 2015, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/jmcb.12281 by Université De Nantes, Wiley Online Library on [16/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License changes. Similarly, the average size of price changes is larger in the United States, but when sales are excluded the difference appears much smaller. This raises two concerns for macromodels. First, it emphasizes the need for a better understanding of the determinants of sales and their macro-implications-for example, [START_REF] Kehoe | Prices Are Sticky After All[END_REF] suggest that the actual degree of price stickiness is mainly driven by the frequency of regular price changes. Second, it underlines the importance of assessing whether structural differences in the costs of adjustments, or differences in the volatility of micro or aggregate shocks, can help us to understand similarities and differences between France and the United States in price adjustment characteristics.

A second set of noticeable facts relates to the distribution of price changes. The shares both of small and of large price changes is substantial. This fact is robust to taking into account sales and product substitutions, although the sizes of price increases and decreases are strongly reduced when we exclude sales. The average price change is about 12% in absolute values when product replacements and sales are included, and about 8% when sales are excluded. The distribution of price changes is quite dispersed and leptokurtic, consistent with what is obtained by [START_REF] Midrigan | Menu Costs, Multi-Product Firms, and Aggregate Fluctuations[END_REF], for instance. The large size of price changes suggests a large variance in idiosyncratic shocks, whereas the extent of small price changes suggest more complicated forms of adjustment costs than a basic menu cost model, as suggested by [START_REF] Costain | Price Adjustments in a General Model of State-Dependent Pricing[END_REF] or [START_REF] Midrigan | Menu Costs, Multi-Product Firms, and Aggregate Fluctuations[END_REF]. A recent theoretical literature emphasizes that designing macro-economic models able to reproduce those facts alters the monetary policy responses to shocks (see, e.g., [START_REF] Alvarez | Sticky Prices, Menu Costs and the Effect of Monetary Shocks: Theory and Micro-Evidence[END_REF].

Third, we also find a strong seasonality of price changes even after controlling for seasonal sales. About 27% of prices are modified in January (versus about 20% on average). We find that this "January effect" on the frequency of price changes still exists even when sales are excluded, and contributes to a large extent to variations of the monthly inflation rate. This is in line with predictions of a nonstaggered Taylor contract model, or could be explained by a strong degree of synchronization of price changes. When sales are excluded, the average sizes of price increases and decreases are broadly flat over the months of the year. Olivei andTenreyro (2007, 2010) show that seasonality in wage setting may have important consequences for the real effects of monetary policy, which may then depend on the quarter where a shock occurs. One can expect similar macroeconomic consequences for prices since regular prices appear-at least-as seasonal as wages.

Fourth, sales contribute significantly to the volatility of the inflation rate, however, at the same time, price changes related to sales and product replacements are found to play a smaller role than regular price changes in the transmission of cost or business cycle conditions to inflation. One explanation may be related to the strong regulation of sales in France. Our results may also suggest that sales respond to idiosyncratic shocks and other long-term firm decisions. In particular, variations in unemployment or the Great Recession are shown to have almost no impact on price changes related to sales or substitutions. This result may be consistent with predictions of rational inattention models where firms' price decisions are more driven by idiosyncratic shocks than by macro ones [START_REF] Mackowiak | Optimal Sticky Prices under Rational Inattention[END_REF].

Fifth, we find that inflation dynamics are mainly driven by fluctuations over time in the frequency of price increases and decreases. We also find that the probability (and to a lesser extent the size) of regular price changes responds to business cycle conditions and sectoral cost proxies. These results are qualitatively consistent with state-dependent models of price setting. However, we find only small changes in price adjustment patterns during the Great Recession. The frequency and the absolute size of price decreases only slightly increased. Moreover, the dispersion of the price change distribution also increased, which is quite consistent with some recent U.S. findings. The stability of the frequency of price changes during the Great Recession raises the question of whether it merely reflects price stickiness, or whether it can be explained by some rigidity in marginal costs.

FIG. 2 .

 2 FIG. 2. Contributions of the Frequency and of the Size of Price Changes to Inflation-Including Product Replacements.

FIG. 3 .

 3 FIG. 3. Contributions of the Frequency and of the Size of Price Changes to Inflation-Nonsales Prices.

FIG. 4 .

 4 FIG. 4. Seasonality of the Frequency of Price Changes. NOTES: Price changes related to product replacements are considered as price changes. Black solid line: frequency of price changes by month. Gray solid line: frequency of price increases by month. Gray dashed line: frequency of price decreases by month.

  FIG. 5. Seasonality of the Frequency of Price Changes-By Sector. NOTES: Price changes related to product replacements are considered as price changes. Black solid line: frequency of price changes by month. Gray solid line: frequency of price increases by month. Gray dashed line: frequency of price decreases by month.

  FIG. 7. Seasonality of the Size of Price Changes. NOTES: Dashed lines: size of price decreases and solid lines: size of price increases. Black lines: weighted average size of price increases or decreases (in percent) including sales. Gray lines: weighted average size of price increases or decreases (in percent) excluding sales. Product substitutions are included.

  FIG. 8. Overall Inflation and Overall Inflation Excluding Energy (in %).

FIG. 9 .

 9 FIG. 9. Frequency of Price Changes, Increases and Decreases Over Time NOTES: Black lines: Monthly weighted frequency of price changes and its moving average over 12 months. Gray line: Moving average (over 12 months) of the monthly weighted frequency of price increases. Black dashed line: Moving average (over 12 months) of the monthly weighted frequency of price decreases. Price changes due to product replacements and sales are excluded. Numbers for the period July 1994 to February 2003 come from results of Baudry et al. (2007); January 2002 is excluded.

  FIG. 10. Average and Median Size of Price Increases and Decreases Over Time. NOTES: Black solid line: Average weighted size of price increases. Black dashed line: median weighted size of price increases. Gray solid line: Average weighted size of price decreases. Dashed gray line: median weighted size of price decreases. Price changes due to product replacements and sales are excluded. Numbers for the period July 1994 to February 2003 come from results of Baudry et al. (2007), January 2002 is excluded.

TABLE 1

 1

	FREQUENCY OF PRICE CHANGES
					France	United States
		France	United States	U.S. weights	U.S. weights
		2003-11	1998-2005
		Mean	Mean	Mean	Median	Mean	Median
	Including sales, including substitutions
	Frequency of price changes	20.1	27.7	20.1	14.9	24.1	16.2
	% of price increases	60.2	-	-	-	-	-
	Excluding sales, including substitutions
	Frequency of price changes	17.4	22.8	17.4	10.6	17.1	9.8
	% of price increases	62.3	-	-	-	-	-
	Including sales, excluding substitutions
	Frequency of price changes	17.7	26.5	17.5	10.4	22.7	14.9
	% of price increases	59.9	55.1	58.0	54.5	53.6	54.4
	Excluding sales, excluding substitutions
	Frequency of price changes	15.0	21.1	14.5	5.7	15.1	6.9
	% of price increases	63.5	59.1	62.4	84.3	60.9	76.0
	% of seasonal sales % of promot. discounts	0.7 1.7	--	--	--	--	--
	% of prod. substitutions	4.1	2.8	-	-	-	-

TABLE 2 FREQUENCY

 2 OF PRICE CHANGES BY SECTOR

				Manufacturing goods
		Food	Durables	Clothing	Other manuf.	Energy	Services
	Including sales
	Frequency of price changes	20.7	22.2	24.9	14.4	77.1	8.2
	% of price increases	56.4	48.3	50.0	63.4	60.7	77.6
	Excluding sales
	Frequency of price changes	17.1	16.5	12.5	12.5	77.0	8.0
	% of price increases	58.0	48.9	55.1	65.9	60.7	78.4
	% of seasonal sales	0.0	1.2	6.7	0.2	0.0	0.0
	% of promot. discounts	3.0	4.5	2.8	1.7	0.1	0.2
	% of prod. substitutions	2.2	9.6	16.2	4.1	0.7	2.0

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TABLE 3

 3

	SIZE OF PRICE CHANGES
		Including sales	Excluding sales
	Price increases
	Mean	12.8	7.9
	Std	26.4	16.2
	Lower quartile	2.0	1.9
	Median	4.3	3.7
	Upper quartile	10.9	7.6
	Price decreases
	Mean	-11.5	-7.8
	Std	13.2	9.6
	Lower quartile	-16.1	-10.0
	Median Upper quartile	-6.1 -2.3	-4.4 -1.8
	% of absolute price change less than 2%	23.7	27.4
	% of absolute price change less than 1%	11.2	13.0

NOTES:

The statistics on the size of price changes are all weighted using CPI disaggregated weights on the period 2003-11. Individual sizes of price changes are here calculated in percentage, and only nonzero price changes are considered (including substitutions).

  15384616, 2015, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/jmcb.12281 by Université De Nantes, Wiley Online Library on [16/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons LicenseNOTES:The statistics on the size of price changes (in log-differences) are all weighted using U.S. ELI disaggregated weights. Average and median price changes are first calculated at product level (on the period 1998-2005 for the United States, Nakamura and Steinsson 2010b, and on the period 2003-11 for France) and then aggregate using U.S. weight structure to obtain the average and median size of price changes.

		France	United States	France	United States
	Price increases
	Including sales	10.0	14.9	6.4	12.3
	Excluding sales	6.0	9.2	5.2	8.0
	Price decreases
	Including sales	-13.4	-18.5	-8.9	-15.3
	Excluding sales	-9.0	-12.0	-7.0	-10.7

TABLE 5 SIZE

 5 OF PRICE CHANGES BY SECTOR

			Price increases			Price decreases
		Mean	Q1	Median	Q3	Mean	Q1	Median	Q3
	Including sales
	Food	10.6	2.0	4.7	11.1	-9.3	-12.7	-5.2	-2.0
	Manufacturing
	Durables Clothing	20.1 53.0	5.1 14.0	12.5 38.5	25.0 75.0	-14.3 -29.1	-20.0 -40.0	-11.5 -30.0	-6.3 -16.7
	Other manuf. Energy	13.1 3.8	2.0 1.7	4.3 3.1	13.2 5.0	-13.0 -3.9	-20.0 -5.2	-8.2 -2.9	-2.5 -1.5
	Services	9.0	2.1	4.0	9.0	-12.8	-17.7	-9.3	-3.8
	Excluding sales
	Food	6.8	1.8	3.7	7.6	-6.4	-8.3	-3.8	-1.6
	Manufacturing
	Durables	16.5	3.5	9.1	20.0	-12.4	-16.7	-9.7	-5.0
	Clothing Other manuf.	21.6 9.6	5.7 1.8	12.7 3.6	25.2 9.0	-17.0 -10.0	-23.8 -13.6	-13.4 -5.7	-7.1 -1.9
	Energy Services	3.8 8.5	1.7 2.1	3.0 3.8	5.0 8.5	-3.9 -12.3	-5.2 -16.7	-2.9 -8.8	-1.5 -3.4

NOTES:

The statistics on the size of price changes are all weighted using CPI disaggregated weights. Individual sizes of price changes are here calculated in percentage, and only nonzero price changes are considered (including substitutions).

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TABLE 6 RECOMPOSING

 6 AGGREGATE MONTHLY INFLATION AT THE DISAGGREGATED PRODUCT LEVEL :We recompose monthly inflation rates at a disaggregated level of product (level 4 of the COICOP classification, 134 different products) using all individual price quotes under different hypotheses on sales and product replacements. We compute the monthly inflation rates for all 134 microprice indices recomposed with our microdata and for the corresponding 134 indices computed and published by INSEE. Then,

		Average monthly	Standard	Corr. with actual
		inflation	deviation	inflation (INSEE)
	Including sales and including subst.	0.185	0.454	0.826
	Excluding sales and including subst.	0.185	0.366	0.700
	Including sales and excluding subst.	0.150	0.341	0.871
	Excluding sales and excluding subst.	0.154	0.268	0.742
	Actual inflation (INSEE)	0.170	0.460	1

NOTES

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TABLE 7 CORRELATION

 7 BETWEEN INFLATION, FREQUENCY, AND SIZE OF PRICE CHANGES

		Including sales	Excluding sales
		Correlation	OLS est.	Correlation	OLS est.
		coef.	Dep. var.: π	coef.	Dep. var.: π
	Frequency of price changes	-0.22	0.01	0.56	0.02
		(0.03)	(0.21)	(0.00)	(0.00)
	Size of price changes	0.97	0.32	0.73	0.12
		(0.00)	(0.00)	(0.00)	(0.00)
	Freq. increases	0.02	0.14	0.76	0.06
		(0.81)	(0.00)	(0.00)	(0.00)
	Freq. decreases	-0.60	-0.30	-0.20	-0.08
		(0.00)	(0.00)	(0.05)	(0.00)
	Size increases	0.57	0.38	-0.38	0.02
		(0.00)	(0.00)	(0.00)	(0.02)
	Size decreases	0.52	0.21	0.16	0.01
		(0.00)	(0.00)	(0.13)	(0.01)

NOTES:

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TABLE 8 PROBABILITY

 8 AND SIZE OF PRICE CHANGES ON INFLATION, UNEMPLOYMENT, AND RECESSION : The sample excludes prices of the energy sector and consist of price changes excluding sales and including substitutions. The table reports marginal effects obtained from the estimation of Tobit models. "Cumulative inflation" is the cumulative product-level inflation rate (at the four-digit product level) since the last price change in a given outlet i. The product-level inflation rate is computed using individual price data excluding sales but including substitutions. "Unemployment" is the unemployment rate in France (source Eurostat). "Great Recession" is a dummy variable equal to 1 when France was in recession; we use the datation of CEPR Euro Area Business Cycle for France (January 2008 to June 2009). Year, month, and product (five-digit product level) controls are included. *** significant at 1%, ** significant at 5%, * significant at 10%. Standard deviations of estimates are reported in parentheses.

		Price increases	Price decreases
		Probability	Size	Probability	Size
	Cumulative inflation	0.269 ***	0.238 ***	-0.194 ***	0.254 ***
		(0.004)	(0.011)	(0.003)	(0.013)
	Unemployment	-1.090 ***	-0.044	0.533 ***	-0.089
		(0.040)	(0.058)	(0.032)	(0.083)
	Great Recession	-0.423 ***	-0.360 ***	0.266 ***	-0.202 *
		(0.060)	(0.084)	(0.045)	(0.104)
	N observations	8,022,198	682,295	8,022,198	477,654

NOTES

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TABLE 9 PROBABILITY

 9 AND SIZE OF SALES ON INFLATION, UNEMPLOYMENT, AND RECESSION : The sample excludes service and energy sectors, in which the incidence of sales is marginal. The table reports marginal effects obtained from Tobit models where the endogenous variable is the size of price decrease during sales (equal to "." when there is no sales or promotions and equal to the log size of price decrease during the sale period). "Cumulative inflation" is the cumulative product-level inflation rate (at the four-digit product level) since the last price change in a given outlet i. The product-level inflation rate is computed using individual price data excluding sales but including substitutions. "Unemployment" is the unemployment rate in France (source Eurostat). "Great Recession" is a dummy variable equal to 1 when France was in recession: we use the datation of CEPR Euro Area Business Cycle for France (January 2008 to June 2009). Year, month, sales period, and product (five-digit product level) controls are included. For identification, monthly dummies and sales period dummies are excluded from the second equation of the Tobit models. *** significant at 1%, ** significant at 5%, * significant at 10%. Standard deviations of estimates are reported in parentheses.

		Sales		Excluding seasonal sales
		Probability	Size	Probability	Size
	Cumulative inflation	-0.092 ***	-0.001	-0.069 ***	0.039 ***
		(0.002)	(0.013)	(0.002)	(0.012)
	Unemployment	0.208 ***	-0.107	0.118 *	-0.429 *
		(0.080)	(0.195)	(0.062)	(0.266)
	Great Recession	0.236 **	0.490 *	-0.151 *	0.082
		(0.10)	(0.265)	(0.077)	(0.270)
	N observations	2,894,231	170,163	2,894,231	115,513

NOTES

TABLE 10 PROBABILITY

 10 AND SIZE OF PRICE CHANGES AT PRODUCT SUBSTITUTIONS ON INFLATION, UNEMPLOYMENT, AND RECESSION : The sample includes all sectors; we consider price changes excluding sales. The table reports marginal effects obtained from Tobit models where the endogenous variable is the size of price decrease or increase when the product is replaced (equal to "." when there is no substitution and equal to the log size of price decrease/increase at the product substitution). "Cumulative inflation" is the cumulative product-level inflation rate (at the four-digit product level) since the last price change in a given outlet i. The product-level inflation rate is computed using individual price data excluding sales but including substitutions. "Unemployment" is the unemployment rate in France (source Eurostat). "Great Recession" is a dummy variable equal to 1 when France was in recession: we use the datation of CEPR Euro Area Business Cycle for France (January 2008 to June 2009). Year, month, and product (five-digit product level) controls are included. *** significant at 1%, ** significant at 5%, * significant at 10%. Standard deviations of estimates are reported in parentheses.

		Price increases		Price decreases
		Probability	Size	Probability	Size
	Cumulative inflation	-0.024 ***	0.029	-0.047 ***	0.122 ***
		(0.002)	(0.019)	(0.002)	(0.019)
	Unemployment	0.083 ***	-0.221	0.160 ***	0.081
		(0.030)	(0.231)	(0.028)	(0.261)
	Great Recession	0.023	-0.093	0.107 ***	0.107
		(0.042)	(0.298)	(0.039)	(0.329)
	N observations	4,515,950	132,571	4,515,950	112,925

NOTES

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See, for example,[START_REF] Gautier | The Dynamics of Gasoline Prices: Evidence from Daily French Micro Data[END_REF] for an analysis of gasoline prices at higher frequency. 15384616, 2015, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/jmcb.12281 by Université De Nantes, Wiley Online Library on [16/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

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