Understanding price stickiness: firm-data evidence on price adjustment lags and their asymmetries

Transcription

1 Understanding price stickiness: firm-data evidence on price adjustment lags and their asymmetries Daniel A. Dias, Carlos Robalo Marques, Fernando Martins, and J.M.C. Santos Silva January 8, 2014 Abstract We study the speed of price reactions to positive and negative demand and costs shocks. In line with the predictions of optimal price setting models, we find that price adjustment lags vary with firm s characteristics that are related to the importance of menu costs, the variability of the optimal price, and the sensitivity of profits to sub-optimal prices. We also find that the majority of firms react faster to positive than to negative cost shocks, and more quickly to negative than to positive demand shocks. However, the direction and magnitude of these asymmetries vary across firms and with the type of shock in a way that cannot be fully explained by any single theoretical model of asymmetric price adjustment. Overall, these results suggest that the reaction to monetary policy shocks may depend on which firmsorsectorsareparticularlyaffected by them and, therefore, that richer models are needed to fully understand the effects of monetary policy. JEL classification codes: C41, D40, E31. Key Words: Asymmetries in price rigidity, Firm heterogeneity, Ordered data, Survey data. Department of Economics, University of Illinois at Urbana-Champaign and CEMAPRE. ddias@illinois.edu. Banco de Portugal. cmrmarques@bportugal.pt. Banco de Portugal, ISEG (Technical University of Lisbon) and Universidade Lusíada de Lisboa. fmartins@bportugal.pt. Department of Economics, University of Essex and CEMAPRE. jmcss@essex.ac.uk 1

2 1. INTRODUCTION Price stickiness has a central role in macroeconomics and, besides a vast theoretical literature, it has generated numerous empirical studies trying to explain its origins and gauge its importance. Most of the literature aimed at identifying the reasons of price stickiness has focused on the frequency of price changes. 1 However, an important issue that arises when using observed price changes to measure price rigidity at the micro-level is that the differences in the frequency of price changes across products are not expected to strictly correspond to differences in firm behaviour. Rather, the frequency of price changes is likely to also depend in a significant way on the frequency and magnitude of the shocks that hit the firms in the period under consideration. This suggests that the frequency of price changes is not the best variable to use in empirical studies on the nature and origins of price rigidity. As Blinder (1991, p. 94) puts it: From the point of view of macroeconomic theory, frequency of price change may not be the right question to ask, for it depends as much on the frequency of shocks as on the firms pricing strategies. We are more interested to know how long price adjustments lag behind shocks to demand and cost. Therefore, rather than looking into the reasons for infrequent price changes, in this paper we use survey data to directly investigate the deeper and more meaningful question of the determinants of the speed of price reactions to demand and cost shocks. 2 Furthermore, we study two important and intertwined forms of heterogeneity in the speed with which firms respond to shocks. 1 See among others, Bils and Klenow (2004), Alvarez and Hernando (2005), Dhyne et al. (2006), Munnick and Xu (2007), Klenow and Kryvtsov (2008), Gopinath and Itskhoki (2010), Klenow and Malin (2011), Druant et al. (2012), and Vermeulen et al. (2012). 2 Other authors have studied similar survey data; see, e.g., Small and Yates (1999), Fabiani et al. (2004), Loupias and Ricart (2004), Alvarez and Hernando (2005), Kwapil et al. (2005), and Martins (2010). However, the main objective of these papers was to document and explain the existence of price rigidity and not so much to study the determinants of the speed of price adjustments. 2

3 First, we study between-firm heterogeneity by identifying firm-, product-, and market-level characteristics that explain why some firms react faster than others to each of the four types of shock on which we have information. In line with theoretical models on optimal price-setting rules (e.g., Barro, 1972, Caballero, 1989, and Alvarez et al., 2011), we find evidence that the degree of price stickiness is influenced by variables that are related to the importance of menu costs, the variability of the optimal price, and the sensitivity of profits to sub-optimal prices. These results, therefore, lend support to the idea that firms optimally choose the degree of price stickiness. Second, we study within-firm heterogeneity by checking whether firms react differently to demand and cost shocks, and asymmetrically to positive and negative shocks (in a slight abuse of terminology we refer to all these differences as asymmetries). We find that, in line with similar evidence reported in the literature, most firms in our sample react faster to positive than to negative cost shocks, and more quickly to negative than to positive demand shocks. However, and more importantly, we also find that the direction and magnitude of the asymmetries varies across firms and with the type of shock in a way that cannot be fully explained by any single existing theoretical model of asymmetric price adjustment. The results we present are important because the forms of heterogeneity in the speed of firms responses toshocksthatwefind have implications for macroeconomic models and monetary policy. First, it has been shown that the between-firm heterogeneity in price stickiness leads monetary shocks to have larger and more persistent real effects (see, e.g., Carvalho, 2006, and Nakamura and Steinsson, 2009). Second, the existence of within-firm heterogeneity has important consequences for the relationship between inflation and aggregate demand. The literature suggests that whether the Phillips curve is linear, concave, or convex depends on the existence and sign of the asymmetries in price rigidity at the firm level (see, e.g., Buckle and Carlson, 1996, Laxton et al., 1999, Dolado et al., 2004, and Dolado et al., 2005). Our results show that asymmetries of different signs can coexist in the same economy and therefore the reaction to monetary policy shocks may depend on which firms or sectors are particularly affected by them. Overall, these results suggest that economic models should try to account for the 3

4 documented heterogeneity in firms responses to shocks, and that richer and more eclectic models are needed to fully understand firms reactions to different types of shocks and to better predict the effects of monetary policy. The rest of the paper is organised as follows. Section 2 describes the novel dataset used in the paper. Section 3 introduces the econometric model we use and describes its links to the literature on price stickiness. Section 4 presents and analyses the estimation results, and Section 5 summarizes and discusses our main findings. Finally, the appendices provide a detailed description of the econometric model used, and information on how the different variables were constructed. 2. THE DATA Most of the data used in this study come from a survey about price setting practices carried out by the Banco de Portugal. 3 The idea of using survey data to study price setting behaviour was pioneered by Blinder et al. (1998), and is becoming increasingly popular (see, e.g., Fabiani et al., 2004, Loupias and Ricart, 2004, Alvarez and Hernando, 2005, Kwapil et al., 2005, Lünnemann and Mathä, 2006, and Martins, 2010). A potential disadvantage of this type of data is that it corresponds to reported, not actual, behaviour and it is impossible to know whether the answers provided are close to reality. However, in our model we will use only the ordinal information in the answers given by the firms, which significantly mitigates potential measurement errors. 4 3 For further details on this survey, see Martins (2005, 2010). 4 Another potential disadvantage of the type of data we use is that it does not distinguish between aggregate and idiosyncratic shocks. Indeed, the economic literature has stressed that the reaction of firms to shocks may depend on whether these are aggregate or idiosyncratic (Lucas, 1973), and recently Mackowiak and Wiederholt (2009) developed a model in which prices react quickly to idiosyncratic shocks, but only slowly to aggregate shocks (see also Dhyne et al., 2011). The fact that our data has no information on whether the firm sees the shock as aggregate or idiosyncratic is an important limitation. In any case, we do not expect this fact to seriously limit the interpretation of our results because, since we have four observations for each firm, our panel data model will to some extent account for the heterogeneity resulting from firms interpreting the nature of the shock in different ways. 4

5 Intheparticularsurveyforwhichwehavedata,firms were asked how long they would take to react to significant cost and demand shocks. More specifically, they were asked the following four questions: 1) After a significant increase in demand how much time on average elapses before you raise your prices? ; 2) After a significant increase in production costs how much time on average elapses before you raise your prices? ; 3) After a significant fall in demand, how much time on average elapses before you reduce your prices? ; and 4) After a significant decline in production costs how much time on average elapses before you reduce your prices?. The responses to these questions, which will be the dependent variable in our model, are recorded as continuous interval data with six categories: 1 - less than one week; 2 - from one week to one month; 3 - from one month to three months; 4 - from three to six months; 5 - from six months to one year; 6 - the price remained unchanged. With the expression significant increase or significant decline the authors of the survey had in mind inducing respondents to interpret the shock as significant enough to lead firms to react to it by changing their price. Therefore, we interpret option 6 as indicating that the price will eventually change, but the adjustment lag is longer than one year. 5 Table 1 displays the distribution of the observed price adjustment lags for each type of shock. These distributions make it clear that there is a substantial degree of heterogeneity in the way firms respond to shocks. Indeed, for each of the shocks considered, the response lags vary between less than one week to more than a year. Naturally, this heterogeneity reflects the fact that firms differ from one another in some important characteristics; in the next section we present an econometric model that partially explains this heterogeneity. 5 Some authors who have looked at similar surveys for other European countries have interpreted option 6 literally as meaning that such firms do not react to shocks (see, for instance, Kwapil et al., 2005, and Fabiani et al., 2004). This interpretation implies that the distribution of the lags is defective (i.e., there is a positive probability that the lag is infinite). The model we use does not depend on the particular interpretation that is given to option 6 because all we will assume is that firms choosing option 6 do not have price adjustment lags of less that one year. As a robustness check we also estimated models grouping categories 5 and 6 together and found that the results change very little. 5

6 Table 1: Distribution of the price responses to demand and cost shocks Cost shocks Demand shocks Price adjustment lag Positive Negative Positive Negative 1 - less than one week from one week to one month from one month to three months fromthreetosixmonths fromsixmonthstooneyear more than one year Total The results in Table 1 also suggest that firms react differently to different shocks. Specifically, firms in the sample are generally quicker to react to cost shocks, in particular when they are positive, than to demand shocks. For example, the share of the firms that do not change their prices in the first year after a positive cost shock is around 10 percent, while for a positive demand shock the corresponding share is just below 35 percent. Interestingly, firms in the sample seem to react more quickly to positive than to negative cost shocks, but to be slower to react to positive than to negative demand shocks. 6 Formal tests for the hypotheses that the reaction time is the same both for positive and negative shocks and for demand and cost shocks, will be performed in Section 4. Besides the questions on price adjustments lags, the survey also contains information on a large set of firms characteristics, some of which will be used as regressors in our model. In addition, we supplemented the survey data with information from Central de Balanços, a comprehensive dataset maintained by Banco de Portugal in which the balance sheets and income statements of most Portuguese firms are registered. combining these datasets through the individual tax identification number of each firm, we are able to obtain detailed information on 903 firms from different sectors. More specifically, our sample includes firms with 20 or more employees, from which almost 90 percent belong to Manufacturing (NACE - classification of economic activities - 15 to 6 Similar results concerning the relative speed of price adjustment to cost and demand shocks using survey data were obtained for Austria, Italy, France, Luxembourg, Spain and the US (see, respectively, Kwapil et al., 2005, Fabiani et al., 2004, Loupias and Ricart, 2004, Lünnemann and Mathä, 2006, Alvarez and Hernando, 2005, and Blinder et al., 1998). 6 By

7 37) and the remaining to Services (NACE 60 to 64, 80 and 85 - Transport, Storage and Communication, Education and Healthcare). Sectors such as agriculture, construction, or wholesale and retail trade are not included. 3. A MODEL FOR PRICE ADJUSTMENT LAGS In this section we briefly present the model used to study the determinants of the priceadjustmentlags. Westartbyexplaininghowthenatureoftheavailabledata shaped the particular type of econometric model used, and then we turn to the literature on optimal price setting to guide our choice of regressors. The section concludes with a description of the regressors used and of the rationale for including them in the model The econometric model The econometric model we use to study the determinants of the price adjustment lags takes into account both the interval nature of the data and the fact that each firm contributes to the sample with four observations. Specifically, we model the latent variable, which represents the time firm takestoreacttoashockoftype, asa function of a set of firm characteristics and of a firm-specific random-effect. Because is not fully observable, and due to the potential existence of reporting errors, our model uses only the ordinal information provided by the firms. That is, the dependent variable in our model is e =1 6, the indicator of one of the six possible response categories. We therefore use a panel-ordered probit model that allows for the presence of unobserved firm-specific effects. Because the results in Table 1 suggest that the speed of price adjustment is shock specific, we estimate a model which allows for the possibility of different coefficients for each type of shock, including different cut-off parameters and different variances for the non-observed stochastic components. This is almost equivalent to estimating four different models, one for each type of shock, with the difference being that in our case the models are linked by the unobserved heterogeneity component, which is assumed to 7

8 be common to the four shocks. 7 A more detailed description of the model is provided in Appendix A. To complete the model specification it is necessary to define the set of regressors to use; we next turn to the literature on price stickiness for guidance on this Theoretical background There is now an extensive theoretical literature aiming at explaining why prices at the micro level may remain unchanged for large periods of time. Here, we focus on the recent contribution by Alvarez et al. (2011) because it combines both menu and information costs, the leading explanations for the existence of price stickiness, and thus may be seen as encompassing most of the previous literature. 8 The model of Alvarez et al. (2011) describes how firms optimally choose the time between price reviews and price changes, and how they set the optimal price as a function of the adjustment costs. This model can be used to identify firm s characteristics that may be related to their degree of price stickiness. Alvarez et al. (2011) assume that: i) the out-of-equilibrium cost for a firm may be captured by the quadratic function, = [ ( ) ( )] 2,where measures the sensitivity of profits to the price gap, i.e., the deviation of the actual (log) price, ( ), fromtheoptimal(log)price, ( ); ii) the optimal (log) price follows a random walk with Gaussian innovations with variance 2 per unit of time; iii) the firm incurs in a fixed information cost,, in order to determine the optimal price and on a fixedmenucost,, in order to change the price; and iv) the rate of inflation, or the drift of the stochastic process ruling ( ), is0 or approximately 0. 9 Under these hypotheses, Alvarez et al. (2011) showed that the expected 7 Qualitatively, the results do not change if the model is estimated without the random effects or assuming that the random effects are independent across the four equations. 8 Other relevant contributions in this field include, for instance, Barro (1972), Caballero (1989), Dixit (1991), Bonomo and Carvalho (2004), Reis (2006), Woodford (2009), Gopinath and Itskhoki (2010), and Bonomo et al. (2010). 9 Note that depends on the parameters of the demand and costs functions, and that, in particular, it is increasing with the elasticity of demand faced by the firm. The parameter 2 may be seen as measuring the volatility of demand and cost functions. 8

9 time between price reviews,, can be approximated by v ³ ³ u t ³ +2 1 Φ = 2, (1) 2 where is some threshold such that the firm opts for not adjusting the price if ( ) ( ), andφ ( ) denotes the CDF of the standard normal distribution. Because appears on both sides of (1), and also because depends on some of the parameters, obtaining comparative statics is not a straightforward task. However, using some of the results and assumptions in Alvarez et al. (2011), it is possible to show that: i) increases with the information cost ( 0); ii) forsmall, increases with the menu costs ( 0); iii) forsmall 2, the more volatile the optimal price is the smaller will be ( 2 0); and iv) decreases with the sensitivity of profits to the price gap ( 0). One may expect the price adjustment lags for a firm following this model to be positively correlated with the average time between price reviews, 10 and therefore the results above also give us information about the possible determinants of price adjustment lags. In the absence of direct measures for,, 2,and, we use as regressors sectoral, product, and firm-level characteristics which can be seen as indirect measures of these parameters The covariates In the remainder of this section we briefly present the covariates used as indirect measures of,, 2,and, and discuss how they can be linked to these parameters. 11 To make clear the connection between the regressors and the parameters in the optimal price-setting model, we group the regressors into four categories. 10 This, of course, does not imply that looking at the frequency of price changes or at the speed of price adjustment will deliver the same conclusions about the determinants of price rigidity. The reason for this is that, as noted by Blinder (1991), the observed frequency of price changes depends on non-observable shocks and it does not allow one to disentangle the effects of firm characteristics from the effects of the shocks. We avoid this problem by looking at the lags of price adjustment after a shock rather than at the frequency of price changes which may reflect the effect of multiple shocks. 11 Appendix B provides detailed descriptions of all the regressors, as well as basic summary statistics. 9

10 1) Menu and information costs In the survey there are two questions about the importance of costs related to adjusting prices and of costs related to information gathering for the purpose of reviewing prices. We use the answers to these two questions to construct the dummy variables Importance of menu costs and Importance of information costs, which are equal to one if the firm considers that the corresponding cost is a very important reason to postpone price changes. 2) Variability of the optimal price This group includes five regressors: three variables related to the cost structure of the firm (Share of labour costs, Share of capital costs, andshare of intermediate input costs), and two variables related to the relation between the firm and its customers (Explicit contracts, i.e., the proportion of sales under written contracts, and Implicit contracts, i.e., whether the relation with the customers is essentially of a long- or short-term nature). If prices of different inputs have different volatilities, it is expectable that the cost structure of a firm will matter for the variability of the optimal price. For example, if input costs are relatively stable, such as wages which are changed on average once a year, the variability of the optimal price will be low. On the contrary, if input costs are volatile, as it is the case of some raw materials, the variability of the optimal price will also be high and therefore prices are likely to be reviewed and/or changed more frequently leading on average to faster reactions to shocks. Economic theory suggests that the existence of explicit and/or implicit contracts may be an important source of price stickiness at the firm level (see, for instance, Fisher, 1977, and Okun, 1981). With explicit contracts firms aim at building long-term relationships with their customer in order to stabilise their future sales. Customers, on the other hand, are attracted by a constant price because it makes their future costs more predictable and helps to minimize transaction costs (e.g., shopping time). In turn, the theory of implicit contracts is based on the idea that firms try to win customer loyalty by changing prices as little as possible. Overall, the presence of explicit and/or implicit contracts may be expected to reduce firm s demand variability 10

11 and thus to reduce the frequency with which prices are reviewed and/or changed, leading on average to slower reactions to shocks. 3) Sensitivity of profits to sub-optimal prices This group includes a set of six covariates: Competition, Price competitiveness, Quality competitiveness, Delivery competitiveness, Intermediate goods and Services. The variable Competition identifies firms with five or more competitors. It is known that the more competitive a sector is, the more sensitive profits are to sub-optimal prices, i.e., the higher is (see, for instance, Martin, 1993). Thus, ceteris paribus, stronger competition may be expected to translate into quicker responses to shocks. The covariates Price competitiveness, Quality competitiveness, anddelivery competitiveness distinguish firms by their competitiveness source: price, quality, and time to deliver; these are dummy variables that are equal to one if the firm considers price, quality, or the delivery period, respectively, as very important factors of competitiveness. We may think of the regressors identifying the competitiveness factors as reflecting different product characteristics which translate into different demand elasticities and thus into different values for (higher demand elasticity for firms for which price is an important factor, and lower elasticity for firms that emphasize the other factors). 12 The two remaining variables, Intermediate goods and Services, are, respectively, dummies indicating whether the firm produces mainly for other companies and the sector in which the firm operates. These variables are expected to have a bearing on the sensitivity of profits to the price gap because final goods and services are typically more differentiated than manufacturing and intermediate goods, respectively, and thus face a less elastic demands. 4) Other controls Finally, we include a set of covariates that we believe may be related to the speed of price adjustments through more than one of the parameters in the optimal price-setting 12 Martin (1993) showed that the speed of price adjustment increases with the elasticity of demand, that is, firms react faster to shocks when the demand schedule facing them is flatter. This same idea was used by Gopinath and Itskhoki (2010) to show the link between the frequency of price adjustment and exchange rate pass-through. 11

12 model. The first of these variables, Size, is a dummy indicating that the firm has more than 250 employees. This variable may be seen as a measure of the firms market power (which is expected to affect ), but can also be seen as an indirect measure of. Indeed, Zbaracki et al. (2004) have argued that the importance of information costs is likely to be higher in large firms (see, however, Buckle and Carlson, 2000). The remaining variables in the group are directly related to price setting practices. These covariates (Price discrimination, Quantity discount, Price set by customers, and Price set by competitors) identifyfirms that discriminate prices either by deciding the price on a case-by-case basis or by practising quantity discounts, and firms that do not have price autonomy (the price is set or strongly influenced by its main customers or competitors). These variables may be related to the information and menu costs faced by the firm, but may also reflect the competitiveness of the market in which the firm operates and therefore may also be related to the sensitivity of the firms profits to sub-optimal prices. 4. EMPIRICAL RESULTS 4.1. Between-firm heterogeneity: what explains price stickiness? Table 2 presents the estimates of the main parameters of the panel-ordered probit model, as well as the corresponding standard errors. For ease of presentation, we organize the discussion of the results around the groups of regressors described before and that correspond to the four parameters of the theoretical model in (1). 13 As could be expected, the results in Table 2 show that firmsforwhichmenucosts are important tend to adjust prices more slowly than other firms, but this effect is statistically significant only for demand shocks. Interestingly, we find that the information costs dummy does not emerge as a statistically significant factor in explaining differences in the price adjustment lags across firms. Given the crucial role that information costs play in theoretical models of price rigidity, this result may seem somewhat surprising. However, it is in line with the finding that very few firms in the sample 13 Table A1 in Appendix A presents the estimation results of the remaining parameters of the model. 12

13 ranked information costs as an important obstacle to adjusting prices (a similar pattern is found for the Euro area, as documented by Fabiani et al., 2006). It is important to emphasizethatalthoughwedonotfind direct evidence of the importance of the information costs, our results obviously do not imply that these are not a relevant source of price rigidity. Indeed, it may just be that in our model the effect of the information costs is being accounted for by the other regressors that we know can be related to these costs (Price discrimination, Quantity discount, Price set by customers, Price set by competitors, and Size), all of which are statistically significant for at least one type of shock. Turning now to the indirect measures of the variability of the optimal price, our findings confirm that, ceteris paribus, the cost structure of the firm affects the speed of price adjustment. In particular, we see that the firms with a share of labour costs above the median are slower to adjust to all the four shocks considered. 14 However, the coefficientsontheothervariablesthatweassumedtobeinformativeaboutthevariability of the optimal price (Explicit contracts and Implicit contracts) arenotstatistically different from zero for either of the four shocks. The results in Table 2 show that all the regressors that we considered to be related to the sensitivity of firms profits to non-optimal prices emerge as having a significant impact on the speed of price adjustment. Firms operating in more competitive environments, or that consider price as an important factor of competitiveness, tend to be faster to react to shocks, while firms that emphasize the quality of the product or the delivery period as competitiveness factors tend to adjust their prices at a slower pace (specially so, in face of demand shocks). Our results also show that the speed of price adjustment varies with the type of market for the product and with the sector where firms operate. Firms that operate in the services sector are substantially slower to react to shocks than firms that operate in the manufacturing sector: for each of the four shocks, Services shows up as having one of the largest coefficients. In turn, 14 This is a very robust result that has been extensively documented in the literature for the frequency of price adjustments (see, among other, Altissimo et al. 2006, and the references therein). Our results show that the same result is valid for the speed with which firms react to shocks. 13

14 firms that sell their products to other firms (Intermediate goods) tend to be quicker to adjust their prices than firms whose products are mainly for final demand (whose main destinations are wholesalers, retailers or consumers). These results are consistent with previous evidence on the frequency of price changes which suggested a significantly higher degree of price stickiness in the services sector and also that producer prices are changed more frequently than consumer prices. The remaining regressors also emerge as having significant impacts on price adjustment lags. In particular, our results indicate that whether or not firms follow a single price policy has important consequences for the speed of price adjustment: firms that decide the price on a case-by-case basis, or do quantity discounts, tend to be faster to adjust to both cost and demand shocks. The speed of price adjustment also varies with the differences in the price autonomy of the firm: Price set by customers has a positive and significant impact in the case of positive cost shocks, suggesting that for these firms customers have enough power to delay the firms reaction when costs push prices up. Regarding Price set by competitors, our results show that firms that have their prices significantly affected by the main competitors are faster to respond to demand shocks than firms that set their own prices. This suggests that firms whose prices are set by the main competitors may be acting as market followers in a market wherethepresenceofmarketleadershelpsreducing potential coordination problems. Finally, our results also suggest that size matters for the speed of price adjustment: inthefaceofcostshocks,largefirms tend to be slower at adjusting their prices than small firms. In summary, the results in Table 2 can be interpreted as confirming that optimal price-setting models such as the one presented by Alvarez et al. (2011) provide an adequate description of the forces determining how firms choose the degree of price stickiness. Perhaps more importantly, our results also suggest that the degree of price stickiness varies substantially across firms and depends on firm s characteristics such as the menu costs, the cost structure, the type of good, and the degree of competition. The implications of these results will be further explored below. 14

15 Table 2: Panel-ordered probit estimates for the price adjustment lags (main results) Cost shocks Demand shocks Covariates Positive Negative Positive Negative Constant Menu and information costs: Importance of menu costs Importance of information costs Variability of the optimal price: Labour costs Intermediate input costs Capital costs Explicit contracts Implicit contracts Sensitivity of profits to the price gap: Competition Price competitiveness Quality competitiveness Delivery competitiveness Intermediate goods Services Other controls: Price discrimination Quantity discount Price set by customers Price set by competitors Size (0 298) (0 198) (0 287) (0 122) (0 127) (0 110) (0 128) (0 149) (0 132) (0 113) (0 129) (0 111) (0 123) (0 204) (0 160) (0 152) (0 183) (0 164) (0 158) (0 412) (0 240) (0 349) (0 149) (0 154) (0 135) (0 155) (0 183) (0 161) (0 139) (0 158) (0 135) (0 150) (0 254) (0 195) (0 185) (0 222) (0 199) (0 195) (0 294) (0 196) (0 276) (0 117) (0 121) (0 105) (0 122) (0 142) (0 126) (0 109) (0 123) (0 106) (0 117) (0 196) (0 155) (0 147) (0 173) (0 155) (0 150) (0 350) (0 227) (0 324) (0 139) (0 142) (0 123) (0 143) (0 169) (0 149) (0 129) (0 147) (0 125) (0 139) (0 233) (0 183) (0 173) (0 205) (0 184) (0 178) Standard errors computed from analytical second derivatives are in parenthesis; ***marks significance at 1% level, **marks significance at 5% and *marks significance at 10% level. 15

16 4.2. Within-firm heterogeneity: symmetric or asymmetric lags? As discussed before, the results in Table 1 suggest that firms may react differently to different types of shocks. Moreover, the results in Table 2 show that there are substantial differences between the parameters of the four equations, 15 which also suggests the existence of within-firm heterogeneity, that is, that a firm may have different reactions to different types of shocks. The possible existence of firm-level asymmetric price rigidity is a relevant issue because it has consequences for the relationship between inflation and aggregate demand, and thus may have important implications for monetary policy. There is now a vast theoretical literature that focuses on the question of whether prices are stickier in response to a shock that warrants a price decrease or to shocks in the opposite direction, or whether prices react more quickly to cost or to demand shocks. A survey of this literature tells us that there are many possible justifications for the existence of differences between the speed of adjustment to different types of shocks, but there seems to be no consensus about the sign and magnitudes of these differences. 16 Based on the argument that wages are flexible upwards but rigid downwards, some literature favours the idea that prices are stickier downwards than upwards. If this is the case, the relationship between inflation and aggregate demand (Phillips curve) must be non-linear, calling for asymmetric monetary policy rules. In particular, negative monetary policy shocks (interest rate increases) must be larger when inflation is above target than positive shocks (interest rate cuts) when inflation is below target (see, e.g., Laxton et al., 1994, Laxton et al., 1999, Dolado et al., 2004, Dolado et al., 2005, and Dobrynskaya, 2008). However, if prices react faster to negative than to positive 15 See also Table A1 in Appendix A. 16 For models of aymmetric price reactions to positive and negative shocks, see, among many others, Okun (1981), Maskin and Tirole (1988), Tsiddon (1993), Ball and Mankiw (1994), Hansen et al. (1996), Kovenock and Widdows (1998), Bhaskar (2002), Rotemberg (2005), Ellingsen et al. (2006), Devereux and Siu (2007), Chen et al. (2008), Yang and Ye (2008), Tappata (2009), Anderson and Simester (2010), Lewis (2011), and Cabral and Fishman (2012). 16

17 demand shocks, things may be expected to work the other way around. The conclusions in Buckle and Carlson (1996) and Fabiani et al. (2006) favour this alternative view. In the context of our model, the existence of within-firm heterogeneity can be investigated formally by testing restricted models imposing symmetry, against the unrestricted model we have estimated. These tests can be easily implemented as tests of the significance of the differences between the shock-specific parameters in the different equations; we consider both differences within shocks (differences in the responses to positive and negative cost shocks and positive and negative demand shocks) and the difference between shocks (differences in the responses to positive shocks to costs and demand and to negative shocks to costs and demand). Table 3 presents the results of the four tests; in all cases the null of symmetry is rejected at all usual significance levels. These results, therefore, strongly suggest that firms react differently to negative and positive shocks, and to cost and demand shocks. In order to investigate how price stickiness varies with the type of shock, we used the estimated econometric model to compute, for each firm in the sample and for each shock, the probability that it takes more than a year for the firm to adjust its price; 17 then we computed the differences between these probabilities for each pair of shocks. As before, we consider both the differences within shocks and the differences between shocks. Table 3 - Tests of symmetry Symmetry within shocks Symmetry between shocks Positive and Positive and Positive cost Negative cost negative negative and demand and demand cost shocks demand shocks shocks shocks 2 (24) = (24) = (24) = (24) = ( =0 000) ( =0 000) ( =0 000) ( =0 000) 2 (24) stands for the Wald test statistic with 24 degrees of freedom and for the corresponding p-value. 17 We focus on the category e =6(i.e., price adjustment does not take place in the first year after the shock) because it is more meaningful than the category e =1(see Table 1), and it is well known that in models for ordered data only the results for the first and last categories can be unambiguously interpreted; see, e.g., Winkelmann and Boes (2006). 17

18 10 9 Differences in the probabilities within shocks positive negative shocks 10 9 Differences in the probabilities between shocks cost demand shocks Cost shock Demand shock Positive shock Negative shock Differences in probabilities Differences in probabilities Fig 1: Distribution of differences between probabilities for the category e =6. Figure 1 presents the distribution of these differences in our sample, revealing that, for the majority of firms, prices adjust more quickly upwards than downwards following cost shocks, but more slowly upwards than downwards in reaction to demand shocks (differences in probabilities are mostly negative in the first case and mostly positive in the second). Also, the majority of firms tend to be faster to respond to cost than to demand shocks either positive or negative. 18 In addition, Figure 1 also shows that there is a high degree of heterogeneity in the size and even in the direction of the asymmetry. In fact, a non negligible mass of firms adjust prices more quickly downwards than upwards following cost shocks and more slowly downwards than upwards in reaction to demand shocks. The results regarding the asymmetry between positive and negative cost shocks for the majority of firms in the sample are consistent with the predictions of a model with 18 Similar results concerning the relative speed of price adjustment to cost and demand shocks using survey data were obtained for Austria, Italy, France, Luxembourg, Spain and the US (see, respectively, Kwapil et al., 2005, Fabiani et al., 2004, Loupias and Ricart, 2004, Lünnemann and Mathä, 2006, Alvarez and Hernando, 2005, and Blinder et al., 1998). Comparable results for positive and negative cost shocks were obtained by Peltzman (2000), for the U.S., and by Loupias and Sevestre (2013), for France. 18

19 menu costs and trend inflation (see Tsiddon, 1993, Ball and Mankiw, 1994, Ellingsen et al., 2006), with a model that incorporates search costs or consumer inattentiveness (Chen et al., 2008, Yang and Ye, 2008, Tappata, 2009, Lewis, 2011, Cabral and Fishman, 2012), and with the predictions of some models considering firms strategic behaviour (e.g., Devereux and Siu, 2007). However, it is at odds with the predictions of the oligopoly models with kinked demand curves of the type considered by Maskin and Tirole (1988), which suggest that firms may react more quickly to negative than to positive shocks, as is the case of a smaller share of firms in the sample. In turn, the finding that the majority of firms in the sample react faster to negative than to positive demand shocks is consistent with a model where customer anger is taken into consideration (Okun, 1981, Anderson and Simester, 2010), but could have not been anticipated, for instance, by menu-cost models with positive trend inflation. However, the latter models will be able to explain the behaviour of the firms for which the adjustment is faster after a positive than after a negative demand shock. Finally, the results regarding the asymmetry between cost and demand shocks which show that most firms in the sample react faster to cost than to demand shocks are consistent with models of customer anger or fair pricing. These models predict that consumers will more easily accept a price increase caused by a change in costs than a price increase that is caused by an increase in demand. Some important conclusions emerge from the analysis in this subsection. First, there is evidence of significant asymmetries in the speed of price responses to positive and negative demand and cost shocks. Second, for the majority of firms, prices adjust more quickly upwards than downwards following cost shocks, but more slowly upwards than downwards in reaction to demand shocks. However, there is a non negligible mass of firms for which the asymmetry is the other way around. Third, there does not seem to be a single theoretical model that can explain all the different results we obtained. Finally, as regards the implications for monetary policy, our results show that asymmetries with different signs can coexist in the same economy and, therefore, the reaction to monetary policy shocks may depend on which firms or sectors are particularly affected by them. 19

20 5. SUMMARY AND CONCLUDING REMARKS This paper uses survey data to study the length of price adjustment lags in reaction to positive and negative demand and cost shocks. Price adjustment lags are a direct measure of price rigidity and therefore are a better measure of price stickiness than the commonly used frequency of price changes, which is expected to also depend on the number and magnitude of the shocks that affect the optimal price during the observation period. Moreover, the survey data we use has the advantage of providing information on the reaction time to different types of shock, and therefore allows us to study both between- and within-firm heterogeneity. We find evidence that the degree of price stickiness is influenced by variables that can be construed as measuring the importance of menu costs, the variability of the optimal price, and the sensitivity of profits to sub-optimal prices, which are key ingredients in standard optimal price-setting models, such as the ones suggested in Barro (1972), Caballero (1989), or Alvarez et al. (2011). More specifically, we find that the lags of price adjustments vary with the firm, market and product, characteristics, such as the menu costs, the cost structure of the firm, the competitive environment, or the type of good. We also find evidence of the existence of asymmetries in the speed with which firms adjust their prices in response to positive and negative demand or cost shocks. In line with similar evidence reported in the empirical literature, most firms in our sample seem to react faster to positive than to negative cost shocks, and more quickly to negative than to positive demand shocks. However, we also find that the direction and magnitude of these asymmetries vary both across firms and with the type of shock in a way that cannot be explained by any single existing theoretical model of asymmetric price behaviour. This suggests that more eclectic models are needed to better understand this phenomenon. Our results on within- and between-firm heterogeneity in the speed of price reactions to shocks have important implications for macroeconomic models and for the understanding of the effects of monetary policy. First, the evidence on price stickiness being 20

21 optimally set by firms in response to market conditions and the firms specific characteristics suggests that it may be important for monetary models to try to accommodate the fact that price stickiness may change in response to changes in the economic structure as well as to monetary policy itself. Second, the fact that firms react differently to different types of shocks has the implication that the relationship between inflation and aggregate demand (Phillips curve) must be non-linear, calling for asymmetric monetary policy rules. However, in contrast to most of the theoretical literature which tends to favour the idea that prices are stickier downwards than upwards, the evidence obtained in this study suggests that the type of asymmetry prevailing at the aggregate levelmaydependontherelativeimportanceofdifferent types of firms in the economy andonhowtheyareaffected by the monetary policy shocks. Therefore, whether the relation between inflation and aggregate demand is linear, concave, or convex is still an open issue and thus more empirical evidence is required before definite conclusions can be drawn on this matter. ACKNOWLEDGEMENTS We are most grateful to the Editor Christopher Bowdler and to an anonymous referee for their many insightful and helpful suggestions. We also thank Nuno Alves, Mário Centeno, Ana Cristina Leal, José Ferreira Machado, Stefan Niemann, and Pedro Portugal for helpful discussions and useful suggestions. The opinions expressed in this paper are those of the authors and do not necessarily coincide with those of Banco de Portugal or the Eurosystem. Daniel Dias and João Santos Silva gratefully acknowledge the partial financial support from Fundação para a Ciência e Tecnologia, (Programme PEst-OE/EGE/UI0491/2013). The usual disclaimer applies. 21

22 APPENDIX A In this appendix we explain in detail the panel-ordered probit with random effects introduced in Section 3. We are interested in modelling the response of each firm to four different shocks. These four responses are likely to depend on common unobserved firm characteristics, suggesting the use of a panel data set-up in which the four seemingly unrelated equations are linked by a common random effect representing the unobserved firm characteristics. However, because we let different covariates have different coefficients in different equations, we allow the impact of the random effects to be shock-specific. Besides providing potential efficiency gains, the inclusion of the random effects with a flexible distribution makes the model more general and therefore less sensitive to distributional assumptions. The resulting model is very similar to a standard ordered probit with the only differencebeingthefactthatwetakeintoaccountthepanelstructureofthedata. As in the common ordered probit, we assume that there is a latent variable,,which represents the time firm takestoreacttoashockoftype. Recall that the different typesofshocksare: 1)positivedemandshock;2)positivecostshock;3)negativedemand shock; and 4) negative cost shock. We also assume that is related to a set of firm characteristics by = Λ (A1) where Λ ( ) is a strictly increasing invertible function that is specific toshocksoftype ; is a set of firm characteristics whose impact, measured by vectors,isshock specific; is a non-observed firm-effect whose impact, measured by, is shock specific; and is a non-observed stochastic term that is firm and shock specific. Equation (A1) implies that = Λ 1 the linear model ( ) is related to the firm characteristics by =

23 In our data, is not fully observed and instead we observe e, which is related to as follows. For =1 2 6 e = 1, (A2) where the constants are the limits of the intervals into which the domain of is partitioned due to the fact that is observed as interval data. At this point, two approaches can be followed. Because the price lags are reported in the form of known time intervals, we could specify the form of Λ ( ) and use this information to determine the cut-off parameters. Alternatively, we can estimate the cut-off parameters, which avoids the need to specify Λ ( ). This is the approach we follow because by not specifying Λ ( ) the model gains an interesting degree of flexibility. Specifically, for identification purposes, we set 0 =, 1 =0,and 6 =+, estimating freely the remaining four cut-off parameters. Inordertobeabletoestimatetheparametersofthemodel,weneedtomakedistributional assumptions on the unobserved random components. We start by assuming that (0 1), where the normalization of the variance to 1 implies no loss of generality. Then, based on (A2), the conditional probability of observing e = is given by Pr (e = ) = Pr( 1 ) = Pr( ) Pr ( 1 ) = Φ 0 + ª Φ ª = (e ) where, as before, Φ ( ) denotes the normal distribution function. Assuming that the disturbances are conditionally independent (given and ) across and, we can write the probability that for a certain firm we observe (e 1 = 1 e 2 = 2 e 3 = 3 e 4 = 4 ) as Pr (e 1 = 1 e 2 = 2 e 3 = 3 e 4 = 4 )= 23 4Y (e ) =1