Daniel Levy
email: levyda@mail.biu.ac.il.

Guest

Price Rigidity and Flexibility: Recent Theoretical Developments Introduction to the Special Issue

Keywords: Price Rigidity, Price Flexibility, Cost of Price Adjustment, Menu Cost, Adjustment, New Keynesian Economics, Price System

The price system, the adjustment of prices to changes in market conditions, is the primary mechanism by which markets function and by which the three most basic questions get answered: what to produce, how much to produce and for whom to produce. To the behaviour of price and price system, therefore, have fundamental implications for many key issues in microeconomics and industrial organization, as well as in macroeconomics and monetary economics. In microeconomics, managerial economics, and industrial organization, economists focus on the price system efficiency. In macroeconomics and monetary economics, economists focus on the extent to which nominal prices fail to adjust to changes in market conditions. Nominal price rigidities play particularly important role in modern monetary economics and in the conduct of monetary policy because of their ability to explain short-run monetary non-neutrality. The behaviour of prices, and in particular the extent of their rigidity and flexibility, therefore, is of central importance in economics.

INTRODUCTION

The price system, the adjustment of prices to changes in market conditions, is perhaps the single most important mechanism in a market-based economy. It is the price system that ensures that markets produce and offer the goods and the services that people want. It is the price system that ensures that the quantities produced are indeed the quantities that people and consumers would like to purchase. It is the price system that ensures that the products and services produced will end up in the hands of those that value them most. In short, the price system is the primary mechanism by which marketbased economies function and by which the three most basic questions get answered: what to produce, how much to produce and for whom to produce.

To the behaviour of price and price system, therefore, have fundamental implications for many key issues in microeconomics and industrial organization, as well as in macroeconomics and monetary economics. In microeconomics, managerial economics, and industrial organization, historically the economists' interest has been in the efficiency of the price system and in the resulting market outcomes. That is, the process by which price adjustments to changes in market conditions lead to efficiency of the market system and the resulting equilibrium allocations. In macroeconomics and monetary economics, the primary focus of the economists has been on the extent to which nominal prices fail to adjust to changes in market conditions. This type of nominal price rigidities play central role in modern monetary economics because of their ability to explain short-run monetary non-neutrality.

The behaviour of prices, therefore, is of central importance in economics. At the theoretical level, it is important to study models with various types of rigidities. For example, all models with Keynesian or New Keynesian flavour rely on some form of price (or wage) rigidity in order to generate predictions that fit the behaviour of the aggregate data. Therefore, it is critical to study and understand what is the nature of the barriers to price adjustments, how these barriers lead to sluggishness in price adjustment, and what do these mechanisms imply for various issues and questions at the level of both microeconomics as well as macroeconomics.

During the last 15-20 years, we have witnessed a remarkable revival in the popularity of New Keynesian models, that is, models that incorporate various forms of price rigidities as the main source of friction that generates monetary non-neutrality. Some of these studies have been published in the edited volumes by Mankiw andRomer (1991a, 1991b) and Sheshinski and Weiss (1993), which also contain references to other related studies. Since the publication of these volumes, however, there have been numerous developments in the theoretical literature. The goal of this special issue is to report some of these developments.

At the empirical level, it is important to assess the extent of price rigidity and flexibility. In particular, studying whether or not prices adjust to changes in market conditions as the standard New Classical model predicts seems to be of particular importance. In response to recent theoretical developments, the literature has also begun producing during the last 10-15 years empirical studies of price rigidity using various types of micro-level data from the US as well as from the European Union member countries. Two forthcoming special issues of the Managerial and Decision Economics [START_REF] Young | Explicit evidence on an implicit contract[END_REF][START_REF]Managerial and Decision Economics, a special issue on "Price Setting and Price Adjustment in Some European Union Countries[END_REF] will include some of these empirical studies.

IN THIS ISSUE

This special issue of the Managerial and Decision Economics contains eight theoretical contributions. These papers address the topics of price rigidity and flexibility from various angles. Of the eight studies, the first is a broad and updated survey paper.

The second paper provides a sociological perspective on price rigidity and offers a new methodological contribution. The third paper offers a marketing perspective on price rigidity linking it to the issue of reference price. The latter plays a central role in marketing, both in theory as well as in practice. The fourth paper focuses on non-price adjustment mechanisms by suggesting that prices may be rigid, if waiting time, i.e., the delivery lag, can respond endogenously to changes in market conditions.

The remaining four papers focus on macroeconomic implications of rigid prices and costs of price adjustment. One of the four papers studies the optimality of price stability, which is a topic of particular interest to monetary policy makers and to students of monetary policy. The second paper studies a model which can yield a hump-shaped inflation response to monetary policy shocks of the type frequently documented by empirical studies using variety of US as well as other countries' aggregate data. The third paper analyses an equilibrium optimization model to explore the interaction between price rigidities and inventories and its role in the propagation of business cycles. Finally, the fourth paper compares the real effects of trend inflation and monetary shocks in discrete and continuous time versions of a simple New Keynesian model.

The paper by Alex Wolman, "The Frequency and Costs of Individual Price Adjustment," is a remarkably thorough survey of over 100 theoretical and empirical studies, all focusing on price rigidity, one way or another. The theoretical studies Wolman surveys, all use rigid prices as one of the key ingredients of their modelling strategy. The empirical studies-and Wolman surveys no less 50 of them, all try to assess the extent of price rigidity directly or indirectly, or study various issues relevant for price rigidity and flexibility, such as measurement of price adjustment costs such as menu costs or managerial and customer costs, and assessing the relevance of these costs for price rigidities that have been documented by empirical studies.

Besides its broad coverage, Wolman's study is unique because of the attention it gives to earlier studies of [START_REF] Mills | The Behaviour of Prices[END_REF] and Means (1935aMeans ( , 1935b[START_REF] Means | Notes on inflexible prices[END_REF] In addition, Wolman provides a fascinating discussion of the early literature, including [START_REF] Keynes | Review of The Behavior of Prices[END_REF], [START_REF] Hicks | Annual survey of economic theory: the theory of monopoly[END_REF] and Scitovsky (1941), as well as less known correspondence between Means and Galbraith (1936). It turns out that these studies and the exchange between Means and Galbraith, discusses and suggest the idea of price adjustment cost and its various facet, perhaps anticipating the ideas of Akerlof andYellen (1985a, 1985b) and [START_REF] Mankiw | Small menu costs and large business cycles: a macroeconomic model[END_REF].

In the paper titled "A Sociological View of Costs of Price Adjustment: Contributions from Grounded Theory Methods," Mark Zbaracki offers a sociologist's and organizational behaviour scientist's perspective on the empirical approach that is based on hypothesis testing, which dominates the economics discipline. Zbaracki argues that the economic theory and data often pose problems that cannot be addressed with the existing econometric methods that are designed to test hypotheses. For example, theories of price adjustment costs rely on variables that cannot be observed. Although in principle such costs could be measured, in practice there is little hope to expect such measurements with the existing statistical data-gathering and econometric methods.

Zbaracki argues that the grounded theory methods developed by sociologists can be used to demonstrate the importance of price adjustment costs and to address deeper questions about how firms adjust prices. Properly matched to economic problems, Zbaracki suggests, grounded theory may help economists in developing better theories and in improving the testing of the existing theories.

Grounded theory methods are discovery oriented and thus they are especially useful for generating new theories based on data and observations. In this respect, grounded theory methods differ from the more common approach used in economics and other social sciences. Rather than beginning with a priori theory and using data for hypothesis testing and falsification of the existing theory, grounded theory methods enable the social scientist to use data for generating new theories.

Zbaracki uses price adjustment and cost of price adjustment as an example to demonstrate the advantages of grounded theory approach in economics. He argues that discovery-oriented methods can be used not only for examining the validity of existing theories, but also, and perhaps more importantly, it allows us to ask deeper questions about how firms adjust prices.

Zbaracki argues that grounded theory can provide three kinds of evidence: (i) observation relevant to existing theory, (ii) discovery of behaviours that alter existing theory, and (iii) process these observations and data for developing new theories and models. Zbaracki addresses the three approaches to the use of evidence that emerges from the use of grounded theory methods. In the context of the cost of price adjustment, he interprets the first approach, observation, as a tool for measuring the managerial and customer costs of price adjustment [START_REF] Zbaracki | Managerial and customer costs of price adjustment: direct evidence from industrial markets[END_REF]. Zbaracki argues, however, that focusing only on these costs would mean ignoring most of the relevant data from such observations. According to Zbaracki, the second approach, discovery, results from careful analysis of what pricing managers and their teams must do to adjust prices. Such evidence can help us discover new theory relevant to costs of adjustment. The third approach, process theory, can be used to develop more comprehensive models of adjustment.

From this evidence, Zbaracki discuss existing methods, distinguishing the methods of grounded theory from other interview methods (see, for example, [START_REF] Blinder | Asking About Prices: A New Approach to Understanding Price Stickiness[END_REF] that might be more familiar to economists. Zbaracki concludes by arguing that grounded theory and firm-level data could be useful to economists who seek to overcome certain theoretical and empirical barriers. While these methods cannot resolve all unanswered questions, Zbaracki argues, they may help economists develop better theories and better empirical tests of existing theories when they are properly matched to certain problems and methods.

Gadi Fibich, Arieh Gavious, and Oded Lowengart offer a marketing perspective on price rigidity. In their paper "Optimal Price Promotion in the Presence of Asymmetric Reference-Price Effects," Fibich, et al. study the role of asymmetric reference-price effects in promotional pricing decisions, and demonstrate that reference pricing can be a possible source of price rigidity. An additional contribution of their study is exploring the role of reference price in price promotions.

As Fibich, et al. note, price promotion is a common managerial practice employed for a variety of reasons such as luring customers into stores to buy other products at regular price (i.e., loss leader), increasing repeat buying, increasing market share among brand switchers, and targeting deal-prone consumers. Although there is a large body of literature on the effects of price promotions on demand and profitability of firms, Fibich, et al. argue, relatively little has been done to explore the effect of promotional activities on the reference price of a specific brand. Specifically, the concept that both deal frequency and depth of price cut can affect reference price has gained virtually no attention by researchers.

In "Production, Inventory and Waiting Costs," Gil Epstein models an environment with a non-price adjustment mechanism. That is, Epstein argues that often prices are rigid because adjustment occurs through waiting time. This idea has been proposed by [START_REF] Carlton | Equilibrium fluctuations when price and delivery lag clear the market[END_REF][START_REF] Carlton | Delivery lags as a determinant of demand[END_REF] who described it as a situation where "markets clear through delivery lags."

Epstein assumes that demand is a negative function of the waiting time. In many settings sellers with fixed capacities serve randomly arriving customers. From time to time queues form and customers end up paying two prices, an explicit price to the seller and, in addition, an implicit price in the time spent waiting. Some studies cited by Epstein find that indeed, the retail demand is sensitive to service time: customers are willing to pay about one percent more for a six percent reduction in congestion, on average. Consistent with these observations, [START_REF] Blinder | Asking About Prices: A New Approach to Understanding Price Stickiness[END_REF] report in their interview study that firms often prefer to respond to variations in demand by changing delivery time and improve other auxiliary services rather than change prices.

Epstein derives conditions under which an inventory policy, with regard to changes in waiting times and prices, will be optimal, i.e., preferred to a policy where sales are from current production. Epstein shows that a possible reason for the necessity of holding inventory is that it gives the firm the ability to sell its products with different waiting times. At any given price level, as the waiting time for receiving a product increases, the cost facing the buyer increases and thus demand decreases. The producers can use this fact in order to increase sales and profits.

Thus, Epstein's paper offers a possible explanation for price rigidity: the demand is more sensitive to the consumer's waiting costs than to the price of the product and thus, firms may whish to change the waiting time for a product to be supplied rather than to change the product's price.

The last four papers of the special issue focus on macroeconomic implications of price rigidity and cost of price adjustment. In "Costly Price Adjustment and the Optimal Rate of Inflation," Jerzy Konieczny studies the optimality of price stability. As Konieczny argues, stable price level, that is zero inflation, has become a reference point for many students of monetary economics and for central bankers. Konieczny develops a model in which price stability is optimal. Konieczny's economy consists of monopolistically competitive firms that face costs of nominal price adjustment.

Konieczny considers the effects of different, constant rates of inflation on welfare by assuming that money pays interest. In his model, money is indexed while prices are not.

The main friction in Konieczny's the model is the presence of the costs of adjusting nominal price and so the effects of inflation stem from the accounting role of money.

In Konieczny's model, inflation has there types of effects on welfare. First, the firm in his model has to bear the price adjustment costs as inflation affects its desired nominal price. Second, inflation affects the average desired real price over the pricing cycle. Third, inflation affects the average productivity of the monopolistic firms. Focusing on the two latter effects, Konieczny argues that they arise because firms change nominal prices infrequently and, in the presence of inflation, real prices vary over time. The effect of desired real prices on welfare is due to the fact that the economy is monopolized and real wages and output are too low. Inflation may strengthen the monopolistic distortion by increasing the average desired real price over the pricing cycle.

This productivity distortion arises from the effect of inflation-induced real price variability on the average productivity. As the pricing period is typically short relative to the lifetime of fixed factors such as capital, firms satisfy demand by changing the variable factor input and so they face increasing marginal costs. Inflation increases the variability of real prices over the pricing cycle. Since more output is sold by firms whose price is relatively low and marginal costs high, inflation reduces the average productivity of the variable factor and shrinks the economy's production-possibilities set. The productivity distortion is symmetric around zero and both inflation and deflation are detrimental.

Konieczny finds that the net effect of inflation on welfare depends on the balance of the two distortions. The monopolistic distortion depends on the properties of the demand function while the productivity distortion depends on the convexity of the cost function.

The more convex is the cost function, the more likely is the productivity distortion to dominate and welfare to fall, regardless of the monopolistic distortion, as inflation departs from zero. If the cost function is close to linear, inflation may increase welfare if it induces monopolistic firms to reduce their desired real prices. A superior policy, however, is to maintain a constant price level and subsidize labor services. Such policy lowers the desired real price in terms of wages and increases output but does not generate the productivity distortion.

In "Explaining Hump-Shaped Inflation Responses to Monetary Policy Shocks," James Yetman notes that according to conventional wisdom, the output effects of a monetary policy shock commence within months of the shock, while most inflationary effects lag significantly. This conventional wisdom is based both on specific historical events, as well as empirical estimates. For example, [START_REF] Mankiw | The inexorable and mysterious tradeoff between inflation and unemployment[END_REF] argues that while the monetary policy tightening of the Volcker disinflation commenced in October 1979, large declines in inflation only started in 1981, while output growth rates declined coincident with the monetary policy tightening. This phenomenon has been documented using data from other countries as well.

Studies that use the popular VAR methodology have reported similar findings. For example, [START_REF] Bernanke | Inside the black box: the credit channel of monetary policy transmission[END_REF] find that the largest declines in real output occur between eight and twenty-four months after a tightening of monetary policy. In contrast, prices are essentially stable for the first 12 months, before declining steadily.

As Yetman notes, many existing theoretical models have problems explaining these findings. Standard sticky price models, for example, are unable to generate a humpshaped inflationary response that lags the output response to any significant degree. In a recent contribution, [START_REF] Mankiw | Sticky information versus sticky prices: a proposal to replace the New Keynesian Phillips Curve[END_REF] introduce a model of sticky information and argue that the model can explain the above phenomenon. Within their model, firms do not set a single price for their good, but instead a pricing plan that may entail a new price in each future period. They combine their assumption of sticky information with [START_REF] Calvo | Staggered prices in a utility-maximizing framework[END_REF] timing of price adjustment, in which the probability that firms update their pricing plan is assumed to be constant and independent of the length of time since the pricing plan was last adjusted.

Yetman examines the robustness of [START_REF] Mankiw | Sticky information versus sticky prices: a proposal to replace the New Keynesian Phillips Curve[END_REF] finding by exploring whether the assumption of optimal updating of pricing plans on the part of price setters influences the results reported by Mankiw and Reis, by incorporating state-contingent (rather than time-contingent) price setting. Firms are assumed to optimally choose whether to reset their pricing plan each period, after observing the state of the economy.

Thus firms' price setting decisions are fully consistent with profit maximization, given the existence of costs of changing pricing plans.

Yetman finds that for the specific experiment Mankiw and Reis examine-a ten percent reduction in aggregate demand, state-contingent price adjustment implies an almost uniform inflation response over the first several periods following a monetary policy shock, and for the more realistic case of a smaller shock-a one percent reduction in aggregate demand, the inflation response is greatest either in the period of the shock, or the following period. Thus the hump-shaped response reported by [START_REF] Mankiw | Sticky information versus sticky prices: a proposal to replace the New Keynesian Phillips Curve[END_REF] is not robust to optimal price path adjustment by firms.

Yetman proposes a solution that remains consistent with profit maximizing price setting decisions by firms that can recover a hump-shaped response of inflation for small nominal shocks, and is consistent with empirical evidence on sources of nominal rigidity.

As Yetman notes, there is clear empirical evidence that points to the importance of both, menu costs [START_REF] Levy | The magnitude of menu costs: direct evidence from large U.S. supermarket chains[END_REF][START_REF] Levy | Price adjustment at multiproduct retailers[END_REF](Levy, et al. , 2002;;Dutta, et al.1999Dutta, et al. , 2002;;[START_REF] Levy | The real thing: nominal price rigidity of the nickel coke, 1886-1959[END_REF][START_REF] Young | Explicit evidence on an implicit contract[END_REF][START_REF] Zbaracki | Managerial and customer costs of price adjustment: direct evidence from industrial markets[END_REF]), as well as contractual obligations as sources of price rigidity. therefore, models firms as choosing both the price and the average contract length optimally, conditional on their information at the time of price setting. In particular, he assumes that there is a prohibitive cost of renegotiating contracts currently in effect in response to a shock.

Yetman demonstrates that with fixed average lengths contracts, and combined with menu costs, his model can retrieve the hump-shaped inflation response for realistically sized shocks. He also argues that sticky contracts remedy another limitation of the sticky information model. Sticky contracts imply that the level of trend inflation affects the inflation dynamics of the economy, which is consistent with existing empirical evidence, whereas sticky information combined with time-contingent price-path adjustment implies that stable trend inflation has no effect on inflation dynamics.

In "Price Rigidities, Inventories and Business Cycles,"Chris Tsoukis and Naveed Naqvi set up an equilibrium optimization model to study the interaction between price rigidities and inventories and its role in the emergence and propagation of business cycles. According to Tsoukis and Naqvi, this interaction may be important at both the micro and macro levels. When firms fix prices, they meet demand by varying supply, but when supply cannot be varied instantaneously then they adjust the inventories. Thus, price fixity and inventory fluctuations are closely linked. At the macro level, the (temporary) decoupling of demand and supply allowed by the existence of inventories could provide important insights into business cycles.

Tsoukis and Naqvi note that despite the attention received in the existing literature by price rigidities and inventories in isolation, the interactions between the two has been largely ignored. With the goal of filling this gap in the literature, Tsoukis and Naqvi investigate the effects of greater price flexibility and storability of the inventory goods on business cycle dynamics. They also show how inflation persistence can arise in an optimization framework. They link the inflation persistence to price flexibility and the storability of goods.

The strategy adopted by Tsoukis and Naqvi is to pursue a general equilibrium analysis in terms of growth rates rather than the more popular HP-filtered levels. That is because the public and policy-making discourse is cast in terms of growth rates, and also because the time-series properties of growth rates (log differences) are easier to interpret than those of HP residuals.

The model of Tsoukis and Naqvi assumes profit maximizing firms with an AK technology and proportional capital adjustment costs. The firm maintains a stock of inventories as a buffer between supply and demand, which allows it to meet fluctuations in demand. The firm is a monopolistic competitor with the ability to set its own price.

Price adjustment, however, is sluggish because of the menu costs and follows the wellknown Calvo pattern, which gives rise to a forward-looking inflation equation.

Tsoukis and Naqvi derive analytically a number of results about the effect of greater price flexibility and inventory good storability on the persistence and volatility of the macro system. They find that greater price flexibility reduces the persistence of growth fluctuations but does not necessarily reduce the overall volatility of the macro system.

Tsoukis and Naqvi also find that inflation is negatively related to growth and the inventory ratio regardless of the origin of the shock. Finally, they show how persistence of inflation can arise in a general equilibrium system. Overall, Tsoukis and Naqvi note, their analysis points to rather complex interactions between price rigidities and storability of inventory goods.

In the last paper of the special issue, "The Real Effects of Inflation in Continuous versus Discrete Time Sticky Price Models," Wai-Yip Alex Ho and James Yetman compare the real effects of trend inflation and monetary shocks in discrete and continuous time versions of a simple model of a New Keynesian style economy. As Ho and Yetman note, many New Keynesian models incorporate time-dependent sticky prices. These models often use a discrete time framework, which effectively imposes an arbitrary minimum length of time over which prices must be fixed. With many authors defining a period as corresponding to one quarter, this implies that a complete price flexibility corresponds to a situation where prices are updated once a quarter. If one removes this restriction, then continuous time modes are obtained. Ho and Yetman assume that nominal prices are sticky because of menu costs, but that firms optimally choose their average contract length.

Based on the analysis of this model, Ho and Yetman conclude that for given menu costs, continuous time setting implies a shorter average contract length, and larger real effects of both trend inflation and monetary shocks, than discrete time unless inflation is very low. Further, Ho and Yetman find that while discrete time models result in complete price flexibility above some finite level of trend inflation, price flexibility arises only asymptotically in continuous time models. Finally, consistent with common wisdom, Ho and Yetman find that if changing prices requires labor input (see, for example, [START_REF] Levy | The magnitude of menu costs: direct evidence from large U.S. supermarket chains[END_REF][START_REF] Levy | Price adjustment at multiproduct retailers[END_REF][START_REF] Dutta | Menu costs, posted prices, and multiproduct retailers[END_REF][START_REF] Zbaracki | Managerial and customer costs of price adjustment: direct evidence from industrial markets[END_REF], then continuous time models lead to large welfare costs of high rates of inflation, while discrete time models do not.

  , which have not been reviewed thoroughly in the post 1980s literature. The studies by Mills and Means have been extremely influential, although as Wolman notes, they are not without shortcomings.

Acknowledgements

I am grateful to numerous anonymous scholars for serving as referees, and for helping me assess the papers, comment on them, and help the authors improve the manuscripts. Some of these referees have read two, three, and two of them even four versions of the manuscript, which have substantially delayed the completion of this special issue. I am grateful to the authors for patiently waiting for the completion of this editorial process. I also thank my colleagues and coauthors, Bob Barsky, Mark Bergen, Allan Chen, Sourav Ray, Paul Rubin, Avichai Snir, Andy Young, and Mark Zbaracki for numerous conversations, comments, and advice throughout the editorial process. Soyong Chong, Mike Hammock, and Shireen Meer provided efficient editorial assistance in the editing and processing of the special issue. Finally, I thank Wiley's production personnel of the MDE for their assistance in processing the papers for publication.


Daniel Levy
email: levyda@mail.biu.ac.il.

Guest

Price Rigidity and Flexibility: New Empirical Evidence Introduction to the Special Issue

Keywords: D21, D40, E12, E31, E50, E52 Price Rigidity, Price Flexibility, Cost of Price Adjustment, Menu Cost, Managerial Pricing, Price System, Price Setting, New Keynesian Economics, Store-Level Data, Micro-Level Data

The marketplace, along with its price system, is the single most important institution in a western-style free enterprise economy. The ability of prices to adjust to changes in supply and demand conditions enables the market to function efficiently and lies behind the magical invisible hand mechanism. To the behaviour of prices and in particular to the ability of prices to adjust to changes in market conditions, therefore, have fundamental implications for many key issues in many areas of both microeconomics as well as macroeconomics. It is, therefore, critical to study and understand whether there are barriers to price adjustments, what are the nature of these barriers, how the barriers lead to price rigidity, what are possible implications of these rigidities, etc. This introductory essay briefly summarizes the fourteen empirical studies of price rigidity that are included in this special issue.

INTRODUCTION

The marketplace, along with its price system, is the single most important institution in a western-style free enterprise economy. It is the ability of prices to adjust to changes in supply and demand conditions that enables the market to function efficiently.

It is the ability of prices to adjust to changes in market conditions that lies behind the magical invisible hand mechanism. To the behaviour of prices, therefore, have fundamental implications for many key issues in many areas of both microeconomics as well as macroeconomics.

One of the key questions of interest in this context is to what extent do prices indeed adjust to changes in market conditions. In other words, how rigid or how flexible are the prices? In microeconomics and industrial organization, this question is important as the extent of price rigidity and flexibility may serve as an indicator of the efficiency of the price system and market outcomes. In macroeconomics and in monetary economics this question is important because of the role rigid prices play in explaining short-run monetary non-neutrality and therefore in the study and conduct of macroeconomic and monetary policy. It is, therefore, critical to study and understand whether prices are rigid or not, that is, whether there are barriers to price adjustments, what are the nature of these barriers, how the barriers lead to price rigidity, what is the extent of the price rigidity, what are the microeconomic and macroeconomic consequences of the price rigidity, how widespread price rigidities really are, etc.

Certainly, these and many similar questions about price rigidity are not new. The rigidity of prices and wages is one of the key ingredients of the traditional Keynesian economics. Until about early 1990s, however, there were only a handful of empirical studies that studied price rigidity using micro level (i.e., store-level and product-level) data on actual transaction prices.

During the last 15-20 years, the literature has witnessed a remarkable revival in the popularity of New Keynesian models, that is, models that incorporate various forms of price rigidities as the main source of friction that generates monetary non-neutrality. See, for example, Mankiw andRomer (1991a, 1991b) and Sheshinski and Weiss (1993), which contain references to other related studies.

The revival of the theoretical New Keynesian research program has rekindled the economists' interest in the empirical aspects of price rigidity. The literature, therefore, began producing empirical studies of price rigidity using various types of micro-level data from the US as well as from the European Union member countries.

A previous special issue of the Managerial and Decision Economics [START_REF] Levy | Managerial and Decision Economics, a special issue on "Price Rigidity and Flexibility: Recent Theoretical Developments[END_REF] was devoted to reporting some of the recent theoretical developments in this line of research. The goal of the current special issue of the Managerial and Decision Economics is to report the findings of some of the most recent empirical studies of price rigidity. A forthcoming special issue of the Managerial and Decision Economics (Levy and Smets, 2007) will report the results of some recent additional empirical studies that use micro level retail and wholesale transaction price data as well as survey data from several European Union member countries.

IN THIS ISSUE

This special issue of the Managerial and Decision Economics contains 14 empirical contributions. These papers address empirically various aspects of price rigidity and flexibility from different angles using different types of data from different sources. Of the 14 papers, eight of them use data from the US, three studies use data from Germany, one study uses data from Hungary, one from the Netherlands, and one from Israel. The types of data range from internet prices, to scanner data, to store-level hand-collected price data, to mail order catalogue price data, and to individual product level price data that are collected by national statistical agencies. The nature of the products and goods covered also varies, from books and CD's, to various food items, computer hardware, mortgages, consumer products, gasoline, etc.

The analysis of price data from the internet is particularly beneficial because on the internet the information gathering and search cost is substantially lower in comparison to more traditional settings. For example, consumers can conduct easy and quick price comparisons by going to various price comparison sites. Individual sellers can track the prices of their competitors continuously at almost no cost by having special data gathering software monitor, access, and download the relevant price information. This, presumably, allows the sellers react to competitors' prices, or study the competitors' reactions to their pricing and price adjustment decisions. The resulting reduction in the extent of the information asymmetry and in search cost, it has been suggested, should reduce the price dispersion and could potentially lead the markets to converge to a single price. Further, the internet setting is relatively free of menu cost type price adjustment costs, making the internet price data particularly useful for conducting controlled experiments for assessing the relevance of various types of menu cost models by confronting the menu cost models' predictions against the data behaviour found on the internet.

Two papers in the special issue study the relevance of menu cost type price adjustment costs directly, although as discussed below, several other papers address the question as well, but not necessarily directly.

In the paper "Small Price Changes and Menu Costs," Saul Lach and Daniel Tsiddon use monthly store-level transaction price data for wine and meat products, sampled at Israeli wine and grocery stores, respectively. These are the same data used by the Israeli Central Bureau of Statistics for constructing the monthly consumer price index. Lach and Tsiddon use these data to address one of the central questions of the literature on menu costs: if the cost of price change is a "small fixed" amount as the menu cost literature usually envisions, then we should not see small price changes. However, many data sets, it turns out, contain small price changes. In addition to current study of Lach and Tsiddon, which they have also used in their earlier studies (Lach andTsiddon, 1992, 1996), small price changes have been documented, for example, by [START_REF] Carlton | The Rigidity of prices[END_REF] for intermediate good price data, by [START_REF] Kashyap | Sticky prices: new evidence from retail catalogues[END_REF] for mail-order catalogue price data, and more recently by Levy, et al. (2005) for retail prices of food products and by [START_REF] Ray | Asymmetric wholesale pricing: theory and evidence[END_REF] for wholesale prices of food products.

Lach and Tsiddon argue that there is no contradiction between the presence of small price changes on the one hand, and menu costs on the other, as long as many different products are sold by the same firm and the firm is subject to price adjustment costs that have a firm-specific component. Lach and Tsiddon argue that in such an environment, the optimal change in the price of a single product may indeed be small as long as the average price change of different products by the same firm is large. The findings Lach and Tsiddon report are consistent with this explanation. For example, Lach and Tsiddon find that the smaller a price change of a given product, the larger the average price change of the remaining products sold by the firm.

Rajesh Chakrabarti and Barry Scholnick argue in the paper "The Mechanics of

Price Adjustment: New Evidence on the (Un)importance of Menu Costs" that if menu cost is the main cause of nominal price rigidity, then no nominal rigidities should exist in the internet prices because in the internet setting price changes can be made with a click of a keystroke at virtually zero cost. In other words, Chakrabarti and Scholnick argue, the internet is free of menu costs.

In their paper, Chakrabarti and Scholnick examine the price change behaviour of two well-known online booksellers, Amazon.com and BarnesandNoble.com, and find strong evidence that nominal price rigidities indeed persist on the internet. Given the virtual absence of menu costs in the internet setting, they conclude that other types of costs besides menu costs, for example managerial thinking costs [START_REF] Zbaracki | Managerial and customer costs of price adjustment: direct evidence from industrial markets[END_REF][START_REF] Zbaracki | The anatomy of a price cut: discovering organizational sources of the costs of price adjustment[END_REF], must be causing these rigidities.

In the paper "Thick Markets, Market Competition and Pricing Dynamics: Evidence from Retailers," Kostas Axarloglou uses store-level transaction price data for books collected in Ann Arbor, Michigan, and for music CDs collected in Natick, Massachusetts, to study the implications of thick markets and of the intensity of market competition on price markups and the synchronization in price adjustments.

Axarloglou finds that price markups decline in the presence of thick market effect due to extensive market competition among retailers. Furthermore, he finds evidence that the likelihood of price adjustments as well as the cross-store price adjustment synchronization is closely related to the intensity of market competition among price setters over fairly standardized products with relatively short product life cycle.

In the paper "Follow the Leader: Price Change Timing in Internet-Based Selling," Robert Kauffman and Charles Wood examine pricing strategies and competitive interactions for internet sellers in books and music CD markets. Using customized internet data collection agent which run daily and gathered price data from various internet sellers and price comparison sites, Kauffman and Wood examine the pricing strategies that are observed among internet sellers, and attempt to identify the theories that best explain these observations. They use the VAR methodology to study the competitive strategies employed by internet sellers for pricing identical goods in the books' and music CDs' markets and explore the variation in these strategies across the sampled firms.

Kauffman and Wood find that the theory of Bertrand competition seems to be insufficient for explaining the competitive pricing interactions that are occurring among internet-based sellers in terms of the timing of the competitive price changes. Instead, their results show that the firms operating in the electronic marketplace appear to pursue different market segments. Moreover, they argue that within each segment different types of competitive interactions are feasible. Kauffman and Wood also find that rather than pricing at or near marginal costs, as predicted by Bertrand competition, internet sellers try to anticipate the price changes of their rivals and accordingly time their own price changes. They do this by either using similar business rules that cause their price adjustments to react to the same external events as the other sellers do, or by monitoring price changes directly and responding accordingly.

Three papers in the special issue address the question of asymmetric price adjustment directly or indirectly. The possibility that prices might adjust asymmetrically to cost increases and decreases (or to demand increases and decreases), has received considerable attention in the empirical price rigidity literature. The three studies of asymmetric price adjustment that are included in this special issue continue that line of research.

In the paper "Why Do Prices Rise Faster than They Fall? With an Application to Mortgage Rates," Linda Toolsema and Jan Jacobs study asymmetric price adjustment of mortgage rates in the Netherlands. They use two main interest rate series for their study.

The first is the average interest rate the Dutch banks charge for a mortgage with fixed interest term of five year. The second is the long-term (10-year) interest rate. This longterm interest rate is interpreted and treated as the capital market rate. Thus the former series is interpreted as the price, while the latter series is interpreted as the cost. Using these two series, Toolsema and Jacobs estimate an error correction model of a cointegration relationship in the framework of a bivariate VAR, where the change in the mortgage rate is explained by the deviation from the long-run equilibrium in the previous month and by the current and lagged increases as well as decreases in the capital market rate.

Toolsema and Jacobs find that the Dutch mortgage rates adjust asymmetrically to changes in their costs. Specifically, the find that the response of the mortgage rate is stronger if the cost, that is the capital market rate, increases in comparison to the situation where the cost decreases. Given the reduced form framework of the econometric estimation strategy they employ in their estimations, and given the absence of important exogenous determinants of the mortgage rates, they are unable to offer a clear-cut explanation to the findings they report. Instead, they suggest that the asymmetric interest rate adjustment may be due to (i) tacit collusion, (ii) consumer search or switching costs (where the search cost is primarily caused by the lack of transparency in mortgage markets), and (iii) prepayment risk.

In the paper, "The Dynamics of Dailey Retail Gasoline Prices," Michael Davis studies the behavior and the dynamics of daily gasoline prices in the US. Using two years of daily retail gasoline price data from four gas stations (two Mobil and two Citgo) located in Newburgh, New York, Davis studies asymmetric price adjustment of the gas prices and assesses the relevance of the existing menu cost models by estimating a structural dynamic model of firms' price adjustment behavior that incorporate menu costs, and finds that although the menu cost can explain the behavior of gas prices, menu fully.

Davis explores the asymmetry in gas price adjustment using a version of the autoregressive conditional hazard rate model as well as the more standard logit model.

Both models enable him to assess probabilistically the likelihood of price adjustments. He finds that in his sample, a price adjustment is more likely to occur upward than downward. Moreover, Davis explores the validity of a version of partial adjustment model and lagged information model and concludes that neither of them are consistent with the gas price behavior he documents. He concludes that a likely explanation for his finding is related to the consumers search behavior.

In the paper "Asymmetric Price Adjustment: Evidence from Weekly Product-Level Scanner Price Data," Georg Müller and Sourav Ray use Dominick's supermarket chain's scanner price data for both the retail as well the wholesale price for 30 commonly used food products in 6 categories in order to explore asymmetric price adjustment. Dominick's is a large Midwestern supermarket chain, operating about 95 large supermarket stores in and around Chicago metro area. The chain controls about 25 percent of the market share in Chicago and its vicinity, making it an economically significant representative of a large retail supermarket industry.

The paper is a follow-up of [START_REF] Peltzman | Prices rise faster than they fall[END_REF] study in which he uses the same basic data set (along with several other data sets) to explore the asymmetry. The difference between the two studies is that while Peltzman uses the data at a monthly frequency, Müller and Ray use the data at a weekly frequency, which the frequency at which the original scanner data is actually recorded. Their findings indicate that there is some limited asymmetry in the price behaviour of some individual products, but they do not find any evidence of pervasive chain-wide asymmetric pricing strategy. Müller and Ray discuss the issues of operational efficiencies, competition, and consumer perceptions as possible explanations for their findings, but in the end they rule them out. Instead, they conclude that models based on a version of costs of price adjustment offer most plausible explanation for the findings.

In the paper, "Price Rigidity and Market Power in German Retailing," Sascha Weber and Sven Anders study the scope of market power in the German retail market.

They also try to assess the magnitude of the effect of the market power on the extent of price rigidity and flexibility in the retail markets for beef and pork in Germany. Weber and Anders use a panel of weekly retail scanner price data for the two year period from January 2000 to December 2001 from 207 different retail outlets for 24 product categories. Amongst the sampled stores are small corner grocery stores as well as large self-service warehouses and discount chain stores. They also compare their findings to the findings reported for the US (see, for example, [START_REF] Barsky | What can the price gap between branded and private label products tell us about markups[END_REF]).

Weber and Anders conduct two types of analysis with this rich data set: extensive mean analysis and structural conjectural variation analysis. The extensive mean price analysis of the data shows that the hypothesis of competitive behaviour in the German retail food market can be rejected, because in their data items are sold at varying and temporarily rigid prices across different types of retail store. Weber and Anders find significant differences in the pricing behaviour across store types with discount stores featuring the highest degrees of price rigidity for beef and pork products. When Weber and Anders employ a structural conjectural variation approach to parameterize the retail industry-level equilibria, and they again find significant deviations from perfectly competitive behaviour. Thus, both approaches seem to suggest that the hypotheses of perfect competition in German retailing can be rejected, indicating that German retailers have some market power.

The link between individual price dynamics and the aggregate inflation unfortunately is not well-understood and is not often studied. The next four papers try to fill this gap in the literature by studying individual product-level price behaviour under various inflationary and monetary regimes using various types of data from three different countries.

In the paper "The Frequency and Size of Price Adjustment: Microeconomic Evidence," Attila Rátfai documents some basic facts about price adjustment patterns at the level of individual price setter using high frequency panel data set of retail prices of 14 processed meat products collected in 9 distinct stores in Hungary during the 1993-1996, when Hungary was experiencing moderate and stable inflation rates.

As Rátfai notes, the findings from a moderate inflation regime are particularly interesting because other related studies have typically focused on data from either low or high inflation countries. Studies of low-inflation period might suppress the role trend inflation may play in microeconomic pricing decisions, while the studies of high-inflation periods might end up reporting biased result because at high inflation the price adjustment frequency may exceed its "true" frequency.

Rátfai finds that stores typically change their prices in large, discrete and infrequent jumps. He also finds that the prices are set for about three months on average and when they are changed, the average change is 9 percent. Rátfai finds heterogeneity across both, stores and products, but the heterogeneity seems to be more prevalent in the frequency of price changes. The fraction of stores making large adjustments varies considerably over time and is strongly correlated with the inflation. Overall, Rátfai concludes that none of the popular pricing models is fully able to account for microeconomic realities found in the price settings that exist in the stores that are contained in his sample. Nevertheless, the pricing patterns Rátfai finds appear to be most consistent with two-sided S-s price adjustment models.

In the paper, "Retail Prices during a Change in Monetary Regimes: Evidence from Sears, Roebuck Catalogues, 1938Catalogues, -1951," Andrew Young and Alexander Blue study micro-level price dynamics immediately before and immediately after the establishment of the Bretton Woods monetary regime. For this they use price data from Sears, Roebuck and Company catalogues for 49 different consumer goods, representing fairly wide range of products both nationally branded as well as private label products.

Young and Blue find that over the entire sample period the average length between nominal price changes was over 2 years. That average was longer in the pre-Bretton Woods period in comparison to the later period, but only by less than half a month.

Additionally, they find that prices of nationally branded products were considerably more rigid than private labels (consistent with the findings reported by [START_REF] Barsky | What can the price gap between branded and private label products tell us about markups[END_REF]. Moreover, they identify three goods that did not experience a single price change. In terms of the size of the price changes, the price changes of both nationally branded products and private label products were larger by 0.60-1.83 percent on average during the period from 1945 to 1951 than during the pre-Bretton Woods period. Young and Blue do not find evidence of decreased price inertia in the higher inflation time period. Instead, they find that the price changes in their sample display a higher correlation with inflation from 1938 through 1944. Thus, Young and Blue conclude, the evidence favours a time-dependent pricing model that did not change significantly in response to the establishment of the Bretton Woods regime.

In the paper "Are They Always Offering the Lowest Price? An Empirical Analysis of the Persistence of Price Dispersion in a Low Inflation Environment," Sebnem Bahadir-Lust, Jens-Peter Loy, and Christoph Weiss study the nature of price distributions and the intra-distribution dynamics for 10 food products across 131 retail stores in Germany in 2000, when the ongoing aggregate inflation rate was relatively low. Using Varian's (1980) model of sales and weekly transaction price data, they investigate whether the position of stores within the cross-sectional price distribution is persistent or perhaps it changes over time.

Bahadir-Lust, Loy, and Weiss report that posted prices vary considerably across stores. Store heterogeneity, it turns out, accounts for roughly 30% of this price dispersion and significant amount of dispersion remains even after controlling for unobserved store heterogeneity. Bahadir-Lust, et al. also document some changes in the position within the cross-sectional price distribution over time, but still they find more persistence in ranks than reported in previous studies. Finally, their regression analysis suggests that the degree of rank persistence varies across products, regions, as well as the type of stores.

In the paper "Price Variability and Price Dispersion in a Stable Monetary Environment: Evidence from German Retail Markets," Matthias Fengler and Joachim Winter study the relationship between inflation and price variation using weekly price data for consumption goods, collected by a German consumption analysis agency in 1995. The data includes prices for 23 product categories and cover a total of 560 individual products, each identified by the manufacturer, the products' size, the products' brand, etc.

Using these data, Fengler and Winter construct three measures of price dispersion and find significant positive correlation between the rates of price change and price dispersion, both at the level of individual products and product groups. They, however, find no correlation between the rates of price changes and price variability. After comparing their findings with those reported by other studies in this literature, they conclude that when aggregate nominal shocks are small-that is, during low inflation periods, only price dispersion is correlated with price changes. As the rate of inflation rises, both the variability as well as the dispersion becomes affected. During particularly high inflations periods such as during hyperinflationary periods, the systematic movements in the price dispersion seem to disappear. The price dispersion, Fengler and Winter conclude, is best explained by microeconomic frictions in price adjustment, whereas price variability appears to be related to costly price search and informational problems.

The only evidence the existing literature offers on the relevance of hierarchical delays for price rigidity, is the survey evidence of [START_REF] Blinder | Asking About Prices: A New Approach to Understanding Price Stickiness[END_REF] and several other replication survey studies that were conducted more recently by several EU central banks, some of which are included in the forthcoming special issue of the MDE (Levy and Smets, 2007). This is puzzling because [START_REF] Blinder | Asking About Prices: A New Approach to Understanding Price Stickiness[END_REF] include the theory of hierarchical delays amongst the twelve leading theories of price rigidity.

In the paper, "Hierarchical Delays as a Source of Nominal Price Rigidities:

Evidence from the Microcomputer Industry," Michael Hicks investigates the market for microcomputers in the United States from 1993-1995 and offers evidence of nominal price rigidities that are attributable to hierarchical delays. Hicks explores alternative explanations for these rigidities and is able to rule them out.

Hicks' data include price listings of the manufacturer's suggested retail prices for 80486SX computers and components in the 25-50MHZ range, including central processing units, partially and fully assembled systems and memory add-ons for the period from January 1993 through December 1995. Hicks argues that the prices in his data are sticky in a monopolistically or workably competitive industry, which he argues is consistent with the new Keynesian interpretation of his findings.

The last paper of the special issue focuses on a non-price adjustment mechanism.

The entire existing literature on market behavior in both microeconomic theory and industrial organization focuses almost exclusively on situations in which markets clear through price adjustment. The Walrasian model is exclusively devoted to the study of such markets.

Unfortunately, very few studies consider settings in which markets clear through some other mechanism [START_REF] Carlton | Equilibrium fluctuations when price and delivery lag clear the market[END_REF][START_REF] Carlton | Delivery lags as a determinant of demand[END_REF][START_REF] Blinder | Asking About Prices: A New Approach to Understanding Price Stickiness[END_REF][START_REF] Levy | The real thing: nominal price rigidity of the nickel coke, 1886-1959[END_REF][START_REF] Young | Explicit evidence on an implicit contract[END_REF]. However, we know that the equilibrium quantity depends on not only the product's price but also on its quality, on the delivery time, on the delivery place, etc. Therefore, markets in principle could clear through the adjustment of one of these non-price factors. It is, therefore, both interesting as well as important to understand how firms undertake such non-price adjustment activities, especially in situations where prices may be rigid despite changes in demand and supply conditions.

For example, it might be that the observed nominal prices are rigid only because the market adjusts through quality changes, or through changes in the delivery time (e.g., waiting in queues or in lines), or perhaps through changes in the delivery place, etc. In that case, the nominal price rigidity is not necessarily an indicator of market failure or of market inefficiency.

In the paper "Holiday Non-Price Rigidity and Cost of Adjustment," Georg Müller, Mark Bergen, Shantanu Dutta, and Daniel Levy use scanner price data from a large supermarket chain, to study one component of retailers' non-price retail activity, product additions and deletions. The data, which is used also by [START_REF] Müller | Asymmetric price adjustment: evidence from weekly productlevel scanner price data[END_REF], comes from the scanner data set of Dominick's, a large US supermarket chain in the Chicago metropolitan area, operating 94 stores with a market share of about 25 percent. According to [START_REF] Levy | The magnitude of menu costs: direct evidence from large U.S. supermarket chains[END_REF][START_REF] Levy | Price adjustment at multiproduct retailers[END_REF] and [START_REF] Dutta | Menu costs, posted prices, and multiproduct retailers[END_REF], the sales of large multi-store U.S. supermarket chains of this type comprised 86.3 percent of the total US retail grocery sales. Thus the market they are studying has a quantitative economic significance, as well.

The database Müller, Bergen, Dutta, and Levy use represents approximately 30 percent of Dominick's revenues. The data come from the chain's scanner database, which contains the actual retail transaction prices of the products by each SKU code. This enables them determine when a new product is introduced or when an old product is discontinued. The retail prices are the actual transaction prices: the price customers paid at the cash register each week. The subset of the data Müller, Bergen, Dutta, and Levy use consists of 4,532 products in 18 product categories covering a four-year period, from the week of September 14-20, 1989 to the week of September 16-22, 1993, a total of 210 weeks. The specific time series they use for the analysis come from 6 stores of the chain that face similar competitive environments. In total, they use 27,192 price time series.

The same data set has been used by Chevalier, et al. (2003), Levy, et al. (2002), Levy et al. (2005a, 2005b[START_REF] Müller | Private label price rigidity during holiday periods[END_REF][START_REF] Ray | Asymmetric wholesale pricing: theory and evidence[END_REF].

Using these data, Müller, Bergen, Dutta, and Levy document periods of rigidity in the activities related to new products' introduction and old products' deletion. Specifically, they find that new products are less likely to be introduced, and existing products are less likely to be discontinued during major US holiday periods than throughout the rest of the year. Müller, Bergen, Dutta, and Levy argue that this is likely due to higher costs of undertaking these kinds of product assortment activities during holiday periods. They discuss how this conclusion relates to the exiting literature on price adjustment costs, non-price adjustment, price adjustment during holiday periods, and price rigidity.

ACKNOWLEDGEMENTS

I am grateful to the following scholars for serving as anonymous referees, and for helping me assess the papers, comment on them, and help the authors improve the manuscripts: Maria Arbatskaya, Michael Baye, Erik Brynjolfsson, John Carlson, Allan Chen, Todd Clark, Andrew Eckert, Benjamin Eden, William Hamlen, Michael Hicks, Andreas Hornstein, Kevin Huang, James Kahn, Jurek Koniezny, Praveen Kopalle, Stefan Krauss, Saul Lach, Zheng Liu, Bernd Lucke, Attila Ratfai, John Roufagalas, Barry Scholnick, Michael Schwarz, Avichai Snir, Claus Thustrup, Eric Toulemonde, Russell Winer, Alex Wolman, and Andrew Young. Some of these referees have read two, three, and eight of them even four versions of the manuscript, which has substantially delayed the completion of this special issue. I am grateful to the authors for patiently waiting for the completion of this editorial process. I also thank my colleagues and coauthors, Bob Barsky, Mark Bergen, Allan Chen, Sourav Ray, Paul Rubin, Avichai Snir, Andy Young, and Mark Zbaracki for numerous conversations, comments, and advice throughout the editorial process. Soyong Chong, Mike Hammock, and Shireen Meer provided efficient editorial assistance in the editing and processing of the special issue. Finally, I thank Wiley's production personnel of the MDE for their assistance in processing the papers for publication.