Bargaining, Fairness, and Price Rigidity in a DSGE Environment

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 900 July 2007 Bargaining, Fairness, and Price Rigidity in a DSGE Environment David M. Arseneau Sanjay K. Chugh* *NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgement that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp. This paper can be downloaded without charge from Social Science Research Network electronic library at http://www.ssrn.com/.

Bargaining, Fairness, and Price Rigidity in a DSGE Environment∗ David M. Arseneau † Sanjay K. Chugh‡ Federal Reserve Board University of Maryland and Federal Reserve Board July 31, 2007 Abstract A growing body of evidence suggests that an important reason why firms do not change prices nearly as much as standard theory predicts is out of concern for disrupting ongoing customer relationships because price changes may be viewed as “unfair.” Existing models that try to capture this concern regarding price-setting are all based on goods markets that are fundamentally Walrasian. In Walrasian goods markets, transactions are spot, making the idea of ongoing customer relationships somewhat difficult to understand. We develop a simple dynamic general equilibrium model of a search-based goods market to make precise the notion of a customer as a repeat buyer at a particular location. In this environment, the transactions price plays a distributive role as well as an allocative role. We exploit this distributive role of pricestoexplorehowconcernsforfairnessinfluencepricedynamics. Usingpricingschemeswith bargaining-theoretic foundations, we show that the particular way in which a “fair” outcome is determined matters for price dynamics. The most stark result we find is that complete price stability can arise endogenously. These are issues about which models based on standard Walrasian goods markets are silent. Keywords: Sticky prices, fair pricing, customer markets, search models JEL Classification: E20, E30, E31, E32 ∗The views expressed here are solely those of the authors and shouldnot be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. †E-mail address: david.m.arseneau@frb.gov. ‡E-mail address: chughs@econ.umd.edu. 1

Contents 1 Introduction 4 2 Baseline Model 8 2.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Walrasian Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Non-Walrasian Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Price Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4.1 Nash Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4.2 Proportional Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4.3 Fair Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5 Goods Market Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.6 Resource Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.7 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 Partial Equilibrium Analytics 21 4 Quantitative Results in Baseline Model 24 4.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2 Steady State Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.3 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3.1 Nash Bargaining with No Menu Costs . . . . . . . . . . . . . . . . . . . . . . 28 4.3.2 Nash Bargaining with Menu Costs . . . . . . . . . . . . . . . . . . . . . . . . 29 4.3.3 Proportional Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.3.4 Fair Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.3.5 Customer Bargaining Power and Price Volatility . . . . . . . . . . . . . . . . 33 5 Intensive Quantity Adjustment 34 5.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.2 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.3 Price and Quantity Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.3.1 Nash Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.3.2 Proportional Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.3.3 Fair Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.5 Quantitative Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2

5.5.1 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.5.2 Steady State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5.5.3 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6 Demand Shocks 39 7 Conclusion 40 A Tables and Figures 43 B Nash Bargaining 59 C Fair Bargaining 62 D Steady-State Analytics 64 E Intensive Quantity Adjustment 65 F Advertising Data 67 3

1 Introduction Agrowingbodyofevidencesuggeststhatanimportantreasonwhyfirmsdonotchangepricesnearly as much as standard theory predicts is out of concern for disrupting ongoing customer relationships because price changes may be viewed as “unfair.” Several recently-developed models try to capture this concern regarding price-setting, but in all of them the underlying model of the goods market is Walrasian. InWalrasiangoodsmarkets,transactionsarespot,makingtheideaofongoingcustomer relationships somewhat difficult to understand. Instead, models that feature explicit bilateral relationships between customers and firms seem to be called for in order to study the interactions between customer relationships and price rigidities. We develop a simple model that embeds a search-based goods market in an otherwise-standard dynamic general equilibrium model, making the notion of a customer as a repeat buyer at a particular location well-defined. In this framework, the transactions price (the terms of trade) plays a distributive role as well as an allocative role. We exploit this distributive role of prices to explore how concerns for fairness influence price dynamics. Themoststarkresultwefindisthatifpricingisguidedbya“fairnessnorm,”completepricestability can arise endogenously. More generally, the consequences of menu costs of price adjustment on the dynamics of prices and allocations depend crucially on the manner in which price and quantity in specific relationships are determined, something about which standard models based on Walrasian goods markets are silent. Thetwofoundationsofourmodelareaspecificnotionofcustomerrelationshipsandmenucosts of changing prices in those customer markets. In our model, customer relationships are valuable to both consumers and firms because of search frictions that each must overcome before goods trade canoccur. Thepresenceofsearchfrictionsleadstoasurpluswhenacustomerandafirmmeet, and the parties must decide how to share the local monopoly rents. Regarding menu costs, we do not claim we have an explanation any deeper than existing ones for why there may be costs of changing prices; for convenience, such costs can be thought of in the typical fashion of costs associated with recording, reporting, and implementing new prices. By situating menu costs in a clearly-defined concept of a customer relationship, however, we are able to show that the consequences of price rigidities as typically formulated may depend critically on how prices and quantities traded are determined in specific relationships. Wefocusonbargainingschemesasthemechanismbywhichpricesandquantitiesaredetermined in customer markets. Despite using the formalisms of bargaining theory, we do not need to take literally the idea that customers and firms haggle over prices in every meeting. Rather, it seems to us that the idea that customers wield some “bargaining power” accords with the evidence of Blinder et al (1998) and others that firms often try to avoid upsetting their existing customers. Given this interpretation, we adopt three bargaining protocols to pin down terms of trade 4

between customers and firms: Nash bargaining, proportional bargaining, and a pricing system that we refer to as fair bargaining. We adopt Nash bargaining as a benchmark because of its familiarity: ithasrecentlybecomerelativelywell-understoodinmacroeconomicsduetotheongoing explosion of quantitative labor search models that employ it. Both proportional bargaining and fair bargaining implement an idea of a fairness norm under which parties always split the surplus in a fixed proportion, a feature that Nash bargaining does not always respect. The main difference betweenproportionalbargainingandfairbargainingisthemannerinwhichpartiesarriveatthefair outcome. Proportional bargaining assumes that the fair outcome is achieved through a mechanical sharing rule. In contrast, our notion of fair bargaining, although not axiomatic like the Nash and proportional outcomes, attempts to retain Nash bargaining’s strategic foundation by imposing fairness as a constraint on the standard Nash optimization problem. Akerlof (2007) makes the case that incorporating norms in macroeconomic models may be an evolutionary step for the field. We view our fairness norm, whether captured through proportional bargaining or fair bargaining, as in this spirit. We also view our idea as complementary to Rotemberg (2005, 2006), who has also stressed the notion that modeling fairness in pricing may be important. The crucial way in which our models of fair-pricing differ from Rotemberg (2005, 2006) is that we embed fairness as a feature of the trading structure of the environment, rather than altering preferences to account for it. In our model, if there are no menu costs, the Nash-bargaining outcome, the proportionalbargaining outcome, and the fair-bargaining outcome all coincide. In the presence of menu costs, however, the three bargaining protocols imply quite different dynamics of prices and allocations. Under proportional bargaining, menu costs turn out to be completely irrelevant for both quantity and price dynamics, which seems to accord with survey evidence, such as Blinder et al (1998) and Fabiani et al (2006), that menu costs are not a very important friction in practice. Under fair bargaining,pricesalwaysremainattheirsteady-statevaluesanddynamicallocationsarecompletely unaffected by price rigidity. The key to understanding the dynamics under both proportional bargaining and fair bargaining is the fact that under Nash bargaining, price movements cause a time-varyingwedgebetweenshort-runandlong-runsharesofthesurplusaccruingtocustomersand firms. With a fairness norm, parties eliminate such wedges, but the way in which the wedges are eliminatedmatters. Ifthewedgesareeliminatedaccordingtoproportionalbargaining’smechanical sharing rule, customers and firms efficiently and equally share the consequences of menu costs and are able to engineer the zero-menu-cost Nash outcome. On the other hand, if the wedges are eliminated with the strategic considerations of fair bargaining in the background, menu costs are borne entirely by firms and eliminating the wedges requires complete price stability. Duetothepresenceoflocalmonopolyrents, ourmodelalsohassomethingtosayaboutmarkup 5

behavior irrespective of menu costs. There lately has been a surge of interest in developing models in which markups are endogenously time-varying for reasons other than the presence of price rigidities.1 Our flexible-price models deliver a time-varying markup; moreover, the flexible-price markup is countercyclical with respect to demand shocks, which seems to accord with empirical evidence and which has been the attention of much modeling effort. However, with fair bargaining and the presence of menu costs, the markup is constant, which is simply a reflection of the fact that both prices and marginal cost are time-invariant under fair bargaining. In terms of bringing to bear data on our model, we exploit a central idea captured by our model: firms and consumers expend resources looking for trading partners. In our model, firms directresourcestowardsadvertisinginordertoattractcustomers, andshoppersspendtimelooking forandpurchasinggoodsfromfirms. Empiricalevidenceshowsthattheresourcesexpendedinsuch search activities are not negligible. Firm expenditures on advertising constitute over two percent of GDP, and time-use surveys show that individuals spend an average of about one hour per day shopping. Using such evidence, we can calibrate two deep features of our model. A by-product of our structure is that our model reproduces remarkably well the cyclical dynamics of aggregate advertising behavior in U.S. data. We articulate our ideas in a non-monetary model, meaning the price dynamics on which we focus are those of real (relative) prices. It is apparent that much interest would lie in whether and to what extent our results carry over to monetary environments. We have reason to believe that the crucial aspects of our results — namely, that the consequences of menu costs depend critically on how customers and firms determine prices and quantities and, in particular, the conclusion that some trading arrangements would lead to the endogenous emergence of price stability — would carry over to monetary economies because the core mechanisms at work in our environment do not depend on things being cast in nominal or real terms. However, adding a monetary dimension to our model may not be as straightforward as imposing an ad-hoc cash-in-advance constraint or other typical monetary formulation used in the literature because once customer relationships are modeled explicitly, we may have to be careful about issues such as which consumers carry cash, which firms require payment in cash, etc. A monetary extension seems a logical next step; here, though, we concentrate on understanding some basic principles of the interactions between price rigidity and customer relationships. Hall (2007) takes a very similar view of product markets as we take here and does use it to think about monetary policy issues. As in our model, the price at which goods change hands in Hall’s (2007) model plays a distributive role in additional to the standard allocational role. 1Some examples are Jaimovich (2006), Ravn, Schmitt-Grohe, and Uribe (2006), and Gust, Leduc, and Vigfusson (2006). 6

Different prices inside a customer relationship achieve different distributions of the surplus between the consumer and the firm, but this does not affect the underlying efficiency of a trade. This admits the possibility of, in Hall’s (2007) language, equilibrium sticky prices in customer markets. Given what we perceive as a growing sense of frustration with pricing models currently used in macroeconomic models, stemming from the growing body of micro pricing facts that challenge standard time-dependent or state-dependent pricing rules, allowing a distributional role for prices, as both our model and Hall’s (2007) model do, may be a useful new direction for macroeconomic models. It seems to us that allowing this additional role for prices accords better with the idea that firms do not re-set prices out of worry for upsetting customers than do standard views of price rigidity. Besides the difference in focus on monetary versus non-monetary issues, we think another aspect of our model that sets it apart from Hall’s (2007) is that we embed it from the start in a fully-articulated, quantitativeDSGEenvironment, makingcomparisonswithpredictionsofexisting DSGE models straightforward. Indeed, there lately has been a general surge of interest in developing simple structures of customer-firm interactions that can be tractably incorporated into state-of-the-art quantitative macroeconomic models. Our work here also falls into this broad category. A few recent examples of work in this broadly-defined area are the deep habits models of Ravn, Schmitt-Grohe, and Uribe (2006) and Nakamura and Steinsson (2007) and the switching-cost model of Kleschelski and Vincent (2007). As we mentioned, in terms of some basic motivation — the idea that fairness norms may interact with or may lead to price rigidity — the studies by Rotemberg (2005, 2006) are the closest in spirit to what we set out to achieve here. We view our work as complementary to all these recent efforts because we model customer relationships and fairness concerns through trading arrangements rather than essentially just through preferences. One could of course go back much further and tie ideas to the rich customer-markets literature, which includes studies by, among many others, Diamond (1971) and Klemperer (1995). Okun (1981) voices some of the ideas — namely, that search frictions in goods markets may have important consequences for aggregate phenomena — that we formalize through a modern search and matching framework. We certainly cannot do justice to the rich history of thought on these topics. The rest of our paper is organized as follows. In Section 2, we lay out our baseline model with standard Nash bargaining, proportional bargaining, and fair bargaining. In the baseline model, only an extensive margin of consumption exists, and bargaining occurs just over the price paid by the customer. We provide some partial equilibrium analytics in Section 3, which illustrate the core forces at work in our environment. We examine the fully general equilibrium baseline model’s numerical properties in Section 4, including a discussion of how and why fair bargaining leads to complete price rigidity in the face of arbitrarily small menu costs of price adjustment. 7

In Section 5, we enrich our environment to allow for bargaining over both price and quantity in a given customer relationship, thus allowing for extensive and intensive margins of consumption. Finally, in Section 6, we briefly extend our model to include exogenous government purchases to demonstrate that our basic results carry over to an environment with demand shocks. Section 7 concludes and offers some ideas for continuing work. Most of the derivations of key relationships in our model are relegated to the appendices. 2 Baseline Model Our key point of departure from standard macro models is that, for some goods trades, households and firms each have to expend resources finding individuals on the other side of the market with whom to trade. A fraction of goods market exchange is thus explicitly bilateral, in contrast to all trades happening against the anonymous Walrasian auctioneer. Our model also does feature standard Walrasian goods for which search frictions are absent. We believe this view of goods markets is quite natural — some goods require effort to find and some goods do not. For search goods, households spend time looking for firms from which to purchase goods, while firms direct part of their revenues towards trying to attract customers. We think of these two search activities as shopping and advertising, respectively. Because we want to avoid taking a specific stand on the details of why it is that goods-market trading is costly — there are probably a great many reasons — we adopt the modeling device of an aggregate matching function from the labor search literature. Hall (2007) also takes this route. We describe more fully this matching mechanism below.2 For our purposes, the important consequence ofthesesearchandmatchingfrictionsisthatonceacustomerrelationshipisformed, eachpartyhas an incentive to keep the match intact because dissolving the relationship would mean each has to re-enterthecostlysearchprocess. Theexistenceofasurplustobesharedinacustomerrelationship means that we must think beyond standard Walrasian marginal pricing conditions because prices play both distributional and allocative roles. In the rest of this section, we describe in detail the households and firms in our model as well as the rest of the economic environment. 2.1 Households There is a measure one of identical households, with a measure one of individuals that live within each household. In a given period, an individual member of the representative household can be engaged in one of four activities: purchasing goods (shopping) at a firm, working, searching for 2Those familiar with the basic labor search model as described by Pissarides (2000, chapter 1), will find close analogies in several of our modeling choices. 8

goods, or leisure. More specifically, l members of the household are working in a given period; s t t members are searching for firms from which to buy goods; Nh members are shopping at firms with t which they previously formed relationships; and 1−l −s −Nh members are enjoying leisure. Note t t t ourdistinctionbetweenshoppingandsearchingforgoods. Individualswhoaresearchingarelooking to form relationships with firms, which takes time. Individuals who are shopping were previously successful in forming customer relationships, but the act of acquiring and bringing home goods itself takes time.3 We assume that the members of a household share equally the consumption that shoppers acquire. With this atomistic structure, we assume that lifetime discounted household utility is ∞ " Z Nh ! # E X βt u(x )+ϑv t c di +g(1−l −s −Nh) (1) 0 t it t t t 0 t=0 where x is consumption of a standard Walrasian good and c is the quantity of the search good i that shopper i brings back to the household. The household costlessly (aside from the direct purchase price) and instantaneously purchases the good x, which is of course what it means for the good to be traded in a Walrasian market. Total consumption RNh c di of the search goods 0 i obtained by shoppers is pooled by the household and divided equally amongst all family members. Instantaneous utility over leisure is g(.), and the parameter ϑ governs how the household prefers to divide its total consumption between search and non-search goods. Note that consumption of the search good potentially has two dimensions in our model: an extensive margin (the number of shoppers who buy goods) and an intensive margin (the number of goods each shopper buys). For the results in this section, we shut down adjustment at the intensive margin by setting c = c¯. We begin by closing down the intensive margin for two reasons: doing so i emphasizes the extensive margin, which is the most novel aspect of our model, and it also allows us some flexibility in calibrating our model. We discuss this issue further below when we present the calibration of the baseline model. In section 5, we endogenize adjustment at the intensive margin of consumption. In the remainder of this section, then, we specialize to the case c = c¯, it and our notation reflects this. Finally, we point out that searching and shopping each detract from household leisure in the same, linear, manner.4 3Forexample, evenifone knowsexactlywheretogotobuy certaingoods, onemaystillhave towalkaroundthe aisles, stand in the checkout line, etc. 4WerecognizethatinmakingN andsperfectsubstitutesinhowtheydetractfromutility—eachunitofN ors is equivalent to forgoing one unit of leisure — we are taking a particular stand on the relative disutility of what we term searching versus shopping. A more general specification that allows for finer distinction between the disutility from shopping versus from searching would be u(x,l,s,N). Because we think we would not have sufficient guidance fromdataorexistingmodelsonhowtocalibrate,letaloneconstruct,suchafunction,weadopttheformulationthat we do. Despite limitations imposed by data and the lack of previous such modeling efforts, it has been suggested 9

Whether or not we allow intensive adjustment, note that the aggregator inside v(.) is linear in the total amount of search goods, meaning what we have in mind is a world in which all search goods are perfect substitutes in utility. Our baseline model focuses on this polar case because it means that any “monopoly markups” that arise in our model are due solely to search and matching frictions that create temporary bilateral monopolies, rather than to any ex-ante differentiation of products that create pure monopolies. That is, beginning with this assumption again allows us to isolate effects stemming from the search frictions in goods markets. As we will see in section 5, in order to endogenize the intensive quantity traded, we must add some curvature to the consumption aggregatorinside v(.). Theeconomic contentofsuchcurvature is thatgoods obtainedfrom distinct matches are imperfect substitutes. We defer further discussion on this point until we encounter the full model in section 5. Using c = c¯for now, then, the flow budget constraint the household faces is i Z Nh t x + p c¯di+b = w l +R b +d , (2) t it t t t t t−1 t 0 where b is holdings of a state-contingent one-period real private bond at the end of period t−1, t−1 which has gross payoff R at the beginning of period t, w is the real wage, and d is firm dividends t t t received lump-sum by the household. The Walrasian good x serves as the numeraire, hence the price p of a given search good is measured in units of x. With this structure so far, the household’s i first-order conditions with respect to Walrasian consumption x , labor l , and bond holdings b are, t t t respectively, u0(x )−λ = 0, (3) t t −g0(1−l −s −Nh)+λ w = 0, (4) t t t t t −λ +βE {λ R } = 0, (5) t t t+1 t+1 whereλ istheLagrangemultiplierassociatedwiththetime-tflowbudgetconstraintandmeasures, t in equilibrium, the marginal value of wealth to the household. Conditions (3), (4), and (5) are completely standard and imply the usual consumption-leisure optimality condition g0(1−l −s −Nh) t t t = w (6) u0(x ) t t to us that perhaps shopping does not entail disutility at all and that it is only searching that is associated with disutility. In that case, we may consider writing u(c,1−l−s), in which s continues to detract from leisure, which has some precedent from “shopping-time” models, but N does not. We do not have a strong prior regarding this latterviewthatshoppingandsearchingaresufficientlydistinctactivities. Thus,ratherthanpresentadizzyingarray of alternative preference specifications, our approach is to simply lump shopping and searching together in terms of utils and see how much progress we can make on our core ideas. If the primitive trading arrangements our model emphasizes(whichareindependentofhowwewishtowritepreferences)aredeemedsufficientlyuseful,onemaywant to consider alternative preference specifications. 10

and consumption-savings optimality condition u0(x ) = βE (cid:8) u0(x )R (cid:9) . (7) t t t+1 t+1 The household must also choose how much effort to devote to searching and a desired number offutureshoppers; Nh isnotfreetobechosenatthebeginningofperiodtbecausethatdependson t how many searchers were previously successful in forming customer relationships. The household faces a perceived law of motion for the number of active customer relationships in which it is engaged, Nh = (1−ρx)(Nh+s kh(θ )), (8) t+1 t t t where kh is the probability that a searcher finds a good. This matching probability depends on θ ≡ a/s, which measures the tightness of the goods market — how many advertisements there are per searcher — and is taken as given by the household. With fixed probability ρx, which is known to both households and firms, an existing customer relationship dissolves at the beginning of a period. The dissolution of a customer relationship may occur for any of a number of reasons: the customer may move away, the firm may close shop, the customer may simply choose to stop visiting the same store for some reason, and so on. A natural potential future extension would be to endogenize the rate at which customer-firm relationships break up. Finally, then, the household first-order conditions with respect to s and Nh are t t+1 −g0(1−l −s −Nh)+(1−ρx)µhkh(θ ) = 0 (9) t t t t t and ( Z Nh ! ) t+1 −µh+β(1−ρx)E µh −βE {λ p c¯}+βE ϑv0 c¯di c¯−g0(1−l −s −Nh ) =0, t t t+1 t t+1 Nt+1 t t+1 t+1 t+1 0 (10) where µh is the Lagrange multiplier on the law of motion for shoppers, p is the relative price t Nt+1 of the N-th good at time t+1, and c¯ is the fixed quantity consumed of the N-th good at time t+1. As we present below, the price p is determined in bargaining. From here on, we conserve on i (cid:18) (cid:19) notation by using v0 to stand for v0 RN t h c¯di , g0 to stand for g0(1−l −s −Nh), and u0 to stand t 0 t t t t t for u0(x ). t Having taken first-order conditions and given that we restrict attention to symmetric equilibria in which p = p for all i 6= j, the first-order condition on Nh becomes i j t+1 −µh+β(1−ρx)E µh −βE {λ p c¯}+βE (cid:8) ϑv0 c¯−g0 (cid:9) = 0, (11) t t t+1 t t+1 t+1 t t+1 t+1 where p now stands for the real (measured in units of x) price of any given good for which there t+1 exists a customer-firm relationship. Condensing this expression with the household first-order 11

condition on s, we have ( ) g0 g0 t = β(1−ρx)E ϑv0 c¯−g0 −λ p c¯+ t+1 . (12) kh(θ ) t t+1 t+1 t+1 t+1 kh(θ ) t t+1 Using (3) and re-grouping terms, we have ( ) g0 g0 t = β(1−ρx)E c¯ (cid:2) ϑv0 −p u0(x ) (cid:3) −g0 + t+1 , (13) kh(θ ) t t+1 t+1 t+1 t+1 kh(θ ) t t+1 whichwerefertoasthehousehold’sshoppingcondition. Theshoppingconditionsimplystatesthat attheoptimum,thehouseholdshouldsendanumberofindividualsouttosearchforgoodssuchthat the expected marginal cost of shopping (the left-hand-side of (13)) equals the expected marginal benefit of shopping (the right-hand-side of (13)). The expected marginal benefit of shopping is composed of two parts: the utility gain from obtaining c¯more goods via the search market rather than via the Walrasian market (net of the direct disutility g0 of shopping) and the benefit to the household of having one additional pre-existing customer relationship entering period t+1. If all trades were frictionless, household optimal choices would imply ϑv0 = p u0(x ). With frictions, in t t t order to engage in costly search, it must be that on the margin, the household expects ϑv0 > t+1 p u0(x ).5 This positive flow return ensures that the household finds it worthwhile to send t+1 t+1 some of its members shopping. 2.2 Walrasian Firms To make pricing labor simple, we assume that there is a representative firm that buys labor in and sells the Walrasian good x in competitive spot markets. The firm operates a linear production technology that is subject to aggregate TFP fluctuations, y = z lW, where lW denotes the labor t t t hired by Walrasian firms. Profit-maximization yields the standard result that w = z , (14) t t which all participants in the economy, including the non-Walrasian firms described next, take as given.6 5In the calibrated version of the model, this condition does indeed hold, but it is likely not a theorem that this condition must hold. For some parameterizations, it is likely that the condition fails, in which case a participation constraint would be needed to ensure an equilibrium in which search goods are desirable. We echo and expand on thispointinthecontextoffirmincentivesinthisenvironmentwhenwediscussthemodelwithintensiveadjustment in section 5. 6AstructureisomorphictoourdivisionintoWalrasianfirmsandnon-Walrasianfirmsdescribednextistosuppose thatthereisasinglerepresentativefirmthathireslabortoproduceoutput,someofwhichitsellsdirectlytoconsumers via Walrasian markets and some of which it sells via search-based channels. One could labels these two channels of sales to consumers as “wholesale” and “retail” channels, which would make the environment look more similar to that of Hall (2007). 12

2.3 Non-Walrasian Firms We also assume that there is a representative firm that sells a large number of goods in bilateral trades. For each good that it sells, the representative search firm must first attract customers. To attract customers, the firm must advertise, and how any given level of advertisements it posts mapsintohowmanycustomersitfindsisgovernedbyamatchingtechnologytobedescribedbelow. Owing to frictions associated with finding customers, the firm views existing customers as assets. Its total stock of customers evolves according to the perceived law of motion Nf = (1−ρx)(Nf +a kf(θ )), (15) t+1 t t t where a is the number of advertisements the firm posts in period t, and kf is the probability that t one of the firm’s advertisements attracts a customer, which depends on goods market tightness θ; θ is taken as given by the firm. As with competitive firms, the production technology is linear in labor and subject to an exogenous aggregate productivity shock. Total output of the non-Walrasian firm is thus y = z lA, t t t where lA denotes the labor hired by the non-Walrasian firm. Because we assume a constant-returns production technology with no fixed costs of production (there is a fixed cost of advertising, but no fixed cost of producing), its real marginal cost of production is constant and coincides with average cost.7 Denoting marginal production cost by mc in period t, we can express the firm’s t total production costs as the sum of production costs across all of its customer relationships, RNf t mc c di. 0 t it The firm also faces a menu cost of adjusting the per-unit price of each good it sells to a given customer. Specifically, we use a Rotemberg-type quadratic cost of price adjustment, which is a fairly conventional way of modeling menu costs. As we mentioned earlier, our goal is not to provide acompellingmicro-foundationforwhypriceadjustmentmayentailcosts; rather,adoptingatypical reduced-form specification is just a tractable way to get at our ultimate objective. With this structure in place, total profits of the representative search firm in a given period t are Z Nf Z Nf Z Nf κ (cid:18) p (cid:19)2 t t t it p c di− mc c di− −1 −γa , (16) it it t it t 2 p 0 0 0 it−1 where p is the relative price (which is, recall again, measured in units of x) of good i, γ is the it flow cost of an advertisement, thus γa is the total flow advertising cost the firm incurs. We again t specialize right away to the case c = c¯ and, as we have already mentioned, defer considering i intensive adjustment until section 5. The parameter κ measures how large menu costs are; setting κ = 0 of course means there are no menu costs. The firm’s customer base Nf is pre-determined t 7To preview the equilibrium, mc =1 ∀t in our model because we have w =z . t t t 13

entering period t. Discounted lifetime profits of the firm are thus X ∞ " Z N t f Z N t f Z N t f κ (cid:18) p it (cid:19)2 # E Ξ p c¯di− mc c¯di− −1 −γa , (17) 0 t|0 it t 2 p t t=0 0 0 0 it−1 where Ξ is the period-0 value to the household of period-t goods, which we assume the firm uses t|0 to discount profit flows because the households are the ultimate owners of firms.8 The problem of the firm is thus to maximize (17) subject to the evolution of its customer base (15) by choosing {a ,Nf }. In the firm’s pursuit of customers, it takes p and c¯ as given t t+1 i becausethosewillbedeterminedinthetradingprotocolstobedescribedbelow. Noteanimportant pointofdeparturefromstandardmacromodelsofgoodsmarkets: thefirmisnot aunilateralpricesetter here.9 The first-order conditions with respect to {a ,Nf } thus are t t+1 −γ +(1−ρx)µfkf(θ ) = 0 (18) t t and   !2  n o  κ p  −Ξ t|0 µf t +(1−ρx)E t Ξ t+1|0 µf t+1 +E t Ξ t+1|0p N,t+1 c¯−mc t+1 c¯− 2 p N,t+1 −1  = 0, (19)  N,t  where µf is the Lagrange multiplier on the firm’s customer constraint. Condensing these first-order t conditions, we arrive at the firm’s optimal advertising condition,   !2  γ  κ p γ  kf(θ ) = (1−ρx)E t Ξ t+1|tp t+1 c¯−mc t+1 c¯− 2 p N,t+1 −1 + kf(θ )  , (20) t  N,t t+1  where Ξ ≡ Ξ /Ξ is the household discount factor (again, technically, the real interest t+1|t t+1|0 t|0 rate) between period t and t+1. In equilibrium, Ξ = βλt+1, which in turn, by the household t+1|t λt optimality condition (3), is Ξ = βu0(xt+1). In writing (20), we have also imposed symmetric t+1|t u0(xt) equilibrium, in which p = p = p for any i 6= j. it jt t The advertising condition states that at the optimum, the expected marginal cost of posting an ad (the left-hand-side of (20)) equals the expected marginal benefit of forming a relationship with a new customer (the right-hand-side of (20)). The expected marginal benefit takes into account the revenuefromsellingtooneextracustomer, theproductioncostsincurredforproducingtosellthose 8Technically, of course, it is the real interest rate with which firms discount profits, and in equilibrium the real interest rate between time zero and time t is measured by Ξ . Because there will be no confusion using this t|0 equilibrium result “too early,” we skip this intermediate level of notation and structure. 9The fact that price is “taken as given” as the firm optimally chooses its level of advertising might lead some to interpret this model as one in which firms have a primitive concern for maximizing their market share, an objective that some models of customer relations do posit. While this is somewhat a semantic point, we note that it is in fact profits that the firms in our environment maximize. It is just that firms are not free to unilaterally set prices to achieve maximum profits, rather they must form relationships before determining prices jointly with customers. 14

extraunits, futuremenucostsinthatcustomerrelationship, andthecostsavingsoffindinganother customer in the future due to the pre-existing (in time t+1) customer relationship. Condition (20) is a free-entry condition in advertising. The fact that an entry decision must be made before a firm can enjoy any profit flows means that profit flows from sales of goods are not pure rents as they are in commonly-employed formulations of goods markets. 2.4 Price Determination With bilateral relationships between customers and firms, there is an array of ways to think about how prices are determined. We focus on three bargaining schemes, two that are axiomatic and one that, although it is not axiomatic, seems to us to capture important intuitive elements underlying each of the two axiomatic schemes. In considering bargaining, we do not need to take literally the ideathatcustomersandfirmshaggleoverpricesineverymeeting,eventhoughthatistheformalism we use. Rather, it seems to us that the idea that customers wield some “bargaining power” accords with the evidence that firms often try to avoid “upsetting their existing customers.” Tomakeprogresswiththisidea,then,weconsiderthreebargainingprotocols. Thefirstprotocol isNashbargaining, thesecondisproportionalbargaining, andthethirdisamodifiedNashproblem in which the two parties always divide the match surplus in a fixed proportion. We refer to this third trading protocol as fair bargaining, although we recognize that bargaining theorists would not accord this trading protocol “bargaining” status. Conceding this point, we nonetheless use the term fair bargaining to make the discussions symmetric. Proportional bargaining and fair bargaining implement the idea of “fairness” in trading outcomes in similar, but distinct, ways. Our specific notion of fairness is one in which the surplus accruing to customers is always a fixed ratio of the surplus accruing to firms. Clearly, as discussed by Binmore (2007) and many others, there are a great many ways to operationalize the concept of fairness. Given our environment of explicit relationships between consumers and firms, we think ours is at least one natural definition. As we show below, and is well-known in bargaining applications (see Aruoba, Rocheteau, and Waller (2007) for a particularly recent application), the Nash solution does not generally satisfy this definition of fairness. It is well-understood that Nash bargaining has explicit strategic foundations. Specifically, Rubinstein (1982) shows that the Nash bargaining solution is the limiting solution of a strategic alternating-offers bargaining environment. In contrast, proportional bargaining, while it does, as we show below, capture our definition of fairness, does not have as clear a strategic foundation. Instead, it accords better with the concept of a focal-point equilibrium, an outcome that, perhaps for some evolutionary reason, simply is the accepted social norm. Experimental evidence on bilateral games people play, summarized by, among others, Binmore (2007, Chapter 6), suggests that 15

both strategic and focal-point elements are typically at work. This motivates us to construct our fair-bargaining scheme in an attempt to retain the strategic element inherent in Nash bargaining as well as the fairness/focal-point element inherent in proportional bargaining. 2.4.1 Nash Bargaining In Nash bargaining over the i-th product, the firm and the customer jointly choose p to maximize it the Nash product (M −S )ηA 1−η, (21) t t t where M is the value to a household of having a member engaged in a relationship with a firm, t S is the value to a household of having a member searching for goods, A is the value to a firm of t t beingengagedinarelationshipwithacustomer,andη isastandardtime-invariantNashbargaining weight. The value to a firm of an advertisement that failed to attract any customers is normalized to zero. As we show in Appendix B (where we present the definitions of M, S, and A), the price p that emerges from Nash bargaining in any particular customer-firm relationship satisfies the it sharing rule (1−ω )(M −S ) = ω A , (22) t t t t t in which ω is the effective bargaining power of the customer and 1−ω is the effective bargaining t t power of the firm. Specifically, η ω ≡ , (23) t η+(1−η)∆F/∆H t t where ∆F and ∆H measure marginal changes in the value of a customer relationship for the firm t t and the household, respectively. WeprovidemoredetailsinAppendixB,butthreepointsareworthmentioninghere. First,timevariation in ω means that the household’s surplus M −S from an active customer relationship t t t is not a fixed ratio of the firm’s surplus A . The Nash solution thus does not generally satisfy our t definition of fairness. Second, with zero costs of price adjustment in period t (which may arise for two reasons: either κ = 0 or κ > 0 but p = p ), ω = η (because in that case ∆F/∆H = 1). It it it−1 t t t is thus variation in prices coupled with the presence of menu costs that drives a time-varying wedge between effective bargaining power and the Nash bargaining weights. Indeed, if the Nash product the customer and firm maximized were (M t −S t )ωtA t 1−ωt rather than (21), the outcome would be the sharing rule (22). Third, in the long run (i.e., the deterministic steady state), ω = η because p = p = p¯ (recall these are real prices). Thus, the wedge between η and ω is a business-cycle it it−1 i t phenomenon. With time-varying effective bargaining power, the price solves ω " κ (cid:18) p (cid:19)2 γ # u˜(c¯) t it p c¯−mc c¯− −1 + = −p c¯+ (24) 1−ω it t 2 p kf(θ ) λ it t it−1 t t 16

" (cid:18) ω (cid:19) " κ (cid:18)p (cid:19)2 γ ## + (1−θ kf(θ ))E Ξ t+1 (1−ρx) p c¯−mc c¯− it+1 −1 + . t t t t+1|t 1−ω it+1 t+1 2 p kf(θ ) t+1 it t where u˜(c¯) is the utility function defined over the quantity consumed of a good obtained from a given customer relationship (rather than the utility v(.) defined over the household’s aggregate consumption of search goods RN c¯di.).10 The pricing condition (24) shows that price-setting is 0 forward-looking for two distinct reasons. One reason is a standard sticky-price reason: with costs of price adjustment, a setting for p has ramifications for future setting of p . But note that it it+1 even with κ = 0, p is affected by expectations regarding p . This forward-looking aspect of it it+1 pricing has to do with the long-lived customer relationship: with probability 1−ρx, the customer and firm will bargain over the same good again in the future. In typical models, price-setting is static in the absence of menu costs; in our framework, it is dynamic even in the absence of menu costs.11 Finally, we note that with κ = 0, the Nash sharing rule (22) reduces to the more standard (1−η)(M −S ) = ηA , and the pricing equation (24) simplifies dramatically to t t t (cid:18)u˜(c¯)(cid:19) p = (1−η) +η(mc −γθ ), (25) it t t λ t which one can obtain by working through the derivations in Appendix B. 2.4.2 Proportional Bargaining Condition (22) shows that in the presence of menu costs, the surplus is split between consumers and firms according to time-varying shares. Suppose instead that some fairness norm in pricing were in place in which the customer and firm ensure that they always split the total surplus in a time-invariant ratio. An axiomatic solution (see Kalai (1977) for the original exposition) that guarantees constant splits is the proportional bargaining solution. Under proportional bargaining, the price p solves it (1−η)(M −S ) = ηA , (26) t t t 10With intensive adjustment not allowed here in our basic model, we could just as well use the notation u¯≡u˜(c¯) ratherthanthestructurewepresent. Lookingforwardtoourfullmodelinsection5,though,theadditionalnotation here will prove useful in comparing features across models. 11InRavn,Schmitt-Grohe,andUribe’s(2006)andNakamuraandSteinnson’s(2007)models,pricingisalsoforwardlookingdespitetheabsenceofmenucosts. Intheirsetups,“deephabits,”whicharelong-livedpreferencerelationships consumershavewithparticulargoods,arethesourceofforward-lookingpricing. Atthecoreoftheirmodels,though, is still the typical Walrasian goods market, making, in our view, relationships perhaps a more tenuous idea than in our framework. No matter the relative merits of our approach versus others, a broader idea that emerges is that one can model long-lived customer relationships through preferences, as Ravn, Schmitt-Grohe and Uribe (2006) and Nakamura and Steinsson (2007) both do, or through trading arrangements, as we do here. 17

without any reference to an underlying maximization problem.12 Substituting the definitions of M , S , and A presented in Appendix B, the proportional-bargaining price solves t t t η " κ (cid:18) p (cid:19)2 γ # u˜(c¯) it p c¯−mc c¯− −1 + = −p c¯+ (27) 1−η it t 2 p kf(θ ) λ it it−1 t t (cid:18) η (cid:19) " " κ (cid:18)p (cid:19)2 γ ## + (1−θ kf(θ )) E Ξ (1−ρx) p c¯−mc c¯− it+1 −1 + , t t 1−η t t+1|t it+1 t+1 2 p kf(θ ) it t which differs from (24) only in that η/(1−η) replaces ω /(1−ω ). t t 2.4.3 Fair Bargaining As we discussed above, Nash bargaining has clear strategic foundations, while those underlying proportional bargaining are less clear. To try to capture both the strategic element underlying Nash bargaining and the focal-point element underlying proportional bargaining — both elements thattheevidenceofBinmore(2007)suggestsareimportantforunderstandingbilateralinteractions — we construct a pricing scheme that draws on both. The way in which we implement this idea is to continue using the Nash product as the objective the parties seek to maximize; however, constant shares are now enforced. Specifically, p is chosen it to maximize (M −S )ηA 1−η (28) t t t subject to a constant-split rule (1−ϕ)(M −S ) = ϕA . (29) t t t The most straightforward constant-split rule to understand is the case ϕ = η, which amounts to enforcing the standard Nash sharing condition despite the presence of menu costs. We focus just on this case.13 We provide the details behind this problem in Appendix C, but the outcome of fair bargaining over price is h i κ(π −1)π −(1−ρx)κE Ξ (π −1)π = 0, (30) it it t t+1|t it+1 it+1 in which π is defined as the gross rate of price change between period t−1 and t, π ≡ p /p . it it it it−1 If this were a monetary model, we would of course call π inflation and thus may be tempted to 12Technically,onecouldwriteanunderlyingmaximizationproblemthatgivesrisetothissharingrule,aswell,but for most practical applications, one does not need to do so. For more on the relationship between Nash bargaining and proportional bargaining, see Kalai (1977). 13AlthoughNashbargainingisostensiblyatthecoreofthispricingprotocol,wepointoutthatwhileNashbargaining,duetoitsaxiomaticnature,isacooperativeequilibriumconcept,fairbargainingisanon-cooperativeequilibrium concept. Inparticular,becausebyconstructionNashbargainingplacesthebargainingpartiesontheParetofrontier, the fact that the fair-bargaining solution differs necessarily means that it does not place the parties on the Pareto frontier. 18

refer to condition (30) as a modern Phillips curve because it links period-t price growth (inflation) to expected future price growth (inflation). What prevents condition (30) from being a Phillips curve (aside from the fact that our model is not cast in nominal terms) is that it contains nothing at all about allocations. To show how tantalizinglyclose(30)istoastandardNewKeynesianPhillipscurve,compareitwiththestandard pricing equation that emerges from New Keynesian models; for example, the analogous condition in Chugh (2006, equation 7) is h i f(mc )+κ(π −1)π −κE Ξ (π −1)π = 0, (31) t t t t t+1|t t+1 t+1 wheref issomefunctionthatdependsonthemarginalcostofproduction.14 Thefactthatmarginal cost, which reflects something about allocations, appears in a standard New Keynesian Phillips curve of course provides the linkage between real activity and price movements in that class of models. Our fair-pricing condition (30), missing marginal costs, is thus of course not a Phillips curve because it does not link price changes to real activity. Indeed, it is quite the opposite of the spirit of a Phillips Curve: condition (30) describes only the dynamics of prices and demonstrates that the dynamics of allocations are divorced from the dynamics of prices. Thus, price rigidity coupled with a fairness norm in bargaining effectively decouples prices from quantities in our model. Finally, we point out that our notion of fairness in pricing is an assertion about the bargaining protocol. We are not modeling deeper-rooted reasons that may underlie why fair bargaining (or proportionalbargaining,forthatmatter)maybeadoptedinthefirstplace. Onepotentialcandidate explanation is the recent model of Rotemberg (2006), in which customer “anger” over prices that are perceived to be exploitative may lead to a fairness norm. More broadly, Akerlof (2007), in his overture to macroeconomics to adopt more “norm-based” behavior into standard models, discusses why incorporating norms and, at least as a first step, ignoring endogeneity of norm adoption may be an important evolutionary step for the field. Such issues are quite interesting to consider, and if our model proves to be useful in thinking about some aspects of goods-market relationships, one may want to embed such mechanisms in our model in future work. For now, our focus is on the consequences of menu costs of price adjustment given a fairness norm in pricing. 2.5 Goods Market Matching The number of new customer-firm relationships that are formed in any period t is described by an aggregate matching function m(s ,a ). We assume the matching technology is Cobb-Douglas, t t 14In New Keynesian models, the Phillips curve is essentially just the first-order condition of firms facing rigidities in their price-setting choices and of course has nothing to do with bargaining. 19

m(s ,a ). With Cobb-Douglas matching, the probabilities that shoppers and firms, respectively, t t find partners is m(s,a) (cid:18) a(cid:19) kh(θ) = = m 1, = m(1,θ) (32) s s m(s,a) (cid:18)s (cid:19) kf(θ) = = m ,1 = m(θ−1,1), (33) a a with θ ≡ a/s a measure of how thick (the ratio of firms searching for customers to individuals searching for goods) the goods market is. As in the labor search literature, the matching function is meant to be a reduced-form way of capturing the idea that it takes time for parties on opposite sides of the market to meet. Rogerson, Shimer, and Wright (2005, p. 968) note that the ability to be agnostic about the actual mechanics of the process by which parties make contact with each other may be a virtue. Our modeling motivation is very much in line with this idea. With the matching function describing the flow of new customer relationships, the aggregate number of active customer relationships evolves according to N = (1−ρx)(N +m(s ,a )). (34) t+1 t t t 2.6 Resource Constraint Total output of the economy is absorbed by Walrasian consumption, non-Walrasian consumption, price adjustment costs, and advertising costs. The resource constraint is thus Z Nt Z Nt κ x + c di+ (π −1)2+γa = z l . (35) t it t t t t 2 0 0 2.7 Equilibrium We restrict attention to a symmetric equilibrium in which the price p is identical across all active customer relationships. Because (part of) goods trade is carried out in non-Walrasian markets, the core notion of equilibrium in our model is that of a search equilibrium, rather than a competitive equilibrium. This motivates the definition of a symmetric search equilibrium for our model. Asymmetricsearchequilibriumisendogenousprocessesforthehousehold’schoice{x ,l ,s ,Nh ,b }∞ , t t t t+1 t t=0 the Walrasian firm’s choice {lW}∞ , the non-Walrasian firm’s choice {a ,Nf ,lA}∞ , the real t t=0 t t+1 t t=0 wage {w }∞ , bond returns {R }∞ , dividends {d }∞ , prices in the non-Walrasian goods market t t=0 t t=0 t t=0 {p }∞ , and matching probabilities {kh,kf}∞ such that t t=0 t t t=0 • given {p ,w ,R ,d ,kh,kf}∞ , the household maximizes (1) subject to (2) and (8); t t t t t t t=0 • given {w }∞ , the Walrasian firm chooses labor to maximize profit; t t=0 • given {p ,w ,kh,kf}∞ , the non-Walrasian firm maximizes (17) subject to (15); t t t t t=0 20

• {p }∞ satisfies either (24) (Nash bargaining) or (30) (fair bargaining); t t=0 • the resource constraint (35) holds for t = 0,1,....; • the labor market clears, {l = lW +lA}∞ ; t t t t=0 • the customer market clears, {Nh = Nf}∞ ; t t t=0 • the aggregate law of motion for active customer relationships is given by (34) for t = 0,1,....; • the bond market clears, {b = 0}∞ ; t t=0 • dividends {d }∞ are determined residually from the non-Walrasian firm’s profit function; t t=0 • {kh,kf}∞ are given by (32) and (33). t t t=0 Collecting conditions that summarize the equilibrium, equilibrium is endogenous processes {x ,N ,p ,s ,a ,l ,w ,R }∞ thatsatisfy(6),(7),(13),(14),(20),either(24)or(30),(34),and(35), t t t t t t t t t=0 for given exogenous process {z }∞ . t t=0 3 Partial Equilibrium Analytics Our main interest lies in some general equilibrium business cycle consequences of search frictions in goods trade and price rigidity. However, we can gain a lot of intuition for the economic forces at work in our model by examining both analytically and numerically its steady-state equilibrium. The triple (p,θ,s) are the most important endogenous variables describing our frictional goods market.15 Features such as the intensive quantity c, presence of a production technology, and endogenous labor force participation are all present to make our model quantitatively realistic and readily comparable to other quantitative macroeconomic models. We again emphasize that the fundamental notion of goods-market equilibrium here is that of a search equilibrium, not a Walrasian (or Walrasian-based) equilibrium.16 Tomakesomeanalyticalprogress,then,forthemomentsupposethegeneralequilibriumfeatures of our model were shut down. Specifically, suppose c = 1 and labor is not needed (l = 0).17 In 15In this regard, there is a very tight analogy with the basic static labor search model, as described by Pissarides (2000, chapter 1), as we mentioned earlier. Those familiar with the textbook labor search model will find the analyticalexpositionhereextremelyfamiliar;becausethereareacoupleofdetailsthatdonotcarryovercompletely (but, admittedly, nearly completely) identically, we think it worthwhile to explain the basics. 16Asisapparent,whatwediscussinthissectionisequilibriuminthesearch-goodsmarket; Walrasianequilibrium is of course the relevant equilibrium concept for the good x. 17Really all we require for this partial equilibrium steady-state analysis is just that labor is fixed at l =¯l. Going all the way to essentially an endowment model — in which when a firm finds a customer to whom to sell, product magically appears — in which l=0 just eases the ensuing exposition a bit. 21

this partial equilibrium version of our model, then, imposing steady-state on the firm advertising condition gives us γ β(1−ρx) = (p−mc), (36) kf(θ) 1−β(1−ρx) in which we have used the fact that in the deterministic steady state, prices do not change (remember, these are real prices), hence there are no menu costs of price adjustment. With Cobb-Douglas matching, the probability a firm that has advertised matches with a customer is kf(θ) = θ−ξ. Imposing this and rearranging, we have β(1−ρx) β(1−ρx) p = mc+γθξ, (37) 1−β(1−ρx) 1−β(1−ρx) whichshowsthatthemarkupofpriceovermarginalcostofproductionisgovernedbytheadvertising cost γ and customer market tightness θ. If γ = 0, we have p = mc, which makes perfect sense because in that case it is costless for firms to find customers and we have assumed that goods are ex-ante perfect substitutes; in other words, the goods market is (nearly) Walrasian with γ = 0. With γ = 0, firms make normal profits by charging simply their marginal production cost as in a textbook model. Clearly, then, it is the search friction embodied in γθξ that drives a wedge between price and marginal production cost. Indeed, because γθξ ≥ 0, p ≥ mc. Figure 1 shows that the advertising condition is upward-sloping in (p,θ) space.18 To preview some of the intuition behind the dynamics of markups we present soon: because θ in general will vary over time as part of business cycle fluctuations, the markup of price over marginal production cost should be expected to be time-varying, and this markup is endogenous. Time-variation in search costs drives time-variation in markups in our framework.19 To determine the steady-state (p,θ), we must also examine (the steady-state version of) the pricing condition (24), which is the relevant pricing condition for both Nash and fair bargaining (because, recall again, both bargaining schemes deliver the same outcome when there is no cost of price adjustment, which is true in the steady-state of all our models). Again assuming c = 1 and afteralsousingthesteady-stateversionoftheadvertisingcondition,wecanexpressthesteady-state pricing condition as (cid:18)u˜(1)(cid:19) p = (1−η) +η(mc−γθ), (38) λ where we have used the fact that in steady state, ω = η. The first term on the right-hand-side of this expression, because it itself depends on θ in general equilibrium (because the marginal utility of wealth λ is a general equilibrium object), makes analyzing this expression prohibitively more 18In constructing Figures 1 and 2, we use the parameter values described in Section 4.1. 19Inadifferentnotionof“consumersearch”(oneinwhichsearchmeansthatconsumersexplicitlyfaceadistribution of prices from which to choose), Alessandria (2005) makes the very similar point that search costs are reflected in prices. 22

complicatedthananalyzingthesteady-stateadvertisingcondition. Tofocusideas, though, suppose it were simply a constant, A. In that case, we have the very simple pricing equation p = (1−η)A+η(mc−γθ), (39) which states that the price lies inside an interval bounded above by the firm’s production cost net of savings on search costs and bounded below by the household’s utility of consumption A. The convex weights are simply the Nash bargaining weights.20 The locus (39) is downward-sloping in (p,θ) space, as illustrated in Figure 1; the steady-state equilibrium (p,θ) is determined where it and the pricing condition cross in Figure 1. Conditions (37) and (39) characterize (p,θ) in terms of deep parameters. It is fairly straightforward to show (we provide the details in Appendix D) that the steady-state price is strictly decreasing in customer bargaining power η. This result makes a lot of intuitive sense: the more bargaining power customers wield, the less rents the firm can extract out of the match surplus, meaning the smaller is the markup of unit price over unit marginal production cost. So far, we have characterized the equilibrium pair (p,θ). To complete the description of the steady-state equilibrium core of our model, it remains to characterize s (or, equivalently, a, because θ ≡ a/s)foragiven(p,θ). Todothis,webeginbynotingthatinasteady-stateequilibrium,theflow of individuals from search into customer relationships equals the flow of individuals from customer relationships (gone sour) back into search. Equating these flows, kh(θ)s = ρxN = ρx(1 − s).21 Rearranging, ρx s = . (40) ρx+kh(θ) Cobb-Douglas matching implies kh(θ) = θkf(θ) = θ1−ξ. In (a,s) space, then, the flow condition (40), which characterizes activity on the household side of the goods market, defines the downward-sloping locus shown in Figure 2. Finally, to describe equilibrium in (a,s) space, we need a description of activity on the firm side of the goods market; such adescription comes from combining (37) and (39). Specifically, solving (37) for p, substituting in (39), and using the implicit function theorem to compute the slope of a with respect to s (we again relegate the details to Appendix D), we can show that the resulting form of the advertising condition is the upward-sloping ray in (a,s) space shown in Figure 2; the steady-state equilibrium (a,s) is determined where it and the locus (40) cross 20Once again, to those familiar with the modern theory of labor markets, this is all very familiar. Indeed, as we pointed out at the outset, our steady-state analysis is parallel to the analysis of the basic labor search model in Pissarides (2000, Chapter 1). 21Here it is critical that it is only searching and shopping that are the two possible activities for individuals, meaning s+N =1. If individuals could also work/take leisure and work/leisure were a possible state to transit to after a failed customer experience, it would be much more difficult to conduct the ensuing analysis. 23

in Figure 2. In combination, then, Figures 1 and 2 fully characterize the steady-state (partial) equilibrium triple (p,θ,a) that describes goods-market trade. 4 Quantitative Results in Baseline Model With these analytics in mind, we turn to characterizing the full deterministic steady state of our model numerically (i.e., fully endogenizing u˜/λ by re-introducing elastic labor supply). We begin by describing the calibration we use. 4.1 Calibration For instantaneous utility, we choose the common functional forms u(x) = logx, (41) v(y) = logy, (42) and ζ g(z) = z1−ν. (43) 1−ν The time unit of our model is meant to be one quarter, so we set β = 0.99, in line with an average annual real interest rate of about four percent. We fix the curvature parameter for the subutility function over leisure to ν = 0.4. We set the preference parameter ϑ = 1 as a baseline. With this baseline setting and given the rest of the calibration described below, the fraction of equilibrium total consumption that is comprised of consumption obtained through search is 43 percent. That is, ϑ = 1 delivers Nc = 0.43, which does not seem unreasonable. Varying ϑ varies this share; Nc+x in the limit, of course, ϑ = 0 collapses our model to one in which all goods are exchanged via Walrasian trade. As we mentioned earlier, we choose a Cobb-Douglas specification for the matching function, m(s,a) = ψsξsa1−ξs, (44) and set the elasticity to ξ = 0.5. We choose Cobb-Douglas because of its convenient properties — s in particular, the fact that matching probabilities depend only on goods-market tightness θ ≡ a/s, as we already mentioned — but recognize that it would be desirable to test how empirically useful the Cobb-Douglas description is for goods-market frictions.22 For the Nash bargaining weight η, we choose a middle-of-the-road calibration η = 0.50 for most of the results we report, but do vary it in some of our experiments. One virtue of setting η = ξ , well-known to search theorists, is that, as s 22Petrongolo and Pissarides (2001) survey the empirical usefulness of Cobb-Douglas matching for labor markets. 24

Hosios (1990) first showed in the context of labor search models, the underlying search equilibrium is socially efficient. We of course do not know if an efficient search equilibrium in the goods market is the best description of the data, but it seems useful as a starting point. We calibrate a number of other parameters in the version of our model in which there are zero costs of price adjustment (κ = 0). In this flexible-price version of our model, we set ζ = 4.3 so that the household spends 30 percent of its time working (equivalently, the household sends 30 percent of its family members to work) and then hold this value fixed as we move to other versions of our model. We also calibrate γ, c¯, and ψ, all of which we discuss in more detail immediately below, in the zero-menu-cost version of our model and hold the resulting values constant throughout all versions of our model. Two novel properties of our model about which we can obtain some empirical evidence are the amountoftimeconsumersspendshoppingandfirms’expendituresonadvertising. Accordingtothe American Time Use Survey (ATUS), conducted annually by the U.S. Bureau of Labor Statistics, the average American consumer spends just under one hour per day shopping, which is roughly one-fourth as much time spent working.23 The questionnaire that is the basis for the survey does not distinguish between, in the terminology of our model, “searching” for goods and “shopping” for goods. Thus, we calibrate our model so that, in the deterministic steady state, (N+s)/l = 0.25 and allow the model to endogenously determine N and s separately. Hitting this target requires setting the intensive quantity traded in a customer relationship to c¯= 1.4. Regarding advertising expenditures, we use data from the BLS and Universal McCann, an advertising agency that tracks and projects developments in the industry.24 According to these data, total nominal advertising expenditures in the U.S. in 2005 were about $276 billion and are estimated to have been about $290 billion in 2006, putting the share of advertising in total nominal GDP around 2.25 percent. This figure strikes us as non-neglible: firm spend quite a lot attracting and retaining customers. Going back to 1950, this share has generally fluctuated within the range 2 percent to 2.5 percent. Because the notion of advertising in our model is likely a bit more general than activities typically expensed as advertising, we use the upper limit of 2.5 percent as our guidepost.25 We thus calibrate γ so that γa in our model is 2.5 percent of GDP in steady state. In Appendix F, we provide for interested researchers annual aggregate advertising data. Unfortunately, neither the shopping data nor the advertising data gives us any guidance (at least not that we have been able to discern) about how to calibrate our model’s matching and separation probabilities. Lacking solid evidence, we calibrate the matching function parameter ψ 23Data on the American Time Use Survey, which began in 2003, can be accessed at http://www.bls.gov/tus/. 24A summary of the data through 2005 can be found in the BLS’s 2007 Statistical Abstract of the United States, Table 1261. 25In our model, any activity that potentially helps a firm attract customers is “advertising.” 25

in the flexible-price version of our model so that kh = 0.4. The resulting value is ψ = 0.45, which we hold fixed as we move to other versions of our model. We simply set the parameter that governs the breakup of a customer relationship at ρx = 0.10, which states that a firm loses ten percent of its existing customers in any given period. Equivalently, this parameter setting means that a newly-formedcustomer-firmrelationshipisexpectedtolastfor1/ρx = 10periods(quarters), which we think does not seem implausible. We also face a problem in terms of calibrating the price-adjustment parameter κ. Ideally, we would like to set it so that in the deterministic steady state, resources devoted to price adjustment absorb some empirically-relevant portion of output. However, because all prices are real in our model,price-adjustmentcostsarealwayszeroinanydeterministicsteadystate,makingκirrelevant for the steady state. Hence, we report results for several values of κ, corresponding to no, small, moderate, and large menu costs. We think this strategy is sufficient because the main results we wish to convey are conceptual rather than quantitative. Finally, the exogenous TFP process follows an AR(1) in logs, logz = ρ logz +(cid:15)z , (45) t+1 z t t+1 with (cid:15)z ∼ iidN(0,σ ). We choose ρ = 0.95 and σ = 0.007 in keeping with the RBC literature — z z z see, forexample, KingandRebelo(1999, p. 955). Asourresultsshow, thissettingforthevolatility of the shock to TFP delivers volatility of total output in our model of about 1.6 percent, in line with empirical evidence. Thus, the amplification of TFP shocks to GDP fluctuations in our model is no different than in a standard RBC model. 4.2 Steady State Numerical Results Steady-state prices and quantities are reported in Table 1 for our baseline calibration. At our benchmark value η = 0.50, the markup in the search goods sector is just above eight percent, in line with empirical evidence and with the settings for product-market markups employed by many quantitative macroeconomic models. Thebasicmotivationofourworkisthatcustomerbargainingpowermaybeimportantinpricing (andother)decisions. Assuch, onewouldwanttoknowthepredictionsofourframeworkregarding key endogenous variables as customer bargaining power changes. Figure 4 illustrates how a number of steady-state variables vary with customer bargaining power η regardless of whether or not there are menu costs of price adjustment. The results in Figure 4 are invariant to both the menu cost parameter κ and the specific bargaining protocol because in the steady state, π = 1 (i.e., prices are unchanging) because the interesting price in our model is a real price — in the steady state, real prices are of course constant. 26

As shown in Figure 4, an increase in consumer bargaining power depresses the bargained price (thetopleftpanel), confirmingouranalyticalresults. Becausemarginalproductioncostisconstant at unity by construction, the markup declines as η rises, as well. A lower price leaves the household with a larger gain M − S from forming a match (the top right panel), which also induces it to put more effort into search. The firm, on the other hand, loses from a rise in η, as the fall in A shows. The firm reduces its advertising because lower prices eat directly into profits, making customer relationships less valuable to it. With lower a and higher s, market thickness θ (≡ a/s) unambiguously falls. Regarding the flow of new relationships formed, the reduction in advertising expenditures dominates the increase in search activity, and the number of customer-firm relationships (N) falls. For our calibration, even though s rises, the total amount of time that households spend engaged in shopping-relatedactivities(N+s)declines. Householdsoptimallyreallocatethisadditionaltimebetween labor and leisure according to the consumption-leisure optimality condition (expression (6)), and it turns out that total labor declines, which, in turn, leads to lower total output. The latter result highlights an interesting point of contrast with the standard Dixit-Stiglitz model of monopolistic competition. In the standard model, reducing the degree of firms’ pricing power (in the form of a higher elasticity of demand for its output) pushes price closer to marginal cost, causing output to rise. Figure 4 shows that in our model, reducing firms’ pricing power (here, in the form of lower bargaining power for the firm) causes households to devote less time to production activities and enjoy more leisure, causing output to decline. Thereasonforthedifferenceintheresponseofoutputasthemarkupofpriceovermarginalcost falls is of course a direct result of the non-Walrasian features of our model. Advertising activities open up a supply-side channel missing in a standard model. When the firm has less to gain from trading in the non-Walrasian market, it simply chooses to reduce its activity there by cutting back on advertising. The resulting number of transactions in the non-Walrasian market declines. Shopping becomes less of a burden for households, who enjoy more leisure and devote less time to production activities.26 4.3 Dynamics To study dynamics, we approximate our model by linearizing in levels the equilibrium conditions of the model around the non-stochastic steady-state. Our numerical method is our own implementation of the perturbation algorithm described by Schmitt-Grohe and Uribe (2004b). We conduct 26One way to interpret this is that firms can indirectly manage labor demand through the non-Walrasian market. By changing advertising behavior, the firm can influence the number of long-term relationships in the economy and, hence the amount of time households spend in shopping activities. Shopping time, in turn, is closely linked to the household labor supply decision. 27

5000simulations,each100periodslong. Foreachsimulation,wecomputefirstandsecondmoments and report the medians of these moments across the 5000 simulations. To make the comparisons meaningful as we vary model parameters, the same realizations for productivity shocks are used across versions of our model. Because by construction marginal production cost is always mc = 1 t in our model, we will speak interchangeably about the dynamics of prices and markups. Depending on the issue at hand, one or the other language will typically be more convenient to use, which we think is clear in the ensuing discussion. 4.3.1 Nash Bargaining with No Menu Costs Table2presentssimulation-basedfirstandsecondmomentsforkeyvariablesunderNashbargaining andzeromenucosts. Examiningbasicbusinesscyclestatisticsrevealsthatthesearchgoodsmarket is a source of consumption smoothing, in the sense that the volatility of total consumption is lower than the volatility of GDP.27 In our model, total consumption is Nc+x. The volatility of total search consumption Nc, at 1.13 percentage points, is noticeably lower than the volatility of Walrasian consumption x. In our baseline calibration, search consumption makes up 43 percent of total consumption in the steady-state Nc+x. The volatility of total consumption, at 1.55 percent (not shown in the table), is thus a bit lower than volatility of total output. The consumption smoothing, although obviously not as quantitatively strong as in an RBC model with capital, arises because active customer-firm relationships are a state variable in our environment, making part of total consumption pre-determined. At roughly 0.94% ( = 1.55/1.66), the relative volatility of aggregate consumption in our model is clearly not as low as that which obtains in an RBC model with capital (see, for example, Table 3 in King and Rebelo (1999, p. 957)). Thus, we are clearly not claiming that search consumption induces as quantitatively strong a smoothing effect as does capital. The fact that consumption smoothing can arise in a model with completely perishable goods and no capital, though, is novel. Nevertheless, in terms of developing intuition for the basic dynamics of the model, we find it useful to think of the formation of customer-firm relationships as an investment decision for participants on both sides of the market. Households invest time searching for retailers, and firms invest advertising dollars in order to attract shoppers. A comparison of the volatility of advertising expenditures in our model to the volatility of investment in a standard RBC model with capital supports this analogy. We have more to say about the business cycle properties of advertising expenditures below. The final point worth emphasizing is that even with flexible prices, our model delivers a time- 27Trivially, in a model with no search markets and in which labor is the only production input, the volatility of GDP would be identical to the volatility of consumption simply because all output is absorbed by consumption. 28

varying markup, a result that is of some interest on its own. Our baseline model predicts that markups are procyclical, as the fifth column in Table 2 documents. However, most empirical evidence — for example, Rotemberg and Woodford (1999) or, more recently, Jaimovich (2006) — suggests that markups are countercyclical. We do not view this as a shortcoming of our model for two reasons. First, our basic goal was not to model markup behavior per se. Second, our baseline model features only TFP shocks. Our reading of the empirical evidence is that it is not even clear whether countercyclicality of markups observed in the data is due to demand shocks or supply shocks. In Section 6, we briefly extend our model to include demand shocks and demonstrate that our model is in fact capable of delivering countercyclical markups. 4.3.2 Nash Bargaining with Menu Costs We now turn on menu costs. Table 3 presents simulation-based first and second moments for key variables under Nash bargaining and for several values of κ. Comparing results across models, one feature that stands out is that the volatility and correlation properties of the typical quantity variables GDP, (Walrasian) consumption x, and time spent working l are virtually invariant to the size of the menu cost κ. The same is true of the correlation and volatility properties of time spent shopping N and time spent searching s. Quantity variables as a whole are thus largely unaffected by the magnitude of menu costs. An exception is goods-market tightness θ, which becomes a bit less volatile as κ rises. Because, as we just noted, the volatility of s changes little with κ, changes in the volatility of θ are driven by fluctuations in firms’ incentives to advertise. We document and discuss this latter feature of our model further at the close of this section. With most quantity variables largely unaffected by the degree of price rigidity, then, we focus most of the rest of our discussion on the dynamics of prices (equivalently, markups) and effective bargainingpower. AsTable2shows, withzerocostsofpriceadjustment, effectivebargainingpower is constant over the business cycle at ω = η. We pointed out in Section 2.4.1 that this must be the t casewithnocostsofpriceadjustment, andAppendixBprovesthis. Nevertheless, prices, andhence markups, do vary. Recall that for the case κ = 0, the Nash pricing condition can be expressed as in(25),whichmakesclearthatingeneralpricesvaryovertimedespiteconstanteffectivebargaining power because the marginal utility of wealth λ and aggregate goods-market tightness θ are both t t time-varying. As Table 3 shows, prices (markups) become more volatile and more persistent as κ rises, mirroring what happens to customers’ effective bargaining power ω . In fact, ω and p are negatively t t t correlated over the business cycle: their mean correlation across simulations is -0.11 with κ = 5, -0.64 with κ = 20, -0.79 with κ = 50, and -0.81 with κ = 100. Figure 5 provides more evidence of this phenomenon. We think this result is quite easy to understand: at times when consumers’ 29

effective bargaining power is low, firms are more likely to be to able to push through higher prices. The relationship holds in the opposite direction as well, of course: at times when consumers’ effective bargaining power is high, firms must lower their profit margins. Our model predicts that such phenomena hold at a business-cycle frequency, perhaps opening a new way to empirically thinking about how and why markups change over time. Regardless of the ability to empirically test this idea with currently available data, eliminating the phenomenon that prices are higher the lower is consumers’ bargaining power (and vice-versa) is precisely the goal of the fair-bargaining norm that we examine below. Finally, we noted above that firms’ incentives to advertise fluctuate over time. Changes in these incentives are reflected in shifts of the firm advertising condition, the steady-state version of which, recall, is the downward-sloping locus in Figure 1. In Figure 6, we scatter the dynamic realizations of (θ,p) for a representative simulation with κ = 0. Comparing the results with Figure 1, clearly both the advertising condition and the Nash pricing condition shift over the business cycle, but shifts in the advertising condition dominate because the resulting scatter is upward-sloping. This resultcarriesovertotheenvironmentwithpositivemenucosts, asthecomparableresultspresented in Figure 7 show. For brevity, we omit plotting the dynamic realizations of (a,s) in the space of Figure 2, which all show that it is dynamic shifts in the flow condition (40) that dominate. The reason that a fluctuates so much more than s is that firm profits are linear in a, while household utility displays diminishing returns in leisure (which depends on s). All else equal, the household has an incentive to limit fluctuations in its search activity in a way that firms do not. Whether in the face of zero menu costs (Table 2) or positive menu costs (Table 3), the standard deviation of advertising, at over 4 percent, lines up well with the cyclical volatility of advertising behavior in the U.S. economy. In Appendix F, we present data and summary statistics for U.S. aggregate advertising. The cyclical volatility of advertising over the past 50 years is 4.2 percent, and its contemporaneous correlation with GDP is 0.73; our model predictions are quite close to these. We did not set out to match advertising dynamics per se, but the fact that our basic model matchesquitewellthevolatilityandcorrelationofadvertisingbehaviormeansthatitisnotsubject to the same critique Shimer (2005) leveled at labor search models.28 28Specifically, in work that has sparked much subsequent modeling effort, Shimer (2005) demonstrated that the standardMortensen-PissaridesstructurecoupledwithNashbargainingfailstomatchthevolatilitiesofunemployment and vacancies, the two inputs to the aggregate matching function, observed in the data. Our model employs a Mortensen-PissaridesstructurecoupledwithNashbargaining,yetatleastoneoftheinputstotheaggregatematching function — advertising — is as volatile as observed in the data. Regarding the volatility of the other input to the matchingfunction—householdsearchbehavior—theAmericanTimeUseSurveyonlybeganin2003,sowecannot compute meaningful time-series summary statistics for it. We can only note that over the four years of its survey, household time spent shopping has been remarkably stable, which also qualitatively matches our model’s prediction regarding the volatility of N and s. 30

In summary, regardless of the presence of menu costs, the dynamics of prices and quantities are largely divorced from each other in the search goods market. The price p plays much more of a distributive role (determining how the surplus in a customer relationship is split) than the purely allocative role it plays in standard Walrasian views of goods markets. This point is made quite clearly in Figure 8, which shows impulse responses to a one-time, persistent TFP shock for κ = 0 and κ = 20. Output dynamics are essentially identical (the two responses in the top panel of Figure 8 lie virtually on top of each other) despite large differences in price dynamics. Because the price plays a distributive role, our model seems ideally suited to study notions of fairness in pricing. With some understanding of the dynamic results under Nash bargaining in hand, we thus turn next to dynamics under our two fairness schemes, proportional bargaining and fair bargaining. We again point out that these fairness schemes are only relevant in the presence of menu costs (κ > 0) because, as we discussed in Section 2.4, all three bargaining schemes collapse to standard Nash bargaining, both in steady state and dynamically, if κ = 0. 4.3.3 Proportional Bargaining The proportional-bargaining price always solves (27), which is identical to the Nash sharing condition (22) when ω = η, which occurs, recall, if κ = 0. Thus, no matter the magnitude of κ, all t dynamics under proportional bargaining, both those of prices and quantities, are identical to the dynamics under Nash bargaining and κ = 0 reported in Table 2. The way in which fairness is captured by proportional bargaining thus renders menu costs completely irrelevant. To understand this, recall from the analysis of the results under Nash bargaining and positive menu costs that the primary channel through which menu costs affected price dynamics was through time-variation in effective bargaining power ω . In proportional bargaining, in contrast, t there is no notion of “bargaining power” — indeed, this is what we mean when we say that proportional bargaining lacks clear strategic foundations. In proportional bargaining, parties’ adherence to the ad-hoc rule that splits the surplus according to fixed shares no matter what shuts down the transmission of menu costs to prices intermediated through effective bargaining power. As a consequence, price dynamics are governed entirely by the dynamics of the underlying surplus, and any price adjustment is simply an efficient response to a shock and neutralizes the distributive role of prices. Finally, to square proportional bargaining with Nash bargaining in a different way and to motivate fair bargaining from a quantitative perspective, we conduct the following thought experiment. For a given value of κ and using Nash bargaining, we can construct the sequence {ωPROP} of t effective bargaining power that would make the Nash outcome coincide with the proportionalbargaining outcome. In other words, {ωPROP} is a series we can construct residually to make t 31

the Nash dynamics for a given κ identical to the Nash dynamics for κ = 0. Using κ = 20, the last row of Table 2 reports the dynamics of this counterfactual effective bargaining power series. This residual measure of effective bargaining power is much more volatile than any of the actual effective bargaining power series reported in Table 3. In proportional bargaining, ωPROP is indeed nothing but a residual; there is no notion of bargaining power at all in proportional bargaining. This fact, coupled with the observation that if there were a notion of bargaining power behind fairness it would apparently fluctuate a great deal, is part of our motivation for constructing our fair-bargaining protocol, the results of which we now turn to. 4.3.4 Fair Bargaining Table 4 compiles results using fair bargaining for the same set of experiments as in Table 3. The central result here is that the presence of menu costs makes the price of the search good completely rigid. In the discussion surrounding expression (23), we noted that ω = η if and only if the t cost of price adjustment in period t is zero. The menu cost can be zero either because κ = 0 or because p = p . Under fair bargaining, the customer and firm are constrained to share the t t−1 surplus according to ω = η ∀t. With κ > 0, the only way this sharing norm can be achieved is t if prices never vary. One way of understanding this result is that the “fairness constraint” on the Nash bargaining problem effectively eliminates the efficient adjustment of the price that obtains under proportional bargaining. Echoing the result under proportional bargaining, however, the magnitude of menu costs (here, as long as they are positive) is irrelevant for price, as well as quantity, dynamics. However, it is not a theorem that would hold in any goods-search model of the type we propose that fair bargaining necessarily requires complete price stability. With the features present in our model, it is only time-variation of prices that create a wedge between η and ω . One can easily t extend our model to include other features that would affect this wedge. For example, in Arseneau and Chugh (2007), time-varying labor taxes also induce such a wedge (albeit in a model of wage bargaining, but we think the idea would translate readily to our environment). Suppose exogenous tax movements and (endogenous) price movements were both present in our model. In such an environment, there may be situations in which variations in the two offset each other in such a way as to leave no wedge at all between η and ω . Indeed, the fair-bargaining norm may require t customers and firms to engineer price movements in precisely the right way to offset exogenous tax shifts. We have not conducted such experiments with our model and so cannot assert this definitively, but based on our work here and the results and intuition in Arseneau and Chugh (2007), this hypothesis seems sound. Quantity dynamics, which are also invariant to κ, are very nearly, but not completely, identical 32

to the flexible-price Nash baseline. The most obvious difference is in the volatility of goods-market tightness θ. Its standard deviation of about 1.2 percent in Table 4 is roughly half that of all the results under Nash bargaining displayed in Tables 2 and 3. Because the volatility of s is virtually the same across models, the smaller fluctuations in θ under fair bargaining must be due to smaller fluctuationsina. Toverifythisconjecture, weplotinFigure9thedynamicrealizationsofthepairs (θ,p) and (a,s) for a representative simulation.29 The reason that advertising does not fluctuate as much under fair bargaining is simple: because p does not fluctuate, a firm’s incentives to advertise do not vary nearly as much as they do under Nash bargaining. With the return to advertising thus much less variable over time, actual advertising is less variable as well. Related to a point we made earlier, we do not need to take literally the idea that customers and firms calculate deviations of ω from η and use that to inform what prices they consider acceptable. Our model is obviously a metaphor for more subjective forces underlying the kinds of evidence that Blinder et al (1998) and others tabulate that suggest that avoiding customer anger is often a major concern of firms when determining prices. 4.3.5 Customer Bargaining Power and Price Volatility In the dynamic results so far, we have focused on the case η = ξ , which corresponds to the Hosios s (1990) parameterization. In our model with Nash bargaining, even though effective bargaining power ω generally is different from η along the business cycle, in the long-run (i.e., in steadyt state), ω = η. Thus, using the Hosios setting implies that customers’ long-run bargaining power is such that the underlying search equilibrium is efficient, which is a useful benchmark. Of course, long-run bargaining power may not satisfy the Hosios condition. A basic goal of our study is to shed some light on the consequences of bargaining and bargaining power for pricing outcomes. We need not limit ourselves to short-run changes in bargaining power; we can also easily investigate how changes in long-run bargaining power affect pricing. We thus repeat our basic experiments for alternative values of long-run customer bargaining power η. Table 5 reports results for Nash bargaining (the issue at hand here is moot with fair bargaining because fair bargaining renderspricesconstant),fixingκ = 0,usingalowersettingforcustomerbargainingpower(η = 0.20) and a higher setting for customer bargaining power (η = 0.50) (the middle panel repeats results from the top panel of Table 2). As the results make apparent, the means, volatilities, and correlations of almost all variables change little as we vary long-run bargaining power. The exception, though, is prices (equivalently, the markup): the standard deviation of prices in the search goods sector falls about four-fold as long-run customer bargaining power rises from η = 0.20 to η = 0.80. Thus, not only does higher 29The setting for κ does not matter here because equilibrium dynamics are invariant to κ. 33

average customer bargaining power lower the average markup (from 15 percent to less than 5 percent in Table 5), it lowers its volatility as well. To demonstrate this point a bit further, we plot in Figure 10 the mean volatility of prices across simulations for a wide range of values of η and for several values of κ.30 The rate at which price volatility declines as long-run customer bargaining power rises is larger the higher is κ. Figure 10 thus illustrates two implications of our model that may be testable using time-series data on, say, sectoral-level prices: the relationship between volatility of prices and the fraction of repeat customers (which may serve as a proxy for average customer bargaining power), and how this relationship changes with the importance of pure menu costs in that sector. Such empirical investigation is left for future work. The main point that emerges from our experiments here, though, is that average bargaining power has implications not only for average prices (as illustrated in Figure 4) but also for price volatility. 5 Intensive Quantity Adjustment In order to highlight the consequences of the formation and dissolution of customer relationships, we have so far limited fluctuations in consumption of search goods to fluctuations at the extensive margin (fluctuations in N). In goods markets, it is natural to think that fluctuations also occur at the intensive margin, the quantity traded per transaction; indeed, this is the only margin at which fluctuations occur in standard models. We now relax the assumption in our baseline model that c = c¯in every trade i and instead endogenize c. it In order to open up the intensive margin of adjustment, we modify one feature of our baseline model. In our baseline model, the aggregator over search goods over which subutility v(.) is defined is linear in the number of goods obtained, y = RN c di. In a symmetric equilibrium, y = Nc, 0 i which makes clear that from the point of view of just preferences, the household does not care whether a given amount of total search consumption comes from many matches, each with a small per-match quantity, or a small number of matches, each with a large per-match quantity. From a cost perspective, however, the latter is cheaper than the former because finding and engaging in many customer relationships takes time. Thus, were we to stick with the formulation of y we have used thus far as we endogenize c, the number of matches would be driven very low and quantity traded per match would be very large. This poses both a conceptual and a quantitative problem. Conceptually, our model is meant to be one in which consumers “must” engage in search and shopping to obtain goods; a model in which N and s are extremely small and c extremely large goes against this spirit. The agents in our model would cleverly circumvent the frictions we have placed in their way. Quantitatively, it could easily be the case that we would need to employ an 30Theexperimentsweconductinthissectionofcoursewouldbetrivialunderfairbargainingbecausepricesnever change under fair bargaining. 34

incentive-compatibility constraint in the baseline model to ensure that firms would actually want to participate in such an equilibrium because if a given customer is able to bargain a large c, price could easily be driven below marginal production cost, in which case it of course does not make sense for firms to want to engage in advertising to find customers in the first place.31 To sidestep such conceptual and quantitative issues, we modify the aggregator inside v(.) to be a CES composite of the goods obtained from distinct matches, " #1/ρ y = Z Nt cρ , (46) t it 0 with ρ < 1, which indicates that households have a preference for obtaining consumption from different matches. With sufficiently diminishing returns to consumption at the intensive margin, N will not be driven too low. Aside from the reasons we have already mentioned, introducing such diminishing returns to intensive consumption may be natural in its own right. For example, were sweaters to never carry labels, two sweaters from Banana Republic may be completely indistinguishablefromtwosweatersfromJCrew. Withlabels,however,itisplausiblethatahouseholdmay desire one sweater from Banana Republic and one sweater from JCrew. This type of preference idea often goes under the name “preference for variety,” and the label, so to speak, applies well enough to our idea here, as well.32 Finally, note that in a symmetric equilibrium, y = cN1/ρ. We briefly describe the main modifications to the baseline model of Section 2 and leave most detailstoAppendixBandC. Inprinciple, themodificationstothemodelaresimple: inadditionto the introduction of curvature in the consumption aggregator, c¯from the baseline model is replaced by c in all equilibrium conditions, and we must describe the protocol by which quantity traded t 31A bit more precisely, we tried, holding fixed the calibration in our baseline model, endogenizing c (using the mechanisms described below) with the linear aggregator and indeed found that firms need to be subsidized (i.e., γ < 0) to be induced to advertise and produce for customers (and the resulting equilibrium featured p < mc). It couldbethecasethatforsomeotherconstellationofparametersofourbaselinemodel,thiswouldnotoccur,butwe didnotfindone. Assumingthatsuchaparameterconstellationdoesnotexistorthatsuchaparameterconstellation is unrealistic on other grounds, one would need to impose a constraint that would guarantee that firms enjoy nonnegativeprofitsfrompayingfor advertising. Becausethisentrydecisionoccurseveryperiod,suchaconstraintwould inprinciplebeanoccasionally-bindingconstraint,whichwouldrequirequitedifferentnumericaltoolsthanweuseto solve the model and would likely be difficult to implement in any case due to the size of our model. 32We could also call this formulation “differentiation” of products, as is typical in models that use this type of consumptionaggregator. Wehesitatetousethisterminology,though,becausewhatwehaveinmindisnot anex-ante notionofdifferentiation,butratheranex-postnotionofdifferentiation. Tocontinuewiththeexample,whatwehave in mind is that at a primitive level the household does not care whether it finds sweaters at Banana Republic or JCrewordoesnotevencarewhetheritobtainseitheratall. Moresubtly,given thatonesweaterhasbeenpurchased from Banana Republic, in our formulation the household would prefer if the second sweater were purchased from JCrew. Intheend,however,thisisasomewhatsemanticpoint,andifonewantstocallthisformulationofourmodel one in which there is differentiation of goods, we do not strongly object. 35

in a customer relationship is determined. We assume that the customer and firm bargain (either Nash-bargain or fair-bargain) simultaneously over price and quantity. 5.1 Households Discounted household utility is now E 0 X ∞ βt  u(x t )+ϑv   " Z N t h cρ it di # ρ 1 +g(1−l t −s t −N t h)  , (47) 0 t=0 and in the flow budget constraint (2), we simply replace c¯ by c . Because the household takes it as given c in its unilateral utility maximization problem, all household first-order conditions are it identical to those in the baseline model, with appropriate replacement of c¯by c . For example, in it a symmetric equilibrium, the shopping condition is now ( ) g0 g0 t = β(1−ρx)E c (cid:2) ϑv0 −p u0(x ) (cid:3) −g0 + t+1 . (48) kh(θ ) t t+1 t+1 t+1 t+1 t+1 kh(θ ) t t+1 5.2 Firms Walrasian firms are no different than in our baseline model. Search firms are also no different, except that in the profit-maximization problem c¯is replaced by c , which has the consequence that it c appears in the period-t advertising condition, t+1 γ ( " κ (cid:18)p (cid:19)2 γ #) t+1 = (1−ρ )E Ξ p c −mc c − −1 + . (49) kf(θ ) x t t+1|t t+1 t+1 t+1 t+1 2 p kf(θ ) t t t+1 Just as households do, search firms take c as given in their unilateral optimzation problem. it 5.3 Price and Quantity Determination We extend both Nash bargaining and fair bargaining to now include simulataneous bargaining over (p ,c ). it it 5.3.1 Nash Bargaining In simultaneous Nash bargaining over (p ,c ), the customer and firm continue to maximize the it it Nash product (21). The bargained price continues to satisfy condition (24), with appropriate replacement of c¯by c . The bargained quantity c solves a condition that takes a similar form, it it ø " κ (cid:18) p (cid:19)2 γ # u˜(c ) t it it p c −mc c − −1 + = −p c + (50) 1−ø it it t it 2 p kf(θ ) λ it it t it−1 t t " (cid:18) ø (cid:19) " κ (cid:18)p (cid:19)2 γ ## + (1−θ kf(θ ))E Ξ t+1 (1−ρx) p c −mc c − it+1 −1 + , t t t t+1|t 1−ø it+1 it+1 t+1 it+1 2 p kf(θ ) t+1 it t 36

except with bargaining weights ø and 1−ø , and ø 6= ω . The main conceptual difference between t t t t ø and ω is that the former depends on u˜0(c ) whereas the latter does not. If κ = 0, a more t t it convenient characterization of the solution for the quantity traded is available. With κ = 0, c it satisfies g0 t = z . (51) u˜0(c ) t it Further details are provided in Appendix B and Appendix E. 5.3.2 Proportional Bargaining As we know from the presentation and discussion of proportional bargaining in the baseline model, the outcome replicates that of Nash bargaining with κ = 0. The irrelevance of menu costs under proportional bargaining thus readily extends to simultaneous bargaining over price and quantity. 5.3.3 Fair Bargaining Simultaneous fair bargaining over price and quantity means that the customer and firm choose (p ,c ) to maximize (M −S )ηA 1−η subject to the constant-split rule (1−η)(M −S ) = ηA . it it t t t t t t Price continues to be characterized by (30), while the quantity satisfies g0 t = z , (52) u˜0(c ) t it exactly as in the Nash case with κ = 0. Thus, fair bargaining, in eliminating the wedge in pricebargaining,alsoeliminatesthewedgeinquantity-bargaining. FurtherdetailsappearinAppendixC and Appendix E. 5.4 Equilibrium ThevariablesandconditionsdefiningasymmetricsearchequilibriumarethesameasinSection2.7 (withappropriatereplacementofc¯byc ),withtheadditionofc asanendogenousstochasticprocess t t and, depending on whether we are using Nash bargaining or fair bargaining, either condition (50) or (52) to pin down quantity traded. 5.5 Quantitative Results 5.5.1 Parameterization Thefunctionalformsweusearethesameasinthebaselinemodel, and, aswealreadydiscussed, we h i1 usetheaggregator RNtcρ ρ insidethesubutilityfunctionv(.). Wekeepallparametersettingsfixed 0 it at their values in the baseline model to try to achieve some comparability. However, the models are not readily comparable because we also must choose ρ < 1; by thus changing a structural 37

parameter of the economy relative to the baseline economy, cross-model comparisons inherently become difficult to interpret. In our setting for ρ, we choose to make the steady-state markup the same as in the baseline model when η = 0.50. Setting ρ = 0.19 delivers a gross markup of 1.0835 here, identical to that in the baseline calibration of the model of Section 2. 5.5.2 Steady State Steady-state prices and quantities are reported in Table 6 for the model with intensive adjustment. Comparing with Table 1, the main difference is that the fraction of time spent in shopping-related activitiesismuchhigher. Boththenumberofactivecustomerrelationshipsandtimespentsearching are much higher. Larger N reflects the curvature we introduced in the search goods aggregator, which, as we discussed at the start of this section, gives households a preference for obtaining consumption from many matches. Absent some other counteracting feature of the environment, thisversionofourmodelthuscannotaccountforthetime-useevidencethatshows(N+s)/l = 0.25. Because relationships occasionally dissolve, households must also search more in order to maintain the larger N, explaining the higher level of s in the model here compared to the baseline model. Figure 11 illustrates how key steady-state variables change with customer bargaining power η. As the middle left panel shows, the extensive quantity N falls, as it did in Figure 4; the difference here is that the intensive quantity c simultaneously rises the larger is η. This substitution reflects the fact that with higher η, households know they can leverage a higher quantity out of each customer relationship. Given that match formation is costly, it makes sense for the household to essentially substitute out of extensive consumption and into intensive consumption. The levels and responses of all other variables are very similar to those in Figure 4, so we do not discuss them further. 5.5.3 Dynamics Tables7and8catalogresultsforthesamesetofdynamicexperimentsweconductedinSection4.3; endogenizing the intensive quantity does not change the main quantitative results presented there. A few new notable results do arise, though. First, endogenizing the intensive quantity imparts more persistence to household search behavior. Second, as shown in Tables 2, 3, and 4, with fixed c¯, search activity is weakly procyclical no matter the bargaining protocol. In contrast, with endogenous intensive quantity, the cyclicality of s depends crucially on the bargaining protocol in place. In turn, the cyclicality of search mirrors the cyclicality of the intensive quantity c. With Nash bargaining, c is always countercyclical with respect to total GDP. This result is the dynamic manifestation of the substitution between N and c just discussed above: because of the “preference for variety” in this version of the model, all else equal, the household prefers 38

that expansions in search consumption come at the extensive margin rather than at the intensive margin. It is also striking how much less volatile c is than N is: between five- and six-fold less volatile depending on the value of κ. A standard model’s notion of consumption-smoothing is thus pusheddowntothelevelofintensiveconsumptioninthisversionofourmodel. Wethinkthismakes sense because it is intensive consumption that is essentially governed by a MRS-type of optimality condition; this can be seen most clearly in condition (51), which is also the core of condition (50). As in the baseline model without intensive adjustment, the proportional bargaining outcome, no matter the value of κ, is identical to the Nash outcome with κ = 0, so this notion of fairness leaves c countercyclical. In contrast, under fair bargaining, c is procyclical with respect to total GDP. This seems to be related to the result that the volatility of c relative to the volatility of N is not nearly as small under fair bargaining as it is under Nash bargaining. As in the baseline model, fair bargaining mutes the volatility of p, which in turn governs the incentives of firms to cyclically alter their advertising behavior. With advertising not nearly as volatile as under Nash bargaining, the equilibrium stock of active customer relationships does not fluctuate nearly as much, which in turn means that the scope for substitution between N and c is dramatically reduced. Thus, despite the primitive “preference for variety,” households must accept procyclical movements of c to vary their consumption of search goods. 6 Demand Shocks We noted in Section 4.3 that, although our basic model driven by only TFP shocks does not deliver countercyclical markups, extending our model to allow for demand shocks can overturn this prediction. To the extent that it is not clear whether the countercyclicality of markups observed in the data is due predominately to demand shocks or supply shocks, we think it is useful to at least know that our model is capable of matching this stylized fact for some shocks. We introduce demand shocks by allowing exogenous government purchases. For the sake of simplicity, we only conduct the experiments in this section in the baseline model with fixed c¯. Total output is now absorbed by consumption (of both Walrasian and search goods), advertising costs, price adjustment costs, and government spending, so the resource constraint is κ x +N c¯+g +γa + (π −1)2N = z l . (53) t t t t t t t t 2 No other features of the baseline model of Section 2 change, hence all equilibrium conditions, with the obvious exception of the resource constraint, are unchanged. Government spending is assumed to follow an AR(1) in logs, logg = (1−ρ )logg¯+ρ logg +(cid:15)g , (54) t+1 g g t t+1 39

with (cid:15)g ∼ iidN(0,σ ), and the shock to government spending is uncorrelated with the shock to g TFP. We set g¯= 0.05 so that government spending makes up about 19 percent of total output, set ρ = 0.97, in line with Schmitt-Grohe and Uribe (2004a), and set σ so that the standard deviation g g of government purchases is 6 percent of the mean level g¯ — the resulting value is σ = 0.03. g We examine the dynamics of this model in the face of just shocks to government spending. The upper panel of Table 9 shows that with κ = 0 and Nash bargaining as the pricing mechanism, the contemporaneous correlation of the markup with GDP is -0.32. As κ increases, however, the correlation turns positive. So our claim is not that our model with demand shocks always predicts a countercyclical markup, just that it can. Finally, we do not need to consider fair bargaining here becausemarkupsaretime-invariantunderthatprotocol. Weleavetofutureworkafullinvestigation of the cyclicality properties of the markup in our model. 7 Conclusion Weconstructedamodelinwhichlong-livedcustomerrelationshipsallowonetothinkaboutanarray of pricing schemes in goods-market transactions. Our focus here was on bargaining arrangements between firms and customers in which fairness was of paramount concern. Depending on exactly how our concept of fairness is operationalized, menu costs may be either completely irrelevant for dynamics (proportional bargaining) or may lead endogenously to complete price stability (fair bargaining). Under proportional bargaining, consumers and firms effectively share the menu costs efficiently, making them irrelevant. Under fair bargaining, price changes are the only source of time-variation in effective bargaining power between a firm and a customer. Avoiding this timevariation in effective bargaining power requires ensuring price stability. As we noted, in a richer model (one that includes, for example, labor or consumption taxes), stabilizing surplus shares need not require complete price stability. Understanding how pricing decisions are affected by bargaining power is an understudied topic, at least in the context of modern quantitative macroeconomic models. Survey evidence seems to repeatedly support the view that firms often avoid changing prices out of concern for upsetting their existing customers. It is difficult to articulate very precisely such views in standard models of goods markets because in the basic Walrasian framework, of course, there simply are no clear notions of customers and bargaining. We think we have made some progress in at least pointing out a potentially useful direction, one that is immediately tractable in modern quantitative macroeconomic models. An even deeper bargaining-theoretic explanation for price rigidity is provided by Menzio (2007), but the tension there is that his framework seems likely not readily tractable in standard DSGE models. More broadly than the fair-bargaining result around which we centered much of our analysis, 40

we think the general framework we developed of search-based frictions in goods markets holds the promise of being usefully incorporated into standard quantitative macroeconomic models. Such a line of research immediately allows one to think beyond the standard marginal pricing conditions present in most models and therefore is likely to be useful in bringing to bear new ideas about a host of issues in macroeconomics. As we have admitted, more work needs to be done in thinking about the empirical counterparts of and calibration of some elements of our model. But at least these are testable parts of our model. It is well-understood from standard macro models that wedges between consumption-leisure marginal rates of substitution and marginal rates of transformation must stem from frictions in goods markets or from frictions in labor markets or both. Chari, Kehoe, and McGrattan (2006), among others, have emphasized that understanding this (to use their terminology) “labor wedge” is quite important for macro modeling efforts. Our model posits search frictions in product markets alongside a perfectly-competitive labor market, so the wedge between the MRS and the consumption-leisure MRT stems from goods market frictions. Labor search models, especially their recent DSGE incarnations, have made clear that such wedges arise from primitive labor matching frictions as well. A model featuring labor search and goods search frictions may have even more to offerintermsofexplaininglaborwedges. Inaddition,anominalversionofsuchamodel,inwhichit is nominal prices and nominal wages over which parties bargain, would have some potentially very interesting things to say regarding dynamics of real wages. Hall’s (2007) model does incorporate both goods search and labor search frictions and points out some interesting tradeoffs regarding stabilizing goods markets versus stabilizing labor markets that monetary policy may face. We see a great many other possible applications of our framework. One application is to asset pricing: the fact that marginal utility of consumption is tied to consumer search frictions opens up a new mechanism for thinking about asset prices. Another possible use for our framework is to provide a micro-foundation behind habit-based consumption models: part of consumption is a state variable in our model, as it is in habit-based models, because it directly reflects the number of pre-existingcustomerrelationships. Ourframework, sufficientlyenrichedonthepricing/bargaining side of the model, may also provide a different way to think about time-varying markups in goods markets, an issue we only scratched the surface of here. Finally, another important motivation behind the construction of our model is the eventual design of optimal macroeconomic policy in such an environment. Arseneau and Chugh (2006, 2007) study optimal policy in the presence of deep-rooted frictions in labor markets, with all other macro markets quite standard. Aruoba and Chugh (2006) study optimal policy in the presence of deep-rooted frictions in money markets, with all other macro markets quite standard. Both of these studies uncover policy channels and implications about which standard models used to 41

study dynamic optimal policy are silent, and several of the policy prescriptions obtained in these studies are indeed opposite those reached using standard frameworks. However, each of these studies considers goods trade in more or less standard Walrasian fashion. We conjecture that thinking about deep-rooted frictions in goods markets is likely to also yield new insights about how macroeconomic policy ought to be conducted, a topic rising on our research horizon. 42

A Tables and Figures Figure 1: Steady-state firm advertising condition and Nash pricing condition. Figure 2: Steady-state flow condition and firm advertising condition 43

µ a s θ N Nc x gdp 1.0835 0.0151 0.0189 0.8000 0.0680 0.0952 0.1919 0.2943 Table 1: Steady-state prices and quantities under benchmark calibration. markup A M-S 1.4 3 8 1.3 6 2 1.2 4 1 1.1 2 1 0 0 0 0.5 1 0 0.5 1 0 0.5 1 advertising search θ 0.04 0.06 6 0.03 0.04 4 0.02 0.02 2 0.01 0 0 0 0 0.5 1 0 0.5 1 0 0.5 1 Nc x gdp 0.11 0.1921 0.31 0.3 0.1 0.192 0.29 0.09 0.1919 0.28 0.08 0.1918 0.27 0 0.5 1 0 0.5 1 0 0.5 1 Figure 3: Steady-state allocation as function of customer bargaining power η. 44

Variable Mean Std. Dev. SD% Autocorr. Corr(x,Y) Corr(x,Z) Nomenucost,κ=0 µ 1.0835 0.0036 0.0033 0.1751 0.5557 0.5850 gdp 0.2945 0.0049 0.0166 0.9342 1.0000 0.9993 x 0.1918 0.0036 0.0190 0.9246 0.9996 1.0000 c 1.4000 0 0 — — — N 0.0681 0.0008 0.0113 0.9274 0.9345 0.9212 Nc 0.0954 0.0011 0.0113 0.9274 0.9345 0.9212 l 0.2945 0.0007 0.0025 0.7866 -0.9626 -0.9718 w 0.9997 0.0190 0.0190 0.9216 0.9993 1.0000 p 1.0835 0.0036 0.0033 0.1751 0.5557 0.5850 s 0.0189 0.0007 0.0360 0.0187 0.0885 0.1237 θ 0.7996 0.0233 0.0292 0.9209 0.9992 1.0000 ω 0.5000 0.0000 0.0000 — — — a 0.0152 0.0007 0.0494 0.2868 0.6624 0.6878 Addendum ωPROP 0.5000 0.0138 0.0277 -0.3752 -0.2030 -0.1776 Table 2: Simulation-based moments in baseline model with Nash bargaining, zero menu costs, and TFP shocks as driving force. 45

Variable Mean Std. Dev. SD% Autocorr. Corr(x,Y) Corr(x,Z) Menucost,κ=5 µ 1.0835 0.0032 0.0030 0.8008 0.9387 0.9488 gdp 0.2945 0.0049 0.0166 0.9344 1.0000 0.9993 x 0.1918 0.0036 0.0190 0.9245 0.9995 1.0000 c 1.4000 0 0 — — — N 0.0681 0.0008 0.0113 0.9285 0.9346 0.9211 Nc 0.0954 0.0011 0.0113 0.9285 0.9346 0.9211 l 0.2945 0.0007 0.0025 0.7864 -0.9623 -0.9716 w 0.9997 0.0190 0.0190 0.9216 0.9993 1.0000 p 1.0835 0.0032 0.0030 0.8008 0.9387 0.9488 s 0.0189 0.0007 0.0356 0.0256 0.0940 0.1295 θ 0.7996 0.0230 0.0287 0.9227 0.9994 1.0000 ω 0.5000 0.0015 0.0031 0.1087 -0.3572 -0.3246 a 0.0152 0.0007 0.0488 0.2934 0.6642 0.6898 Menucost,κ=20 µ 1.0834 0.0050 0.0047 0.9775 0.9533 0.9467 gdp 0.2945 0.0049 0.0165 0.9344 1.0000 0.9993 x 0.1918 0.0036 0.0190 0.9244 0.9995 1.0000 c 1.4000 0 0 — — — N 0.0681 0.0008 0.0113 0.9293 0.9346 0.9211 Nc 0.0954 0.0011 0.0113 0.9293 0.9346 0.9211 l 0.2945 0.0007 0.0025 0.7882 -0.9627 -0.9720 w 0.9997 0.0190 0.0190 0.9216 0.9993 1.0000 p 1.0834 0.0050 0.0047 0.9775 0.9533 0.9467 s 0.0189 0.0007 0.0353 0.0296 0.1076 0.1432 θ 0.7996 0.0221 0.0277 0.9242 0.9995 1.0000 ω 0.5000 0.0031 0.0061 0.5501 -0.4542 -0.4233 a 0.0152 0.0007 0.0481 0.2940 0.6618 0.6876 Menucost,κ=100 µ 1.0833 0.0093 0.0086 0.9967 0.5995 0.5909 gdp 0.2945 0.0048 0.0164 0.9344 1.0000 0.9993 x 0.1918 0.0036 0.0190 0.9244 0.9995 1.0000 c 1.4000 0 0 — — — N 0.0681 0.0008 0.0111 0.9298 0.9345 0.9210 Nc 0.0954 0.0011 0.0111 0.9298 0.9345 0.9210 l 0.2945 0.0008 0.0026 0.7967 -0.9658 -0.9747 w 0.9997 0.0190 0.0190 0.9216 0.9993 1.0000 p 1.0833 0.0093 0.0086 0.9967 0.5995 0.5909 s 0.0189 0.0007 0.0349 0.0293 0.1570 0.1922 θ 0.7997 0.0190 0.0237 0.9256 0.9996 0.9999 ω 0.5001 0.0058 0.0117 0.8008 -0.1332 -0.1113 a 0.0152 0.0007 0.0459 0.2750 0.6429 0.6691 Table 3: Simulation-basedmomentsinbaselinemodelwithNashbargaining, positivemenucosts, andTFP shocks as driving force. 46

Variable Mean Std. Dev. SD% Autocorr. Corr(x,Y) Corr(x,Z) Menucost,κ=5 µ 1.0835 0 0 — — — gdp 0.2945 0.0048 0.0161 0.9341 1.0000 0.9993 x 0.1918 0.0036 0.0190 0.9242 0.9995 1.0000 c 1.4000 0 0 — — — N 0.0681 0.0007 0.0106 0.9299 0.9342 0.9210 Nc 0.0954 0.0010 0.0106 0.9299 0.9342 0.9210 l 0.2945 0.0009 0.0029 0.8184 -0.9737 -0.9812 w 0.9997 0.0190 0.0190 0.9216 0.9993 1.0000 p 1.0835 0 0 — — — s 0.0189 0.0007 0.0346 0.0474 0.3010 0.3341 θ 0.7998 0.0098 0.0123 0.9294 0.9999 0.9998 ω 0.5000 0 0 — — — Menucost,κ=20 µ 1.0835 0 0 — — — gdp 0.2945 0.0048 0.0161 0.9341 1.0000 0.9993 x 0.1918 0.0036 0.0190 0.9242 0.9995 1.0000 c 1.4000 0 0 — — — N 0.0681 0.0007 0.0106 0.9299 0.9342 0.9210 Nc 0.0954 0.0010 0.0106 0.9299 0.9342 0.9210 l 0.2945 0.0009 0.0029 0.8184 -0.9737 -0.9812 w 0.9997 0.0190 0.0190 0.9216 0.9993 1.0000 p 1.0835 0 0 — — — s 0.0189 0.0007 0.0346 0.0474 0.3010 0.3341 θ 0.7998 0.0098 0.0123 0.9294 0.9999 0.9998 ω 0.5000 0 0 — — — Menucost,κ=50 µ 1.0835 0 0 — — — gdp 0.2945 0.0048 0.0161 0.9341 1.0000 0.9993 x 0.1918 0.0036 0.0190 0.9242 0.9995 1.0000 c 1.4000 0 0 — — — N 0.0681 0.0007 0.0106 0.9299 0.9342 0.9210 Nc 0.0954 0.0010 0.0106 0.9299 0.9342 0.9210 l 0.2945 0.0009 0.0029 0.8184 -0.9737 -0.9812 w 0.9997 0.0190 0.0190 0.9216 0.9993 1.0000 p 1.0835 0 0 — — — s 0.0189 0.0007 0.0346 0.0474 0.3010 0.3341 θ 0.7998 0.0098 0.0123 0.9294 0.9999 0.9998 ω 0.5000 0 0 — — — Menucost,κ=100 µ 1.0835 0 0 — — — gdp 0.2945 0.0048 0.0161 0.9341 1.0000 0.9993 x 0.1918 0.0036 0.0190 0.9242 0.9995 1.0000 c 1.4000 0 0 — — — N 0.0681 0.0007 0.0106 0.9299 0.9342 0.9210 Nc 0.0954 0.0010 0.0106 0.9299 0.9342 0.9210 l 0.2945 0.0009 0.0029 0.8184 -0.9737 -0.9812 w 0.9997 0.0190 0.0190 0.9216 0.9993 1.0000 p 1.0835 0 0 — — — s 0.0189 0.0007 0.0346 0.0474 0.3010 0.3341 θ 0.7998 0.0098 0.0123 0.9294 0.9999 0.9998 ω 0.5000 0 0 — — — Table4: Simulation-basedmomentsinbaselinemodelwithfairbargainingandTFPshocksasdrivingforce. 47

Variable Mean Std. Dev. SD% Autocorr. Corr(x,Y) Corr(x,Z) Lowcustomerbargainingpower(η=0.20) µ 1.1526 0.0059 0.0052 0.2616 0.6868 0.6778 gdp 0.3021 0.0051 0.0168 0.9167 1.0000 0.9999 x 0.1918 0.0036 0.0190 0.9236 0.9998 1.0000 c 1.4000 0 0 — — — N 0.0691 0.0007 0.0107 0.9256 0.9163 0.9213 Nc 0.0968 0.0010 0.0107 0.9256 0.9163 0.9213 l 0.3021 0.0007 0.0022 0.9498 -0.9942 -0.9955 w 0.9997 0.0190 0.0190 0.9216 0.9999 1.0000 p 1.1526 0.0059 0.0052 0.2616 0.6868 0.6778 s 0.0105 0.0004 0.0342 0.0311 0.0357 0.0235 θ 2.6707 0.0916 0.0343 0.9215 0.9999 1.0000 ω 0.2000 0 0 — — — a 0.0281 0.0014 0.0494 0.3186 0.7270 0.7188 Equalbargainingpower(η=0.50) µ 1.0835 0.0036 0.0033 0.1751 0.5557 0.5850 gdp 0.2945 0.0049 0.0166 0.9342 1.0000 0.9993 x 0.1918 0.0036 0.0190 0.9246 0.9996 1.0000 c 1.4000 0 0 — — — N 0.0681 0.0008 0.0113 0.9274 0.9345 0.9212 Nc 0.0954 0.0011 0.0113 0.9274 0.9345 0.9212 l 0.2945 0.0007 0.0025 0.7866 -0.9626 -0.9718 w 0.9997 0.0190 0.0190 0.9216 0.9993 1.0000 p 1.0835 0.0036 0.0033 0.1751 0.5557 0.5850 s 0.0189 0.0007 0.0360 0.0187 0.0885 0.1237 θ 0.7996 0.0233 0.0292 0.9209 0.9992 1.0000 ω 0.5000 0 0 — — — a 0.0152 0.0007 0.0494 0.2868 0.6624 0.6878 Highcustomerbargainingpower(η=0.80) µ 1.0452 0.0015 0.0015 0.2316 0.5364 0.5951 gdp 0.2846 0.0047 0.0165 0.9448 1.0000 0.9974 x 0.1919 0.0036 0.0189 0.9282 0.9985 0.9998 c 1.4000 0 0 — — — N 0.0635 0.0007 0.0116 0.9368 0.9459 0.9202 Nc 0.0889 0.0010 0.0116 0.9368 0.9459 0.9202 l 0.2846 0.0008 0.0027 0.6392 -0.8747 -0.9072 w 0.9997 0.0190 0.0190 0.9216 0.9974 1.0000 p 1.0452 0.0015 0.0015 0.2316 0.5364 0.5951 s 0.0326 0.0011 0.0343 0.0824 0.1325 0.2022 θ 0.2338 0.0059 0.0251 0.9196 0.9970 1.0000 ω 0.8000 0 0 — — — a 0.0076 0.0004 0.0468 0.3301 0.6403 0.6914 Table 5: Simulation-based moments, for various values of η, in basic model with Nash bargaining, κ = 0, and TFP shocks as driving force. 48

markup A M-S 1.4 3 8 1.3 6 2 1.2 4 1 1.1 2 1 0 0 0 0.5 1 0 0.5 1 0 0.5 1 advertising search θ 0.04 0.06 6 0.03 0.04 4 0.02 0.02 2 0.01 0 0 0 0 0.5 1 0 0.5 1 0 0.5 1 Nc x gdp 0.11 0.1921 0.31 0.3 0.1 0.192 0.29 0.09 0.1919 0.28 0.08 0.1918 0.27 0 0.5 1 0 0.5 1 0 0.5 1 Figure 4: Steady-state allocation as function of customer bargaining power η. µ a s θ N c Nc x gdp 1.0835 0.0267 0.1851 0.1443 0.2830 0.5951 0.1684 0.1276 0.3088 Table 6: Steady-state prices and quantities with intensive adjustment. 49

1.12 1.11 1.1 1.09 1.08 1.07 1.06 0.5 ω p κ = 100 1.105 1.1 1.095 1.09 1.085 1.08 1.075 1.07 1.065 1.06 0.5 ω p κ = 50 1.095 1.09 1.085 1.08 0.5 0.51 ω p κ = 20 Figure 5: Dynamic relationship between customer effective bargaining power ω and Nash price for various degrees of price rigidity. 50

Variable Mean Std. Dev. SD% Autocorr. Corr(x,Y) Corr(x,Z) Flexibleprices,κ=0 µ 1.0834 0.0030 0.0027 0.8317 0.9196 0.9701 gdp 0.3088 0.0044 0.0143 0.9613 1.0000 0.9874 x 0.1276 0.0022 0.0173 0.9484 0.9982 0.9952 c 0.5951 0.0012 0.0020 0.8868 -0.7597 -0.6487 N 0.2829 0.0035 0.0123 0.9783 0.9466 0.8840 Nc 0.1684 0.0018 0.0105 0.9827 0.9672 0.9151 l 0.3088 0.0016 0.0053 0.7549 -0.8355 -0.9115 w 0.9997 0.0190 0.0190 0.9216 0.9874 1.0000 p 1.0834 0.0030 0.0027 0.8317 0.9196 0.9701 s 0.1851 0.0032 0.0173 0.6639 -0.3275 -0.1772 θ 0.1442 0.0067 0.0466 0.9224 0.9878 1.0000 ω 0.5000 0.0000 — — — — a 0.0267 0.0013 0.0473 0.7884 0.8672 0.9329 Menucost,κ=5 µ 1.0833 0.0084 0.0078 0.9802 0.9892 0.9553 gdp 0.3088 0.0044 0.0141 0.9601 1.0000 0.9882 x 0.1276 0.0022 0.0174 0.9459 0.9979 0.9960 c 0.5951 0.0012 0.0020 0.8827 -0.7379 -0.6274 N 0.2829 0.0034 0.0120 0.9791 0.9432 0.8816 Nc 0.1684 0.0017 0.0101 0.9834 0.9668 0.9165 l 0.3088 0.0017 0.0054 0.7710 -0.8540 -0.9233 w 0.9997 0.0190 0.0190 0.9216 0.9882 1.0000 p 1.0833 0.0084 0.0078 0.9802 0.9892 0.9553 s 0.1851 0.0031 0.0165 0.6694 -0.3077 -0.1616 θ 0.1442 0.0064 0.0447 0.9258 0.9903 0.9999 ω 0.5000 0.0034 0.0068 0.9397 -0.8392 -0.7470 a 0.0267 0.0012 0.0454 0.7967 0.8759 0.9375 Menucost,κ=20 µ 1.0832 0.0173 0.0160 0.9947 0.8147 0.7554 gdp 0.3088 0.0043 0.0138 0.9580 1.0000 0.9898 x 0.1276 0.0022 0.0176 0.9428 0.9978 0.9970 c 0.5951 0.0012 0.0020 0.8750 -0.6628 -0.5526 N 0.2829 0.0032 0.0112 0.9799 0.9375 0.8788 Nc 0.1684 0.0016 0.0095 0.9836 0.9676 0.9220 l 0.3088 0.0018 0.0057 0.7932 -0.8851 -0.9423 w 0.9997 0.0190 0.0190 0.9216 0.9898 1.0000 p 1.0832 0.0173 0.0160 0.9947 0.8147 0.7554 s 0.1851 0.0028 0.0151 0.6623 -0.2531 -0.1158 θ 0.1442 0.0058 0.0404 0.9294 0.9933 0.9996 ω 0.5001 0.0089 0.0178 0.9685 -0.5538 -0.4626 a 0.0267 0.0011 0.0416 0.8032 0.8857 0.9410 Menucost,κ=50 µ 1.0830 0.0225 0.0208 0.9973 0.5805 0.5337 gdp 0.3088 0.0041 0.0134 0.9559 1.0000 0.9912 x 0.1276 0.0023 0.0178 0.9401 0.9978 0.9977 c 0.5951 0.0011 0.0018 0.8415 -0.5144 -0.4056 N 0.2829 0.0029 0.0103 0.9803 0.9324 0.8771 Nc 0.1684 0.0015 0.0089 0.9837 0.9689 0.9277 l 0.3088 0.0018 0.0060 0.8133 -0.9109 -0.9574 w 0.9997 0.0190 0.0190 0.9216 0.9912 1.0000 p 1.0830 0.0225 0.0208 0.9973 0.5805 0.5337 s 0.1851 0.0025 0.0136 0.6410 -0.1672 -0.0388 θ 0.1442 0.0050 0.0347 0.9318 0.9953 0.9993 ω 0.5002 0.0126 0.0252 0.9681 -0.1732 -0.1076 a 0.0267 0.0010 0.0368 0.8038 0.8900 0.9407 Table 7: Simulation-basedmomentsinmodelwithintensiveadjustment, Nashbargaining, andTFPshocks as driving force. 51

Variable Mean Std. Dev. SD% Autocorr. Corr(x,Y) Corr(x,Z) Flexibleprices,κ=5 µ 1.0835 0 0 — — — gdp 0.3088 0.0037 0.0120 0.9475 1.0000 0.9952 x 0.1276 0.0024 0.0186 0.9325 0.9982 0.9993 c 0.5951 0.0007 0.0012 0.6530 0.6820 0.7494 N 0.2829 0.0018 0.0064 0.9805 0.9193 0.8768 Nc 0.1684 0.0012 0.0070 0.9821 0.9743 0.9477 l 0.3088 0.0022 0.0071 0.8677 -0.9664 -0.9869 w 0.9997 0.0190 0.0190 0.9216 0.9952 1.0000 p 1.0835 0 0 — — — s 0.1851 0.0018 0.0095 0.5763 0.3775 0.4645 θ 0.1443 0.0017 0.0121 0.9428 0.9998 0.9969 ω 0.5000 0 0 — — — a 0.0267 0.0005 0.0181 0.7691 0.8605 0.9062 Menucost,κ=20 µ 1.0835 0 0 — — — gdp 0.3088 0.0037 0.0120 0.9475 1.0000 0.9952 x 0.1276 0.0024 0.0186 0.9325 0.9982 0.9993 c 0.5951 0.0007 0.0012 0.6530 0.6820 0.7494 N 0.2829 0.0018 0.0064 0.9805 0.9193 0.8768 Nc 0.1684 0.0012 0.0070 0.9821 0.9743 0.9477 l 0.3088 0.0022 0.0071 0.8677 -0.9664 -0.9869 w 0.9997 0.0190 0.0190 0.9216 0.9952 1.0000 p 1.0835 0 0 — — — s 0.1851 0.0018 0.0095 0.5763 0.3775 0.4645 θ 0.1443 0.0017 0.0121 0.9428 0.9998 0.9969 ω 0.5000 0 0 — — — a 0.0267 0.0005 0.0181 0.7691 0.8605 0.9062 Menucost,κ=50 µ 1.0835 0 0 — — — gdp 0.3088 0.0037 0.0120 0.9475 1.0000 0.9952 x 0.1276 0.0024 0.0186 0.9325 0.9982 0.9993 c 0.5951 0.0007 0.0012 0.6530 0.6820 0.7494 N 0.2829 0.0018 0.0064 0.9805 0.9193 0.8768 Nc 0.1684 0.0012 0.0070 0.9821 0.9743 0.9477 l 0.3088 0.0022 0.0071 0.8677 -0.9664 -0.9869 w 0.9997 0.0190 0.0190 0.9216 0.9952 1.0000 p 1.0835 0 0 — — — s 0.1851 0.0018 0.0095 0.5763 0.3775 0.4645 θ 0.1443 0.0017 0.0121 0.9428 0.9998 0.9969 ω 0.5000 0 0 — — — a 0.0267 0.0005 0.0181 0.7691 0.8605 0.9062 Menucost,κ=100 µ 1.0835 0 0 — — — gdp 0.3088 0.0037 0.0120 0.9475 1.0000 0.9952 x 0.1276 0.0024 0.0186 0.9325 0.9982 0.9993 c 0.5951 0.0007 0.0012 0.6530 0.6820 0.7494 N 0.2829 0.0018 0.0064 0.9805 0.9193 0.8768 Nc 0.1684 0.0012 0.0070 0.9821 0.9743 0.9477 l 0.3088 0.0022 0.0071 0.8677 -0.9664 -0.9869 w 0.9997 0.0190 0.0190 0.9216 0.9952 1.0000 p 1.0835 0 0 — — — s 0.1851 0.0018 0.0095 0.5763 0.3775 0.4645 θ 0.1443 0.0017 0.0121 0.9428 0.9998 0.9969 ω 0.5000 0 0 — — — a 0.0267 0.0005 0.0181 0.7691 0.8605 0.9062 Table 8: Simulation-based moments in model with intensive adjustment, fair bargaining, and TFP shocks as driving force. 52

1.095 1.09 1.085 1.08 1.075 1.07 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 θ p κ = 0 Figure 6: Dynamic relationship between goods market tightness θ and Nash price p in baseline model with κ=0. 53

κ = 5 1.1 1.09 1.08 1.07 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 p κ = 20 1.1 1.08 0.74 0.76 0.78 0.8 0.82 0.84 0.86 p κ = 100 1.1 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 p θ RESULTS Figure 7: Dynamic relationship between goods market tightness θ and Nash price p in baseline model with D N P P M C YNAMICSκ> –0. ASH RICING, OSITIVE ENU OSTS TFP impulse Main result: GDP Menu costs affect price/markup dynamics, but have minimal impact on real quantities Price of search goods positive menu costs “Price”plays much more of a zero menu costs distributive role than an allocative role Customer effective bargaining power - Admits the possibility of equilibrium sticky prices(Hall, 2007) - Admits discussion about “fairness” Figure 8: Impulse response in baseline model. May 21, 2007 IF Workshop 32 54

0.018 0.0175 0.017 0.0165 0.016 0.0155 0.015 0.0145 0.014 0.0135 0.017 0.018 0.019 0.02 0.021 s a 1.0835 1.0835 1.0835 1.0835 1.0835 1.0835 1.0835 0.76 0.78 0.8 0.82 0.84 θ p Figure 9: Dynamic relationship between goods market tightness θ and Nash price p (left panel) and advertisements a and consumer search activity s in baseline model with fair bargaining. 55

1.5 κ = 100 1 κ = 20 0.5 κ = 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 η Figure 10: Volatility of price (expressed in standard deviation percentage points) as function of customer bargaining power η in baseline model with Nash bargaining for various values of κ. 56

markup gdp x 1.2 0.35 0.13 1.15 0.129 1.1 0.3 0.128 1.05 1 0.25 0.127 0 0.5 1 0 0.5 1 0 0.5 1 c N Nc 0.75 0.4 0.2 0.7 0.35 0.65 0.3 0.15 0.6 0.25 0.55 0.2 0.1 0 0.5 1 0 0.5 1 0 0.5 1 labor search θ 0.35 0.5 0.8 0.4 0.6 0.3 0.3 0.4 0.2 0.2 0.25 0.1 0 0 0.5 1 0 0.5 1 0 0.5 1 Figure 11: Steady-state allocation as function of customer bargaining power η in model with intensive adjustment. 57

Variable Mean Std. Dev. SD% Autocorr. Corr(x,Y) Corr(x,Z) Corr(x,g) Zeromenucost µ 1.0835 0.0006 0.0006 -0.0650 -0.3222 — -0.3065 gdp 0.3368 0.0020 0.0061 0.7678 1.0000 — 0.9999 x 0.1868 0.0002 0.0013 0.7927 -0.9992 — -0.9997 c 1.4000 0 0 — — — — N 0.0663 0.0001 0.0014 0.7949 -0.7672 — -0.7777 Nc 0.0929 0.0001 0.0014 0.7949 -0.7672 — -0.7777 l 0.3368 0.0020 0.0061 0.7678 1.0000 — 0.9999 w 1.0000 0 0 — — — — p 1.0835 0.0006 0.0006 -0.0650 -0.3222 — -0.3065 s 0.0184 0.0002 0.0084 -0.0386 -0.5131 — -0.4988 θ 0.8000 0.0002 0.0002 0.8108 0.9974 — 0.9984 ω 0.5000 0 0 — — — — a 0.0147 0.0001 0.0084 -0.0354 -0.4917 — -0.4773 Menucost,κ=5 µ 1.0835 0.0004 0.0003 0.6454 0.1137 — 0.1277 gdp 0.3368 0.0020 0.0061 0.7676 1.0000 — 0.9999 x 0.1868 0.0002 0.0013 0.7923 -0.9992 — -0.9997 c 1.4000 0 0 — — — — N 0.0663 0.0001 0.0014 0.7978 -0.7669 — -0.7776 Nc 0.0929 0.0001 0.0014 0.7978 -0.7669 — -0.7776 l 0.3368 0.0020 0.0061 0.7676 1.0000 — 0.9999 w 1.0000 0 0 — — — — p 1.0835 0.0004 0.0003 0.6454 0.1137 — 0.1277 s 0.0184 0.0002 0.0084 -0.0334 -0.5106 — -0.4961 θ 0.8000 0.0001 0.0001 0.6178 0.9807 — 0.9773 ω 0.5000 0.0003 0.0005 -0.1895 -0.4863 — -0.4741 a 0.0147 0.0001 0.0084 -0.0259 -0.5016 — -0.4871 Menucost,κ=20 µ 1.0835 0.0006 0.0006 0.9711 0.5143 — 0.5230 gdp 0.3368 0.0020 0.0061 0.7674 1.0000 — 0.9998 x 0.1868 0.0002 0.0013 0.7922 -0.9992 — -0.9997 c 1.4000 0 0 — — — — N 0.0663 0.0001 0.0014 0.8000 -0.7664 — -0.7774 Nc 0.0929 0.0001 0.0014 0.8000 -0.7664 — -0.7774 l 0.3368 0.0020 0.0061 0.7674 1.0000 — 0.9998 w 1.0000 0 0 — — — — p 1.0835 0.0006 0.0006 0.9711 0.5143 — 0.5230 s 0.0184 0.0002 0.0084 -0.0329 -0.4990 — -0.4840 θ 0.8000 0.0002 0.0002 0.8626 -0.9820 — -0.9851 ω 0.5000 0.0004 0.0008 0.2115 -0.5358 — -0.5267 a 0.0147 0.0001 0.0085 -0.0150 -0.5191 — -0.5044 Menucost,κ=100 µ 1.0835 0.0008 0.0007 0.9923 0.3406 — 0.3461 gdp 0.3368 0.0020 0.0060 0.7668 1.0000 — 0.9998 x 0.1868 0.0002 0.0013 0.7926 -0.9991 — -0.9997 c 1.4000 0 0 — — — — N 0.0663 0.0001 0.0015 0.8012 -0.7658 — -0.7774 Nc 0.0929 0.0001 0.0015 0.8012 -0.7658 — -0.7774 l 0.3368 0.0020 0.0060 0.7668 1.0000 — 0.9998 w 1.0000 0 0 — — — — p 1.0835 0.0008 0.0007 0.9923 0.3406 — 0.3461 s 0.0184 0.0002 0.0086 -0.0390 -0.4679 — -0.4518 θ 0.8000 0.0008 0.0010 0.8114 -0.9972 — -0.9984 ω 0.5000 0.0005 0.0011 0.5698 0.0485 — 0.0582 a 0.0147 0.0001 0.0090 0.0013 -0.5519 — -0.5368 Table 9: Simulation-based moments in basic model with government spending, Nash bargaining, and government purchase shocks as driving force. 58

B Nash Bargaining Here we derive the Nash-bargaining solution between an individual customer and the firm. We present the most general case in which bargaining occurs over both price and quantity, and at the end of the section we show how to simplify things if the quantity is fixed and bargaining occurs only over price. For notational simplicity, we omit the conditional expectations operator E where t it is understood. Themarginalvaluetothehouseholdofafamilymemberwhoisalreadyengagedinarelationship (a shopper) with a firm is u˜(c ) g0(1−l −s −N ) h i M = it − t t t −p c +E Ξ ((1−ρx)M +ρxS ) . (55) t λ λ it it t t+1|t t+1 t+1 t t Here, p denotes the price of the consumption good traded between a firm and a customer, and it c denotes its quantity. The function u˜ is the marginal utility to the household of obtaining it consumptionfromthei-thmatch. Thepreciseexpressionforu˜ dependsonwhetherthehousehold’s aggregator over search consumption goods is linear (as in the baseline model) or displays curvature (as in the model with intensive adjustment). For simplicity, here we assume that the aggregator is linear, and the expression for u˜ for the case with curvature is derived in Appendix E. Thus, let y be defined as simply the sum of the c ’s, y ≡ RN c di, in which case u˜(c ) is defined as u (.)∂y, i 0 i i 1 ∂ci which reduces to u˜(c ) = u (.). Because the units of u˜ are utils, we convert it into units of the final i 1 composite by dividing by the period-t marginal utility of wealth for the household, λ , which has t units of utils per final good. The marginal value to the household of an individual who is searching for goods is g0(1−l −s −N ) h (cid:16) (cid:17)i S = − t t t +E Ξ θ kf(θ )(1−ρx)M +(1−θ kf(θ )(1−ρx))S . t λ t t+1|t t t t+1 t t t+1 t (56) The only instantaneous components of S is the marginal reduction in utility due to the marginal t reduction in total household leisure time because of searching. The value to a firm of an existing customer is κ (cid:18) p (cid:19)2 h i A = p c −mc c − it −1 +E Ξ (1−ρx)A , (57) t it it t it 2 p t t+1|t t+1 it−1 where the instantaneous components takes into account the revenue from sales to the customer, the total cost of production, and the cost of price adjustment. Bargaining occurs every period over the price p and quantity c . The firm and customer it it maximize the Nash product (M −S )ηA 1−η, (58) t t t 59

where η ∈ (0,1) is the fixed weight given to the customer’s individual surplus. The first-order condition of the Nash product with respect to p is it (cid:18)∂M ∂S (cid:19) ∂A η(M −S )η−1 t − t A 1−η +(1−η)(M −S )ηA −η t = 0, (59) t t t t t t ∂p ∂p ∂p it it it which can be condensed as usual to ∂A (cid:18)∂M ∂S (cid:19) t t t (1−η)(M −S ) = −ηA − . (60) t t t ∂p ∂p ∂p it it it We have ∂Mt = −c , ∂St = 0, and ∂pit it ∂pit ∂A (cid:18) p (cid:19) 1 (cid:20) (cid:18)p (cid:19) p 1 (cid:21) t = c −κ it −1 +(1−ρx)E Ξ κ it+1 −1 it+1 , (61) ∂p it p p t t+1|t p p p it it−1 it−1 it it it which reveals a second forward-looking element to pricing, independent of the forward-looking element that arises due to the long-lived customer relationship. Defining π ≡ p /p as the gross growth rate of the price of the i-th good, it it it−1 ∂A 1 (cid:20) π (cid:21) t = c −κ(π −1) +(1−ρx)κE Ξ (π −1) it+1 . (62) ∂p it it p t t+1|t it+1 p it it−1 it Next, define ∆H ≡ −∂M /∂p , ∆F ≡ ∂A /∂p , and thus t t it t t it η ω ≡ (63) t η+(1−η)∆F/∆H t t (1−η)∆F/∆H 1−ω = t t (64) t η+(1−η)∆F/∆H t t as time-varying bargaining weights. With these definitions, the sharing rule that determines p is it (1−ω )(M −S ) = ω A . (65) t t t t t The surplus is split proportionally according to time-varying weights, which is a generalization of the usual Nash-sharing rule. Note that if κ = 0 (i.e., there are no menu costs), ω = η, in which t case the typical Nash sharing rule (1−η)(M −S ) = ηA emerges. t t t Using the Bellman equation for the value to a firm of an existing customer along with the (cid:16) (cid:17)2 advertising condition, we have A = p c − mc c − κ pit −1 . Using this along with the t it it t it 2 pit−1 definitions of M and S and going through several algebraic rearrangements, we can, after some t t tedious algebra, show that the price p is characterized by it ω " κ (cid:18) p (cid:19)2 γ # u˜(c ) t it it p c −mc c − −1 + = −p c + (66) 1−ω it it t it 2 p kf(θ ) λ it it t it−1 t t " (cid:18) ω (cid:19) " κ (cid:18)p (cid:19)2 γ ## + (1−θ kf(θ ))E Ξ t+1 (1−ρx) p c −mc c − it+1 −1 + . t t t t+1|t 1−ω it+1 it+1 t+1 it+1 2 p kf(θ ) t+1 it t 60

Note there are two reasons why price-setting is forward-looking. One reason is a standard stickyprice reason: with costs of price adjustment, a setting for p has ramifications for future setting of it p . But note that even with κ = 0, p is affected by expectations regarding p . This has to it+1 it it+1 do with the long-lived customer relationship: with probability 1−ρx, the customer and firm will bargain over the same good again in the future. If κ = 0, we have that ∂A /∂p = c , and the t it it bargaining weight collapses to ω = η. t Bargaining over the quantity c traded yields it (cid:18)∂M ∂S (cid:19) ∂A η(M −S )η−1 t − t A 1−η +(1−η)(M −S )ηA −η t = 0. (67) t t t t t t ∂c ∂c ∂c it it it We have ∂Mt = u˜0(cit) −p , ∂St = 0 (because of our maintained assumption that u is separable in ∂cit λt it ∂cit its two arguments), and ∂At = p −mc . Thus, the sharing rule that determines c is ∂cit it t it ∂A ∂M t t (1−η)(M −S ) = −ηA . (68) t t t ∂c ∂c it it Similar to how we proceeded above in Nash bargaining over the price, we can define the following: δH ≡ −∂M /∂c , δF ≡ ∂A /∂c , and thus t t it t t it η ø ≡ (69) t η+(1−η)δF/δH t t (1−η)δF/δH 1−ø ≡ t t (70) t η+(1−η)δF/δH t t as time-varying bargaining weights. Note that ø 6= ω . Proceeding completely analogously as t t above (i.e., using the Bellam equations for the value to a firm of an existing customer along with the advertising condition and going through several tedious steps of algebra), we can show that the quantity c is characterized by it ø " κ (cid:18) p (cid:19)2 γ # u˜(c ) t it it p c −mc c − −1 + = −p c + (71) 1−ø it it t it 2 p kf(θ ) λ it it t it−1 t t " (cid:18) ø (cid:19) " κ (cid:18)p (cid:19)2 γ ## + (1−θ kf(θ ))E Ξ t+1 (1−ρx) p c −mc c − it+1 −1 + , t t t t+1|t 1−ø it+1 it+1 t+1 it+1 2 p kf(θ ) t+1 it t which is expression (50) in the text. Clearly, the only difference between (66) and (71) is in the relevant bargaining weights. In particular, note that ø depends on u˜0(c ) through ∂M /∂c , t it t it whereasω doesnot. Withcurvatureintheaggregatoroversearchconsumptiongoods, derivingthe t expressionforu˜0(c )requiressometediousalgebra,thedetailsofwhichareprovidedinAppendixE. it If κ = 0, a more convenient representation of the solution for the quantity traded is available. Using the derivatives of M and A , (68) becomes t t (cid:18) u˜0(c )(cid:19) t (1−η)(p −mc )(M −S ) = η p − A . (72) t t t t t t λ t 61

Next, recognize that, with κ = 0, the Nash solution for the price satisfies (1−η)(M −S ) = ηA . t t t Imposing this on the previous expression, we have that the quantity c traded solves t u˜0(c ) t mc = . (73) t λ t Recall that households’ optimal choice of labor implied λ = g0/w , meaning t t t mc u˜0(c ) t t = . (74) w g0 t t Finally, because marginal cost is identically equal to the ratio of the real wage to the marginal product of labor w /z , in equilibrium, the quantity traded in any given customer-firm relationship t t satisfies g0 t = z , (75) u˜0(c ) t t which is a goods-market efficiency condition stating that the household’s MRS between leisure and consumption of a particular good equals the marginal product of labor. Thus, with simultaneous bargaining over price and quantity traded of any given good, quantity (the intensive margin of consumption) is privately efficient, which is a standard outcome of Nash bargaining. One implication of this result is that if consumption were subject to proportional taxation, the intensive margin of trade would be unaffected by the consumption tax, given a number of customer-firm relationships (which in general would be distorted by a consumption tax). In our baseline model without the intensive margin, the customer and firm asset values M and t A simplify to t u˜(c¯) g0(1−l −s −N ) h i M = − t t t −p c¯+E Ξ ((1−ρx)M +ρxS ) (76) t λ λ it t t+1|t t+1 t+1 t t and κ (cid:18) p (cid:19)2 h i A = p c¯−mc c¯− it −1 +E Ξ (1−ρx)A . (77) t it t 2 p t t+1|t t+1 it−1 That is, quantity exchanged in a customer match is fixed at c¯. Maximization of the Nash product is now with respect to only p . Proceeding similarly as above, it ω " κ (cid:18) p (cid:19)2 γ # u˜(c¯) t it p c¯−mc c¯− −1 + = −p c¯+ (78) 1−ω it t 2 p kf(θ ) λ it t it−1 t t " (cid:18) ω (cid:19) " κ (cid:18)p (cid:19)2 γ ## + (1−θ kf(θ ))E Ξ t+1 (1−ρx) p c¯−mc c¯− it+1 −1 + , t t t t+1|t 1−ω it+1 t+1 2 p kf(θ ) t+1 it t which is expression (24) in the text. C Fair Bargaining Rather than the surplus being split according the time-varying rule (1−ω )(M −S ) = ω A , t t t t t here we impose fair bargaining, in which it is required that (1 − η)(M −S ) = ηA . That is, t t t 62

suppose that the customer and firm arrange the effects of inflation so that the shares of the surplus each gets are not time-varying. In fair bargaining, the customer and firm jointly choose (p ,c ) to maximize the Nash product it it (M −S )ηA 1−η (79) t t t subject to the constraint (1−η)(M −S ) = ηA . (80) t t t Letting ι be the Lagrange multiplier on the constraint, the first-order conditions of the bargaining t problem are (cid:20)∂M ∂S ∂A (cid:21) ∂A A η (cid:20)∂M ∂S (cid:21) A η t t t t t t t t ηA − + +ηι = (1−η)ι − (81) t ∂p ∂p ∂p t ∂p (M −S )1−η t ∂p ∂p (M −S )1−η it it it it t t it it t t and (cid:20)∂M ∂S ∂A (cid:21) ∂A A η (cid:20)∂M ∂S (cid:21) A η t t t t t t t t ηA − + +ηι = (1−η)ι − . (82) t ∂c ∂c ∂c t ∂c (M −S )1−η t ∂c ∂c (M −S )1−η it it it it t t it it t t In obtaining these, we used the constraint to make the substitution (1−η)(M −S ) = ηA . Next, t t t h i because (1−η)(M −S ) = ηA , clearly (1−η) ∂Mt − ∂St = η∂At, and similarly for derivatives t t t ∂pit ∂pit ∂pit with respect to c . The two first-order conditions thus reduce to it (cid:20)∂M ∂S ∂A (cid:21) t t t ηA − + = 0 (83) t ∂p ∂p ∂p it it it and (cid:20)∂M ∂S ∂A (cid:21) t t t ηA − + = 0. (84) t ∂c ∂c ∂c it it it Because ηA 6= 0, the terms in brackets characterize the fair bargaining solutions for p and c . t i i With the definitions of M , S , and A , ∂Mt = u˜0(cit)−p , ∂St = 0 (because of our maintained t t t ∂cit λt it ∂cit assumption that u is separable in its two arguments), and ∂At = p −mc . Inserting these in the ∂cit it t latter FOC, u˜0(c ) it = mc . (85) t λ t Once again, using the equilibrium condition λ = g0/w and the fact that mc = w /z = 1, t t t t t t g0 t = z (86) u˜0(c ) t t characterizes the solution for the quantity traded, just as in the Nash case with κ = 0. Thus, in fair bargaining, eliminating the wedge in price-bargaining has the associated effect of eliminating the wedge in quantity-bargaining as well. As was the case in Nash bargaining, the derivation of u˜0(c ) is presented in Appendix E. it 63

Proceeding similarly, the price is characterized by h i κ(π −1)π −(1−ρx)E Ξ κ(π −1)π = 0, (87) it it t t+1|t it+1 it+1 which reveals something very interesting. If this were a monetary model and thus π were the rate of change of the nominal price level, this condition would be identical to a standard New Keynesian Phillips curve except for the fact that nothing at all about allocations appears. D Steady-State Analytics Using conditions (37) and (39), we first prove our claim in Section 4.2 that the steady-state price (and hence the steady-state markup) decreases as customer bargaining power η rises. Using the fact that Cobb-Douglas matching implies the probability a firm finds a customer is kf(θ) = θξ, from (37) we can solve for θ: (cid:20) β(1−ρx) p−mc(cid:21)1 ξ θ = . (88) 1−β(1−ρx) γ Inserting this in (39): (cid:20) (cid:18) β(1−ρx) p−mc(cid:19)(cid:21) p = (1−η)A+η mc−γ . (89) 1−β(1−ρx) γ Defining an implicit function F(p,η) = 0 using this last expression, we can compute the partials ηγ (cid:18) β(1−ρx) (cid:19)(cid:18) β(1−ρx) p−mc(cid:19)1 ξ −1 F = 1+ (90) p ξ γ[1−β(1−ρx)] 1−β(1−ρx) γ and   (cid:18) β(1−ρx) p−mc(cid:19)1 ξ F η = A−mc−γ 1−β(1−ρx) γ . (91) With search frictions, γθξ > 0; the advertising condition then guarantees that p > mc. Hence, given that all other parameters are of appropriate sign and magnitude (i.e., β ∈ (0,1), ρx ∈ (0,1), η ∈ (0,1), ξ ∈ (0,1), and γ > 0), F > 0. Next, note that we can write F compactly as p η F = A−(mc−γθ). If A < (mc−γθ), forming customer relationships would not even be socially η beneficialbecausethesocialmarginalbenefit(theutilityAofconsuming)wouldnotcoverthesocial marginalcostofformingrelationshipsandproducing. Thus, wesimplyassumethatA > (mc−γθ), implying F > 0, Finally, then, we have by the implicit function theorem that the bargained price η decreases the higher is customer bargaining power, dp = − Fη < 0. dη Fp Next, to characterize the firm advertising condition in (a,s) space, first solve for p from (37): 1−β(1−ρx) p = mc+ γθξ. (92) β(1−ρx) 64

Inserting this in (39) gives us a version of the advertising condition that embeds the pricing condition: 1−β(1−ρx) mc+ γθξ = (1−η)A+η(mc−γθ). (93) β(1−ρx) Replacing θ by a/s, we can define an implicit function G(a,s) = 0 using this last expression and compute the partials 1−β(1−ρx) G = γξaξ−1s−ξ +ηγs−1 (94) a β(1−ρx) and 1−β(1−ρx) G = − γaξs−ξ−1−ηγas−2. (95) s β(1−ρx) By the implicit function theorem, the slope of the advertising condition in (a,s) space is thus da = −Gs. With a couple of steps of algebra, it is not difficult to show that da = θ, meaning that ds Ga ds in (a,s) space, the advertising condition is a ray through the origin with angle θ to the s axis, as illustrated in Figure 2. E Intensive Quantity Adjustment For use in the Nash-bargaining and fair-bargaining solutions for quantity, we require an expression for u˜0(c ). Recall that with curvature, the household subutility function over search consumption it goods is " #1/ρ  v Z Nt cρ jt dj . (96) 0 With u˜(c ) defined as the marginal utility to the household of obtaining consumption from the it i-th match, we have " #1/ρ  " #1−1 u e (c it ) = v0  Z Nt cρ jt di  ρ 1 Z Nt cρ jt dj ρ ρcρ it −1. (97) 0 0 Note the distinction between the indices i and j: j is a dummy index of integration, while i denotes a good obtained from the i-th customer relationship. For use in the bargaining solutions for the intensive quantity, what requires some work is obtainingu˜0(c )because,note,c appearsthreetimesinexpression(97): asoneoftheconsumption it it terms in the argument to v(.), as one of the consumption terms in the integral RN cρdi, and by 0 i itself in the last term on the right-hand-side. To make the problem manageable, define " #1/ρ  f(c it ) ≡ v0  Z Nt cρ jt dj , (98) 0 " #1−1 g(c ) ≡ 1 Z Nt cρ dj ρ , (99) it ρ jt 0 65

h(c ) ≡ ρcρ−1. (100) it it Letting z ≡ u˜(c ), what we are interested in deriving is ∂z = f0gh+fg0h+fgh0. Proceeding, it ∂cit " #1/ρ  " #1−1 f0 = v00  Z Nt cρ jt dj  ρ 1 Z Nt cρ jt dj ρ ρcρ it −1, (101) 0 0 g0 = 1 (cid:18)1 −1 (cid:19)" Z Nt cρ dj # ρ 1−2 ρcρ−1, (102) ρ ρ jt it 0 h0 = ρ(ρ−1)cρ−2. (103) it We limit attention to symmetric equilibria, so having computed derivatives, we can impose symmetry, c = c, on f, g, h, f0, g0, and h0, yielding i (cid:16) (cid:17) f = v0 c N 1/ρ , (104) t t 1 1−ρ g = c1−ρN ρ , (105) ρ t t h = ρcρ−1, (106) t (cid:16) (cid:17) 1−ρ f0 = v00 c N 1/ρ N ρ , (107) t t t 1−ρ 1−2ρ g0 = c−ρN ρ , (108) ρ t t h0 = ρ(ρ−1)cρ−2. (109) t Constructing the symmetric version of f0gh+fg0h+fgh0 and rearranging, 1−ρ (cid:20) (cid:16) (cid:17) 1−ρ (cid:16) (cid:17) (cid:18) 1 (cid:19)(cid:21) u˜0(c ) = N ρ v00 c N 1/ρ N ρ +v0 c N 1/ρ (1−ρ)c−1 −1 , (110) t t t t t t t t N t which goes into the Nash- and fair-bargaining solutions for the intensive quantity traded. Note (cid:16) (cid:17) that if we we were to remove curvature by setting ρ = 1, this collapses to u˜0(c ) = v0 c N 1/ρ . t t t 66

F Advertising Data The aggregate advertising data are from two separate sources. The data for 1951 to 1999 are obtainedfromanupdatedversionofRobertJ.Coen’s(McCann-Erikson,Inc.) originaldatapublished in Historical Statistics of the United States, Colonial Times to 1970. The data for 2000 to 2005 are obtained from the Newspaper Association of America (NAA). The aggregate data include spending for advertising in newspapers, magazines, radio, broadcast television, cable television, direct mail, billboards and displays, Internet, and other forms. The GDP figures are from the US Bureau of Economic Analysis (BEA). Using the nominal data in Table 10, we construct a real advertising series by deflating by the all-items Consumer Price Index (results were quite similar deflating by the GDP deflator). Logging andHP-filteringtheresultingseries,wefindthatovertheentiresamplethecyclicalvolatilityofreal advertising is 4.2 percent, the contemporaneous correlation with GDP is 0.73, and its first-order serial correlation is 0.6. 67

Year Aggregatenominaladvertisingexpenditure($B) NominalGDP($B) ShareofGDP(%) 1950 5.7 293.8 1.9 1951 6.4 339.3 1.9 1952 7.1 358.3 2.0 1953 7.7 379.4 2.0 1954 8.2 380.4 2.1 1955 9.2 414.8 2.2 1956 9.9 437.5 2.3 1957 10.3 461.1 2.2 1958 10.3 467.2 2.2 1959 11.3 506.6 2.2 1960 12.0 526.4 2.3 1961 11.9 544.7 2.2 1962 12.4 585.6 2.1 1963 13.1 617.7 2.1 1964 14.2 663.6 2.1 1965 15.3 719.1 2.1 1966 16.6 787.8 2.1 1967 16.9 832.6 2.0 1968 18.1 910.0 2.0 1969 19.4 984.6 2.0 1970 19.6 1,038.5 1.9 1971 20.7 1,127.1 1.8 1972 23.2 1,238.3 1.9 1973 25.0 1,382.7 1.8 1974 26.6 1,500.0 1.8 1975 27.0 1,638.3 1.7 1976 33.3 1,825.3 1.8 1977 37.4 2,030.9 1.8 1978 43.3 2,294.7 1.9 1979 48.8 2,563.3 1.9 1980 53.6 2,789.5 1.9 1981 60.5 3,128.4 1.9 1982 66.7 3,255.0 2.0 1983 76.0 3,536.7 2.1 1984 88.0 3,933.2 2.2 1985 94.9 4,220.3 2.2 1986 102.4 4,462.8 2.3 1987 110.3 4,739.5 2.3 1988 118.8 5,103.8 2.3 1989 124.8 5,484.4 2.3 1990 129.6 5,803.1 2.2 1991 127.6 5,995.9 2.1 1992 132.7 6,337.7 2.1 1993 139.5 6,657.4 2.1 1994 151.7 7,072.2 2.1 1995 162.9 7,397.7 2.2 1996 175.2 7,816.9 2.2 1997 187.5 8,304.3 2.3 1998 201.6 8,747.0 2.3 1999 215.3 9,268.4 2.3 2000 243.3 9,817.0 2.5 2001 231.3 10,128.0 2.3 2002 236.9 10,469.6 2.3 2003 245.6 10,960.8 2.2 2004 263.8 11,712.5 2.3 2005 271.1 12,455.8 2.2 Table 10: Advertising Data 68

References Akerlof, George A. 2007. “The Missing Motivation in Macroeconomics.” American Economic Review, Vol. 97, pp. 5-36. Alessandria, George. 2005. “Consumer Search, Price Dispersion, and International Relative Price Volatility.” Federal Reserve Bank of Philadelphia Working Paper No. 05-9. Arseneau, David M. and Sanjay K. Chugh. 2006. “Ramsey Meets Hosios: The Optimal Capital Tax and Labor Market Efficiency.” International Finance Discussion Paper no. 870 , Board of Governors of the Federal Reserve System. Arseneau, David M. and Sanjay K. Chugh. 2007. “Optimal Fiscal and Monetary Policy with Costly Wage Bargaining.” International Finance Discussion Paper no. 891 , Board of Governors of the Federal Reserve System. Aruoba, S. Boragan and Sanjay K. Chugh. 2006. “Optimal Fiscal and Monetary Policy When Money is Essential.” International Finance Discussion Paper no. 880 , Board of Governors of the Federal Reserve System. Aruoba, S. Boragan, Guillaume Rocheteau, and Christoper J. Waller. 2007. “Bargaining and the Value of Money.” Journal of Monetary Economics. Forthcoming. Binmore, Ken. 2007. Does Game Theory Work? The Bargaining Challenge. MIT Press. Blinder, Alan S., Elier D. Canetti, David E. Lebow, and Jeremy B. Rudd. 1998. Asking About Prices: A New Approach to Understanding Price Stickiness. Russell Sage Foundation. Chari, V.V., Patrick J. Kehoe, and Ellen R. McGrattan. 2006. “Business Cycle Accounting.” Econometrica. Forthcoming. Chugh, Sanjay K. 2006. “Optimal Fiscal and Monetary Policy with Sticky Wages and Sticky Prices.” Review of Economic Dynamics, Vol. 9, pp. 683-714. Diamond, Peter A. 1971. “A Model of Price Adjustment.” Journal of Economic Theory, Vol. 3, pp. 156-168. Gust, Christopher, Sylvain Leduc, and Robert J. Vigfusson. 2006. “Trade Integration, Competition, and the Decline in Exchange-Rate Pass-Through.” International Finance Discussion Paper no. 864 , Board of Governors of the Federal Reserve System. Fabiani, Silvia, Martine Druant, Ignacio Hernando, Claudia Kwapil, Bettina Landau, Claire Loupias, Fernando Martins, Thomas Matha, Roberto Sabbatini, Harald Stahl, and Ad Stokman. 2006. “What Firms’ Surveys Tell Us About Price-Setting Behavior in the Euro Area.” International Journal of Central Banking, Vol. 2, pp. 3-47. Hall, Robert E. 2005. “Equilibrium Wage Stickiness.” American Economic Review, Vol. 95, pp. 50-65. Hall, Robert E. 2007. “Equilibrium Sticky Prices.” Stanford University. 69

Hosios, Arthur J. 1990. “On the Efficiency of Matching and Related Models of Search and Unemployment.” Review of Economic Studies, Vol. 57, pp. 279-298. Jaimovich, Nir. 2006. “Firm Dynamics, Markup Variations, and the Business Cycle.” Stanford University. Kalai, Ehud. 1977. “Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons.” Econometrica, Vol. 45, pp. 1623-1630. King, Robert G. and Sergio T. Rebelo. 1999. “Resuscitating Real Business Cycles. In Handbook of Macroeconomics, edited by John B. Taylor and Michael Woodford, Vol. 1B. Elsevier. Klemperer, Paul. 1995. “Competition When Consumers Have Switching Costs: An Overview with Applications to Industrial Organization, Macroeconomics, and International Trade.” Review of Economic Studies, Vol. 62, pp. 515-539. Kleshchelski, Isaac and Nicolas Vincent. 2007. “Market Share and Price Rigidity.” Northwestern University. Menzio, Guido. 2007. “A Search Theory of Rigid Prices.” University of Pennsylvania. Nakamura, Emi and Jon Steinsson. 2007. “Price Setting in Forward-Looking Customer Markets.” Harvard University. Okun, Arthur M. 1981. Prices and Quantities. The Brookings Institution. Petrongolo, Barbara and Christopher A. Pissarides. 2001. “Looking into the Black Box: A Survey of the Matching Function.” Journal of Economic Literature, Vol. 39, pp. 390- 431. Pissarides, Christopher A. 2000. Equilibrium Unemployment Theory. MIT Press. Ravn, Morten, Stephanie Schmitt-Grohe, and Martin Uribe. 2006. “Deep Habits.” Review of Economic Studies, Vol. 73, pp. 195-218. Rogerson, Richard, Robert Shimer, and Randall Wright. 2005. “Search-Theoretic Models of the Labor Market: A Survey.” Journal of Economic Literature, Vol. 43, pp. 959-988. Rotemberg, Julio J. 2005. “Customer Anger at Price Increases, Changes in the Frequency of Price Adjustment, and Monetary Policy.” Journal of Monetary Economics, Vol. 52, pp. 829-852. Rotemberg, Julio J. 2006. “Fair Pricing.” Harvard University. Rotemberg, Julio J. and Michael Woodford. 1999. “The Cyclical Behavior of Prices and Costs. In Handbook of Macroeconomics, edited by John B. Taylor and Michael Woodford, Vol. 1B. Elsevier. Rubinstein, Ariel. 1982. “Perfect Equilibrium in a Bargaining Model.” Econometrica, Vol. 50, pp. 97-109. 70

Schmitt-Grohe, Stephanie and Martin Uribe. 2004a. “Optimal Fiscal and Monetary Policy Under Imperfect Competition.” Journal of Macroeconomics, Vol. 26, pp. 183-209. Schmitt-Grohe, Stephanie and Martin Uribe. 2004b. “Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function.” Journal of Economic Dynamics and Control, Vol. 28, pp. 755-775. Shimer, Robert. 2005. “The Cyclical Behavior of Equilibrium Unemployment and Vacancies.” American Economic Review, Vol. 95, pp. 25-49. 71