Long-term contracts, bargaining and monetary policy

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1 Long-term contracts, bargaining and monetary policy VERY PRELIMINARY VERSION Mirko Abbritti Universidad de Navarra Asier Aguilera-Bravo Universidad Pública de Navarra January 22, 27 Abstract A growing empirical literature documents the importance of long-term contracts and bargaining for price rigidity and firms dynamics. This paper introduces long-term business-to-business (B2B) relationships and price bargaining into a standard monetary DSGE model. The model is based on two assumptions: first, both wholesale and retail producers need to spend resources to form new business relationships. Second, once a B2B relationship is formed, the price is set in a bilateral bargaining between firms. The model provides a rigorous framework to study the effect of long-term contracts and bargaining on monetary policy and business cycle dynamics. It shows that these contracts reduce both the allocative role of intermediate prices and the real effects of monetary policy shocks. We also find that the model does a good job in replicating the second moments, cross-correlations and persistence of the data, and that it improves over the benchmark New Keynesian model in explaining some of them. JEL classification: E52, E3, D4, L Keywords: Monetary Policy, Price Bargaining, Product Market Search, B2B. INTRODUCTION The typical business environment often differs dramatically from the standard Dixit-Stiglitz monopolistic competition framework usually adopted in modern DSGE monetary models. As evidenced by recent empirical research, most firms engage mainly in long-term relationships with their customers, and most of their customers are other firms (see e.g. Blinder et al. (998) for the US, Fabiani et al. (26) for the Euro Area and Apel et al. (25) for Sweden). Most of these long-term relationships are governed by contracts, and these contracts last on average between one and two years. Negotiations of prices and quantities are the rule rather than the exception. In fact, in surveys firms report that the main reason they wish to keep prices stable is that they are concerned about losing

2 customers relationships. For instance, Fabiani et al. (26) find, on the basis of surveys conducted by nine Eurosystem national central banks, that the existence of implicit and explicit contracts with customers is the most important explanation for rigid prices. Zbaracki et al. (24) find that customer communications and price negotiation costs account for almost 75% of the total price adjustment cost and are 2 times bigger than the size of the menu costs. Motivated by this evidence, in this paper we introduce business-to-business (B2B) long-term relationships and price bargaining into a standard monetary DSGE model. In the model there are two types of firms, upstream producers (wholesalers) and downstream producers (retailers). Wholesalers produce intermediate goods, which are transformed by retailers into final goods and sold to households. The intermediate goods market is characterized by search and matching frictions à la Mortensen & Pissarides (994). Both wholesalers and retailers need to spend time and resources to match and form long-term relationships with other firms. Once a business relationship is formed, the price is bargained between wholesalers and retailers according to a standard Nash bargaining protocol. The presence of quadratic customer communications and price negotiation costs introduce nominal stickiness in intermediate prices and gives a role to monetary policy. The model provides a rigorous framework to study the effect of long-term contracts and bargaining on monetary policy and business cycle dynamics. The model is calibrated to capture the main features of the US product market. We consider three shocks: a shock to the technology of wholesalers, a shock to the technology of retailers and a monetary policy shock. While the calibration of the monetary shock is standard, the two technology shocks are calibrated to match the volatility of output and the cross-correlation of output with intermediate prices. We compare the performances of the model with the ones of a benchmark two-sector New Keynesian (NK) model with sticky intermediate prices. We find that the model does a good job in replicating the second moments, cross-correlations and persistence of the data, and that it improves over the benchmark NK model in explaining some of them. In particular, introducing B2B long-term relationships helps to improve the volatility of investment, employment, intermediate prices, consumption and wages as well as the cross-correlation of investment, intermediate price inflation and consumption. It also allows to increase the persistence of the system and get closer to the data for output, investment, intermediate price inflation, employment and wages. Recent research has started to investigate the importance of long-term relationships between firms and customers for price and business cycle dynamics. The vast majority of these papers, however, have focused the attention on retail firms to consumer relationships, and do not allow for bilateral negotiations between the parties. These are important distinctions, because the business environment See, e.g, Hall (28), Arseneau & Chugh (27), Kleshchelski & Vincent (29), Ravn et al. (2), Gourio & Rudanko (24), Paciello et al. (24), Den Haan (23). 2

3 in B2B transactions is very different from the one in business-to-consumer (B2C) transactions. To the best of our knowledge, only three papers analyze the implications of B2B relationships and bargaining for price and business cycle dynamics. Drozd & Nosal (22) introduce dynamic frictions of building market shares into an international real business cycle model and show that the model can account for several pricing puzzles of international macroeconomics. Mathä & Pierrard (2) introduce two-sided search and matching between wholesalers and retailers into the standard RBC model to study the effect of long-term relationships on business cycle dynamics. Abbritti & Trani (25) study incomplete pass-through and the allocative power of intermediate goods prices in a model with product market frictions and bargaining over intermediate prices and quantities. Our paper differs from Drozd & Nosal (22), Mathä & Pierrard (2) and Abbritti & Trani (25) in two main aspects: First, we endogenize the match destruction margin. Therefore, the stock of B2B contracts changes not only through endogenous creation, but also through endogenous destruction of matches. Endogenous destruction is modeled by assuming that the productivity of each match is match-specific, and that inefficient matches are destroyed. Second, we allow for price adjustment costs in the bargaining problem between wholesalers and retailers. These costs, which are meant to capture customer communications and price negotiation costs, introduce nominal price stickiness and give a role to monetary policy. We show in the following that endogenous match destructions and sticky prices potentially play an important role in B2B and pricing dynamics. The structure of the paper is as follows. Sections 2 and 3 describe the theoretical B2B model and the benchmark NK model, respectively. In Section 4 the calibration strategy is explained and the results and robustness check are detailed in Section 5. Section 6 concludes. 2. THE MODEL 2.. Firms and Product Market The product market is composed by two different types of firms, wholesalers and retailers, and follows the search and matching structure developed by Mortensen & Pissarides (994). In order to sell their products, wholesale producers need to establish long-term customer relationships with retailers. Once both types of firms meet they bargain over the intermediate price at which retailers buy intermediate goods to wholesalers. The productivity of each match contains an idiosyncratic element a t (i). Every period, match-specific productivities are drawn from a time-invariant distribution with c.d.f. F (a t (i)) and p.d.f. f (a t (i)). We assume that the aggregate number of business to business (B2B) relationships T t, follows the law of motion T t+ = ( δ t+ ) (T t + m t ) where m t, the number of new B2B relationships at time t, is a constant returns to scale function of the search effort of retailers V t (purchase managers) and the search effort of wholesalers S t (advertising and marketing): m t = ms ξ t V ξ t 3

4 The separation rate is defined as δ t = δ x + ( δ x ) F (ã t (i)), where ã t (i) is an endogenously determined productivity threshold below which matches are not profitable and hence terminated Wholesalers There is a continuum of wholesale producers with unit mass. Each wholesaler j maximizes the expected present value of future profits {( ) PIt (j) β,t c W t (j) P t E t= subject to the production function and the law of motion of the customer base T t (j) ( r k t + δ k ) Kt (j) w t N t (j) γ W κ Y W t (j) = qt t (j) = A W t K t (j) α N t (j) α T t+ (j) = ( δ t+ (j)) (T t (j) + S t (j) µ W (θ t )) ( ) κ St (j) T t (j)} T t (j) The wholesaler chooses how much search effort, S t, he will execute to find new buyers for his product. Think of this as the firm choosing the number of sales managers it is going to hire. Each unit of effort will provide him with a average of µ W (θ t ) = mθ ( ξ) t retailers at the end of the period, where θ t = V t /S t is the product market tightness, and the cost of this effort is captured by the last term of the objective function above. P It (j) denotes the price of the intermediate good, that is decided after the succesfull match in a bilateral bargain with the retailers. c W t = φ 2 (P It(j)/P It (j) π) 2 captures quadratic price adjustment costs. We assume that this cost, which is intended to capture price negotiation and communication costs, is proportional to the number of B2B relationships T t. The wholesaler also decides how much capital, K t (j), and labor, N t (j), he is going to rent. A W t is an AR() technology shock and, for simplicity, we normalize q =. The rental rate of capital is r k t, its depreciation rate δ k and the real wage is denoted by w t = W t /P t. From the first-order necessary conditions we get that both the capital-labor ratio and the marginal cost mc t = ( A W t K t (j) N t (j) = α w t α rt k + δ k ( ) wt ) α ( ) r k α t + δ k α α are equal across wholesalers. This is because ex-ante all the wholesale producers are identical since the match-specific productivity draws are not realized until the matches occur and intermediate prices are bargained. Further combinations of the FOCs give us the following expression: J W t (j) = P It (j) P t c W t (j) mc t + ( (κ ) St (j) γ W κ T t (j) ) κ + E t β t,t+ ( δ t+ (j)) J W t+ 4

5 This equation captures the expected value (across matches) of a B2B relationship for wholesaler j. This depends positively on the intermediate price that the retailer pays him and negatively on the marginal cost of production. A successful match is not only valuable in terms of production but also because it establishes a long-term relationship that saves both parties the cost of searching ( ) for an alternative match, (κ ) κ γ St(j) κ. W T t(j) The last term, Et β t,t+ ( δ t+ (j)) Jt+, W captures the expected continuation value of a match. This brings dynamic effects into the model coming from the fact that in the next period only a fraction equal to ( δ t+ (j)) of the matches survives and both wholesalers and retailers benefit from them. Optimal amount of search is chosen chosen to equate the expected marginal cost and the marginal benefit of a new business relationship: ( ) κ γ St(j) W T t(j) = E t β t,t+ ( δ t+ (j)) Jt+ W µ W (θ t ) This equation makes it clear once again that the search effort is executed in one period but it does not pay off until the next period and only if the match resulting from it is not destroyed Retailers There is a continuum of retail producers with unit mass that buy the intermediate goods from wholesalers and sell it to consumers in perfectly competitive markets. Each retailer draws a matchspecific productivity from a time-invariant distribution with c.d.f F (a) and p.d.f. f(a). We assume that the draw of productivity takes place after intermediate price bargaining. This timing assumption simplifies considerably the bargaining problem and the solution of the model because it implies that the bargined price is identical for every match. The total production of retailer i is given by where A R t A R t T t (i) ã f (a) a F (ã) da = AR t T t (i) H (ã t (i)) is an AR() technology shock, T t (i) is the number of productive or functional matches and H (ã t (i)) is the conditional expectation of the idiosyncratic shock E [a a ã t (i)]. The productivity threshold ã t (i) is endogenously determined such that below it matches are not profitable and hence destroyed. In a similar way to the case of the wholesale producers, the number of B2B relationships of retailer i follows a law of motion that depends on the current-period separation rate and the previous-period number of functional matches and search effort exercised, V t (i) where µ R (θ t ) = mθ ξ t of effort. T t+ (i) = ( δ t+ (i)) (T t (i) + V t (i) µ R (θ t )) is the average number of wholesalers attracted in the current period per unit Retailers maximize the expected present value of profits before the realization of the idiosyncratic shock a, i.e. based on the expected output E a Yt R (i) = A R t T t (i) H (ã it ). Specifically, every retailer i 5

6 maximizes: E t= ( ) β t,t+ {A R PIt (i) t T t (i) H (ã t (i)) + c R t (i) T t γ R P t κ ( ) κ Vt (i) T t (i)} T t (i) subject to the law of motion of the customer base. Retailers also face a cost of changing the bargained price, which is defined as c R t = φ 2 (P It(i)/P It (i) π) 2 and it is also proportional to the number of B2B relationships T t. The last term of the equation captures the cost of effort. At the beginning of each period the retailer chooses the level of production and the search effort. The intermediate price P It is decided after the successful match in a bilateral bargaining between retailers and wholesalers. From the first-order necessary conditions we get the expected value (across matches) of a customer relationship for the retailer J R t (i) = A R t H (ã t (i)) P It (i) P t c R t (i) + ( ) κ (κ ) Vt (i) γ R + E t β t,t+ ( δ t+ (i)) Jt+ R (i) κ T t (i) The value of a match depends positively on its production and negatively on the marginal cost, which is the relative price the retailer has to pay to the wholesaler. Once again we can see, from the fourth term, that a match saves on searching cost. The last term in the equation connects the value of the matches in two subsequent periods bringing the dynamic effects into the model. Keeping in mind that this is a general equilibrium model and that all the variables are somehow connected, we can notice a ceteris paribus effect of the threshold on the value of the matches. In particular, a higher threshold implies a higher average value of the matches because the previously least productive matches are destroyed, leaving operative those with higher productivity. In equilibrium, the marginal cost of searching in a given period is equal the marginal benefit that will be realized in the subsequent periods: ( ) κ γ Vt(i) R T t(i) = E t β t,t+ ( δ t+ ) Jt+ R (i) µ R (θ t ) Endogenous separation We assume that a successful match is endogenously destroyed whenever the realization of the idiosyncratic shock does not make it profitable for at least one of the parties. Since prices are determined before the realization of a t, the value of a B2B relationship for a wholesaler, J W t depend on a t. Let us define by J R t (j), does not (a t ) the marginal value for the retailer of a match with idiosyncratic productivity a t. The threshold ã t is endogenously determined as solution of J R t (ã t ) =. Combining this equation with the first-order conditions of the retailer the critical threshold below which matches are terminated is implicitly defined as: ã t (i) = ( A R t ) P It (i) P t + c R t (i) ( ) κ (κ ) Vt (i) γ R κ T t (i) γ R ( Vt(i) T t(i) µ R (θ t ) ) κ 6

7 The threshold ã t is increasing on the relative intermediate price and on the cost of changing prices because the higher these are the more profitable the match has to be to allow the retailer to pay for them. On the other hand a higher technology shock of the retailers makes them more productive and can compensate for a lower idiosyncratic draw Bargaining After wholesalers and retailers are matched, intermediate prices are determined through a Nash bargaining scheme between them. Precisely, for each match v, intermediate goods prices are determined as the outcome of the following bargaining scheme [ (J W max SU t = t (v) ) η ( J R t (v) ) ] η P It where η is the bargaining power of wholesalers. We assume that prices are determined before the productivity draw of the retailers. Hence, the bargaining problem is the same across matches and the intermediate price will be unique. Dropping the subscript v, maximization gives: ( ηjt R ( η) ( H t ã t ) J W t ) ϕ t = τ t ( ηj R t + ( η) J W t where τ t = (φ (π It ) π It β t,t+ ( δ t+ ) φ (π It+ ) π It+ ) captures the marginal cost of changing the intermediate price and ϕ t = P It /P t is defined as the intermediate relative price Households There is a representative household in the economy and his total lifetime utility is given by: { c E β t σ t σ κ N t +ν } + ν t= which depends positively on consumption, c t, and negatively on labor, N t. The household faces a sequence of flow budget constraints which denoted in real terms can be written as: c t + b t+ R t π t+ + k t+ ( δ k ) k t = w t N t + b t + (r k t + δ k )k t + d t where b t denote purchases of bonds, R t is the nominal interest rate on bonds, w t is the real wage and d t are the dividends net of lump sum taxes. From the first-order necessary conditions we obtain the standard Euler Equation, the labor supply and the no arbitrage condition on the assets: c σ t = βc σ t+ R tπ t+ w t = κn ν t c σ t R t π t+ = + r k t+ These equations will determine the level of consumption, the demand for bonds and physical capital and the supply of labor. ) 7

8 2.3. Aggregate Constraints and Prices To close the model we need to aggregate the quantities and the markets to clear. The total output in the economy is the result of adding up the production of every match whose productivity draw was above the threshold: Y R t = A R t T t H (ã t ) and T t = A W t K α t N α t Aggregate physical capital evolves according to K t+ = ( δ k )K t + I t And finally notice that output can be either consumed, invested in physical capital or used to pay the cost of changing bargained prices and/or search efforts. Y t = c t + I t + φ (π It ) 2 T t + γ R κ ( Vt T t ) κ T t + γ W κ ( St T t ) κ T t From the definition of the relative price, ϕ t = P It /P t, we are able to establish the relationship between Consumer Price Index and Producer Price Index inflations: 2.4. Monetary Policy π It π t = ϕ t ϕ t The monetary policy is described by a simple Taylor-type rule where the nominal interest rate set by the monetary authority depends on core inflation, output and the previous-period nominal interest rate: [ ( R t R = exp( z PIt t) P It ) φπi ( Yt Y ) φy ] φr ( Rt where φ R, φ πi and φ Y are the relative weights on the previous period interest rate, current core (intermediate price) inflation and output, respectively, and z t is an AR() shock. R ) φr 3. BENCHMARK NEW KEYNESIAN MODEL We compare the results of the model with product market frictions (B2B) with the ones of a benchmark New Keynesian (NK) model with monopolistic competition. To make the models comparable, we assume that also in the benchmark model there are two sectors of production, wholesalers and retailers. Wholesalers are monopolistically competitive and face quadratic price adjustment costs. Retailers combine the varieties of the intermediate goods in a single bundle and sell it to households. Specifically, in the benchmark NK model retailers operate under perfect competition and flexible [ prices. Their production function is y rt = A R t y It, where y It = y It(j) εnk ] ε NK ε NK ε NK dj is a bundle 8

9 of intermediate varieties bought from different wholesalers. The optimal demand of each variety j is ( ) εnk y It (j) = PIt (j) yit. A R t Pt c P t Each wholesaler j operates under monopolistic competition and faces quadratic adjustment costs ( ) (j) = ψp PIt (j) 2. 2 P It (j) π Wholesaler j maximizes the expected present value of future profits E t= {( ) PIt (j) β,t c P t (j) y It (j) ( } r k ) t + δ k Kt (j) w t N t (j) P t subject to the production function y It (j) = A t K t (j) α N t (j) α and the demand for each variety ( ) εnk y It (j) = PIt (j) yit. From the wholesaler s maximization problem we obtain the following A R t Pt FOCs: mc t = ( ) α ( ) wt r k α t + δ k A t ( α) α () K t (j) (2) w t rt k = α + δ k α P It (j) P t = N t (j) ε NK ε NK where τ P t (j) = ψ p (π It (j) π) π It (j) β t,t+ y It+ (j) y It (j) ( mc t + c P t (j) τ ) P t (j) ε NK (3) {ψ p (π It+ (j) π) π It+ (j)} captures the marginal costs of changing prices. The first two equations capture the marginal costs and the capital labor ratio. Equation (3) is instead a version of the Phillips curve relating present and future inflation rates to marginal costs. In fact, aggregating across firms and log-linearizing around steady state one can rewrite equation (3) as: ˆπ It = βe tˆπ It+ + (ε NK ) ( ) mc t ψ ÂR t p where variables with hats denote log deviations from steady states. 4. CALIBRATION In the baseline calibration the parameters are set to capture the main structural features of the US product market. The model is calibrated at the quarterly frequency. Standard parameters. Many parameters are set to standard values. In particular, the discount factor is β =.99, consistent with an annual average interest rate of 4%. The utility function is assumed to be log in consumption, i.e. σ =. We set ν =.5, consistent with a Frisch elasticity equal to 2. This is inside the range of values typically used in general equilibrium models 2. The elasticity of wholesalers production with respect to capital is α =.33. The quarterly capital depreciation rate is δ =.3 corresponding to an annual depreciation rate of 2%. Following Mathä & Pierrard (2),the parameter κ is chosen to match N =.2, which means that 2% of total available time is 2 See e.g. Peterman (26) for a discussion. 9

10 used for work. The parameter governing the degree of price rigidities, φ, is set to 4, as in Krause & Lubik (27), which is an intermediate value of the ones used in the literature. Product market frictions. The calibration of the parameters of the frictional matching market is more challenging, because there is scant evidence on the size of these parameters. The separation rate is set to δ =.2, which implies an average duration of a contract of around 2 years. This is broadly in line with the survey evidence of Blinder et al. (998). Since we do not have direct information on the match destruction process, we calibrate the other parameters determining δ following the labor search literature. We set the exogenous part of the separation rate to 2/3 of the total separation rate, i.e. δ x =.8. Consequently, the endogenous separation rate can be computed as δ n = F (ã) = (δ δ x ) / ( δ x ). The implied steady state threshold for idiosyncratic productivity is ã = F (δ n ). We assume that idiosyncratic productivity a t is i.i.d. lognormally distributed with c.d.f. F (a). In order to calibrate the parameters µ LN and σ LN of the lognormal distribution, we normalize µ LN = and set σ LN =.5. To calibrate the matching process, we start by calibrating the wholesalers search effort x w =.9 as in Abbritti & Trani (25), who build a proxy for the search effort based on the nationallevel Occupational Employment Statistics (OES) dataset. In the baseline calibration, the parameters governing the elasticity of matching to the search effort of wholesaler, ξ, and the bargaining power of wholesalers, η, are set to the standard values ξ = η =.5 (see e.g. Mathä & Pierrard (2) and Abbritti & Trani (25)). Therefore, in the baseline calibration we study a situation where wholesalers and retailers have equal bargaining power. We will however relax this assumption in the sensitivity analysis. Search costs are assumed to be quadratic in the search intensities of the parties, i.e. κ = 2. The other parameters of the matching process follow endogenously from steady state relationships. Monetary policy and shock processes. As commonly assumed in the literature, we assume that the central bank reacts to PPI inflation with with an elasticity φ πi of.5, to output growth with an elasticity φ Y =.5 and a persistence in interest rates φ R =.85. The standard deviation of monetary policy shocks is set to.25 percent, consistent with the estimates by Christiano et al. (24). Finally, the two technology shock processes are calibrated to reproduce some stylized facts of the US economy. Specifically, we set the persistence of the two technology shock processes to ρ AR = ρ AW =.95, while their volatility is set to match two targets: the absolute volatility of aggregate output and the cross-correlation of output with intermediate goods prices. This gives σ AW =.96 and σ AR =.42. Calibration of the NK benchmark model. For the calibration of the benchmark model, we choose the same parameters value of the baseline B2B model. The only additional parameter of the NK model is the elasticity of demand for the intermediate varieties, which is set to ε NK =, consistent with a mark-up of %. To make the results comparable with the ones of the baseline B2B

11 model, we follow the same strategy as in the baseline model, and re-adjust the volatility of the two technology shocks to match the absolute volatility of aggregate output and the cross-correlation of output with intermediate goods prices. This gives σ AW =.5 and σ AR =.. 5. RESULTS 5.. LONG-TERM CONTRACTS AND MONETARY POLICY The repeated nature of the interactions between wholesalers and retailers points toward an important issue: bargained intermediate prices may not be allocative, in the sense that they may not affect the final production of firms. For example, if the real intermediate price decreases, wholesale firms may decide not to adjust production if they expect buyers to compensate them in the future for the reduced profits incurred in the current period. This issue is especially relevant if one considers the recent empirical evidence, which suggests that nominal price stickiness arises mainly at the intermediate rather than at the retail level. In fact, as first shown by Barro (977), the real effects of monetary policy when prices are sticky crucially depends on prices being allocative 3. In the B2B model intermediate prices still play an allocative role through two different channels. First, they affect the value of a B2B relationship to wholesalers and retailers and thus the incentives of firms to engage in costly search activities. Notice, however, that this effect is opposite for firms in the two sides of the market: while an increase in ϕ induces wholesalers to increase their search effort, it also reduces the search effort of retailers. The two effects thus tend to cancel out. The overall effect on the formation of new matches depends on the initial product market tightness, on the presence of search externalities and on the separation rate. However, the bargained price ϕ also has a direct effect on the separation threshold ã. Ceteris paribus, a higher ϕ reduces the value of the marginal match for the retailer and thus increases the threshold ã. Consequently, both the separation rate δ and the average productivity of surviving matches H (ã) increase. Through this mechanism, intermediate good prices have a direct allocative role on the number of B2B relationships and final output. Therefore, in the presence of sticky prices monetary policy can affect directly the number of endogenous separations, the average productivity of surviving relationships and final and intermediate output. To gauge the quantitative size of these two channels, Figure shows the effect of an expansionary monetary policy shock. The reduction of interest rates stimulates the economy increasing the levels of consumption and investment which lead to an increase in aggregate demand. Firms respond to the shock mainly through the endogenous separation margin. To increase production, firms respond by keeping alive matches with lower productivity: the productivity threshold and the destruction rate decrease. The search effort of both wholesalers and retailers instead goes down because the shock 3 See also Abbritti & Trani (25) for a discussion.

12 Figure : Impulse Responses to a Standard Deviation Shock to the Monetary Policy Rule.3 Production. Search Retailers Search Wholesalers B2B relationships 5 5 Relative Interm. Price Separation Rate PPI Inflation Average Idiosyncratic Shock CPI Inflation σ is short-lived and firms anticipate the need to reduce their stock of B2B relationships in the future. Final price inflation increases more than the intermediate price inflation because of the rigidity of the latter and hence the intermediate relative price goes down. Figure 2 compares the effect of a monetary policy shock in the B2B model with the ones in the benchmark NK model. Results are qualitatively similar but quantitatively very different. Two main facts stand out. First, the effects of a monetary policy shocks are much larger in the NK model than in the B2B model. This is consistent with the idea of a much lower allocative role of intermediate prices in B2B relationships. Second, the effects of a monetary policy shock are much more persistent in the model with B2B relationships. In fact, in the NK model the effects of the shock almost disappear after 3 quarters while in the B2B model they persist much longer TECHNOLOGY SHOCKS TO WHOLESALERS AND RETAILERS PRODUCTION Once we distinguish between sectors of production, it is interesting to study how the effects of technology shocks that affect primarily the production of wholesalers differ from the ones that affect 2

13 Figure 2: Comparison of the IRFs of the B2B and NK Models to a Monetary Policy Shock.4 Output.5 Core Inflation t t 6 Investment 2 Employment NK B2B t t the production of retailers. For simplicity, we assume that the two shocks are uncorrelated. Adding a degree of cross-correlation between the two shocks does not change the main results. Let us consider first a technology shock to the wholesalers production function, shown in Figure 3. A positive shock makes the wholesalers more productive increasing total production (Y t ). The increase in T t comes from two different sources. On one hand, the reduction of wholesalers marginal costs increases the total value of each match and induces both wholesalers and retailers to increase their search efforts, which results in the creation of a higher number of new matches. On the other hand, the threshold of the idiosyncratic shock, ã t goes down, which reduces the endogenous destruction rate of matches, δ t, as well as the average productivity of the retailers. The high persistence of output is driven by the high persistence of the number of B2B relationships (T t ), which is mainly caused by the higher searching efforts. On impact, the shock reduces the intermediate relative price, which is accompanied by a lower intermediate price inflation and a higher final price inflation. As we can see in Figure 4, a positive technology shock to the retailers production function has, to some extent, a similar effect as a shock to the technology of wholesalers. The search effort and the 3

14 Figure 3: Impulse Responses to a Standard Deviation Shock to Wholesalers Technology.5 Production 2 Search Retailers 4 Search Wholesalers B2B relationships Separation Rate Average Idiosyncratic Shock Relative Interm. Price PPI Inflation CPI Inflation σ number of B2B relationships both increase, exhibiting high persistence. At the same time the matchspecific productivity threshold declines and this reduces the endogenous destruction rate of matches. There is however one important difference between the two shocks: while the relative intermediate price is negatively correlated with output following both a monetary policy shock and a wholesalers technology shock, it is positively correlated with output after a retailer s technology shock. For this reason, the introduction of the retailer s technology shock is crucial for the ability of our model to match the cross-correlation of intermediate good prices with output, which is slightly positive in the data. We use this fact to provide a reasonable calibration of the volatility of the technology shock to retailers and show, in the following section, that the combination of these three shocks allows the B2B model to explain remarkably well the second moments of the data SECOND MOMENTS Even though the main goal of this paper is not to perfectly replicate the data we can show that it does a fairly good job in replicating some key second moments statistics of the data. To assess the quantitative validity of our model, we show in the following tables the relative standard deviation, the 4

15 Figure 4: Impulse Responses to a Standard Deviation Shock to Retailers Technology.6 Production.6 Search Retailers.3 Search Wholesalers B2B relationships Separation Rate Average Idiosyncratic Shock. 5 5 Relative Interm. Price PPI Inflation CPI Inflation σ contemporaneous correlation with output and the serial correlation generated by it and we compare them not only with the data but also with those generated by the benchmark NK model with which the main difference is the structure of the product market. As we can see in Table both models match the standard deviation of output. However the NK model overestimates the volatility of investment as well as that of employment. Our model also does a better job approximating the relative volatilities of the intermediate price, consumption and wages. The fact that the model replicates about half of the volatility of the intermediate price (as opposed to the percent reached by the NK model) is a satisfactory result, especially since the novelty of our model is the structure of the product market that determines the intermediate price. On the other hand our model does not generate enough volatility to match the intermediate inflation rate. Table 2 displays the contemporaneous correlation with output of the main variables. The performances of the two models are quite similar as both do a good job in matching the cross-correlation of the data. However Table 3 clearly shows that our model does a better job in terms of matching the serial correlation of macroeconomic series, especially the one of output, investment, wages and 5

16 Table : Relative Standard Deviation US Data B2B NK Output. (.5). (.5). (.5) Investment Employment Intermediate Price Consumption Wages CPI Inflation PPI Inflation Interest Rate Table 2: Contemporaneous Correlation with Output US Data B2B NK Output... Investment Employment Intermediate Price Consumption Wages CPI Inflation PPI Inflation Interest Rate core inflation. The autocorrelation of the intermediate price is reasonably well approximated by both models but in the case of the NK model it comes at the cost of underestimating that of output, investment, employment, wages and both inflation rates SENSITIVITY ANALYSIS Tables 4 and 5 present two different robustness exercises. Table 4 analyzes the seconds moments of the model for different values of the bargaining power of the wholesalers η. This parameter is essential to the outcome of the bargaining problem since it determines how the total surplus of a match is split between wholesalers and retailers. In our calibration we have followed a rather cautious approach and have set it equal to.5. In this exercise we see how the variables react to the extreme values of. and.9. The first thing we notice is that the volatility of output is increasing in η, especially from.5 to.9. As a consequence of this increment, with the exception of investment and 6

17 Table 3: Serial Correlation US Data B2B NK Output Investment Employment Intermediate Price Consumption Wages CPI Inflation PPI Inflation Interest Rate employment, the relative standard deviation of all the variables decreases as the bargaining power of wholesalers increases. The variables whose relative volatility seems to be more reactive to changes on η are investment, intermediate prices, core inflation and the interest rate. It seems interesting that the cross-correlation of the intermediate price becomes negative for high values of η, but this can come from the fact that the intermediate price is the outcome of the bargaining problem so its sensitivity to the bargaining power is not very surprising. By looking at the relative volatility one might be tempted to set η =. to match the intermediate price, core inflation and the interest rate with the data. However doing so would come at the expense of a higher volatility of employment and investment and, more importantly, a lower volatility of output, setting them further apart from their real counterparts. Table 4: Sensitivity to the Bargaining Power of Wholesalers η Relative Standard Deviation Correlation with Output Serial Correlation η =. η =.5 η =.9 η =. η =.5 η =.9 η =. η =.5 η =.9 Output. (.33). (.5). (2.35) Investment Employment Intermediate Price Consumption Wages CPI Inflation PPI Inflation Interest Rate Finally, in Table 5 we repeat the same exercise but now for the volatility of the idiosyncratic shock 7

18 Table 5: Sensitivity to the Volatility of the Idiosyncratic Shock σ LN Relative Standard Deviation Correlation with Output Serial Correlation σ LN = σ LN =.5 σ LN =.3 σ LN = σ LN =.5 σ LN =.3 σ LN = σ LN =.5 σ LN =.3 Output. (.35). (.5). (.5) Investment Employment Intermediate Price Consumption Wages CPI Inflation PPI Inflation Interest Rate parameter, σ LN. In our baseline calibration we have set it equal to.5 and in this exercise we want to see how the different variables react if we cancel it from the model, by setting it equal to, and if we do a mean preserving spread of the distribution of the idiosyncratic shock, by giving it a value of.3. The variable that seems more sensitive to σ LN is investment, whose relative volatility is increasing with the mean preserving spread, specially for values above.5. On the other hand the relative volatility of the other variables seems to decrease as σ LN increases but these changes do not appear to be quantitatively significant. Notice that one might be tempted to eliminate the volatility of the idiosyncratic shock to increase the relative volatility of the intermediate price and core inflation as well as their persistence in order to bring the data and the model closer together. However, doing so will reduce the volatility of output and increase the relative volatilities of employment and CPI inflation. 6. CONCLUSIONS This paper has introduced search and matching frictions and bargaining between firms into an otherwise standard monetary DSGE model. We show that, for reasonable calibrations, the long-term nature of the contracts between firms reduces the allocative role of intermediate good prices and the real effects of monetary policy shocks. At the same time, the presence of search frictions and endogenous match separations increases the persistence of most macroeconomic variables. We show that the model does a good job in replicating the second moments, cross-correlations and persistence of US product market and business cycle data. 8

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