The Role of Intermediate Goods in International Monetary Cooperation Job Market Paper

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1 The Role of Intermediate Goods in International Monetary Cooperation Job Market Paper Tian Xia University of California, Davis November 7 Abstract This paper investigates the implication of intermediate goods on optimal monetary policy in open economies, and in particular, focusing on the welfare gains from monetary cooperation. In a relatively standard two country dynamic stochastic general equilibrium model with input-output relations, I demonstrate that introducing intermediate goods can amplify the welfare gains caused by cost-push shocks by an order of magnitude larger. A detailed analysis on the equilibrium dynamics highlights a new channel that is absent in the previous literature: non-cooperative central banks respond differently to shocks in the intermediate goods market versus shocks in the final goods market, even if these shocks generate the same distortions when the two central banks cooperate. Furthermore, I find that increasing the degree of openness in the intermediate goods market can reduce the welfare gains from monetary cooperation. This casts doubt on whether the recent trend in international economic integration may justify the potential need for international monetary cooperation. I would like to thank my advisors Alan M. Taylor, Paul Bergin, Athanasios Geromichalos, and Katheryn Russ for their advice and comments. I am grateful to Nicolas Caramp, James Cloyne, Assaf Razin, Mingzhi Xu, and participants at UC Davis International/Macro Brownbag for useful suggestions. Department of Economics, University of California, Davis, One Shields Ave., Davis, CA 9. txxia@ucdavis.edu

2 Introduction As countries become more interdependent through the globalization of markets for goods and services, whether central banks should conduct monetary policies independently or cooperatively is a central question in the intellectual discussions on open economy optimal monetary policy. Following the recent financial crisis, there have been increasing concerns regarding monetary policy spillovers across countries, and policymakers have been asked to consider the need for internalizing such spillovers through cooperation. Yet, academic debate on the desirability of international monetary cooperation is far from settled. There are divergent views on two central questions relevant on the topic of monetary cooperation. What are the possible monetary policy spillovers that central banks need to internalize in their policy reactions in order to enhance welfare? How large would the welfare loss be if they fail to do so? The nature of optimal monetary policy in open economies under cooperation vs. non-cooperation has been widely discussed in the academic literature. A key insight highlighted in the past literature is that the benefit of monetary cooperation gains lies in the internalization of policy spillovers. Early contributions to the discussion, such as Hamada [97] and Cooper [98] analyze the gains from monetary cooperation with models featuring ad hoc stabilization goals. Yet, such framework lacks micro foundations, and further development in models is needed to consider optimizing behaviors under rational expectations. The New Open Economy Macroeconomics (NOEM) literature, which features strong micro foundations combined with imperfect competition and nominal inertia, identifies spillovers in the terms of trade that central banks need to internalize to maximize global welfare under monetary cooperation. The pioneering work by Obstfeld and Rogoff [] shows that the welfare gains from monetary cooperation theoretically exist in the NOEM model, but the gains are quantitatively far from sufficient to be policy relevant. The remarkably disappointing conclusion on the lack of welfare gains has stimulated a growing strand of literature incorporating realistic features into the simple framework of Obstfeld and Rogoff [] in search of potential gains from monetary cooperation. In particular, the literature has shown that increasing economic integration through trade could generate sizable welfare gains (eg. Coenen et al. [7], Pappa []), which suggests that the recent trend in international economic integration may broaden the scope of international monetary cooperation. Yet, it may be premature to conclude that central banks will start coordinating if Blanchard et al. [] of the International Monetary Fund comment: Today, policy coordination has resurfaced as a hot topic: while the worst of the global financial crisis is behind us, no one would claim that a return to Great Moderation is in the cards, and policymakers around the globe appear worried about policy transmissions across many dimensions.

3 there is further globalization in the world economy. So far, the current debate on how economic integration affects the welfare gains from monetary cooperation does not distinguish between final goods and intermediate goods. As demonstrated in the past literature, assuming trade only happens in final goods, then the recent trend in international economic integration is indeed in favor of monetary cooperation due to larger terms of trade spillovers. However, a number of empirical studies show that intermediate goods actually account for a substantial share of total trade, and cross-border intermediate input linkages are important conduits of shocks (eg., Jones [7], Chen et al. [], Huang and Liu [7], Hummels et al. [998, ], Yi [, ]). Furthermore, certain characteristics relevant for monetary policy analysis, such as the elasticity of substitution and price stickiness, are different between intermediate goods and final goods. Given the importance of intermediate goods in both theoretical and empirical studies, it is natural to examine the role of intermediate goods in shaping optimal open economy monetary policy, and whether increasing economic integration in the intermediate goods market can result in the same favorable outcome on the welfare gains of monetary cooperation. This paper fills in the gap in the literature by examining the role of intermediate goods in monetary policy cooperation. I introduce intermediate goods according to an input-output production structure in a standard two country model with monopolistic competition and nominal rigidities. Following the tradition in studies on optimal monetary policy, the economy is disturbed by productivity shocks and cost-push shocks. The governments in the two countries provide sales subsidies raised in a lump-sum fashion to eliminate the monopolistic distortion in the steady state. The model is characterized by three features that generate second-order welfare distortions: price stickiness, exogenous disturbances in markups due to cost-push shocks, and cross country spillovers through the terms of trade externality. The welfare gains from monetary cooperation arise due to independent central banks fail to internalize the terms of trade externality. Based on the equilibrium conditions, introducing intermediate goods in an otherwise standard two country model results in two additional channels on the welfare gains from monetary cooperation. The first channel is the direct effect of the terms of trade on marginal cost due to trade in intermediate goods. Clarida et al. [] predicts this channel to be an interesting avenue through which the gains from monetary cooperation arise, and recently it has been identified in Gong et al. [] s study on optimal cooperative monetary policy. The second channel, which is specific to the input-output production structure, is the feedback mechanism in the price transmission in intermediate goods market. In the presence of intermediate goods, a share of output is used as material inputs in the production itself, thus fluctuations in the producer price index feed into the marginal cost, which further amplifies the changes in the price level. As shall be demonstrated, these two addi-

4 tional channels from the intermediate goods market may cause central banks to respond differently to shocks in the intermediate goods market and the final goods market under non-cooperation, even if the shocks are equally distortionary under cooperation. This creates another source of welfare gains from monetary cooperation. To the best of my knowledge, the difference in central banks response to shocks in the intermediate goods market versus the final goods markets has not been identified in the previous literature. My main findings can be summarized as follows. In general, introducing intermediate goods amplifies the welfare gains from monetary cooperation, compared to a benchmark model with labor as the only factor of production. Thus, I demonstrate a missing piece in the previous literature that may have caused underestimation in the gains of monetary cooperation. However, increasing openness in the intermediate goods market can reduce the welfare gains from monetary cooperation, which is at odds with the predictions on the effect of openness on the welfare gains from models with final goods only. Consistent with the previous findings, under plausible parameterization, cost-push shocks are the major source of gains from international monetary cooperation. Furthermore, introducing intermediate goods amplifies the contribution of cost-push shocks to the welfare gains. Detailed analysis on the central banks policy responses shows that in the non-cooperative equilibrium, central banks strategically respond to cost-push shocks in the intermediate goods market much more aggressively compared to cost-push shocks in the final goods market. This is the main reason for the sizable amplification from intermediate goods on the welfare gains from monetary cooperation. I interpret the above results as evidence for the two additional channels of intermediate goods on monetary policy cooperation. This paper is mostly related to the literature on the welfare gains of monetary cooperation. Following Obstfeld and Rogoff [], many have generalized their framework and discussed how certain key parameters and distortions can affect the welfare gains of monetary cooperation. Clarida et al. [], Benigno and Benigno [, ] and Pappa [] show that the existence and the size of the welfare gains strongly depend on the intertemporal and the intratemporal elasticities of substitution. Sutherland [], Rabitsch [] and Engel [a] examine how incomplete financial asset market affects the welfare gains. The welfare gains under incomplete exchange rate pass-through have been discussed in Devereux and Engel [], Duarte [], Corsetti and Pesenti [] and Fujiwara and Wang [7]. Coenen et al. [7] quantify the welfare gains using a large-scale DSGE model that is calibrated to represent the U.S. and the Euro area. Engel [b] offers a recent survey on the current state of monetary cooperation literature. This paper is not the first to incorporate intermediate goods in the analysis of optimal open economy monetary policy. However, with the exception of Tchakarov [], most existing literature focuses only on cooperative monetary policy or optimal monetary

5 policy in a small open economy. Furthermore, my approach in introducing intermediate goods in the production function is through an input-output structure, which is absent in the previous studies on optimal open economy monetary policy. Tchakarov [] and Lombardo and Ravenna [] show that imported inputs in production have important implications on optimal monetary policy. Compared to their models, the input-output structure in my model allows for price to feed back into the marginal cost. This feedback mechanism is weaker when the intermediate goods market is more integrated. Therefore my model shows that integration in the intermediate goods market can cause a reduction in the welfare gains of monetary cooperation, as opposed to the increase in the welfare gains found in Tchakarov []. Gong et al. [], Devereux and Engel [7] and Shi and Xu [7] analyze optimal monetary policy in models with vertical integration. As intermediate goods and final goods are connected via forward-backward linkages in their models, due to multiple price stickinesses their production structure generates relative price distortions across different stages of production. In contrast to their model, the input-output production structure in my framework does not include any relative price distortions across multiple production stages, as there is only a single stage of production. In this regard, my model shares similar features with Petrella and Santoro [9, ] that analyze optimal monetary policy in a closed economy with multiple sectors and input-output structure. The rest of the paper is laid out as follows. Section describes the model. Section discusses the model s parameterization. Section discusses the theoretical intuition of the relevance of intermediate goods in optimal monetary policy design, and its implication on the welfare gains from monetary cooperation, with numerical results presented to support the theory. Section summarizes and concludes. Model The world economy consists of two symmetric countries, called Home and Foreign. Each country specializes in one type of tradable good. A unit mass of identical, infinitely lived households are populated in each country. Each household produces a single differentiated good and consumes a basket of final goods produced in both economies. Due to the imposed symmetry between the two countries, in the following I only discuss the prob- In Tchakarov [], due to the assumption that intermediate goods are all imported, increasing the integration in the intermediate goods market also increases the share of intermediate goods used in production. Thus, the increase in the welfare gains is the outcome of the increase in both the economic integration and the usage of intermediate goods. The input-output production function adopted in my model has enough flexibility to increase the openness in the intermediate goods market without changing the share of intermediate goods used in the production process.

6 lems of Home households, unless necessary otherwise. The variables related to Foreign households are marked with an asterisk (*) for clarity.. Households The preference of household k in Home country is described by the following utility function W (k) = E t= β t ( C(k) σ t σ χ L(k) +ν t + ν + χ log M(k) t ), () P C,t where C(k) denotes consumption, L(k) denotes labor supply, M(k) t /P C,t denotes real money balance that is adjusted using the consumer price index P C,t, and β is the discount factor. I follow Obstfeld and Rogoff [] in assuming the limiting case where χ, so that the weight of real money balance in the household preference is negligible. Household k maximizes equation () subject to the budget constraint. Consumption expenditure is financed by the household s labor income, profit income, nominal money balance, and lump-sum transfers from the government. In addition, the household has access to an international financial market, where a full set of state-contingent (Arrow- Debreu) securities are traded. The individual budget constraint under period t is given by P C,t C(k) t +E t D t,t+ B(k) t+ +M(k) t+ = W t L(k) t +B(k) t +Π(k) t T (k) t +M(k) t, () where B(k) t+ is the holdings of state contingent nominal bonds that promise to pay one unit of domestic currency in period t + if a specified state is realized. D t,t+ is the price of such bond, denominated in the domestic currency. The nominal interest rate i t can be equivalently expressed as /E t D t,t+. W t L(k) t is the wage income, Π(k) t is the profit income, and T (k) t is the lump-sum transfer from the government. The consumption basket in Home country, C t, is defined as the following CES aggregator C t = [γ φc c φc φc CH,t + ( γ c ) φc φc φc CF,t ] φc φc, () where γ c is the degree of home bias in consumption, and is the intratemporalelasticity of substitution between Home and Foreign goods. The consumption indices of Home and Foreign goods are defined as aggregations of all the imperfectly substitutable differentiated goods produced in the respective country, with a constant elasticity of substitution ɛ between the differentiated goods C H,t = [ C(j) ɛ ɛ H,t dj] ɛ ɛ, CF,t = [ C(j) ɛ ɛ F,t dj] ɛ ɛ. ()

7 .. Firms For a firm operated by household k, the production technology is Y (k) t = Z t M(k) α t L(k) α t, () where Z t is the country specific productivity shock, which is given an exogenous AR() process with standard deviation σ z and serial correlation ρ z. L(k) t is the number of hours hired by the firm, and M t is the amount of intermediate goods used as material inputs for production. Similar to consumption, intermediate goods combine Home and Foreign produced goods into a CES aggregator M t = [γ φm m φm φm MH,t + ( γ m ) φm φm φm MF,t ] φm φm. () For the sake of flexibility, for intermediate goods I specify the intratemporal elasticity of substitution φ m, and the home bias γ m as a new set of parameters. This allows me to examine how varying the parameters in the intermediate goods market affect my results, while keeping the market condition for final goods unchanged. The aggregations of the varieties for intermediate goods produced in Home and Foreign are assumed to be the same with their respective consumption indices M H,t = [ M(j) ɛ ɛ H,t dj] ɛ ɛ, MF,t = [ M(j) ɛ ɛ F,t dj] ɛ ɛ. (7) This means that in Home, the aggregate prices for Home produced goods and Foreign produced goods are defined as: P H,t = [ P (j) ɛ H,t dj] ɛ, PF,t = [ P (j) ɛ F,t dj] ɛ, (8) and the prices for the bundles of Home final goods and intermediate goods are respectively: P C,t = [γ c P φc H,t + ( γ c )P φc F,t ] φc, P M,t = [γ m P φm H,t + ( γ m )P φm F,t ] φm. (9) Firms are price takers in factor markets, and operate under monopolistic competition when selling goods in the intermediate goods market and the finals good markets. I assume a producer currency pricing scenario where firms set prices in the foreign market in their own currency. Thus, the law of one price holds and changes in exchange rate are

8 fully reflected in export price. The demand schedule for firm k can be written as Y (k) t = ( P (k) H,t P H,t ) ɛ Y t. () Firms set their prices following a partial adjustment rule à la Calvo [98]. Given the demand schedule above, in each period, firm k receives a random signal with a probability of θ that allows it to adjust its price. If firm k is able to adjust its price in period t, it sets its optimal price P (k) opt t to maximize the expected present value of profits n= (βθ) n Ω t+n [P (k) opt t ( + τ t+n ) MC t+n ]Y (k) t+n, () where Ω t+n is the household s nominal stochastic discount factor, MC t+n is the nominal marginal cost, which is not firm specific due to the joint assumptions of perfectly competitive factor market and Cobb-Douglas production function, and τ t+n is the sales subsidy. I assume that the sales subsidy is time-varying, which translates to inefficient cost-push shocks that deviate the flexible price allocation from the socially efficient allocation. Furthermore, the stochastic process τ t fluctuates around an optimal level of subsidy that completely eliminates the distortion created by monopolistic competition in the steady state. Thus the steady state subsidy τ satisfies the condition ɛ (ɛ )(+ τ) =. In addition, I assume that shocks in the model are small enough such that no firm would ever receive negative profit. Based on equation (), the solution for the optimal price is P (k) opt t = ɛ ɛ E t n= (βθ)n Ω t+n MC t+n Y (k) t+n E. () t n= (βθ)n Ω t+n ( + τ t+n )Y (k) t+n In every period, for given factor prices, firm k solves a cost minimization problem to determine the amount of factors used in production. The first order condition from the problem implies: MC t Y (k) t = W tl(k) t α = P M,tM(k) t. () α Equation () would result in the following condition between nominal marginal cost and factor prices:. The market clearing condition MC t = a α ( α) ( α) PM,t α W t α. () Z t The output produced in each country will partly be sold to the final goods markets in the two countries, and the rest be sold as intermediate goods used by firms in the two 7

9 countries. The resource constraints for the aggregate outputs, are respectively: Y t = C H,t + C H,t + M H,t + M H,t, () Y t = C F,t + C F,t + M F,t + M F,t. (). Relative prices and the terms of trade Due to the difference in the CES aggregations between final goods and intermediate goods, I define the real exchange rates for the two markets separately. The consumption based real exchange rate, RER C,t, is defined as the price of Foreign consumption bundle relative to Home consumption bundle εtp C,t P C,t, where ε t is the nominal exchange rate. Based on the assumption of complete financial market, in equilibrium RER C,t is determined by the following risk sharing condition: ( C t C t ) σ = RER C,t. (7) Similarly, the material inputs based real exchange rate, RER M,t, is defined using the aggregate prices for intermediate goods. The two real exchange rates are related through the following equation: RER M,t = RER C,t P M,t P M,t P C,t P C,t. (8) The terms of trade is defined as the price of Home imports over Home exports, T OT t = P F,t P H,t. Using the definition of the aggregate prices P C,t and P M,t, it is possible to show that the two real exchange rates RER C,t and RER M,t are related to the terms of trade: T ] φc T ] φc RER C,t = [( γ c) + γ c T OT φc [γ c + ( γ c )T OT φc, RER M,t = [( γ m) + γ m T OT φm [γ m + ( γ m )T OT φm T ] φm T ] φm. (9). Equilibrium conditions and optimal monetary policy Central banks in the two countries act as Ramsey policymakers that maximize welfare, under a set of private sector optimality constraints (shown in Appendix A.). Given exogenous processes for technology shocks and cost-push shocks, and sequences of Home and Foreign policy instruments, the equilibrium dynamics of the endogenous variables (shown in Appendix A.) can be fully determined with the inclusion of the system of equations characterizing private sector optimality conditions. In the cooperative equilibrium, the two central banks jointly commit to policies that 8

10 maximize the global welfare of the representative households in the two countries: W global = W + W. () If the central banks are uncoordinated, each central bank maximizes the welfare of its own country, while taking the entire path of policy moves from the other central bank as given. This non-cooperative equilibrium corresponds to an open-loop Nash equilibrium. To derive the optimal policy responses and the equilibrium dynamics, I employ the method used in Bodenstein et al. [] to obtain the optimal policies from a timeless perspective as in Benigno and Woodford [, ]. This method produces the same result as the standard linear-quadratic approach that is widely used in the optimal monetary policy literature, with the advantage that there is no need to analytically derive the secondorder approximation of equilibrium conditions to obtain the quadratic loss functions that central banks aim to minimize when applying the linear-quadratic approach. In section, the calculation of welfare is based on a second-order perturbation method, while the impulse responses are derived with first-order approximated solutions. As discussed in Lombardo and Sutherland [] and Wang [], the outcome of the open-loop Nash equilibrium crucially depends on the policy instruments chosen by the two policy makers, which in turn affect the estimated welfare gains from monetary cooperation. A variety of policy instruments have been chosen in the open economy literature, including producer price inflation (e.g., Benigno and Benigno [8]), nominal money balance (e.g., Obstfeld and Rogoff []), and interest rate (e.g., Rabitsch []). I follow Coenen et al. [7] in assuming that the growth rate of nominal money balance is the policy instrument employed by the central banks. The reason for this choice is that it would be more realistic to consider central banks being able to directly control money supply and indirectly influence inflation rate though the equilibrium conditions, rather than vise versa. A reasonable alternative option would be using interest rate as the policy instrument. However, in the timeless perspective this choice would yield equilibrium indeterminacy. Parameterization The parameterization of the model is as follows. The choices are comparable to those in Corsetti et al. [] and Bodenstein et al. []. I consider a quarterly model, so that the discount factor β is set to.99, implying an annual interest rate about %. The literature has not reached a consensus on the inverse Frisch elasticity ν. The value ranges The model is solved numerically using Dynare (Adjemian et al. []) 9

11 from a low value of.7 that is used in Rotemberg and Woodford [998], to a high value such as in Benigno [9]. I consider an in-between value of ν =. The price stickiness parameter θ is equal to.7, meaning on average the frequency of adjustment in prices would be quarters. I consider the elasticity of substitutions in goods varieties ɛ to be, which implies a markup of % in the steady state. For the exogenous shock processes, the parameters capturing the persistence and the variance of productivity shocks are set as ρ z =.9, and σ z =.8. As for cost-push shocks, I follow the convention in the literature in assuming purely transitory shocks with standard deviation σ τ =.. The relative magnitudes of cost-push shocks and productivity shocks are in line with the calibrated estimates in Coenen et al. [7]. The share of material inputs α in production is assumed to be., which is consistent with the average cross country intermediate goods share shown in Jones [7]. As documented in Chen et al. [], the intermediate goods trade as a share of the total trade in the US is roughly % over the period between the 97s and 99s. I assume in my model that when both final goods and intermediate goods are traded, the home bias parameters for both consumption and material inputs, γ c and γ m, are assigned with a value of.8. For the rest of the parameters, I allow for a wide range of values since the literature has proved that these parameters are crucial in determining welfare gains from monetary cooperation. The parameters include the relative risk aversion σ, the intratemporal elasticity of substitution between Home and Foreign final goods, and the intratemporal elasticity of substitution between Home and Foreign intermediate goods φ m. The literature on open economy monetary policy has offered insights on how σ and affect the optimal monetary policy under non-cooperation. As discussed in Benigno and Benigno [] and Benigno and Benigno [], there would be no gains from monetary cooperation only under very spacial cases for the two parameters. Pappa [] calculates the welfare gains of monetary cooperation and shows that results are sensitive to the choices of the two parameters. Despite their importance, estimations on these parameters vary widely in the literature. Depending on the identification strategy, micro data evidence on relative risk aversion ranges from around, as suggested in Chetty [], to a value around, as implied by the estimation in Best et al. []. For the intratemporal elasticity of substitution, the business cycle literature typically assumes a value of unity, yet estimates based on individual product groups generate values as high as. For robustness analysis, in section, the welfare gains from monetary cooperation are calculated based on σ ranging between -, and ranging between -. If the result shown does not specify values for σ and, then it means that the average values of. and are chosen for the See, for example, Lai and Trefler [], Imbs and Mejean [].

12 two parameters respectively. As for φ m, I make two alternative assumptions. Under the first assumption, φ m is assumed to be, implying a Cobb-Douglas production function in labor, domestic material inputs, and foreign material inputs. The other assumption assumes that intermediate goods and final goods are equally elastic in terms of cross country substitution, so φ m takes the same value as. Gains from monetary cooperation Before analyzing how intermediate goods would affect the monetary policies in the two countries, it is useful to first focus on the trade-offs that central banks have to consider in conducting optimal monetary policy. As widely known in the open economy literature, the terms of trade is central in understanding economic spillovers across different economies. Fluctuations in the terms of trade may create cross country misalignments in the relative prices of consumption and material inputs, which lead to inefficient resource allocation. Under cooperation, central banks maximize the global welfare, thus fully recognizing the effect of the terms of trade spillover to the other country. A non-cooperative central bank, on the other hand, has the incentive to strategically tilt the terms of trade to its own country s favor, while disregarding the spillover effect of this self-serving strategy on the other country. However, any central bank s attempt to strategically manipulate the terms of trade would be self defeating, as the other central bank would implement exactly the same policy to offset the spillovers from the terms of trade. The strategic interactions between the two countries create inefficient distortions, which give rise to welfare gains from monetary cooperation. Apart from the cross country terms of trade distortion, central banks also have to accommodate the distortions within their own economy. In this model, the two countries are both characterized by a distortion due to price stickiness, and a distortion due to markup fluctuations caused by cost-push shocks. The presence of the price stickiness prevents the economy to efficiently adjust to disturbances. In the absence of cost-push shocks, cooperating central banks can optimally respond to productivity shocks by keeping domestic inflation stable in a floating exchange rate regime, thus achieving the flexible price allocation, which is also the socially optimal allocation. This is no longer possible with the presence of cost-push shocks, as markup fluctuations create a wedge between the socially optimal allocation and the flexible price allocation. When a disturbance in the markup occurs, the optimal monetary policy balances the goals of inflation stabilization and output stabilization, which implies that keeping domestic inflation stable would no longer be optimal (e.g., Woodford [] and Woodford []). Taking into account the relevant welfare cost of the two within country distortions, the two central banks max-

13 imize their respective countries welfare by balancing the trade-offs between the benefit in manipulating the terms of trade, and the loss caused by internal distortions under the non-cooperative scenario. How do intermediate goods influence the welfare gains from monetary cooperation? In the model economy, the introduction of intermediate goods in the production function does not by itself add any distortion. From the central banks perspective, they still face the same internal distortions due to price stickiness and cost-push shocks, and adjust the terms of trade optimally to maximize welfare. However, this does not necessarily imply that the central banks would conduct monetary policies that are similar to an economy without intermediate goods. Based on how the production function is constructed in the model, having intermediate goods in the production function creates an input-output structure across the two countries. This changes the private sector optimality constraints on the Ramsey policy makers. Even though goods sold in the intermediate goods market and the final goods market are essentially the same goods produced by the same firms, the two markets transmit shocks differently through different equilibrium conditions. To see how this makes a difference, here I stress two channels related to intermediate goods that are relevant to optimal monetary policy. The first channel is that through the intermediate goods market, the terms of trade exert a direct effect on real marginal cost, while the existing indirect effect via the labor market diminishes as the share of material inputs increases. In order to understand the intuition, it is useful to rewrite equation () in terms of real marginal cost RMC t and real wage RW t that are detrended with Home producer price index RMC t = a α ( α) ( α) [γ m + ( γ m )T OT φm t ] φm RWt α. () Z t In a standard model where intermediate goods are absent, the terms of trade affect real marginal cost indirectly through its impact on real wage. With a higher share of material inputs in the production function, this effect is dampened. However, as long as the intermediate goods market is not in a state of autarky, the terms of trade can directly influence real marginal cost via material inputs in production. This is because the price of intermediate goods bundle directly enters the nominal marginal cost equation (), correspondingly there exists a terms of trade externality directly observable in real marginal cost. As Clarida et al. [] point out, this adds an additional effect of openness on real marginal cost. Thus fluctuations in the terms of trade cause substitution between Home and Foreign goods both in the final goods market and the intermediate goods market. Since central banks ignore the terms of trade spillover across borders in the non-cooperative equilibrium, the additional intermediate goods market terms of trade α

14 distortion that directly impacts on real marginal cost may affect the welfare gains from monetary cooperation. Even if assuming firms can only use intermediate goods produced in their own country, which shuts down the terms of trade distortion in the intermediate goods market, the intermediate goods market is still relevant when central banks weigh the trade-offs between different distortions. The second channel where intermediate goods market affects open economy optimal monetary policy is that it may give rise to different transmission mechanisms to the distortions. This is particularly relevant following a disturbance from a cost-push shock. As inflation stabilization is infeasible under the optimal monetary policy, price transmission mechanism in the private sector optimality constraints is critical in determining how central banks respond to a cost-push shock. In the presence of intermediate goods market, inflation caused by an external shock will feed back into nominal marginal costs through the intermediate goods price P M,t, creating further upward pressure on the produce price. This feedback mechanism, which is absent in the final goods market, may cause central banks to perceive the price transmission mechanisms in the intermediate goods market and the final goods market differently. As shall be demonstrated in detail in the next section, the difference in the perception will result in central banks establish different monetary policy responses depending on the market disturbed by the shocks.. Gains from cooperation: baseline results To appreciate how intermediate goods matter in determining the welfare gains from international monetary cooperation, I compare the welfare gains between the following scenarios. The first scenario is where labor is the only factor used in production (α = ). Starting with the second scenario, I incorporate intermediate goods in the production function. The second scenario is where firms produce goods under a roundabout structure, so that only goods produced domestically are used as material inputs (α =., γ m = ). To demonstrate how economic integration in the intermediate goods market can affect the welfare gains, the third scenario introduces a realistic amount of openness in the intermediate goods market, which means there is an input-output relation across the two countries in the model (α =., γ m =.8). The production function is assumed to be Cobb-Douglas, so that φ m =. The last scenario also allows for trade in intermediate goods, but assumes that intermediate goods and final goods have equal intratemporal elasticity of substitution (φ m = ). Given the parameterization of the model, the fourth scenario demonstrates how a higher intratemporal elasticity of substitution in intermediate goods can affect the welfare gains. The welfare gains are reported as the global welfare difference between cooperation and non-cooperation, in terms of

15 equivalent percentage increase in the steady state consumption. Figure : of monetary cooperation: baseline results No material inputs Roundabout Input-output,low φ m Input-output,high φ m σ.. σ.. σ.. σ Notes: This figure reports the welfare gains of monetary cooperation for varying σ and. The values of welfare gains refer to the percentage increase in the steady state consumption. are reported under four different settings: (i) the model with no intermediate goods (α = ); (ii) the model with roundabout production (α =., γ m = ); (iii) the model with input-output production, with low φ m (α =., γ m =.8,φ m = ); (iv) the model with input-output production, with high φ m (α =., γ m =.8,φ m = ) Figure shows the welfare gains from monetary coordination. Consistent with existing findings in the literature, the welfare gains are generally very small under the scenario with labor being the only factor used for production. The welfare gains are monotonically increasing in σ and. Within the range of feasible σ and, the largest welfare gain is equivalent to a negligible.% of steady state consumption units. The results change drastically when intermediate goods are introduced in the production structure. Regardless of whether intermediate goods can be traded or not, the welfare gains are significantly larger compared to the scenario without intermediate goods. In the case with a roundabout production structure, the maximum welfare gain within empirically relevant values of σ and increases to.9%, which is more than times larger compared to the first scenario. However, the third panel shows that economic integration through the input-output interaction between the two countries attenuates the increase in the welfare gains significantly. Yet, compared to the scenario without intermediate goods, on average the welfare gains are still times larger. Allowing a larger intratemporal elasticity of substitution in intermediate goods has similar effect as enlarging the corresponding parameter for final goods, and the largest welfare gain under this scenario is a relatively large.% equivalence in the steady state consumption. Overall, the baseline results shown in Figure provide evidence that disregarding intermediate goods does lead to underestimation in the welfare gains from monetary cooperation. Under realistic parameterization for the share of intermediate goods in the production function and the degree of openness in the intermediate goods market, allowing intermediate goods in the production function can amplify the welfare gains by at

16 least times larger, and even by an order of magnitude larger with larger substitutability between domestic and foreign produced intermediate goods.. The degree of openness in intermediate goods market As Figure may imply, increasing the openness in the intermediate goods market generally reduces the welfare gains from monetary cooperation, unless there is high substitutability between Home and Foreign intermediate goods. To confirm this conjecture, Figure plots the welfare gains from monetary cooperation for various degrees of the home bias γ m and the intratemporal elasticity of substitution φ m in the intermediate goods market, with a similar graph for the final goods market for comparison. The figure shows that in both markets, raising the intratemporal elasticity of substitution between Home and Foreign goods increases the welfare gains. However, goods market integration yields different results depending on the market that is being economically integrated. Consistent with prior literature, economic integration in the final goods market raises the welfare gains of monetary cooperation significantly. On the other hand, in general the welfare gains are decreasing in the degree of openness in the intermediate goods market. Only under the specific joint conditions where the market is close to autarky and the intratemporal elasticity of substitution is high in the intermediate goods market do we observe the positive correlation between the welfare gains and the degree of openness. Figure : of monetary cooperation: economic integration in the different markets. Intermediate goods market Final goods market.. φ m = φ m =. φ m = φ m =. φ m = = =. = =. = γ m γ c Notes: This figure reports the welfare gains of monetary cooperation as a function of home bias parameter and intratemporal elasticity of substitution in the intermediate goods market and the final goods market. The values of welfare gains refer to the percentage increase in the steady state consumption. The left panel shows the welfare gains for the intermediate goods market. The right panel shows the welfare gains for the final goods market. For each panel the parameters of the unreported market are held constant.

17 It is interesting to note that the decreasing relationship between the openness in the intermediate goods market and the welfare gains from monetary cooperation is in contrast with the literature s suggestion that increasing openness is needed to justify for large enough welfare gains that are of policy relevance. My results show that whether larger economic integration would give grounds for further international monetary cooperation crucially depends on the counteracting effects that happen in the final goods market and the intermediate goods market. Goods market integration leads to higher monetary cooperation welfare gains under the condition that the positive effect in the final goods market outweighs the negative effect in the intermediate goods market. To further illustrate this point, Figure provides the evidence that there does not exist a monotone relationship between openness and monetary cooperation welfare gains when economic integration in the final goods market and the intermediate goods market happens simultaneously. Thus, the figure presents a scenario where economic integration does not alter the share of intermediate goods in trade (γ c = γ m ). As before, I plot the welfare gains under two alternative assumptions on the intermediate goods substitutability. Based on the figure, it is evident that increasing openness does not necessarily suggest larger welfare gains from monetary cooperation. Figure : of monetary cooperation: openness in the intermediate goods market and the final goods market..8 φ m = φ m = = γ and γ m c Notes: This figure reports the welfare gains of monetary cooperation when economic integration happens simultaneously in both the intermediate goods market and the final goods market. The values of welfare gains refer to the percentage increase in the steady state consumption.

18 . The contribution of shocks To isolate the optimal monetary responses to different shocks, I separately reestimate the welfare gains from monetary cooperation with only productivity shocks and only cost-push shocks. Figure reports the welfare gains with productivity shocks only, while Figure reports the results for cost-push shocks. Consistent with the findings in Coenen et al. [7] and Corsetti et al. [], under all scenarios cost-push shocks are the most important source of welfare gains from monetary cooperation. In fact, the contribution from productivity shocks is negligible, as the welfare gains from cost-push shocks are orders of magnitude larger within the range of and σ considered. This is apparent in Figure, as cost-push shocks alone replicate the welfare gains estimated with all the shocks present in Figure. Figure : of monetary cooperation: only productivity shocks No material inputs Roundabout Input-output,low φ m Input-output,high φ m σ.. σ.. σ.. σ Notes: See Figure Figure : of monetary cooperation: only cost-push shocks No material inputs Roundabout Input-output,low φ m Input-output,high φ m σ.. σ.. σ.. σ Notes: See Figure That the large welfare gains from monetary cooperation are explained by cost-push shocks do not, however, imply that it is based on arbitrarily setting a high volatility in the shock process itself. Nor does the importance of cost-push shocks in the welfare evaluation suggests that cost-push shocks are important in explaining the business cycle behavior. 7

19 To see this, Table reports the variance decomposition for Home variables under optimal monetary policy. For the sake of space, I only report two scenarios, as the differences in the variance decomposition between different scenarios are quantitatively small. As the table reveals, productivity shocks are the most important drivers of fluctuations in the real variables. Home and Foreign productivity shocks together explain more than 9% of variations in all the real variables shown in the table. Cost-push shocks, on the other hand, mainly contributes to the volatility in the nominal variable: producer price inflation. The intuition for this result is simple: productivity shocks do not generate policy trade-offs within a country, while cost-push shocks are distortionary and create trade-offs between domestic inflation stabilization and domestic output stabilization. When a disturbance in the markup happens, central banks may reduce the internal distortions by adjusting the terms of trade, which offers an incentive to export some of the distortions to the other country. When the two central banks do not cooperate, the spillovers in the terms of trade distortion result in the occurrence of large global welfare losses due to the central banks adopting beggar-thy-neighbor monetary policies. Thus, the distortionary nature in cost-push shocks creates a large wedge between the allocation of the cooperative and the non-cooperative policies, yet cost-push shocks by themselves do not generate large fluctuations in real variables. As for productivity shocks, since stabilizing inflation replicates the efficient allocation, the real variables exactly replicate the dynamics of the flexible price allocation in cooperation. Without suffering from any distortion in the cooperative scenario, the incentive for the terms of trade manipulation is small. Thus much of the dynamics of real variables can be explained by productivity shocks without generating a sizable wedge between the cooperative and the non-cooperative equilibrium. Table : Variance decomposition Cooperation Nash Model with no material inputs Z t Zt τ t τt Z t Zt τ t τt Consumption Labor Output Inflation Terms of trade Model with input-output production, low φ m Consumption Labor Output Inflation Terms of trade To examine the equilibrium dynamics, Figure and Figure 7 respectively report the 8

20 impulse responses following an one standard deviation productivity shock and cost-push shock in Home country. Following a disturbance in Home productivity, the discrepancies between the cooperative policy responses and the non-cooperative policy responses are tiny, which is consistent with the welfare estimation. Furthermore, as introducing intermediate goods into the model does not add any distortion to the economy, inflation stabilization is always optimal under monetary cooperation across all four scenarios. The non-cooperative optimal monetary policy responses do not display any significant differences across all four scenarios. When the two central banks do not cooperate, Home central bank tends to slightly under-stabilize deflation following a positive productivity shock. If Foreign central bank does not respond, there will be an improvement in the terms of trade. Since Home and Foreign goods are substitutes under the baseline parameterization, Home households enjoy the benefit of appreciated terms of trade by working less, well maintaining the consumption level by substituting Home goods with Foreign goods. However, as both policy makers simultaneously adopt the same policy responses against each other, the attempt to manipulate the terms of trade is unsuccessful, which results in overall loss in the social welfare. The impulse responses following a favorable Home cost-push shock, on the other hand, show that intermediate goods are critical in determining optimal monetary policy. Across all four scenarios, Home and Foreign monetary stances exert contractionary biases when they do not cooperate. However, with intermediate goods introduced into the model, the differences between the cooperative allocations and the non-cooperative allocations are significantly larger. In fact, in the scenarios with intermediate goods, the tendency for monetary contraction is so large that it completely reverts the sign of on impact interest rate responses when central banks do not cooperate. As the model is symmetric and both countries play against each other in an open loop Nash game, such beggar-thy-neighbor policy is of course self-defeating. Compared to the cooperative monetary policies, the non-cooperative policies cause both countries to severely lower the level of consumption and production in the presence of intermediate goods. Moreover, the discrepancies between the non-cooperative policies and the cooperative policies are consistent with the welfare estimation. I find that the contractionary bias in the noncooperative policies lessens when I increase the openness of intermediate goods market, and it increases when intermediate goods become more substitutable.. Transmission of cost-push shocks In the previous subsection, my results indicate that cost-push shocks are the major source of welfare gains from monetary cooperation. Furthermore, the optimal monetary policy responses to cost-push shocks are significantly different when intermediate 9