سیاست پولی بهینه در حضور قیمت گذاری ارائه محصول به بازار

This paper presents a general-equilibrium framework to revisit the issues of optimal monetary policies and international policy coordination in a two-country model, focusing on the role of a pricing-to-market (PTM) policy by firms. Both countries may be different with respect to PTM. Using the set-up developed by Corsetti and Pesenti [Corsetti, G., Pesenti, P., 2001. Welfare and macroeconomic interdependence. Quarterly Journal of Economics 116, 421–445] and Betts and Devereux [Betts, C., Devereux, M., 2000a. International monetary policy coordination and competitive depreciation: A reevaluation. Journal of Money, Credit, and Banking 32, 722–745; Betts, C., Devereux, M., 2000b. Exchange rate dynamics in a model of pricing-to-market. Journal of International Economics 50, 215–244], we show that (i) for a given Foreign monetary stance, a Home monetary expansion is beneficial for both countries only if Home PTM is at an intermediate range; (ii) in a world Nash equilibrium Home and Foreign welfare are bell-shaped in the degrees of PTM; (iii) relative welfare crucially depends on the degrees of PTM; (iv) there is a welfare gain from cooperation even in the cases of no and full PTM.

It is a truism that in a world with increasingly integrated national economies, monetary policy in each country affects economic welfare both at home and abroad. Due to the presence of beggar-thy-neighbor and beggar-thyself effects, however, the welfare effects are difficult to sign. The exploration of the international spillovers and the design of an optimal monetary policy in closed and open economies has become a cottage industry for that reason (see, e.g., Corsetti and Pesenti, 2001, Corsetti and Pesenti, 2005, Obstfeld and Rogoff, 2002, Devereux and Engel, 2003 and Sutherland, 2004). Given that wages and/or prices are predetermined, the core of the problem is a simple trade-off: monetary policy is useful for closing the output gap arising from monopolistic competition but may have an adverse terms-of-trade effect. The purpose of this paper is to ask whether monetary policy is beggar-thy-neighbor or beggar-thyself and to compare non-cooperative and cooperative optimal monetary policies. To address the issues of interest, we set up a non-stochastic two-country general equilibrium model with imperfect competition on goods and labor markets and nominal wage and price rigidities. Some firms segment markets by country, they can charge different prices in domestic and foreign markets. In a similar framework Betts and Devereux, 2000a and Betts and Devereux, 2000b have shown that the sign of the terms-of-trade effect very much depends on the pricing policy of firms. If firms pre-set their export prices in the currency of the producer (consumer), the terms of trade of the expanding country will worsen (improve). In their model, the fraction of exporters who set prices in local currency of sale (pricing to market PTM) is symmetric across countries. Our framework instead allows the fraction of PTM firms to differ across the home and the foreign country, so that any change in the terms of trade can be separated in a change in export prices depending on home PTM and a change in import prices depending on PTM abroad. This distinction is crucial, since the increase in world aggregate demand is a function of the difference of the degrees of PTM, and since a given movement of the terms of trade is now compatible with various consumption and output (employment) allocations.1 Optimal policies are derived using as objective criterion welfare of the representative agent defined over the discounted flow of consumption, the utility of real balances and the disutility of work effort. Somewhat surprisingly, this most natural criterion is not very common in the related literature, where many contributions assume away the real balance term (see, e.g., Corsetti and Pesenti, 2005 and Sutherland, 2004). If, however, real balances are important for determining allocations of agents, and monetary authorities are maximizing the welfare of agents, then it should be included in the policymakers’ problem. But this comes at a price. To get an exact solution for the welfare term we have to choose specific functional forms. In particular, utility is logarithmic in consumption and the elasticity of substitution between home and foreign goods is restricted to unity. The latter precludes current account imbalances and thus shuts off any long-run effects of money. But since the unitary value is within the range of empirical estimates of this parameter and no approximations of welfare are needed in order to characterize the optimal policy functions, the gain of this assumption, at least from our point of view, outweigh the costs in form of a loss in generality.2 In our two-country (Home and Foreign) set-up we show the following: (i) Home’s terms of trade improve (worsen), if the sum of PTM-degrees in Home and Foreign is greater (less) than unity. (ii) For a given Foreign monetary stance, a Home monetary expansion is beggar-thyself (beggar-thy-neighbor), if Home PTM is “low” (“high”). Only if Home PTM is at an intermediate range, welfare will raise in both countries. This range vanishes in the case of perfect competition of labor and goods markets. (iii) In a world Nash equilibrium Home and Foreign welfare are bell-shaped in the degrees of PTM. (iv) The country which exhibits a higher degree of PTM than its neighbor will come up with a higher (or at least the same) welfare level. (v) If there is no terms-of-trade effect at the aggregate level, the Nash optimal monetary stance is identical for both countries; it does not matter which country experiences a higher degree of PTM in its economy. (vi) There is always a welfare gain from cooperation independently of the degrees of PTM. The superiority of cooperation contrasts to parts of the literature. Assuming a world of no PTM Rogoff (1985) finds that the worsening of the terms of trade puts a brake on the policymakers’ incentive to inflate in order to fill the output gap. Cooperation removes this brake, so that the equilibrium inflation rate rises implying a decline in welfare compared to the case of policy competition. Our result is different since we leave wages and prices as predetermined, not forward looking variables. We consider policies under commitment, which are not, in general, time-consistent in the Barro-Gordon sense. Betts and Devereux (2000a) find that the degree of PTM determines whether cooperation is good or bad. This result, however, hinges on an arbitrary assumed cost of inflation, which is absent in the welfare of private agents but part of the objective function of the policymaker.3Corsetti and Pesenti (2005) analyze a stochastic two-country model and show that there are gains from cooperation when the degrees of PTM are strictly between zero and unity. In the polar cases of no and full PTM the movement in the terms of trade has no impact on relative consumption and output, there is no incentive to use the terms of trade strategically and thus no gain from cooperation (see also Benigno and Benigno, 2003 and Devereux and Engel, 2003). Obstfeld and Rogoff (2002) argue that even in the case where there are some gains from cooperation, these are likely to be very small. Benigno (2002), on the other hand, shows that these gains will be non-trivial if utility is not logarithmic in consumption. Sutherland (2004) makes a similar point emphasizing the case where the cross-country elasticity exceeds unity (for a discussion of the importance of this parameter for the sign of the welfare spill-over see also Tille, 2001 and Michaelis, 2004). Pappa (2004) provides a most general model and discusses how sensitive welfare responds to changes in key parameters like the intertemporal elasticity of substitution, the labor supply elasticity, the degree of openness etc. The paper is structured as follows. The model is presented in Section 2. Section 3 presents the solution of the model and a discussion of the transmission mechanism of monetary shocks. Section 4 discusses the design of an optimal monetary policy distinguishing between a world Nash equilibrium and a cooperative equilibrium. Section 5 concludes.

The key message of our paper is that both the magnitude of the degree of pricing to market and its asymmetry between countries is decisive for the transmission mechanism and the welfare effects of monetary policy. In particular, these parameters are decisive for the question whether monetary policy is beggar-thy-neighbor or beggar-thyself. By comparing non-cooperative and cooperative optimal monetary policies we find, firstly, that there is always a gain from cooperation, and secondly, that the gain reaches a maximum at the polar cases of no and full pricing to market since in these cases the movement in the terms of trade and thus the welfare spill-over is at a maximum in the non-cooperative setting. Our framework can be extended in several ways, for instance by a less restrictive preference specification. Most prominent is the role of the cross-country elasticity of substitution. Assuming a value different from unity would imply long-term effects of monetary policy via current-account imbalances opening up interesting interactions with various distortions like monopolistic competition on goods and labor markets or imperfections concerning the financial market structure. Further research will show whether the second-order approximation technique put forward by Sutherland (2004) overcomes the problem of obtaining exact and explicit solutions when the cross-country elasticity of substitution differs from unity. Another promising line of research is the joint determination of optimal fiscal and monetary policy. Steps in this direction have been taken by Schmitt-Grohé and Uribe (2004b). If policymakers were able to neutralize the monopolistic competition distortions by subsidies on wages and production, the flexible price equilibrium would be efficient, and monetary policy could be used for some other objectives. Stochastic open economy models à la Obstfeld and Rogoff, 2000 and Obstfeld and Rogoff, 2002 take up this idea and analyze how alternative monetary policy rules perform in mitigating demand, supply and liquidity-preference shocks. If, however, the government has no access to non-distortionary instruments, we will be back in a second-best world where the design of optimal policies will be an exciting subject of further research.