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Non-coordinated monetary policy is analyzed in a stochastic two-country general equilibrium model. Non-coordinated equilibria are compared in two cases: one where policy is set in terms of state-contingent money supply rules, and one where policy is set in terms of state-contingent nominal interest rate rules. In general, the non-coordinated equilibrium differs between the two types of policy rule, but a number of special cases are identified where the equilibria are identical. The endogenous choice of policy instrument is analyzed and the Nash equilibrium in the choice of policy instrument is shown to depend on the interest elasticity of money demand.

There is currently an active literature analyzing a wide range of issues relating to monetary policy in open economies. This has been prompted by the development of tractable microfounded general equilibrium models of open economies where sticky prices give a role for monetary policy. These models provide a natural basis for studying the welfare implications of coordinated and non-coordinated monetary policy.1 In many respects, this new literature has developed a more or less common theoretical framework which includes such features as real money balances in the utility function, imperfectly competitive goods or labor markets, and sticky nominal prices or wages. There are, however, some differences in approach between authors. One such difference is the way in which the monetary policy instrument is specified. Some authors, such as Obstfeld and Rogoff, 1998, Obstfeld and Rogoff, 2002 and Devereux and Engel, 2003 and Sutherland (2004) adopt the traditional approach of specifying monetary policy in terms of choices for the nominal money stock. But other authors, such as Corsetti and Pesenti (2001b) and Clarida et al. (2001) adopt an alternative approach which is to specify monetary policy in terms of choices for the nominal interest rate. An important question which, hitherto, has not been addressed in the new literature is whether, and to what extent, it matters which instrument is used to implement monetary policy. This is the focus of the current paper. Using a simple model which is consistent with those used in the current literature, we investigate the circumstances in which the choice of monetary policy instrument affects the equilibrium outcome. The appropriate choice of policy instrument has, of course, been the subject of an extensive earlier literature starting with Poole (1970). The issue at stake in this previous literature was the stabilizing properties of a fixed money supply target compared to a policy of fixing the nominal interest rate. Typically the conclusion from this earlier literature was that the choice of instrument could have a substantial effect on the volatility of macrovariables and that the ‘welfare’ ranking of instruments depended on the mixture of shocks hitting the economy. An important feature of the question addressed by this earlier literature, which distinguishes it from the issue we are investigating in this paper, is the focus on non-state-contingent rules for the monetary policy instrument. The earlier literature focused on a policy of fixing the quantity of money as compared to a policy of fixing the nominal interest rate. In this paper, on the other hand, we analyze monetary policy rules which allow the monetary authority to react to shocks. Thus, in our framework (in common with many of the contributions to the recent open economy literature) the monetary authority chooses a feedback rule for the policy instrument which specifies a reaction to the exogenous shocks hitting the economy. The comparison to be made, therefore, is between a feedback rule for the money supply and a feedback rule for the nominal interest rate. 2 In this context one obvious reaction is to argue that, if the parameters of the rule are chosen optimally by the monetary authority (as is typically the case in the recent literature), it should not matter which policy instrument is determined by the rule. A welfare maximizing monetary authority is only concerned with the real equilibrium that is delivered by the rule. If the policy instrument is the money supply, then the monetary authority will choose parameters for the feedback rule which deliver the desired real equilibrium. Likewise, if the policy instrument is the interest rate the monetary authority can (and will) choose feedback parameters which deliver exactly the same desired real equilibrium. Thus (in contrast to the literature following Poole, 1970) one may be tempted to assume that the choice of policy instrument is irrelevant when the monetary authority chooses a welfare maximizing state-contingent rule. We show in this paper that, although this logic may be correct in a closed economy (where, by definition, there is only one monetary authority), it does not carry over to an open economy setting. We show that, in general, when one is considering non-coordinated policymaking represented by a Nash game between national policymakers, the real equilibrium (and thus the level of welfare) delivered by the Nash equilibrium in the choice of feedback parameters does depend on the particular way in which monetary policy is specified. It is therefore not correct to assume that the choice of policy instrument is irrelevant. There are, however, some special cases where the Nash equilibrium is unaffected by the choice of policy instrument. These cases are identified and explained.3 Having shown that the real equilibrium delivered by the Nash game over the choice of policy feedback parameters differs depending on the choice of policy instrument, a natural further question to analyze is the endogenous choice of the policy instrument itself. This issue has already been addressed within the context of the earlier Poole-style analysis by Turnovsky and d'Orey (1989). They consider a simple Nash game between national policymakers in a two-country model where the policymakers make a choice between the money supply or the nominal interest rate as the monetary policy instrument. In a similar spirit we analyze an extension to our model where policymaking is a two-stage process. In the first stage there is a Nash game over the choice of policy instrument and in the second stage there is a Nash game over the choice of parameters for feedback rules (which determine the setting of the policy instruments chosen in the first stage).4 We show that, when the choice of policy instrument makes a difference to the equilibrium in the Nash game over feedback parameters, there is a unique Nash equilibrium in the game over policy instruments. The Nash equilibrium in the choice of policy instrument can either result in the choice of money supply rules or interest rate rules depending on the elasticity of money demand with respect to the nominal interest rate. The paper proceeds as follows. Section 2 describes a simple two-country model which is used as a framework for analyzing the implications of policy instrument choice. Section 3 analyzes the comparison between interest rate rules and money supply rules. In this section the choice of policy instrument is assumed to be exogenous. Section 4 considers the endogenous choice of policy instrument. Section 5 discusses the implications of some generalization of our model. Section 6 concludes the paper.

This paper has compared state-contingent money supply rules with state-contingent interest rate rules in a two-country sticky-price general equilibrium model. It has been shown that, in general, the equilibrium outcome of non-coordinated policymaking can differ depending on whether monetary policy is specified in terms of money supply rules or interest rate rules. A number of special cases are identified where the two types of rule yield the same equilibrium. The endogenous choice of policy instrument was analyzed as part of a two-stage game and it was shown that a unique Nash equilibrium exists in the choice of monetary instrument. This paper has concentrated on deriving explicit results for a fairly restrictive model (which is nevertheless representative of the recent literature). The results are, however, robust to a number of important generalizations of the model.