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This paper studies the national welfare maximizing inflation tax in an open economy with imperfect competition. It shows that the presence of a monopolistic distortion dampens the incentive to engage in strategic use of the inflation tax. If this dampening effect is strong enough, monetary policy becomes completely inward-looking, restoring the Friedman rule as an equilibrium strategy regardless of the actions of the foreign government. This aspect of the policy interaction—driven entirely by the presence of imperfect competition—is important because it determines the underlying structure of the policy game and is therefore crucial for determining whether or not there exist welfare gains from international monetary cooperation.

This paper studies the national welfare maximizing inflation tax in an open economy with imperfect competition. In previous work, Cooley and Quadrini (2003)—henceforth CQ—use a model with perfect competition to show that in a two-country world, non-cooperative governments face an incentive to use the domestic inflation tax to gain an advantage over the terms of trade. This incentive leads to a systematic inflationary bias, giving rise to potentially large wel- fare gains from international monetary cooperation—on the order of one half to a full percentage point of steady state consumption when policy is set under commitment. However, imperfect competition is widely regarded to be an important feature of the economy. 1 It is particularly important in an open economy context because it helps to explain a number of important issues in international trade.2 In particular, imperfect competition arising from product differentiation is one of the core assumptions underlying Obstfeld and Rogoff (1996, 2000), which from the basis for what has become the workhorse model in open economy macroeconomics. Given its central role in the open economy literature, it seems natural then to ask what imperfect competition implies for the national welfare maximizing inflation tax. This paper shows that it has important consequences for the equilibrium inflation tax as well as for the resulting gains from international monetary cooperation.3 As in CQ, the model presented in this paper assumes a transactions demand for money which enters through a cash-in-advance constraint. Anticipated inflation causes the nominal interest rate to rise above zero, implying that money is dominated by bonds in rate of return. Agents respond by inefficiently economizing on real cash balances, substituting out of consumption and into leisure. Intuitively, anticipated inflation can be thought of as a tax on consumption, or equivalently, a subsidy for leisure. In a closed economy setting, the representative agent both bears the entire burden of the consumption tax and enjoys the full benefit of the leisure subsidy. Accordingly, the optimal policy is to minimize the consumption-leisure distortion by eliminating the inflation tax altogether.4 This story does not necessarily hold in an open economy because leisure is a non-traded good. Holding constant foreign inflation, higher domestic inflation creates a leisure subsidy that primarily benefits the domestic representative agent. At the same time, the adjustment of the exchange rate allows for expenditure switching in both countries away from the domestically produced good and into the foreign produced good. The expenditure switching channel allows the burden of the consumption tax to be shared equally across countries. As long as the welfare gain from the leisure subsidy (which accrues mainly to the domestic household) outweighs the welfare loss from the consumption tax (which is shared across countries), there is an incentive to inflate away from the Friedman rule to gain an advantage over the terms of trade.5 Doing so creates a “beggar-thy-neighbor” spillover to the foreign agent. The primary contribution of this paper is to show that this trade-off depends crucially on the degree of imperfect competition in the world economy. When world product markets are perfectly competitive, the trade-off unambiguously favors the terms of trade distortion, generating a strong incentive to engage in policy competition. In this case, the policy game takes on a prisoner’s dilemma structure that results in potentially large welfare gains: over ten percent of steady state consumption, assuming symmetry in country size. Quantitatively, the welfare gains found in this paper are significantly larger that those reported in CQ, resulting mainly from differences in the underlying structure of the two models. In particular, whereas in CQ anticipated inflation affects the terms of trade through the relative price of intermediate inputs into production, here it distorts the consumption/leisure margin. In doing so, it alters the terms of trade through the relative price of a non-traded good. This latter channel implies significantly larger welfare consequences for anticipated inflation. Introducing imperfect competition dampens the incentive to engage in policy competition. Output and consumption are inefficiently low in the presence of a monopolistic distortion and, as a result, the marginal utility of consumption is high relative to the case of perfect competition. This makes anticipated inflation more costly, thereby worsening the trade-off between the monetary distortion and the terms of trade distortion. As a result, non-cooperative governments become more inward-looking when setting policy. If this dampening effect is strong enough, monetary policy becomes completely inward-looking and the Friedman rule is restored as an equilibrium strategy regardless of the actions of the foreign government. This aspect of the policy interaction—driven entirely by the presence of imperfect competition— is important because it changes the underlying structure of the policy game. As a result, it also is crucial for determining whether or not there exist welfare gains from international monetary cooperation. If the monopolistic distortion is large such that the Friedman rule is restored as an equilibrium strategy in either of the two countries, the prisoner’s dilemma structure of the policy game breaks down, eliminating any welfare gains from cooperation. This result is markedly different from the conclusions of CQ, who find gains from cooperation in all but the most asymmetric of world economies.6 The remainder of this paper proceeds as follows. The next section presents the model. Section 3 describes the three distortions operating in the economy. Section 4 presents the equilibrium solution of the non-cooperative policy game. Section 5 focuses on the effect of imperfect competition on the incentive to engage in policy competition and the resulting implications for the welfare gains to cooperation. Section 6 concludes.

This paper studies the national welfare maximizing inflation tax in an open economy with imperfect competition. As in Cooley and Quadrini (2003), we find that with perfect competition both governments have an incentive to engage in strategic use of the inflation tax. In this case, the policy game takes on a prisoner’s dilemma structure that can result in potentially large welfare gains from international monetary cooperation. However, this result is highly sensitive to the presence of imperfect competition. Introducing imperfect competition to the model dampens the incentive to engage in policy competition, thereby lowering the gains from cooperation. If this dampening effect is sufficiently strong, policy becomes strictly inward-looking and the Friedman rule is restored as an equilibrium strategy regardless of the actions of the foreign government. This aspect of the policy interaction is important because it determines the underlying structure of the policy game and is therefore crucial for determining whether or not there exist welfare gains from international monetary cooperation. In particular, if the monopolistic distortion is large such that policy turns strictly inward-looking in either of the two countries, the prisoner’s dilemma structure of the policy game breaks down thereby eliminating the gains from cooperation. Two aspects of this paper deserve further attention. First, we have assumed throughout that governments have access to a commitment device. Relaxing the commitment assumption and introducing nominal rigidities would significantly change the results by introducing a time consistency problem. Arseneau (2004) shows that whether the optimal monetary surprise is inflationary or deflationary depends importantly on initial inflation expectations. If expectations are sufficiently anchored, each government faces an incentive to create a deflationary surprise in order to manipulate the short run terms of trade. The noncooperative discretionary equilibrium in this case is the global Friedman rule. Thus, even though a national welfare maximizing government might want to use the inflation tax to manipulate the long run terms of trade, lack of commitment may prevent it from doing so. Furthermore, lack of commitment eliminates the gains from cooperation. A second direction for future research is to study a noncooperative public finance problem in the spirit of the Ramsey literature, where each government chooses the national welfare maximizing mix of monetary and fiscal policy to finance an exogenous stream of domestic government expenditures. Along these lines, it might also be interesting to study the link between the optimal monetary/fiscal mix and trade policy. In particular, an open question is whether or not the introduction of an optimally chosen tariff would restore the optimality of the Friedman rule by giving government access to a fiscal instrument that influences the terms of trade more directly than the inflation tax.