دام نقدینگی و سیاست پولی بهینه در اقتصاد باز

We consider an open-economy model with the Calvo-type sticky prices. We mainly analyze the situation in which the monetary authority in each country cooperates so as to maximize the world welfare. In the case where the zero lower bound (ZLB) on nominal interest rates never binds, the optimal inflation targeting rule in our open-economy model has exactly the same form as in the closed-economy model. This is not the case, however, when the ZLB may bind. The optimal paths are characterized in such a situation. In contrast with what has been suggested in the existing literature, the optimal paths of the nominal exchange rate in our model typically exhibit appreciation of the currency of the country where the ZLB binds. J. Japanese Int. Economies22 (1) (2008) 1–33.

How should monetary policy be conducted when the zero lower bound (ZLB) for nominal interest rates may bind? The recent experience of Japan is a well-known example of such a “liquidity trap.” There, the call rate1 has been below 0.5 percent per annum since October 1995 and below 0.1 percent since March 1999 (except for the period August 2000–March 2001). Krugman (1998) argues that, even when the nominal interest rate hits the zero bound, the central bank could still stimulate the current level of output by raising expectations of future inflation. This point is further elaborated in a more fully dynamic framework with staggered pricing by Eggertsson and Woodford (2003).2 Based on an optimization-based, quadratic approximate welfare measure, they analyze the state-contingent paths of inflation, output gap, and nominal interest rates under optimal policy commitment. Furthermore, they derive a price-level targeting rule that could implement the optimal paths. In this paper, we extend the analysis of Eggertsson and Woodford (2003) to a two-country open-economy model.3 A continuum of differentiated products are produced in each country, and each good price is adjusted at random intervals as in Calvo (1983). We assume perfect exchange-rate pass-through, so that the law of one price holds. We analyze the optimal state-contingent paths of various variables, and compare our results to the proposal of Svensson, 2001, Svensson, 2003 and Svensson, 2004 that the currency of a country in a liquidity trap should depreciate. We start with a result on equilibrium shares of consumption across countries. In the literature on open-economy monetary models, it is often assumed that the equilibrium shares of consumption across countries are determined independently of the monetary policy rule adopted by each country. This assumption is a bit problematic. It is true that with complete asset markets (and isoelastic preferences), given initial financial asset holdings and policy rules, the equilibrium shares of consumption are constant at all dates and all contingencies. In general, however, even under these assumptions, given initial asset holdings, different policy rules would result in different equilibrium shares of consumption across countries. We provide sufficient conditions on preferences and initial asset holdings for the equilibrium shares of consumption across the two countries to be independent of the policy rule adopted by each country. They include unit elasticity between goods produced in different countries. For simplicity, we assume that those conditions hold in this paper. As for the policy objective, we mostly focus on the case in which the two monetary authorities cooperate each other to maximize the world welfare, which is defined as the world average of expected lifetime utility of households. Based on a second-order approximation, the objective function of the monetary authorities is given by a quadratic loss function in output gaps and inflation rates. Here, the welfare-relevant inflation rates are not the CPI inflation rates, but the producer-price inflation rate in each country, as in Benigno and Benigno (2003) and Clarida et al. (2001). Thus, fluctuations in the nominal exchange rate per se does not affect the welfare. We first examine the optimal policy rule when the ZLB is assumed never to bind. Surprisingly, in this case, the optimal inflation targeting rule in our open economy model takes exactly the same form with the same parameter value as the one obtained for the closed economy by Woodford (2003, Section 7.5). That is, the (producer-price) inflation rate in each country must be targeted at the level given by a constant times the rate of change of its output gap. This is true even though the aggregate supply relation shows international dependence, that is, the inflation–output-gap tradeoff in each country is affected by the output gap in the other country. Thus, as long as the ZLB never binds, the monetary authority in each country may forget about international dependence and set the target rate of inflation independently, in order to maximize the world welfare. This is not the case when the ZLB may bind. In such a case, as our optimal price-level target rule shows, the price-level target in each country is not determined independently. To examine quantitative properties of the optimal state-contingent paths of key variables, we conduct a numerical experiment similar to the one in Eggertsson and Woodford (2003). It shows that the optimal state-contingent paths of inflation, output gaps, and nominal interest rates of the country in a liquidity trap look very similar to those obtained for the closed economy by Eggertsson and Woodford (2003). Such paths in our open economy model are, however, made possible by active policy coordination of the other country. Regarding exchange rates, our numerical experiment shows that the currency of a country in a liquidity trap must appreciate, rather than depreciate. This makes a sharp contrast to what Svensson, 2001, Svensson, 2003 and Svensson, 2004 proposes. A theoretical justification for his proposal is made in Svensson (2004). While our model and Svensson's (2004) differ in several ways,4 the difference in the evolution of nominal exchange rates under optimal policy arises from his assumption that (i) the shock that generates a liquidity trap lasts only for one period and (ii) the country in a liquidity trap has a productivity level which is higher than the steady-state level. Note that a country falls into a liquidity trap, say, at date 0, if the expected growth rate of productivity in that country from date 0 to date 1 is sufficiently negative. Svensson (2004) creates such a situation by assuming that the productivity of a country at date 0 is unusually high (and the expected level of productivity at date 1 is normal). This is why he observes depreciation at date 0 under optimal policy: Since the country produces more than normally the relative price of goods produced in that country to those produced abroad must fall. Because the price of a good is set one period in advance, this fall in the relative price is achieved by a depreciation. However, even in this scenario, if the shock lasts for more than one period so that the expected growth rate of productivity is negative, say, for dates t=0,…,τt=0,…,τ, then the currency would appreciate at all t=1,…,τt=1,…,τ under optimal policy commitment. In this sense, our claim that the currency of a country in a liquidity trap appreciates under optimal policy commitment holds more robustly. The rest of the paper is organized as follows. In Section 2, we describe households and give a proposition on the equilibrium share of consumption. In Section 3, the aggregate-supply relations are derived. In Section 4, a quadratic approximate world welfare measure is computed, and an optimal inflation targeting rule is derived for the case where the ZLB is assumed never to bind. In Section 5, the natural rates of interest are defined and the “intertemporal IS equations” are obtained. In Section 6, optimal policy in a liquidity trap is analyzed. In Section 7, the state-contingent paths of nominal exchange rates under optimal policy is discussed. Section 8 is concluding remarks.

We have analyzed optimal policy in an open economy. First, when the ZLB for nominal interest rate is assumed never to bind, the optimal inflation targeting rule for each country is exactly the same with the same parameter value as the one for the closed-economy model (Woodford, 2003). Indeed, in such a case, each monetary authority can forget about international dependence in setting its inflation target, in order to maximize the world welfare. Second, this is not the case when the ZLB may bind. The optimal price-level target rule shows significant international dependence. The optimal state-contingent paths of inflation, output gaps, and nominal interest rates for the country in a liquidity trap look very similar to those obtained for the closed-economy model by Eggertsson and Woodford (2003). However, such paths are made possible by policy coordination by the other country. Third, in spite of the proposal of Svensson, 2001, Svensson, 2003 and Svensson, 2004, the nominal exchange rate of the country in a liquidity trap appreciates under optimal policy (except possibly at the initial date). For simplicity, we have made some restrictive assumptions. First, for instance, the elasticity of substitution between home-goods and foreign-goods is assumed to be unity. Second, we have assumed full exchange-rate pass-through. Third, only productivity shocks are examined. Fourth, the steady-state distortions due to market power is (close to) zero, and so on. Extending our model in these respects is left for future research.