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This paper sets up an endogenous growth model of an open economy in which the monetary authority implements a gradualist interest-rate rule with targets for both inflation and economic growth. We show that, under a passive rule, a monetary equilibrium exists and is unique. Moreover, the equilibrium is locally determinate. By contrast, an active rule implies either two equilibria, one high-growth and one low-growth, or none. In the case of two equilibria, the high-growth equilibrium is locally determinate, while the low-growth equilibrium is a source. Besides, the stabilization and growth effects of alternative target policies are also explored in this study. Moreover, in departing from the existing literature, we turn to focus on the analysis of transition with a particular emphasis on the case of imperfect credibility.

The interest of economists in interest-rate rules has been sparked by early studies by Sargent and Wallace (1975) and McCallum (1981) and revived by Taylor (1993) in the light of description for U.S. monetary policy.1Taylor (1993) shows that since 1987 U.S. monetary policy can be well described in terms of a simple rule whereby the central bank sets the short-term nominal interest rate as an increasing linear function of a measure of inflation and the output gap with coefficients of 1.5 and 0.5, respectively. According to various coefficients of inflation, interest-rate rules can be divided into two distinctive styles. If a feedback rule has an inflation coefficient greater than unity (which satisfies the Taylor principle), it is dubbed an active interest-rate rule (or Taylor's rule). By contrast, a passive rule involves an inflation coefficient of less than unity. Taylor (1999) claims that the active feedback rule is widely judged to have been unusually successful in the United States, suggesting that the rule is worth adopting as a principle of behavior. In fact, in many industrialized countries their monetary policies can be also classified into various styles of interest-rate rules (see Clarida et al., 2000). Ever since Taylor's (1993) seminal work, the related issues have been extensively analyzed in a wide variety of models that include interest-rate rules aimed at inflation targets and/or output targets.2 Nevertheless, this is still a contentious issue that deserves more careful investigation. There exist two facts which are neglected by the theoretical literature. First, traditionally, interest-rate rules followed by central banks have been regarded as devices for macroeconomic stabilization in the short run. However, in practice, central banks do not focus solely on welfare gains from stabilization in economic environments with uncertainty (the short run goal), but they also pursue long run development goals, such as economic growth. 3 For example, since 1997 the Bank of England's Inflation Report has reported projections for four-quarter inflation and real GDP growth for an eight-quarter forecast horizon. Since 1992 Sweden's Riksbank has published forecasts for Q4/Q4 real GDP growth and December/December CPI inflation for the current year and the two following “out” years (see Kuttner, 2004). Similar projections were also made by the central bankers of New Zealand, Australia and Canada though some of these projections may be not available publicly. Second, there is an evident fact that in an open-economy environment, real-world central banks have the option to trade foreign assets at a world interest rate. The presence of foreign assets, traded freely by home agents (including the central bank), and the prevalence of a (fixed) world interest rate, will redefine the mechanics that underlie interest-rate targeting by central banks. Once this extra device in the hands of central bankers – the foreign assets – creates an essential mechanism for managing real money balances, the capital account and the foreign interest rates will become very important forces behind the impact of interest-rate targeting on the macro-economy. However, in spite of its importance, with few exceptions (Taylor, 2001, McCallum and Nelson, 2001 and Erceg, 2002), economists have paid relatively little attention to the discussion regarding the performance of interest-rate rules in an open economy. Based on these two facts, this paper makes a theoretical attempt to analyze the macroeconomic and growth implications by viewing interest-rate targeting as a policy regime that can also influence sustainable long-run growth. In our analysis it is crucial that the private sector reacts to the interest-rate rule with long-run growth targets in mind. 4 Specifically, we extend the interest-rate rule that is gradualist, in the sense that it feeds back to both the inflation and income-growth targets in an open economy with endogenously-determined growth rates. Moreover, in this open-economy setup, the roles of the capital account and foreign interest rates become particularly important. The core questions we ask are: (i) what happens to the macro-economy in the long run under the gradualist passive and active interest-rate rules with respect to inflation targeting in an open economy? (ii) what are the stability properties and the transition dynamics in each case? and (iii) what is the role of policy credibility in answering the above two questions? i.e. what is the impact of the non-credibility of policy (along the lines of Lahiri, 2000) with special emphasis on the impact of the duration of credibility for the resulting paths and steady state(s)? These issues are obviously unexplored in the existing literature in which interest-rate rules are thought of as devices for macroeconomic stabilization in the short run. Besides, more recent studies focus on whether appropriately designed policy institutions reduce the probability of asset pricing bubbles and other self-fulfilling prophecies that can be generated in models with multiple equilibria (see, for example, Benhabib and Farmer, 1999, McCallum, 2003, Woodford, 2003 and Benhabib et al., 2003). Our paper will depart from this issue and focus on the analysis of transition. In order to come up with these answers, our model comprises some novel characteristics.5 First of all, we specify that the central bank's operating procedure is implementing a gradualist interest-rate rule, i.e. it gradually adjusts the nominal interest rate toward the targeted level, rather than adjusting the interest rate by an immediate once-and-for-all jump. As is commonly believed by economists, this is the way several central bankers have conducted their monetary policy. Such a belief is also supported by evidence that the official interest rates in major countries have been adjusted by small amounts with infrequent reversals (see, for example, Goodhart, 1996, Sack, 1998, Woodford, 1999 and Martin, 1999). Second, we adopt the “Ak” production function as the source of endogenous growth in a deterministic environment. 6 Such a specification is the simplest resolution to abstracting from externalities, which can blur the role of the policy analysis for growth. 7 Yet, technically, the AK technology can lead to a problem in an open economy, namely, that this technology with fixed physical capital returns tends to lead to such consumption/investment decisions of households that imply instant transition to a steady state (infinite speed of convergence). To avoid this problem, we follow the resolution of Barro and Sala-i-Martin (1995, ch. 3), and include adjustment costs for investment, which becomes an essential ingredient for our analysis. Third, money is introduced into our model by employing a transactions' cost technology a-la Sims. Specifically, a higher velocity of money comes together with an extra cost in terms of the consumable good. As a result, money is no longer a simple “veil” of the economy, leading our model to transcend the (neo)classical dichotomy between real and monetary variables. Compared to other popular approaches to breaking the classical dichotomy, namely, the money-in-the-utility-function and cash-in-advance approaches, the transaction costs approach seems to be more plausible because its assumption is less restrictive.8 In addition, Feenstra (1986) has shown that the transaction costs and the money-in-the-utility-function approaches can be functionally equivalent. Wang and Yip (1992) have also proved that these three approaches can yield the same qualitative results. According to their finding, our main results can be easily applied to the other two approaches. By characterizing the balanced growth equilibrium, several interesting findings emerge from our analysis which are summarized as follows. First of all, a well-known result obtained in the literature is that an equilibrium is locally unique if the central bank follows an active rule, and locally indeterminate if the passive rule is implemented (see, for example, Clarida et al., 2000). This result is challenged by more recent studies. Generally speaking, the indeterminacy in dynamic general equilibrium models associated with the interest-rate feedback rule hinges crucially on the specific economic environment in which money enters preferences and technology (Benhabib et al., 2001a and Benhabib et al., 2001b), the monetary-fiscal regime (Benhabib et al., 2001a and Benhabib et al., 2001b), the investment and its adjustment costs of investment (Dupor, 2001, Dupor, 2002 and Carlstrom and Fuerst, 2005), the endogenous labor supply (Meng and Yip, 2004), and the exact definition of inflation measurement (Bernanke and Woodford, 1997, Benhabib et al., 2001b, Benhabib et al., 2003, Carlstrom and Fuerst, 2000 and Carlstrom and Fuerst, 2005), etc. Apart from the issues raised in this literature, this paper shows that, in an open-economy endogenous growth model, whether interest-rate rules are active or passive plays a decisive role in affecting the overall economy's dynamic stability properties. If the central bank implements a passive rule, then the monetary equilibrium exists and is unique. Moreover, this unique passive monetary equilibrium is locally determinate. However, if the central bank implements an active rule, then the open economy either has two equilibria, one high-growth and one low-growth, or none. In the case of two equilibria, the high-growth equilibrium is locally determinate, while the low-growth equilibrium is a source. By focusing on the steady-state effects, we find that there can be an appropriately chosen interest-rate rule that feeds back to both inflation and economic growth, which can lead to a double gain: it can lead to both more price stability and to higher economic growth. To be more specific, we find that, in the long run, an anticipated rise (rather than decline) in the inflation target unexpectedly leads to this double gain. This result holds true for unanticipated policies as well. For the transitional dynamics, we show that in response to an anticipated permanent decrease in the inflation target, the growth rate of the open economy will decline on impact and then continuously fall toward its new stationary level. However, the nominal interest rate and the inflation rate will exhibit a mis-adjustment: they will fall during the period between the policy's announcement and its implementation; once the lower inflation target is realized, the nominal interest and inflation rates will start to increase toward their new and higher stationary levels. Finally, as argued by Gavin (2003), inflation targeting has been successful because the policy-maker decides on objectives and announces them. In line with Calvo (1986) and Drazen and Helpman (1988), the framework with imperfect credibility of the monetary authority is analyzed. We point out that the economy can enjoy higher growth during the entire transition if the commitment in regard to the growth target policy is imperfectly credible. This provides a theoretical explanation as to why the government often overstates its intended growth target and implements a non-credible policy. In particular, we show that in response to different credibility horizons, the economy will experience quite distinct transitional dynamics.

This paper sets up an endogenous growth model of an open economy in which the central bank implements a gradualist interest-rate rule with targets for inflation and economic growth. We show that under a passive rule the monetary equilibrium exists and is unique; moreover, it is locally determinate. By contrast, an active rule implies either two equilibria, one high-growth and one low-growth, or none. In the case of two equilibria, the high-growth equilibrium is locally determinate, while the low-growth equilibrium is a source. Our results clearly differ from those in previous studies (see, for example, Carlstrom and Fuerst, 2000 and Carlstrom and Fuerst, 2005 and Fiore and Liu (2002)), and hence provide new insights for policy implications. We have also shown that, under a nominal interest-rate rule that feeds back to both inflation and economic growth, regardless of whether it is passive or active, an immediate rise in the inflation target stabilizes the price level and promotes economic growth both in the transitional period and in the long run. Nevertheless, under a pre-announced inflation target policy, price stability and the expansion of economic growth cannot be achieved simultaneously during the period between the policy's announcement and its implementation. We also show that, under such an interest-rate rule, a higher growth target has a favorable effect on both inflation and economic growth in the long run. In addition, the policy authority always has incentives to overstate its intended growth target and hence will implement a non-credible policy. The credibility of the central bank's commitment is shown to play an important role in influencing the transitional dynamics of the macroeconomic variables.