باز بودن و نرخ بهره: تجزیه و تحلیل با استفاده از مدل MIUF و معامله مدل هزینه پول

This paper discusses the manner in which the difference in the specification, which generates a demand for money by agents, alters the optimal interest rate in open economies by taking into account that the prices reflect the producers' optimization. In acanonical money-in-the-utility function (MIUF) model, the Friedman rule is optimal. On the other hand, in the transaction cost model, the optimal interest rate is positive and increases, in terms of the share of imports in consumption.

Over the last two decades, trade liberalization has significantly integrated the world's economies, and citizens are now able to have increased access to imported goods. In light of globalization, recent movements in prices of imported foods and raw materials have aggravated worldwide concerns and now threaten to weaken governments' control over general consumer prices. Does such an exposure to the overseas market alter the costs and benefits of changing the domestic policy? Since Romer (1993) documented the empirical evidence and theoretical framework that support the negative correlation between the openness to trade and monetary expansion, the merits and demerits of his study have been widely discussed. Among affirmative opinions, the theoretical background primarily depends on the sticky-price argument where monetary policies face the time-inconsistency problem. However, such a defense sometimes suffers the empirically almost zero correlation between the openness and the slope of Phillips curve (Temple (2002)), resulting in the puzzle. This motivates us to explore the alternative explanation of the association between the openness of economy1 and the optimal interest rate in a flexible-price framework, which does not rely on the time-inconsistency hypothesis. Since the specification of money can affect the optimality of the Friedman rule,2 we examine two types of monetary models: money-in-the-utility function (MIUF) model and transaction cost model of money. As is usually assumed in the literature, only domestic currency facilitates the transaction in both the models.3 We find that, in an open economy, the optimal interest rate is zero in the MIUF model, while it is positive in the transaction cost model. This difference in optimal interest rates stems from the existence of the channel through which the real balance can affect the labor supplies and product prices. In both models, the real balance is assumed to facilitate the consumer's transaction. In the MIUF model, money does not affect the economy further, and thus, the zero interest rate is optimal regardless of the economy's openness, in order not to raise the opportunity cost of holding money. On the other hand, in our transaction model, the decrease in the interest rate additionally increases the value of domestic producer's income, which encourages its labor supply and decreases the price of home goods. Since the overall consumption increases only by the share of home goods, the home country is less motivated to exploit the expansionary policy. The optimal transaction cost is positive and is supported by the positive nominal interest rate. Another finding of this paper is that our version of the transaction cost model of money can produce a bliss point in the overall utility from money with a finite level of the real balance. This contrasts with the MIUF model with CRRA formula, in which the zero interest rate is optimal in the limit. Our result in the transaction cost model that the country's openness, that is, the import share in consumption, is negatively associated with the optimal real balance is also documented in the previous studies by using other frameworks. Romer (1993) illustrated the inverse association between inflation and openness to trade using cross-country data. He argued that the monetary authority in a more open economy is less motivated to an expansionary policy because the Phillips curve is steeper. Since, Lane, 1997 and Rogoff, 2003 among others have developed sticky-price models in which the gain from a surprise monetary expansion is smaller in a more open economy. Rogoff (2003) also argues that globalization and deregulation might make the economy more competitive and the Phillips curve steeper, which reduces the potential benefit of surprise monetary expansion. Terra (1998) propounds an alternative view that openness is an empirically important determinant of inflation only for severely indebted countries. Temple (2002) further argues that the costs of monetary expansion are greater in open economies because it generates unwelcome variability in real exchange rates. Hau (2002) demonstrates this negative relationship between volatility and openness in a model with nominal rigidities. In contrast, this paper predicts that the openness of economy leads to the monetary contraction even in a flexible price model. As is usually assumed in the recent literature of open macroeconomics, for instance, by Chari et al., 2002 and Devereux et al., 2006, this paper assumes that only the consumer's currency facilitates transactions in both models. This is in contrast to the models of currency substitution discussed in Calvo and Rodriquez, 1977 and Kareken and Wallace, 1981, and recently in Heimonen (2008). Therefore, the positive interest rate in the transaction cost model does not stem from the currency substitution, whose mechanism is extensively discussed by, for instance, Végh, 1989 and Guidotti and Végh, 1993a. In order to model the demand for money, many techniques have been proposed in the literature. A direct technique is to assume that money produces positive utility and to incorporate money in the utility (Sidrauski (1967)). Another technique includes assuming a certain transaction cost in purchasing goods, in which money has a role as a medium of exchange facilitating transactions.4 This transaction cost can be modeled by considering the “shopping time” or by assuming that real resources are used in the process of exchange. Feenstra (1986) prefers the latter approach and considers consumption but not leisure. Our transaction cost model belongs to the last classification of the transaction cost model, but the utility considered includes leisure as well as consumption. By employing the transaction cost model, we demonstrate that consumption, leisure, or transaction cost are not satiated from money, but the net utility from money yields a bliss point.5 The implementation of the optimal monetary policy has been a potential concern in the literature. To ensure the monetary equilibrium, economists have tactfully imposed some restrictions on the level of money. One direct technique is to assume that the utility of money is satiated at a finite level of money. Some models have a bliss point, while others just assume that money does not yield the utility when it exceeds the level of satiation. The satiation can be imposed on the money in the utility function as well as over the transaction cost technology. Examples can be found in Friedman (1969), Phelps (1973), Brock (1975), Correia and Teles (1996), Eggertsson and Woodford (2003), and Alvarez, Kehoe, and Neumeyer (2004) among others. We provide one validation for assuming a satiation in the MIUF model by analyzing the transaction cost model, in which the sum of the terms related to the transaction cost in the utility has a bliss point. The remainder of this paper is organized as follows. Section 2 presents a formal description of the MIUF model. Section 3 introduces the transaction cost model of money. Section 4 concludes the paper.

We have compared the MIUF model and the model of the transaction cost of money in open economies by extending the approach of Feenstra (1986). Our contributions in considering the transaction cost model are twofold: (1) providing one validation to assume a bliss point in the utility from money and (2) illustrating that the openness of economy makes the optimal interest rate positive even when there is no time-inconsistency issue. The violation of the qualitative equivalence of the models is based on transmission mechanisms that money affects the economy. In both the models, the accumulation of money facilitates the consumer's transaction and basically increases utility. At the same time, only in the transaction cost model, the decrease in the liquidity cost enables people to purchase the same quantity of real goods with a smaller expenditure. Such increased value of income encourages the labor supply and increases disutility. Therefore, the optimal size of the transaction cost balances these conflicting effects and yields a bliss point in the overall utility. Our analysis also demonstrates that the Friedman rule of zero nominal interest rate is optimal in the MIUF model, but not in the transaction cost model. In the MIUF model, since there is no mechanism through which the real balance affects other real allocations, imposing the opportunity cost of holding money is not optimal regardless of the openness to imports. On the other hand, in the latter model, the existence of import goods ameliorates the positive effect of decreasing interest rate on consumption. Since the labor supply is independent of the openness to import, the optimal interest rate is positive, which is higher than the case under autarky. In a real world, the effect of openness on the national economy can certainly be a hybrid of various factors. Our argument for the monetary contraction caused by the openness can coexist with the time-inconsistency hypothesis, such as Romer (1993), but is also applicable to economies with well-disciplined central banks. Since policymakers nowadays are generally believed to refrain from creating a monetary surprise, our prediction is important, especially in OECD countries. Empirical researches are called for in order to measure the degree to which our transaction cost hypothesis explains the overall monetary stance in each country. Another possibility for future research is to introduce the foreign currency as an alternative means of payment. Since the currency substitution might introduce another factor to impede the domestic policy, it is also interesting to see whether our results are modified in the presence of the use of foreign currency.