The Comparative Analysis of Exchange RateRegimes

Transcription

1 The Comparative Analysis of Exchange RateRegimes Yoshino, Naoyuki Kaji, Sahoko Suzuki, Ayako 1. Introduction The purpose of this paper is to analyze the optimal exchange rate regime by use of a simple open macro economic model. Three exchange rate regimes, namely, the fixed exchange rate, the flexible exchange rate and the basket currency systems are compared both theoretically and empirically. Different policy objective functions are introduced in order to obtain optimal exchange rate policy. Furthermore, the optimal weight for the basket currency system is obtained in order to minimize the objective loss function. Both static and dynamic models are compared by use of Thai data. The major conclusions obtained here are as follows; (i) The weight for the basket currency system is different based on the policy objectives. (ii) The trade weight is optimal only when the policy objective is the current account stability and the case where both export and import elasticity are identical. (iii) In an empirical analysis, the Thai macro econometric model is estimated. By use of Thai data, it is shown that the basket currency system yields the minimum value of the loss function when the optimal basket weight is chosen. (iv) In the dynamic model, the same conclusion is reached, namely the currency basket yields the minimum value for the loss function. There are some restrictions in the model. The model deals with three countries, namely US, Japan and Thailand. The theoretical model is based on one small open economy with two large countries. The model does not deal with the case of multiple small countries. The structure of this paper is as follows. yoshino@econ.keio.ac.jp kaji@econ.keio.ac.jp dk995208@mita.cc.keio.ac.jp 41

2 The section 2 compares three exchange rate regimes by static analysis and calculate the optimal weights under the basket-peg regime. It is shown that the optimal values of weights varies depending on policy objectives. Thus the common practice of choosing trade weights as weights in a currency-basket is not always optimal. The section 3 conduct the dynamic analysis. We introduce the aggregate supply function into the model and consider the case in which the price is explicitly shown in the loss function. The large gap pointed by Rockett and Nsouli (1977) is modeled by Dornbusch(1976) as an overshooting of exchange rate. Our model is based on the Dornbusch model and consider the overshooting under the flexible regime. From the result of our empirical analysis, it takes much time from the initial equilibrium to the next equilibrium under the fixed regime and the loss value becomes larger. However, the basket-peg regime with the optimal weights can minimize the loss value. The section 4 gives the conclusion. 2. Comparative Static Analysis In this section, we conduct the static analysis using the macro economic model of goods and financial markets. The main results from this section is as follows. Firstly, the optimal choice of exchange rate regime for a small open economy depends on its policy objectives. However, the basket-peg can minimize the loss value under the any loss function by moving the weights. Secondly, when adopting a basket-peg, the optimal weights in the basket also depends on its policy objective. Thirdly, the common practice of choosing trade weights as basket weighs is optimal only under special conditions A macroeconomic model of goods and financial markets As in Yoshino and Fujimaru!J1999!K, ours is a general equilibrium model comprising five markets; those for -!domestic money, -"domestic bonds, -# assets denominated in dollars, -$ assets denominated in yen, and -% goods and services. Our analysis differs from Yoshino and Fujimaru (1999) in the following ways. We (1) adopt the stock-equilibrium approach to exchange rate determination, (2) explicitly take exchange risk into account and (3) analyze the relationship between 8 For the details, see Yoshino, Kaji and Suzuki (2000) 42

3 the policy objectives and exchange rate regimes. There are three sectors: -! the public sector (the government and the central bank), -" the private sector, and -# the foreign sector. There are also three countries: the USA, Japan and Thailand. We assume that Thailand is a small country. Among other things, this means that the yen-dollar exchange rate is exogenous to Thailand. Thus the bahts-yen rate is endogenously determined as follows. bahts/yen = bahts/dollar * dollar/yen Putting the dollar denominated assets together with yen dominated assets in one equation, the equilibrium conditions for financial and goods markets can be shown as follows. 9 (1) The equilibrium condition for domestic money is The left-hand side is the real value of the stock of money supplied. The right-hand side is the real value of money demand. Money demand depends on the domestic rate of interest, rates of interest on dollar and yen denominated assets, GDP and real value of stock of assets. (2) The equilibrium condition for domestic bonds is The left-hand side is the real value of the stock of domestic bonds supplied by the government. The right-hand side is the real value of demand for domestic bonds. Because this is a small country, foreigners do not hold domestic bonds. Domestic demand for domestic bonds depends on its own return, rates of interest on dollar- and yen- denominated assets, GDP and the real value of stock of assets. The last two terms on the right-hand side show that demand for domestic bonds increase with the increase in foreign exchange risk. 9 All partial derivatives are defined to be positive. 43

4 (3) The equilibrium condition for foreign bonds is The left-hand side is the real value of the stock of dollar- and yen- denominated bonds supplied. The right-hand side is the real value of demand for such bonds. This time, the demand comes from the private and public sectors at home. Domestic demand for dollar- and yen- bonds depends on the returns as well as exchange risk on the respective bonds, domestic rate of interest, GDP and real value of stock of assets. The demand for these bonds decline with the increase in foreign exchange risk. (4) The equilibrium condition in the goods and services market is This is the IS equation. Consumption depends on GDP, investment depends on the rate of interest. Net exports depend on the bahts-dollar rate, bahtsyen rate, US GDP, Japanese GDP, domestic GDP and exchange risk. (5) The real wealth held by private sector The domestic private sector holds domestic money, domestic bonds, dollar-bonds and yen-bonds. This equation is an identity that defines the stock of nominal assets, rather than an equilibrium condition. (6) The exchange rate The one of three exchange rates is not independent. Thus Bahts/yen rate can be derived as fellows. (7) The currency basket The basket we consider is a weighted average of the 44

5 bahts-dollar rate and the bahts-yen rate. That is, Where ν is the basket weight on the bahts-dollar rate. 2.2 Objective functions and the optimal basket weights In this section we ask which among the basket-peg, dollar-peg and floating exchange rate regimes result in the lowest value of the different loss functions corresponding to the different policy objectives 10. we compare the value of the different loss functions when there is the external shock or dollar/yen exchange rate change. We also calculate the optimal weights in a currency basket. Due to Walras law in the asset market, only two out of the three equilibrium conditions (1) to (3) in section 2.1 are independent. Thus we eliminate the equilibrium condition for domestic money and derive the reduced forms of three endogenous variables. Two of the three endogenous variables, which are GDP and the domestic interest rate, are common to all the analyses below. The remaining endogenous variable will differ depending on the type of exchange rate regime we consider. Under floating exchange rates, this endogenous variable is the bahts-dollar rate. Under the dollar-peg regime and the basket-peg regime, it is the stock of dollar denominated assets held publicly (foreign exchange reserves). We drive the reduced forms of these endogenous variables and conduct the analyses below Trade balance equilibrium as the policy objective We begin with a special case. In analyses of currency baskets, often the trade weights are used as the weights on the currencies in the basket. In fact, Gan Yeo and Lim (1999) find that Singapore uses trade weights as the weights in its 10 See Yoshino Kaji and Suzuki(2000) 11 The reduced forms are driven in terms of the exogenous variable of dollar/yen exchange rate. Other exogenous variables are considered to be constant (=0). In other words, we analyze the case in which the dollar/yen exchange rate is moved from its equilibrium value in the following subsections. 45

6 currency basket. But as we show in the analyses below, optimal currency weights are often complicated functions of partial derivatives. The purpose of this subsection is to show one set of sufficient conditions for trade weights to be indeed the optimal weights in a currency basket, and thereby emphasize how special such a case is. Assume that the small country (Thailand) cares only about its trade. The country s authority s loss function can be described as where BT is Thailand s total trade (exports plus imports) with the rest of the world, and BT is its target value. Thailand is assumed to trade only with the USA and Japan, whose respective trade weights are ω1 and ω2. For reasons that become clear shortly, we assume that Thailand s trade depends only on nominal exchange rates, and that the elasticity of total trade with respect to the nominal exchange rate takes the same value _ for trade with USA and trade with Japan. Then we have In the following subsections, we compare the performance of different exchange rate regimes in minimizing loss functions such as equation (8). But here, we consider only one exchange rate regime, the basket-peg, because the purpose is to show a set of conditions under which the trade weights turn out to be the optimal currency weights in the basket. From the equation (6) and (7), bahts/dollar and bahts/yen rate can be derived as e = α- (1- ν) yen e $ /, yen yen e = α+v e $ /. Substituting those into equation (9) we have Substituting this into the objective function (8), the.rst order condition for L minimization with respect to ν or = 0 gives us v 46

7 indicating that the optimal weights are indeed the trade weights. This case is definitely a special case, which satisfies the following conditions; -! the country s objective is to minimize fluctuations in the value of total trade, -"exports and imports depend only on nominal exchange rates and -# the elasticity of total trade with respect to the nominal exchange rate is the same for all trade-partner countries whose currencies are in the basket, -$there are only two trading partners whose currencies are the only two currencies in the basket, and -%the shock to the economy takes the form of a change in the exchange rate between the two currencies in the basket. It can be said that it is unlikely that those conditions are met, and trade weights are unlikely to be an optimal weights. These are not necessary conditions, and there be other cases in which trade weights are optimal as currency weights. However, the following analyses show that, under several different policy goals, the optimal values for currency weights are functions of partial derivatives which would not in general be equal to trade weights GDP stability as the policy objective Now we begin comparing different exchange rate regimes for each policy objective. Consider the case where the Thai government wants to minimize fluctuations in GDP when there is the external shock in dollar/yen exchange rate. The loss function which the authorities minimize is Substituting the reduced form of GDP derived from the equation (1) to (7) and calculating the optimal weights which minimize this loss function, the first order condition L/ ν = 0 gives us where, yen e $ / yen - e $ /!". e*- e * show, respectively, the initial change in the yen-dollar exchange rate and the induced increase in exchange risk. 6 47

8 We can see that the optimal weights depend on the following partial derivatives: (i) response of domestic bond demand to changes in the domestic interest rate, (ii) response of domestic bond demand to changes in the returns on foreign bonds, (iii) response of domestic bond demand to changes in real wealth, (iv) response of domestic bond demand to changes in exchange risk, (v) response of domestic investment to changes in the domestic interest rate, (vi) response of demand for domestic product to changes in real exchange rates, (vii) response of demand for domestic product to changes in real exchange rates Current account stability as the policy objective Some countries choose current account stability as their policy objective. In that case, the objective function is The optimal weight in the basket is derived as the subsection 2.2.2, where, We can see that the optimal weight depends on the following. (i) response of domestic bond demand to changes in the domestic interest rate, (ii) response of domestic bond demand to changes in the returns on foreign bonds, (iii) response of domestic bond demand to changes in real wealth, (iv) response of domestic bond demand to changes in exchange risk, (v) response of domestic bond demand to changes in GDP, (vi) response of domestic investment to changes in the domestic interest rate, (vii) response of demand for domestic product to changes in real exchange rates, (viii) response of demand for domestic product to changes in exchange risk, (ix) response of demand for domestic product to changes in GDP, (x) response of foreign bond demand to changes in the domestic interest rate, (xi) response of foreign bond demand to changes in the rate of return on foreign 48

9 investment, (xii) response of foreign bond demand to changes in GDP, (xiii) response of domestic bond demand to changes in real wealth Exchange rate stability as the policy objective We assume that the policy goal is to stabilize the bahts-dollar rate. The objective function is Evidently, the best choice is the regime that fixes the bahts-dollar rate at a constant level or the dollar peg. When adopting the basket-peg, the optimal weight is obtained by solving the first-order condition L v = 0, which gives us ν = 1. This means dollar peg regime. 2.3 Empirical analysis using Thai data We use Thailand s annual data from 1971 to 1999, and the Instrumental Variables Method to estimate the equations in the section 2.1. The results are shown in Table 1. Because the exogenous variables are different according to whether floating or fixed exchange rates are adopted, we have two sets of results. The functions we estimated are the consumption function, the investment function, the export function (to the USA and to Japan), the import function (from the USA and from Japan), the demand function for domestic bonds, the demand function for foreign bonds, the demand function for money. The first column of the table shows the explanatory variables. The second and third columns show the coefficients. The t-values are shown in parentheses and two asterisks on t-values indicate the level of significance is 1%, one asterisk indicates it is 5%. Thailand had fixed exchange rates against the US dollar, but has been devaluing since To take this fact into account, we introduced a coefficient dummy on the exchange rate for the year 1981 and 1984 (when there is a large devaluation.). We also introduced a constant dummy variable in estimating the investment function for 1986 and 1987, because there was a marked drop in investment during these years. For exchange risk, we used the variance of monthly exchange rate data as proxy. Using the estimated coefficients, we calculated the basket weights that 49

10 minimize the loss functions corresponding to the three different policy goals in the section 2.2. The result is shown in Table 2. Table 3 shows the values of loss functions under the floating, dollar-peg and basket-peg regimes calculated by using the estimated coefficients. The loss values under the basket-peg is calculated by using both the trade weights and the optimal weights in Table 2. In the former case, we used Thai data to find that is equal to 0.4. As it can be seen from Table 2, the optimal weights depend on the policy objectives and none of the optimal weights equal to the trade weights (0.4). Comparing the loss value in Table 3, the order of optimality is 1. basketpeg, 2. dollar-peg, 3. flexible under the loss function of GDP and current 8 account, 1. dollar-peg (or the basket with the weight 1), 2. flexible under the loss function of bahts/dollar exchange rate. Table 3 also indicate that using trade-weights as basket-weights under the basket-peg leads to higher losses and here again we can also see that the trade weights is not optimal. We used the variance of monthly exchange rate data for exchange risk in this estimation. However, the result shows that the coefficient of this exchange risk is ignorable. Thus the reason of higher loss under the floating is the coefficient of bahts/dollar exchange rate rather than exchange risk. However, it is worth to note that our estimation is based on the data in the period Thailand adapted the fixed regime. Thus it is not reliable to use these estimation for floating regime. It is possible that the coefficient of exchange risk become larger in the floating regime, and in such a case, the loss of floating regime might be much larger. 50

11 51

12 52

13 53

14 3. Dynamics analysis 54

15 In this section, we conduct the dynamic analysis. We introduce the aggregate supply function into the model and consider the case in which the price is explicitly shown in the loss function. Specifically, we analyze the GDP and the price movement from the initial equilibrium value to the next equilibrium value when there is the external shock or dollar/yen exchange rate change. Our model takes into account of the exchange rate overshooting under the flexible regime. From the result of our empirical analysis, it can be seen that it takes much time for the objective variables to move from the initial equilibrium to the next equilibrium under the fixed regime and the loss value becomes larger. However, the basket-peg regime with the optimal weights can minimize the loss value. 3.1 Model There are three countries: the USA, Japan and Thailand. We assume that Thailand is a small country. Among other things, this means that the yendollar exchange rate is exogenous to Thailand. We assume that assets are imperfectly substituted between Thailand and foreign countries whereas US assets and Japanese assets are indifferent for Thai investors. 12 Thus the equation of interest rate parity is where, the fourth term shows the risk premium. The depreciation of home currency increase the stock of foreign assets held by domestic investors and decrease home interest rate. The equilibrium condition for home money market is Assume that demand for goods depend only on real exchange rates. Thus Since the one of three exchange rates is not independent, the bahts/yen exchange 12 55

16 rate can be induced as below. The inflation depends on the excess demand for goods and the expected inflation, where the second terms shows the expected inflation. Among the above variables, p e, y, i *,p*, yen p and yen e $ / are common exogenous variables under any exchange rate regimes. We assume that those exogenous variables except dollar/yen rate is constant (=0) and conduct the analyses below. 3.2 Floating exchange rate regime Under the floating regime, money (mt!kbecomes the exogenous and exchange rate (et) becomes endogenous. From the equation (1) to (7), we can drive two difference equations as below. Since pt+1 = pt and et+1 = et in the long-run equilibrium, we can derive the long-run equilibrium values of price, p and exchange rate, e. Checking the characteristic roots of above difference equations, this system has 56

17 the saddle path stability.7 The saddle path is where, Since 0 < ω2 <1, 13 it can be shown that β > 0 when ω2 > 1 - ψ(δ + θ). That is, the coefficient of Saddle path is positive in this case. Thus when the price is above its equilibrium value, the exchange rate is above its equilibrium value, overshooting the equilibrium value. Now assume that dollar/yen rate moves from its initial equilibrium value (=0) to yen e ˆ $ /. From the equation (8) (9), the initial equilibrium value of the price and the exchange regime are p o = e o = 0 and the new equilibrium values after the dollar/yen change are The new saddle path is 13 See appendix 1 57

18 Now assume the agents are rational and can always be on the saddle path. Thus the economy can jump on this new saddle path. Also assume that the price is sticky in the short-run and does not move from the initial value. Thus at time 0 (the short-run period after the dollar/yen change), p0 = 0. Substituting this into the new saddle path, the exchange rate at time 0 is which shows that the exchange rate under-shoots its new equilibrium value. Now using p0 and e0 as the initial values, time t values of the price and exchange rate can be derived as follows. 14 Substituting those equations into the equation (3) yields the time t value of GDP as 3.3 Dollar-peg regime Under the fixed regime, the exchange rate (et) becomes exogenous and assumed to be e = 0. Money supply mt becomes endogenous. Risk premium now depends on the expected devaluation of home currency and we assume this expectation is exogenous. Solving the model in 3.1 for the price and the money supply, Since pt+1 = pt in the long-run equilibrium, the long-run equilibrium values of the 14 See appendix1 58

19 price and the money supply are Now assume again that dollar/yen rate moves from its initial equilibrium value yen (=0) to e ˆ $ /. Since the price is sticky in the short run, p0 = 0 at the time 0. Using this time 0 value as the initial value, the difference equation of (34) can be solved as Substituting this equation into (3), we can obtain the time t value of GDP. 3.4 Basket peg regime As basket peg is one of the fixed regimes, endogenous and exogenous variables are same as dollar peg regime. As the section 2, the basket we consider is a weighted average of the bahts-dollar rate and the bahts-yen rate. That is, From this equation and the equation (4), we can obtain two equations of exchange rate. Using those two equations of exchange rates, solve the model for price and money supply. 59

20 The long-run equilibrium value is derived as usual, As before, assume the dollar/yen rate moved from its initial value to difference equation (43) can be solved as usual. e ˆ $ / yen. The Substituting this into the equation (4), we can obtain the time-t value of GDP. 3.5 Loss functions In this section, we clarify the difference in the way the policy objective variables are affected by an exogenous shock under floating, dollar-peg and basket-peg regimes. The policy objectives we consider here are the stability in GDP and price. The loss functions clarified in this section is actually calculated in the next section by using the estimated values and compared GDP Assume that the government aims to reduce the distance between the initial equilibrium to the new equilibrium when there is external shock, which is the dollar/yen rate change. The government s loss function can be described as below. 60

21 where, βd is the discount rate. For simplicity, we assume βd = 1. Now the loss function under the floating, the dollar-peg and the basket-peg can be introduced from (33)(39) and (48). 3.6 Price Now consider the case in which the price is the government s objective variable. The government s loss function is Loss function under the three regimes can be derived from (31)(38)(47). 61

22 3.6.1 Price and GDP Consider the case in which the government aims to stabilize both GDP and Price. The loss function can be set as where μ1 and μ2 are policy weights. The loss functions under the three regimes can be derived as 3.7 Empirical analysis We use Thailand s quarterly data from 1990:1 to 2000:4, and the Instrumental Variables Method to estimate the equations in the section 3.1. The results are shown in Table 4. Because the exogenous variables are different according to whether floating or fixed exchange rates are adopted, we have two sets of results. Thailand had fixed exchange rates against the US dollar, but has floated it since 1997:3. To take this fact into account, we introduced a coefficient dummy on the exchange rate for the period before 1997:3 and after that. We use the coefficients shown before this period for fixed regimes and those after this period for floating regime. The estimated result show that ω2 > 1- ψ(δ+θ) does not hold and thus the exchange rate does not overshoot. However, since the estimated term of flexible exchange rate is quite short, it can be said that it is fragile to believe this 62

23 estimation for floating regime. Thus the possibility of overshooting cannot be eliminated. Table 5 shows the value of loss function calculated by using estimated values in Table 4. The policy weights and basket weights are set as 0.5:0.5. It can be seen from this table that the loss value is the smallest under the floating and the largest under the dollar-peg in the any case of loss functions. This is because firstly, the initial change in GDP is smaller under the floating (because the overshooting does not occur) and secondly, the distance between the initial value and the next equilibrium value of price is smaller under the floating. In addition, the economy settle in the new equilibrium faster in the floating regime. Regarding to Basket peg, the loss is always less that those under the dollar-peg even with weights of 0.5. However, as expected, if the optimal weights are used as basket weights, we can minimize the loss. The optimal weights is 63

24 4. Conclusion In this paper, we compared the relative superiority of floating, the dollar-peg ad the basket-peg regime in a small open economy under several different policy objective. We have shown which exchange rate regime can minimize the value of loss function under the dollar/yen exchange rate change. In the section 2, we compare three regimes by the comparative static analysis and introduced the optimal weights in the currency basket. It has been seen both analytically and empirically that the optimal values of weights varies depending on policy objectives and the common practice of choosing trade weights as weights in a currency-basket is not always optimal. Our empirical analysis also showed that the basket regime can minimize the loss under any loss functions. The loss was always larger under the floating regime than the dollar-peg. In the section 3, we conducted the dynamic analysis introducing the aggregate supply function into the model. We analyze the GDP and the price movement from the initial equilibrium value to the next equilibrium value when there is the external shock or dollar/yen exchange rate change. Our empirical result suggests that the loss value is the smallest under the floating and the largest under the dollar-peg in the any case of loss functions. The fact that the overshooting of the exchange rate did not occur from our estimated coefficients may be the reason of this small loss under the floating. The basket-peg with the optimal weights can minimize the loss in this case as well. In conclusion, it can be said that the optimal choice of exchange rate regimes depend on the policy objectives. However, since we can minimize the loss function by moving the basket weights, the basket-peg regime seems to be desirable in both short-run and long-run. 5. Appendices Appendix 1 The characteristic roots of difference equations (7) and (8) can be derived by solving the equation below. 64

25 Solving this equation, Since, both ω1 and ω2 are real and distinct. Then it is easily found that ω1 > 1. Now, when φ- ψ > 0, and thus ω2 > 0. Also since, 0 < ω2 < 1. Thus the system is described by the unique stable saddle path. The solution for the original variable #p and e are derived as 65

26 From the equations above, the saddle path is where, 66

27 5.0.2 Appendix 2 Our notation for variables are as follows. All variables except for the rates of interest are natural logarithm values of the originals. 67

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