I. Introduction

“In a world where exchange rates can fluctuate by 2 percent per day and 20 percent per year, economists are asked to evaluate the causes and consequences of such fluctuations. If we are to go beyond the Panglossian response that ‘the market knows best,’ we need some concept of an equilibrium rate of exchange as a standard against which to measure actual exchange rate changes.” (Black (1994), p. 279). The second amendment of the IMF’s Articles of Agreement (1977) states that the Fund shall exercise firm surveillance over the international monetary system and members’ exchange rate policies. To do so requires a consistent theoretical framework, which is empirically implementable, to explain the fundamental determinants of the evolution of the equilibrium real effective exchange rate in the medium to longer run.

This paper attempts to provide such a framework. It focusses on the real exchange rate of the U.S. dollar relative to the currencies the other G-7 countries. In the theoretical framework adopted here the fundamental determinants of the equilibrium real exchange rate are measures of productivity and thrift in the G-7 countries. The equilibrium real exchange rate generated by these fundamentals, when short-term speculative and cyclical factors are ignored, is referred to as the natural real exchange rate (NATREX). Section II summarizes the stylized facts and explains why there is a need for a new model to explain real exchange rates. Section III explains the NATREX approach, discusses the structural equations, and relates the NATREX equations to other optimization approaches. Section IV describes the solution of the model. There is a medium-run solution when foreign debt and capital are given, and its trajectory to the longer run when debt and capital evolve endogenously. This explains why the real exchange rate is not stationary. Section V describes the data and the econometric results and Section VI shows how the NATREX explains the econometric results. Section VII shows (a) to what extent the actual real value of the U.S. dollar deviates from its medium-run and longer-run equilibrium values, and (b) what were the factors producing the medium- to the longer-run trends in the real value of the U.S. dollar. The NATREX analysis thus provides a response to the issues posed in the opening paragraph.

The NATREX is a benchmark for the medium- to longer-run equilibrium real exchange rate. We use the NATREX to estimate “misalignments” and to infer whether the observed real exchange rate movements are transitory or longer lasting. The NATREX, unlike Williamson’s (1994) FEER or the DEER of Bayoumi et al. (1994), is a positive rather than a normative concept.

The NATREX is the real exchange rate which equates the current account to ex ante social saving less social investment generated by the fundamentals, productivity and thrift, when the U.S. fundamentals are corrected for cyclical variations in the rate of capacity utilization and incomplete adjustments in asset markets. Cyclical elements represented by the variation in the rate of capacity utilization from its stationary mean, or deviations of the unemployment rate from the equilibrium rate of unemployment, are not considered among the sustainable fundamentals because they average out to zero. Speculative capital flows and changes in reserves are not considered in the determination of the NATREX because they are not sustainable, and have only short-run, but not medium-run effects on the real exchange rate. The excess of saving over investment, under these conditions, represents a capital outflow. The NATREX equates the current account to the nonspeculative capital outflow, evaluated at capacity output and when there is a complete adjustment in asset markets.

The real exchange rate R(t) used here is the real effective exchange rate shown in equation (1) below, which is measured by the ratio of normalized unit labor costs, in a common currency, in the main tradable sector (manufacturing) in the United States relative to the other G-7 countries. The nominal effective exchange rate is denoted by N(t), w(t) represents U. S. normalized unit labor costs and w’(t)is the counterpart in the rest of the G-7. A prime refers to the foreign variable. A rise in the exchange rate signifies an appreciation of the U.S. dollar. Equation (1) below thus defines the actual real exchange rate.

We show below that the NATREX at any time is a function of the capital intensity, k(t), the foreign debt intensity, F(t), and the fundamentals denoted by the vector Z(t) of productivity and thrift in the United States and the other G-7 countries. The NATREX is represented by R[k(t), F(t); Z(t)]. The actual real exchange rate, R(t), can be decomposed into three parts in equation (1a).

The first term, which is denoted by e(t)=[R(t) - R[k(t), F(t); Z(t)], refers to the transitory short-term factors. It is the deviation of the actual real exchange rate R(t) from the NATREX. The deviation results from speculative forces, cyclical factors or from incomplete adjustments in asset markets. ^2/ Our hypothesis is that the expectation of this deviation is zero, i.e., E[e]=0, so that the real exchange rate converges to the NATREX.

The fundamentals of productivity and social thrift, denoted by Z(t), affect the NATREX directly, given endogenous capital and foreign debt, and also affect the rate of capital formation and the current account. The induced evolution of capital and debt produce a trajectory of the NATREX to a steady state R^*(Z(t)) conditional upon the fundamentals. The trajectory of the NATREX to the steady state is the second term, [R[k(t), F(t); Z(t) - R^*(Z(t)], and the steady state is the third term, R^*[Z(t)]. The actual real exchange rate moves over the medium run to the NATREX, and the latter moves over the long run to the steady state value.

The NATREX model does not address itself to the question of how much of the variation in the real exchange rate will occur through variations in the nominal exchange rate and how much through relative unit labor costs. The deviation e(t) representing the short-run speculative and cyclical factors will go to zero but the model does not specify whether it will do so with a change in nominal exchange rates or from changes in nominal unit labor costs via differential wage inflation.

II. What Is To Be Explained

1. Stylized facts ^3/

There are several stylized facts that motivate the construction of the NATREX model. They explain why we do not use either the PPP hypothesis, the model with monetary dynamics and rational expectations, or the representative agent-intertemporal optimization model to determine what is the equilibrium real exchange rate. Many of these stylized facts are described in terms of their stationarity properties. A stationary variable is defined as one which reverts to a constant mean, i.e., whose mean and variance are finite and are independent of time. Ten stylized facts are considered below:

a. The real effective exchange rate of the U.S. dollar relative to the other G-7 currencies (USREUG7 in Figure 1), as well as the overall U.S. real effective exchange rate (USREU), are not stationary, as shown by the Dickey-Fuller (DF) and the augmented Dickey-Fuller (ADF) statistics in Table 1. Figure 1 plots, in normalized form, the real effective exchange rate (USREUG7), the nominal effective exchange rate (USNEUG7), and purchasing power parity (PPP) defined as the ratio of the G-7/U.S. GDP deflators. It is seen that the real and nominal rates move together and that the nominal value of the dollar is not related to the PPP during the floating rate period.

United States: Nominal and Real Effective Exchange Rate and Purchasing Power Parity

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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United States: Nominal and Real Effective Exchange Rate and Purchasing Power Parity

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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United States: Nominal and Real Effective Exchange Rate and Purchasing Power Parity

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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Table 1.

Description of the Data, Stationarity or Nonstationarity Properties of Basic Variables: DF/ADF Statistics

Note: MacKinnon critical value, significant at 5 percent (^*); 1 percent (^**). The C or N indicates whether a constant (C) was or was not (N) used, and the integer refers to the number of lags. Variables, and line in IFS: four-quarter moving averages are denoted by prefix MA, and are used for USDISRAT (MADISRAT) and USGROWTH (MAUSGROWTH). (i) The index of time preference was derived as follows: call DISRAT or time preference the sum of total private (US96fc) plus public consumption (US91ffc-US93gfc) to GDP(US99bc). A four-quarter moving average is MADISRAT. For the G-7, the time preference G7DISRAT is government expenditures national income accounts plus private consumption divided by GDP. The four quarter moving average is MAG7DIS. (ii) The growth variables were growth of real GDP over the past year. For the United States we used a four-quarter moving average (MAUSGROW). (iii) The total short-term capital flow is US77gd, the component involving bank liabilities, called deposit money banks, is US77gbd. (iii) portfolio plus direct investment is (US77bbd + US77bad). (iv) The terms of trade are US74/US75. The foreign interest rate and price deflators refer to the G-7 less the United States. The foreign variables from national income accounts refer to all the G-7.

Table 1.

Description of the Data, Stationarity or Nonstationarity Properties of Basic Variables: DF/ADF Statistics

		ADF/DF
Variable		I (1)	I (0)
(1975.1-1993.3)
Real exchange rate (USREUG7)		(C, 0) = -0.97
U.S.-G-6 real long-term interest			(N, 0) = -2.0*
U.S. time preference: moving average (MADISRAT)		(C, 2) = -1.31
U.S. growth moving average (MAUSGROW)			(C, 2) = -3.8**
G-7 time preference moving average (MAG7DIS)			(C, 2) = -2.85
G-7 growth moving average (MAG7GR0W)			(C, 1) = -3.87**
	current account/GDP	(C, 1) = -1.97
U.S. net foreign assets/GNP		(C, 1) = -1.13
U.S. rate of capacity utilization (USCUR)			(C, 1) = -3.39**
(1973.1 - 1994.1)
Short-term capital flows total: (US77gd)			(C, 1) = -3.2**
	deposit money banks		(N, 1) = -4.4**
Portfolio plus direct investment:		(C, 1) = -1.76
	U.S. terms of trade		(C, 1) = -3.27**
Real effective exchange rate (USREU)		(C, 1) = -1-37

Note: MacKinnon critical value, significant at 5 percent (^*); 1 percent (^**). The C or N indicates whether a constant (C) was or was not (N) used, and the integer refers to the number of lags. Variables, and line in IFS: four-quarter moving averages are denoted by prefix MA, and are used for USDISRAT (MADISRAT) and USGROWTH (MAUSGROWTH). (i) The index of time preference was derived as follows: call DISRAT or time preference the sum of total private (US96fc) plus public consumption (US91ffc-US93gfc) to GDP(US99bc). A four-quarter moving average is MADISRAT. For the G-7, the time preference G7DISRAT is government expenditures national income accounts plus private consumption divided by GDP. The four quarter moving average is MAG7DIS. (ii) The growth variables were growth of real GDP over the past year. For the United States we used a four-quarter moving average (MAUSGROW). (iii) The total short-term capital flow is US77gd, the component involving bank liabilities, called deposit money banks, is US77gbd. (iii) portfolio plus direct investment is (US77bbd + US77bad). (iv) The terms of trade are US74/US75. The foreign interest rate and price deflators refer to the G-7 less the United States. The foreign variables from national income accounts refer to all the G-7.

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Table 1.

Description of the Data, Stationarity or Nonstationarity Properties of Basic Variables: DF/ADF Statistics

		ADF/DF
Variable		I (1)	I (0)
(1975.1-1993.3)
Real exchange rate (USREUG7)		(C, 0) = -0.97
U.S.-G-6 real long-term interest			(N, 0) = -2.0*
U.S. time preference: moving average (MADISRAT)		(C, 2) = -1.31
U.S. growth moving average (MAUSGROW)			(C, 2) = -3.8**
G-7 time preference moving average (MAG7DIS)			(C, 2) = -2.85
G-7 growth moving average (MAG7GR0W)			(C, 1) = -3.87**
	current account/GDP	(C, 1) = -1.97
U.S. net foreign assets/GNP		(C, 1) = -1.13
U.S. rate of capacity utilization (USCUR)			(C, 1) = -3.39**
(1973.1 - 1994.1)
Short-term capital flows total: (US77gd)			(C, 1) = -3.2**
	deposit money banks		(N, 1) = -4.4**
Portfolio plus direct investment:		(C, 1) = -1.76
	U.S. terms of trade		(C, 1) = -3.27**
Real effective exchange rate (USREU)		(C, 1) = -1-37

Note: MacKinnon critical value, significant at 5 percent (^*); 1 percent (^**). The C or N indicates whether a constant (C) was or was not (N) used, and the integer refers to the number of lags. Variables, and line in IFS: four-quarter moving averages are denoted by prefix MA, and are used for USDISRAT (MADISRAT) and USGROWTH (MAUSGROWTH). (i) The index of time preference was derived as follows: call DISRAT or time preference the sum of total private (US96fc) plus public consumption (US91ffc-US93gfc) to GDP(US99bc). A four-quarter moving average is MADISRAT. For the G-7, the time preference G7DISRAT is government expenditures national income accounts plus private consumption divided by GDP. The four quarter moving average is MAG7DIS. (ii) The growth variables were growth of real GDP over the past year. For the United States we used a four-quarter moving average (MAUSGROW). (iii) The total short-term capital flow is US77gd, the component involving bank liabilities, called deposit money banks, is US77gbd. (iii) portfolio plus direct investment is (US77bbd + US77bad). (iv) The terms of trade are US74/US75. The foreign interest rate and price deflators refer to the G-7 less the United States. The foreign variables from national income accounts refer to all the G-7.

b. The U.S. real long-term interest rate (USRLT) and the real long-term interest rate in the rest of the G-7 (G6RLT) converge to each other. These real interest rates are defined as the nominal rate on long-term bonds less the change in the GDP deflator over the previous four quarters (see Figure 2). The real long-term interest rate differential (USRLT-G6RLT) is stationary with an expected value of zero.

Long-Term Real Interest Rates: United States vs. Other G-7 Countries

(In percent)

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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Long-Term Real Interest Rates: United States vs. Other G-7 Countries

(In percent)

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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Long-Term Real Interest Rates: United States vs. Other G-7 Countries

(In percent)

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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c. The ratio of net foreign assets to GNP is not stationary. ^4/ The net foreign asset position is defined as total U.S. investment abroad less total foreign investment in the United States. The United States went from a creditor country with net foreign assets of 6.56 percent of GNP in 1950 and 10.66 percent in 1970, to a debtor position of -7.66 percent in 1990.

d. The ratio of the U.S. current account/GNP, or a four-quarter moving average of the current account/GNP, is not stationary. This nonstationarity is consistent with the stylized fact that countries vary their net creditor/debtor positions.

e. As found by Faruqee (1995), the net foreign asset position of the United States appears to be a significant determinant of the U.S. real exchange rate.

f. U.S. short-term capital flows are stationary with an expected value of zero. We use two measures of these flows. One is the balance of payments component described in the IFS as “other capital, deposit money banks” (US77gbd), which represents private capital flows reported by banks, and the second is the total short-term capital flow “other capital nie” (US77gd). ^5/ Both are stationary and the expected value of the deposit money bank flow is zero.

g. The sum of portfolio investment (US77bbd) and direct investment (US77bad), and as a proportion of GNP (US99ac) are not stationary; their means are not constant over time.

h. During the period 1973:1-1994:1, the U.S. terms of trade were stationary, whereas the U.S. real effective exchange rate (USREU) was not stationary. Hence, the U.S. terms of trade (export prices/import prices) behave differently over time than the U.S. real effective exchange rate.

i. The U.S. ratio of private consumption plus total government consumption expenditure to GDP is not stationary. This ratio is referred to as the U.S. rate time of preference and a four-quarter moving average of this variable is labelled MADISRAT in Table 1. It does not have a mean that is independent of time during the period 1973:1-1994:2. The corresponding ratio in the other G-7 countries, called G-6 time preference and labelled MAG6DIS, is also not stationary.

j. The nominal deutsche mark/U.S. dollar is not cointegrated with the ratio of M3 to output in Germany divided by the ratio of M2 to output in the United States. ^6/

III. The NATREX Approach

Our optimization and structural equations are more general than the standard approach. First, we have independent saving and investment equations. There is no “representative agent” that describes a country, or whose decisions at time zero describe the pattern of consumption and saving over an infinite horizon. There is a market mechanism operating via the real exchange rate, that produces the ex post equality between social saving and the sum of investment and the current account. The “representative agent” models have no such market mechanism. Second, our optimization is based upon the view that agents know that they do not and cannot know the evolution of the fundamentals and do not have perfect knowledge of the structural equations of the system. As the real exchange rate and the underlying fundamentals vector Z are not stationary, as shown in Table 1, one cannot predict the values of Z(t) in the future. At each point in time, our agents use all available information efficiently and there is a feedback control mechanism which ensures that the economy converges to the unknown and changing optimal steady state which depends upon the fundamentals. We explain the evolution of the debtor/creditor position over time to a dynamically stable steady state, where the trade balance is sufficient to pay the interest on the debt. When the ratio of net foreign assets/GDP converges to a constant steady state value, the present value of the steady state net foreign assets/GDP goes to zero as time goes to infinity. This requirement will be the NATREX “intertemporal budget constraint.”

1. The structural equations

Equations (2)-(7) below describe the NATREX model for large economies. ^10/ The endogenous variables are defined as follows, where a prime refers to the foreign country: R=real effective exchange rate, k (k’) = capital intensity; F = foreign debt intensity (positive for debtor, negative for creditor), r (r’) - real domestic long-term interest rate, C = social consumption per unit of effective labor and S = social saving/effective labor, y = y (k; Z) capacity output/effective labor. Investment I is dk/dt. The current account deficit -CA=Df/dt, is the rate of change of the foreign debt. ^11/ All variables except the exchange rate, interest rate and prices are measured per unit of effective labor. The exogenous variables are Z, the fundamentals: k’ = G-6 capital intensity, productivity of capital is (u, u’), index of time preference is (g, g’).

a. Internal equilibrium in the goods market

In the NATREX model, investment less social saving (I-S) determines the nonspeculative capital flow (L). Investment depends upon the Keynes-Tobin q-ratio. Social saving depends upon wealth and time preference. In turn, investment less saving is determined by the capital intensity k, the debt intensity F, and the fundamentals Z. The equilibrium real exchange rate, R, is determined such that the current account CA = N(R, k, F; Z), plus the nonspeculative capital flow L = (I-S)(k, F; Z) sum to zero, at capacity output, as shown by equation (2). We ignore speculative factors in the determination of medium to long-run equilibrium. ^12/

We write this equilibrium condition equating the current and capital accounts separately for the United States in equation (2) and for the rest of the G-7 in equation (3). The foreign variables are denoted by a prime.

$\begin{array}{cc}\left(I-S\right)\left(k,F;Z\right)+N\left(R,k\text{,}F;Z\right)\text{= 0}& \left(2\right)\end{array}$

$\begin{array}{cc}\left(I^{\prime }-S^{\prime }\right)\left(k^{\prime },F;Z\right)-N\left(R,k\text{,}F;Z\right)\text{=}\text{0}& \left(3\right)\end{array}$

Equations (2)-(3) can be expressed in terms of the balance of payments. There is a set of real exchange rates and real long-term rates of interest which equates the current account to the capital flow S-I in both the United States and the rest of the G-7. We shall refer to equation (2), graphed in the (R, r) space as the IX curve, and equation (3), graphed in the (R, r’) space as the IX’ curve in Figure 4. Additional equations involve the determinants of investment (7), saving (6), capital flows (8), and the current account N(k, F, Z) in (2) and (3).

Basic Variables

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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Basic Variables

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Basic Variables

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Determination of Real Exchange Rate and Real Interest Rate

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Determination of Real Exchange Rate and Real Interest Rate

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Determination of Real Exchange Rate and Real Interest Rate

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b. Portfolio balance: interest rate parity

The interest rate parity theory is that the real interest rate differential will be such that investors are indifferent between domestic and foreign assets. Investors have long horizons and contemplate both direct and portfolio investment. The expected real return on U.S. long-term assets is the real long-term rate of interest, r, plus the expected long-term real appreciation of the U.S. dollar, which is the average annual expected change in the exchange rate over a long horizon, denoted E(DR). The expected return in the rest of the G-7 is the real long-term interest rate r’. Using all available information, the investors are assumed to know from Table 1 that the real effective exchange rate is integrated of order 1 such that the first differences are stationary. The equilibrium real exchange rate reflects the properties of the underlying fundamentals. As the fundamentals have been shown to be integrated I(1), the real exchange rate is also I(1). Therefore, in making their long-term investment decisions, investors in the United States and the foreign countries are assumed to know that E (OR) = 0 and therefore base their investment decisions only the real long-term interest rate differential (r-r’). Short-run exchange rate expectations are irrelevant for long-term investment decisions. Using all available information that the fundamentals and real exchange rate can be described as martingales R(t) = R(t-1) + e(t), E(e) = 0, portfolio balance of long-term investment implies the convergence of real long-term rates of interest, r=r’.

$\begin{array}{cc}r=r^{\prime }\left(4\right)& \end{array}$

Figure 2 compares the foreign ^13/ (G6RLT) and U.S. (USRLT) real long-term interest rates. As is clear from stylized fact (b), Figure 2, Table 1, the differential (r-r’) is stationary and its expected value is zero. The portfolio balance equation (4) implies is that the foreign real long-term rate and the USRLT converge to each other, which is shown by the intersection of the IX and IX’ curves in Figure 4. The world real rate of interest r=r’ is such that world saving less investment (I-S) + (I’-S’)= 0 is zero, from equations (2)-(3).

c. Independent investment and saving decisions

In the NATREX model, firms make the investment decisions and households and government make saving decisions. We start with the fact that the crucial fundamentals Z(t) are I(1), such that there is no stationary distribution function and the uncertainty increases as one looks further into the future. The future is characterized by uncertainty rather than risk, in the sense of Frank Knight. ^14/ The agents change over time with new generations, waves of immigration and new governments. In each case, the relevant agents, including the government, are assumed to adopt an optimizing feedback control algorithm that assures stability and convergence to the unknown steady state values. This is a major difference from the RAIOM discussed above. ^15/

(1) The consumption and saving functions

The NATREX uses a consumption or saving function based upon intertemporal optimization which implies an intertemporal budget constraint that the foreign debt intensity stabilizes even though the future evolution of income is unknown. In our model, consumption and saving include both public plus private sector. From standard optimization theory, social consumption C is proportional to permanent income Y^*. The latter is based upon the expectation that current income will grow at the rate of growth of effective labor n, and it is discounted at the real long-term rate of interest r. This implies that social consumption is proportional to current capacity output y=y (k;Z), where k is the capital intensity. Included in the exogenous vector Z is a parameter of productivity. ^16/ This is the first part of consumption equation (5).

$\begin{array}{cc}C/y=g-hF/y& \left(5\right)\end{array}$

When there is no foreign debt, the coefficient g is the ratio of private plus public consumption to capacity output. This is what we call time preference and reflects social tastes. A rise in g can occur in several ways: (i) a rise in the cyclically-adjusted government expenditures, not offset by a decrease in private consumption; (ii) a rise in private consumption induced by a tax cut, not offset by a decline in government expenditures; (iii) a change in the demographic composition of the population toward groups whose consumption to income ratio is high (the very young, and very old). Stylized fact (i) and Table 1 show that the ratio of social consumption to GNP is not stationary.

When the foreign debt rises to a level that the government realizes is unsustainable, then it changes its fiscal policy to reduce the deficit or increase government saving. This is a feedback control that is reflected in coefficient h. All of the decisions are based upon current measurements of variables in a way that is guaranteed to drive the system to the steady state, regardless of the disturbances. ^17/

Social saving is GNP less public plus private consumption. The general consumption function (5) implies saving function (6).

$\begin{array}{cc}S=\left(1-g\right)y\left(k;Z\right)+\left(h-r\right)F=S\left(k,F;Z\right)h>r,S_k>0,S_F>0& \left(6\right)\end{array}$

Thus, social consumption, via the government budget deficit, is negatively related, and the social saving is positively related, to the foreign debt, dS/F>0. This will satisfy our intertemporal budget constraint if feedback control h is greater than the real rate of interest r. A rise in capital increases wealth and permanent income, and we expect that to raise saving, DS/dk>0.

(2) Investment equation

Equation (7) below is the independent investment equation. A similar investment equation applies abroad. In the standard optimal growth models, the Maximum Principle is used to derive the optimal rate of investment. This is an open loop control where we must have perfect knowledge. We must know with certainty the steady state capital intensity, denoted k^*, and the production function. Then the optimal growth path is a saddle point path. The slightest error in our knowledge, the slightest deviation from the path, will send the economy off on an errant trajectory; and the economy will never reach the steady state.

For this reason, Infante and Stein (1973), developed a closed loop suboptimal feedback control (SOFC) based upon dynamic programming. We proved that if the rate of investment is a nonlinear function of the difference between the current marginal product of capital and the social discount rate, then the trajectory of the rate of investment will be very close to the unknowable optimal trajectory. Our SOFC is guaranteed to home in on the unknowable optimal steady state capital intensity, and will be extremely close to the unknown optimum path. We have synthesized the optimal control for the realistic situation of imperfect knowledge and where the basic parameters are changing in an unknowable way. All that we require are observable measurements of the marginal product of capital.

Infante and Stein analyzed the situation for an economy where the saving and investment decisions are identical. When saving and investment decisions are made independently, as in the NATREX model, and when the capital good is not the same as the output, then Stein (1994) and (1995, Chapters 2-3) made two changes in the SOFC. The optimal rate of investment is a nonlinear function of the Keynes-Tobin q-ratio based upon current measurements of variables, dk/dt=J(q) in equation (7).

$\begin{array}{cc}dk/dt=I=J\left(q\right)=J\left(k;Z\right)J_{k<0}& \left(7\right)\end{array}$

The q-ratio is based on current measurements. The q-ratio is positively related to the current marginal physical product of capital y’(k(t);Z(t)), negatively to the current real rate of interest r, and to external factors such as the price of imported materials, contained in Z.

The rate of investment dk/dt will be positively related to the q-ratio so defined. When q>1, the rate of change of the capital intensity will be positive, and when q<1 the rate of change of the capital intensity will be negative. In the steady state, the capital intensity k=k^*, such that q=1. This function is designed to produce convergence to the unknown and changing optimal trajectory.

d. The rate of change of the foreign debt and the current account

The rate of change of the foreign debt, Df/dt, is given by equation (8), which is equal to investment less saving and equal to the current account deficit.

$\begin{array}{cc}Df/dt=J\left(k;Z\right)-S\left(k,F;Z\right)=L\left(k,F;Z\right)L_k=J_k-S_k<0;L_F=-S_F<0& \left(8\right)\end{array}$

Foreign debt is an endogenous variable, and countries may and do change from debtor to creditor and vice versa. The NATREX intertemporal budget constraint is that the value of the foreign debt converges to a steady-state value F^*. The system is dynamically stable: the debt does not explode. In the steady state, where the debt is constant, investment less saving equal to the current account deficit is equal to zero. Then, the trade balance B^* must equal the interest payments rF on the foreign debt.

The current account is the trade balance less interest payments on the foreign debt. The trade balance depends negatively upon the real exchange rate, positively upon foreign income and negatively upon domestic real GNP equal to y(k;Z) - Rf, which is GDP less interest payments Rf. We may therefore write the current account CA=N(R, k, F, r;Z) in equations (2) and (3).

Equation (2) states that the real exchange rate adjusts to make the current account equal to saving less investment (S-I). Therefore the ex post current account will be as forward looking as are the saving and investment equations above.

IV. Solution of the Model

The equilibrium real exchange rate and real rates of interest are simultaneously determined in equations (2)-(4), using (5)-(8), as functions of capital, debt and the exogenous variables Z. This is described in Figure 4. The evolution of capital and debt are described by equations (7)-(8), described in phase diagram Figure 5. Debt and capital feed back on the real exchange rate described in Figure 4. This dynamic system is the NATREX model, which explains the medium to longer-run evolution of the real exchange rate in equation (1a).

Dynamics of Capital and Debt Intensities

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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Dynamics of Capital and Debt Intensities

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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Dynamics of Capital and Debt Intensities

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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The system can be analyzed graphically. ^18/ The IX and IX’ curves in Figure 4 are the sets of real effective exchange rates R and real rates of interest (r, r’), which equate the current account to the capital account, which is determined by planned saving less investment at capacity output in each country. The IX curve for the U.S. relates to R and r, and the IX’ is related to R and r’ in the rest of the world. Output in each country is equal to capacity output. The IX curve is negatively sloped because a rise in the real rate of interest r raises saving less investment (S-I), which is the capital outflow. To maintain the equality of the capital flow to the current account evaluated at capacity output, the real effective exchange rate must depreciate (decline) and thereby increase the current account. The foreign IS’ curve is positively sloped because a rise in R is a depreciation of the foreign currency.

Given the IX and IX’ curves, there will be portfolio adjustments between U.S. and foreign long-term assets when real long-term interest rates differ. At real exchange rate R(B), the U.S. real rate of interest at point B is less than the foreign rate at point b. The excess demand for foreign assets and excess supply of U.S. assets will lead to a rise in the U.S. rate, a decline in the foreign rate and a depreciation of the dollar. The medium run NATREX is at point H in Figure 4, and is equation (9), and the world rate of interest is equation (10). At that point, in both the United States and the foreign countries, the current account plus the capital account is zero, world saving equals world investment, and there is portfolio balance such that real long-term rates of interest have converged. Neither country can control its real exchange rate or real long-term rate of interest; they are simultaneously determined.

The foreign debt affects the real exchange rate in (9), but it does not affect the world rate of interest in (10) because the debt does not affect world saving and world investment.

The rate of change of the real exchange rate is equation (11), which depends upon the evolution of capital and debt. The rate of change of the debt is the current account deficit.

When there is balance of payments equilibrium and portfolio balance at point H in Figure 4, the q-ratio need not be equal to unity, nor need investment less saving (equal to the capital inflow) be equal to zero. In that case, the capital and foreign debt will vary according to equations (7)-(8). These variations, as well as variations in the fundamentals, produce movements in the IX curve. Hence, the medium run NATREX in equation (9) is not stationary, and neither will be the observed real effective exchange rate.

Figure 5 describes equations (7) and (8), the endogenous movements in capital and debt. We have substituted the world rate of interest in equation (10) into the q-ratio. Hence the q-ratio depends upon capital k(t) and exogenous forces Z(t). The curve dk/dt=J (k^*; Z)=0 indicates the capital intensity k^*, where the q-ratio is unity. Then the marginal return on capital is equal to the world real rate of interest given by equation (12) below. For k below (above) k^*, the q-ratio is greater (less) than unity. The capital stock converges monotonically to k^* in the direction of the horizontal vectors. This is the substance of equation (7).

The curve L=0 described by Df/dt= L(k,F;Z)=0 is the relation between debt and capital such that investment less saving, which equals the capital account, is equal to zero i.e., J-S=L=0. Along the L=0 curve, the current account is zero, and the foreign debt is not changing. A rise in the foreign debt above the L=0 curve reduces wealth, which reduces consumption and raises saving. The rise in saving less investment produces a capital outflow, which reduces the foreign debt back to the L=0 curve. The vertical vectors describe the movement of the foreign debt. The element of stability d(Df/dt)/Df<0, derived from our saving function, produces our intertemporal budget constraint whereby the debt stabilizes at a value along the L=0 curve.

If, at the medium run NATREX point H in Figure 4, (i) the q-ratio exceeds unity and (ii) saving less investment (equal to the current account) is positive, then capital will increase and debt will decrease along one of the trajectories such as E0-E1 to the steady state at El in Figure 5. At the steady state position the following holds: the q-ratio is equal to unity, such that the marginal return on capital is equal to the world rate of interest; investment less saving, i.e., the current account, is zero; and the trade balance is equal to the interest payments. A zero current account equal to S-I=0, is described by equation (13), where the asterisk denotes a steady state value. ^19/

We may solve (9), (12), and (13) for the steady state values of the real exchange rate, the capital and debt intensities as functions of the fundamentals Z, which involve foreign and domestic productivity and thrift variables. The steady state value of the NATREX, R*, is given by equation (14).

This completes the explanation in an abstract way of the determination of the three components of the medium to longer-run real exchange rate in equation (1a).

V. Empirical Analysis

The NATREX model is suited to empirical analysis using the logic of the cointegration techniques. The observed real exchange rate consists of two large parts: a disequilibrium component and a moving equilibrium (NATREX). The disequilibrium effects of the deviation of the actual real exchange rate from the NATREX, given by the term [R(t) - R[k(t),F(t);Z(t)], are associated with deviations of the rate of capacity utilization from its stationary mean and with disequilibrium in the asset markets, before real long-term rates of interest have converged. This is one measure of “misalignment.” The NATREX itself consists of two parts. One part is the trajectory of the NATREX to the steady state, which describes how the endogenous evolution of capital and debt in Figure 5 move the IX and IX’ curves in Figure 4 to generate a trajectory for the NATREX. The second part is the longer-run equation (14), which is based on IX curves associated with steady state values of capital (k^*) and debt (F^*). Formally, this can be described by a dynamic process econometric equation (15), which corresponds to equation (1a). The system is stable when 1>a>0. The longer-run effect is term BZ(t). The trajectory is the error correction term [R(t-1) - BZ(t-1)]. The disequilibrium effect is in impact term [Z(t) - Z(t-1)].

Equation (15), the sum of the moving equilibrium and disequilibrium elements, indicates the extent to which our model can explain the actual evolution of the real exchange rate. We have two concepts of the equilibrium real exchange rate. The first two terms concern the evolution of the equilibrium real exchange rate when there is portfolio balance and the rate of capacity utilization is at its stationary value. This is the medium-run equilibrium. We can therefore calibrate the moving equilibrium real exchange rate on the rate of capacity output and when there is portfolio adjustment. This calibration has been sought by Williamson (1994), Clark et al. (1994), Bayoumi et al. (1994) and Clark (1995) in attempting to determine the equilibrium rate of exchange. Hence we can separate the moving equilibrium from the disequilibrium effects. A comparison of the actual with the medium-run equilibrium is one measure of “misalignment.” Finally, the first term represents the longer-run equilibrium which is just a function of the exogenous variables. The deviation of the actual real exchange rate from the longer-run equilibrium is the second measure of misalignment. In this part, we discuss the data and present the empirical results. In the next part, we explain the empirical results in terms of the model.

2. Econometrics ^26/

We display two estimation methods. First (Table 2) is an ordinary least squares OLS estimate of the real exchange rate (USREUG7) regressed on the fundamentals and disequilibrium components. An AR(1) transformation was used to reduce the effects of serial correlation. The second method (Table 3) is a nonlinear least squares NLS estimate of equation (15). Similar results are obtained in both cases. The basic results are as follows: (1) A rise in U.S. time preference (MADISRAT) depreciates the equilibrium real value of the dollar; (2) an increase in foreign-time preference (MAG7DIS) appreciates the equilibrium value of the U.S. dollar. These effects are always significant; (3) neither the U.S. growth (MAUSGROW) nor the foreign growth variable (MAG7GR0W) has a significant effect; (4) the disequilibrium deviation of the rate of capacity utilization from its stationary mean value (DEVCUR) significantly depreciates the real value of the dollar; (5) the disequilibrium deviation of the U.S. real long-term rate of interest from the foreign real long-term real rate of interest (INTDIF) significantly appreciates the dollar.

Table 2.

OLS Regression of Real Effective Exchange Rate USREUG7 on Fundamentals and Disequilibrium Terms - AR(1) Transformation Used

Sample Period 1975:2-1993:3

Note: Residuals: (1) From the LM test the F statistic has a probability of 0.05 indicating some serial correlation. (2) From de ARCH test, the F-statistic has a probability 0.85 thus indicating no heteroskedasticity. (3) The ADF(N.l) statistic for the residuals -4.42 is significant at the 1 percent level. The residuals are stationary.

Table 2.

OLS Regression of Real Effective Exchange Rate USREUG7 on Fundamentals and Disequilibrium Terms - AR(1) Transformation Used

Sample Period 1975:2-1993:3

Variable	Coefficient	Std. Error	T-Stat.	Prob.
CONSTANT	192.7397	118.0197	1.633115	0.1076
MADISRAT	-582.7147	107.0164	-5.445098	0.0000
MAUSGROW	-0.335879	0.532291	-0.631007	0.5304
MAG7DIS	473.9907	191.2641	-2.478200	0.0160
MAG7GROW	-0.183023	0.284273	-0.643830	0.5221
INTDIF	1.928176	0.409621	4.707219	0.0000
DEVOUR	-0.259351	0.324519	-0.799186	0.4273
AR(1)	0.825274	0.055837	14.78017	0.0000
R-squared	0.949495	Mean dependent var		78.02342
Adj. R-squared	0.943699	S.D. dependent var		10.63447
S.E. of regression	2.523319	Akaike info criterion		1.959802
Sum squared resid	388.3956	Schwartz criterion		2.218829
Log likelihood	-157.5199	F-statistic		163.8289
Durbin-Watson stat	1.474129	Prob(F-statistic)		0.000000

Note: Residuals: (1) From the LM test the F statistic has a probability of 0.05 indicating some serial correlation. (2) From de ARCH test, the F-statistic has a probability 0.85 thus indicating no heteroskedasticity. (3) The ADF(N.l) statistic for the residuals -4.42 is significant at the 1 percent level. The residuals are stationary.

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Table 2.

OLS Regression of Real Effective Exchange Rate USREUG7 on Fundamentals and Disequilibrium Terms - AR(1) Transformation Used

Sample Period 1975:2-1993:3

Variable	Coefficient	Std. Error	T-Stat.	Prob.
CONSTANT	192.7397	118.0197	1.633115	0.1076
MADISRAT	-582.7147	107.0164	-5.445098	0.0000
MAUSGROW	-0.335879	0.532291	-0.631007	0.5304
MAG7DIS	473.9907	191.2641	-2.478200	0.0160
MAG7GROW	-0.183023	0.284273	-0.643830	0.5221
INTDIF	1.928176	0.409621	4.707219	0.0000
DEVOUR	-0.259351	0.324519	-0.799186	0.4273
AR(1)	0.825274	0.055837	14.78017	0.0000
R-squared	0.949495	Mean dependent var		78.02342
Adj. R-squared	0.943699	S.D. dependent var		10.63447
S.E. of regression	2.523319	Akaike info criterion		1.959802
Sum squared resid	388.3956	Schwartz criterion		2.218829
Log likelihood	-157.5199	F-statistic		163.8289
Durbin-Watson stat	1.474129	Prob(F-statistic)		0.000000

Note: Residuals: (1) From the LM test the F statistic has a probability of 0.05 indicating some serial correlation. (2) From de ARCH test, the F-statistic has a probability 0.85 thus indicating no heteroskedasticity. (3) The ADF(N.l) statistic for the residuals -4.42 is significant at the 1 percent level. The residuals are stationary.

Table 3.

Nonlinear Least Squares Estimation

Sample Period 1975:2-1993:3

Note: The residuals have the following characteristics: (1) From the LM test for serial correlation with two lags, the F-statistic is 2.99 with a probability of 0.057, so there is some serial correlation coming from the first lagged residual. (2) The ARCH test for heteroskedasticity with one lag has an F-statistic 0.45 with a probability 0.50. The White test for heteroskedasticity has an F-statistic 0.71 with a probability 0.73. Hence we do not find any heteroskedasticity. (3) The Jarque-Bera test for normality is 0.91 with a probability 0.91. Thus we cannot reject normality. (4) The ADF statistic for the residual from the entire equation (15) is -6.2 which is significant at the 1 percent level. The residuals are stationary. The Chow breakpoint was 1980:2. The F-statistic 1.00 has a probability 0.42. Hence there is no evidence of a structural break.

^1/USREUG7=C(1)+C(2)^*MADISRAT+C(3)^*MAG7DIS+C(4)^*(USREUG7(-1)-C(1)-C(2)^*MADISRAT(-1)-C(3)^*RAG7DIS(-1))+C(5)^*INTDIF+C(6)^*DEVCUR.

Table 3.

Nonlinear Least Squares Estimation

Sample Period 1975:2-1993:3

Variable 1/	Coefficient	Std. Error	T-Stat.	Prob.
C(1)	335.9549	151.0658	2.223898	0.0297
C(2)	-660.0887	97.26102	-6.786776	0.0000
C(3)	370.8803	209.0170	1.774402	0.0808
C(4)	0.787841	0.052184	15.09745	0.0000
C(5)	0.404234	0.131753	3.068127	0.0032
C(6)	-0.420673	0.134209	-3.134453	0.0026
R-squared	0.945686	Mean dependent var		78.04067
Adj. R-squared	0.941443	S.D. dependent var		10.55811
S.E. of regression	2.554907	Akaike info criterion		1.957848
Sum squared resid	417.7631	Schwartz criterion		2.150576
Log likelihood	-161.8504	F-statistic		222.8684
Durbin-Watson stat	1.475414	Prob(F-statistic)		0.000000

Note: The residuals have the following characteristics: (1) From the LM test for serial correlation with two lags, the F-statistic is 2.99 with a probability of 0.057, so there is some serial correlation coming from the first lagged residual. (2) The ARCH test for heteroskedasticity with one lag has an F-statistic 0.45 with a probability 0.50. The White test for heteroskedasticity has an F-statistic 0.71 with a probability 0.73. Hence we do not find any heteroskedasticity. (3) The Jarque-Bera test for normality is 0.91 with a probability 0.91. Thus we cannot reject normality. (4) The ADF statistic for the residual from the entire equation (15) is -6.2 which is significant at the 1 percent level. The residuals are stationary. The Chow breakpoint was 1980:2. The F-statistic 1.00 has a probability 0.42. Hence there is no evidence of a structural break.

^1/USREUG7=C(1)+C(2)^*MADISRAT+C(3)^*MAG7DIS+C(4)^*(USREUG7(-1)-C(1)-C(2)^*MADISRAT(-1)-C(3)^*RAG7DIS(-1))+C(5)^*INTDIF+C(6)^*DEVCUR.

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Table 3.

Nonlinear Least Squares Estimation

Sample Period 1975:2-1993:3

Variable 1/	Coefficient	Std. Error	T-Stat.	Prob.
C(1)	335.9549	151.0658	2.223898	0.0297
C(2)	-660.0887	97.26102	-6.786776	0.0000
C(3)	370.8803	209.0170	1.774402	0.0808
C(4)	0.787841	0.052184	15.09745	0.0000
C(5)	0.404234	0.131753	3.068127	0.0032
C(6)	-0.420673	0.134209	-3.134453	0.0026
R-squared	0.945686	Mean dependent var		78.04067
Adj. R-squared	0.941443	S.D. dependent var		10.55811
S.E. of regression	2.554907	Akaike info criterion		1.957848
Sum squared resid	417.7631	Schwartz criterion		2.150576
Log likelihood	-161.8504	F-statistic		222.8684
Durbin-Watson stat	1.475414	Prob(F-statistic)		0.000000

Note: The residuals have the following characteristics: (1) From the LM test for serial correlation with two lags, the F-statistic is 2.99 with a probability of 0.057, so there is some serial correlation coming from the first lagged residual. (2) The ARCH test for heteroskedasticity with one lag has an F-statistic 0.45 with a probability 0.50. The White test for heteroskedasticity has an F-statistic 0.71 with a probability 0.73. Hence we do not find any heteroskedasticity. (3) The Jarque-Bera test for normality is 0.91 with a probability 0.91. Thus we cannot reject normality. (4) The ADF statistic for the residual from the entire equation (15) is -6.2 which is significant at the 1 percent level. The residuals are stationary. The Chow breakpoint was 1980:2. The F-statistic 1.00 has a probability 0.42. Hence there is no evidence of a structural break.

^1/USREUG7=C(1)+C(2)^*MADISRAT+C(3)^*MAG7DIS+C(4)^*(USREUG7(-1)-C(1)-C(2)^*MADISRAT(-1)-C(3)^*RAG7DIS(-1))+C(5)^*INTDIF+C(6)^*DEVCUR.

It is shown in Table 1 that the real effective exchange rate and U.S. rate of time preference are integrated I(1) and the other G-7 rate of time preference is close to I(1). ^27/ On the other hand, the two growth variables are stationary I(0). Hence the longer-run movements in the real effective exchange rate are expected to be due primarily to the U.S. and other G-7 time preference variables. Since only the time preference variables and the disequilibrium variables were significant in Table 2, the NLS estimation in Table 3 uses for the fundamentals Z=[MADISRAT, MAG7DIS] only the U.S. and other G-7 rates of time preference. The disequilibrium variables, reflected in the U.S. less the foreign real long-term rate of interest, INTDIF, and the deviation of the U.S. rate of capacity utilization from its stationary mean, DEVCUR, are the same as before. Figure 6, discussed below, plots the actual real exchange rate, the fitted value based upon Table 3 and the residuals. In terms of equation (15), the longer-run effects BZ are that a rise in U.S. time preference depreciates the dollar and a rise in other G-7 time preference appreciates the dollar. Coefficient a, of the error correction term R(t-l)-BZ(t-l) in equation (15), is 0.78. Hence the system converges to a stable equilibrium. The disequilibrium effects are that a rise in the U.S. less foreign interest rate appreciates the dollar. A rise in the rate of capacity utilization above its stationary mean depreciates the dollar. The residual e(t) from equation (15) is stationary at the 1 percent level. ^28/ Moreover, it is normal and there is no heteroskedasticity. Using the Chow breakpoint test at 1980:2, there is no significant difference between the early and later subperiods.

United States: Real Effective Exchange Rate Relative to Rest of G-7 and Fit from NLS Estimate

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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United States: Real Effective Exchange Rate Relative to Rest of G-7 and Fit from NLS Estimate

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United States: Real Effective Exchange Rate Relative to Rest of G-7 and Fit from NLS Estimate

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VI. The NATREX Explanation of the Econometrics

In this part we use the NATREX model to explain the econometric results. In the concluding Section VII we then use the model and empirical results to answer the questions posed at the beginning of the paper concerning what is the equilibrium value of the U.S. dollar and what were the causes and degree of misalignment.

1. Impact and medium-run effects: a rise in U.S. time preference or the productivity of capital

Along the IX or IX’ curve in Figure 7, the current account plus the nonspeculative capital inflow, equal to investment less saving, evaluated at capacity output, is equal to zero. At the intersection of the two curves there is portfolio balance and the real long-term rates of interest are equal in the United States and in the rest of the G-7. Let there be a rise in investment less saving, produced by either a rise in time preference or in productivity of capital in the United States. The rise in time preference could occur because there is a tax cut that increases private consumption, or a direct rise in government consumption that is not offset by private consumption. ^29/ The rise in the investment occurs because of a rise in the q-ratio.

Effects of Changes in Time Preference and Productivity

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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Effects of Changes in Time Preference and Productivity

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Effects of Changes in Time Preference and Productivity

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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The IX curve shifts to IX(1) in Figure 7 because, given the real exchange rate R(0) and the trade balance, a rise in the U.S. interest rate to H’ is required to keep I-S unchanged. Initially, the U.S. real rate of interest will exceed the foreign rate by H-H’, and there will be a shift toward U.S. long-term assets and away from those in the foreign country. The real value of the dollar will rise to R(1) and interest rate convergence at r1 will occur at point H1. This is picked up by the disequilibrium effects in both the NLS estimation Table 3 and OLS estimate Table 2, where the differential between the U.S. and rest of the G-7 real rate of interest INTDIF leads to an appreciation of the U.S. dollar.

At point H1, there is an appreciated dollar R(1)>R(0), a trade deficit equal to the capital inflow to finance the excess of investment less saving and the world real rate of interest that has risen to rl. This is the conventional medium-run effect.

VII. Conclusion: The Equilibrium Real Exchange Rate

The NATREX model and empirical analysis respond to the issues raised in the opening paragraph of this paper: they provide a theoretical explanation of the movement of the real rate of exchange in the medium to long run and an estimate of the degree of misalignment. The longer-run equilibrium exchange rate depends upon the fundamentals of social time preference at home and abroad. These fundamentals have not been stationary. Since the real exchange rate inherits the properties of the fundamentals, insofar as the fundamentals seem to be martingales, the observed real exchange rate will have the time series property of a martingale. This does not mean that the real exchange rate is a random variable unrelated to the theory. Quite the contrary: it is related to the fundamentals in the manner described by the NATREX model. Misalignment means that the exchange rates are not in line with the fundamentals when there is internal and external balance. To have internal balance, output should be at capacity output. To have external balance requires (i) there should be no deviation between the domestic and foreign real long-term real rates of interest, (ii) the real exchange rate should equate the current account to the nonspeculative capital outflow, and (iii) speculative capital flows and changes in reserves are excluded.

We now show how the NATREX model estimates the degree of misalignment. The nonlinear least squares estimates of the dynamic system, described by equation (15), are presented in Table 3. The model and econometric tests show that the actual real effective exchange rate of the U.S. dollar R(t) depends upon the fundamentals of productivity and time preference at home and abroad, contained in vector Z(t), an error correction mechanism driving the system to the longer-run equilibrium, and disequilibrium factors denoted DZ which represent the deviation between actual and capacity output (DEVCUR) and between the U.S. and the foreign real long-term rates of interest (INTDIF). The equilibrium real exchange rate is obtained when the disequilibrium vector is zero and there is no longer an error correction. We calibrate the equation in Table 3 such that output is at capacity (DEVCUR-0) and there is real long-term interest rate convergence (INTDIF-0). This calibration allows us to estimate the equilibrium and degree of misalignment.

Figure 6 compares the actual real exchange rate with the fitted value from nonlinear least squares estimates in Table 3, and also displays the stationary residuals. The regressors are the fundamentals and the disequilibrium terms. The fundamentals Z(t) used in Table 3 and Figure 8 are time preference in the United States and the G-7 countries. The U.S. growth relative to its stationary mean is positively correlated with the deviation DEVCUR between the actual rate of capacity utilization and its stationary mean. Hence the U.S. growth variable was not used as a fundamental in the empirical work, though it is a fundamental in the theoretical part. The foreign growth variable is also stationary and hence excluded from NLS Table 3. The residuals reflect speculative capital flows, since the cyclical elements are contained in the disequilibrium terms in the equation.

United States: Actual and Equilibrium Real Effective Exchange Rate

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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United States: Actual and Equilibrium Real Effective Exchange Rate

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United States: Actual and Equilibrium Real Effective Exchange Rate

Citation: IMF Working Papers 1995, 081; 10.5089/9781451955149.001.A001

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The misalignment estimates are shown in Figure 8, which compares the actual real effective exchange rate (USREUG7) with the longer-run equilibrium part. The latter is the first term BZ(t) in equation (15), and is called the NATNLS ^35/ in Figure 8. To obtain the equilibrium, the NATNLS, the error correction term and the disequilibrium terms are set equal to zero. We use NATNLS as our estimate of the equilibrium exchange rate in Figure 8. ^36/ Misalignment is measured as the deviation (UREUG7 - NATNLS). The depreciation of the equilibrium value of the U.S. dollar since 1982 is indeed closely related to social time preference. ^37/ As is seen in Figure 8, there were substantial misalignments from 1976-80 and from 1982-85. From then until the end of the sample period in 1993:3 the real exchange rate was close to its estimated equilibrium value.

The FEER/DEER models, of Williamson, Bayoumi et al., Clark et al. and Clark, calibrate the equilibrium exchange rate on an exogenously determined “desirable” current account. These are normative concepts. The NATREX model takes time preference as an exogenous variable without any normative significance, and the current account is an endogenous variable. The NATREX concept of equilibrium can be related to the FEER/DEER by setting our measure of time preference MADISRAT equal to their “desirable” time preference, and evaluating the equilibrium exchange rate with this component of vector Z. ^38/

We have shown that the NATREX model has explanatory power and that it is useful for interpreting the behavior of exchange rates because it provides: (1) an estimate of misalignment between the actual real effective exchange rate and the equilibrium rate associated with internal and external balance; and (2) an estimate of how the fundamentals affect the equilibrium rate.