AS THEORY of exchange rate determination, the doctrine of purchasing power parity (PPP) posits an underlying tendency for movements in the nominal exchange rate to offset movements in the ratio of national price levels, assuring constancy of the real exchange rate.¹ Based on this static measure of equilibrium relative prices, deviations in the real exchange rate from its PPP benchmark can then be viewed as gains or losses in external competitiveness.

However, real exchange rate movements do not completely coincide with perceived changes in competitiveness, reflecting a basic flaw in the PPP approach. Instead, the likely effects of exchange rate changes on the trade balance are often difficult to predict without further information regarding the source of the shock. Moreover, it may be quite misleading to view the real exchange rate as an isolated measure of external competitiveness without further reference to developments within the overall macroeconomic environment.²

Like other relative prices, real exchange rates are affected by real disturbances. In turn, real exchange rate movements stemming from real shocks may often represent fundamental shifts in the relative prices compatible with international equilibrium. Hence, a more general view of real exchange rate determination than the one offered by PPP is needed. Specifically, a distinction needs to be made between relative-price movements that represent lasting changes in the level of competitiveness and short-term fluctuations that reflect transitory departures from a given PPP level. Consequently, whether the long-run real exchange rate actually remains constant over a given time horizon (and PPP obtains) depends upon the behavior of its underlying economic determinants.

Viewing PPP as a fixed steady-state condition rather than as a long-run equilibrium condition, this paper investigates the sources of trend variation in the real exchange rate. Focusing on the United States and Japan, the empirical analysis examines the long-run relationship between the real exchange rate and the fundamental determinants that underlie the trend decline in the real value of the dollar and the trend appreciation in the real yen over the postwar period.

In examining real exchange rate determination, this paper implements a version of the macroeconomic balance approach,³ which broadly defines the sustainable real exchange rate as that value or path consistent with internal and external macroeconomic balance. Internal balance corresponds to output being at its potential level in conjunction with a nonaccelerating rate of inflation. External balance requires a balance of payments position in which any current account imbalance is financed by a sustainable rate of capital flows.

Since capital flows are simply international transfers of financial claims, sustainability of the capital account in turn rests upon the desired stock of external assets and liabilities between nations.⁴ Integrating stock variables and stock-equilibrium relationships directly into the analysis has the advantage that flow equilibrium must follow as a necessary condition. Hence, a sustainable real exchange rate within a stock-flow framework can in principle account for both internal and external macroeconomic (flow) balance.⁵

Determinants of the equilibrium real exchange rate also include factors that affect the net trading position of the home country in world markets, as well as the underlying propensity of the home country to be a net lender or borrower of capital. In other words, the interaction between the permanent structural components in both the current and capital account jointly determine the sustainable real exchange rate.

On the trade side, among the factors that primarily operate through the current account, ‘“the productivity approach,” based on the seminal work of Balassa (1964) and Samuelson (1964), has perhaps received the most attention.⁶ Other structural determinants, such as the stance of trade policy, variations in the terms of trade,⁷ and the composition of fiscal spending, may also have a long-run impact on relative prices. In a developing country context, Edwards (1989) presents an empirical analysis of exchange rate determination emphasizing these and other factors affecting international equilibrium.⁸

Using cointegration techniques, this paper examines empirically the long-run determinants of the real exchange rate for the United States and Japan over the postwar era. In particular, structural components in both the current and capital accounts—underlying each country’s net trade and net foreign asset positions—-are shown to influence the path of the long-run real exchange rate for each country. The empirical analysis also provides estimates for the sustainable real value of the dollar and the yen over the postwar period, conditional on the stock of net foreign assets and real factors affecting trade flows.

I. Illustrative Model

Consider a world economy consisting of two countries—designated as home and foreign—engaging in the trade of two distinct goods and one financial asset.⁹ The home country produces and consumes a domestic good, and purchases the foreign good through trade with the rest of the world. With the price of the foreign good serving as the numeraire, variables are expressed in real terms (measured in units of the foreign good) unless specified otherwise, and output is taken to be fixed at its full employment level.

Assets pay a fixed real rate of return, r*, and the net stock of real assets held by home country is denoted by f. By assumption, the large foreign country absorbs any excess spending or saving in the home country through a flow of securities without affecting its demand for the home good. From goods market equilibrium, the trade balance for the home country, which also equals the difference between the value of domestic output and domestic spending, depends on the relative price of home and foreign goods plus an exogenous shift parameter. Specifically, net exports nx for the home country can be written as

where q is the (log) real exchange rate defined as the real price of the domestic good so that an increase denotes a real appreciation at home; and x represents the shift parameter incorporating exogenous factors that affect the relative demand and supply of domestic and foreign goods, and thus the trading position of the home country.¹⁰ Note that equation (1) embodies the traditional elasticities approach to the balance of payments, allowing the contemporaneous relative price of exports versus imports (abstracting from J-curve effects) to impact on the trade balance, where the parameter γ captures the familiar Marshall-Lerncr condition.¹¹

Abstracting from detailed aspects of the service account, the current account is defined simply by the net trade in goods plus the interest income received (or paid) on a country’s net foreign asset (or debt) position: ca = nx + r*f. The current account balance also equals the rate of accumulation of net foreign assets held domestically:¹²

where dot variables throughout denote time derivatives, i.e.,$\dot{y}=dy/dt\mathrm{.}$ Hence, $\dot{f}$ in equation (2) represents the instantaneous change in the stock of net foreign assets held by the home country resulting from a given current account position.

Determining the equilibrium real exchange rate over the medium term revolves around the issue of sustainability. A sustainable balance of payments position is one that reflects a current account balance financed by a desired or sustainable rate of capital flows.¹³ In turn, a sustainable capital account position is based on the underlying determinants of net foreign asset equilibrium. That desired rate of net foreign asset accumulation (or decumulation) which mirrors a desired amount of excess saving (or spending) is characterized by the following behavioral equation:

where the desired rate of accumulation ${\dot{f}}^d$ is a function of the difference between the domestic real interest rate r and the domestic long-run rate ρ, and the difference between the target level f^d and the actual level of net foreign assets.¹⁴ The target variable measures the stock of net foreign assets that domestic residents would prefer to hold if the short-run rate of interest equaled p. As a baseline case, the long-run real interest rate is assumed fixed equal to the world rate of interest (ρ - r*).¹⁵

In addition, the prevailing domestic real rate of interest r, which influences desired consumption and saving decisions implicit in equation (3), reflects the ex ante rate of return on assets measured in terms of home consumption:

where α is the expenditure share of domestic goods in home consumption, and E_t[.] is the rational expectations operator conditional on the information set at time t. Equation (4) can be interpreted generally as an arbitrage condition equating real rates of return across borders with international capital mobility. In this very simple model with only one financial asset, equation (4) is also simply the Fisher equation, where the real interest rate is equal to the nominal interest rate less the rate of (CPI) inflation (both measured in units of the foreign good).

A sustainable balance of payments position, associated with flow equilibrium over the medium term, is identified by the relation $\dot{f}={\dot{f}}^d\mathrm{.}$ In conjunction with internal balance, this condition ensures that the corresponding real exchange rate represents a sustainable equilibrium value or path consistent with underlying macroeconomic balance. Using equations (2), (3), and (4), this relation can be written as:

The balance of payments equilibrium condition in equation (5) requires that the net flow of goods and services be equal to the rate of desired excess spending over income (desired current account). Equivalently, from a flow of funds perspective, this condition specifies that the actual rate of net foreign asset accumulation be consistent with the desired net flow of financial claims (desired capital account). Hence, based on equation (5), the current account position over the medium term is financed by a sustainable rate of international capital flows.

Equations (2) and (5) together form a system of simultaneous linear equations consisting of two endogenous state variables,f and q, and two exogenous or forcing variables, f^d and x. Conditional on initial and terminal conditions for f and q respectively to ensure an economically sensible, nonexplosive solution,¹⁶ the fundamental solution for q, derived in the Appendix, is given by:

In expressions (6)-(9), bars over variables indicate long-run (stock) equilibrium values, while other variables reflect current (flow) equilibrium values. The forward-looking nature of the solution depicted above incorporates the fact that anticipations of future economic conditions are important for current variables, and, thus, the exchange rate is affected by market expectations.¹⁷

From equation (8), equilibrium holdings of net foreign assets $\overline{f}$ (t) depend on the expected forward evolution in the target level of net foreign assets {f^d(t)}∞. Similarly, as seen from equation (9), the exogenous permanent component in net exports $\overline{x}$(t) relies on the present discounted value of the expected path of future trade disturbances $\{x\left(t\right){\}}_t^{\infty }\mathrm{.}$ Finally, the central result is seen by equation (7), defining the long-run equilibrium real exchange rate $\overline{q}$ as a function of these under lying components in both the current account and the net foreign asset position.

The relationship between sustainable adjustment over the medium term and long-run equilibrium is captured by equation (6). The sustainable (saddle) path for the real exchange rate q(t)—associated with internal and external macroeconomic balance—differs from its long-run value $\overline{q}$ until full stock equilibrium is attained.

In transition, the real exchange rate may move away from its long-run equilibrium value to assure a convergent path for net foreign assets toward its steady-state value. For example, a permanent increase in the target level of net foreign assets, which requires an eventual and lasting real appreciation, initially depreciates the real exchange rate in order to improve the trade balance and increase the current stock of net foreign assets toward its higher desired long-run level.¹⁸

Steady-state equilibrium, characterizing a stable level of net foreign assets or liabilities, implies: $\dot{f}={\dot{f}}^d=0.$ With exogenous forcing variables being constant at their steady-state values $(f^d\left(t\right)=\overline{f},x\left(t\right)=\overline{x}),$ equilibrium in stationary state is summarized by the following set of conditions:

Note that only when the economy reaches steady state and fundamentals have settled down to their stationary values does PPP obtain in terms of constancy of the real exchange rate. Meanwhile, with long-run movements in the fundamentals, a clear distinction exists between equilibrium exchange rate movements associated with changing steady states (and changing saddle paths), and a constant PPP value associated with a given stationary state.

In steady state, the trade balance is determined solely by the equilibrium level of net foreign assets.²⁰ This result can be interpreted as a “stock” version of the absorption approach. The desired net foreign asset position anchors the sustainable series of net saving flows (Y - A or S - I balances) and trade balances. In steady state, net exports attain a sufficient “primary” surplus (deficit) to offset interest obligations (receipts) on the stable level of external debt (assets). Consequently, those disturbances that impact on the current account over the short term without affecting net foreign assets in the long run, translate into changes in the real exchange rate, without affecting net exports, in steady-state equilibrium.²¹

To summarize, determinants of the equilibrium real exchange rate include factors that affect both the net trading position of the home country in world markets and the underlying propensity of the home country to be a net lender or borrower of capital. In other words, the interaction between the permanent structural components in both the current account and the capital account jointly determine the sustainable real exchange rate.

On the trade side, determinants that operate primarily through the current account may include variables such as productivity growth differentials affecting the relative price of nontraded goods or commodity-price shocks affecting the terms of trade. On the finance side, fundamentals that essentially determine the economy’s long-run net foreign asset position may include variables such as demographic factors, which affect net saving behavior through life-cycle effects, or the stock of government debt, which affects net national borrowing in the absence of Ricardian equivalence.²²

II. Econometric Methodology

Of course, determining the relevant set of economic variables that underlie the sustainable real exchange rate remains an empirical issue, and devising an econometric framework based on the preceding discussion becomes the focus here. The central considerations involve the identification and estimation of the long-run relationship between the real exchange rate and its fundamental determinants.

In that regard, cointegration analysis provides a natural conceptual framework for examining long-term comovements between a set of time-series variables. As a matter of definition, a set of N difference-stationary variables are said to be cointegrated if there exists at least one linear combination—i.e., cointegrating vector—of these variables that is stationary, defining their long-run relationship(s).²³

Intuitively, cointegrated variables may drift apart temporarily, but must converge systematically over time. Hence, any model that imposes a deterministic long-run relationship between a set of integrated economic variables, while allowing those variables to deviate over the short term, will exhibit cointegration.

In the case of the real exchange rate, the presence of short-run speculative factors (reflecting asset market disturbances) and cyclical factors (given the sluggish adjustment of prices and wages) may cause the real exchange rate to deviate temporarily from its sustainable path, defined by the movement of its (nonstationary) fundamentals. Over time, the self-correcting mechanisms of an open economy ensure sustainable adjustment in the real exchange rate to its long-run value compatible with stock-flow equilibrium.²⁴

Cointegration analysis generates empirical estimates for the long-run sustainable path of the real exchange rate, conditional on the time-series evolution of its fundamentals. Using the estimated cointegrating vector to identify the underlying stochastic trend, observed exchange rate movements can be decomposed into its transitory and permanent components (cycle and trend).

Annual data for the United States and Japan were obtained for the postwar period. For the real exchange rate, a CPI-based index of the real effective exchange rate (REER) was used.²⁵ Explanatory variables included stock data on net foreign assets as a share of GNP (NFA)²⁶ and a term of trade index [TOT)—constructed as the ratio of export unit value to import unit value.²⁷ As for productivity, two measures were implemented. First, following Kakkar and Ogaki (1993), a comparative index of the relative price of traded versus nontraded goods (TNT)— composed of the ratio of the domestic CP1 to WPI relative to the corresponding (trade-weighted) index for the remaining G-7 countries (except Canada)—was constructed.²⁸ Second, a comparative index of labor productivity levels (PROD), constructed from rates of growth in real output per manhour in manufacturing at home versus the (trade-weighted) values for the rest of the G-7, was also used.²⁹

In other contexts, the variable TNT, representing the relative price of nontraded goods, may actually serve as a measure of the real exchange rate. Of course, the two variables TNT and REER should in principle be closely related, depending on the source of the shock. Specifically, shocks that irreversibly alter the relative price of tradables versus nontradables should be manifested in the stochastic trend in each series, reflecting the influence of the fundamentals common to both.³⁰ It is precisely for this reason that including TNT as a proxy for trends in sectoral productivity may help explain long-run trends in the real exchange rate.³¹

Under the assumption that (average) labor productivity in manufacturing reflects overall productivity in traded goods, the variable PROD provides a more direct measure of existing productivity differentials in tradables at home and abroad. Unfortunately, the equivalent measure for nontradables, which is inherently more difficult to define and measure, is not available. Since productivity in traded versus nontraded goods is the critical comparison, it should be noted that the measure PROD may be appropriate only under the further assumption that trend movements in relative productivity in services are insignificant among the major industrial countries.

III. Empirical Results

Cointegration estimation is conducted using the multivariate maximum likelihood estimation (MLE) technique proposed by Johansen (1988). The Johansen procedure provides test statistics for the number of cointe-grating relationships that may exist, as well as empirical estimates for each of the cointegrating vectors.³²

Before estimating the cointegration parameters. Augmented Dickey-Fuller (ADF) test statistics were calculated to indicate the order of integration in each of the univariate time series. The results of unit root tests—based on a unit-root null versus a trend-stationary alternative—are reported in Table 1. In every case, the ADF tests are consistent with each series being characterized as I(1) variables. Specifically, the ADF test fails to reject the presence of a unit root for each series in levels, but not in first differences.³³

Table 1.

Tests of Order of Integration^a

^aThe null hypothesis is a unit root versus a trend-stationary alternative. The ADF(k) test statistic for a variable x_t is given by the t-statistic on the estimated coefficient π₂ in the following auxiliary regression (including constant and trend):

$\mathrm{\Delta }{x}_t={\pi }_0+{\pi }_{1}trend+{\pi }_2{x}_{t-1}+\underset{j=1}{\overset{k}{\mathrm{\Sigma }}}{\gamma }_j\mathrm{\Delta }{x}_{t-j},$

where k is determined by the highest order lag for which the corresponding γ_i is significant. If the underlying data generating process is an AR(p), then k = p - 1. See Campbell and Perron (1991). Unless otherwise specified, k = 0 (Dickey-Fuller test).

^bIndicates significance at 5 percent level.

^cIndicates significance at 1 percent level; based on Mackinnon (1991) critical values.

Table 1.

Tests of Order of Integration^a

		ADF(k) test statistic
Variable		United States (1950-90)	Japan (1951-90)
	REER	-3.31 (k = 1)	-2.64
ΔREER		-3.85b	-4.11c (k =3)
	NFA	-1.44 (k = 1)	-2.46 (k = 1)
ΔNFA		-3.65b	-4.71c
TOT ΔTOT		-1.53 -6.61c	-2.68 (k = 1) -4.98c
	TNT ΔTNT	-1.25 -6.02c	-2.77 (k = 1) -5.03c(k = 1)
	PROD ΔPROD	-0.69 -5.63c	-0.92 -5.84c

^aThe null hypothesis is a unit root versus a trend-stationary alternative. The ADF(k) test statistic for a variable x_t is given by the t-statistic on the estimated coefficient π₂ in the following auxiliary regression (including constant and trend):

$\mathrm{\Delta }{x}_t={\pi }_0+{\pi }_{1}trend+{\pi }_2{x}_{t-1}+\underset{j=1}{\overset{k}{\mathrm{\Sigma }}}{\gamma }_j\mathrm{\Delta }{x}_{t-j},$

where k is determined by the highest order lag for which the corresponding γ_i is significant. If the underlying data generating process is an AR(p), then k = p - 1. See Campbell and Perron (1991). Unless otherwise specified, k = 0 (Dickey-Fuller test).

^bIndicates significance at 5 percent level.

^cIndicates significance at 1 percent level; based on Mackinnon (1991) critical values.

View Table

Table 1.

Tests of Order of Integration^a

		ADF(k) test statistic
Variable		United States (1950-90)	Japan (1951-90)
	REER	-3.31 (k = 1)	-2.64
ΔREER		-3.85b	-4.11c (k =3)
	NFA	-1.44 (k = 1)	-2.46 (k = 1)
ΔNFA		-3.65b	-4.71c
TOT ΔTOT		-1.53 -6.61c	-2.68 (k = 1) -4.98c
	TNT ΔTNT	-1.25 -6.02c	-2.77 (k = 1) -5.03c(k = 1)
	PROD ΔPROD	-0.69 -5.63c	-0.92 -5.84c

^aThe null hypothesis is a unit root versus a trend-stationary alternative. The ADF(k) test statistic for a variable x_t is given by the t-statistic on the estimated coefficient π₂ in the following auxiliary regression (including constant and trend):

$\mathrm{\Delta }{x}_t={\pi }_0+{\pi }_{1}trend+{\pi }_2{x}_{t-1}+\underset{j=1}{\overset{k}{\mathrm{\Sigma }}}{\gamma }_j\mathrm{\Delta }{x}_{t-j},$

where k is determined by the highest order lag for which the corresponding γ_i is significant. If the underlying data generating process is an AR(p), then k = p - 1. See Campbell and Perron (1991). Unless otherwise specified, k = 0 (Dickey-Fuller test).

^bIndicates significance at 5 percent level.

^cIndicates significance at 1 percent level; based on Mackinnon (1991) critical values.

United States

The test statistics for cointegration for the United States based on the Johansen procedure are reported in Table 2. using TNT. Tests for the number of cointegrating relationships in the data consist of the maximal eigenvalue and trace test statistics, where λMAX tests for at most r cointegrating vectors against a point alternative of exactly r + 1 cointegrating relationships, while TRACE tests for at most r cointegrating vectors against an alternative of at least r+1 vectors.

Table 2.

Johansen Maximum Likelihood Tests and Parameter Estimates: United States (1950-90)^a

Eigenvalues in descending order: 0.553, 0.391, 0.373, 0.190, 0.000)

^aEstimation involved a VAR with four lags and a restricted constant in the cointegrating vector. The Jacque-Bera test for normality and the Box-Pierce test against serial correlation (not reported) suggest that the selection of lag length is suitable. As a check for robustness, alternate lag length specifications were tested and do not affect the results.

^bIndicates significance at 5 percent level.

^cIndicates significance at 1 percent level; critical values based on Johansen and Juselius (1990).

Table 2.

Johansen Maximum Likelihood Tests and Parameter Estimates: United States (1950-90)^a

Eigenvalues in descending order: 0.553, 0.391, 0.373, 0.190, 0.000)

Cointegration Likelihood Ratio Tests
Number of cointegrating vectors:
null hypothesis				λMAX			Trace
	r = 0			29.82b			73.30c
	r ≤1			18.35			43.47c
	r≤2			17.30b			25.12c
	r≤3			7.82			7.82
Parameter Estimates
		(Corresponding maximal eigenvector)
		REER	NFA	TOT		TNT	Constant
Unrestricted		-39.38	41.56	6.03		35.20	-10.86
Normalized		-1.00	1.06	0.15		0.89	-0.28
Restricted Estimates
	REERt = 1.54NFAt + 0.91TNTt - 0.30;
	(Exclusion on TOT, x2(1) = 1.95)
	REERt = 1.47NFAt + TNTt - 0.30;
	(Exclusion on TOT and homogeneity on TNT, x2(2) = 3.33)

^aEstimation involved a VAR with four lags and a restricted constant in the cointegrating vector. The Jacque-Bera test for normality and the Box-Pierce test against serial correlation (not reported) suggest that the selection of lag length is suitable. As a check for robustness, alternate lag length specifications were tested and do not affect the results.

^bIndicates significance at 5 percent level.

^cIndicates significance at 1 percent level; critical values based on Johansen and Juselius (1990).

View Table

Table 2.

Johansen Maximum Likelihood Tests and Parameter Estimates: United States (1950-90)^a

Eigenvalues in descending order: 0.553, 0.391, 0.373, 0.190, 0.000)

Cointegration Likelihood Ratio Tests
Number of cointegrating vectors:
null hypothesis				λMAX			Trace
	r = 0			29.82b			73.30c
	r ≤1			18.35			43.47c
	r≤2			17.30b			25.12c
	r≤3			7.82			7.82
Parameter Estimates
		(Corresponding maximal eigenvector)
		REER	NFA	TOT		TNT	Constant
Unrestricted		-39.38	41.56	6.03		35.20	-10.86
Normalized		-1.00	1.06	0.15		0.89	-0.28
Restricted Estimates
	REERt = 1.54NFAt + 0.91TNTt - 0.30;
	(Exclusion on TOT, x2(1) = 1.95)
	REERt = 1.47NFAt + TNTt - 0.30;
	(Exclusion on TOT and homogeneity on TNT, x2(2) = 3.33)

^aEstimation involved a VAR with four lags and a restricted constant in the cointegrating vector. The Jacque-Bera test for normality and the Box-Pierce test against serial correlation (not reported) suggest that the selection of lag length is suitable. As a check for robustness, alternate lag length specifications were tested and do not affect the results.

^bIndicates significance at 5 percent level.

^cIndicates significance at 1 percent level; critical values based on Johansen and Juselius (1990).

The null hypothesis of no cointegration (r = 0) among the four time series in Table 2 is soundly rejected by both the TRACE and λMAX statistics.³⁴ Indeed, based on the test statistics, multiple cointegrating relationships may possibly exist.³⁵ The cointegrating vector corresponding to the maximal eigenvalue (i.e., the dominant long-run relationship) is also reported in Table 2. The long-run coefficients have the correct signs, and the point estimates on the normalized coefficients are of plausible magnitude.³⁶

Tests of exclusion restrictions reported in Table 3 confirm that each variable enters the reported cointegrating vector and thus shares a deterministic long-run relationship with the real exchange rate, with the exception of the terms of trade measure TOT. Moreover, the test results of joint exclusion restrictions also shown in Table 3 support the finding that neither NFA nor TNT alone can explain permanent movements in REER³⁷ Both productivity differentials and net wealth are found to be relevant in the long-run determination of the U.S. real exchange rate.

Table 3.

Tests of Exclusion Restrictions: United States (1950-90)^a

Model: β₁REER + β₂NFA + β₃TOT + β₄TNT + μ ∼ I(0)

_^a Also, exclusion restrictions for the constant μ are rejected at the 1 percent level of significance assuming either a single or multiple cointegrating vectors.

_^b The likelihood ratio test statistic LR(k) is distributed as x²(rk), where k is the number of restrictions and r is the number of cointegrating vectors.

_^c Indicates significance at 1 percent level.

Table 3.

Tests of Exclusion Restrictions: United States (1950-90)^a

Model: β₁REER + β₂NFA + β₃TOT + β₄TNT + μ ∼ I(0)

Single Exclusion Restrictions
		LR(1) statistic	LR(2) statistic
		assuming	assuming
Null hypothesis		1 cointegrating vectorb	2 cointegrating vectors
	β = 0	9.96c	10.18c
	β= 0	7.81c	8.83c
	β3= 0	1.95	2.13
	β4 = 0	8.78c	8.88c
Joint Exclusion Restrictions
		LR(2) statistic
Null hypothesis		assuming 1 cointegrating vector
	β2 = β3 = 0	10.08b
	β3 = β4 = 0	9.75b

_^a Also, exclusion restrictions for the constant μ are rejected at the 1 percent level of significance assuming either a single or multiple cointegrating vectors.

_^b The likelihood ratio test statistic LR(k) is distributed as x²(rk), where k is the number of restrictions and r is the number of cointegrating vectors.

_^c Indicates significance at 1 percent level.

View Table

Table 3.

Tests of Exclusion Restrictions: United States (1950-90)^a

Model: β₁REER + β₂NFA + β₃TOT + β₄TNT + μ ∼ I(0)

Single Exclusion Restrictions
		LR(1) statistic	LR(2) statistic
		assuming	assuming
Null hypothesis		1 cointegrating vectorb	2 cointegrating vectors
	β = 0	9.96c	10.18c
	β= 0	7.81c	8.83c
	β3= 0	1.95	2.13
	β4 = 0	8.78c	8.88c
Joint Exclusion Restrictions
		LR(2) statistic
Null hypothesis		assuming 1 cointegrating vector
	β2 = β3 = 0	10.08b
	β3 = β4 = 0	9.75b

_^a Also, exclusion restrictions for the constant μ are rejected at the 1 percent level of significance assuming either a single or multiple cointegrating vectors.

_^b The likelihood ratio test statistic LR(k) is distributed as x²(rk), where k is the number of restrictions and r is the number of cointegrating vectors.

_^c Indicates significance at 1 percent level.

Based on the estimated vectors of cointegration reported in Table 2, estimates for the trend component of dollar real exchange rate can be computed.³⁸ The underlying stochastic trend depicting the long-run path for the dollar real exchange rate is calculated based on the second set of restricted estimates reported in Table 2.

Figure 1 displays the dollar real exchange rate index (in logs, 1985 = 0) and its estimated trend component over the sample period. The vertical axis is measured in percentage terms. Based on the fitted trend, the variance ratio of permanent (trend) innovations to actual innovations in the real exchange rate is about 30 percent for the entire sample, and 20 percent for the subsample under floating exchange rates (1973-90). In other words, about one fifth of the variability of observed real exchange rate changes can be attributed to permanent shocks and the variation of changes to the long-run real exchange rate.

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U.S. Real Exchange Rate: Actual and Trend Values

Citation: IMF Staff Papers 1995, 001; 10.5089/9781451957068.024.A004

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The most salient feature of the time-series behavior of the U.S. real exchange rate over the postwar period is the overall steady decline in both its actual and sustainable values as evident in Figure 1. An explanation for the long-run real depreciation of the dollar becomes clear upon examining the path of its underlying fundamentals.

A well-known stylized fact of the postwar era is that industrial countries have experienced more rapid productivity growth and a tendency toward convergence in per capita income vis-a-vis the United States.³⁹ In turn, economic convergence among this group since World War II has had important consequences for the real value of the dollar.

With productivity gains accruing mainly in the traded goods sector, the relative price of traded versus nontraded goods declined more slowly in the United States (CP1/WPI ratio rose less quickly) than in the rest of the world. Consequently, the measure TNT exhibits a steady trend decline over the sample, only leveling off since the mid-1970s in conjunction with the productivity slowdown.⁴⁰ This downward secular trend, resulting from differential rates of biased productivity growth at home and abroad, appears to have been largely responsible for the declining real value of the dollar since the Second World War.

Meanwhile, net foreign assets, NFA, remained relatively stable over the entire sample until the 1980s. Since that time, however, the U.S. net foreign asset position has declined significantly, representing the transformation of the United States from the world’s largest creditor to the world’s largest debtor country.⁴¹ The result has been a further decline in the sustainable value of the dollar real exchange rate toward the end of the sample period.

Based on estimates of the permanent component, cyclical fluctuations in the dollar real exchange rate—obtained as the difference between the actual and trend values—are shown in Figure 2. The vertical axis is once again measured in percentage terms. This (stationary) residual component can be interpreted as transitory deviations from the long-run path, resulting from short-term cyclical and speculative factors.⁴²

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U.S. Real Exchange Rate: Cyclical Component

Citation: IMF Staff Papers 1995, 001; 10.5089/9781451957068.024.A004

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From Figure 2, note that the real dollar appears to have been above trend on more than one occasion during the Bretton Woods period.⁴³ This result may not seem surprising considering trie dollar’s unique role as the reserve currency under the gold-exchange standard. Under the Bretton Woods system, U.S. payments deficits were essentially financed through an accumulation of dollar reserves abroad, as central banks maintained fixed parities vis-a-vis the dollar. Although, in principle, dollar reserves could have been converted into gold to offset the overall increase in world reserves, authorities generally accepted the increase in currency reserves as part of the mechanism providing international liquidity in a growing global economy,⁴⁴

Figure 2 indicates that the largest divergence in the dollar real exchange rate relative to trend during the Bretton Woods period occurred toward the end of the regime. Substantiating this result, the last few years of the fixed exchange rate system witnessed a tremendous increase in outstanding dollar liabilities (up 250 percent between 1969-72), as the system ultimately collapsed. Although the observed value of the real exchange rate had actually shown a general decline until that time, the critical fact remains that the underlying trend value of the dollar fell even further.⁴⁵

In comparing the behavior of transitory fluctuations across fixed and floating exchange rate regimes, a sharp difference is apparent in Figure 2. In particular, cyclical variation in the dollar real exchange rate has, not surprisingly, been much higher since 1973.⁴⁶ As for the more recent behavior of the dollar, note that the period of massive nominal (and real) appreciation from 1980 to 1985 reflects a large divergence in the real dollar from its estimated long-run path.⁴⁷ Of course, ex post, this episode in fact proved to be unsustainable in the long run.⁴⁸

Japan

The test statistics for cointegration in the case of Japan are reported in Table 4, using PROD. The null hypothesis of no cointegration among the four time series is again rejected by the TRACE statistic at the 1 percent level and by λMAX statistical the 10 percent level of significance (critical value = 24.9), with the possibility of two cointegrating vectors. The vector corresponding to the maximal eigenvalue for Japan is reported in Table 4. Note that only the long-run coefficient on NFA has the correct sign, but the point estimate is quite large. However, the point estimates and coefficient signs appear sensitive to the choice of lag length of the VAR, and must be interpreted carefully.

Table 4.

Johansen Maximum Likelihood Tests and Parameter Estimates: Japan (1951-90)^a

(Eigenvalues in descending order: 0.522, 0.490, 0.130, 0.096)

^aEstimation involved a VAR with four lags and an unrestricted constant to allow for possible deterministic trends. The Jacque-Bera test for normality and the Box-Pierce test against serial correlation (not reported) suggest that the selection of lag length is suitable. Similar results obtain with TNT instead of PROD.

^bIndicates significance at 5 percent level.

^cIndicates significance at 1 percent level; critical values based on Johansen and Juselius (1990).

Table 4.

Johansen Maximum Likelihood Tests and Parameter Estimates: Japan (1951-90)^a

(Eigenvalues in descending order: 0.522, 0.490, 0.130, 0.096)

Cointegration Likelihood Ratio Tests
Number of cointegrating vectors:
null hypothesis			λMAX				Trace
	r = 0		29.62				59.50c
	r ≤1		24.62b				43.47b
	r≤2		8.62				8.62
	r≤3		3.61				3.61
Parameter Estimates
		(Corresponding maximal eigenvector)
		REER	NFA	TOT			Constant
Unrestricted		-12.95	-104.99	16.92			13.31
Normalized		-1.00	-8.11	1.31			1.03
Restricted Estimates
	REERt = 0.66PRODt
	(Exclusion on TOT, and NFA, x2(2) = 1.95)

^aEstimation involved a VAR with four lags and an unrestricted constant to allow for possible deterministic trends. The Jacque-Bera test for normality and the Box-Pierce test against serial correlation (not reported) suggest that the selection of lag length is suitable. Similar results obtain with TNT instead of PROD.

^bIndicates significance at 5 percent level.

^cIndicates significance at 1 percent level; critical values based on Johansen and Juselius (1990).

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Table 4.

Johansen Maximum Likelihood Tests and Parameter Estimates: Japan (1951-90)^a

(Eigenvalues in descending order: 0.522, 0.490, 0.130, 0.096)

Cointegration Likelihood Ratio Tests
Number of cointegrating vectors:
null hypothesis			λMAX				Trace
	r = 0		29.62				59.50c
	r ≤1		24.62b				43.47b
	r≤2		8.62				8.62
	r≤3		3.61				3.61
Parameter Estimates
		(Corresponding maximal eigenvector)
		REER	NFA	TOT			Constant
Unrestricted		-12.95	-104.99	16.92			13.31
Normalized		-1.00	-8.11	1.31			1.03
Restricted Estimates
	REERt = 0.66PRODt
	(Exclusion on TOT, and NFA, x2(2) = 1.95)

^aEstimation involved a VAR with four lags and an unrestricted constant to allow for possible deterministic trends. The Jacque-Bera test for normality and the Box-Pierce test against serial correlation (not reported) suggest that the selection of lag length is suitable. Similar results obtain with TNT instead of PROD.

^bIndicates significance at 5 percent level.

^cIndicates significance at 1 percent level; critical values based on Johansen and Juselius (1990).

Results of exclusion restrictions shown in Table 5 indicate that, in the presence of exactly one stationary linear combination, no single variable need enter the cointegrating vector, including REER itself. However, each variable must enter at least one of the vectors in the presence of two such long-run relationships. This finding suggests that different subsets of the real exchange rate and the explanatory variables are probably cointegrated. Based on tests of joint exclusion reported in Table 5, only productivity and the real exchange rate cointegrate alone, with the restricted estimates reported in Table 4.⁴⁹

Table 5.

Tests of Exclusion Restrictions: Japan (1951-90)

Model: β₁REER + β₂NFA + β₃TOT + β₄PROD ~ I(0)

^aIndicates significance at 1 percent level.

Table 5.

Tests of Exclusion Restrictions: Japan (1951-90)

Model: β₁REER + β₂NFA + β₃TOT + β₄PROD ~ I(0)

Single Exclusion Restrictions
	LR(1) statistic	LR(2) statistic
	assuming	assuming
Null hypothesis	1 cointegrating vector	2 cointegrating vectors
β1 = 0	1.89	21.07a
β2 = 0	1.61	20.27a
β3 = 0	1.76	19.39a
β4 = 0	0.81	19.78a
Joint Exclusion Restrictions
	LR(2) statistic
Null hypothesis	assuming 1 cointegrating vector
β2 = β3 = 0	1.95
β3 = β4 = 0	10.29a
β2 = β4 = 0	15.57a

^aIndicates significance at 1 percent level.

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Table 5.

Tests of Exclusion Restrictions: Japan (1951-90)

Model: β₁REER + β₂NFA + β₃TOT + β₄PROD ~ I(0)

Single Exclusion Restrictions
	LR(1) statistic	LR(2) statistic
	assuming	assuming
Null hypothesis	1 cointegrating vector	2 cointegrating vectors
β1 = 0	1.89	21.07a
β2 = 0	1.61	20.27a
β3 = 0	1.76	19.39a
β4 = 0	0.81	19.78a
Joint Exclusion Restrictions
	LR(2) statistic
Null hypothesis	assuming 1 cointegrating vector
β2 = β3 = 0	1.95
β3 = β4 = 0	10.29a
β2 = β4 = 0	15.57a

^aIndicates significance at 1 percent level.

Cointegration estimates using TNT instead of PROD in the case of Japan (not reported) yield very similar results. With either measure of productivity, the results of various exclusion tests appear somewhat sensitive (unlike the case of the United States) to the selection of the lag length of the VAR. In particular, exclusions restrictions on NFA and TOT may or may not be rejected under different specifications.

However, the empirical results on the role of PROD (and TNT) are robust, consistently rejecting its exclusion from any long-run relationship with the real exchange rate for Japan, and yielding consistent parameter estimates in the restricted vector of cointegration. In combination with the results for the United States, the empirical findings thus lend strong support for the “productivity approach” as described in Hsieh (1982), Marston (1987), and others, recast here in a cointegration framework.⁵⁰

As a part of the convergence club. Japan like Western Europe has experienced a period of sustained productivity catch-up with the United States—the likely result of faster capital-deepening, technological spillovers, or some combination thereof. Moreover, productivity gains in Japan have been more heavily concentrated in tradables than in other industrial countries, as evidenced by the manufacturing data. The comparatively faster rate of productivity growth in traded goods in Japan underlies the yen’s real appreciation vis-a-vis not only the United States but other industrial countries as well.

Trend-cycle decompositions for the real value of the yen are shown in Figures 3 and 4. The (filtered) trend components in Figure 3 are based on the long-run relationship between REER and PROD in Table 4 and the corresponding estimates using TNT.⁵¹ Both measures yield similar results, although the long-run estimates based on PROD generate a larger transitory component, probably as a result of omitting comparative productivity in nontradables. Based on the fitted trends, the variance ratios of innovations in the stochastic trend to innovations in the observed real exchange rate are 16 and 27 percent, using PROD and TNT respectively.

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Japanese Real Exchange Rate: Actual and Trend Values

Citation: IMF Staff Papers 1995, 001; 10.5089/9781451957068.024.A004

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Both estimates of the cyclical component for Japan in Figure 4, indicate, interestingly, that the largest disparity in the actual rate relative to trend under Bretton Woods also occurred toward the end of the regime. Also of note, the quantitative estimates of misalignment for both the dollar and the yen real exchange rates during the breakup of Bretton Woods are broadly in line with the simulation results reported in Bayoumi and others (1994).

IV. Concluding Remarks

Viewing PPP as a fixed steady-state condition rather than as a long-run equilibrium condition, this paper has sought to explain long-run movements in the real exchange rate from a stock-flow perspective. Focusing on the United States and Japan, the empirical methods have applied recent cointegration techniques to examine the long-run determinants of the real exchange rate, in order to understand trend movements in the real value of the dollar and the yen over the postwar period.

For the United States, cointegration tests suggest that net foreign assets and productivity differentials share a long-run relationship with the real exchange rate. This finding supports the proposition that the structural components of both the current and capital accounts—underlying a country’s net trade and net foreign asset positions—jointly determine the long-run sustainable real exchange rate.

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Japanese Real Exchange Rate: Cyclical Component

Citation: IMF Staff Papers 1995, 001; 10.5089/9781451957068.024.A004

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For Japan, the results are a bit less clear, except for the fact that productivity certainly matters in the long run. Cointegration tests for Japan suggest that various measures of productivity differentials share a long-run relationship with the real exchange rate. Historically, Japan has enjoyed tremendous productivity growth, particularly in manufacturing, along the path to economic convergence, thereby leaving room for little else to explain the extraordinary rate of real appreciation of the yen over the postwar period.

On the other side of convergence, the relative gains that industrial countries have made relative to the United States in terms of productivity and output explain much of the downward secular trend in the dollar real exchange rate since World War II. Thus, the empirical findings firmly support the view that sectoral productivity differentials explain a large portion of the trend variation in the real exchange rate for the United States and Japan.