Journal Issue

United States of America: Background Papers

International Monetary Fund
Published Date:
October 1995
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III. The Real Effective Value of the U.S. Dollar, the Fiscal Deficit, and Long-Run Balance of Payments Equilibrium 1/

1. Introduction

The relationship between the fiscal deficit and the equilibrium U.S. dollar exchange rate has been the focus of much recent interest. The notion that concerns about persistent U.S. fiscal deficits may underlie the recent decline in the dollar against the yen and deutsche mark has led to a debate over whether lowering the U.S. fiscal deficit would strengthen or weaken the dollar. 2/ The debate stems mainly from the polar predictions made by different models. Models that focus on flows, such as the Mundell-Fleming model, predict that deficit reduction would cause the dollar to depreciate, while stock-flow models such as the Fund’s MULTIMOD predict short-run depreciation but long-run appreciation. 3/

This chapter examines this issue by extending Faruqee’s (1994) empirical analysis of the long-run real effective exchange rate of the U.S. dollar. The model developed below describes short-run and long-run relationships among stocks, flows, and relative prices in the context of balance of payments equilibrium. Empirical tests confirm that in the long run, the real exchange value of the U.S. dollar is significantly influenced by the U.S. fiscal balance relative to the average fiscal balance of its trading partners. The model also accurately tracks (in sample) the real effective U.S. dollar over the last 40 years. 4/

Section 2 briefly discusses the model, Section 3 discusses the data, and Section 4 presents empirical results. Section 5 concludes the chapter.

2. Long-run balance of payments equilibrium and the real exchange rate

a. A model of balance of payments equilibrium

Faruqee’s (1994) analytical model is an integration of flow and stock equilibrium into a continuous-time model of the balance of payments. Asset flows, asset stocks, and variables that influence the current account balance (including the real exchange rate) are jointly determined in equilibrium. Equilibrium in this context is defined to mean a sustainable balance of payments, in particular a sustainable stock of net foreign assets in the long run. The model has four main components: the trade balance (modeled in terms of the real exchange rate and other shift factors), short-run balance of payments equilibrium, interest rate parity, and a long-run constraint on the accumulation of net foreign assets. From these relationships, Faruqee derives a long-run equilibrium relationship among the steady-state real exchange rate, steady-state asset stocks, and shift factors for the trade balance.

Net exports, nx, are assumed to depend on the real exchange rate, q (the real price of the domestic good, as the foreign good serves as the numeraire), and shift factors, x, that affect the trade balance:


Ignoring nonfactor services, or including them implicitly in nx, the current account is the sum of net exports and interest on the stock of net foreign assets, denoted by a (the real rate of return on foreign assets is denoted by r*):

Since the current account equals the capital account when the balance of payments is in equilibrium, 2/

where the dot denotes the derivative with respect to time. 3/ In addition, domestic interest rates are given by foreign interest rates less the expected effect of depreciation, or

where α is the share of domestic goods in home consumption (recall that q is the price of domestic goods relative to foreign goods), Et[·] is an expectations operator, and r is the domestic real interest rate.

In the long run, asset accumulation must be consistent with its desired (or sustainable) path, ȧd. This path is assumed to be given by

Desired foreign asset accumulation is thus a positive function of the spread between domestic and foreign real interest rates and the gap between desired and actual foreign assets.

A sustainable balance of payments means that ȧ - ȧd, or combining the previous two equations and the real interest-rate parity condition,

Solving Equations 1 and 2 for the steady-state values of a, x, and q (denoted by a¯,x¯,andq¯) yields

plus other conditions governing the steady-state level of foreign assets, the shift factors, and the evolution of q. Equation 3 implies that, for example, an increase in the steady-state level of net foreign assets is consistent with an appreciation of the real effective exchange rate, all else equal. The empirical analysis thus is based on the steady-state specification for the real exchange rate shown in Equation 3.

b. Long-run balance of payments equilibrium and the fiscal deficit

In the absence of Ricardian equivalence, the fiscal balance can influence the equilibrium exchange rate in the long run. 1/ In particular, an increase in net foreign indebtedness (resulting from a deterioration in the fiscal balance) decreases the net interest receipts from abroad. In the long run, the balance on goods and services must improve in order to restore the current account to a sustainable level. This improvement requires a real depreciation. This long-run effect stands in contrast to the short-run effects, mediated by interest rates, that obtain in models that focus solely on flow equilibrium, (e.g., the Mundell-Fleming model), in which a large fiscal deficit increases domestic real interest rates, attracting capital from abroad and causing the real exchange rate to appreciate. In more general settings with uncertainty, changes in the fiscal balance might also affect confidence or risk premiums. 1/

The fiscal balance is used in the empirical model rather than the corresponding stock of debt. This is of no consequence for the long run; when the target stock of government debt, B, is fixed as ratio to nominal GDP, which in the steady state is growing at the rate g, the steady-state deficit, D, and the steady-state stock of government debt are related by the identity D = gB. 2/ Also, in practice, fiscal plans focus on deficits as much as or more so than on the stock of debt, so it is relevant from a policy perspective to focus on the effects of deficit reduction on the exchange rate. With FBAL denoting the fiscal balance, the long-run model will then be

where the coefficient ζ embodies both the proportionality factor, g, and any other effects (such as effects on confidence or risk premiums) that the fiscal deficit might have on the long-run real exchange rate. 3/ The empirical analysis that follows assesses the significance of this modification for the United States, with special focus on its implications for the long-run real exchange rate.

3. Data

The choice of variables follows directly from the theoretical framework of the previous section. 4/ The Appendix describes data sources and the details of how each series is computed.

The real exchange rate is measured by the multilateral real effective exchange rate based on consumer prices (REER). Two other relative price series serve to capture movements in trade that are unrelated to changes in REER. An index of the ratio of traded-goods prices to non-traded goods prices (TNT) for the United States relative to partner countries serves as a proxy for trends in sectoral productivity that may not be captured by the CPI-based REER. The terms of trade (TOT), the ratio of export unit value to import unit value, captures fluctuations in the prices of foreign traded goods that may not be fully reflected in either foreign CPIs (through REER) or in the domestic prices of traded goods (through TNT). While it may seem peculiar to use three relative price variables, no single measure of the real exchange rate fully explains international competitiveness. 1/ In addition, there is broad theoretical and empirical support for a specification linking TOT and TNT with the real exchange rate. 2/ Of course, in practice each of the series is at best a proxy for its theoretical counterpart.

In addition, the analysis below includes consideration of the effect of the fiscal balance in the United States relative to its G-7 trading partners (the G-7 accounts for about 70 percent of U.S. trade). The series is limited to the G-7 since expanding coverage to the most heavily-weighted non-G-7 partner country (Mexico) would have reduced the sample period by one third. This series is denoted FBAL. 3/

REER is treated as the real exchange rate in this discussion, in contrast to much theoretical work where other relative prices (such as the relative price of traded to nontraded goods) play the role of the real exchange rate. Williamson (1994) argues that a real effective rate based on relative price levels is preferable to a series based on narrower measures of relative prices. 4/ As the three relative prices, REER, TOT, and TNT, are jointly determined, in equilibrium the relationship of TNT and TOT to the real exchange rate is ambiguous, and will depend on the source of shocks and the structure of demand and supply. 5/

The likely effects of changes in NFA and FBAL on REER are considerably more straightforward. 1/ NFA should be positively related to the real exchange rate in the long run; an increase in net foreign assets leads to an increase in net interest receipts from abroad, which requires an appreciation to generate offsetting flows in the trade and nonfactor service components. 2/ Finally, the fiscal balance should be positively related to the real exchange rate, for essentially the same reasons as for the net foreign asset position. In the absence of Ricardian equivalence, a decrease in the fiscal deficit lowers net foreign debt and improves the income component of the current account, requiring an offsetting appreciation. 3/ Including both NFA and FBAL in the exchange rate equation permits inference on the effects of changes in FBAL holding NFA constant, including channels other than the current account, e.g. effects on confidence or risk premiums.

All series are annual and span 1955-90. Chart III-1 shows the data plotted over time. Several patterns are worth noting: for example, REER declines steadily after the end of Bretton Woods, with a spike in the mid-1980s. The next task is to analyze these patterns in the context of the empirical model.


4. Results

The empirical model employed is an error-correcting model (ECM). It incorporates a long-run relationship among the variables of interest in a model of their joint short-run dynamics. Specifically, if the variables are collected into a (5 × 1) vector Yt = [REERt, TOTt, TNTt, NFAt, FBALt] the model is

Here, μ is a (5 × 1) vector of constants (intercepts for each of the five equations), Γ1,…,Γk are (5 × 5) matrices of short-run coefficients, π is the (5 × 5) matrix of long-run coefficients, and ut is a (5 × 1) vector of random disturbances. The long-run relationships among the variables in Y are embedded in the (n x n) matrix π, where n is the number of variables (here, n is 5). These long-run relationships are estimated using the full information maximum likelihood method of Johansen. 4/ The details of estimation and inference in ECMs are readily available elsewhere, so they are omitted here. 1/ As in Faruqee (1994), the constant μ is restricted to impose consistency between the condition that there is a constant in the ECM and the condition that the differenced series are driftless (i.e., that E(ΔYt)=0). 2/

The remainder of this section presents the main empirical results. The first task is to ascertain that the variables have long-run (unit-root) components, so that the asserted long-run relationship among them is statistically justifiable. The tabulation below presents augmented Dickey-Fuller tests for a unit root, including a constant and trend. 3/ The number of lags for each test was chosen to be the same as employed by Faruqee.

Tests for Unit Roots 4/

The results are mixed; for REER and NFA, neither the level or difference of the series can reject the null of a unit root. However, small changes in the specification of the test lead it to reject the null of a unit root for both ΔREER and ΔNFA. 1/ There is thus evidence to suggest that all the variables are difference-stationary, and hence are good candidates for a cointegrating relationship.

Cointegration results are presented next. These are performed using an ECM with four lags, and with the constant constrained as described above. 2/ These tests give an idea of the number of long-run relationships -among the series, and the qualitative features of those relationships. The maximum eigenvalue and trace tests are presented in the tabulation below. The maximum eigenvalue test pits the null of r cointegrating relationships against the alternative of r+1 cointegrating relationships, while the trace test pits the null of r cointegrating relationships against the alternative of η cointegrating relationships.

The trace and eigenvalue tests imply at least four cointegrating relationships among the variables. The tests strongly reject the null of no more than 3 cointegrating relationships, and so four cointegrating relationships are assumed to be present for the rest of the analysis. 3/

Tests for the Number of Cointegrating Relationships 4/

Maximum Eigenvalue


rank = 044.4**131.8**
rank ≤ 132.4*87.4**
rank ≤ 222.8*55.0**
rank ≤ 320.5**32.2**
rank ≤ 411.8*11.8*

Tests for the significance of each of the variables in the cointegrating relationship are presented in the tabulation below. These are likelihood ratio tests for joint restrictions across the four cointegrating relationships. 1/ For each model, all of the variables are significant at the ten percent level; indeed, except for the fiscal balance, all are significant at the one percent level. The more modest significance of the fiscal balance might result from some mild redundancy in including both FBAL and NFA. In fact, when NFA is excluded from the model, the restriction that FBAL does not enter any of the cointegrating relationships is easily rejected at the one percent level. This indicates that NFA, which includes foreign holdings of U.S. government debt, probably already captures some of the effects that fiscal policy has on exchange rates. 3/

Tests of Exclusion Restrictions 2/
VariableTest Statistic
REER:X2 = 20.3**
NFA:X2 = 13.7**
TOT:X2 = 17.4**
TNT:X2 = 15.5**
FBAL:X2 = 7.9*

Chart III-2 gives a view of the in-sample fit of the model. The model tracks the changes in the real effective exchange rate well, including the decline after Bretton Woods and the appreciation of the mid-1980s. The correlation between fitted and actual values is about 98 percent.


The final assessment of the model involves an examination of the signs of the relationships among the variables. The focus will be on estimates of the long-run matrix π. 4/ Note that these estimates provide information solely about the long-run relationships among the variables. There are several possible long-run relationships to be examined, in particular one for each row of π, but the natural choice is the one associated with ΔREER, i.e., the first row of π. Estimates of this first row are presented in Equation 5 below, normalized so that the first element (corresponding to REER) is equal to -1, hence putting the coefficients in regression format. Since the variable FBAL is large in magnitude, its estimated coefficients are relatively small. Here the coefficients are multiplied by 100 to make the presentation cleaner. FBAL is an index number and hence unitless, so this transformation is of no real consequence.

The coefficients of NFA and TNT have positive signs. These are consistent with arguments about intersectoral resource allocation (for TNT) and the arguments made above about the long-run effects of NFA shifts on the composition of the current account. TOT, on the other hand, has a negative sign. It may be that supply effects dominate trade in manufactures, but demand effects dominate for trade in goods and services. FBAL also has the predicted sign in the equation, e.g. a positive sign.

5. Conclusions

Discussions of the relationship of the fiscal balance to exchange-rate trends have increased in relevance since the most recent decline of the dollar against the yen and deutsche mark. These discussions have focused largely on the predictions of theoretical models. This chapter provides some simple evidence on the potential long-run relationship between the fiscal deficit and the multilateral real effective exchange rate for the United States.

The notion that the fiscal balance plays an important role in the long-run real exchange rate has some empirical support. The fiscal balance of the United States relative to that of its major trading partners bears a significant and positive relationship to the real exchange rate as measured by the CPI-based REER after accounting for the effects of other variables in the long run. Specifically, an increase in the fiscal deficit of the United States relative to its trading partners, all else equal, tends to depreciate the real exchange rate in the long run. In-sample, the predictions of the model for the real effective rate are quite close to the actual value of REER, tracking the mid-1980s appreciation and depreciation.

Nonetheless, the results should be viewed with considerable caution. First, the long-run relationship of the fiscal variable to the other variables is not particularly strong. The results suggest that the effect of fiscal policy on the real exchange rate is largely subsumed in the net foreign asset position. Second, given the nature of the relative fiscal variable, in particular the fact that it is a flow and that it appears to revert to its mean, it may be inappropriate to model it as containing a unit root process, even though the unit-root tests support this specification. Such tests can be quite unlikely to reject the unit-root null hypothesis even when that null hypothesis is false. 1/ Third, it could be argued that fiscal balances can have important short-run effects on short-run real exchange rate dynamics, while the corresponding stock of debt is relevant for the long-run equilibrium exchange rate. Future analysis could remedy both these problems by including public debt stocks and fiscal balances as separate variables.

In addition, a more detailed analysis could consider a richer array of fiscal variables. For example, the real effective exchange rate could be affected in the long run by both taxation and spending policies. In particular, a reduction in fiscal spending that is matched by reduced taxes (leaving the fiscal deficit unchanged) may still affect the long-run real exchange rate if government preferences for traded over nontraded goods differ from those of the private sector. Hence, it would be useful to examine the significance (in both economic and statistical senses) of each separately. Further work in this vein would include such variables in the analysis.

Finally, the empirical work focused on the long-run relationship between fiscal policy and the real effective exchange rate. A possible avenue for future research on the topic would be to examine the implications for short-run dynamics in the exchange rate. Such analysis would be especially pertinent given the disparate predictions that theory yields for the short run and long run. This would also provide an opportunity to extend the data set in order to include recent episodes, and to increase the frequency to quarterly if possible, in order to explore richer short-run dynamics.


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    WilliamsonJohn“Introduction” inJohnWilliamsoned. Estimating Equilibrium Exchange Rates (Washington: Institute for International Economics1994).


The data series were calculated as follows. All the series are identical to those used in Faruqee (1994), except for the fiscal balance series, which was not used in Faruqee (1994).

REER: Multilateral CPI-based real effective exchange rate. The series is rebased to equal 100 in 1985, then expressed in logarithms. Source: International Financial Statistics.

TOT: Terms of trade (export unit value divided by import unit value). The series is rebased to equal 100 in 1985, then expressed in logarithms. Source: International Financial Statistics.

TNT: Index of the price of traded goods relative to the price of non-traded goods, proxied by the ratio of CPI to WPI, for the United States relative to G-7 partner countries excluding Canada. The index is constructed as log(TNTUS) - Σj Wj log(TNTOther G-7), where Wj is the weight used in REER for country j rescaled for the omission of non-G-7 countries. Each TNTj series is scaled to equal 1 in 1985. Source for basic data: International Financial Statistics.

NFA: Net foreign assets as a percentage of GDP, in units where 0.01 = one percent. Source: Masson, Kremers, and Horne (1993).

FBAL: Fiscal balance as a percentage of GDP relative to partner countries. Source: International Financial Statistics. The index is constructed as FBALUS - Σj Wj FBALOther G-7, where Wj is the weight used in REER for country j rescaled to account for the omission of non-G-7 countries. Each FBALj is rescaled to equal 100.0 in 1985, in order to account for differences in coverage and other non-comparabilities across countries.

Prepared by Charles Kramer. The provision of data by Hamid Faruqee is gratefully acknowledged.

See for example “Every Which Way,” The Economist, June 3, 1995; Martin Feldstein, “Lower Deficits, Lower Dollar,” Wall Street Journal, May 15, 1995; and Paul Krugman, “Why Higher Savings May Hit the Dollar,” Financial Times, May 24, 1995.

This issue is discussed further in Section 3. See also the accompanying background paper by Laxton and Symansky.

Of course, a more rigorous test of the model’s predictive ability would be to assess its out-of-sample forecasting performance.

x is defined here as a (1 x k) vector, with a conformable coefficient vector θ.

In this definition, the capital account includes movements in official reserves (e.g., official intervention in foreign exchange markets). The same is true for the data on net foreign assets used in the empirical work.

This analysis rules out valuation effects by denominating all securities in terms of one numeraire (the foreign good); in fact, the securities of the two countries are assumed to be perfect substitutes for one another. In principle, in a more general model, short-run valuation effects due to changes in the exchange rate (with stocks held fixed) might enter the equation for the evolution of the stock in the non-numeraire quantity.

Loosely, Ricardian equivalence is the proposition that changes in the mix of taxes and debt used to finance spending are offset by changes in private behavior in a way that leaves real economic variables unchanged. For details in the context of exchange-rate determination see Macklem, Rose, and Tetlow (1994) and the accompanying background paper by Laxton and Symansky.

For further discussion see Black, Laxton, Rose, and Tetlow (1994) and Macklem, Rose, and Tetlow (1995). The accompanying background paper by Laxton and Symansky also provides details on these effects and simulations using MULTIMOD.

The accompanying background paper by Laxton and Symansky shows that changes in net foreign assets can affect both the size and the composition of the current account balance. These are not explicitly modeled in their effects on foreign assets and net exports in augmenting the model here, however.

The productivity variable (PROD) mentioned in Faruqee is not included in the analysis. It did not show up significantly in his results, and his main findings omitted it.

See e.g. Marsh and Tokarick (1994), who recommend using a diverse set of competitiveness indicators.

Since data on the fiscal balance for Japan is not available from the data source (IFS) before 1955, the index starts at that date. It is conceivable that two variables--one for United States and another for trading-partner balances--ought to be employed, rather than one comparative measure. After all, different interest rates prevail on the debt of different countries, and a reduction in the U.S. deficit may have a different effect on confidence than an increase the deficit of a partner country. However, empirical tests (not shown) do not reject the restriction that the cointegrating coefficients are the same size and opposite in sign for United States and aggregated partner-country deficits, so proceeding with the data as defined is reasonable.

Williamson (1994) illustrates this with a simple model of the real exchange rate. If there are no nontraded goods, his real exchange rate expression collapses to the terms of trade; if the home country is small in the traded-goods market, it collapses to the price of nontraded goods relative to the price of domestic exportables. Clearly, neither of these circumstances describes the United States.

Again, the focus here is on long-run relationships. As noted above, short-run dynamics may differ considerably in nature from the steady-state relationship.

Valuation effects might play a role in the short run, but here two long-run steady states are compared. Valuation effects are not present since the exchange rate is constant in the steady state.

The absence of Ricardian equivalence is necessary so that an increase in public saving is not offset dollar for dollar by a decrease in private saving, leaving total saving unchanged.

See Hamilton (1994), Chapter 20.

See, e.g., Hamilton (1994), Chapters 19 and 20.

See Hamilton (1994), p. 581.

Strictly speaking, the restriction that the constant term in the ECM lies in the cointegrating space, which involves the assumption that E(ΔYt) = 0, has implications for the correct specification of these tests. In particular, it implies that including a trend term in tests for the level, and a constant and trend term in tests for the difference, is inefficient. However, the tests were run with trend terms anyway, for comparability with the results in Faruqee (1994). At most one might expect some loss of test power from including these terms if they are irrelevant; in fact, the test results improve when these terms are omitted.

The asterisk denotes significance at the 5 percent level. Note that k = 0 except in the case of REER and NFA, where k = 1.

For each of the differenced variables, the null of a unit root is rejected (using no lags) when the constant and trend terms are omitted. These results make sense if the trend and constant do not belong in the test regression--the failure to reject may indicate low power caused by the presence of irrelevant variables.

The results of the cointegration tests using an unconstrained constant were qualitatively similar--the test still finds r > 1 cointegrating vectors, though fewer of them. Also, a test rejected the restriction that the fourth lag of all variables in all equations could be excluded at the one percent level.

The statistics could be interpreted as rejecting the null of four cointegrating vectors in favor of the alternative that there are five such vectors, but this would make no sense; it would imply that the variables are all stationary, which is almost surely false given the results of the unit root tests.

One asterisk indicates significance at the 5 percent level. Two asterisks denotes significance at the 1 percent level.

The tests turn out to be sensitive to the number of cointegrating relationships assumed to be present. The previous results clearly imply the presence of four cointegrating relationships, though, so these results rest on safe ground.

One asterisk denotes significance at the 10 percent level, two asterisks denotes significance at the 5 percent level. Note that k = 0 except in the case of REER and NFA, where k = 1.

A more detailed study would break NFA into private and public components of assets and liabilities, and include domestically-held public debt as an auxiliary variable. This endeavor awaits future research efforts.

The use of statistical, rather than economic, restrictions to identify the cointegrating vectors in the Johansen technique makes it impossible to ascribe a structural interpretation to their estimates. This point is discussed in more detail by Pesaran and Shin (1994).

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