The conceptual framework described in Section II emphasizes the fact that the current account can be viewed from at least two different perspectives. On the one hand, the current account is the result of intertemporal decisions that influence domestic saving and investment. On the other, it corresponds to net exports, and thus reflects the intratemporal choices between home and foreign goods and services, which are influenced importantly by their relative price, that is, the real exchange rate. If an equilibrium saving-investment balance can be defined, and other factors affecting net exports can be controlled for, then the equilibrium real exchange rate can be calculated as that rate which makes these two ways of viewing the current account consistent with each other at a position of internal balance (full employment). This is the core of the macroeconomic balance approach.

In the rest of this section, the accounting identities are first explained, and a simple conceptual model involving saving and investment flows is described in some detail, with attention to several elaborations that are needed to make the simple model more realistic and relevant. A discussion of several different notions of equilibrium then follows. One important distinction relates to underlying policies, namely, whether actual or desirable policies are used in the assessment. Another important distinction concerns flow and stock equilibria; full long-run equilibrium should reflect both. The section concludes with a derivation of a globally consistent reduced-form system of saving and investment equations. This general reduced-form system provides the basis for the specific equation estimates that are reported in Section VI.

## Accounting Identities

As noted above, the conceptual framework rests on the fact that the current account can be expressed as domestic saving minus investment, or as net ex-ports of goods and services. In particular, the national accounting identity that relates output to the components of demand,

can be written as

where the terms on the left-hand side are measures of national saving and investment, respectively. A more elaborated version of this identity distinguishes private sector saving from the government’s position, using the government’s budget constraint that relates the deficit *(DEF)* to government spending on goods and services (G) and on transfers *(TR*, including interest payments on outstanding debt) minus taxes (*T*):

This allows rewriting equation (4.2) as

where the first term is private disposable income minus consumption, that is, private saving (on the assumption that taxes are paid only by domestic residents and that government transfer payments are not made abroad, and hence do not affect *X* - *M*). Other elaborations, including accounting for government investment (and hence distinguishing between the government deficit and government dissaving) and accounting for factor income flows between house-holds, firms, and foreigners, can be important in some contexts but do not materially affect the conceptual framework.

For present purposes, it is convenient to rewrite equation (4.4) in the form

where *S* denotes national (private plus public) saving, *I* denotes national investment, and *N* = *X* - *M* represents net exports of goods and services, that is, the current account.^{1} To motivate the specification forms of the econometric relationships presented in Section VI, the following subsection describes a simple model of the components of equation (4.5), which is developed further in subsequent subsections.

## A Simple Model

Several key features of the framework we want to develop are captured in the simple model presented in Knight and Masson (1988), which for expository purposes is essentially repeated here. The simple model abstracts from short-run output fluctuations due to fluctuations in demand, adopting instead the classical assumption that flexible prices maintain equality between aggregate demand and aggregate supply. Again, as in the classical model, saving and investment are assumed to depend on the world real interest rate (*r*), which, for the moment, will be taken to be exogenous.^{2} In addition, national saving will be allowed to depend on the government deficit (assumed exogenous), as implied by the assumption that private saving behavior does not reflect full Ricardian equivalence. To the extent that changes in public saving are not fully offset by changes in private saving, an increase in the government deficit will lower national saving. Net exports are assumed to depend on the real exchange rate (*R*). Writing these relationships in functional notation, macroeconomic balance (with no gap between aggregate demand and potential output) will require that

If the rest of the world has a similar schedule describing saving and investment, then there is an additional relationship that allows determination of the world real interest rate. (The net export function *N* already combines both domestic and foreign goods preferences, and hence there is no additional relationship for the rest of the world.) In particular, *r* brings about balance between world saving and investment in this classical framework, while *R* influences the relative demands for domestic and foreign goods.

An equation such as equation (4.6), with parameter values empirically estimated, can serve as the basis for equilibrium exchange rate calculations. It would seem especially useful if the long-run factors determining saving and investment are thought to be better estimated than short-run influences (such as cyclical factors), and hence the equilibrium exchange rate is thought of as a medium-term or a long-term concept. Such a framework also gives a clear role to fiscal policy, through the government deficit; and it may be useful to distinguish the current (or projected deficit) from one that is desirable or sustainable when defining equilibrium rates. But to make applications of such an approach empirically relevant, complications need to be introduced into the simple framework.

## Cyclical Influences and Lags

An important complication is that prices are not completely flexible. Output is demand determined in the short run and is not necessarily equal to potential output, given by the supply side. As a result, net ex-ports tend to be lower, the greater is the difference between actual and potential output *(GAP)*, and conversely for the foreign output gap *(GAPF)*. The business cycle may also have implications for saving and investment levels through its implications for domestic interest rates, which may deviate from the world interest rate. For example, investment may vary procyclically, to the extent that expected returns on investment or access to credit is affected by the cycle. Similar factors may also affect saving. A further complication that is important if a medium-term equilibrium is to be defined is the existence of lags in the effects of variables; for our purposes here, the key lag is in the effect of the exchange rate on the trade balance.

These various complications can be written in functional form as follows:

where the polynomial function *a(L)* of the lag operator *L*, with weights summing to one, describes lags in the real exchange rate’s effect on net exports. It should be noted that the government deficit *(DEF)* can be expected to depend on the output gap as well, but the fact is ignored for now; different fiscal policy concepts will be discussed below. Also, nothing requires that saving and investment must respond only to current values of their determinants, a question we will return to below.

Focusing on the right-hand side of equation (4.7), lags and cyclical effects can be removed in order to calculate an *underlying current account*, which we can label *N*:

representing the current account that would result if the current exchange rate were to prevail into the in-definite future and if output gaps both domestically and abroad were to be eliminated. The underlying current account is one important building block in the IMF’s evaluation of medium-term equilibrium exchange rates, because in the medium term the effects of lags on trade would be expected to be eliminated, and output gaps would be expected to have narrowed to zero. We now turn to factors that may influence the medium-term equilibrium for saving and investment.

## Dynamic Considerations Affecting Saving and Investment

Saving and investment, because of their essential intertemporal nature, depend not only on the current values of variables (such as interest rates and output) but also on expected future values, and, if there are adjustment costs, on lagged asset stocks.^{3} There may be good reasons, therefore, to estimate more complicated saving and investment equations including expectations and asset stock dynamics. Moreover, calculated medium-term equilibrium values for saving and investment should remove the effect of temporary fluctuations in the explanatory variables due to cyclical fluctuations, and longer-term equilibrium should adjust for lagged adjustment to equilibrium asset stocks.

For example, the equilibrium real interest rate, given technology and labor supply, pins down the desired or equilibrium capital stock. In the presence of adjustment costs, however, this level of the capital stock is only attained over time. Along the transition path, the existing stock of capital (relative to output or labor) influences the rate of return on capital, which in turn determines the rate of capital accumulation or investment. So, for example, in countries that are initially capital poor (low stage of development), the rate of return to capital, and hence the rate of investment, should be high.

An important intertemporal aspect of saving behavior is the effect of demography. The life-cycle model of saving would suggest that the economy’s household saving rate should depend on the age pro-file of the population. If saving is primarily for retirement, a larger proportion of retirees should be associated with a lower saving rate; the same may be true if there is a high proportion of children, who do not work but increase household consumption. Conversely, when a large fraction of the population is at their peak earning years, the country’s saving rate should be higher. Therefore, we can express saving as a function not only of the interest rate, but also of the dependency ratio, defined as the dependent population^{4} divided by the remaining population. An increase of this ratio should lower the saving rate. Investment may also depend negatively on this ratio, since at given factor prices a smaller equilibrium capital stock will be associated with lower employment.

Unlike the adjustments made for cyclical fluctuations in output, demographic factors move very slowly. Thus, from a medium-term perspective there is no cause for adjusting the value of these variables to a “normal” level when calculating the equilibrium exchange rate. Rather, their role is in explaining the observed differences in saving and investment rates, and relating them to economic fundamentals.

## Concepts of Equilibrium

No single concept of equilibrium is appropriate in all circumstances. It is necessary to be aware of several important issues. One distinction relates to what is assumed about macroeconomic policies, in particular fiscal policy. One possible assumption is that structural fiscal policy remains unchanged. In the framework described above, the calculation of a medium-term equilibrium exchange rate then involves adjusting both sides of equation (4.7) only for short-term effects. One aspect of this is correcting for movements in the fiscal deficit that are due to the economic cycle. This involves calculating a cyclically adjusted, or structural deficit, which we can label *DEF _{S}*. Corresponding to this is the saving-investment balance that removes the effect of the cycle from both private sector balances and the government fiscal position. When the result for the saving-investment balance is set equal to the underlying current account balance, an equilibrium value can be calculated for the exchange rate. This is sometimes called the

*shadow equilibrium exchange rate, R*:

_{S}An alternative assumption with respect to fiscal policy would be that it is modified in a way that is consistent with policy advice. In particular, the actual deficit, even adjusted for cyclical factors, may not be at a desirable or sustainable level. Policy ad-vice often includes a recommendation to reduce the fiscal deficit, for instance, to a level that would prevent government debt as a ratio to GDP from growing. Defining such a normative concept of the fiscal deficit, which we could label *DEF _{D}*, has an associated concept for the exchange rate, which can be called the

*desired equilibrium exchange rate, R*:

_{D}Another important distinction is between flow equilibrium and stock equilibrium; both must hold in the long run, but more emphasis may be given to flow equilibrium in a medium-term perspective. In stock equilibrium, asset stocks should be constant as ratios to the size of the underlying economy, as measured for instance by GDP. These asset stocks would include household wealth, the capital stock, and net foreign assets. It may therefore be reasonable to impose a saving-investment balance that is consistent with stabilizing these asset stocks, as ratios to GDP, at their current levels—especially if current levels are viewed as sustainable.

Ideally, the flow approach and the asset-related approach should be reconciled, with the former providing the transition path to the latter. Indeed, the mapping between net foreign asset stocks and current account flows in principle allows for consistency in examining external balance and equilibrium exchange rates from either a stock or flow perspective. Thus, precise notions about equilibrium ratios of net foreign assets *(NFA)* to GDP would provide estimates of a path for equilibrium current account ratios and exchange rates that could be combined with the saving-investment model to derive estimates of desirable or sustainable policies. But establishing consistency between assessments of equilibrium based on the saving-investment model and the asset-related methodology is difficult in practice without precise notions of desirable or sustainable levels for either the current account ratio or the *NFA* ratio, and without fully dynamic stock-flow models.^{5}

## Implementation of Saving-Investment Equilibrium

During recent years, the IMF staff has considered two different ways of implementing saving-investment equilibrium for exchange rate assessment. The first is inspired by long-run asset stock equilibrium; it focuses on the current account position that would be consistent with a stable ratio of net foreign assets *(NFA)* to GDP. In particular, writing that ratio as

and relying on the approximation that the change in the stock of net foreign assets equals net exports (abstracting from valuation effects and other complications),

then the cyclically adjusted current account ratio that stabilizes the net foreign asset ratio at its level *f* is simply^{6}

Needless to say, the usefulness of this type of saving-investment norm in assessing current account and exchange rate positions very much depends on one’s judgment as to whether a stable *NFA/GDP* ratio would represent a reasonable outcome for the particular countries in question. Alternative variants on this type of norm can easily be constructed based on alternative judgments about appropriate levels or time paths for *NFA/GDP* ratios. Such judgments may involve notions of desirability as well as sustainability.

The second implementation of saving-investment balance in the assessment of equilibrium exchange rates, which underpins the discussion in Section II and the analysis in Section VI, involves using esti-mated equations for saving and investment. The assessments then adjust for short-run influences (to obtain the shadow equilibrium) or for both these influences and policy changes (to obtain the desired equilibrium). A globally consistent reduced-form system of such saving-investment equations is derived in the next section. The approach of implementing a system of saving-investment equations has the advantage of using empirical evidence on the factors influencing saving and investment, including estimates of the effects of fiscal policies.

## Globally Consistent Equation Specifications

To derive the specification forms that are estimated empirically, we work with the simple saving-investment model described above and solve out for the world interest rate. If we write these equations in linear form as functions of the output gap *(GAP)*, the dependency ratio *(DEM)*, and the fiscal deficit *(DEF)*, as well as the world real interest rate *r* (supposing that all countries have the same coefficients),^{7} then

Averaging across the world implies:^{8}

where a bar over a variable indicates a global average. Therefore, the world interest rate will be given by:

This allows us to write each country’s saving and investment equations as reduced forms that depend on both country-specific (or relative) variables and world aggregates:

and

The coefficients on aggregate variables are derived as follows: *s*_{5} = *s*_{4}(*i*_{1} – *s*_{1})/(*s*_{4} – *i*_{3}), and so forth.

Each country’s current account equation (for *CA _{i}* =

*S*–

_{i}*I*) can also be derived. It can be shown, in this example where all countries have identical coefficients, that the current account does not depend on global variables, because changes in the world interest rate do not affect saving-investment balances, and that the equation can therefore be written

_{i}where *c*_{1} = *s*_{1} – *i*_{1}, *c*_{2} = *s*_{2} — *i*_{2}, and *c*_{3} = *s*_{3}.

The fact that a country’s saving-investment balance depends on differences between own-country variables and global averages implies, for example, that fiscal consolidation at home will not lead to an improvement in the current account balance unless it outpaces fiscal consolidation abroad, other things equal. Nevertheless, as seen in equations (4.18) and (4.19), a general global trend toward fiscal consolidation, which could not affect the aggregate global current account and might not affect current account positions of individual countries, could raise saving and investment levels across all countries. As evi-dent from the above derivations, one can think of the inclusion of the aggregate variables as capturing the (equilibrating) effects of changes in the world real interest rate on saving and investment in accordance with equations (4.14), (4.15), and (4.17).^{9}

^{}1

There are accounting differences between national accounts and balance of payments concepts, which will not be discussed here.

^{}2

By specifying saving and investment as a function of the world interest rate but not the domestic interest rate, the discussion here abstracts from the implications of possible divergences between these two rates. Such interest differentials can emerge for a variety of reasons, including the stage of the business cycle and the stance of monetary policy. To account for the effects on saving and investment of transitory interest rate differentials stemming from the cycle, the role of the output gap is explicitly considered later in this section. The issues of accounting for the effects of transitory movements in interest differentials not captured by the output gap, and for the effects of persistent interest rate differentials, are also discussed further below.

^{}3

A modern treatment of these issues is given, for example, in Blanchard and Fischer (1989), and Dixit and Pindyck (1994).

^{}4

For the empirical analysis discussed elsewhere in this study, the dependent population is defined as those 19 and under or 65 and over.

^{}5

See Section VIII for an assessment based on such a fully dynamic stock-flow model, namely, the Japan block of MULTIMOD.

^{}6

In calculating an asset-related norm for assessing the appropriateness of external positions in the medium term, two adjustments to the current account ratio have been regarded as important in recognition of factors that are thought to influence the desired path of assets over the medium run but assumed to lose relevance in the long run. The first adjustment is for differences in dependency ratios across countries. The other is for German unification, as the rebuilding of the eastern half of the economy is assumed to imply that Germany should be borrowing from the rest of the world.

^{}7

Including the output gap in the equations is intended to partially account for the fact that domestic interest rates may differ from the world interest rate, with implications for saving and investment levels. To allow for the effects of systematic (i.e., seri-ally correlated) albeit transitory movements in interest differentials *not* captured by the domestic output gap, the empirical framework can be further extended to include a lagged dependent variable in these equations (see Section VI), which may also reflect the effects of other sources of inertia (e.g., adjustment costs). The empirical analysis in Section VI also allows for country-specific values of the constant terms *s*_{0} and *i*_{0}. To the extent that for many countries domestic interest rates persistently differ from the world interest rate, the effects of the average differences are implicitly captured by the country-specific constants.

## References

Blanchard Olivier J. & Fischer Stanley 1989,

(Cambridge, Massachusetts: MIT Press).*Lectures in Macroeconomics*Dixit Avinash & Pindyck Robert S. 1994,

(Princeton, New Jersey: Princeton University Press).*Investment Under Uncertainty*Knight Malcolm D. & Masson Paul R. Frenkel Jacob 1988, “

*Fiscal Policies, Net Saving, and Real Exchange Rates: The United States, the Federal Republic of Germany, and Japan,” in*ed. by (Chicago: University of Chicago Press), pp. 21–59.*International Aspects of Fiscal Policies*,