The methodology described in previous sections of this study involves calculating the real effective exchange rate consistent with “medium-term macroeconomic balance.” This state of balance is defined when a country’s current account position equals the domestic saving-investment gap at conditions of full employment. As the current account position is assumed to be a function of the real exchange rate, while the saving-investment balance depends on exogenous factors, such as fiscal and demographic variables, this approach leads to a simple, recursive method for determining the equilibrium exchange rate.

Such a framework has proven useful in assessing the exchange rates of the major industrial countries. From a conceptual point of view, however, it involves simplifications of the full dynamic model that implicitly underlies exchange rate determination. Two issues, in particular, stand out. The first is the truncation of the analysis at the end of a fixed medium-term horizon. This necessarily abstracts from developments beyond this horizon that can, when markets are forward looking, influence the estimates of equilibrium saving-investment balances within the medium-term horizon. An example is expectations of longer-run movements in real exchange rates. With a high degree of international capital mobility, nonstationary exchange rate expectations will drive a wedge between domestic real interest rates relative to those in other countries, as investors equalize expected returns in domestic currencies adjusted for expected exchange rate movements. Deviations in domestic real interest rates from world levels, in turn, will affect the equilibrium saving-investment balance and thus the *level* of the real exchange rate consistent with macroeconomic balance. In this sense, the initial equilibrium level of the exchange rate is determined jointly with its longer-term equilibrium *path* in a full dynamic framework.

A second, related, issue involves the near-term dynamics of the exchange rate. In particular, a gap between the current exchange rate and its medium-term equilibrium level may not indicate misalignment if the movements in the exchange rate required to close this gap are already incorporated in market expectations. In this case, closing the gap would not imply “surprises” in financial markets over the medium term. This suggests a definition of misalignment that applies only when the movements in the exchange rate required to take it to its medium-term equilibrium level would lead to unanticipated shocks in financial markets. This consideration has sometimes been incorporated on an ad hoc basis in the IMF staff’s methodology, by taking into account observed market interest rate differentials in judging the medium-term path of the exchange rate. While useful, the approach has two drawbacks. First, the market interest rate differentials may not themselves seem appropriate in light of expected economic developments. Second, it does not allow an assessment of the effects of alternative assumptions about medium-term developments—including policy settings—on the current equilibrium exchange rate, as there is no mechanism for determining how interest rate differentials would move in response to changes in the economic environment.

This section extends the macroeconomic balance methodology by explicitly incorporating these dynamic considerations in a forward-looking model. In particular, the equilibrium exchange rate path is defined as the model-consistent solution for both current and future exchange rates. The advantage of this approach is that it allows for a fully simultaneous determination of exchange rates, interest rates, and saving-investment balances that highlights the intertemporal aspects of exchange rate determination. The disadvantages are its relatively high “information requirements”—including presumed knowledge of both the underlying economic model and the paths of the exogenous variables that drive the simulations. These requirements go well beyond those needed to apply the standard methodology, making the results more sensitive to model misspecification or forecasting errors. In addition, the complexity of the approach may make it more difficult to clearly motivate the factors contributing to the results and the implications of the underlying assumptions. Thus, there is a tradeoff between greater intellectual purity on the one hand, and the robustness and transparency of the results on the other.

The dynamic extension of the macroeconomic balance approach focuses on a single country, Japan. The next subsection discusses the conceptual issues raised above in more detail, highlighting the simplifications of the full dynamic model implied by the staff’s basic methodology. The third subsection presents simulation paths for the Japanese yen obtained from an empirical model that incorporates forward-looking behavior in financial markets. The fourth subsection assesses the sensitivity of the results to alternative assumptions about economic policies and longer-run developments, such as the impact of population aging. The section concludes with a summary of the results and a discussion of how the methodology could be further refined.

## Conceptual Issues

### Standard Methodology Revisited

The standard macroeconomic balance approach ties down the equilibrium exchange rate via the identity that links the current account balance to the domestic saving-investment (SI) balance. Under conditions of full employment, which are assumed to obtain by the end of the medium term, the SI balance of a given country is determined by structural factors such as its fiscal position, demographic structure, and stage of development. In addition, the SI balance depends on the real interest rate through its effect on consumption and investment. The full-employment SI balance can then be represented in stylized form as:

where *r* is the real interest rate, α is a parameter that indicates the sensitivity of the SI balance to the real interest rate, and *X*^{SI} is a vector of structural determinants of the SI balance. Making the further assumptions that exchange rate expectations are static and that capital is highly mobile between countries, the domestic real interest rate will equal the world rate. This allows the SI balance in equation (8.1) to be expressed only in terms of the world real interest rate, *r ^{w}*, and the vector of other structural determinants.

^{1}

The full-employment (or “underlying”) current account balance, *CA*, is a function of the real effective exchange rate, *rer* (defined in logarithms such that a rise indicates domestic currency appreciation), and a vector of exogenous variables that affect trade flows, *X*^{CA}:

The identity that the SI balance must equal the current account balance then allows equations (8.1) and (8.2) to be solved recursively for the external balance and the equilibrium real exchange rate, conditional on assumed values for the exogenous variables.

### A More General Framework

The above model is a specialized case of a more general framework in which exchange rate expectations may not be static and there may be less than perfect capital mobility between countries. Under these conditions, equations (8.1) and (8.2) must be supplemented by a relationship that describes external capital flows—the third “dimension” of the external balance. For current purposes, the net outflow of foreign capital, *KA*, is assumed to be a function of the expected return on foreign versus domestic as-sets, adjusted for expected exchange rate movements:

where *r* is the domestic real interest rate, *rer ^{e}* is the expected future level of

*rer*,

^{2}and the

*X*represents a vector of other factors that influence capital flows. The parameter γ indicates the sensitivity of capital flows to expected yield differentials. As there is now a distinction between the domestic and world real interest rate, the domestic SI balance in equation (8.1) will now depend not only on the world real interest rate but also on expectations of future real exchange rate movements.

^{KA}Through accounting identities, all three measures of the external balance must be equal: *SI* = *CA* = *KA*. Equations (8.1)—(8.3) then simultaneously determine three endogenous variables—the external balance, the real interest rate, and the real exchange rate—conditional on the *X* vectors, the world interest rate, and the expected exchange rate. It can be seen that the recursive model consisting only of equations (8.1) and (8.2) represents a specialized case when two restrictions are imposed on equation (8.3): that the parameter γ is infinite (i.e., there is perfect international capital mobility); and that *rer ^{e}* equals

*rer*(i.e., real exchange rate expectations are static). Under these assumptions, equation (8.3) collapses to a relationship where the domestic real interest rate equals the world rate, allowing it to be substituted out of equation (8.1).

We are particularly interested in a variant of equation (8.3) where there are no barriers to international capital mobility, thus γ is infinite, but where exchange rate expectations are not constrained to be static. This yields the familiar “open interest parity” (OIP) condition, which equates the domestic real interest rate to the world rate adjusted for expected exchange rate movements:^{3}

Under this assumption, the solution to equations (8.1)—(8.3) can be shown in two dimensions, as in Figure 8.1.^{4} Curve 1, with slope -β/α, indicates the combinations of *r* and *rer* that equate the current account balance and the saving-investment balance, based on equations (8.1) and (8.2). The curve is downward sloping, as a higher interest rate raises the SI balance, which in turn requires a reduction in the exchange rate to raise the current account balance by an equivalent amount. Curve 2 reflects the interest parity condition (equation (8.3’)), conditional on the world interest rate and the expected future exchange rate. This curve slopes up, as a rise in the domestic interest rate causes the exchange rate to appreciate such that the expected future *depreciation* offsets the higher yield on domestic assets. In the limiting case of static exchange rate expectations, curve 2 would be horizontal at the world real interest rate, as any movement in the current exchange rate would be matched by a shift in the expected future rate.

The positions of the two curves—and thus the equilibrium interest rate (*r**) and exchange rate *(rer*)*—depend on the *X* vectors, the world real interest rate, and the expected future exchange rate. For instance, a fiscal expansion would shift curve 1 upward, causing *r* and *rer* to both rise holding world interest rates and the expected exchange rate constant. The effect on the exchange rate would be smaller than when exchange rate expectations are static (i.e., where curve 2 is horizontal), as expectations of future exchange rate depreciation drive up domestic interest rates, thus crowding out domestic spending and moderating the drop in the SI balance. As the deterioration in the current account surplus would also be smaller, the required appreciation of the exchange rate would be reduced.

A second example involves a shock to the expected future exchange rate—due, for instance, to an anticipated *future* fiscal expansion. This would correspond to a shift to the right in curve 2, as the current exchange rate would have to increase by the same amount as the expected future rate holding domestic interest rates constant. Such an outturn, though, would have a contractionary effect on domestic output, causing domestic real interest rates to fall. This decline would moderate the impact on the exchange rate; in the new equilibrium, the exchange rate would rise, but not by as much as the expected future rate, as the decline in domestic interest rates would be accompanied by expectations of future exchange rate appreciation.

This simple framework is intended to illustrate how exchange rates and interest rates are simultaneously determined in a dynamic model with nonstationary exchange rate expectations. In particular, the above example of a shock to the expected exchange rate shows how the solution for the exchange rate and the interest rate in the current period is affected by future shocks via financial market linkages. The framework is not, of course, a complete description of longer-run interest rate and exchange rate determination, as it does not explicitly address the issue of how expectations are formed. In this sense, it is a singleperiod representation of the solution to a more general model in which expectations are endogenous.

Foreshadowing the discussion of the empirical model, it is convenient to assume that expectations of future exchange rates are consistent with the model outlined in a stylized form in equations (8.1)—(8.3). In this case, the expected value for the exchange rate in the next period, *t*+1, formed in period *X* vectors *t*+2. By repetitive substitution, all future values of the exchange rate can be replaced by expected realizations of the *X* vectors. In this way, the current equilibrium levels of the real exchange rate and the real interest rate can be expressed as a function of expected future values of the *X* vectors:

Defining a long-run steady state as a situation in which the X vectors assume the same values in successive time periods (perhaps scaled by a trending variable such as technology), the equilibrium real exchange rate will be stationary, and thus the domestic real interest rate will equal the world rate (assuming open interest parity). As in the simpler model described initially, this again allows equations (8.1)—(8.2) to be solved recursively for the equilibrium exchange rate. Specifically, the domestic SI balance is “tied down” by the world real interest rate, and the exchange rate is determined by the conditions that the current account equal the SI balance. The dynamic relationship for the exchange rate represented by equation (8.3’) can then be thought of as an Euler equation, the solution to which must satisfy the transversality condition given by these long-run conditions.

Turning to short-run dynamics, the impact of cyclical fluctuations in output, prices, and financial variables that arise from price level stickiness was suppressed in the above discussion by assuming continuous conditions of full employment. With this assumption, the model can be entirely expressed in terms of real variables, leaving no role for nominal shocks to affect equilibrium exchange or interest rates. Yet nominal shocks will, in general, influence real variables in the presence of sticky prices, as illustrated in the well-known exchange rate overshooting model of Dornbush (1976).

The standard methodology is not well suited for explicitly taking cyclical factors into account, as it is based on the configuration of real variables under conditions of full employment. The dynamic model outlined above, however, when suitably augmented by equations describing the short-term adjustment of prices, output, and financial variables, can incorporate the impact of nominal shocks in solving for a general, expectations-consistent path for the exchange rate. Consider, for example, an unanticipated easing of monetary policy. Assuming that the real effects of such a shock dissipate by the end of the medium term, it would not alter the assessment of the equilibrium real exchange rate based on the standard macroeconomic balance approach. It would, however, tend to drive down real interest rates over the intervening period, resulting in a depreciation of the initial level of the real exchange rate in the more general dynamic model. In this way, the general model can consistently incorporate cyclical and monetary factors into the assessment of equilibrium exchange rates.

In summary, the standard methodology implicitly assumes that real exchange rate expectations are static, which would be consistent with the economy being in a steady state by the end of the medium term. This substantially simplifies the analysis by making the derivation of equilibrium exchange rates recursive—the full-employment SI balance determines the current account balance, which in turn determines the exchange rate. Allowing for nonstationary expectations, in contrast, makes the framework simultaneous, as interest rates depend on exchange rate expectations, leading to feedback effects on the SI balance and the equilibrium level of the exchange rate. This simultaneity extends beyond the current period, as the outturn in future periods will influence—and be influenced by—present developments. These dynamic considerations are likely to be particularly important in two types of situations: when there are long-lived and changing shocks to the exogenous variables for a given country that lead to long periods of nonstationary real exchange rates; and when short-term cyclical forces drive the current real exchange rate away from its expected medium-term level.

### Meaning of Misalignment in a Dynamic Context

Before turning to the empirical analysis, it is useful to briefly discuss what misalignment means in the context of the above framework. At any given time, the observed values of *rer* and *r* determined by markets must reflect the intersection of the curves in Figure 8.1, in the sense that they reflect a market-clearing equilibrium. Looked at from this static perspective, the only issue is how to solve “backwards” for the values of the *X* vectors, the expected future exchange rate, and the structural parameters that are consistent with the observed market outturn for the exchange rate. In this sense, the market exchange rate is always in equilibrium at a point in time. Misalignment, then, must be framed in terms of the consistency of the current exchange rate with its expected future path—specifically, whether this path represents a full expectational equilibrium.

Put more concretely, the exchange rate is in a full expectational equilibrium only when market expectations of its path are consistent with the predictions of the “true” model underlying equations (8.1)—(8.3), based on all available information. When these paths coincide, the current exchange rate is intertemporally consistent in the sense that there is no reason, ex ante, to expect future surprises in exchange markets. Ex post, of course, unanticipated shocks can occur that redefine the equilibrium and move the exchange rate away from the original path. But as long as such shocks are not predictable, the initial exchange rate is not misaligned.

Suppose, in contrast, that market expectations and the true equilibrium path do not coincide. As the future unfolds, even in the absence of unanticipated shocks, markets will discover that actual interest rates and exchange rates are higher or lower than expected. As a result, there will be unanticipated gains or losses on holding domestic versus foreign assets. Agents whose expectations are closer to the true values will make windfall gains, while others will make losses. Assuming that markets learn over time from their mistakes, expectations will converge on the true path, and the exchange rate will adjust toward its equilibrium level.

## Simulations Using a Dynamic Model

This section provides an empirical implementation of the above concepts by simulating a forward-looking macroeconomic model to obtain consistent dynamic paths for the exchange rate and interest rates. For this purpose, we employ a modified version of the Japanese block of MULTIMOD—the IMF staff’s multicountry macroeconomic model.^{5}

Japan is particularly appropriate to use for illustrating the full dynamic analysis for two reasons. The first is that the real effective value of the Japanese yen has been nonstationary over a long period when defined in terms of broad-based price indices, such as the consumer price index (CPI) or wholesale price index (WPI). This phenomenon is illustrated in Figure 8.2, which shows a trend real appreciation of the CPI-based index of about 3 percent a year over the past four decades, while the WPI-based index has risen by about 1½ percent a year since the early 1970s. The index constructed using export unit values, in contrast, has been broadly constant over the past twenty-five years, suggesting that the upward trend in the CPI- and WPI-based indices can be attributed to so-called Balassa-Samuelson effects. In particular, high productivity growth in Japan’s traded goods sector relative to the domestic goods sector has allowed an upward trend in Japan’s overall price level relative to those in trading partners without jeopardizing international competitiveness.^{6}

**Japan: Alternative Measures of the Real Effective Exchange Rate ^{1}**

(Log scale; 1951 = 100)

Sources: Nikkei Telecom; WEFA; and IMF staff estimates.^{1}CPI-based rate employs an average of major industrial partner countries; WPI-based rate employs an average of major industrial partner countries for which WPIs are available (the United States, Germany, and the United Kingdom); relative export unit values are based on major industrial partner countries.

**Japan: Alternative Measures of the Real Effective Exchange Rate ^{1}**

(Log scale; 1951 = 100)

Sources: Nikkei Telecom; WEFA; and IMF staff estimates.^{1}CPI-based rate employs an average of major industrial partner countries; WPI-based rate employs an average of major industrial partner countries for which WPIs are available (the United States, Germany, and the United Kingdom); relative export unit values are based on major industrial partner countries.

**Japan: Alternative Measures of the Real Effective Exchange Rate ^{1}**

(Log scale; 1951 = 100)

Sources: Nikkei Telecom; WEFA; and IMF staff estimates.^{1}CPI-based rate employs an average of major industrial partner countries; WPI-based rate employs an average of major industrial partner countries for which WPIs are available (the United States, Germany, and the United Kingdom); relative export unit values are based on major industrial partner countries.

As noted in the discussion of conceptual issues, the dynamic analysis is likely to be particularly appropriate in the face of pronounced trends in real exchange rates, such as those evident for Japan. To the extent that they are expected to continue, such trends will drive a wedge between Japanese and foreign real interest rates, and thus affect Japan’s equilibrium saving-investment balance. Furthermore, the prospect of a rapid shift in Japan’s demographic structure in coming decades toward a more elderly population is likely to have important repercussions on saving-investment balances and potential growth rates relative to those in other countries. These, in turn, will affect the future equilibrium path of the real exchange rate, with implications for its current level when agents are forward looking.

The second factor that makes Japan appropriate for the dynamic analysis is short term in nature. Japan experienced a prolonged slowdown in economic activity in the first half of the decade, and output growth has faltered again in 1997. In response to weak cyclical conditions, monetary policy has been eased substantially, leading to historically low levels of short- and long-term interest rates. Under the assumption of open interest parity, these low interest rate levels will be associated with expectations of yen appreciation over the medium term, as cyclical im-balances unwind. Again, an assessment of the appropriate path for the exchange rate in the face of large cyclical imbalances is more tractable with the full dynamic model than with the standard framework.

### Outline of MULTIMOD

Before presenting the simulation results, it is useful to sketch out how the structure of MULTIMOD relates to the stylized framework described above. MULTIMOD embodies neoclassical relationships for domestic spending and external trade, as well as dis-equilibrium relationships that determine how output and prices adjust to excess demand or supply conditions. It also reflects forward-looking behavior in financial markets, in that the predicted paths for the financial variables are “model consistent.” Specifically, it solves for paths for interest rates and the exchange rate such that there are no unanticipated surprises in financial markets over the simulation horizon. For the exchange rate, this means that the open interest parity condition represented by equation (8.3’) holds for all simulation periods—with the important exception of the first period, when the exchange rate can “jump” to its equilibrium path. This jump indicates the extent to which the exchange rate is initially misaligned, in the sense that it reflects an excess yield on either the domestic or foreign asset that was not incorporated in market expectations.

MULTIMOD has been extensively used within the IMF for policy simulation analysis. The present application, however, required constructing a forecasting version of the model that could be used to derive baseline projections for the key variables. Adapting it required several modifications, as described in Appendix I. The most important changes involved reestimating the parameters in the trade and spending blocks to make them more Japan-specific;^{7} modifying the definitions of human and capital wealth to allow for forward-looking behavior without making the associated expectations fully model consistent; and changing the policy reaction function of the monetary authorities such that the real short-term interest rate responds to deviations in nominal income from a target path.^{8} In addition, it was necessary to modify the monetary reaction function to prevent nominal interest rates from assuming negative values—a situation that was frequently observed in un-constrained simulations given the very low starting point for Japanese interest rates. The role of this constraint is discussed in more detail below.

An additional issue that arose in constructing a baseline path was how to tie down the terminal conditions for the forward-looking variables.^{9} Models are generally simulated over a finite horizon, yet values for the forward-looking variables are needed beyond the simulation horizon to tie down their paths in the last periods of the simulation. In the case of the exchange rate, for instance, its value in the last simulation period depends on its expected value in the first period beyond the simulation horizon. To solve this issue, a technique was used that has become increasingly popular in the solution of such models. Specifically, a steady-state version of the dynamic model was constructed that yielded long-run solutions for the endogenous variables for given levels and growth rates of the exogenous variables (as described in Appendix II).^{10} These steady-state values were then used as terminal conditions for the dynamic model.

### Exogenous Assumptions

The model simulations reported here were performed using annual data for 1997–2070, starting from the database and projections underlying the October 1997 *World Economic Outlook*. The first step was to construct paths for the exogenous variables, specifically: foreign activity, inflation, and interest rates; world oil and commodity prices; and domestic productivity growth, labor force growth, and population dependency ratios. For the external variables, the IMF staff’s World Economic Outlook projections were used to the end of the medium-term horizon (i.e., the year 2002). Over the period, growth in foreign activity (defined as the weighted average of partner-country GDP) converges to just over 4 percent a year; foreign inflation (average growth in partner-country export prices and GNP deflators, in U.S. dollars) converges to 1½ percent a year; and the foreign interest rate (the short-term interest rate on U.S. dollar assets) stabilizes at 5¾ percent. World oil and commodity prices remain broadly constant in real terms. Beyond 2002, we assume that foreign growth gradually declines to 1 percent by 2050, as growth rates in developing Asian economies slow toward the steady-state rates assumed for the developed countries. The real interest rate on U.S. dollar assets also falls by about 1 percentage point to reflect the slowing in global growth.

On the domestic side, exogenous variables include the rate of labor-augmented productivity growth and demographic factors. For labor productivity, growth is assumed to converge to the (roughly) 1 percent rate that has been observed in the United States since the early 1970s. The demographic assumptions are based on the projections for Japan released by the Ministry of Health and Welfare in January 1997, which cover the period to 2070. The total population, the population of labor-force age, and the dependency ratio come directly from these projections. To project the active labor force, the participation rate is assumed to rise gradually through 2002 and then to remain constant thereafter.

Regarding economic policies, the baseline assumption is that no medium-term fiscal consolidation measures are introduced beyond 1997, except those associated with the 1994 pension reform plan.^{11} On monetary policy, the implicit nominal growth target equals potential output growth plus a fixed growth rate for the GDP deflator. The latter was set at ½ of 1 percent a year—the rate at which inflation stabilizes in the medium-term World Economic Outlook forecast.

After defining paths for the exogenous variables, it was necessary to adjust the model’s stochastic equations to yield reasonable predictions for the endogenous variables, especially over the near-term horizon. In particular, a completely model-based forecast, with no judgmental adjustments, yielded simulation values that in many cases were not plausible. This is not surprising, given the highly aggregated nature of MULTIMOD and the fact that it was constructed as a policy simulation as opposed to a forecasting model.

To address this problem, “add factors” were introduced to some of the model’s stochastic equations such that they would replicate the World Economic Outlook forecast over the 1997–2002 period *if the values for the exchange rate and interest rates corresponded to their WEO assumptions*.^{12} To better understand this approach, it is necessary to explain the basis of the WEO assumptions for financial variables. Specifically, real exchange rates remain unchanged over the forecast horizon, with the starting level being determined by observed market data at the beginning of the forecast period. For interest rates, paths are assumed consistent with output re-turning to potential over the medium term, conditional on the given level of the real exchange rate. Looked at in terms of the conceptual framework, the WEO projection for Japan first solves equation (8.2) for the current account based on the exogenous exchange rate assumption; equation (8.1) is then solved recursively for the interest rate that equates the SI balance to the current account.^{13} No attempt is made in the WEO framework, then, to impose a consistent path for interest rates and the exchange rate (i.e., equation (8.3’) does not generally hold).^{14}

Taking this WEO forecast as a starting point, MULTIMOD was used to impose consistency in financial markets via equation (8.3’), and then to assess the impact on the other endogenous variables. The model simulations then differ from the WEO projections for two reasons: (1) the paths for the financial variables are fully expectations-consistent through the medium-term projection period, as op-posed to being arbitrarily imposed, and (2) the paths for the forward-looking variables are consistent with the model’s predictions beyond 2002, as opposed to relying on implicit assumptions in the WEO (the horizon of which formally ends in 2002).

### Baseline Path

The baseline paths for the real exchange rate and some other key variables are shown in Figure 8.3. The real effective value of the yen declines by about 4 percent in 1997 (the first simulation period) from its historical level in 1996, in spite of a real interest rate differential in 1996 favoring foreign assets of about 3 percentage points.^{15} Taken together, this implies (under model-consistent expectations) an “excess return” on dollar assets of about 7 percent at the starting point of the simulation, indicating the extent to which the yen is estimated in this framework to have been overvalued in 1996.^{16}

It is interesting to note that the simulated level of the exchange rate in 1997 is about 15 percent below the trend implied by the historical experience. Two factors are at work here. The first is the cyclical position of the Japanese economy discussed above: the large output gap and the absence of inflationary pressures result in very low real interest rates in the initial years of the simulation. This, in turn, pushes down the initial level of the exchange rate, while at the same time increasing its rate of appreciation over the medium term. The second factor is structural changes in Japan’s trade flows in recent years, which have boosted imports and reduced exports beyond the levels predicted by traditional trade equations. These shifts tend to lower the level of the exchange rate consistent with a given external balance, and thus lower the equilibrium exchange rate for given determinants of saving and investment.

From its 1997 level, the real exchange rate appreciates at a rate averaging slightly over 3 percent a year through the medium-term horizon ending in 2002, consistent with the model’s projection of a continuing large real interest differential between dollar and yen assets. In the event, the model’s prediction for the yield differential is similar to that observed in bond markets as of late 1997, suggesting that the ad hoc adjustments for market expectations of exchange rate movements, as made in the staff’s application of the standard methodology, are broadly consistent with the model predictions. While the yen appreciates at a rate similar to the historical trend, the *level* of the exchange rate remains well below trend over the medium term. This reflects, among other things, the assumed continuation of structural changes in Japan’s trade patterns referred to above.

The level of real GDP gradually returns to potential over the medium term, as cyclical factors unwind, while the current account surplus declines to about 1 percent of GDP by 2002. Given that output has returned to full employment, this external surplus corresponds to the medium-term SI balance that plays a central role in the standard approach to exchange rate assessments. In the event, the value obtained is similar to that predicted by the reduced-form estimation framework described in Section II. It is apparent, though, that the current account surplus has not stabilized by the end of the medium term. Instead, it continues to narrow until about 2010, before falling into a deficit of ½ of 1 percent of GDP by 2020. This reversal of Japan’s external position is associated with the most pronounced phase of the population aging process, as the population dependency ratio rises from about 45 percent at the beginning of the century to nearly 70 percent by 2020.^{17} The current account surplus falls because the elderly are assumed to have a lower saving rate than the working-age population, so an increase in their population share puts downward pressure on the overall saving rate. Consistent with downward pressure on aggregate saving, the real exchange rate appreciates sharply over this period, rising by almost 3½ percent a year from 2005–2020.

While these effects of population aging are quite striking, the impact on Japan’s current account is significantly smaller than some other analyses have suggested.^{18} There are four reasons for this. The first three are fairly straightforward: (1) the assumed effect of demographic changes on saving is smaller in this version of the model than some time-series evidence that has been used in other studies would suggest;^{19} (2) private investment declines in relation to GDP as growth in the labor force and potential output slows; and (3) fiscal consolidation measures are assumed to be gradually implemented beyond 2002 that would prevent an unsustainable rise in government debt, so higher government saving partly off-sets lower private saving. The fourth reason is more subtle, involving the intertemporal dynamics of exchange rate and interest rate determination in the model. In particular, as the population age structure stabilizes from about 2020 to 2035, downward pressures on the saving rate and consequent upward pressures on the real exchange rate ease. In the face of expectations of reduced yen appreciation, real long-term interest rates in Japan rise relative to those in the rest of the world, further compressing domestic investment and thus offsetting part of the impact of lower saving on the external balance.

Beyond 2020, the path of the yen exhibits three distinct phases. From 2020 to roughly 2030, its real value stabilizes, followed by a further sharp rise from about 2030 to 2045. Beyond 2045, the yen again levels off. Over the simulation period as a whole, the real value of the yen rises to roughly 37½ times its 1996 level, implying an average annual growth rate of about 1¾ percent.^{20} As discussed below, the swings in the yen’s longer-term growth rate are due primarily to demographics, as the economy experiences various phases of the aging process. In addition to a stabilization of Japan’s demographic structure, the eventual leveling off of the yen’s value is also due to the assumption that the technological and other factors that have contributed to its trend increase in the past will decay over the longer term, consistent with the eventual achievement of a steady-state growth path.

## Alternative Scenarios

This section presents several alternative scenarios based on different paths for some of the key exogenous variables. The expected future settings of economic policies, for instance, can have important effects on the initial level of the exchange rate in forward-looking models. In this context, the baseline assumes no new fiscal policy initiatives toward consolidation during 1997–2002 beyond those adopted in the budget for 1997/98.^{21} As this scenario would leave the deficit at an unsustainably high level at the end of the medium term, we explore here the implications of medium-term fiscal consolidation actions that would substantially reduce the deficit by early in the next decade. Regarding monetary policy, the baseline assumes a very low (implicit) target for inflation of ½ of 1 percent a year through the medium term. The alternative examined here is a rise in the authorities’ assumed objective for inflation to 1½ percent a year, implying a somewhat easier monetary stance than assumed in the baseline. In both cases, we examine the implications for the exchange rate of the constraint that nominal interest rates are prevented from turning negative in the simulations by hypothetically relaxing it, and allowing short-term nominal interest rates to assume the values that would otherwise be generated by the reaction function.

Regarding the role of structural factors, the alternative scenarios focus on the causes of the longerrun appreciation of the yen observed in the baseline. The role of three factors is assessed: (1) the shift toward a more elderly population structure in Japan; (2) the assumption of continued robust growth in Japan’s developing trading partners; and (3) ongoing Balassa-Samuelson effects that continue to reduce the price of Japan’s exports relative to overall prices.

### Alternative Policy Assumptions

For fiscal policy, the alternative scenario assumes that medium-term consolidation plans are implemented to put the fiscal situation on a sustainable footing. As discussed in Okamura (1996), past staff estimates have suggested that measures amounting to roughly 4 percent of GDP would be needed to achieve this goal. To assess the impact of the credible implementation of such a plan on the exchange rate, both spending and taxes were adjusted in the model in a way that divided the burden of deficit reduction roughly equally between these two components over the 1998–2002 period.

The results are shown in Figure 8.4 for the period 1997–2015, both for the scenario in which there is a liquidity trap (i.e., a floor of zero on nominal interest rates) and when this constraint is hypothetically relaxed. The results are expressed as deviations from the baseline simulation, except for the nominal short-term interest rate, which is shown in levels to indicate the role of the liquidity trap.^{22} When the liquidity trap is binding, the real exchange rate depreciates on impact by about 3 percent from its baseline, reflecting expectations of lower future real returns on yen assets in the face of fiscal consolidation.^{23} On impact, though, the real long-term interest rate actually rises slightly, as nominal interest rates are constrained from turning negative, while expected inflation declines in response to weaker real activity. Long-term interest rates gradually decline through the next five years of the simulation, as the floor on nominal interest rates becomes less binding; at the same time, expected inflation rises as agents anticipate a future recovery in real activity. Thus, the exchange rate depreciates further (relative to baseline) until 2001, falling at that time about 7 percent below baseline. The exchange rate subsequently recovers as the effects of front-loaded fiscal consolidation on aggre-gate demand are reversed over the longer run.^{24}

**Front-Loaded Fiscal Consolidation Scenario**

(Deviation from baseline simulation unless otherwise indicated)

**Front-Loaded Fiscal Consolidation Scenario**

(Deviation from baseline simulation unless otherwise indicated)

**Front-Loaded Fiscal Consolidation Scenario**

(Deviation from baseline simulation unless otherwise indicated)

The results in the fiscal consolidation scenario in which the liquidity trap is hypothetically removed are more typical of the standard results obtained with forward-looking models.^{25} Both real interest rates and the real exchange rate fall sharply on impact, as monetary conditions can be relaxed by more in response to fiscal consolidation than in the scenario discussed above. Given the assumed reaction function, short-term nominal interest rates would fall about 1½ percentage points below the floor imposed by the liquidity trap in the initial years of the simulation. Easier monetary conditions cushion the impact on output and inflation, resulting in a decline in output that is less than half as large by 2001. Beyond the first year of the simulation, rather than declining further, the real exchange rate steadily appreciates back toward the baseline level, as the effects of deficit reduction on aggregate demand unwind.

The alternative scenario for monetary policy assumes a rise in the implicit objective for inflation to 1½ percent from the ½ of 1 percent rate assumed in the baseline.^{26} The results are shown in Figure 8.5, again in terms of deviations from baseline. In the presence of the liquidity trap, the real exchange rate depreciates by roughly 3 percent on impact, as easier monetary policy results in lower real interest rates in the initial years of the simulation. Output and inflation are both initially boosted by the stimulative effects of monetary easing; in contrast, the current account balance is little affected, as a weaker exchange rate and stronger domestic demand have offsetting effects on the net trade position. Over time, the inflation rate stabilizes at 1 percent above its baseline, consistent with the change in the assumed objective. The real exchange rate does not return to baseline over this horizon, however, because the impact of a shock to target inflation is not fully neutral in terms of its real effects. In particular, higher inflation raises nominal interest rates, which lowers real money balances and wealth. Households compensate by reducing spending, which raises (slightly) the current account surplus and reduces the equilibrium exchange rate over this horizon.

**Higher-Inflation Target Scenario**

(Deviation from baseline simulation)

**Higher-Inflation Target Scenario**

(Deviation from baseline simulation)

**Higher-Inflation Target Scenario**

(Deviation from baseline simulation)

In the absence of the liquidity trap, the introduction of a higher inflation target would cause the real effective exchange rate to depreciate more sharply, as there would be a somewhat larger initial decline in nominal and real interest rates. Output and inflation would also be subject to more pronounced cycles in the initial years of the simulation, as the liquidity trap would not constrain the instruments of monetary policy. This is the reverse of the situation in the fiscal consolidation scenario, where the liquidity trap limits the extent to which monetary easing can offset the contractionary impact of a tighter fiscal stance.

### Long-Term Structural Factors and Yen Appreciation

The baseline scenario envisages a continuation of the appreciation of the yen that has been observed during the postwar period well into the next century. What are the main factors that would explain a further substantial rise in Japan’s equilibrium real exchange rate? To answer this question, alternative scenarios were performed that isolated the role of the main features of both the model and the baseline data that could explain trend movements in real exchange rates. It turned out that almost all of the projected rise in the real value of the yen could be explained by three factors: (1) changes in Japan’s demographic structure, and specifically a combination of slowing population growth and an aging population;^{27} (2) the assumption of rapid trend growth in trading partners; and (3) a further secular decline in Japan’s export prices relative to the overall price of output.

Before looking at the results, it is useful to summarize the channels through which these factors affect the real exchange rate in the model. Consider first an increase in the population dependency ratio, holding the total population constant. Such a shift will both raise the level of consumption relative to income and lower the size of the labor force and thus potential output. The increase in consumption puts upward pressure on the exchange rate in the near term, as higher spending raises the real interest rate, making domestic assets more attractive. Over the long run, however, higher spending lowers Japan’s stock of foreign assets and thus foreign income, which reduces both total spending and the equilibrium level of the yen. The reduction in the labor force and potential output tends to cause the yen to appreciate at all horizons, as it reduces the supply of Japan’s output relative to foreign output. Given that Japanese and foreign output are imperfect substitutes in MULTIMOD, the “supply” effect puts upward pressure on the relative price of Japanese output and thus the real exchange rate. Similarly, higher foreign growth raises Japan’s real exchange rate, other things equal, by increasing foreign demand for Japanese output and thus raising its equilibrium relative price. Finally, continued declines in export prices relative to the price of overall output allow Japan’s equilibrium real exchange rate to rise over time without undermining external competitiveness.

It is apparent from Figure 8.6 that demographic factors have an important impact on the exchange rate in the baseline simulation. In particular, in the absence of demographic changes beyond 2002 (the scenario labeled alternative 1), the swings in the long-run growth rate of the yen would be almost entirely eliminated. In addition, the real exchange rate in this scenario would be about 40 percent lower than in the baseline by the end of the long-term simulation. The longer-term depreciation of the yen (relative to baseline) is due to the effect of unchanged demographics on the labor force and potential output—both would be about 40 percent *higher* by 2070 than under the baseline population projection, reducing the long-run level of the yen through the channels described above.

**Alternative Long-Run Assumptions**

**Alternative Long-Run Assumptions**

**Alternative Long-Run Assumptions**

The scenario labeled alternative 2 shows the impact of turning off Balassa-Samuelson effects beyond 2002, in addition to assuming no further demographic changes. In particular, it was assumed that there was no further secular downward trend in Japan’s export prices relative to the GDP deflator after 2002, as opposed to the baseline assumption that this trend continues well into the next century. The absence of continuing Balassa-Samuelson effects reduces the real exchange rate by a further 35 percent by the end of the long-term simulation horizon.

Finally, alternative 3 imposes the additional assumption that foreign real output growth declines to its assumed steady-state level of 1 percent a year starting in 2002, as opposed to the much more gradual reduction in growth over the first half of the next century assumed in the baseline. Combined with the assumption of no further demographic or Balassa-Samuelson effects, this results in a simulated level of the real exchange rate that is basically constant over the long-term horizon, confirming that the above three factors fully explain the yen appreciation observed in the baseline. Decomposing the relative importance of each factor, slightly over one-third of the rise is due to the assumption of continued rapid growth in trade partners through the middle of the next century; about one-third is explained by population aging in Japan and the associated drop in the labor force and potential output; and somewhat less than one-third is explained by continued Balassa-Samuelson effects.

It is interesting to note that, in all of the longer-term alternative simulations, the level of the real exchange rate in the starting years of the simulations is affected by developments beyond 2002, the period over which the exogenous assumptions are changed. For instance, in alternative 3, the value of the yen in 1997 is about 24 percent below its baseline. Again, this reflects the intertemporal dynamics of exchange rate determination. Eliminating the long-run factors that cause yen appreciation beyond 2002 tends to drive up real long-term interest rates in Japan in the initial years of the simulation, as forward-looking agents no longer expect lower yields on domestic assets to be offset by future exchange rate appreciation. This, in turn, raises the domestic saving-investment balance and thus the equilibrium current account balance, lowering the equilibrium real exchange rate. In the event, real long-term interest rates in Japan would be about 3½ percentage points higher by 2002 in the absence of future yen appreciation, while the current account surplus would be about 3 percent of GDP or larger.

## Conclusions

This section has described a dynamic framework for assessing equilibrium exchange rates and implemented it for the Japanese yen using simulations of a forward-looking model. The baseline results suggest that the yen was somewhat overvalued in 1996 and very significantly overvalued in 1995. Consistent with the projected continuation of a large real interest differential between yen and foreign assets, the simulated real value of the yen appreciates substantially over the medium term. In the event, the 20 percent real appreciation predicted between 1997 and 2002 is similar to that implied by existing market interest differentials, providing support for the type of adjustments that the staff has made to incorporate market expectations into the standard methodology.

The alternative simulations illustrate how both the starting point and the future path of the yen are affected by different assumptions regarding economic policies and other exogenous variables. Implementation of a front-loaded fiscal consolidation plan, for instance, would significantly lower the equilibrium exchange rate in the short run, but cause it to appreciate relative to the baseline level in the long run. The results for Japan, though, are importantly affected by the constraint that nominal interest rates are prevented from becoming negative in the simulations. Given the low initial level of nominal interest rates, this limits the extent to which monetary easing can offset tighter fiscal policy, resulting in larger initial output losses. On the monetary side, the assumption of a higher implicit target for inflation than assumed in the baseline would also cause the real exchange rate to depreciate on impact, but to appreciate in subsequent years. Again, the results are affected by the presence of a liquidity trap, which limits the initial drop in nominal interest rates that would otherwise be observed.

Regarding the long-run path for the yen, the simulations suggest that the upward trend in its real value will continue well into the next century, although at a more modest pace than in recent decades. The key factors explaining the continuing upward trend are: (1) rapid growth in developing Asian economies; (2) continued Balassa-Samuelson effects; and (3) the effect of population aging in lowering the labor force and potential output in Japan. As these factors are assumed to dissipate in the very long run, the yen eventually stabilizes. The long-run path for the yen also has implications for its near-term equilibrium level. In the absence of expectations of real exchange rate appreciation beyond 2002, real interest rates in Japan would be higher in the initial years of the simulation, which would raise the equilibrium current account surplus and lower the equilibrium level of the yen.

While the model-based results provide a useful check on the methodology described in earlier sections, the use of full-scale dynamic models for this purpose has drawbacks. As the sophistication of the approach increases, so do the information requirements and the sensitivity of the results to misspecification or inappropriate assumptions. Given these caveats, the present results should be considered suggestive. One future direction for refining the analysis would be to replicate the methodology for other countries to allow a global perspective on the impact of demographic changes and macroeconomic policies on exchange rates. Such an approach, though, could well magnify the sensitivity of the results to errors in the assumptions and reduce the transparency of the analysis. Another refinement would be to revisit the specification of certain key blocks of MULTIMOD. The production sector, for instance, models output as a single commodity; dis-aggregation would allow a richer analysis of the effects on the exchange rate of factors such as deregulation and structural reform.

Finally, it would be useful to incorporate “market learning” processes into the financial sector of MULTIMOD to allow an analysis of how misalignments might be resolved over time. The current approach only describes the extent to which misalignments may exist, but not their dynamic implications for variables such as output, prices, and interest rates. Analysis that incorporated learning might also provide a richer basis for examining how macroeconomic policies can and should respond to misalignments.

## Appendix I. Changes to MULTIMOD

The following changes were made to the Japan block in the simulation version of MULTIMOD described in Masson, Symansky, and Meredith (1990) to adapt it to baseline forecasting purposes:

*Human and capital wealth*. In the original version of the model, the (unobserved) levels of human and capital wealth are defined as the discounted values of future simulated earnings streams. It proved difficult to use this specification for baseline forecasting, as unique historical levels for these variables were not defined. Instead, wealth was defined using current flows for income streams adjusted for the expected rate at which they would return to their “potential” levels. This is similar to the approach used in an earlier version of MULTIMOD (see Masson and others (1988)).*Disaggregation of deflators*. MULTIMOD has only one deflator for all components of domestic absorption. Yet there are significant historical trends in the growth rates of different components of spending—investment deflators, for instance, have tended to fall over time relative to consumption prices. To deal with this issue, deflators for the components of absorption were disaggregated and time trends were introduced into the equations explaining their growth to allow for differences in secular growth rates.*Trade parameters and trends*. The trade equations in the original model were estimated using pooled data for the major industrial countries. In some cases, the parameters differed significantly from those generated by Japan-specific trade models (see, for instance, Chadha (1996)). In addition, certain of the equations did not satisfy the long-run homogeneity properties required for a steady-state solution. To resolve this problem, the trade block was reestimated using only Japanese data from 1970–95, and long-run homogeneity was ensured by imposing appropriate parameter constraints.*Demographics and consumption*. In the original version of the model, the population dependency ratio had a very strong impact on consumption and saving, based on time-series estimation. More recent work, including that by Meredith (1995), suggests a smaller effect. Based on these results, the parameter on the demographic ratio in the consumption function was lowered such that a 1 percentage point rise in this ratio lowers the private saving rate by about ⅓ of 1 percentage point, as opposed to almost a full percentage point in the original version of the model.*Reaction function for monetary policy*. The reaction function in the original version of the model was modeled as a money supply rule, where nominal interest rates were adjusted in response to deviations in the money stock from target. The properties of this rule proved problematic for forecasting, and it was replaced by a function that causes the real short-term interest rate to adjust in response to deviations in both the level and the growth rate of nominal GDP from a fixed target. In addition, a constraint was imposed that nominal interest rates could not be negative, by setting the simulated interest rate at zero if the reaction function would otherwise have generated a negative interest rate.*Inflation equation*. The linear relationship between the output gap and inflationary pressures was replaced by the nonlinear relationship described in Laxton, Meredith, and Rose (1995). In this formulation, positive output gaps tended to raise inflation by more than negative gaps lowered it, an asymmetry that seemed consistent with the Japanese experience during the recent economic cycle.

## Appendix II. A Steady-State Version of the Exchange Rate Model

As discussed in the main text, a steady-state version of the dynamic exchange rate model was constructed to derive terminal conditions for the forward-looking variables. This was done by transforming leads and lags on the variables in the dynamic model into their contemporaneous values, using the appropriate steady-state growth rate for each variable. These steady-state growth rates, in turn, were based on the growth rates assumed for the exogenous driving variables in the model.

As a stylized example of the procedure, consider the following dynamic equation for the endogenous variable *x*, where *z* is exogenous (both are measured in logarithms):

In the steady state, *x* will grow at the same rate as *z*, given the homogeneity imposed in the parameter values.^{28} As the variables are measured in logarithms, this growth rate corresponds to *z _{t}* -

*z*, represented as λ. Then the lag and lead on

_{t-1}*x*in the above equation can then be substituted out as follows:

implying that

In this way, the steady-state model can be expressed in terms of only the contemporaneous values of the variables and their steady-state growth rates. Simulating this static model then yields the terminal conditions that were necessary for the dynamic simulations.

The steady-state growth rates themselves were determined as follows. Real growth for the Japanese variables is tied down in the steady state by the exogenous rate of labor-augmented productivity growth, which is assumed to equal 1½ percent a year, similar to the relatively constant growth rate that has been observed since the early 1980s. The inflation rate is determined by the assumed target for monetary policy, which has been set to ½ of 1 percent a year for the GDP deflator, equal to the rate at which inflation is projected to stabilize over the medium-term horizon of the World Economic Outlook. Foreign real growth converges to the same 1½ percent rate assumed for Japan by the middle of the next century (a necessary condition for a steady-state to exist), while foreign inflation is constant at 1½ percent a year.

^{}1

As discussed in Sections II and IV, the IMF staff’s empirical analysis of SI balances is based on a reduced-form version of equation (8.1). In particular, making use of the constraint that SI balances (conceptually) sum to zero across countries, and assuming that the a parameters are the same for all countries, the world real interest rate can be substituted out of equation (8.1) and the *X ^{SI}* vectors replaced by the deviations of domestic variables from their world counterparts. The country-specific constant terms in each of the equations will then reflect, inter alia, the average difference between domestic and world real interest rates over the sample period used for estimation.

^{}3

This “real” interest parity condition can be derived by subtracting expected inflation from both sides of the conventional nominal interest parity condition.

^{}4

The two-dimensional treatment is possible because the external balance drops out of equation (8.3’) with perfect capital mobility. With the general version of equation (8.3), a third axis representing the external balance is needed to show the solution.

^{}5

See Masson, Symansky, and Meredith (1990) for a description of the complete Mark II version of MULTIMOD on which the smaller model used here is based.

^{}6

See Balassa (1964) and Samuelson (1964) for the original expositions of this phenomenon. Meredith (1998) discusses in more detail the evidence for Balassa-Samuelson effects for Japan, while the evidence for Asia more generally is assessed in Isard and Symansky (1996).

^{}7

Most of the equations in the original version of MULTIMOD were estimated using pooled data with common parameters across the major industrial countries.

^{}10

MULTIMOD Mark III (in preparation) explicitly includes such a steady-state analogue to the dynamic model. See Laxton and others (1988).

^{}11

See Okamura (1996) for a discussion of Japan’s longer-term fiscal outlook.

^{}12

This is a standard procedure in constructing a baseline path for MULTIMOD. Beyond 2002, these add factors either were specified to gradually decay or were, in some cases, held constant, where it was judged that there was a permanent shift in the relationship compared with the historical estimates.

^{}13

This is the reverse of the causation that underlies the standard macroeconomic balance approach to assessing misalignment, as discussed above.

^{}14

The implications for Japan of this approach are discussed in IMF (1997), Box 2.

^{}15

This definition of the real exchange rate is based on relative GNP deflators. Historical trend growth is about 2½ percent a year.

^{}16

Combined with an excess return on dollar assets of 17 percent in 1996 relative to the 1995 level, this suggests that the exchange rate was overvalued by almost 25 percent in 1995.

^{}17

The dependency ratio is defined here as the share of the population aged 65 and over or 15 and under to the population aged 16–64. This differs slightly from the definition used in Sections II and IV, which defines the range of nondependent ages as 20–64.

^{}18

Horioka (1990) provides a useful survey of studies on this issue.

^{}19

The effect assumed in this model is based on the analysis in Meredith (1995). The study compares the time-series evidence on the effect of demographics on saving with the results of a stylized life-cycle model for Japan, and explains why the lower effect found in the latter framework may provide a more appropriate benchmark.

^{}21

Beyond 2002, MULTIMOD has a fiscal reaction function that forces taxes and spending to adjust such that the debt-to-GDP ratio converges to a fixed target level.

^{}22

The results for the simulation where there is no liquidity trap are shown as deviations from a hypothetical baseline in which there is also no liquidity trap—in the actual baseline simulation, the liquidity trap is binding in both 1997 and 1998.

^{}23

This initial weakening of the exchange rate in the face of tighter fiscal policy is typical of models with a high degree of capital mobility, and where the ultimate solvency of the government is not doubted by investors. See the Annex of IMF (1995) for a discussion of the exchange rate effects of fiscal consolidation.

^{}24

The effects of aggressive deficit reduction measures on agregate demand unwind because, even in the baseline scenario, fiscal policy is forced to eventually act to prevent an explosive rise in public debt. In this sense, the fiscal consolidation scenario simply “front loads” the adjustments that would ultimately be needed.

^{}25

We use the term “hypothetical,” as it is difficult to envisage a practical situation in which nominal interest rates could be significantly negative for an extended period—in the absence of a tax on cash holdings, the (zero) yield on which would otherwise dominate that on interest-bearing assets.

^{}26

As the Bank of Japan does not currently base monetary policy on any formal framework of inflation targeting, this assumption should be regarded as a stylized characterization of the implicit longer-term objectives of policymakers.

^{}27

For earlier work on demographics using MULTIMOD, see Masson and Tryon (1990).

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