Appendix II Evaluation of Some Simple Coordinated Policy Rules

Paul Masson, Morris Goldstein, and Jacob Frenkel
Published Date:
June 1991
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The gains from policy coordination have often been evaluated in the context of optimal policies when countries act jointly to determine their policies, compared with policies chosen optimally when countries act independently (see, for instance, various articles in Buiter and Marston (1985)). More relevant may be the comparison of simple rules that are not optimal in the context of any single model, but that may be more robust across a range of models, more credible to the general public, and easier to implement.58

In this appendix, we examine several simple rules that have been proposed, by simulating the Fund’s MULTIMOD model.59 The rules that we compare are money and nominal income targeting—rules that can be implemented by countries independently—and fixed nominal exchange rates, target zones, and current account targets—rules that require an element of coordination if implemented by all countries because such targets cannot be chosen independently. For example, if two countries target their bilateral exchange rate, the targets cannot be inconsistent; another example is current account balance targets, which must add up globally. Of course, many other forms of policy coordination are possible; for instance, Frankel (1990) has proposed coordinating around mutually agreed targets for nominal income in each of the major industrial countries.

We first consider the behavior of each of the rules in response to individual shocks (that is, to shocks to individual residuals). Each shock is assumed to be unanticipated when it occurs, and to be an innovation that applies to a single period. Though temporary, such shocks will nevertheless have persistent effects because errors in the model are serially correlated and because the various structural equations of the model contain dynamic effects. Expectations are assumed to be formed in the model in a way that properly takes into account the subsequent dynamics; that is, once the shock has occurred, perfect foresight is assumed to prevail.

The results from single shocks do not of course allow a complete evaluation of policy rules. In general, the relative variance of different kinds of shocks should influence the choice between policy rules. Nevertheless, single-shock exercises can be useful because they allow a characterization of when particular rules are likely to perform better than others.

We follow the single-shock simulations with some stochastic simulations under which errors are consistent with their estimated distribution. One advantage of these stochastic simulations is that the variances of the shocks reflect their relative importance. A formal ranking of the policy rules would require an explicit objective function that specifies the weights to be given to output fluctuations, inflation, and to other objectives. We do not attempt to provide such a ranking, but rather suggest some strengths and weaknesses of each of the rules.

Form of the Reaction Functions

As a prelude to the simulation results, it is necessary to specify exactly how we implement the various policy rules in MULTIMOD. In brief, we imposed reaction functions for the short-term interest rate, assumed to be the instrument for monetary policy, and for real government spending on goods and services, assumed to be the fiscal policy instrument. Details of the feedback rules are given in Frenkel, Goldstein, and Masson (1989b).

The form of the policy rules requires some explanation because there is inevitably some element of arbitrariness in the way they are specified. In general, we have attempted to follow as closely as possible the intentions of their advocates. The final form chosen resulted from some experimentation that identified inadequacies with alternative specifications or with feedback parameters.

Money targeting, rule (1), used the same specification as in the standard version of MULTIMOD. To achieve exactly a money target would produce large swings in short-term interest rates. For that reason, the model includes an equation in which interest rates equate the long-run demand for money, conditional on observed GNP, with the money stock target.

Nominal GNP targeting, rule (2), was specified in terms of a target for the level of nominal income, rather than its rate of change, because of the potential instability from targeting the latter, discussed in Taylor (1985). Some experimentation with feedback coefficients led to a value that yields a flatter aggregate demand schedule (in real output, price space) under nominal income targeting than under money targeting, again as in Taylor (1985).

Fixed nominal exchange rates, rule (3), were implemented by putting a large feedback coefficient on the deviation of the actual from the targeted nominal rate in the equation for short-term interest rates. Variations of exchange rates are thereby kept within narrow margins. It should be stressed that there is an asymmetry in the implementation of this rule as between the United States and other industrial countries. The latter are assumed to subordinate their monetary policies to maintaining dollar parities, whereas the United States is assumed to target monetary aggregates independently of exchange rate considerations, thereby providing a nominal anchor for the system.

Target zones, rule (4), follow as closely as possible the guidelines described in Williamson and Miller (1987) and simulated earlier (using the Federal Reserve Board’s Multi-Country Model) by Edison, Miller, and Williamson (1987). We experimented with various values of the feedback coefficients to achieve the closest control over the targets without producing explosive behavior in the model. As in Edison and others, there is nothing that ensures that the real exchange rate will not in fact depart from the zone (if shocks are large enough). As described in Williamson and Miller (1987), a target for the level of world nominal income serves as the nominal anchor for prices. Note, however, that it is the level, not the rate of change, of world nominal income that appears in our equation;60 the latter is subject to the criticisms made by Taylor (1985) for domestic targeting and did in practice produce problems of nonconvergence in MULTIMOD. The feedback coefficient on world nominal income implies that a 10 percent deviation from baseline raises world interest rates by 1 percentage point.

The extended target zones or “blueprint” proposal, rule (5), contains a policy reaction function for government spending as well as the target zone assignment of monetary policy to the real exchange rate. The equation that endogenizes fiscal expenditures is a feedback rule that aims to close a gap between domestic absorption and its target value. This rule does not hit domestic absorption exactly, but with the feedback coefficient that is imposed, deviations from absorption targets are typically small.

In implementing reversed assignment,61 rule (6), we have specified that the short-term interest rate responds to the proportional gap between nominal absorption and its target, whereas government spending responds strongly to the gap between the current account (as a ratio to GNP) and its target. Instrument instability does not seem to be a problem in the latter case; indeed, in principle, the feedback coefficient could be infinite, forcing deviations of current balances from targets to zero. However, the conclusions derived from the simulations are unlikely to be sensitive to the small deviations from current account targets that result from our specification. If anything, our simulations probably give too much weight to current account targets and not enough to nominal demand targets, and closer control of the latter might have been possible otherwise.

Simulations of Individual Shocks

Four individual shocks are considered:

  • (1) an aggregate demand shock in the United States: a positive innovation in consumption equal to 1 percent.

  • (2) an aggregate supply shock in the United States; in particular, the residual in the equation for the rate of change in the non-oil GNP deflator is increased by 2 percent.

  • (3) a shift in demand toward U.S. goods, equal to 10 percent of U.S. exports.

  • (4) a portfolio preference shift out of U.S. dollar assets, leading to an increase in the required rate of return on dollar assets by 10 percentage points.

Each of the rules is simulated subject to each of the four shocks, one at a time. The results are portrayed in Charts 69.

Chart 6.Shock to U.S. Consumption

(Deviations of U.S. variables from baseline)

The aggregate demand shock, namely, a 1 percent increase in U.S. consumption,62 has quite different effects under the different policy rules (Chart 6). Without any policy changes, such a shock will increase output and put upward pressure on prices, as well as appreciate the real exchange rate and lead to a decline in the current account. It also generates positive spillovers for the output of other countries. Since nominal GNP rises, as does the demand for money, both uncoordinated rules cause interest rates to rise; given the relative steepness of the aggregate demand curves, output and price increases are more moderate with nominal income targeting than with monetary targeting.

Under target zones, the real appreciation of the U.S. dollar leads to a smaller rise in interest rates in the United States than in other industrial countries. However, by limiting the interest rate increases in the United States in response to a demand increase, this rule builds in inflationary pressures, which persist longer than for other rules. Fixed nominal exchange rates yield a similar outcome. In contrast, the extra degree of freedom accorded by fiscal policy in both the blueprint and the reversed assignment rules allows the aggregate demand shock to be almost completely offset by lower government spending. As a result, the output, price, and real exchange rate effects are smallest for these two rules. A comparison of the blueprint with the reversed assignment rule illustrates the relative effectiveness of monetary and fiscal policies. Government spending cuts can easily offset the effects of increased consumption on absorption, allowing the blueprint rule virtually to neutralize the shock. In contrast, control of nominal absorption through the interest rate is not as powerful, at least for values of feedback coefficients that do not produce large swings in interest rates or other variables.

The negative aggregate supply shock (or cost-push inflation shock) likewise yields a variety of responses (Chart 7). This shock has persistent effects because of considerable stickiness in the inflation process. In response to this stagflationary shock, nominal GNP targeting leads to a greater response of interest rates, and hence to greater short-run output losses but smaller increases in prices, than money targeting. Which of the two is preferable depends on the trade-off between the two objectives of output and price level stability, as well as on the discount rate that captures intertemporal trade-offs. Given the very small effects on exchange rates under all rules, fixed rates produce similar results to uncoordinated money targeting.

Chart 7.U.S Aggregate Supply Shock

(Deviations of U.S variables from baseline)

The responses under target zones and blueprint rules are another story. Using monetary policy to counteract the real appreciation of the U.S. dollar requires lower, not higher, U.S. nominal interest rates. However, for both the target zones and blueprint rules there is an additional term that tends to raise interest rates in all countries if world nominal income grows too fast, which happens here. The result with target zones is that U.S. interest rates rise, but by somewhat less than interest rates in other industrial countries. Price level increases continue longer, and are larger in the medium term, than for any other policy rule. It is also true that interest rates have to continue increasing for six years in response to a purely transitory supply shock because of the inertia in the inflation process.

In contrast, interest rates have to rise much less under the blueprint rule because government spending contracts, helping to limit the real appreciation of the dollar. The contraction of government spending is required because the increase in U.S. prices yields an improvement in the terms of trade, which raises real disposable income and stimulates consumption. Though the net effect on output is negative in the short run, output is actually higher after seven years, by which time prices have returned to their baseline levels. It is clear that an aggregate supply shock causes a dilemma for target zones because one instrument—monetary policy—has to wear two hats—resisting inflationary pressures and limiting appreciation of the real exchange rate (in the country experiencing the shock).63 The reversed assignment rule behaves much like the blueprint: both yield relatively small current balance effects.

Chart 8 illustrates the effects of an expenditure-switching shock that corresponds to a shift toward U.S. goods and away from other countries’ goods. The positive shock to U.S. exports of 10 percent shows up in lower exports of other countries in proportions that correspond to their shares in world trade.64 The U.S. current account improves by some 0.6-0.7 percent of GNP in the first period under all rules except reversed assignment, for which the current account change is smaller. For all policy rules, U.S. real output rises initially, and price increases are small. Since neither real exchange rates nor industrial country nominal GNP change much, there is little effect on interest rates under either fixed rates, target zones, or the blueprint.

Chart 8.Shock to U.S. Exports

(Deviations of U.S variables from baseline)

In contrast, under the reversed assignment rule, the increase in the U.S. current account balance leads to increased U.S. Government spending, adding to the stimulus to U.S. output; conversely, government spending declines in other countries. Higher U.S. nominal GNP has to be resisted by higher U.S. interest rates, so that shifts in preferences between countries’ goods lead to a shift in the monetary/fiscal mix under reversed assignment—to tighter monetary/looser fiscal policy in the country facing the increase in its exports, and conversely for those facing lower exports. The contrast between this rule and the others has been heightened by the large feedback coefficient on the current balance: attempts to exert tight control over the current account lead to large swings in other variables under reversed assignment.

The exchange rate shock (Chart 9) puts downward pressure on the dollar relative to the yen, to the deutsche mark, and to other industrial country currencies. The initiating factor is assumed to be a 10 percent increase in the required return on dollar assets.65 Output effects are largest under reversed assignment and under the two uncoordinated rules (money and nominal GNP targeting)—and are smallest under the blueprint rule and fixed rates. The exchange rate always overshoots except under fixed rates, with the U.S. nominal effective exchange rate depreciating by about 15 percent in the first year. Under target zones, despite an initial increase of 6 percentage points in the short-term interest rate, the real effective exchange rate still depreciates considerably. Moreover, the behavior of the GNP deflator suggests that target zones can generate price level instability—a point we return to below in the context of stochastic simulations. Under reversed assignment, government spending rises because of the improvement in the U.S. current account; again, this additional stimulus tends to induce large movements in output.

Chart 9.Shock to Value of U.S. Dollar

(Deviations of U.S variables from baseline)

A money demand shock was also examined. The results are not plotted because they are simple to describe. It is only with money targeting that the money shock has any significant effect on policy settings and on other endogenous variables (the money shock has a small effect on consumption because money is a component of net wealth, but the magnitude is negligible). Under money targeting, the positive innovation to money demand leads to temporarily higher short-term interest rates, and as a result, to lower economic activity for a time. Other policy rules ignore the money demand shock and maintain policy instruments unchanged, allowing macroeconomic variables to remain at their equilibrium levels. This demonstrates the superiority of these rules in the face of money demand shocks, an argument that has long been emphasized by advocates of nominal GNP targeting (for example, Tobin (1980)).

Stochastic Simulations

Simulations of individual shocks, though instructive, do not lend themselves to easy generalizations because no rule dominates the others for all kinds of shocks. It is clear that monetary policy rules (assumed to be credible, and fully understood by the private sector) are relatively ineffective, especially in affecting real variables. Rules using fiscal policy therefore have clear advantages in offsetting shocks, though the assumed flexibility for fiscal policy may be unrealistic. In addition, the proper assignment of monetary and fiscal policies to internal or external balance depends on the nature of shocks. We now turn to simulations where the variances of the shocks reflect their relative importance. Moreover, instead of applying shocks for one period only, we apply shocks in successive periods. By looking at a sufficient number of years, the model should provide useful information about the variances of endogenous variables under the alternative policy rules.

The simulations are performed on the assumption that expectations are formed rationally. The shocks (by definition) are unanticipated at the time they occur. In this context, rational expectations of variables in future periods are formed taking the expected value of those shocks—namely, zero.66 In each period, however, a drawing is made from the covariance matrix describing the shocks. The realized values of endogenous variables are affected by the shocks, and in general will differ from the expectations for those variables formed in previous periods.

The stochastic simulations involve multiple simulations. Not only is it necessary to iterate to a terminal date to force expectations to be consistent with the model’s solution conditional on information available to time t, but it is also necessary to repeat the process each time a new drawing of shocks is made.

In the first set of stochastic simulations, for which root mean square (RMS) deviations from baseline are presented in Table 8, we use a drawing for the shocks that corresponds to residuals in the model’s behavioral equations for 1974–85. These shocks are applied to a baseline for the period 1988–99; the model is simulated another 20 years to minimize the effect of the terminal conditions on the period of interest. The implicit objective is to minimize deviations of target variables from the baseline, so that shocks have as little disruptive effect as possible. We do not make a judgment about how target variables should be weighted in the objective function; however, we presume that macroeconomic performance would be evaluated using some subset of the variables presented in Table 8.67

Table 8.Root Mean Square Deviations from Baseline for Various Policy Rules, Historical Shocks
Policy Rule



Fixed rateTarget


United States
Real GDP13.
Current balance20.
Real effective exchange rate19.
Nominal effective exchange rate17.
Nominal interest rate1.
Real GDP1
Current balance20.
Real effective exchange rate18.
Nominal effective exchange rate111.
Nominal interest rate1.
Real GDP14.
Current balance21.
Real effective exchange rate18.
Nominal effective exchange rate111.
Nominal interest rate2.
Developing Countries
Real GDP13.
Terms of trade15.

Several conclusions emerge from examination of the results.

First, it appears that nominal GNP targeting produces smaller errors in response to typical shocks than money targeting. As noted earlier, nominal GNP targeting has a clear advantage over money targeting when there are shocks to velocity, that is, to the demand for money. For other kinds of shocks, the comparison between the two rules derives from small differences in the elasticity with respect to nominal income and in the speed with which the interest rate reacts to shocks. For the historical shocks considered here, the stabilization properties of the nominal income rule clearly dominated those of base money targeting.

Second, the two rules that ignore domestic variables in setting monetary policy in favor of targeting an exchange rate measure—while keeping fiscal expenditures exogenous—show mixed results: they have some success in reducing the variability of GDP for the United States and for developing countries, but yield no clear advantage for Germany and Japan.

Note also that the behavior of macroeconomic variables is quite different under fixed nominal exchange rates—column (1)—than under target zones. Recall that fixed rates are implemented here through changes in monetary policies of industrial countries other than the United States. The United States is assumed to target the monetary base, as under monetary targeting. As a result, the variability of nominal interest rates is considerably higher abroad than in the United States. The fixity of nominal exchange rates is also associated with more variability of inflation in all industrial countries.

Some might argue that stochastic simulations of fixed rates using historical shocks overstate the need for movements in interest rates. Since the period 1974–85 was characterized by flexible exchange rates, a credible announcement of a set of nominal exchange rate targets could be seen as reducing shifts between currencies. Moreover, our earlier single-shock simulations suggested that target zones could be unstable under exchange rate shocks; response to such shocks could be unfavorably biasing the results against target zones. To examine this question, we also ran some simulations for which shocks to interest parity conditions were assumed to be absent. These results—shown in column (2) under fixed rates— exhibit only slightly less variability. It does not seem therefore that our results are strongly affected by changes in speculative behavior in currency markets that might be associated with the exchange rate regime.

The target zones rule, in contrast to fixed nominal rates, posits a symmetric assignment of monetary policies to real effective exchange rates. As hinted at earlier, achievement of tight target zones is difficult in the model, and RMS deviations from baseline for real exchange rates are quite high; on the other hand, real GDP, at least in the United States, and inflation generally, are quite stable. The policy reaction functions for target zones used here are based on Edison, Miller, and Williamson (1987); our results suggest, however, that a more complicated rule for setting interest rates— perhaps using proportional, integral, and derivative control terms—would be more appropriate.68 Such rules may also be more robust to model misspecification. At the same time, we would argue that the fact that a simple rule does not perform well suggests some skepticism about the practicality of real exchange rate targeting, given the uncertainty associated with the precise dynamics of the economy.

Third, the blueprint rule produces considerably lower errors for most variables,69 but does so with the benefit of an additional policy instrument—namely, real government spending. Somewhat surprisingly, the reversed assignment rule does not succeed in stabilizing either real GDP (except for developing countries) or real effective exchange rates.70 Though current account targets are achieved closely under reversed assignment, they may not be the preferred measure of external balance because shocks that change the terms of trade will change the valuation of trade flows for given trade volumes. Stabilizing the current balance will therefore not be sufficient to neutralize the domestic demand effects of external shocks.

Our historical shocks comprise a small sample—only 12 observations—and it does not seem appropriate to evaluate policy rules on the basis of one historical episode. Our second set of stochastic simulations therefore draws shocks for 61 residuals over 40 years from the distribution describing the historical shocks. The simulations were then performed as described above, one year at a time. Table 9 presents the RMS deviations from baseline for the various policy rules.

Table 9.Root mean Square Deviations from Baseline for Various Policy Rules, Generated Shocks, 1988–2027
Policy Rule
Money targetingNominal GNP targetingFixed rate(1)(2)Reversed assignment
United States
Real GDP115.
Current balance20.
Real effective exchange rate111.612.811.
Nominal effective exchange rate18.18.50.410.38.85.1
Nominal interest rate2.
Real GDP15.
Current balance24.
Real effective exchange rate7.810.
Nominal effective exchange rate11.317.
Nominal interest rate2.
Real GDP115.
Current balance13.
Real effective exchange rate18.
Nominal effective exchange rate114.211.90.515.914.011.8
Nominal interest rate2.
Developing Countries
Real GDP112.
Terms of trade14.

There are several qualitative differences relative to the historical shocks of Table 8. First, the ranking of money and nominal GNP targeting has changed. The reason seems to lie in the timing of shocks to developing country supplies of commodities and manufactured exports. In the historical simulations, these shocks occur mainly at the end of the simulation period; they have persistent effects, but since the RMS deviations are calculated only over the 12 years of the shocks, some of those effects are not captured. In contrast, the generated shocks distribute those effects more evenly over the simulation, and nominal GNP targeting, with its flatter aggregate demand curve, performs more poorly than money targeting.

Second, fixed rates in Table 9 no longer dominate the two uncoordinated rules with respect to real GDP in Japan, nor for the real effective exchange rate of the dollar. Unless a considerable premium is placed on nominal exchange rate stability, there seems little to choose among the first three rules—money and nominal GNP targets, and fixed rates. Unfortunately, the target zones proposal could not be simulated here; with the feedback parameters specified in Edison, Miller, and Williamson (1987), the target zone rule suffers from dynamic instability that eventually prevents MULTI-MOD from converging to a solution. The problem is exacerbated by the longer simulation period, because real shocks push the short-run equilibrium real exchange rate further from its long-run equilibrium value.71

Third, the blueprint rule—column (1)—again seems to yield for most variables lower RMS deviations than the other rules. Its superiority, however, with respect to reversed assignment is less marked than in Table 8. As discussed above, both of these rules assume that real government spending can be flexibly used in the current period to respond to deviations from targets— be it nominal domestic demand (blueprint) or the current balance (reversed assignment). A more realistic assumption, in our view, would be that fiscal spending can respond with a lag of a year to deviations from targets. Taking account of this inflexibility would mean that lower (higher) growth in nominal domestic demand under the blueprint rule would lead to higher (lower) government spending in the following year. In our first attempt to make this constraint operational, we used the same feedback coefficients as in column (1); however, this produced dynamic instability. The results presented in column (2) use a feedback of nominal domestic demand onto government spending that is half of the contemporaneous effect. Interestingly enough, the RMS deviations for this variant of the blueprint rule are now closer to those for the other rules.72 It is a topic for further research to examine the constrained use of fiscal policy to hit other targets—for instance, under the reversed assignment rule.

It should be stressed that simulation results for simple coordinated and uncoordinated policy rules should not be used to draw inferences about the effects of judgmental (discretionary) coordinated policies, including the ongoing coordination exercise among the largest industrial countries. In this connection, the differences between the effects of coordinated policy rules and judgmental coordinated policies may be as large as those between uncoordinated policy rules and coordinated policy rules. A key task of future research in this area should be to learn about the effects of judgmental policies—even though such policies do not lend themselves easily to simulation exercises.

The version of the model used in these simulations is described in Masson and others (1988).

Williamson and Miller (1987) are not specific about the form that this term should take.

The error in this equation has a serial correlation coefficient equal to 0.148, so that roughly 15 percent of the shock persists into the second year, 2 percent into the third year, etc. See Appendix II, Table 3 of Frenkel, Goldstein, and Masson (1989b).

If there is no feedback of inflation on monetary policy—such as through world nominal income—then the target zones rule cannot be simulated, given the absence of a nominal anchor.

The shock is distributed using the weights that serve to allocate the world trade discrepancy in MULTIMOD. As a result, the shock to the United States is also reduced by the U.S. share, so that U.S. exports rise on impact by about 8.6 percent, not the full 10 percent.

As in the historical data, the risk premium shocks are quite persistent (owing perhaps to speculative bubbles as well as to shifts in portfolio preferences), with serial correlation coefficients equal to 0.43 for shocks to interest parity between the United States and Japan, and 0.75 between the United States and Germany.

In fact, the model has to be linear for this to be fully consistent with rationality.

It could be argued that the sole criterion should be the discounted utility of consumption, and the variances of variables would matter only insofar as they reduced the output available for consumption (or increased the variance of consumption itself). The model as currently specified does not incorporate such effects, making it necessary to evaluate rules on the basis of their effectiveness in reducing the variability of key variables. Of course, the absence in the model of links between second and first moments (that is, variances and means) of variables makes it subject to Lucas critique problems.

Such specifications have been used by Currie and Wren-Lewis (1987, 1988a, 1988b), among others.

Though it does not stabilize nominal effective exchange rates in Japan and Germany. Nominal effective exchange rates use MERM weights, and include only industrial country currencies, while real effective exchange rates are calculated using relative manufacturing export prices weighted according to export shares; developing countries are included in this calculation.

Currie and Wren-Lewis (1988a) also find that such a rule performs less well than the blueprint assignment.

Of course, given the assumption that agents know those values, policymakers could (in the model) have moving targets for exchange rates, trying only to offset current shocks, and not the lagged effects of past shocks. But such an experiment—which would in effect involve starting each period’s simulation at baseline values—was not performed.

Except for current account balances. It seems that because of J-curves, the lagged response of government spending actually does better in offsetting the current account effect of most shocks.

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