Abstract
In this paper I take up three policy issues that have been of central concern in recent academic and official discussions of international economic interdependence and macroeconomic policy coordination.
In this paper I take up three policy issues that have been of central concern in recent academic and official discussions of international economic interdependence and macroeconomic policy coordination.
What should be the monetary or fiscal response in the rest of the industrialized world to a unilateral tightening of U.S. fiscal policy, and what should be the U.S. monetary response?
What should be the monetary and fiscal response in the industrialized countries to a sudden, large change in an important exchange rate? For concreteness. I shall refer to this event as a “collapse of the U.S. dollar.”
What should be the policy response in the industrialized world to a disappointing performance of real growth?
All three issues clearly are of more than academic interest. In this paper I attempt to give qualitative answers through use of a simple analytical model. However simple the individual country models may be, the interdependent global economic system very soon outgrows analytical treatment; numerical simulation methods are called for. Recent works by Sachs (1985) and by Sachs and McKibbin (1985) have demonstrated the usefulness of such an approach. The advantages—in both intuition and insight—of keeping things sufficiently small and transparent to permit a simple algebraic and diagrammatic analysis are such, however, that a first pass at this problem “in two dimensions” is justified.
The first subsection of Section I outlines the simple two-country. Dornbusch-style model, which includes a floating exchange rate, perfect capital mobility, rational exchange rate expectations, and gradual price adjustment. The long-run or steady-state comparative statics are reviewed in the second subsection of Section I, whereas the last subsection of Section I characterizes the nature of the dynamic adjustment process. Possible responses to a tightening of U.S. fiscal policy are reviewed in Section II. In Section III, possible responses to a collapse of the U.S. dollar are considered, and Section IV assesses the policy implications of a slowdown in world economic activity. Qualifications and conclusions are given in Section V.
I. An Analytical Approach
The three policy issues can be analyzed by reference to a simple model.
The Model
Consider the simple two-country or two-region version of the Dornbusch (1976) open macroeconomic model with a freely floating exchange rate and perfect capital mobility given in equations (1)–(12) below. It can be viewed as a version of Mundell’s (1968) two-country model, with sluggish price adjustment and rational exchange rate expectations. Except for some inconsequential differences, this model is the one used by Miller (1982). Turnovsky (1985) has used this model to analyze the effects of several anticipated and unanticipated monetary and fiscal shocks (see also Buiter (1985a) for another application). All variables other than interest rates are in natural logarithms.
All coefficients are nonnegative; country 1 will be referred to as “the US,” and country 2 as “the rest of the world” (ROW):
where mj is the nominal money stock of country j, pj is its GDP (gross domestic product) deflator, yj is its real output, ij is its nominal interest rate, and rj is its real interest rate; e is the nominal exchange rate, expressed as the number of units of country 1’s currency per unit of country 2’s currency; fj is a measure of fiscal stance in country j; τj is country j’s tax rate on interest income accruing from abroad and its subsidy rate on the interest cost of borrowing from abroad (these taxes drive a wedge between the domestic nominal interest rate and the interest rate on loans denominated in the same currency overseas); c is the real exchange rate or competitiveness; and lj country j’s stock of real money balances.
The model has rational exchange rate expectations and rational inflation expectations on the part of investors. The exchange rate is set in an efficient, forward-looking asset market, and the exchange rate can make discrete “jumps” at a point in time in response to “news.” Domestic costs pj are predetermined (that is, given at a point in time), but their rates of change respond to excess demand or supply and to “core inflation.”
The model will have short-run “Keynesian” but long-run classical or monetarist features. Each country’s demand for real money balances varies positively with its own national income yj and negatively with its own nominal interest rate ij.1 There is no endogenous direct currency substitution.2 A shift parameter ηj is added to allow for portfolio shifts. The demand for each country’s output depends on its real interest rate rj, on competitiveness c, on the other country’s level of real income, and on the domestic fiscal impulse fj. Domestic costs are governed by an augmented Phillips curve. The (logarithm of the) level of capacity output
The two countries are linked not only through competitiveness and activity effects but also directly through an integrated international financial market. Equation (5) represents the condition for (after-tax) uncovered interest parity. US and ROW currency-denominated interest-bearing assets are perfect substitutes in private portfolios. This will be the case if the international financial markets are efficient and there are risk-neutral speculators.
It will be convenient to represent the essential dynamics of this “mini-world” economic world through three state variables: lj (with j = 1, 2); real money balances in each of the two countries; and c, which is US competitiveness.
Long-Run Equilibrium
The long-run comparative statics in this model are completely classical or monetarist. Output in each country is at its exogenously given, full-employment level, and changes in the levels and growth rates of nominal money stocks are translated into corresponding changes in the levels and proportional rates of change of costs and of the exchange rate. Equations (13a—i) summarize the long-run equilibrium of this economy:
where
In the long run (at full employment), fiscal expansion in the US worsens US competitiveness, whereas fiscal expansion in the ROW causes US competitiveness to improve.3 Neither changes in the levels nor in the rates of growth of the nominal money stocks affect real competitiveness or real interest rates. Fiscal expansion in the US or in the ROW raises the world real interest rate. Note that the US and ROW real interest rates differ only to the extent that US and ROW taxes (subsidies) on foreign interest income (costs) differ. An increase in τ1—τ2 lowers the US real interest rate and raises that in the ROW. Competitiveness therefore must move against the US to restore equilibrium in the market for US output. An increase in
An increase in the level of capacity output
Dynamic Response to Policy Changes and Exogenous Shocks
When the restriction is imposed that the two countries or regions have identical structures, it becomes possible to provide an analytical and diagrammatic exposition of the main policy issues (see Aoki (1981) and Miller (1982)). The assumption of identical structures is of course quite restrictive. All differences in country performance must be attributed solely to different policies, different exogenous shocks, or different initial conditions. A full analysis of two- or three-country models that allows for intercountry differences in the specification of major behavioral relationships will require numerical simulation methods. The simplified two-country model does, however, permit a quite transparent first pass at the major policy issues. Symmetry in this model means that k1 = k2 = k; λ1 = λ2 = λ; γ1 = γ2 = γ; δ12 = δ21 = δ; ε12 = ε21 = ε; and ψ1 = ψ2 = ψ.
The three simultaneous state equations of the unrestricted model can be decomposed into two independent subsystems when the restriction of identical structures is imposed. A two-dimensional system involves the real exchange rate and the difference between the two countries’ real money stocks. Let ld ≡ l1—l2, ṁd ≡ ṁ1 − ṁ2, ηd ≡ η1 − η2, fd ≡ f1 − f2, τd ≡ τ1 − τ2, and
The aij (with i, j = 1, 2) and bij (with i = 1, 2; j = 1,…,5) are given in Appendix I.
A one-dimensional system involves only averages or global magnitudes. Let la ≡ (l1 + l2)/2, ṁa ≡ (ṁ1 + ṁ2)/2, fa ≡ (f1 + f2)/2, ηa ≡ (η1 + η2)/2, τa ≡ (τ1 + τ2)/2, and
The “output equations,” the equations giving the short-run endogenous variables as functions of the state variables and the exogenous variables (in self-explanatory notation), are
and
The matrices Cd, Dd, Da, and Da are given in Appendix II.
The long-run comparative statics for the differences and averages can be obtained easily from equations (13a–i):
Global or average economic performance and the difference between the economic performances of the two countries are “decoupled”: they can be studied independently of each other, with average outcomes a function only of current and past average policy-instrument values and average exogenous shocks, whereas performance differences are a function only of differences in current, past, and expected future differences in policy-instrument values and exogenous disturbances. The “averages” model (equations (14b) and (15b)) can indeed be viewed as a self-contained model of a single closed economy. Because the price deflators are predetermined and the real exchange rate “washes out” through the assumption of symmetrical structures, the “averages” model contains no nonpredetermined, forward-looking or jump variables. Note that, after analyzing averages and differences, one can easily retrieve individual country performance, since l1 = ½ld + la, l2 = -½ld + la, and so on.
The “averages” economy (equation (14b)), with its single predetermined state variable, will be stable if and only if -ψλ-1(Ω - ε)-1γ < 0; that is, if and only if
The “differences” system (equation (14a)), with its predetermined variable ld and its nonpredetermined variable c, will have a unique convergent saddle-point equilibrium if and only if a11a22 - a21a12 < 0; that is, if and only if
Because ε > 0, equation (17a) implies equation (17b).
Equation (17b) is equivalent to the condition that an improvement in US competitiveness will (given ld, ṁd, ηd, fd, and rd) raise the effective demand for US output relative to output in the ROW. It is a weak condition, which amounts to assuming that, in a diagram with the nominal interest rate on the vertical axis and output on the horizontal axis, the IS curve—after the Phillips curve is used to substitute out the (expected) rate of inflation—is either downward-sloping or upward-sloping and steeper than the LM curve. I assume that equation (17a) is satisfied. Given equation (17a) (and thereby equation (17b)), the saddle-point equilibrium and the “differences” system look either like panel A of Figure 1 (when the IS curve is downward-sloping, a22 > 0, and the ċ = 0 locus is upward-sloping) or like panel B of Figure 1 (when the IS curve is upward-sloping and steeper than the LM curve, a22 < 0, and the ċ = 0 locus is downward-sloping and cuts the
Equilibrium and Dynamic Adjustment in the Symmetric Two-Country Model
Citation: IMF Staff Papers 1986, 003; 10.5089/9781451972887.024.A005
First among the policy issues to be considered now is the proper response in the ROW to a unilateral fiscal contraction in the US.
II. Responses to a Tightening of US Fiscal Policy
This section poses three possible responses to a sudden change in one of the world’s major exchange rates—a collapse of the US dollar.
US Fiscal Tightening Without Fiscal or Monetary Response in the ROW and Without Monetary Response in the US
A fiscal tightening in the US without any fiscal response in the ROW is, in the notation of this paper, a reduction in the average fiscal impulse (fa) and a reduction in the difference between the two countries’ fiscal impulses (fd) that is twice as large as the reduction in fa. From equations (16a–e) it is clear that the long-run consequences of this unilateral fiscal contraction will be the following:
an improvement in US competitiveness (c increases)
a lowering of the real interest rate in the US and in the ROW
an increase in the world real money stock because nominal as well as real interest rates are lower in the US and in the ROW.
In panel A of Figure 2 one sees that, for c and ld, the full long-run adjustment from E1 to E2 occurs instantaneously. Relative US-ROW real money balances are unaffected by the US fiscal tightening. The required long-run depreciation in the real exchange rate can therefore be brought about immediately by a jump or step depreciation in the nominal exchange rate of the US.
Effects of US Fiscal Tightening Without Fiscal or Monetary Response in ROW and Without Monetary Response in US
Citation: IMF Staff Papers 1986, 003; 10.5089/9781451972887.024.A005
In the new long-run equilibrium the global stock of real money balances will be larger because lower nominal interest rates raise velocity (panel B of Figure 2). Given nominal money growth rates in the US and the ROW, and without any discrete changes in the levels of the nominal money stocks, the process of increasing real balances requires that the rate of inflation be held below the given rates of growth of the nominal money stocks. There will therefore be a temporary global recession: ya declines. The global recession affects the US and the ROW equally: yd is zero throughout the adjustment process. US output declines because of the fiscal tightening, but the decline is mitigated somewhat as competitiveness improves. The ROW suffers from its loss of competitiveness, which mirrors the improvement in US competitiveness. The recession is therefore concentrated in the nontraded-goods sector of the US and the traded-goods sector of the ROW. Nominal and real interest rates and inflation rates in the US and the ROW are affected equally by the US fiscal contraction: id, rd, and ṗd are zero throughout. Both nominal and real interest rates decline globally (and in each country). As in the familiar closed-economy IS-LM, augmented Phillips-curve model, the decline in nominal and real interest rates mitigates the contraction of aggregate demand but does not undo it completely. There is “crowding out” (in our policy experiment, a reversal of crowding out), but it is less than 100 percent. Note that, because inflation declines during the recession, real interest rates come down by less than nominal interest rates. Figure 3 summarizes the response to the unexpected announcement at time t0 of an immediately implemented permanent tightening of US fiscal policy.4
Global and Regional Response to Unilateral Tightening of US Fiscal Policy
Citation: IMF Staff Papers 1986, 003; 10.5089/9781451972887.024.A005
Monetary Policy Stabilizes the Nominal Exchange Rate
One alternative scenario that is often considered consists of a tightening of US fiscal policy, an unaccommodating US monetary policy, unchanged fiscal policy in the ROW, and monetary policy in the ROW geared to interest rate coupling. Given perfect international capital mobility, interest rate coupling amounts to having a fixed nominal exchange rate. Under a fixed exchange rate regime, a fiscal contraction in the US will, with perfect capital mobility, lead to a stock-shift outflow of capital from the US, a stock-shift loss of US foreign exchange reserves, and (in the absence of sterilization of the US loss of reserves) a corresponding contraction in the US money stock. The ROW experiences the counterpart stock-shift inflow of capital, stock-shift gain in foreign exchange reserves, and expansion of its money stock (again, in the absence of sterilization). It is therefore arbitrary whether one assigns the stabilization of the exchange rate to the monetary policy of the ROW or to that of the US. Under a fixed exchange rate regime (which is expected to be permanent), there is effectively a single global world money market or world LM schedule. Individual countries can choose their own rates of domestic credit expansion and thus collectively determine the growth of the world money stock. The distribution of this world money stock among countries is determined by the individual countries’ money demand functions, with reserve flows making up the difference between changes in domestic money demand and domestic credit expansion.
The formal analysis of the fixed exchange rate regime is quite simple. Let the global stock of gold and foreign exchange reserves be constant and, for notational simplicity, equal to zero. The global money stock is therefore the sum of the two countries’ stocks of domestic credit. Let m be the logarithm of the global nominal money stock, Di, the logarithm of country i’s stock of domestic credit, and v the share of US domestic credit in total domestic credit:
Setting the logarithm of the fixed nominal exchange rate equal to zero, one defines the global price level, p, as
The global money demand stock η is similarly defined as
and global income as
The proportional rate of growth of country i’s domestic credit is μi ≡ Ḋi. (Under a freely floating exchange rate regime, μi ≡ ṁi.) The augmentation term in the Phillips curve is taken to be the policy-determined μi rather than the endogenously determined ṁi. No fixed exchange rate regime is viable unless inflation rates converge. I therefore impose μ1 = μ2 = μ. This still permits short-term divergence of inflation rates. Also define i ≡ i1 = i2 + τ2 - τ1. The model consists of equations (19)—(22) and equations (2), (4), (7), and (9); identical structures are again assumed:
For algebraic simplicity and to retain comparability with the case of a floating exchange rate, both countries are assumed to be of equal size, so that v = ½.
The fixed exchange rate version has two state variables, l and c, which are both predetermined. The equations of motion and the determination of output in the two countries are given in equations (23) and (24), respectively:
The coefficient matrices Af, Bf, Cf, and Df are given in Appendix III.
Several points can be made about the fixed exchange rate system. Define (see Appendix III) K1, K2, and Δ as follows:
It is easily checked that the stability of equation (23) requires that K1 + K2 > 0 and that K1 - K2 > 0; K2, however, could be either positive or negative. With a fixed exchange rate, fiscal contraction in the US will therefore definitely lower US real output (since ∂ y1/∂ f1 = K1Δ-1 > 0), but it may either raise or lower real output in the ROW (since ∂ y2/∂ f1 = -K2Δ-1). If K2 < 0, the depressing effect on the ROW’s exports of a decline in US demand outweighs the beneficial effect of lower worldwide interest rates (
If the US and ROW are of similar size, total world output always contracts, even in the case in which output in the ROW is stimulated by lower interest rates:
Note that average global real liquidity under the fixed exchange rate regime (½ l given in equation (23)) behaves identically to average global real liquidity under the freely floating exchange rate regime (la given in equation (14b)).5 The same holds for average world output. (Compare equation (26) with ya from equation (15b)). It is also easily checked that the long-run, steady-state effects of fiscal policy (or of other real shocks) are the same under fixed and floating rates.
Therefore when one compares the consequences of a tightening of US fiscal policy under a floating exchange rate with that under a fixed exchange rate, holding global monetary policy constant in the sense that the growth rates of domestic credit (hence of the global stock of nominal money) are the same in the two regimes, the recession in the US after the fiscal contraction will be smaller under a floating exchange rate, whereas in the ROW the recession will be deeper with a floating rate.
The global loss of output is the same under the two exchange rate regimes, but, whereas under a floating rate the recessions in the US and the ROW are identical in magnitude (although in the US the nontraded-goods sector will be hit, whereas in the ROW it will be the traded goods sector), under a fixed rate the US will always experience a deeper recession. It is even possible that under a fixed rate the ROW would experience a net boost in output.
The short-run behavior of the real exchange rate is quite different under the two regimes. As shown in Figure 3, under a floating exchange rate US competitiveness, which is a nonpredetermined variable in this case, sharply improves on impact to its new equilibrium level. This jump depreciation of c reflects a jump depreciation of e, the nominal exchange rate. Although this clearly represents a hard landing for the US dollar, it represents a much softer landing for the US real economy than the alternative scenario, in which the nominal exchange rate is kept constant throughout. In the latter case, US competitiveness improves gradually after the US fiscal contraction and converges asymptotically to the same level achieved immediately with a freely floating exchange rate. The improvement in competitiveness is because the US rate of cost inflation falls below that of the ROW as a result of the relatively deeper recession in the US.
An alternative scenario under a fixed nominal exchange rate that is sometimes considered to be more likely is the following, which can be called the “non-McKinnon variant.” The US, instead of accepting the stock-shift contraction in its domestic money stock associated with the stock-shift outflow of capital and loss of reserves, engages in domestic open market purchases to maintain the initial level of the money stock; that is, the US sterilizes the stock-shift loss of reserves by a stock-shift expansion of domestic credit. The ROW does not sterilize. This means that the global money stock expands (through a stock-shift US domestic credit expansion) until the US money stock again assumes its value before the fiscal contraction.
In contrast with the first analysis of the fixed exchange rate case, there now is a one-time increase in the level of the path of the global nominal money stock (relative to what happens under a floating rate) accompanying the US fiscal contraction. Global nominal and real interest rates will decline by more than they do both in the case of a fixed exchange rate without US sterilization and in the case of the floating exchange rate. It is clear that the recession in the US will be less deep with sterilization than without, and that for the ROW the recession will be less deep or the expansion larger. It is easily checked that, with a fixed exchange rate and sterilization in the US, the impact effects of a fiscal change in the US on output in the US and in the ROW are given by
and
If the IS curve is downward-sloping (1 - γψ > 0) and if the denominators of equations (27a,b) are positive, US output declines on impact; the ROW has a recession if the direct activity spillover effects dominate the “crowding-in” effects of lower interest rates (ε - γkλ-1 > 0), a boom if the reverse holds true.
Global economic activity (if the US and the ROW are assumed to be of equal size) can either contract (if 1 - γψ - γkλ-1 + ε > 0) or expand (if 1 - γψ - γkλ-1 + ε < 0). This ambiguity is to be expected because, globally, monetary and fiscal policy move in opposite directions. Strong crowding out (high γ and low λ) increases the likelihood of a net expansionary effect.
Policies That Achieve Improvement in US Competitiveness Without Contraction in World Demand
In this subsection 1 take as given the fiscal tightening in the US as well as the achievement of a lasting improvement in US external competitiveness. A floating exchange rate is again assumed.
ROW Fiscal Expansion to Match US Fiscal Contraction
In the formal setting of the simple model, the transition to improved US competitiveness can be achieved instantaneously and without any contraction of effective demand at home or abroad by having the US fiscal contraction matched by a corresponding ROW fiscal expansion. In terms of the dynamics of equations (14a,b) and (15a,b) and of the steady-state conditions of equations (16a–e), this “package” consists of a reduction in fd with fa unchanged. Figure 4 shows the instantaneous adjustment process.
Response to US Fiscal Contraction and Matching ROW Fiscal Expansion
Citation: IMF Staff Papers 1986, 003; 10.5089/9781451972887.024.A005
There is no change in real or nominal interest rates because the effects on the global capital market of the two opposing fiscal impulses cancel each other out. If the magnitude of the US fiscal contraction is kept the same as before, the improvement in US competitiveness is now doubled (in the linear model) because of the fiscal expansion in the ROW. World aggregate demand is unchanged and so is aggregate demand for each country’s output.
There are several qualifications to be made before this painless adjustment package is recommended for use in the real world. First, although total output stays constant in each country, there is a shift toward the production of tradables in the US and toward the production of nontradables in the ROW. Steelworkers make poor hairdressers, and conversely. The problems associated with changing the sectoral composition of production, employment, and investment are ignored in this simple model.
Second, the selection of dosage and timing for the ROW fiscal expansion is made to look simpler than it would be in practice because of the assumption of known, identical structures. Although relaxing this assumption in no way weakens the case for a flexible policy response in principle, it makes the practical task of selecting the right mix, dose, and timing a much more complicated matter than the simple model may suggest.
Third, a fiscal expansion in the ROW may be opposed for structural or allocative reasons. Increased public spending may be undesirable because of its political irreversibility and because, at full employment, the benefits from the spending are judged to be less than the cost. Lower taxes or higher transfer payments may be undesirable because of possible efficiency losses, undesirable incentive effects, or distributional reasons.
Fourth, fiscal expansions (other than balanced-budget fiscal expansions) entail larger deficits and, in time, a larger public debt. If the real interest rate exceeds the growth rate of the real tax base, explosive debt-deficit spirals are possible unless the primary (noninterest) deficit is planned (and believed) to become a surplus in due course. If there is no reputation for fiscal rectitude, temporary (increases in) deficits will be extrapolated into the future. Fear of possible future monetization of deficits will raise long-term nominal interest rates. Increased uncertainty about the future course of inflation may add a further risk premium to the required rate of return on nominal government debt. In extreme circumstances, fear of partial or complete debt repudiation or of special capital levies and surcharges may build a risk premium into the rate of return on all public debt (see Blanchard, Dornbusch, and Buiter (1986) and Buiter (1985b)). A good reputation for underlying fiscal rectitude would, however, avoid the potential crowding out resulting from such “confidence” effects. It might therefore help if such a program were supervised by, or at least coordinated through, an organization or institution that has a reputation for fiscal restraint.
Finally, it may be judged that the global level of effective demand is currently excessive, and that a net reduction in global demand is in order, as well as a realignment of US competitiveness. A unilateral US fiscal contraction might in that case be the correct policy. The point would seem to be of mainly academic interest if, as many observers have pointed out, there remains a margin of Keynesian slack in the world economy.
US Fiscal Contraction Matched by Effective Demand-Maintaining, Expansionary Monetary Policy Changes
Calls for a change in the U.S. macroeconomic policy mix—from tight money and loose fiscal policy to looser money and tighter fiscal policy—have been heard from all corners of the economic profession in recent years. There are two kinds of monetary policy changes that could be used in the present model: changes in the level of the nominal money stock and changes in the proportional growth rate of the nominal money stock.
Money “jumps.” It is clear from inspection of the steady-state conditions (16a, e) and of the equations of motion (14a, b) and (15a, b) that there is one and only one set of discrete (discontinuous) changes in the levels of the nominal money stocks in both countries that will permit an instantaneous transition at full employment (in both countries) to the new real long-run equilibrium associated with the unilateral reduction in the US fiscal impulse discussed in the first subsection of this section. If df1 < 0 is the size of the US fiscal contraction, these nominal money jumps in both countries are given by
At the predetermined price level, this nominal money jump provides just the right increase in real money balances demanded as a result of the lower nominal (and real) world interest rate associated with the lower global fiscal impulse. There is no need to force the path of the price level below the path of the nominal money stock through a policy of demand deflation and unemployment. The steady-state increase in real money balances, which in a neoclassical model with a nonpredetermined. flexible price level would be brought about by a discrete downward jump in the price-level path, is achieved in the Keynesian. predetermined price-level model by stock-shift open market purchases that increase the nominal money stocks in each country by the required amounts. It is the stickiness of real money balances that makes a recession inevitable when there is any exogenous shock or policy change that raises the long-run demand for money balances. This stickiness of the real money stock reflects both the stickiness of domestic costs (assumed to be a structural property of private market behavior that is invariant to policy and exogenous shocks), and the stickiness of monetary policy. If the level of the nominal money stock is a choice variable at any given instant, policy flexibility can compensate for domestic cost inflexibility.
The great advantage of the kind of once-and-for-all nominal money stock jumps considered here is that they do not result in any change in the rate of inflation, short-run or long-run. They do cause the long-run level of the path of prices to be higher than it would otherwise have been, but, since welfare costs are associated with the rate of inflation rather than with the level of prices (only in a world without uncertainty), this is no cause for concern. The major problem with money-jump policies is their effect on inflationary expectations. The obvious analytical distinction between a discontinuous discrete change in the level of the money stock path and a (finite) change in the instantaneous rate of change of that path may not be as obvious in practice, especially when the money stock path is sampled at discrete time intervals: a once-and-for-all upward change in level at a point in the middle of an observational interval t0 may look much like an increase in the rate of growth between t0 and t0 + 1. If such an apparent increase in the growth rate gets extrapolated into the future, serious instability may result. Governments or central banks with a reputation for monetary rectitude will be able to engineer onetime money jumps without adverse effects on expectations of inflation. Governments or central banks with a reputation for monetary laxity will be prisoners of the markets’ lack of confidence and may have to live with the adverse effects on inflation expectations of any observed increase in the money stock.
Note that if the monetary authorities had nominal income targets rather than monetary targets, there should be no credibility problems associated with a one-time increase in the nominal money stock. Nominal income targets are velocity-corrected monetary targets. They have desirable operating characteristics whenever exogenous shocks or policy changes necessitate a change in velocity.
Changes in money growth. The other monetary policy action (in both countries) that can achieve the transition to an improved level of US competitiveness without any output or employment cost is an equal, permanent increase in the rate of growth of the nominal money stock in each country. It can again be checked, from the steady-state conditions (16a–e) and from the equations of motion (14a, b) and (15a, b), that the following permanent increase in ṁ1 and ṁ2 will achieve an instantaneous transition, at full employment in both countries, to the new real long-run equilibrium associated with the unilateral reduction in the US fiscal impulse discussed in the first subsection of this section:
This monetary policy response would, by raising the rate of inflation in both countries, prevent the global real interest rate decline resulting from the US fiscal contraction from being translated into a decline in nominal interest rates. With nominal interest rates unchanged, there is no increase in the demand for real money balances and consequently no need for a recession to depress the path of the general price level below the path of the nominal money stock. The policy has one obvious undesirable feature: a recession is prevented at the cost of having a permanently higher rate of inflation in the world economy.
III. Responses to a Collapse of the US Dollar
An important question addressed in the World Economic Outlook (International Monetary Fund (1985)) is the proper response (in the US and in the ROW) to a sudden large fall in the value of a key currency, for concreteness taken in this paper to be the US dollar. To determine the nature of the appropriate policy responses, one first must determine the causes of the sudden depreciation of the currency. There are two broad classes of possible causes: the bursting of a speculative bubble that had caused the dollar to be overvalued in relation to the “fundamentals,” and an actual or perceived change in the fundamentals driving the exchange rate. The latter category can be subdivided into several cases: (1) a portfolio shift against the dollar reflecting, say. greater uncertainty about the future prospects for US inflation (in the simple model of this paper, this can be represented by a reduction in US liquidity preference: a fall in η1); (2) an increase in the real risk premium on foreign-owned US assets (this could reflect fear of future increases in taxation of US interest income and. conceivably, a greater perceived risk of repudiation or default; in the model this can be represented by an increase in τ2 - τ1: the real risk premium is like a net tax on US interest income); (3) an unexpected increase in the level of the US money stock or in the rate of US monetary growth; (4) an unexpected tightening of the US fiscal stance.
All four events should be thought of in relative terms; that is, the portfolio shift against the dollar reflects an increase in uncertainty about US inflation relative to uncertainty about inflation in the ROW. Similarly, it is looser US monetary policy relative to monetary policy elsewhere, or tighter US fiscal policy relative to fiscal policy elsewhere, that puts downward pressure on the dollar.
An important issue in determining the appropriate policy response to a sudden drop of the dollar, in response to a change in private sector perceptions about the likely future course of the fundamentals, is whether the national authorities and the international coordinating agency share these new perceptions. A different approach will in general be called for if the authorities believe they have information superior to that used by private agents in forming expectations, but there is no way for the authorities to share this information with private market participants or to convince them of its relevance. In what follows, no superior public sector information is assumed.
A Bursting Bubble
It is well known that the solution of rational expectations models with forward-looking, nonpredetermined state variables (such as the nominal and the real exchange rates in our model) may be characterized by a “bubble”; that is, the behavior of the endogenous variables may be influenced by variables that matter only because, somehow, private agents believe that they matter. These bubble processes, which affect expectations in a self-validating manner, may be functions of the fundamental variables (that is, of those variables that enter into the structure of the model in ways other than merely being part of the information set used to form expectations) or of completely extraneous or spurious variables of the “sunspot” variety (Blanchard (1979), Azariadis (1981), Obstfeld and Rogoff (1983)).
In Figure 5, it is assumed that all fundamentals have constant values, now and in the future, that the steady-state equilibrium corresponding to these constant values for the fundamentals is E0, and that the associated convergent saddle path is S0S0. Suppose, without loss of generality, that the predetermined variable is at its steady-state value
Bursting of an Exchange Rate Bubble
Citation: IMF Staff Papers 1986, 003; 10.5089/9781451972887.024.A005
It seems quite self-evident that the right thing for policymakers to do when a bubble bursts is to sit back and enjoy the sight. Although a well-developed theory of the welfare economics of speculative bubbles in a world with uncertainty and limited and asymmetrically distributed (insider/outsider) information does not exist, there is a strong presumption that such bubbles are costly and harmful as well as unsustainable. It may be that the fundamental valuation to which the exchange rate returns when the bubble bursts represents in itself an unattractive equilibrium because the fundamentals (especially current and anticipated future policy) are in a mess. That, however, is an argument for doing something about the fundamentals once the exchange rate again reflects those fundamentals—a course that would have been desirable had there been no bubble and no sudden drop in the exchange value of the dollar.
In reality, the ending of a speculative bubble is likely to be associated both with major redistributions of wealth and with short-term disruption of financial markets, commerce, and production because of bankruptcies and insolvencies. None of these adjustment costs are included in the formal model presented here. I would be surprised, nevertheless, if it could be shown that it is better to end a bubble with a slow puncture than with a quick burst. A hard landing of the dollar under these circumstances does not preclude a soft landing for the world economy. No policy response in the US or in the ROW seems necessary.
A Reduction in US Liquidity Preference
A downward shift in the US liquidity preference schedule (a fall in η1) has no long-run effects on competitiveness or on real or nominal interest rates. In the short run. the effects are as depicted in Figure 6. An unexpected, immediate, permanent reduction in η1 works just as would a one-time increase in the level of the US money stock. The nominal and real exchange rate jump-depreciates to E01 from E0. After that, the real exchange rate gradually moves back to its initial level, and the system converges to E1. Real economic activity in the US booms because of short-run lower nominal and real interest rates and because of the improvement in competitiveness. Average world economic activity also rises (ya increases), as shown in panel B of Figure 6, because of the short-run downward pressure on nominal and real interest rates. Activity levels in the ROW are depressed, however, because the loss of competitiveness outweighs the effect of lower interest rates. If the initial equilibrium was deemed to be satisfactory, the obvious policy response to the fall in liquidity preference is a matching one-time reduction in the level of the US nominal money stock. Such a reduction would leave all real and nominal variables (other than l1) unchanged.
Dollar Depreciation as Result of Fall in US Liquidity Preference
Citation: IMF Staff Papers 1986, 003; 10.5089/9781451972887.024.A005
If the shift out of US money represents stock-shift currency substitution and has as its counterpart a matching stock-shift increase in foreign money demand η2, the change in competitiveness will be twice as large. Average real world activity (ya, ia,ṗa and ra) are unchanged in the short run and in the long run. The behavior of c and ld is like that illustrated in panel A of Figure 6, but with a shift up and to the left of the saddle path that is twice as large. The US experiences a transitional boom that is matched by a transitional slump in the ROW. The obvious way to neutralize this one-time currency substitution and to stabilize the exchange rate is to make the US money stock contract by -Δη1 and to expand the ROW money stock by Δη2. In addition, such changes in monetary policy may well have favorable effects (not formally modeled here) on the relative changes in inflation uncertainty that may have prompted the money demand shifts in the first place.
An Increase in the Real US Risk Premium
An increase in the relative perceived real riskiness of foreign investment in the US will in the long run raise the US real and nominal interest rates and lower the ROW real and nominal interest rates, leaving the average world rates unchanged. The increase in US riskiness and reduction in ROW riskiness are assumed to apply only to foreign investors, not to domestic capital formation in either country. Figure 7 illustrates the dynamic response pattern to this shock. Global averages (la, ya, ia, ṗa, and ra) are not affected. The US economy experiences an immediate jump depreciation of the nominal and real exchange rate from E0 to E01.
Increase in Relative Perceived Riskiness of Foreign Investment in US
Citation: IMF Staff Papers 1986, 003; 10.5089/9781451972887.024.A005
Note that the real exchange rate overshoots its long-run equilibrium value. After the initial jump there is a gradual depreciation of the US real exchange rate. The new long-run equilibrium at E1 represents a net real depreciation relative to the initial one. The US economy experiences a transitory boom that lowers its real stock of money balances. The ROW goes through a transitory slump that raises its real money balances.
One possible policy response that exactly neutralizes this increase in the US foreign investment risk premium is an equal increase in τ1—τ2, the excess of the US tax rate on interest income accruing from abroad over the ROW’s tax rate on interest income accruing from the US. This response would restore the initial equilibrium immediately. Alternatively, a one-time increase in the ROW’s nominal money stock by λ times the change in the risk premium, and a reduction in the US nominal money stock by the same magnitude, would instantaneously achieve the same long-run change in the real equilibrium shown in Figure 7, without any transitional US inflation and ROW contraction. A permanent increase in the US rate of monetary growth and an equal reduction in the ROW rate of monetary growth, with dṁ1 - dṁ2 ≡ dṁd = -d (risk premium), would in Figure 7 move the economy immediately from E0 to E01, which would now be the new long-run equilibrium.
Policy-Induced Exchange Rate Collapses
The response of the exchange rate to changes in fiscal and monetary policy in the US and ROW has already been discussed in Section II. The only point worth repeating here is that a hard landing for the US dollar need not represent a hard landing for the US economy or for the ROW. If the initial situation is one characterized by current and anticipated future lax US fiscal policy and tight US monetary policy, these fundamentals are likely to be reflected in a strong (an “overvalued”) US real exchange rate. The first-best cooperative, coordinated global policy package to change this unfavorable equilibrium (fiscal contraction in the US; one-time money stock increases in the US and the ROW to meet the resultant fall in velocity) is accompanied by a dollar collapse. It may seem paradoxical that the restoration of confidence in the ability of the US to get and keep its budget under control would be accompanied by a fall in the US dollar, but such a view reflects the mistaken identification of the exchange rate as an index of national economic power.
IV. Policy Responses to a Slowdown in Global Economic Activity
The first question that needs to be answered before one can determine the appropriate US and ROW policy responses to a global economic slowdown concerns the cause(s) of this slowdown. A distinction must be made between a slowdown resulting from an adverse supply-side shock (represented in the simple model by a temporary or permanent fall in
Adverse Supply-Side Developments
Permanent reductions in productive capacity in the US and the ROW raise the long-run real interest rate everywhere and thus bring demand down in line with supply. Nominal interest rates will also rise if money growth rates are unaffected, and the demand for real money balances in both regions will decline, through both real income and real interest rate effects, in the long run. If productive capacity is affected equally in both countries (
Effects of Common Permanent Decline in Productive Capacity in Both Countries
Citation: IMF Staff Papers 1986, 003; 10.5089/9781451972887.024.A005
The policy response that prevents the emergence of excess demand and inflationary pressures during the transition to the lower levels of capacity output involves a contraction of demand that can be achieved by either fiscal or monetary means (or by a combination of the two). If no long-run change in competitiveness is desired, any fiscal contraction should be equal in the two countries. Probably the simplest coordinated policy action that immediately achieves the new long-run equilibrium at E1, in Figure 8 is a reduction in m1 and in m2 equal to
If the common decline in capacity at t0 is expected to be temporary and to be reversed at t1, there is still no action in c - ld space (panel A of Figure 8). The world economy experiences a bout of excess demand between t0 and t1 (moving from E01 to E02 in panel B of Figure 8) and a bout of excess supply after t1 (between E03 and E0). The same reduction in m1 and in m2 at t0 will take the world economy (without excess demand) from E0 to E1, where it will stay until t1. At t1 both nominal money stocks should be increased again by the same percentage by which they were reduced at t0 in order to achieve a painless and instantaneous restoration of full equilibrium at E1.
An adverse permanent supply shock in the US alone, say, would cause a long-run worsening of US competitiveness (required to choke off global demand for US output), some increase in global real and nominal interest rates (but less than that with a common decline in capacity output), a decline in US real money balances, and a smaller decline in ROW real money balances. On impact, there is likely to be a step appreciation of the US dollar. After that the real exchange rate continues to appreciate gradually toward its new long-run equilibrium. Real interest rates in the US will be below those in the ROW during the transition. A reduction in the US nominal money stock by an amount
A Demand-Induced Slowdown in Economic Activity
When the cause of a disappointing level of economic activity is a decline in some component of private demand, appropriately designed demand management can minimize the damage and, in the present model, can be used to avoid it altogether. Increases in private liquidity preference (η1 and η2) can be met with corresponding one-time increases in the levels of the nominal money stocks (m1 and m2). A downward shift in the private consumption functions or a collapse of animal spirits can be offset directly by corresponding fiscal stimuli f1 and f2. If the balanced-budget multiplier theorem retains some validity, these fiscal stimuli can be provided without increasing the deficit. Supply-side consequences from the tax increase or from cuts in transfer payments involved in a balanced-budget expansion should of course be taken into account (the behavioral links, ignored in this paper, between fi and
Note that it is never necessary, in response to any shock, to engineer a permanent change in monetary growth rates. One-time changes in the levels of the nominal money stocks (or temporary changes in money growth rates) are sufficient.
V. Conclusions
This paper has presented a rather old-fashioned study of demand management in an open, interdependent economic system. Three contingencies discussed widely during 1984 and 1985 were analyzed through an eclectic, short-run Keynesian, long-run classical, two-country model. The main conclusion is that an active monetary or fiscal (or combined) response in both countries or regions is in general required to minimize the costs associated with the adjustment process following a variety of demand-side or supply-side shocks. Only in the case of a currency collapse—from the bursting of an exchange market speculative bubble—did a no-response policy appear desirable. A unilateral fiscal contraction in country 1 (the US) will cause a temporary slowdown of world economic activity as well as a sudden drop in the nominal and real value of the US dollar. Merely preventing the nominal exchange rate from changing does not reduce the magnitude of the global recession or alter the long-run real adjustment that takes place, but it would redistribute the unchanged global unemployment and excess capacity burden toward the US and away from country 2 (the rest of the world, ROW). A no-response policy would be appropriate if the initial situation were characterized not only by an undesirable US fiscal-monetary policy mix, resulting in a poor US international competitive position, but also by global excess demand. An expansionary fiscal move in the ROW or a combined expansionary monetary policy move in both the US and the ROW could achieve the desired traverse to a better level of US competitiveness without a global slump. These monetary stimuli need not be permanent increases in the rate of money growth. One-time, credible, open market purchases raising the levels of the nominal money stocks would suffice.
The proper response to a sudden drop in the value of the US dollar depends crucially on the reason(s) for this drop. The bursting of a speculative bubble has no obvious implications for monetary or fiscal policy. Downward pressure on the value of the US dollar, resulting from a one-time fall in US liquidity preference, calls for a matching one-time reduction in the US nominal money stock. Direct currency substitution away from the dollar calls for open market sales in the US and open market purchases in the ROW. The consequences of the emergence of a real risk premium on the return from foreign investment in the US can be neutralized by a matching increase in the difference between the US tax rate on interest income from the ROW and the ROW’s tax rate on interest income from the US. Alternatively, one might accept the depreciation of the nominal and real US exchange rates but avoid the transitional US inflation and ROW contraction by expanding the money stock in the ROW and reducing it in the US.
The appropriate policy response to a slowdown in global economic activity depends on whether this slowdown reflects a deterioration of the supply side or deficient aggregate demand. To avoid the stagflation that would otherwise result from a global adverse supply shock, demand-reducing measures are called for in both countries. If the supply shock is temporary, the restrictive measures should be reversed when capacity output recovers. The appropriate response to a fall in private demand for goods and services is a fiscal stimulus. The contractionary effects of an increase in liquidity preference can be avoided by an accommodating (noninflationary) increase in the level of the money stock.
The fiscal stimuli discussed in this paper are to be interpreted as “discretionary” changes over and above the automatic changes in tax receipts and transfer payments that reflect the workings of existing tax and benefit laws, rules, and regulations as the level of economic activity varies; such automatic stabilizers dampen but never eliminate economic fluctuations.
To provide truly satisfactory answers to the questions raised in this paper, the model would have to be extended in a number of directions. Even an analysis that focuses on the industrial world alone would benefit from a three-region setting: the United States plus Canada, Europe, and Japan. The complexity entailed in expanding to cover three regions virtually obliges one to use numerical rather than analytical methods. The model of this paper ignores all stock-flow asset dynamics, those coming from the government budget identities, those coming from the current account of the balance of payments, and those resulting from real capital accumulation.6 Again, incorporation of these dynamics would require the use of numerical methods. Finally, it would be extremely desirable to allow explicitly for uncertainty. Adding some linear stochastic processes with known coefficients to the deterministic model is feasible but does not constitute much of an advance. Anything more complicated—even linear models with stochastic coefficients, let alone nonlinear stochastic models—would mean entering the mathematical or computational stratosphere. The modeling language one would like to use just does not exist yet.
The logic of the model used in this paper, and indeed of any model that permits persistent disequilibrium or non-Walrasian equilibrium, implies that monetary and fiscal policy instruments can be used actively to stabilize output, employment, and the price level in response to a wide range of demand or supply shocks. To argue against such activist policy responses, or against the adoption of explicit policy rules that would, for example, make monetary growth (or the deviation of actual monetary growth from its expected value) a function of observable contingencies, one must make a case for the technical, political, or institutional impossibility of an active stabilization policy.
The technical impossibility of stabilization policy has been argued on two grounds. There is the Lucas-Sargent-Wallace-Barro argument that, in properly specified macroeconomic models, only unperceived or unanticipated monetary policy can affect the deviations of actual real variables from their “natural” or full-information values. Fiscal policy obviously has allocative effects both in the short run and in the long run, but it too cannot systematically affect the deviation of real output and employment from their capacity, full-employment, or natural levels. If debt neutrality prevails, the substitution of lump-sum taxes for current borrowing has no real effects in the short run or in the long run. These propositions of policy ineffectiveness for a while engaged the interest of a significant part of the macroeconomic profession but are now in general viewed as theoretical curiosities without empirical relevance.
The second technical argument against the active use of stabilization policy is much older (it goes back at least to Milton Friedman’s work in the 1950s and 1960s) but is more relevant. It is a generalization of the “long and variable lags” argument used by Friedman to make the case against active countercyclical use of monetary policy. Clearly, the length of the lag between the policy response and its impact on the variable(s) of interest (the “outside lag”) is irrelevant in itself. It is uncertainty about the coefficients in the model, about the order of the lags, and indeed about the total specification of the appropriate model of the economy that forces one to qualify the confident policy prescriptions that emerge from the manipulation of models such as the one in this paper. The length of the “inside lag,” the lag between identification of the need to respond and the moment the policy handle can finally be cranked, puts further constraints on the ability to stabilize the economy through active demand management. Estimates of the “inside lag” for U.S. fiscal policy range from a few years to infinity.
Uncertainty about the way in which the economy works not only renders the consequences of policy activism harder to predict. It also increases uncertainty about the consequences of refraining from policy activism and sticking to preannounced, unconditional (noncontigent or open-loop) rules. It seems highly unlikely that a cautious, safety-first policy of hedging one’s bets in the face of great uncertainty would ever involve the economic equivalent of locking the steering wheel and closing one’s eyes.
The political or institutional case against active demand management relies in part on alleged observed asymmetries or irreversibilities in monetary and fiscal policy design. Policymakers, according to this view, are happy to cut taxes and raise spending for cyclical reasons during a slump, but they are reluctant to raise taxes and cut spending when the economy is overheating and a countercyclical quid pro quo is needed. Although there is some informal evidence supporting this view, there are also counterexamples (for example, the increase in the overall U.K. tax burden by 4 percent of GDP during Prime Minister Thatcher’s first term). It would be valuable to have more systematic evidence on this important issue of political economy.
The conditions under which optimal, conditional stabilization policy rules would be credible (or time-consistent) also are only just beginning to be studied. The study of economic history since World War II suggests that “stabilizing” monetary and fiscal policy actions have their desired effects only if the monetary or fiscal authorities have “conservative” reputations for underlying monetary soundness and fiscal responsibility and rectitude. Without such reputations, temporary and reversible changes in money growth, tax rates, or spending schedules are likely to be perceived as permanent. Such adverse expectations or confidence effects may lead to inflation premiums in nominal interest rates, and even to “super crowding out” or negative multipliers as a result of increased long real rates (see Buiter (1985b)).
Coordination of international stabilization policy through international agencies with reputations for monetary and fiscal conservatism could therefore be especially effective.
One set of “cautious” global macroeconomic policy recommendations popular among international officials (see, for example. International Monetary Fund (1985)), can be summarized as: (1) adherence to unconditional medium-term monetary growth targets; (2) continued downward pressure on structural fiscal deficits; and (3) limited countercyclical responsiveness of actual deficits to reflect the (partial) operation of the automatic fiscal stabilizers. According to the analysis in this paper, such a policy package will not prevent a global recession if and when the United States tightens its budgetary stance. It is not even sufficient to prevent the slowdown that appears to be already under way. The risks associated with this strategy are very high. Even in the current state of the macroeconomic arts, it is not impossible to design a more flexible and superior set of policy recommendations. Not for the first (or the last) time, caution demands if not action, then certainly preparedness for action should the need arise.
APPENDIX I: Coefficients in Equation (14a)
The aij and bij from equation (14a) are given by
and
APPENDIX II: Coefficient Matrices in Equation (15a)
The coefficient matrices in equation (15a) are
and
The coefficient matrices in equation (15b) are
and
APPENDIX III: Coefficient Matrices in Equations (23) and (24)
The coefficient matrices in equation (23) are given by equations (37)
and (38) (see page 580).
The coefficient matrices in equation (24) are given by equations (39)
and (40) (see page 580), where
APPENDIX IV: Behavior and General Solution of ld and c in Equation (14a)
The behavior of ld and c given in equation (14a) can be summarized as
where A ≡ {aij}, B = {bij}, and z is the vector of exogenous variables. The general solution for c and l can be shown (see Buiter (1984a)) to be
where λ1 is the stable eigenvalue of A, and λ2 is the unstable eigenvalue.
where V is the matrix whose columns are the right eigenvectors of A, and
F is the bubble component; it satisfies EtḞ(t) = λ2F(t) but is otherwise arbitrary.
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Mr. Buiter is Professor of Economics at Yale University. During the period in which this paper was written, he was a consultant in the Research Department of the Fund. He holds degrees from Cambridge University and Yale University.
One could specify the demand for real money balances as a demand for money balances in terms of the country’s consumption bundle. Let country 1’s consumer price index
Adding such currency substitution would not alter the results qualitatively. Let the money demand functions, including direct currency substitution, be given by m1 - p1 = -β1ė - λ1i1 + k1y1 + η1 and m2 - p2 = β2ė - λ2i2 + k2y2 + η2. In the “symmetric” case considered below, β1 = β2 = β, λ1 = λ2 = λ, and k1 = k2 = k. For any variable x, let xd = x1 - x2 and xa = (x1 + x2)/2. It follows that ld = -(λ + 2β)id + kyd - 2β(τ1 - τ2) and ld = -λ ia + kya. The behavior of global averages is completely unaffected by direct currency substitution. Country differences are affected through an increased interest sensitivity of that is, the coefficient of id is now -(λ + 2β) instead of -λ. In addition, the last term on the right-hand side of the ld equation is absent without direct currency substitution. Ignoring this second (minor) difference, the analysis that follows can be applied to the case of direct currency substitution by replacing λ (in the “differences” model only) by λ + 2β. In the limiting case in which the currencies are perfect substitutes (β = +∞), only an ex ante fixed exchange rate regime is viable.
This result is quite robust and does not depend on the assumption of a fixed level of capacity output. In Buiter (1984b) I considered the case in which capacity output is given by a neoclassical production function with exogenous labor supply and a long-run endogenous capital stock. In the perfectly integrated financial markets, an increase in public spending raises the global real interest rate and thus lowers the steady-state capital stocks at home and abroad and, with them, domestic and foreign capacity output. If the contraction in capacity output is not biased toward the foreign country and if the increase in public spending is biased toward home goods, then higher public spending still raises the relative price of home goods. If public debt is not neutral, a lower level of domestic taxes will also (if domestic private spending is, at the margin, biased toward home goods) be associated with an increase in the relative price of home goods.
For ia to decline less on impact than in the long run, one must assume that 1 - γψ - ε > 0. For ra to decline less on impact than in the long run, one must assume that ε < 1.
Since K1 + K2 = Ω - ε.
For a numerical simulation model that incorporates all three sources of asset dynamics in a two-country, full-employment setting, see Buiter (1984b).
