stopping inflation in the dornbusch model: optimal monetary policies with alternative...

DEAN TAYLOR Uniuersity of Colorado at Denuer

Stopping Inflation in the Dornbusch Model: Optimal Monetary Policies With Alternative Price-Adjustment Equations*

This paper compares the optimal monetary policies for reducing inflation in the Dombusch model with various authors’ modifications of his price-adjustment equation. In the cases where the price-adjustment equation is augmented with a forward-looking expectations variable, the optimal policy calls for an increase in the money stock followed by no further monetary growth. On the other hand, when inflation has momentum, the optimum policy may require either an initial increase or decrease in the money stock followed by monetary growth that allows for an increase in real money balances.

Countries frequently have flexible exchange rates because they are pursuing an inflationary monetary policy. Yet one of the most popular models for flexible exchange rates (Dornbusch 1976) does not allow for steady-state inflation. This paper shows that various authors’ modifications of the Dombusch price-adjustment equation which allow for steady-state inflation can lead to very different optimal monetary policies for stopping inflation.

Dombusch specifies the price-adjustment equation as an inflation-output trade-off or a simple Phillips curve. Although his specification may be appropriate in the environment he considers, it is unrealistic with an inflationary monetary policy. As pointed out by Mussa (1982), continuous monetary expansion only generates continuous price inflation by having output persistently exceed its full employment level.

This paper analyzes two cases where a forward-looking variable is added to the price-adjustment equation. The first, suggested by Dombusch (1976) and used by Frankel (1979) and Buiter and Miller (1981), adds the rate of monetary growth to the price-adjustment equation. The second case adds a variable suggested by

*I have benefitted from comments by Betty Daniel and Gerd Schwartz and from seminars at SUNY-Albany and the University of South Carolina.

Journal of Macroeconomics, Spring 1989, Vol. 11, No. 2, pp. 199-216 199 Copyright 0 1989 by Louisiana State University Press 0164-0704/89/$1.50

Dean Taylor

Mussa (1982): the rate of change of the equilibrium price that would result if prices where fully flexible. With either of these price-adjustment equations, the system has the same optimal monetary policy to stop inflation. A jump increase in the money stock followed by no further monetary growth stops inflation costlessly and instantaneously. When either of these forward-looking rate of change variables are added to the price-adjustment equation, the inflation rate is perfectly flexible. That is, with the appropriate jump in the money stock, the economy can go from one steady-state rate of inflation to another without any effect on income.

These results are then contrasted with optimal policy when inflation has momentum. This model follows Buiter and Miller (1981), who use a price-adjustment equation with momentum by augmenting the Phillips curve with a Cagan adaptive expectations term that depends on current and past inflation. In this case, both the inflation rate and prices are sticky, and the underlying rate of inflation can be reduced only by enduring a recession induced by monetary restraint. With a quadratic loss function, the optimal policy may require an instantaneous contraction of the money stock followed by sufficiently rapid monetary growth to allow an increase in real money balances. On the other hand, if the indirect effect of the forward-looking financial variables is strong enough, the optimal policy may require an initial increase in the money stock followed by additional monetary growth.

Following the review of the Dornbusch model in Section 1, Section 2 analyzes the optimal policy when the price-adjustment equation is augmented with a forward-looking variable. Section 3 analyzes the optimal policy when inflation has momentum. Finally, Section 4 gives concluding remarks.

1. The Dornbusch Model

The key assumption to the Dornbusch model is that goods prices are sticky and do not jump, while asset prices are free to adjust instantaneously to clear markets. The primary justification for the sticky price assumption is empirical: goods prices do not move freely. The variable output version of the Dornbusch (1976, 1174-75) model consists of the following equations.

Monetary equilibrium is represented as

m=-Xr+p+qy; (1)

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Stopping Inflation in the Dornbusch Model

where m, p, and y are the logarithms of the money supply, the price level, and income, respectively, and r is the nominal interest rate.

Output responds to changes in aggregate demand, which depend on the relative price of domestic goods and the nominal interest rate,

Y = 8(X - p) - ur + y , (2)

where foreign prices are assumed constant and x is the log of the exchange rate. The model assumes that the real exchange rate con- verges to the initial steady state after a disturbance, which causes a unique equilibrium.

To reflect this paper’s inflationary environment, aggregate demand will be modified to be a function of the difference between the nominal interest rate and the own rate of return on domestic goods, fi (the first derivative of p):’

y = 6(x - p) - a(r - fi) + y . (2’)

The foreign nominal (and real) interest rate, p, is assumed constant. Assets are perfect substitutes if there is a premium to offset the expected appreciation in the exchange rate:

r=p+i. (3)

The interest rate is the shortest term rate (the overnight rate) so that the rate of change of the exchange rate in (3) applies to the next instant in time. The rate of depreciation, 2, is anticipated cor- rectly except at the moment of the unanticipated policy change (at which time [3] does not hold).

For analyzing the problem of inflation, Dornbusch’s price-adjustment equation is troublesome. This equation specifies the rate of price change as proportional to deviations of short-run supply from its equilibrium level and represents the simple Phillips curve:

‘Both Mussa (1982) and Obstfeld and Rogoff (1984) use a weighted average of domestic prices and the exchange rate, pp + (1 - p)x, instead of just domestic prices, p, in Equations (1) and (2’). This alternative specification has no effect on this paper’s basic results.

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where tj is the log of full employment income. Although this specification may be appropriate in the environment that Dornbusch considers, it is inappropriate when trend movements in the money supply are producing inflation. In his specification, continuous monetary expansion can generate continuous price inflation only by having output persistently exceed its full employment level. The following sections consider the optimal monetary policies and the behavior of the system while slowing inflation when using various proposed modifications of the Dornbusch price-adjustment equation, (4). These alternative price-adjustment equations can result in critically different optimal policies for stopping inflation.

2. Stopping Inflation When a Forward-Looking Variable Is Added to the Price-Adjustment Equation

Two forward-looking rate of change variables have been suggested to augment the price-adjustment equation, (4). Since the model’s optimal solution is the same for both cases, they are con- sidered together. Dombusch (1976) suggests adding a term for the rate of monetary growth to the price-adjustment equation. This modification is implemented by Frankel (1979) and Buiter and Miller (1981, 1982) as

$ = Tr(y - ij) + +I) (4’)

where ni is the contemporary rate of monetary growth.’ Mussa (1982), on the other hand, suggests augmenting the price-

adjustment equation by the rate of change of the full-equilibrium solution for the price level, 13, if prices are fully flexible. The price equation then becomes

2; = 7r(y - g) + p’. (4”)

Mussa’s rationale for augmenting the price-adjustment equation with the variable 1; is that it maintains equilibrium once it is achieved.

With either of these price-adjustment equations, the optimal monetary policy stops inflation costlessly and instantaneously without any effect on output.3 With the appropriate jump in the money

The augmentation term, k, is the right-hand derivative. Therefore, if m makes a discrete jump, the price level does not jump.

30bstfeld and Rogoff (1984) discuss the various disequilibrium dynamics of the Dornbusch model when the price-adjustment equation is augmented with different

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stock followed by no further monetary growth, the economy can go from one steady-state rate of inflation to another without any effect on income. Setting the rate of monetary growth, tir, to zero after the policy change eliminates the effect of the second term in (4’). Similarly, a zero rate of monetary growth results in a zero rate of change for the full-equilibrium price level, 1;, eliminating the effect of the second term in (4”). The lower rate of monetary growth results in a lower steady-state inflation and lower interest rates, and consequently, in greater steady-state real money balances. There- fore, to keep income from changing, real balances need to be expanded instantaneously to the quantity demanded at a steady state with zero inflation. Since the price level is sticky, changing the nominal quantity of money changes the real quantity of money.

Assume that the rate of monetary growth, the rate of inflation, and the rate of depreciation are initially all equal to r. As shown in Figure 1, a jump in m by the amount of Ar followed by no further monetary growth will immediately stop inflation without y deviating from its equilibrium level, &. The solution, therefore, requires knowledge about only one parameter in the model: the semi- elasticity of the demand for money, A. The greater the past rate of inflation, the greater the necessary initial jump in the money stock to stop the inflation will be.

To summarize, with either (4’) or (4’7, inflation can be stopped without a recession because, although prices are sticky and cannot jump, the inflation rate is perfectly flexible. The rate of inflation can be lowered instantaneously and costlessly by increasing the money supply to its new equilibrium level at the desired rate of inflation and thereafter keeping monetary growth equal to the desired rate of inflation. 4

3. Stopping Inflation When Inflation Has Momentum A broad range of economists maintain that persistent inflation

develops self-sustaining momentum that is attributed to backward-

forward-looking variables. However, with the optimum policy in this section, the system is always in equilibrium and the paths of the variables are the same re- gardless of which forward-looking variable is used.

4As pointed out by Buiter and Miller (1981, 174), “The intentions of the government are likely to be in doubt when a policy of monetary disinflation is initiated with an expansion of the nominal money stock!” However, the model does not allow for doubts about government intentions and assumes both perfect credibility and perfect foresight.

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m

Y

r 1 i I L

I

t=o

Figure 1.

time

looking, adaptive expectations. Discussing the patterns of inertial inflation, Tobin (1981, 24) states: “The behavior that sustains these patterns may be interpreted as backward-looking-emulating the behavior of other unions and other industries, catching up with ref- erence groups, passing through historical costs, fulfilling explicit or implicit contractual agreements and mutual understandings.” Gor- don (1981, 1982) has carried out extensive empirical studies of the persistence of inflation and concludes that the momentum of inflation is primarily due to institutional and cultural elements and has little to do with the credibility of the disinflation policy.

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Stopping lnflation in the Dornbusch Model

Just as the basis of Dornbusch’s assumption of sticky prices is primarily empirical, the basis for the assumption of sticky inflationary expectations is primarily empirical. To produce a system where inflation is sticky or has momentum, this section follows Buiter and Miller (1981) by using adaptive expectations. They augment the Phillips curve as follows:

fi = n(y - g) + a, (4”‘)

where a is the underlying, expected, or core rate of inflation. This anticipated or expected rate of inflation is adaptively de-

termined according to the Cagan equation:

ci=P(fi-a). (5)

That is, the change in the anticipated rate of inflation is proportional to the discrepancy between the actual and anticipated rates of inflation. The solution to (5) is found so that the anticipated rate of inflation is determined from past rates of inflation. Therefore, like the original Dombusch equation, (4), Equations (4”‘) and (5) have no forward-looking element.5

Substituting (4”‘) into (5) gives

ci=fh(y-ij).

Thus, the underlying rate of inflation can be reduced only by en-

sThis paper uses the traditional approach of the Cagan adaptive expectations model by including only current and Fast values of a variable to predict values of itself. It could be argued that other variables such as the rate of monetary growth or rate of exchange rate depreciation, or other information on the structure of the model, should enter the expectations function. In a later paper, Buiter and Miller (1982) analyze a model where expectations about domestic prices (which they call wages) depend on current and past changes in both domestic prices and the exchange rate. This case has been explored more extensively in Buiter and Miller (1982), DrifBll (1982), Miller (1985), and Miller and Salmon (1984). On theoretical grounds, it is digcult to argue that one specification is better than the other since both specifications are ad hoc and not determined from the structure of the model. Even if a weighted average of domestic prices and the exchange rate is used in Equations (1) and (2’), expectations of domestic prices would not necessarily depend on the current and past changes in both domestic prices and the exchange rate. However, as shown by DriBill (1982), using a weighted average of the changes in domestic prices and the exchange rate complicates the analysis since the optimal trajectory is not time consistent.

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during a recession induced by monetary restraint. The policymaker must trade off unemployment in the short run for less inflation in the long run.

The government’s loss function, L, will be specified in the following discounted quadratic form:

m

L= [(y - 8)’ + q?]e-Qf dt , (7)

where o is the weight attached to the government’s distaste for inflation relative to the loss from income deviating from its equilibrium level and OL is the government’s discount rate. Using the classical calculus of variations, the loss is minimized subject to the constraints (4”‘) and (6) with the boundary conditions a0 = r and a, = 0.6 First, (4”‘) is substituted into (7) to eliminate fi and then (6) is substituted to eliminate the variable y - g. The resulting integrand (or intermediate function), I, has arguments only in a, ci, and t:

L= I

m

Z(a,ci, t) dt 0

= I

m [(i2/p2~2 + o(ci/p + a)‘]eeat dt .

0

The Euler equation is

(8)

g-i;= [Zh(l+~)a+~(-$+o)(ud-ii)]e-“‘=O (9)

or

rCZa+cui-ii=O, 00)

where R = [w/(0 + 1/1?)][p~ + cxp] and ii is the second derivative of a with respect to time. The characteristic equation of the differential equation, (lo), has two roots,

-9 = -V4n + a2/2 + o/2 < 0

The boundary condition, a, = 0, comes from the assumption that both inflation and the expectations of inflation are reduced to zero. As is customary in rational expectations models, the unstable root is suppressed.


and

c+’ = +$iiiz/2 + a/2 > 0.

Also, since o/(o + l/n’) < 1 and 4(p2 + I$) + cx2 = (2p + CX)~, then 4 < p. The greater the value of w in the loss function, the closer C$ is to p; the smaller the value of w, the closer 4 is to zero. The general solution to the second-order differential equation, (lo), is a = Ae-“’ + Be O’* From the boun . da conditions, the second ry term is zero. Therefore,

a = Fe-+’ , (11)

which represents the continuous reduction in the underlying rate of inflation from r to zero. The greater the value of 4, the faster the reduction in the underlying rate of inflation will be.

Equating the derivative of (11) to (6) gives the pattern of income after the change in policy:

y - zj = -(+/@r)re-“” . (12)

The change in income at the time of the policy change is

Ay,, = -+I’/@. (13)

After this initial drop, income then recovers exponentially at the rate + as shown in Figure 2.

Substituting (12) and (11) into (4”‘) gives the rate of inflation after the policy change:

6 = (1 - $/p)re-+’ . (14)

Initially the recession causes the rate of inflation to drop below the underlying rate of inflation by $r/p. However, since + < p the induced recession is not so severe as to immediately stop the inflation. The inflation rate subsequently declines to zero during the adjustment.’

‘If, as in Buiter and Miller’s (1982) later paper, expectations about domestic prices depend on current and past changes of not only domestic prices but also the forward-looking exchange rate, expectations will jump discretely if the exchange rate jumps discretely. Then, as shown by Driffill (19&Q), the optimal trajectory is not time consistent. This means implementing a new policy that causes the ex-

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Substituting the derivative of (3) into the derivative of (2’) and rearranging terms gives the differential equation for the rate of depreciation:

6x! - ax = zj + 8-d - a;. (15)

If the real exchange rate is defined as z = x - p, then (IS) can be expressed as

6i - ai = lj . (16)

In the long run, the real exchange rate is assumed to return to L, its level prior to the change in policy. Since z jumps with the change in policy, the initial conditions are not apparent. However, the ter- minal conditions for z are evident. Since z is assumed to return to its original position in the long run, the value of i approaches zero as time approaches ~0. Therefore, the differential equation, (16), can be solved from time t to ~0 and the result then can be evaluated at t = 0 to obtain the value immediately after the jump. Since d&e-“/“/d7 = -@i - uZ)e-s7’u, multiplying (16) by e-&j0 and integrating from t to CQ gives

co ’ -tit/u _ aze - - $e-S7’0d7 . (17)

Substituting the derivative of (12) into (17) and evaluating the in-

tegral yields the rate of depreciation of the real exchange rate after the policy change:

i= pn(u:+ 6) re-“’ * (18)

The path of the level of the real exchange rate after the change in policy is found by integrating (18):

(Note cont. from p. 207) change rate to appreciate and causes the rate of inflation to drop. The policymaker is always tempted to reoptimize and depart from the original policy so as to produce

another shock to lower the inflation rate. The Buiter and Miller (1982) model has been explored also by Miller (1985) and Miller and Salmon (1984).


I

t=o

Figure 2.

time

The real exchange rate, therefore, initially appreciates by the proportion of +r/[pl~(u$ + S)] and th en depreciates to its original level, IZ. This change in the real exchange rate after the change in policy causes domestic goods to be less competitive and is one of the channels through which income is reduced and inflation is slowed.

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Dean Taylor

Since the price level is sticky and cannot jump, the nominal exchange rate also initially appreciates by the proportion +T/[p,(u+ + S)]. After this initial appreciation, the rate of change of the nominal exchange rate, ?J = i + 6, is found by summing (14) and (18).

The real rate of interest in terms of domestic goods is unambiguously higher after the policy change and is the other channel through which income is reduced.’ Since r - fi = p + i - $ = p + i, the real interest rate in terms of domestic goods prices reflects the behavior of i in (18). Therefore, the real interest rate increases initially by $2r/[@r(u$ + S)] and th en exponentially decreases to p.

The nominal interest rate, on the other hand, may change initially in either direction depending on the model’s parameter values and how adverse the policymaker is to inflation, which, in turn, determine how quickly he reduces inflation. Although the real interest rate increases by @I’/[@r(u+ + S)], the rate of inflation, (8), decreases by @r/p. Therefore, the change in the nominal interest rate at the time of the policy change is

ArO = 4 -1 r

44 + 6) 1 P . W)

The nominal interest rate may rise or fall initially depending on whether the sign of the expression in the brackets is positive or negative. If + is sufficiently small, due to a small o, making the adjustment relatively slow, the value of (20) will be negative, giving an initial decline in the interest rate. Figure 2 is drawn with the assumption that the nominal interest rate rises initially when the government implements its disinflationary policy. Figure 3, on the other hand, is drawn with the assumption that the interest rate falls initially. In this case, the fall in the inflation rate, which is induced by the appreciation of the exchange rate along with higher real interest rate, exceeds the increase in the real interest rate. Conse- quently, the nominal interest rate falls.

Whether the nominal interest rate rises or falls initially, it will decline in the long run below its level prior to the policy change by the decrease in the rate of inflation, I. That is, before the policy

‘The actors in the financial markets have perfect foresight, and therefore, the real rate of interest in (2’) is r - $ rather than r - a. That is, both borrowers and lenders perfectly anticipate prices even though those setting prices in the goods market adaptively form their expectations.

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r

I

t=o

Figure 3.

time

change, the interest rate is p + I’; in the long run, the interest rate adjusts to the level p.’

Now consider the necessary behavior of the money stock to produce the desired slowdown in the economy. Remembering that

‘Even if the initial change in the interest rate as expressed by (20) is negative, this decline is less than r; therefore, the interest rate will decline further during the adjustment.

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p does not jump when the policy changes and taking the first difference of (1) gives the required initial change in the money stock:

Am0 = -XAr,, + qAyO. (21)

Substituting (13) and (20) for At-,, and by, gives

Am0 = 4 1 I q !!r -- 7r(u~ + 6) IT p . (22)

If the nominal interest rate increases initially as shown in Figure 2, the money stock, unambiguously, is contracted initially. This case is, therefore, similar to the optimal policy for a closed economy model without any forward-looking financial variables.”

On the other hand, if the parameters are such that the interest rate falls initially, the optimal policy may require initially either an increase or decrease in the money supply depending on whether the first or second term in (21) is larger in absolute value. Figure 3 is drawn with the assumptions that the interest rate falls initially and that the value of A is sufficiently large where the first term in (21) is larger than the second. Consequently, the money supply is expanded initially. The reason a contractionary policy can begin with an increase in the money supply is that the money stock is pro- jected to be less in the future than previously anticipated. The expectation of a lower money stock in the future causes the exchange rate to appreciate and lowers income.” Also, the consequent decline in inflation raises the real interest rate. Although the price adjustment equation is backward-looking, the model is forward-looking through the financial variables. As a consequence, the optimal path may take on some of the characteristics of the optimal path in Sec- tion 2, where the price-adjustment equation contains a forward- looking variable and requires an initial increase in the money stock.

In either case, the rate of monetary growth exceeds the rate of inflation after the policy change. The derivative of (1) gives the required rate of change of the money stock after the policy change:

GL=---x++~+qtj. (23)

“For instance, in a model without any financial variables consisting of Equations (4”‘) and (5), and money demand proportional to nominal income, m = p + y. the money stock would have to decrease in order to decrease income.

“Wilson (1979) examines a simpler case where the expectation of a fihre change in the money stock affects the Dornbusch model.

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Since + = X = i + p, i zz -&i, and fi = -+ti, Equation (23) can be written

ril = lj + A#$ + xc&i + Tjzj . (24)

After the change in policy, the rate of monetary growth exceeds the rate of inflation by the last three terms in (24) since fi, i, and zj are positive. Substituting gives

GZ = [

(1 + A+)(1 - 4/p) + pT(tz3+ 6) + E 1 Ie-+t . (25)

With the rate of monetary growth exceeding the rate of inflation, real money balances are expanding during the adjustment. In the long run, the public will want to hold larger real money balances with a lower rate of inflation. With full adjustment, the log of real money balances, m - p, increases by AI’ since the inflation rate and the interest rate both decrease by I.

In summary, the optimum policy when inflation has momentum will depend on the parameter values and may require an initial increase or decrease in the money stock followed by monetary growth that allows for growth in real money balances. In addition, because expectations do not depend on a forward-looking variable, this optimal solution is time consistent in the sense of Kydland and Pres- cott (1977). That is, there is no temptation for the policymaker to deviate from this optimal trajectory even if he reoptimizes at a later date.

4. Concluding Remarks This paper shows that the various proposed modifications of

Dornbusch’s price-adjustment equation can produce very different optimal solutions to the problem of stopping inflation. When the price-adjustment equation is augmented with a forward-looking variable, the optimal policy requires an initial increase in the money supply equal to the interest semi-elasticity of the demand for money times the inflation rate. This initial change is then followed by no further monetary growth. With this policy, the inflation is stopped instantaneously and painlessly without any effect on the real variables in the system.

When inflation has momentum from expectations that are

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formed adaptively from past inflation, the economy must suffer a recession in order to reduce the inflation. The optimum policy using a quadratic loss function depends on the parameters of the model and how quickly the authorities want to decrease the inflation rate as determined by their loss function. An appreciation of the exchange rate and a higher real interest rate causes the recession. However, the optimal policy may result in either an initial increase or decrease in the nominal interest rate depending on whether the increase in the real interest rate is greater than the initial decrease in the inflation rate. The money supply is decreased initially if the nominal interest rate increases initially. On the other hand, if the optimal policy results in a decrease in the nominal interest rate, the money supply may need to be increased or decreased initially depending on the relative magnitude of the interest semi-elasticity of the demand for money. A contractionary policy can be initiated with an increase in the money stock because the expected future level of the money stock is lower than previously anticipated. Al- though the price-adjustment equation is backward-looking, the model is forward-looking through the financial variables and therefore reacts to changes in the anticipated path of the money stock. As a consequence, the optimal solution with sticky inflation may have some of the characteristics of the model with the forward-looking variable in the price-adjustment equation in that the money supply may be increased initially.

Received: October 1987 Final version: June 1988

References Buiter, W. H., and M.H. Miller. “Monetary Policy and Interna-

tional Competitiveness: The Problems of Adjustment.” Oxford Economic Papers 33 (July 1981): 143-75.

-. “Real Exchange Rate Overshooting and the Output Cost of Bringing Down Inflation.” European Economic Review 18 (May/ June 1982): 85-123.

Dornbusch, R. “Expectations and Exchange Rate Dynamics.” Jour- nal of Political Economy 84 (December 1976): 1161-76.

D&ill, E.J. “Optimal Money and Exchange Rate Policies.” Greek Economic Review 4 (December 1982): 261-83.

Frankel, J.A. “On the Mark: A Theory of Floating Exchange Rates

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Based on Real Interest Differentials.” American Economic Re- view 69 (September 1979): 610-22.

Gordon, R. J. “Output Fluctuations and Gradual Price Adjustment.” Journal of Economic Literature 19 (June 1981): 493-530.

-. “Price Inertia and Policy Ineffectiveness in the United States, 1890-1980.” JournaZ of Political Economy 90 (December 1982): 1087-117.

Kydland, F.E., and E.C. Prescott. “Rules Rather Than Discretion: The Inconsistency of Optimal Plans.” Journal of Political Econ- omy 85 (June 1977): 473-91.

Miller, M.H. “Monetary Stabilization Policy in an Open Economy.” Scottish Journal of Political Economy 3 (November 1985): 220- 33.

Miller, M. H., and M. Salmon. “Dynamic Games and the Time In- consistency of Optimal Plans in Open Economies.” Economic Journal 95 (Supplement 1984): 124-37.

Mussa, M. “A Model of Exchange Rate Dynamics.” Journal of Po- litical Economy 96 (February 1982): 74-104.

Obstfeld, M., and K. Rogoff. “Exchange Rate Dynamics With Slug- gish Prices Under Alternative Price-Adjustment Rules.” Znter- national Economic Review 25 (February 1984): 159-74.

Tobin, J. “Diagnosing Inflation: A Taxonomy.” In Development in an Znflationary World, edited by M. J. Flanders and A. Razin, 19-30. New York: Academic, 1981.

Wilson, C.A. “Anticipated Shocks and Exchange Rate Dynamics.” Journal of Political Economy 87 (June 1979): 639-47.

Appendix Variables and definitions:

m = logarithm of the money supply. p = logarithm of the price level. y = logarithm of income. g = logarithm of full employment income. x = logarithm of the nominal exchange rate. z = logarithm of the real exchange rate. p = full-equilibrium solution for the price level if prices are fully

flexible. r = nominal interest rate. p = foreign nominal and real interest rate.

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a = anticipated or expected rate of inflation that is adaptively determined.

L = government’s loss function. I = integrand (or intermediate function) for the government’s loss

function. JT = initial rate of inflation.

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stopping inflation in the dornbusch model: optimal monetary policies with alternative...

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