Balance of payments crises and fiscal adjustment measures

MICHAEL FRENKEL University of Mainz

Mainz, Federal Republic of Germany

MARTIN KLEIN University of Bonn

Bonn, Federal Republic of Germany

Balance of Payments Crises and Fiscal Adjustment Measures*

A model with optimizing firms and consumers is used to explore the effects of unannounced and preannounced fiscal adjustment policies that are intended to prevent an impending balance of payments crisis. It is shown that preannouncement unambiguously raises the required fiscal adjustment effort so that, from the government's point of view, "cold turkey" is the preferable policy. The effect of preannouncement on the private sector's adjustment cost is ambiguous since preannouncement induces an externality which may either benefit or harm the private sector, depending on the nature of the measure that is preannounced.

1. Introduction Following the seminal cont r ibu t ion of K r u g m a n (1979) various

authors analyzed the evolut ion of a ba lance of p a y m e n t s crisis which culminates in a specula t ive at tack on the in ternat ional rese rves of the central bank. (See, for example , Calvo 1987; Grilli 1986; and Obstfeld 1984, 1986.) At the core of all these analyses is the clash be tween an over ly high fiscal deficit f inanced by m o n e y crea t ion and a fixed exchange par i ty vis-tt-vis the res t of the world. As o~c i a l international r e se rves are not unl imi ted , such situations cannot con- t inue indefinitely. This basic scenario is also the point of d e p a r t u r e for our contr ibut ion. H o w e v e r , we devia te f rom the res t of the lit- e ra ture by cons ider ing ano the r opt ion for end ing such an unsustainable situation: W e assume that the g o v e r n m e n t takes adjust- men t measures by cut t ing the fiscal deficit. W e then focus on one key quest ion: G iven that the g o v e r n m e n t ' s main objec t ive is to e n d the emerg ing ba lance of p a y m e n t s crisis and p r e v e n t a specula t ive attack, how should the g o v e r n m e n t ' s a d j u s t m e n t policies be imple -

*A prior version of this article was presented at the 1988 Konstanz Seminar on Monetary Theory and Policy. Comments by George yon Furstenberg, Patrick Min- ford, and by two anonymous referees are gratefully acknowledged. The usual dis- claimer applies.

Journal of Macroeconomics, Fall 1991, Vol. 13, No. 4, pp. 657-673 Copyright © 1991 by Louisiana State University Press 0164-0704/91/$1.50

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M i c h a e l F r e n k e l a n d M a r t i n K l e i n

mented? Should they be taken immediately or gradually, and ff they can only be taken later, should they be preannounced or taken without preannouncement? We will address these questions by in- vestigating the time paths of key macroeconomic variables under different adjustment scenarios and assessing the adjustment, effort associated with them.

We use a macroeconomic model of a small open economy with optimizing firms and consumers which has a wider scope than the regular model of balance of payments crises. The structure of the model permits the consideration of several fiscal instruments with different effects on income, output, investment, and other real sector variables. We explicitly model the supply side of the economy and assume that there are costs to adjustment of the capital stock so that output and investment do not adjust instantly after fiscal measures have been taken. Realistically, this complicates and ex- acerbates adjustment problems.

The remainder of the article is organized as follows. The model is presented in Section 2. Sections 3, 4, and 5 investigate various aspects of adjustment measures. Section 6 presents the conclusions.

2. The Model We consider a small open economy which produces and con-

sumes a single composite traded good. In keeping with the rest of the literature on balance of payments crises we assume throughout that purchasing power parity holds and that both the rate of inflation and the interest rate in the rest of the world are exogenous. The model contains three assets--domest ic money, foreign bonds, and domestic real capital--and three types of domestic agen ts - - firms, consumers, and the government. Firms and consumers both have perfect foresight and maximize their respective objective func- tions. Firms choose investment and employment, consumers choose consumption, money holdings, and the stock of private net foreign assets. The government sets the nominal exchange rate and controls different fiscal instruments.

I n v e s t m e n t

We use a standard model of the neoclassical theory of investment. The representative firm maximizes the discounted present value of present and future after-tax dividends:

i" o o

max / [(1 - ~k) (q - w L ) - i] e 4'-x~ d x , (1) 2,

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Balance o f Payments Crises and Fiscal Adjus tment Measures

subject to the following constraints:

k = i - S k ;

iml. -< i --< imax ; (3)

q = q (k ,L ) ; qk, qL > 0 ; qkk, qt~,q/cL < 0 . (4)

All variables in the model are in real terms. Dots over variables represent t ime derivatives and t denotes time; q, k, L, and i, are output, capital stock, employment , and gross investment , respectively; w is the real wage rate and "rk denotes the profit tax rate. The discount rate, r, is assumed to be identical to the after-tax real rate of interest in the rest of the world. The first constraint, Equa- tion (2), defines net inves tment as the difference of gross investment and depreciation, which is assumed to occur at a constant rate, 8. The second constraint, Equat ion (3), implicitly represents installation costs for capital equ ipmen t through the lower (imp.) and upper (/max) bounds placed on gross investment , x We assume that imp. and ima x a r e both finite. The solution to this optimization prob- lem is

F im.~, for k(t) < k* ( t+h) , i(t) = k(t) + 8k(t) = I ~k(t), for k(t) = k* (t+h) , (5)

Limin, for k(t) > k* (t+h) ,

where 0 -< h -< hm,~ < ~. The variable k* is the optimal level of the capital stock which would be chosen without constraints on investment and hm~ is the maximum lead by which anticipated future changes in the optimal capital stock affect current investment . In- tuitively, Equat ion (5) means that ff the actual capital stock diverges from its actual or anticipated optimal level it converges there as fast as possible. With L denot ing full employment , the optimal capital stock, k*, and the real wage, w, are implicitly de te rmined by the first-order conditions

r + 8 q k ( k * , L ) - - - ( 6 )

I - ~k

tThis is modeled after Arrow (1968). An alternative way to introduce installation eost would be to postulate an explicit installation cost function as, for instance, in Hayashi (1982). The approach chosen here is analytically easier to manage and sufficient for the purposes of the investigation.

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Michael Frenkel and Martin Klein

and

qL (k*,L) = w . (7)

The Government Budget For the pu rposes of our analysis it is sufficient to wri te the

g o v e r n m e n t ' s p r ima ry deficit as follows:

b = g - "r k (q - w ) , (8)

w h e r e g deno tes the g o v e r n m e n t ' s purchases of goods and services and "rk (q - w) deno tes profi t tax revenue . ~ Subt rac t ing in teres t earnings on official r ese rves (rf) f rom the p r i m a r y deficit we obtain the total fiscal deficit. W e follow the exist ing l i te ra ture on balance of p a y m e n t s crises in assuming that this deficit is f inanced ent i re ly th rough credi t f rom the centra l bank. In a s teady state wi th no growth this implies that the evolut ion of official r e se rves can be wr i t t en as follows:

j ' = ,-f + b, (9)

w h e r e the p roduc t of the inflation ra te (~) and the real m o n e y stock (m) denotes the inflation tax. 3 G o v e r n m e n t r e v e n u e s and expendi - tures have to satisfy an i n t e r t empora l const ra in t that is crucial for our discussion in la ter sections. W e can der ive this const ra in t by solving (9) forward. Excluding Ponzi s chemes we get

t " ¢0

= ~ (b - ~rm) e "-x) dx . f,

Private Consumption and Money Demand The rep resen ta t ive agen t maximizes the following Sidrauski-

type i n t e r t empora l utility function: / . o o

U = | u(c,m) e "'-x) dx , (10) 3,

2For a more comprehensive discussion of fiscal instruments, including government transfers, see Frenkel and Klein (1989).

3If the rate of growth is lower than the real rate of interest and the government does not run Ponzi schemes, permanent budget deficits cannot be financed by is- suing bonds, only by inflation tax. Thus, in the absence of fiscal adjustment, bond finance can at best be used to postpone a speculative attack, never to forestall it completely. See Buiter (1987) for an analysis of this issue.

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Balance o f P a y m e n t s Crises a n d Fiscal A d j u s t m e n t M e a s u r e s

subject on the wea l th const ra in t

(~ = rv + w + s - c - (r + rr) m , (11)

where v = m + z + k is p r iva te ne t weal th and c and z deno t e private consumpt ion and holdings of ne t foreign assets, respectively. Fol lowing Claessens (1988) we use the following pa rame t r i - zation for the ins tantaneous utility function:

1 u(c ,m) = ~ (c~ml-~) 1-R (12)

1 - R

where 0 < a < 1 and R > 0 are constant pa ramete r s . Solving the represen ta t ive consumer ' s opt imizat ion p r o b l e m and consol idat ing the constraints of firms, the g o v e r n m e n t , and consumers yield the following e c o n o m y - w i d e resource constraint :

j c+ ~ = r ( f + z) + q - - i - g - c . (13)

In tegra t ing and solving for consumpt ion yields

c = r [ ( f + c), + (q - i - g) e ~'-x~ dx] . (14)

The r ight -hand side of this equa t ion provides a definit ion of aggre- gate p e r m a n e n t ineome as the income flowing f rom financial and human capital. M o n e y d e m a n d is t hen d e t e r m i n e d as follows: 4

(1 - a ) c m = . (15)

a (r + rr)

The Evo lu t i on o f Ba l anc e o f P a y m e n t s Crisis In o rder to i l lustrate the working of the mode l we give a b r i e f

account of the evolut ion of a ba lance of p a y m e n t s crisis h la Krug- man (1979). F igu re 1 p resen t s the t ime paths of official r ese rves

4This money demand function implies that the partial elasticity of money demand with respect to the nominal interest rate is minus one. However, note that this applies only to variations in the interest rate that are caused by changes in anticipated inflation. Changes in the real interest rate affect permanent income and consumption through (14) and thus the absolute value of the elasticity is smaller than unity.

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and private foreign assets. Before time "0" the fiscal stance is sustainable and the economy is in a steady state. At time "0", the world rate of inflation drops unexpectedly due to, for instance, a new austerity policy pursued in the rest of the world. With purchasing power parity and with a fixed exchange rate the domestic inflation rate then also must drop. The resulting drop in domestic inflation tax revenue increases the fiscal deficit so that official reserves begin to decline, reflecting central bank intervention in the foreign exchange market to support the exchange rate:

j " = r f ' + rr'm' + b0 < 0 ,

where primes denote values during the transition period. At time T official reserves are depleted in a sudden speculative attack and the authorities are forced to abandon the fixed exchange rate. The rate of inflation jumps to a new higher level and money demand drops to a lower level. 5

3. Fiscal Adjustment Policies Now we turn to the investigation the effects of fiscal adjust-

ment measures intended to prevent a balance of payments crisis. Our discussion will be divided into two parts. In Section 4 we assume that the adjustment measures are implemented without prior announcement and without anticipation by the public, and in Sec- tion 5 we then investigate the economic effects of a preannouncement of adjustment policies. We see this as an exercise in positive economics. We do not seek to determine the welfare-maximizing adjustment policy; rather we discuss the policy options from the point of view of a government with a given set of political preferences which inherits an exogenously given set of economic struc- tures from the past. All adjustment policies in our model ultimately amount to cutting the government's primary budget deficit and there are two ways to do this: First, by cutting government consumption; second, by raising profit taxes. Of course these two options do not cover the whole range of policy measures available to governments

5In Figure 1 we assume that the parameter R in the utility function of the representative consumer is equal to unity. We use this assumption to simplify the exposition of the figures throughout the paper. However, note that neither our formal model nor our discussion in the text depends on this assumption. See Claes- sens (1988) for a discussion of this issue.

662

Balance of Payments Crises and Fiscal Adjustment Measures

~ te foreign assets

e s e r v e s

i , i

0 T

Figure 1. Balance of Payments Crisis

total foreign assets of the economy

~--time

in reality. But, the key point here is not the range of available options; it is the fact that the government can accomplish adjustment only by choosing between measures that are in some way non-neutral. In such a situation there is no first-best policy and all adjustment measures will impinge on the real allocation in the economy.

We assume that the government's actions are determined by three objectives. First, the overriding objective is the government's desire to maintain the fixed parity with the rest of the world. This provides the reason for pursuing the adjustment policy. Second, the government wishes to maintain a certain level of consumption for its own purposes. We assume that the current level is at or below the government's optimum so that further cuts in government eon- sumption will imply a disutility for the government. Third, the government wishes to keep profit taxes as low as possible so that increases in the prof i t tax ra te also prov ide d i su t i l i ty for the government. Note that all these objectives under suitable assump- tions could be given a public choice rationale but in order to keep the model as simple as possible we prefer to treat them as state- ments of facts. Summing up we can say that adjustment policy in

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Michael Frenkel and Mart in Klein

our setup can be characterized as a choice between "a rock and a hard place," that is, between two alternatives that are both un- pleasant for the government--and possibly for the consumers as well.

4. Unannounced Adjustment Policies

Cuts in Governmen t Consumpt ion A permanent cut in government purchases of goods and ser-

vices reduces the fiscal deficit and increases both private permanent income and consumption. Assuming that the new level of government consumption is gl, private consumption after the cut is at the level

c , = r ( f + z ) o + q - ~ k - g , = c o + ( g o - g , ) > c o , (16)

where

Co = r ( f + Z)o + q - 8k - go (17)

de.notes the level of private consumption before the cut. Note that the stock of total foreign assets remains constant at the level ( f + Z)o but its composition changes because private agents increase their money balances by reducing their holdings of foreign assets. As Figure 2a illustrates, this results in a sharp inflow of official reserves. At the same time, the loss of reserves is halted and the overall balance of payments swings into equilibrium. The current account remains in equilibrium throughout. For each unit of a cut in government consumption the budget improves by more than one unit. The reason is that the increases in official reserves and money holdings jointly contribute to a further improvement in the fiscal stance by raising interest earnings and the revenue from seigniorage.

Increases in the Profit Tax Rate It is evident that increases in the profit tax rate are not the

only viable adjustment policy because in the long run the economy faces a Laffer curve. Profit tax revenue may either rise or fall after a rate increase because the revenue-enhancing effect of the higher rate is offset by the decline in the capital stock. If the economy is on the downward-sloping part of the Laffer curve, a tax cut is a feasible and effective adjustment policy because short-run and long-

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total foreign assets of the economy

i I l .... ~" ~ time 0 I

Figure 2a. Unannounced Cut in Government Purchases

run effects combine to produce a strong adjustment effect. The fiscal deficit declines, official reserves increase, and since the capital stock increases only gradually due to the constraint on investment, the long-run adjustment effect is even stronger than the impact effect. But note that a government with the postulated set of political preferences would never settle on the downward-sloping branch of the Laffer curve because this is an inefficient allocation where the same revenue can be raised at a lower tax rate.

The interesting case for the investigation of adjustment policies is a situation where profit tax revenue can be raised only by increasing the profit tax rate. The long-run effect of a profit tax increase is a reduction of the capital stock and thus a reduction in permanent income, In anticipation of this, consumption and money demand drop immediately although the actual capital stock declines only gradually toward its new optimal level. The stock of reserves initially declines as private agents substitute foreign assets for money. This is illustrated in Figure 2b by a discrete drop in official reserves. Note that ff reserves are below a critical level, the profit tax increase would immediately trigger a speculative attack. After the initial drop in reserves and assuming that the stock of reserves

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J total foreign assets of the economy

official reserves

I I ~ time 0 I

Figure 2b. Unannounced Increase of the Profit Tax Rate

is high enough to prevent an immediate balance of payments crisis, the overall balance of payments swings into surplus because of higher profit tax revenues. This effect is somewhat attenuated by the fact that lower private money holdings and lower official reserves cause a decline in the inflation tax and interest earnings, respectively. Thus the increase in the profit tax rate needed to close the fiscal gap is larger than initially apparent.

The adjustment effect on impact is higher than the long-run adjustment effect because the revenue-enhancing effect of the tax rate increase appears immediately whereas the revenue-diminishing effect of the base shrinkage builds up only gradually. Thus, if the profit tax increase is calibrated in such a way that it leads to fiscal equilibrium on impact it will not be enough to guarantee sustain- ability of the fiscal stance in the long run. Further fiscal adjustment will be necessary. This also points to a particular difficulty in using the profit tax rate as an instrument of adjustment policy: If the reserve loss continues after a profit tax increase, policy makers cannot conclude that further tax increases are necessary. It could also mean that the initial tax increase was too high. For the same reason a trial and error policy is a dangerous strategy. For example, if profit

666


taxes are cut and it turns out later that this was the wrong policy, a reversal of the cut may be impossible if the remaining stock of reserves is too low to sustain the resulting drop in reserves.

5. Preannounced Adjustment Policies A clear-cut implication of our analysis so far is that the re-

quired adjustment effort increases the longer the adjustment measures are delayed. The reason for this is that while adjustment is delayed, official reserves and interest revenue on them continue to decline so that the necessary cut in the primary fiscal deficit is larger than with timely adjustment. The implication of this is that adjustment measures should be taken immediately at the beginning of the unsustainable fiscal stance. Of course, in the real world of pol- itics "immediately" may not always be possible; "as soon as possible" may be more realistic. This raises the question of whether a government that is committed to adjustment but unable to take immediate action could gain by preannouncing the intended adjustment measures. This is the question which we consider in this section. We assume that adjustment is announced at time A after the inception of the unsustainable stance and implemented at time I > A, both before the occurrence of a speculative attack. We assume that the government does not try to "cheat," and all adjustment measures are implemented exactly as they were announced.

Cuts in Government Consumption The announcement of a cut in government consumption leads

to immediate upward jumps in permanent income, consumption and money demand (Figure 3a). From (14) and (16) we get the new level of consumption:

CA = CO + e-"1-A) (g0 -- gA), (18)

where gA is the level of government consumption that is announced at time A for implementation at time I. The elevated levels of consumption and money demand have two consequences. First, the stock of official reserves increases immediately as private agents shift their portfolio composition from foreign assets to domestic money in response to the increase in permanent income. Second, the com- bined effect of the increase in private consumption and the not-yet- implemented cut in government consumption turns the eurrent account into deficit. The deficit in the overall balance of payments

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total foreign assets . of the economy

official reserves

i t i ~-- time 0 A I

Figure 3a. Announced Cut in Government Purchases

continues after the announcement, albeit at a somewhat slower pace than before as interest earnings on official reserves are now higher because of the reserve inflow. At time A the current account and the overall balance of payments move into equilibrium without a further change in the stock of official reserves.

Does the preannouncement of adjustment measures reduce the required adjustment effort for the government? The answer is unambiguously negative: our analysis implies that the cut in government consumption necessary to establish a sustainable fiscal stance is larger if it is preannounced. The reason for this is that a preannounced cut is preceded by a period of "'overspending" by the private sector, reflecting the (anticipated) rise in permanent income. At the time of the implementation of the cut, the level of private money holdings and of official reserves is therefore lower than with an unannounced cut. As a result, inflation tax revenue and interest earnings on foreign assets are lower so that the size of the cut in government consumption has to be higher in order to establish a sustainable fiscal stance. The immediate implication of this result is that a government that tries to minimize its adjustment effort would not preannounce its measures but take them "cold turkey."

668


Our next question is whether the preannouncement of cuts in government consumption increases the welfare level of domestic private agents? The evidence provided by the model in this respect is mixed, depending on whether we focus on the utility level in certain subperiods or on total utility. The utility level after the cut in government purchases of goods and services is lower for preannounced cuts. The reason is that the increase in permanent income with unannounced cuts in government purchases is higher because no decumulation of foreign assets takes place before the implementation of the cut. However, if we consider the period starting with the time of the announcement of the cut, preannouncement increases the private utility level for two reasons. First, after the p r e a n n o u n c e m e n t pr ivate agents can engage in consumpt ion smoothing by anticipating already today some of the increase in income announced for later. Because of the concavity of the utility function, consumption smoothing unambiguously increases utility. Second, as the preannouncement forces the government to cut consumption by more than otherwise, government absorption of domestic output is lower and private consumption is correspondingly

J total foreiqn assets of the economy

!

official reserves

! I ! ~__time

0 A I

Figure 3b. Announced Increase of the Profit Tax Rate

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higher. This is a positive externality for private consumers. 6 In a way, the preannouncement of adjustment measures induces a "re- distribution" of resources between the government and consumers, harming the former but benefiting the latter.

Increases in the Profit Tax Rate The preannouncement of a profit tax increase has two im-

mediate effects on the domestic economy: First, expected permanent income drops; second, the economy enters a prolonged period of disinvestment. The drop in permanent income induces a drop in private consumption and money demand so that official reserves also drop. This leads to lower seigniorage and lower interest earnings for the government so that the deficit in the overall balance of payments continues even higher than before. At the same time, however, the current account moves into surplus as the continuing high level of output is met by reduced private consumption and investment. In Figure 3b this is indicated by the increase of the economy's total foreign assets. When the tax increase is implemented at time I, the overall balance of payments swings into surplus and

'stays there until the capital stock has reached its new equilibrium level. Our analysis highlights the difficulties in interpreting the be- havior of the economy during the adjustment process: After the announcement of the profit tax increase, the current account and official reserves move into opposite directions and thus give conflicting signals about the adjustment.

The analysis implies again that the adjustment effort that is necessary to attain a sustainable fiscal stance is higher if adjustment is preannounced. The reason for this is that private agents are now able to eschew some or most of the revenue windfall that accrues to the government during the disinvestment period after a surprise profit tax increase so that the tax rate has to b e raised by more than otherwise. Given the government's political preferences, this implies again that the government would prefer to go "cold turkey" instead of announcing the tax increase before its implementation.

The adjustment cost imposed on the private sector may either be increased or reduced by preannouncement. In order to see why, consider the following example. If a single agent is asked, "Would you like to receive private information on the government's future profit tax policy?" the answer is always yes. If the same agent is

6A formal proof of this result is provided in the appendix.

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asked, "Should the government publicly preannounce its future profit tax policy?" the answer may be negative. The reason for this seem- ing contradiction is that a single agent acting alone can always increase his utility by anticipating a future profit tax raise. But if all agents simultaneously act in this manner, they create a negative externality for each other by forcing the government to raise the profit tax rate by more than initially intended. If this negative externality is strong enough, it will more than offset the positive effect of the preannouncement. This is particularly likely in situations where the initial level of the profit tax rate is close to the peak of the Laffer curve so that further rate increases yield only small revenue gains. In these situations private agents are bet ter off if the government implements the tax hike without preannouncement, thus permitting a smaller rate increase and ultimately a lower output loss than under a preannouncement.

6. Summary and Conclusions In summing up our analysis we can point to two main results.

First we have shown that the fiscal structure of adjustment policies plays a crucial role in determining the success of adjustment. Dif- ferent fiscal adjustment measures require more or less stringent conditions for their successful implementation. The second main result of the analysis is that the postponement and the preannouncement of adjustment policies unambiguously raise the required fiscal adjustment effort. From the government's point of view "cold turkey" is therefore the preferable policy. Regarding the adjustment cost for the private sector, the effects of the preannouncement of adjustment measures are ambiguous. We have shown that prean- n o u n c e m e n t - - a p a r t from the usual consumption smoothing ef- f e c t s - i n d u c e s an externality which may either benefit or harm the private sector, depending on the nature of the measure that is preannounced.

Received: October 1989 Final version: November 1990

References Arrow, Kenneth. "Optimal Capital Policy with Irreversible Invest-

ment." In Value, Capital, and Growth, edited by James N. Wolfe. Papers in Honor of Sir John Hicks, Edinburgh, 1968 .

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Buiter, Willem H. "Borrowing to Defend the Exchange Rate and the Timing and Magnitude of Speculative Attacks." Journal of International Economics 23 (1987): 221-39.

Calvo, Guillermo A. "Balance of Payments Crises in a Cash-in-Ad- vance Economy." Journal of Money, Credit, and Banking 19, no. 1 (1987): 19-32.

Claessens, Stijn. "Balance-of-Payments Crises in a Perfect Foresight Optimizing Model.'" Journal of International Money and Finance 7 (1988): 363-72.

Frenkel, Michael, and Martin Klein. "Balance of Payments Crises and the Structure of Adjustment Policies." International Mone- tary Fund Working Paper, WP/89/37, 1989.

Grilli, Vittorio U. "Buying and Selling Attacks on Fixed Exchange Rate Systems." Journal of International Economics 20 (1986): 14_3- 56.

Hayashi, Fumio. "Tobin's Marginal q and Average q: A Neoclassical Interpretation." Econometrica 50, no. 1 (1982): 213-24.

Krugman, Paul. "A Model of Balance of Payments Crises." Journal of Money, Credit, and Banking 11, no. 3 (1979): 311-25.

Obstfeld, Maurice. "Balance of Payments Crises and Devaluation." Journal of Money, Credit, and Banking 16, no. 2 (1984): 208- 17.

~ . " R a t i o n a l and Self-Fulfilling Balance of Payments Crises." American Economic Review 76, no. 1 (1986): 72-81.

Sidrauski, Miguel. "Rational Choice and Patterns of Growth in a Monetary Economy." American Economic Review 57 (1967): 534- 44.

Appendix Combining (12) and (15), the instantaneous utility function at

the optimal money demand can be written as a function of consumption alone:

U ( c , m d) ~ ~C 1-R '

where

1 1 - a (1-a)(1-R)

13= 1 - R

is constant as long as the inflation rate remains constant. The con-

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sumption trajectory without preannouncement has two distinct parts. During the subperiod [0, I), consumption is equal to co (compare Equation [17]). During the subperiod [I, oo), consumption is equal to c~ (compare Equation [16]). The level of utility during the overall period [0, oo) is then

®U(c,m) = (f~/r) [(1-e-r')c01-R + e-r'c~-R] . (1A) e-"dt

Private consumption with preannouncement can be written as follows:

cA = co + e-~t(go-gA) = ( 1 - e -~) Co + e -~l (ct + gz - gA),

where we have set A = 0 in order to simplify the notation. Since this level of consumption is maintained throughout the whole in- terval [0, ~), private utility is given by

¢c

fo U(CA,mA)e-adt = [(1--e-r')Co + e-rl(c I -~- - - (f~ l r) ga)] I-R . gl (2A)

Comparing (1A) and (2A) shows that there are two reasons why consumers benefit from the preannouncement of cuts in government consumption. First, the strict concavity of c l-a implies that (2A) exceeds (1A) even if the term gl - gA is zero; this is the effect of consumption smoothing. Second, we have gt - ga > 0 because preannounced government spending cuts must be higher than unannounced ones; this adds to the consumption smoothing effect and further increases private utility under preannouncement.

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Balance of payments crises and fiscal adjustment measures