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Temporary monetary and fiscal policy in an optimizing model of exchange rate determination
MARCEL0 BIANCONI Tufts
Medford,
Uniuerstty
Massachusetts
Temporary Monetary and Fiscal Policy in an Optimizing Model of Exchange Rate Determination* This paper considers a monetary model of a small open economy with perfect foresight. We perform temporary monetary and fiscal policy experiments focusing on the intercoordination between both, as well as on intracoordination within the fiscal authority. Specifically, we show that, in a small open economy, the natural means of attaining a steady state that satisfies the overall economy intertemporal budget constraint involves the endogenous adjustment of one of the fiscal or monetary policy instruments. The dynamics of the cases of rate of monetary growth and level of government expenditures accomodation are investigated in some detail.
1. Introduction A monetary model of a small open economy founded on microeconomic optimization principles for consumers and firms under perfect foresight is presented. Such framework originates in Sidrausky (1967) and has been generalized by Brock and Turnovsky (1981) for a closed economy. Recent small open economy applications include Obstfeld (1981), Hodrick (1982), and Tumovsky (1985, 1987). Here, we shall follow Hodrick (1982) and Tumovsky (1987) and assume purchasing power parity and perfect capital mobility. In this case, permanent unanticipated policy changes have no dynamic effects in the economy, and the results that emerge are longrun comparative statics. Obstfeld (1981) avoids such an outcome by adopting an endogenous rate of time preference, and Tumovsky (1985) drops the perfect capital mobility assumption by imposing costs on holdings of foreign bonds, therefore obtaining some dynamics. We consider a small open economy with purchasing power parity and perfect capital mobility when disturbances are of a temporary nature. In this case, there will be dynamic adjustments in response to endogenous movements in the rate of exchange depre*I phen Amy
thank an anonymous referee for helpful comments. Conversations with Tumovsky, Partha Sen, Case Sprenkle, Jose Machado, Daniel Richards, Schwartz were also helpful. All remaining errors are my own.
1991, Vol. Journal of Macroeconomic s, Winter Copyright 0 1991 by Louisiana State University 01&G0704/91/$150
13, No. Press
1, pp.
97-115
Steand
97
MarceEo Bianconi ciation (rate of inflation) and other endogenous variables. The small open economy shows a key aspect that differs from the closed economy. It must satisfy an intertemporal budget constraint with the rest of the world imposing an additional restriction in the dynamic behavior of the sytem. Our temporary monetary policy experiment is in the spirit of Sargent and Wallace (1981), L iviatan (19&I), and Drazen (1984). In addition, we examine temporary fiscal policies because in our framework they highlight the intercoordination between monetary and fiscal authorities as well as the intracoordination within the fiscal authority. The paper is organized as follows. In Section 2, we describe the model and solve for the short- and long-run equilibrium. In Section 3, we perform the temporary monetary and fiscal policy experiments and analyze the dynamic paths of the endogenous variables. Section 4 presents some concluding remarks.
2. The Small Open Economy Framework
in an Intertemporal
Optimization
The decentralized macroeconomy consists of three sectors: consumers, firms, and government. All consumers and firms are assumed to be identical, infinitely lived, and competitive. The economy is small and it produces a single traded good whose foreign price is determined exogenously in the world economy. The assumptions of free trade, perfect foresight, and perfect capital mobility lead to the case of an exogenously determined domestic real interest rate equal to the world real interest rate. There are three assets in the economy: domestic money, M, is non-traded and held only by domestic residents; a traded bond, B, denominated in foreign currency constitutes the nominal stock of bonds held by households and includes issuances by the domestic government and foreigners; and the domestic government may borrow domestically and abroad by issuing a bond, A, denominated in domestic currency. The real stock of both bonds yields the fixed world real interest rate. The representative households optimal consumption, asset demands, and labor supply are determined by solving the intertemporal problem
(14 98
Temporary
u,>o, u,,
rJ,
u,,
Monetary
and Fiscal Policy
V’>O;
u,,
V”
to (dm/dt)
+ (db/dt)
= (wl + ~)(l - 7) + (r* - q) b -(q+e)m-S-c,
given the initial
(lb)
conditions m(O) = DW’(O)l b(O) =
and the transversality
=
L%IQoW)I ;
[WPoIQoW)I
= bo ;
04
conditions lim p(t)(exp - Pt)m(t) = 0 ; lim p(t)(exp - Pt)b(t) = 0 ;
(14
where c = I = m = f3 = b = w = T = T= S= P= Q = E = p,(t)(exp -
Pt) =
real consumption, real labor, the stock of real money balances, the rate of time preference (assumed constant), the real stock of bonds held by domestic residents, the real wage rate, real profit, the income tax rate, the real lump-sum tax, the domestic price level, the foreign price level (exogenously determined), the nominal exchange rate (domestic currency per unit of foreign currency), the discounted Lagrange multiplier, 99
Marcelo
Bianconi Q = the foreign rate of inflation (exogenously determined), e = the actual (equal expected) rate of exchange depreciation, r* = the foreign nominal interest rate (exogenously determined).
The inequality V’ > 0 implies that we are always below the satiation level of real balances, and U,, < 0 implies that consumption and leisure are Edgeworth complements. The household budget constraint (lb) is expressed in real flow terms, and the tax structure is simplified since it is assumed that interest income is untaxed and the tax rate that applies to labor income and profits is uniform. The nominal exchange rate is allowed to undergo discrete jumps in response to policy announcements, and the initial real stock of money balances is endogenously determined, while the initial real stock of bonds is predetermined. The optimal plans are determined taking S, e, q, IT, w, r*, 8, 7, E, Q, and P as parametrically given and subject to the initial and terminal conditions (lc)-(ld).’ The corporate sector is simplified. We define technology according to the usual neoclassical production function exhibiting positive but diminishing marginal product of labor. Physical capital is fixed and labor is the only variable factor of production. Then, firms choose their optimal labor demand according to
l-y" =f(O - wl, where
f(Z) satisfies f’ >
0,
f” <
0
(2)
.
The domestic government obeys a budget constraint (which is also observed by the private sector) and controls five exogenous instruments, M, A, 7, S, and g, which as we may see below are not independent. We assume that the fiscal authority is institutionally independent of the monetary authority (see, for example, Sargent and Wallace 1981). The Central Bank specifies monetary policy in terms of a constant rate of monetary growth, tl = [(dM/dt)/M], implying that real money balances evolve according to
(An/&) ‘The existence of equilibrium Brock (1974, 1975).
100
= (0 - q - e)m . is proved
in Arrow
and
(3) Kurz
(1970,
ch.
2); and
Temporary
Monetary
and Fiscal Policy
The nominal stock of domestic issued bonds is assumed and the government budget constraint is given by (du/dt)
constant
= g + (r* - q)a - 7(wZ + P) - 8m - S ,
(4)
where a is the real stock of traded bonds issued by the fiscal authority {a(O) = [A,JP(O)] = [A,/Q&(O)]}, and g is real government expenditure. The solvency requirement for the domestic government is lim [exp - (r* - q)t]a(t) = 0 , t--J and the inter-temporal is satisfied with
budget
constraint
(5)
with the rest of the world
m (b, - ao) +
I0
{f[&t)]
- c(t) -
g)
[exp - (r* - q)tldt = 0 .
(6)
Perfect Foresight Equilibrium Given the policy parameters, the perfect foresight equilibrium is the one where planned supply and demands clear all markets at all points in time consistently with the asset accumulation equations. Solving the consumer’s problem (la)-(ld) and the fir-m’s problem (2) yields the following set of equations which define the perfect foresight equilibrium:
VW
UC>I) = -f’(Ul - 4)Lc. V(m) = (r* + e)pC.
(74
(dm/dt)
= (0 - 9 - e)m .
(db/dt)
= (1 - ~)f(l) -
(da/dt)
= g - TV
The costate CL,, the marginal
c
(74 - S + (r* - q)b - Bm .
- S + (r* - q)a - 8m . utility
of consumption,
(74 m-1
remains con101
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Bianconi
stant over time (a result well known in this class of models) and the transversality conditions must hold. Equations (7a)-(7c) define the short-run equilibrium conditions for c, 1, and e taking the stocks of m, b, and a as given. The solution for the short-run endogenous variables is given by
c = 4pcr 4 >
c, co,
CT >o;
(84
1= KP,,4 ,
I, >o,
5 co;
(W
e = 4.b 4 ,
e,
e,
(84
The marginal utility of consumption, kc, is negatively related to the level of consumption and positively related to the supply of labor. For a given stock of real balances, an increase in t~.~leads to an appreciation of the exchange rate. The income tax rate has its usual distortionary effect on consumption and labor, the former positive and the latter negative. The stock of real money balances has a negative effect on the exchange rate, while consumption and labor are unaffected due to the additive separability of preferences. Equations (7d)-(7f) determine the accumulation of assets in the economy. The three differential equations give the optimal dynamic paths of m, b, and a given the short-run solutions (8a)-(8c), the policy instruments, and the fixed marginal utility of consumption. Steady-State Equilibrium The long-run equilibrium of the system (7a)-(7f) is obtained by setting (dm/dt) = (da/dt) = (db/dt) = 0 and considering the transversality conditions yielding
(W
V’h) = Kr* - 4) + elk ,
(94
(1 - ~)f(l,) - c, - S + (r* - q)bo - em, = 0,
(94
g - Tf(ZJ - S + (r* - q)aO - em, = 0 .
(94
The most important b, is predetermined 102
Ul (CS> L) = -f’(&)(l - 4P, ,
feature of the steady-state solutions is that, since by previous accumulation and a, is the initial
Temporary
Monetary
and Fiscal Policy
stock of cs, other adjust
of government debt, Equations (9a)-(9e) determine the values l,, m,, Pi, and one of the policy instruments 8, g, T, or S. In words, the government must leave one of its instruments to endogenously; therefore it loses one degree of freedom. This is an important characteristic of the small open economy model mainly in terms of the policy experiments we shall perform below. Temporary monetary policy experiments in a closed economy as in Sargent and Wallace (1981), Liviatan (1984), and Drazen (1984), show that, if the fiscal authority does not coordinate and leave its instruments fixed, the monetary authority loses control over the rate of growth of money to sustain an equilibrium. In our model of the small open economy, this characteristic is independent of the policy experiment and is derived as an intrinsic mean of attaining the steady state that satisfies the overall economy intertemporal budget constraint. In general, we may have a steady state with monetary accommodation which involves having 8 as endogenously determined. We may also have a steady state with fiscal accommodation with one of the three fiscal instruments g, T, or S given endogenously while the other two remain exogenously determined.’ There are indeed four ways to attain a steady state depending on the specific nature of the accommodative instrument. The long-run comparative statics are summarized in Table I. Some of the signs are ambiguous and depend on the relative magnitudes of the marginal responses of preferences and technology. With monetary and lump-sum tax accommodation the system is block recursive with the real part separated from the nominal part. With government expenditure and income tax rate accommodation the block recursivity is not preserved and the system is fully simultaneous. We should note that another means of sustaining a steady-state equilibrium would involve an initial open market operation by means of an appropriate choice of bO and a,. We rule out that possibility mainly because it would take the economy directly to the steady state independent of the permanent or temporary character of the policies adopted. 3. Temporary Policies and Dynamics The dynamics of asset accumulation are described by (7d)-(7f) with the appropriate substitution from (8a)-(8c) yielding ‘Turnovsky (1987) considers the optimal choice objective function that incorporates the consumer’s choice of fiscal accommodation.
of 8 through optimization
an appropriate problem with
social some
103
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TABLE
I.
Steady-State
A. Monetary
Accommodation
Effects of Changes in
C,
Resulting Change in 18 m, i-4
6
-
-
?
?
-
+
?
0
0
-
7 g
S B. Lumn-Sum Effects of Changes in
Effects of Changes in
Expenditure C, ? -
; 0
?
D. Income Effects of Changes in
?
0
Resulting Change in 1, ma CL8 ? + + ? 0 0
0
C. Government
+
-
Tax Accommodation C8 -
7 g 0
& S 8
Solutions
S, ? ? ?
Accommodation Resulting Change in 18 ms I4 ? + ?
? + -
+ ?
? + ?
Tax Rate Accommodation Resulting C, + ?
L ? 2
Change in m8 Ps + + ? ?
,
?S ?
(dmldt)
= 18 + CT* - 9) - [V’(m)/pJ)m
(db/dt)
= (r* - 9)b + (1 - 7)f [Z(k=, T)] - c(&, T) - S - em,
(lob)
(da/&
= g - Tf [lb,,
(W
T)] - S + (T* - 9)a - em .
(104
Notice that Equations (lob) and (10~) are linearly equivalent. The system may be solved recursively by considering, for example, (lOa) and (10~) and substituting the appropriate solution into (lob). In 104
Temporary
Monetary
and Fiscal Policy
that case, considering the characteristic matrix of the two dimension system consisting of (lOa) and (lOc), one may show that the relevant matrix is triangular with two positive roots and the two dimension system is unstable. Substituting the appropriate solution for (lOa) into (lob), one notes that the solution for (lob) is also unstable, therefore rendering the three dimensional system completely unstable. Any permanent unanticipated change in the policy parameters will take the system directly to a new steady state with an appropriate jump in the nominal exchange rate, E(0). We consider below temporary policies with dynamics, of unstable nature, generated in part by discrepancies between the short and long-run equilibrium values of some key variables. The solution to the pair of differential equations (lOa) and (10~) is given by
a(t) = a, + Al (exp Alt) + Bl(exp A&) ,
Wb)
where a,, = - [V”(m,)ms/ps] > 0; a= = (r* - 9) > 0; azl = -OS < 0; and Al and B, are constants to be determined by the appropriate initial and transversality conditions. Those solutions may be substituted into (lob) to determine the solution for the evolution of the real stock of bonds held by households. Temporary Monetary Policy3 It is assumed that the economy is in a steady-state equilibrium with a given vector of fiscal instruments exogenously set to yield a fixed net of interest deficit, Do, that is, II,, = [g - $(Z) - S]. At time t = to a temporary reduction in the rate of monetary growth from 6,, to &, &, > &, is announced and implemented until some future known time T. At t = T, accumulation of assets ceases and the fixed deficit ZI, must be monetized by an appropriate endogenous choice of 0,. The dynamic process consists of two phases: at time to 5 t < T the rate of monetary growth is set exogenously at a lower value; at time t 1 T the rate of monetary growth adjusts endogenously to make B(T) = 8,, and, consequently, m(T), a(T), and b(T) a steady-state equilibrium. 3Drazen anticipated
and Helpman policy changes
(1986) study a version of this at some known (or unknown)
problem in terms of pure time in the future.
105
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Bianconi
The nominal exchange rate, E(O), responds instantaneously. Therefore, m(O) and a(0) will take appropriate initial jumps, while b(0) = b, is predetermined by past accumulation. The endogenous B(T) = 8,, which delivers the steady-state solution to m, a, and b is obtained from the system (lOa)-(1Oc) yielding what has been called the monetary and bond Laffer curves
[m(T)- WI ~v’[w)ll(f-* - dJ%I- 1 ( 1 = [b(T) - b,] = [a(T) - a,] .
(12)
These relationships yield a pair of nonlinear curves between m and a, and m and b, and a straight line between a and b where the rate of monetary growth is such that m, a, and b are steady-state equilibrium. Notice also that, since a(T) and b(F) are long-run equilibrium variables, they must satisfy the transversality conditions such that b(T) = b, and a(T) = a,,.4 The initial condition b(O) = b0 and the terminal condition (12) determine the constants in (11). The initial jump in m(0) and a(0) may be obtained from (lla), noting that dm(0) = da(O) since the nominal exchange rate affects both variables identically. This initial jump will be given by
bp - &T) + (dm,lW [l - bp - hT)l , which, in general, will be less than zero, implying jump in the nominal exchange rate is given by
kwwei
(134
that the initial
= - [~(~)lm(~)l~~m(O)l~~l .
Wb)
Equation (13a) captures the two effects that the policy impinges on the system. The second term on the right hand side would be the long-run equilibrium if the policy was supposed to be sustained forever, that is, T + ~0. The first term is the sensitivity of the new 4A property of the policy experiments we shall perform icy will have a permanent effect. This is associated with teresis which has received some attention recently. Sen and this specific result in a related nonmonetary model with instrument is the investment tax credit.
106
is that a temporary polthe phenomena of hysTurnovsky (1988) show capital when the policy
Temporary
Monetary
and Fiscal Policy
long-run equilibrium at t = T to the initial contraction on the rate of monetary growth. It involves two compounded terms, one is the effect of the initial monetary contraction on the monetary growth that will monetize the deficit, and the other is the effect of the endogenous adjustment of the monetary growth on the real stock of money at time T. Figure 1 illustrates a possible dynamic path for the endogenous assets given the temporary monetary policy. The economy is initially at the steady-state equilibrium represented by point A with a given positive net of interest deficit DO sustained by the monetary authority. The policy is implemented at time t = to until a known time t = T. At t = to, the nominal exchange rate instantaneously appreciates according to (13b) and both the real stock of money and the real stock of government issued bonds are instantaneously re-
,/
/ /’ --B-e--_-__/ )I____-^---------al,01 C __d----------!lJa(T) 4 / Temporary
Figure 1. Monetary
Policy
107
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valuated to point C. Between t,, < t 5 T, the dynamic path is completely unstable, governed by (ll), and relative to the steady state associated with the lower rate of monetary growth at point B. The lines connecting the points BDA are the Laffer curves described by (12). At t = T, the economy reaches point D, where 8(T) is such that no accumulation of assets occurs. The new steady state will be at point D, with a rate of monetary growth larger than the one that sustained the initial equilibrium at point A. Intuitively, the revaluation of assets implied by the instantaneous appreciation of the nominal exchange rate is equivalent to an instantaneous net capital outflow. Since agents have perfect foresight and know with certainty that the deficit will be monetized at t = T, the exchange rate starts depreciating (the inflation rate increases) with an associated real movement equivalent to a net capital inflow. In other words, the economy accumulates domestic and foreign real debt to replace the loss from money creation. However, this process cannot go forever, otherwise it would violate the overall economy budget constraint. At t = T, the rate of money growth must finance interest payments on a larger than previous stock of real debt, therefore implying B(T) > 80 > 81 .
(14)
This is a version of the Sargent and Wallace (1981) result for a small open economy. The difference is that in the closed economy only the real value of domestic government bonds changes. In the small open economy this need not be the case. The movements in the nominal exchange rate (price level) mimic net capital inflows from abroad providing a current account surplus sufficient to partly offset the foregone inflation tax. This represents in Figure 1 that from point C to D the real stock of government issued bonds may move above or below a(0). At any rate, at t = T, the inflation tax must be increased to meet interest payments on the increased real stock of domestic and foreign debt. The possible dynamic path of Figure 1 involves many assumptions. First, we assume that the economy is in the lower inflation equilibrium of the LafIer curve. This is equivalent to the assumption that the elasticity of real balances with respect to the rate of monetary growth is less than one in magnitude. Second, we assume that the real stock of money jumps in the upward direction. This need not be the case. If 8 and T are such that (13a) equals zero, the real money stock would not jump at t = to and the ex-
Temporary
Monetary
and Fiscal Policy
change rate would start depreciating from point A in Figure 1. Equilibrium would be attained at the other side of the Laffer curve with a much higher rate of exchange depreciation (rate of inflation).5 Another possibility would be that the initial jump in the real money stock overshoots the would-be steady state at point B. In Figure 1, if it jumped to point E, the economy would follow a hyperdeflationary path. Third, it is critical that the fiscal authority does not act. If the fiscal authority responds to the monetary shock by altering D,, and leaving one of the fiscal instruments to adjust endogenously, then the economy would jump instantaneously to point B in Figure 1, that is, the new steady-state equilibrium. It is interesting to observe the effect of the policy on the monetary growth rate at t 2 T. At t = T, the endogenous rate of money growth is given by
fU) = W’[m(T)IId - b-* - 4))
05)
and (15) holds all along the Laffer curves in (12). Friedman (1969) proposes an optimum quantity of money where no other asset could dominate real balances holdings in terms of rate of return. In our case, full liquidity would be provided by OF = -p = -(r* - 9). Comparing with (15), we note that B(T) = {V’[m(T)]/pS} + BF, implying that 8(T) distorts from OF by an amount equal to the opportunity cost of holding money against the consumption foregone. Temporary Fiscal Policy Consider a temporary policy which consists of increasing the net of interest deficit between to 5 t < T and, at t 2 T, of some instrument adjusting endogenously to make m(T), a(T), and b(T) a steady-state equilibrium. In this case, the choice of endogenous instrument before and after the policy switch is of critical importance. Suppose that the monetary authority is sustaining an equilibrium with monetary accommodation. Any temporary fiscal change will imply the steady-state comparative statics results described in Section 2 above. Notice also that if any fiscal instrument is adjusting endogenously, a temporary policy involving any of the other two
that put (or KS)
‘This is equivalent to the Sargent and Wallace (1981) “spectacular” result. Notice if the economy started from the high inflation equilibrium, such outcome would the economy on a hyperinflationary path, and only an open market operation fiscal accommodation) could restore equilibrium. Also, (r* - 9) < (-0” ms/ is assumed across Figure 1.
109
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instruments yields the steady-state comparative statics results. Dynamics will arise if the policy involves fixing temporarily a given fiscal instrument while all the others are given as parameters. For instance, suppose that the economy is described by lump-sum accommodation as in Table 1, Panel B. The fiscal authority announces and implements at t = t,,, an instantaneous reduction in the lumpsum tax from So to S1, So > S,, to last until a known date, t = T, when a choice of any of S, g, or 7 adjusts endogenously to sustain an equilibrium. Let us focus on some of these alternatives. First suppose lump-sum tax itself accommodates. The case is that lump-sum taxes S(T) = S, will be such that [dm(Z+j/dt] = [da(T)/ dt] = [db(T)/dt] = 0. s ince agents have full information, they know with certainty that at t = T the system will behave according to Table 1, Panel B, which implies that at t = to the real stock of money balances will not jump, that is, the nominal exchange rate does not jump. The appropriate S(T) that delivers the steady state solution for m, b, and a is obtained from (lOa)-(lOc), yielding the conditions
[b(T)- &I = [a(T)- 4 and
m(T) = mc@);
(16)
where 8 is exogenously given by the monetary authority independent of the policy implemented by the fiscal authority. The results in this case are obviously consistent with Ricardian Equivalence. At the time the policy is implemented, domestic residents foresee that lower taxes in the present imply higher taxes in the future such that they start to accumulate domestic government issued bonds at to anticipating future lump-sum payments. The current account and real money holdings are unchanged. Consider now the case in which government expenditures, g(T), adjust endogenously at t = T to the initial lump-sum tax contraction. Since agents are not informally constrained, they shall predict the future government expenditure adjustment and shall react according to the steady state described in Table 1, Panel C. At t = T, g(T) must be such that m, a, and b do not change over time. The appropriate g(T) from (lOa)-(1Oc) must satisfy 110
Temporary
Monetary
41 =W’[m(T)1~/~,U(~)- g(T)
[O + (r* -
+ (r* - 9)lW) which
and Fiscal Policy
yields the following
- a(T 01,
(17)
relationships
[WT)lW’)l h(~)= -1 ,
(184
[WT)lWJl
084
h(n > 0 .
The initial jump in m(0) and a(O), given the instantaneous jump in the exchange rate, will be given by
initial
[dm(O)ldSl= [da(O)ldSl= {[am(T)lag,l(dg,lds)> (exp - X,T) + (dmJdS)[l
- (exp -X,T)]
,
(19)
which is, in general, greater than zero.6 In our model, when the policy announcement and implementation of the policy takes place (at t = to), the level of the exchange rate instantaneously depreciates reflecting the speculative movements of rational agents who anticipate the future gains involved in the foreseen government exMoreover, given the presence of the penditures accommodation. nominal asset dominated in domestic currency, all arbitrage opportunities are fulfilled at t = to and, at t = T, when the endogenous adjustment in government expenditures actually takes place, no jumps in the exchange rate level occur.‘I Let us examine Figure 2, which illustrates the possible dynamic paths of this policy. The initial steady state is at point A. The policy announcement and implementation at t = to yields a downward jump in real money balances as well as in the real value of government issued bonds to point C, since the exchange rate “The
jump
in the
nominal
exchange
rate
in this
case
is
[dE(O)/dS] = -[E(O)/
~@)l[dm(o)ldsl < 0. ‘This result differs from Drazen and Helpman (1986) and Helpman and Drazen (1988) because they consider only one real asset besides money such that, in their case, at t = T, the endogenous adjustment in government expenditures leads to an anticipated infinite return on both assets, that is, a price level jump. See also Calvo (1989) on a related discussion.
111
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m
I
a Figure 2. Temporary Fiscal Policy Government Expenditure Accommodation
depreciates instantaneously. The dynamics are relative to the steady state at point B associated with the lower lump-sum tax. The relationships in (lSa)-(18c) are the connected points BAD reflecting the points where government expenditure adjusts endogenously. Between to I t < T the government deficit is larger and households hold fewer bonds since they anticipate the future government expenditure reduction. Also, real balances are too low (the rate of inflation is higher than the monetary growth rate), and the exchange rate appreciates (inflation rate falls). The current account, which is at an instantaneous surplus at t = to, reverses and all along points C and D there is a net capital outflow. At t = T, the endogenous adjustment in g takes place and g(T) is such that (17) is satisfied and we reach the new steady state at point D. At point 112
Temporary
Monetary
and Fiscal Policy
D, the cut in government expenditure must be enough to cover the cut in lump-sum taxes plus the inflation tax losses associated with the deflationary process and the current account deficit associated with the net capital outflows. Notice that if the initial jump in real balances undershoots, to point E say, the economy would follow a hyperinflationary path. Finally, the income tax rate, T(T), could adjust endogenously. In that case, private agents would look at the steady state described in Table 1, Panel D. The dynamic adjustment would be conceptually similar to the case described in Figure 2 since, at t = T, the income tax rate must increase to provide revenues to service the debt.’
4. Concluding Remarks We have considered a class of temporary policies first introduced by Sargent and Wallace (1981). Specifically, we have shown that one of the main concerns of those authors, namely that the monetary authority loses control over its instrument to sustain an equilibrium, is an intrinsic characteristic of the small open economy model. The reason is that the small open economy must satisfy an overall inter-temporal budget constraint which includes domestic and foreign solvency. Temporary monetary contraction with a constant net of interest deficit involves movements in the exchange rate which imply movements in the current account since there is a revaluation of assets. In this case, the current account starts and ends in a balanced position and the economy ends with a rate of exchange depreciation (rate of inflation) higher than the one prior to the policy. In the case of government expenditure adjustment all endogenous variables are simultaneously a&cted. The current account will be initially in surplus, and along the dynamic path the surplus will be more than used up. Depending on the relative size of the initial jump in the exchange rate, the economy may follow a(n) (in)deflationary path, but consumers unambiguously end up with a higher stock of real balances and a lower stock of real bond hold‘Tumovsky and Brock (1980) and Tumovsky (1987) examine the trade-off between the rate of monetary growth and the income tax rate when 8 is optimally chosen. Along the lines of the cases presented here, one could think of other combinations of temporary policies with subsequent adjustments.
113
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Bianconi
ings. The government, on the contrary, ends up with a higher stock of debt. Two natural extensions of our model are the explicit inclusion of capital and the introduction of risk. The former would involve a better description of the corporate sector along the lines of Brock and Tumovsky (1981) while the latter would follow the lines of Bizer and Judd (1989). Received: May 1989 Final version: April 1990
References Arrow, Kenneth J., and Mordecai Kurz. Public Znvestment, The Rate of Return, and Optimal Fiscal Policy. Baltimore, MA: Johns Hopkins University Press, 1970. Bizer, David S., and Kenneth L. Judd. “Taxation and Uncertainty.” American Economic Review Papers and Proceedings 79 (May 1989): 331-36. Brock, William A. “Money and Growth: The Case of Long-run Perfect Foresight.” Znternational Economic Review 15 (1974); 75077. -. “A Simple Perfect Foresight Monetary Model.” Journal of Monetary Economics 1 (1975): 133-50. Brock, William A., and Stephen J. Turnovsky. “The Analysis of Macroeconomic Policies in Perfect Foresight Equilibrium.” Znternational Economic Review 22 (1981): 179-209. Calvo, Guillermo A. “Anticipated Devaluations.” International Economic Review 30 (August 1989): 587-606. Drazen, Allan. “Tight Money and Inflation: Further Results.” Journal of Monetary Economics 15 (1984): 113-20. Drazen, Allan, and Elhanan Helpman. “Inflationary Consequences of Anticipated Macroeconomic Policies.” NBER Working Paper Series No. 2006, August 1986. Friedman, Milton. The Optimum Quantity of Money and Other Essays. Chicago: Aldine, 1969. Helpman, Elhanan, and Allan Drazen. “Future Stabilization Policies and Inflation.” In Finance Constraints, Expectations, and Macroeconomics, edited by M. Kohn, and S. Tsiang. New York: Oxford University Press, 1988. Hodrick, Robert J. “On the Effects of Macroeconomic Policy in a 114
Temporary
Monetary
and Fiscal Policy
Maximizing Model of a Small Open Economy.” Journal of Macroeconomics 4 (1982): 195-213. Liviatan, Nissan. “Tight Money and Inflation.” Journal of Monetary Economics 13 (1984): 5-15. Obstfeld, Maurice. “Macroeconomic Policy, Exchange Rate Dynamics, and Optimal Asset Accumulation.” Journal of Political Economy 89 (1981): 1142-61. Sargent, Thomas J., and Neil Wallace. “Some Unpleasant Monetarist Arithmetic. ” Federal Reserve Bank of Minneapolis Quarterly Review 5 (1981): 1-17. Sen, Partha, and Stephen J. Turnovsky. “Investment Tax Credit in an Open Economy: Permanent Effects of a Temporary Policy.” Department of Economics, University of Washington, Seattle, 1988. Mimeo. Sidrausky, Miguel. “Rational Choice and Patterns of Growth in a Monetary Economy.” American Economic Review 57 (1967): 53444. Turnovsky, Stephen J. “Domestic and Foreign Disturbances in an Optimizing Model of Exchange Rate Determination.” JournaZ of International Money and Finance 1 (1985): 151-71. -. “Optimal Monetary Growth with Accommodating Fiscal Policy in a Small Open Economy.” Journal of Znternational Money and Finance 6 (1987): 179-93. Turnovsky, Stephen J., and William A. Brock. “Time Consistency and Optimal Government Policies in Perfect Foresight Equilibrium.” Journal of Public Economics 13 (1980): 182-212.
115
Medford,
Uniuerstty
Massachusetts
Temporary Monetary and Fiscal Policy in an Optimizing Model of Exchange Rate Determination* This paper considers a monetary model of a small open economy with perfect foresight. We perform temporary monetary and fiscal policy experiments focusing on the intercoordination between both, as well as on intracoordination within the fiscal authority. Specifically, we show that, in a small open economy, the natural means of attaining a steady state that satisfies the overall economy intertemporal budget constraint involves the endogenous adjustment of one of the fiscal or monetary policy instruments. The dynamics of the cases of rate of monetary growth and level of government expenditures accomodation are investigated in some detail.
1. Introduction A monetary model of a small open economy founded on microeconomic optimization principles for consumers and firms under perfect foresight is presented. Such framework originates in Sidrausky (1967) and has been generalized by Brock and Turnovsky (1981) for a closed economy. Recent small open economy applications include Obstfeld (1981), Hodrick (1982), and Tumovsky (1985, 1987). Here, we shall follow Hodrick (1982) and Tumovsky (1987) and assume purchasing power parity and perfect capital mobility. In this case, permanent unanticipated policy changes have no dynamic effects in the economy, and the results that emerge are longrun comparative statics. Obstfeld (1981) avoids such an outcome by adopting an endogenous rate of time preference, and Tumovsky (1985) drops the perfect capital mobility assumption by imposing costs on holdings of foreign bonds, therefore obtaining some dynamics. We consider a small open economy with purchasing power parity and perfect capital mobility when disturbances are of a temporary nature. In this case, there will be dynamic adjustments in response to endogenous movements in the rate of exchange depre*I phen Amy
thank an anonymous referee for helpful comments. Conversations with Tumovsky, Partha Sen, Case Sprenkle, Jose Machado, Daniel Richards, Schwartz were also helpful. All remaining errors are my own.
1991, Vol. Journal of Macroeconomic s, Winter Copyright 0 1991 by Louisiana State University 01&G0704/91/$150
13, No. Press
1, pp.
97-115
Steand
97
MarceEo Bianconi ciation (rate of inflation) and other endogenous variables. The small open economy shows a key aspect that differs from the closed economy. It must satisfy an intertemporal budget constraint with the rest of the world imposing an additional restriction in the dynamic behavior of the sytem. Our temporary monetary policy experiment is in the spirit of Sargent and Wallace (1981), L iviatan (19&I), and Drazen (1984). In addition, we examine temporary fiscal policies because in our framework they highlight the intercoordination between monetary and fiscal authorities as well as the intracoordination within the fiscal authority. The paper is organized as follows. In Section 2, we describe the model and solve for the short- and long-run equilibrium. In Section 3, we perform the temporary monetary and fiscal policy experiments and analyze the dynamic paths of the endogenous variables. Section 4 presents some concluding remarks.
2. The Small Open Economy Framework
in an Intertemporal
Optimization
The decentralized macroeconomy consists of three sectors: consumers, firms, and government. All consumers and firms are assumed to be identical, infinitely lived, and competitive. The economy is small and it produces a single traded good whose foreign price is determined exogenously in the world economy. The assumptions of free trade, perfect foresight, and perfect capital mobility lead to the case of an exogenously determined domestic real interest rate equal to the world real interest rate. There are three assets in the economy: domestic money, M, is non-traded and held only by domestic residents; a traded bond, B, denominated in foreign currency constitutes the nominal stock of bonds held by households and includes issuances by the domestic government and foreigners; and the domestic government may borrow domestically and abroad by issuing a bond, A, denominated in domestic currency. The real stock of both bonds yields the fixed world real interest rate. The representative households optimal consumption, asset demands, and labor supply are determined by solving the intertemporal problem
(14 98
Temporary
u,>o, u,,
rJ,
u,,
Monetary
and Fiscal Policy
V’>O;
u,,
V”
to (dm/dt)
+ (db/dt)
= (wl + ~)(l - 7) + (r* - q) b -(q+e)m-S-c,
given the initial
(lb)
conditions m(O) = DW’(O)l b(O) =
and the transversality
=
L%IQoW)I ;
[WPoIQoW)I
= bo ;
04
conditions lim p(t)(exp - Pt)m(t) = 0 ; lim p(t)(exp - Pt)b(t) = 0 ;
(14
where c = I = m = f3 = b = w = T = T= S= P= Q = E = p,(t)(exp -
Pt) =
real consumption, real labor, the stock of real money balances, the rate of time preference (assumed constant), the real stock of bonds held by domestic residents, the real wage rate, real profit, the income tax rate, the real lump-sum tax, the domestic price level, the foreign price level (exogenously determined), the nominal exchange rate (domestic currency per unit of foreign currency), the discounted Lagrange multiplier, 99
Marcelo
Bianconi Q = the foreign rate of inflation (exogenously determined), e = the actual (equal expected) rate of exchange depreciation, r* = the foreign nominal interest rate (exogenously determined).
The inequality V’ > 0 implies that we are always below the satiation level of real balances, and U,, < 0 implies that consumption and leisure are Edgeworth complements. The household budget constraint (lb) is expressed in real flow terms, and the tax structure is simplified since it is assumed that interest income is untaxed and the tax rate that applies to labor income and profits is uniform. The nominal exchange rate is allowed to undergo discrete jumps in response to policy announcements, and the initial real stock of money balances is endogenously determined, while the initial real stock of bonds is predetermined. The optimal plans are determined taking S, e, q, IT, w, r*, 8, 7, E, Q, and P as parametrically given and subject to the initial and terminal conditions (lc)-(ld).’ The corporate sector is simplified. We define technology according to the usual neoclassical production function exhibiting positive but diminishing marginal product of labor. Physical capital is fixed and labor is the only variable factor of production. Then, firms choose their optimal labor demand according to
l-y" =f(O - wl, where
f(Z) satisfies f’ >
0,
f” <
0
(2)
.
The domestic government obeys a budget constraint (which is also observed by the private sector) and controls five exogenous instruments, M, A, 7, S, and g, which as we may see below are not independent. We assume that the fiscal authority is institutionally independent of the monetary authority (see, for example, Sargent and Wallace 1981). The Central Bank specifies monetary policy in terms of a constant rate of monetary growth, tl = [(dM/dt)/M], implying that real money balances evolve according to
(An/&) ‘The existence of equilibrium Brock (1974, 1975).
100
= (0 - q - e)m . is proved
in Arrow
and
(3) Kurz
(1970,
ch.
2); and
Temporary
Monetary
and Fiscal Policy
The nominal stock of domestic issued bonds is assumed and the government budget constraint is given by (du/dt)
constant
= g + (r* - q)a - 7(wZ + P) - 8m - S ,
(4)
where a is the real stock of traded bonds issued by the fiscal authority {a(O) = [A,JP(O)] = [A,/Q&(O)]}, and g is real government expenditure. The solvency requirement for the domestic government is lim [exp - (r* - q)t]a(t) = 0 , t--J and the inter-temporal is satisfied with
budget
constraint
(5)
with the rest of the world
m (b, - ao) +
I0
{f[&t)]
- c(t) -
g)
[exp - (r* - q)tldt = 0 .
(6)
Perfect Foresight Equilibrium Given the policy parameters, the perfect foresight equilibrium is the one where planned supply and demands clear all markets at all points in time consistently with the asset accumulation equations. Solving the consumer’s problem (la)-(ld) and the fir-m’s problem (2) yields the following set of equations which define the perfect foresight equilibrium:
VW
UC>I) = -f’(Ul - 4)Lc. V(m) = (r* + e)pC.
(74
(dm/dt)
= (0 - 9 - e)m .
(db/dt)
= (1 - ~)f(l) -
(da/dt)
= g - TV
The costate CL,, the marginal
c
(74 - S + (r* - q)b - Bm .
- S + (r* - q)a - 8m . utility
of consumption,
(74 m-1
remains con101
Marcel0
Bianconi
stant over time (a result well known in this class of models) and the transversality conditions must hold. Equations (7a)-(7c) define the short-run equilibrium conditions for c, 1, and e taking the stocks of m, b, and a as given. The solution for the short-run endogenous variables is given by
c = 4pcr 4 >
c, co,
CT >o;
(84
1= KP,,4 ,
I, >o,
5 co;
(W
e = 4.b 4 ,
e,
e,
(84
The marginal utility of consumption, kc, is negatively related to the level of consumption and positively related to the supply of labor. For a given stock of real balances, an increase in t~.~leads to an appreciation of the exchange rate. The income tax rate has its usual distortionary effect on consumption and labor, the former positive and the latter negative. The stock of real money balances has a negative effect on the exchange rate, while consumption and labor are unaffected due to the additive separability of preferences. Equations (7d)-(7f) determine the accumulation of assets in the economy. The three differential equations give the optimal dynamic paths of m, b, and a given the short-run solutions (8a)-(8c), the policy instruments, and the fixed marginal utility of consumption. Steady-State Equilibrium The long-run equilibrium of the system (7a)-(7f) is obtained by setting (dm/dt) = (da/dt) = (db/dt) = 0 and considering the transversality conditions yielding
(W
V’h) = Kr* - 4) + elk ,
(94
(1 - ~)f(l,) - c, - S + (r* - q)bo - em, = 0,
(94
g - Tf(ZJ - S + (r* - q)aO - em, = 0 .
(94
The most important b, is predetermined 102
Ul (CS> L) = -f’(&)(l - 4P, ,
feature of the steady-state solutions is that, since by previous accumulation and a, is the initial
Temporary
Monetary
and Fiscal Policy
stock of cs, other adjust
of government debt, Equations (9a)-(9e) determine the values l,, m,, Pi, and one of the policy instruments 8, g, T, or S. In words, the government must leave one of its instruments to endogenously; therefore it loses one degree of freedom. This is an important characteristic of the small open economy model mainly in terms of the policy experiments we shall perform below. Temporary monetary policy experiments in a closed economy as in Sargent and Wallace (1981), Liviatan (1984), and Drazen (1984), show that, if the fiscal authority does not coordinate and leave its instruments fixed, the monetary authority loses control over the rate of growth of money to sustain an equilibrium. In our model of the small open economy, this characteristic is independent of the policy experiment and is derived as an intrinsic mean of attaining the steady state that satisfies the overall economy intertemporal budget constraint. In general, we may have a steady state with monetary accommodation which involves having 8 as endogenously determined. We may also have a steady state with fiscal accommodation with one of the three fiscal instruments g, T, or S given endogenously while the other two remain exogenously determined.’ There are indeed four ways to attain a steady state depending on the specific nature of the accommodative instrument. The long-run comparative statics are summarized in Table I. Some of the signs are ambiguous and depend on the relative magnitudes of the marginal responses of preferences and technology. With monetary and lump-sum tax accommodation the system is block recursive with the real part separated from the nominal part. With government expenditure and income tax rate accommodation the block recursivity is not preserved and the system is fully simultaneous. We should note that another means of sustaining a steady-state equilibrium would involve an initial open market operation by means of an appropriate choice of bO and a,. We rule out that possibility mainly because it would take the economy directly to the steady state independent of the permanent or temporary character of the policies adopted. 3. Temporary Policies and Dynamics The dynamics of asset accumulation are described by (7d)-(7f) with the appropriate substitution from (8a)-(8c) yielding ‘Turnovsky (1987) considers the optimal choice objective function that incorporates the consumer’s choice of fiscal accommodation.
of 8 through optimization
an appropriate problem with
social some
103
Marcel0
Bianconi
TABLE
I.
Steady-State
A. Monetary
Accommodation
Effects of Changes in
C,
Resulting Change in 18 m, i-4
6
-
-
?
?
-
+
?
0
0
-
7 g
S B. Lumn-Sum Effects of Changes in
Effects of Changes in
Expenditure C, ? -
; 0
?
D. Income Effects of Changes in
?
0
Resulting Change in 1, ma CL8 ? + + ? 0 0
0
C. Government
+
-
Tax Accommodation C8 -
7 g 0
& S 8
Solutions
S, ? ? ?
Accommodation Resulting Change in 18 ms I4 ? + ?
? + -
+ ?
? + ?
Tax Rate Accommodation Resulting C, + ?
L ? 2
Change in m8 Ps + + ? ?
,
?S ?
(dmldt)
= 18 + CT* - 9) - [V’(m)/pJ)m
(db/dt)
= (r* - 9)b + (1 - 7)f [Z(k=, T)] - c(&, T) - S - em,
(lob)
(da/&
= g - Tf [lb,,
(W
T)] - S + (T* - 9)a - em .
(104
Notice that Equations (lob) and (10~) are linearly equivalent. The system may be solved recursively by considering, for example, (lOa) and (10~) and substituting the appropriate solution into (lob). In 104
Temporary
Monetary
and Fiscal Policy
that case, considering the characteristic matrix of the two dimension system consisting of (lOa) and (lOc), one may show that the relevant matrix is triangular with two positive roots and the two dimension system is unstable. Substituting the appropriate solution for (lOa) into (lob), one notes that the solution for (lob) is also unstable, therefore rendering the three dimensional system completely unstable. Any permanent unanticipated change in the policy parameters will take the system directly to a new steady state with an appropriate jump in the nominal exchange rate, E(0). We consider below temporary policies with dynamics, of unstable nature, generated in part by discrepancies between the short and long-run equilibrium values of some key variables. The solution to the pair of differential equations (lOa) and (10~) is given by
a(t) = a, + Al (exp Alt) + Bl(exp A&) ,
Wb)
where a,, = - [V”(m,)ms/ps] > 0; a= = (r* - 9) > 0; azl = -OS < 0; and Al and B, are constants to be determined by the appropriate initial and transversality conditions. Those solutions may be substituted into (lob) to determine the solution for the evolution of the real stock of bonds held by households. Temporary Monetary Policy3 It is assumed that the economy is in a steady-state equilibrium with a given vector of fiscal instruments exogenously set to yield a fixed net of interest deficit, Do, that is, II,, = [g - $(Z) - S]. At time t = to a temporary reduction in the rate of monetary growth from 6,, to &, &, > &, is announced and implemented until some future known time T. At t = T, accumulation of assets ceases and the fixed deficit ZI, must be monetized by an appropriate endogenous choice of 0,. The dynamic process consists of two phases: at time to 5 t < T the rate of monetary growth is set exogenously at a lower value; at time t 1 T the rate of monetary growth adjusts endogenously to make B(T) = 8,, and, consequently, m(T), a(T), and b(T) a steady-state equilibrium. 3Drazen anticipated
and Helpman policy changes
(1986) study a version of this at some known (or unknown)
problem in terms of pure time in the future.
105
Marcel0
Bianconi
The nominal exchange rate, E(O), responds instantaneously. Therefore, m(O) and a(0) will take appropriate initial jumps, while b(0) = b, is predetermined by past accumulation. The endogenous B(T) = 8,, which delivers the steady-state solution to m, a, and b is obtained from the system (lOa)-(1Oc) yielding what has been called the monetary and bond Laffer curves
[m(T)- WI ~v’[w)ll(f-* - dJ%I- 1 ( 1 = [b(T) - b,] = [a(T) - a,] .
(12)
These relationships yield a pair of nonlinear curves between m and a, and m and b, and a straight line between a and b where the rate of monetary growth is such that m, a, and b are steady-state equilibrium. Notice also that, since a(T) and b(F) are long-run equilibrium variables, they must satisfy the transversality conditions such that b(T) = b, and a(T) = a,,.4 The initial condition b(O) = b0 and the terminal condition (12) determine the constants in (11). The initial jump in m(0) and a(0) may be obtained from (lla), noting that dm(0) = da(O) since the nominal exchange rate affects both variables identically. This initial jump will be given by
bp - &T) + (dm,lW [l - bp - hT)l , which, in general, will be less than zero, implying jump in the nominal exchange rate is given by
kwwei
(134
that the initial
= - [~(~)lm(~)l~~m(O)l~~l .
Wb)
Equation (13a) captures the two effects that the policy impinges on the system. The second term on the right hand side would be the long-run equilibrium if the policy was supposed to be sustained forever, that is, T + ~0. The first term is the sensitivity of the new 4A property of the policy experiments we shall perform icy will have a permanent effect. This is associated with teresis which has received some attention recently. Sen and this specific result in a related nonmonetary model with instrument is the investment tax credit.
106
is that a temporary polthe phenomena of hysTurnovsky (1988) show capital when the policy
Temporary
Monetary
and Fiscal Policy
long-run equilibrium at t = T to the initial contraction on the rate of monetary growth. It involves two compounded terms, one is the effect of the initial monetary contraction on the monetary growth that will monetize the deficit, and the other is the effect of the endogenous adjustment of the monetary growth on the real stock of money at time T. Figure 1 illustrates a possible dynamic path for the endogenous assets given the temporary monetary policy. The economy is initially at the steady-state equilibrium represented by point A with a given positive net of interest deficit DO sustained by the monetary authority. The policy is implemented at time t = to until a known time t = T. At t = to, the nominal exchange rate instantaneously appreciates according to (13b) and both the real stock of money and the real stock of government issued bonds are instantaneously re-
,/
/ /’ --B-e--_-__/ )I____-^---------al,01 C __d----------!lJa(T) 4 / Temporary
Figure 1. Monetary
Policy
107
Marcel0
Bianconi
valuated to point C. Between t,, < t 5 T, the dynamic path is completely unstable, governed by (ll), and relative to the steady state associated with the lower rate of monetary growth at point B. The lines connecting the points BDA are the Laffer curves described by (12). At t = T, the economy reaches point D, where 8(T) is such that no accumulation of assets occurs. The new steady state will be at point D, with a rate of monetary growth larger than the one that sustained the initial equilibrium at point A. Intuitively, the revaluation of assets implied by the instantaneous appreciation of the nominal exchange rate is equivalent to an instantaneous net capital outflow. Since agents have perfect foresight and know with certainty that the deficit will be monetized at t = T, the exchange rate starts depreciating (the inflation rate increases) with an associated real movement equivalent to a net capital inflow. In other words, the economy accumulates domestic and foreign real debt to replace the loss from money creation. However, this process cannot go forever, otherwise it would violate the overall economy budget constraint. At t = T, the rate of money growth must finance interest payments on a larger than previous stock of real debt, therefore implying B(T) > 80 > 81 .
(14)
This is a version of the Sargent and Wallace (1981) result for a small open economy. The difference is that in the closed economy only the real value of domestic government bonds changes. In the small open economy this need not be the case. The movements in the nominal exchange rate (price level) mimic net capital inflows from abroad providing a current account surplus sufficient to partly offset the foregone inflation tax. This represents in Figure 1 that from point C to D the real stock of government issued bonds may move above or below a(0). At any rate, at t = T, the inflation tax must be increased to meet interest payments on the increased real stock of domestic and foreign debt. The possible dynamic path of Figure 1 involves many assumptions. First, we assume that the economy is in the lower inflation equilibrium of the LafIer curve. This is equivalent to the assumption that the elasticity of real balances with respect to the rate of monetary growth is less than one in magnitude. Second, we assume that the real stock of money jumps in the upward direction. This need not be the case. If 8 and T are such that (13a) equals zero, the real money stock would not jump at t = to and the ex-
Temporary
Monetary
and Fiscal Policy
change rate would start depreciating from point A in Figure 1. Equilibrium would be attained at the other side of the Laffer curve with a much higher rate of exchange depreciation (rate of inflation).5 Another possibility would be that the initial jump in the real money stock overshoots the would-be steady state at point B. In Figure 1, if it jumped to point E, the economy would follow a hyperdeflationary path. Third, it is critical that the fiscal authority does not act. If the fiscal authority responds to the monetary shock by altering D,, and leaving one of the fiscal instruments to adjust endogenously, then the economy would jump instantaneously to point B in Figure 1, that is, the new steady-state equilibrium. It is interesting to observe the effect of the policy on the monetary growth rate at t 2 T. At t = T, the endogenous rate of money growth is given by
fU) = W’[m(T)IId - b-* - 4))
05)
and (15) holds all along the Laffer curves in (12). Friedman (1969) proposes an optimum quantity of money where no other asset could dominate real balances holdings in terms of rate of return. In our case, full liquidity would be provided by OF = -p = -(r* - 9). Comparing with (15), we note that B(T) = {V’[m(T)]/pS} + BF, implying that 8(T) distorts from OF by an amount equal to the opportunity cost of holding money against the consumption foregone. Temporary Fiscal Policy Consider a temporary policy which consists of increasing the net of interest deficit between to 5 t < T and, at t 2 T, of some instrument adjusting endogenously to make m(T), a(T), and b(T) a steady-state equilibrium. In this case, the choice of endogenous instrument before and after the policy switch is of critical importance. Suppose that the monetary authority is sustaining an equilibrium with monetary accommodation. Any temporary fiscal change will imply the steady-state comparative statics results described in Section 2 above. Notice also that if any fiscal instrument is adjusting endogenously, a temporary policy involving any of the other two
that put (or KS)
‘This is equivalent to the Sargent and Wallace (1981) “spectacular” result. Notice if the economy started from the high inflation equilibrium, such outcome would the economy on a hyperinflationary path, and only an open market operation fiscal accommodation) could restore equilibrium. Also, (r* - 9) < (-0” ms/ is assumed across Figure 1.
109
Marcel0
Bianconi
instruments yields the steady-state comparative statics results. Dynamics will arise if the policy involves fixing temporarily a given fiscal instrument while all the others are given as parameters. For instance, suppose that the economy is described by lump-sum accommodation as in Table 1, Panel B. The fiscal authority announces and implements at t = t,,, an instantaneous reduction in the lumpsum tax from So to S1, So > S,, to last until a known date, t = T, when a choice of any of S, g, or 7 adjusts endogenously to sustain an equilibrium. Let us focus on some of these alternatives. First suppose lump-sum tax itself accommodates. The case is that lump-sum taxes S(T) = S, will be such that [dm(Z+j/dt] = [da(T)/ dt] = [db(T)/dt] = 0. s ince agents have full information, they know with certainty that at t = T the system will behave according to Table 1, Panel B, which implies that at t = to the real stock of money balances will not jump, that is, the nominal exchange rate does not jump. The appropriate S(T) that delivers the steady state solution for m, b, and a is obtained from (lOa)-(lOc), yielding the conditions
[b(T)- &I = [a(T)- 4 and
m(T) = mc@);
(16)
where 8 is exogenously given by the monetary authority independent of the policy implemented by the fiscal authority. The results in this case are obviously consistent with Ricardian Equivalence. At the time the policy is implemented, domestic residents foresee that lower taxes in the present imply higher taxes in the future such that they start to accumulate domestic government issued bonds at to anticipating future lump-sum payments. The current account and real money holdings are unchanged. Consider now the case in which government expenditures, g(T), adjust endogenously at t = T to the initial lump-sum tax contraction. Since agents are not informally constrained, they shall predict the future government expenditure adjustment and shall react according to the steady state described in Table 1, Panel C. At t = T, g(T) must be such that m, a, and b do not change over time. The appropriate g(T) from (lOa)-(1Oc) must satisfy 110
Temporary
Monetary
41 =W’[m(T)1~/~,U(~)- g(T)
[O + (r* -
+ (r* - 9)lW) which
and Fiscal Policy
yields the following
- a(T 01,
(17)
relationships
[WT)lW’)l h(~)= -1 ,
(184
[WT)lWJl
084
h(n > 0 .
The initial jump in m(0) and a(O), given the instantaneous jump in the exchange rate, will be given by
initial
[dm(O)ldSl= [da(O)ldSl= {[am(T)lag,l(dg,lds)> (exp - X,T) + (dmJdS)[l
- (exp -X,T)]
,
(19)
which is, in general, greater than zero.6 In our model, when the policy announcement and implementation of the policy takes place (at t = to), the level of the exchange rate instantaneously depreciates reflecting the speculative movements of rational agents who anticipate the future gains involved in the foreseen government exMoreover, given the presence of the penditures accommodation. nominal asset dominated in domestic currency, all arbitrage opportunities are fulfilled at t = to and, at t = T, when the endogenous adjustment in government expenditures actually takes place, no jumps in the exchange rate level occur.‘I Let us examine Figure 2, which illustrates the possible dynamic paths of this policy. The initial steady state is at point A. The policy announcement and implementation at t = to yields a downward jump in real money balances as well as in the real value of government issued bonds to point C, since the exchange rate “The
jump
in the
nominal
exchange
rate
in this
case
is
[dE(O)/dS] = -[E(O)/
~@)l[dm(o)ldsl < 0. ‘This result differs from Drazen and Helpman (1986) and Helpman and Drazen (1988) because they consider only one real asset besides money such that, in their case, at t = T, the endogenous adjustment in government expenditures leads to an anticipated infinite return on both assets, that is, a price level jump. See also Calvo (1989) on a related discussion.
111
Marcel0
Bianconi
m
I
a Figure 2. Temporary Fiscal Policy Government Expenditure Accommodation
depreciates instantaneously. The dynamics are relative to the steady state at point B associated with the lower lump-sum tax. The relationships in (lSa)-(18c) are the connected points BAD reflecting the points where government expenditure adjusts endogenously. Between to I t < T the government deficit is larger and households hold fewer bonds since they anticipate the future government expenditure reduction. Also, real balances are too low (the rate of inflation is higher than the monetary growth rate), and the exchange rate appreciates (inflation rate falls). The current account, which is at an instantaneous surplus at t = to, reverses and all along points C and D there is a net capital outflow. At t = T, the endogenous adjustment in g takes place and g(T) is such that (17) is satisfied and we reach the new steady state at point D. At point 112
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D, the cut in government expenditure must be enough to cover the cut in lump-sum taxes plus the inflation tax losses associated with the deflationary process and the current account deficit associated with the net capital outflows. Notice that if the initial jump in real balances undershoots, to point E say, the economy would follow a hyperinflationary path. Finally, the income tax rate, T(T), could adjust endogenously. In that case, private agents would look at the steady state described in Table 1, Panel D. The dynamic adjustment would be conceptually similar to the case described in Figure 2 since, at t = T, the income tax rate must increase to provide revenues to service the debt.’
4. Concluding Remarks We have considered a class of temporary policies first introduced by Sargent and Wallace (1981). Specifically, we have shown that one of the main concerns of those authors, namely that the monetary authority loses control over its instrument to sustain an equilibrium, is an intrinsic characteristic of the small open economy model. The reason is that the small open economy must satisfy an overall inter-temporal budget constraint which includes domestic and foreign solvency. Temporary monetary contraction with a constant net of interest deficit involves movements in the exchange rate which imply movements in the current account since there is a revaluation of assets. In this case, the current account starts and ends in a balanced position and the economy ends with a rate of exchange depreciation (rate of inflation) higher than the one prior to the policy. In the case of government expenditure adjustment all endogenous variables are simultaneously a&cted. The current account will be initially in surplus, and along the dynamic path the surplus will be more than used up. Depending on the relative size of the initial jump in the exchange rate, the economy may follow a(n) (in)deflationary path, but consumers unambiguously end up with a higher stock of real balances and a lower stock of real bond hold‘Tumovsky and Brock (1980) and Tumovsky (1987) examine the trade-off between the rate of monetary growth and the income tax rate when 8 is optimally chosen. Along the lines of the cases presented here, one could think of other combinations of temporary policies with subsequent adjustments.
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ings. The government, on the contrary, ends up with a higher stock of debt. Two natural extensions of our model are the explicit inclusion of capital and the introduction of risk. The former would involve a better description of the corporate sector along the lines of Brock and Tumovsky (1981) while the latter would follow the lines of Bizer and Judd (1989). Received: May 1989 Final version: April 1990
References Arrow, Kenneth J., and Mordecai Kurz. Public Znvestment, The Rate of Return, and Optimal Fiscal Policy. Baltimore, MA: Johns Hopkins University Press, 1970. Bizer, David S., and Kenneth L. Judd. “Taxation and Uncertainty.” American Economic Review Papers and Proceedings 79 (May 1989): 331-36. Brock, William A. “Money and Growth: The Case of Long-run Perfect Foresight.” Znternational Economic Review 15 (1974); 75077. -. “A Simple Perfect Foresight Monetary Model.” Journal of Monetary Economics 1 (1975): 133-50. Brock, William A., and Stephen J. Turnovsky. “The Analysis of Macroeconomic Policies in Perfect Foresight Equilibrium.” Znternational Economic Review 22 (1981): 179-209. Calvo, Guillermo A. “Anticipated Devaluations.” International Economic Review 30 (August 1989): 587-606. Drazen, Allan. “Tight Money and Inflation: Further Results.” Journal of Monetary Economics 15 (1984): 113-20. Drazen, Allan, and Elhanan Helpman. “Inflationary Consequences of Anticipated Macroeconomic Policies.” NBER Working Paper Series No. 2006, August 1986. Friedman, Milton. The Optimum Quantity of Money and Other Essays. Chicago: Aldine, 1969. Helpman, Elhanan, and Allan Drazen. “Future Stabilization Policies and Inflation.” In Finance Constraints, Expectations, and Macroeconomics, edited by M. Kohn, and S. Tsiang. New York: Oxford University Press, 1988. Hodrick, Robert J. “On the Effects of Macroeconomic Policy in a 114
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Maximizing Model of a Small Open Economy.” Journal of Macroeconomics 4 (1982): 195-213. Liviatan, Nissan. “Tight Money and Inflation.” Journal of Monetary Economics 13 (1984): 5-15. Obstfeld, Maurice. “Macroeconomic Policy, Exchange Rate Dynamics, and Optimal Asset Accumulation.” Journal of Political Economy 89 (1981): 1142-61. Sargent, Thomas J., and Neil Wallace. “Some Unpleasant Monetarist Arithmetic. ” Federal Reserve Bank of Minneapolis Quarterly Review 5 (1981): 1-17. Sen, Partha, and Stephen J. Turnovsky. “Investment Tax Credit in an Open Economy: Permanent Effects of a Temporary Policy.” Department of Economics, University of Washington, Seattle, 1988. Mimeo. Sidrausky, Miguel. “Rational Choice and Patterns of Growth in a Monetary Economy.” American Economic Review 57 (1967): 53444. Turnovsky, Stephen J. “Domestic and Foreign Disturbances in an Optimizing Model of Exchange Rate Determination.” JournaZ of International Money and Finance 1 (1985): 151-71. -. “Optimal Monetary Growth with Accommodating Fiscal Policy in a Small Open Economy.” Journal of Znternational Money and Finance 6 (1987): 179-93. Turnovsky, Stephen J., and William A. Brock. “Time Consistency and Optimal Government Policies in Perfect Foresight Equilibrium.” Journal of Public Economics 13 (1980): 182-212.
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