TIA AVIV 56-2,6
THE FOERDER INSTITUTE FOR ECONOMIC RESEARCH' 'TEL-AVIV UNIVERSITY
RAMAT AVIV ISRAEL
GIANNINI fTON OF AGRICULTURtLWONOMILIBA CS
28 1986
51 11119 1T1PYVP 1.1 vrYt5353 lpnn5 113n 1tatr5n nutTr12P31m v'y EXCHANGE RATE MANAGEMENT: INTERTEMPORAL TRADEOFFS
by
Elhanan Helpman and Assaf Razin
Working Paper No.36-85
December, 1985
This research was supported by funds granted to the Foerder Institute for Economic Research by the NUR MOSHE FUND.
FOERDER INSTITUTE FOR ECONOMIC RESEARCH Faculty of Social Sciences, Tel—Aviv University Ramat Aviv,Israe 1. EXCHANGE RATE MANAGEMENT:
Intertemporal Tradeoffs By
Elhanan Helpman and Assaf Razin*
1. INTRODUCTION the It is now understood that exchange rates cannot be managed without
pursuit of other policies which make the entire package internally consistent
(e.g., Polak (1957)). Governments or central banks can only temporarily
target exchange rates without giving due attention to other policies. which However, eventually they have to choose or are forced to choose measures
validate ex—post the feasibility of their exchange rate policy. These
measures will typically be anticipated by economic agents during the initial in periods of exchange rate management, thereby generating immediate pressure
various markets. Hence, the success of the exchange rate management policy
depends to a large extent on other policies, commitments to future policies,
and their effects on expectations.
A major purpose of this paper is to study the effects of policy—induced an slowdowns in the rate of currency devaluation which are not accompanied by
immediate fiscal contraction that prevents reserve losses, thereby implying
the need for a contraction in future periods. An extreme form of this policy
is an exchange rate freeze. Our interest in experiments of this type stems
This is an expanded version of NBER Working Paper No.1590. We wish to thank the Horowitz Institute and the Foerder Institute for Economic Research, Tel—Aviv University for financial aid and to participants at the Tel—Aviv Workshop on International Economics, the Maale Hachamisha Conference on Exchange Rate Management, the Paris Macroeconomic Seminar, and Western Ontario Money Workshop, the New University of Lisbon Seminar the NBER Summer Institute, for comments. EXCHANGE RATE MANAGEMENT: INTERTEMPORAL TRADEOFFS
Elhanan Helpman and Assaf Razin
ABSTRACT
The management 1f the exchange rate is possible only if the government
pursues a monetary—fiscal policy mix which is consistent with its exchange
rate targets. In this paper we construct a model in which the real
consequences of exchange rate management depend on the precise time pattern of the accompanying fiscal and thonetary policies. We study the macroeconomic constraints on feasible policies and the comparative dynamics of disinflation by means of exchange rate targetting that takes place with an initially overvalued currency and a delayed accompanying contractionary policy. The policy brings about an intergenerational redistribution of wealth, and as a result, spending rises during the initial time periods and falls during later periods, the real exchange rate declines initially and rises eventually, and the country's external debt rises in all time periods. These results are consistent with recent exchange—rate—managed—disinflation attempts in Argentina, Chile and Israel.
Elhanan Helpman and Assaf Razin, Department of Economics Tel—Aviv University Tel—Aviv 69978 ISRAEL 2
from the fact that several countries have attempted in recent years to
disinflate by means of slowdowns in the rate of currency depreciations, with
Argentina, Chile and Israel being the prime examples. Argentina used a
preannounced pattern of exchange rate movements (Tablita) from December 1978
to February 1982; Chile used a Tablita from February 1978 which culminated in
an exchange rate freeze in June 1979. The frozen exchange rate was maintained
until June 1982. Israel used a preannounced rate of currency devaluation from
September 1982 until October 1983 (5 percent per month). In all cases the
currency was overvalued and the managed rate of currency devaluation was below
the inflation rate. Table 1 presents data for these countries. It is clear
from these data that in all cases the policy brought about an appreciation in
the real exchange rate; an increase in private consuiption; a
worsening of the trade balance and a loss of reserves. In all cases the
exchange rate management policy turned out to be unsustainable.
[Insert Table 1 about here]
In order to study these issues we construct a model of
overlapping—generations in which consumers have finitely expected horizons, as
in Blanchard (1985). This model is particularly suitable for the purpose at
hand because it is free of distortions but nevertheless does not have the
Ricardo—Barro neutrality property (see Barro (1974)). It is well known that
in economies without distortions in which individuals have infinite horizons exchange rate managements have no real effects (e.g., Helpman and Razin
(1979)), and therefore these types of models cannot explain the facts depicted in Table 1. On the other hand, in economies with distortions exchange rate management may have real effgcts even when individual horizons are infinitely 3 long (e.g., Aschauer and Greenwood (1981), Helpman and Razin (1984) and
Feenstra (1985)), but it seems to us that it is more reasonable to rely on finite horizons than on distortions in order to explain the macroeconomic performance reported in Table 1.
We present our model in Section 2 and discuss there a benchmark equilibrium with a freely floating exchange rate. In that framework the time pattern of real variables does not depend on monetary injections or withdrawals through the tax—transfer system and the resulting equilibrium is identical with the equilibrium that would have resulted in a barter economy.
This naturally leads to an efficient allocation of resources. Efficiency is also preserved when the exchange rate is managed, but the time pattern of real variables does depend on the policies that support the exchange rate path .
(contrast with Helpman and Razin (1979), Helpman (1981) and Lucas (1982)).
Hence, in this case there exist significant differences between a managed and a floating exchange rate regime. In section 3 we study these issues in general terms. In particular, we explore the feasibility of various exchange rate policies in conjunction with the accompanying fiscal and monetary policy mix. The real effects of exchange rate targetting that arise in this analysis are closely related to the real effects of budget financing that were discussed by Blanchard (1985) and Frenkel and Razin (1984) in frameworks without money. We, naturally, take explicit account of monetary considerations.
In section 4 we study in detail the -extreme form of exchange rate management -- the case of an exchange rate freeze. This is designed to shed light on the economic mechanism underlying disinflation policies by means of exchange rate targetting that were described above. We show that when this 4 policy is pursued with an initially overvalued currency and a delayed accompanying absorption policy, the result is higher spending and a low real exchange rate following the inception of exchange rate management, lower spending and higher real exchange rates in later periods, and larger aggregate external debt in all time periods. The twist in the time profile of spending and the real exchange rate, and the upward shift in the time profile of debt, are larger the larger the initial overvaluation and the longer the delay in the absorption policy. However, the delay in the absorption policy is bounded by the government's taxing capacity. Therefore the feasible delay in the absorption policji is also bounded. The beneficiaries of this policy combination are individuals who are alive during its inception, while all future generations suffer.
2. Floating Exchange Rate
We consider an economy with overlapping generations in which a cohort of size 1 is born in every period. Individuals survive to the next period with probability y and this probability is age independent. The event of death is independent across individuals. Therefore, the proportion of a cohort alive at time t1 which survives to period t2 is:
(t,—t1) Y
The age distribution of the population is constant over time and in every period there are ya individuals of age a. The size of the population is also constant and equal to: -\
1:=6*( a = 1/(1-Y) 5
We assume that those individuals live in a small country facing a given one—period world real interest rate r on sure loans in terms of traded goods. All loans are indexed and foreign prices of traded goods are constant and equal to one. Thus if one borrows b he has to repay Rb the next period, where R = l+r is the interest factor. Since an individual survives to the next period only with probability y, he cannot obtain a loan with this interest rate. Foreign financial institutions who lend to domestic residents will obtain a sure repayment Rb if they charge a real interest rate of (R/y) — 1. In order to see this, suppose that b is being lent to every individual of a given cohort. Then those who will survive to the next period will repay Mph. However, only a proportion y of the individuals will survive. Therefore total payments by the cohort will be Rb. Clearly,
(R/y) — 1 is the risk—adjusted real interest rate (see Blanchard (1985)).
There exist firms that produce yT units of 'traded goods per capita and yN units of nontraded goods per capita. The sectoral output levels are functions of the relative price of nontradables pt and so is GDP per capita in terms of traded goods, which we denote by y(p ). Clearly, dy(pt)/dp t =yN.
Firms sell their output in exchange for domestic money and distribute the proceeds to the living individuals at the beginning of the following period.
Individuals have to pay for goods with money; with home money for home goods and foreign money for foreign goods. Thus, we assume a system with cash—in—advance constraints in which goods are bought with the seller's currency (see Helpman and Razin (1984) for a discussion of alternative monetary mechanisms). A firm pays its owners the proceeds from period t-1 at the beginning of period t. At the beginning of period t every individual 6 receives also the repayment (inclusive of interest) of loans he gave in t-1 and new loans are issued. These transactions result in a stock of money that is allocated between domestic and foreign money by trading in the foreign exchange market. These final stocks of money are then used during period t to purchase goods. Local firms absorb during period t the entire stock of domestic money and pay it out as dividends at the beginning of period t+1.
This sequence of transactions is repeated in every period.
The budget constraint of an individual of age a in period t is:
c b — (R/y)b + [e y(p ) — (1) a,t = a,t —1,t-1 t-1 t-1 tt
c (E + ptcNa,t) is his total consumption in terms of where a,t cTa,t traded goods; ba,t is his new debt; (R/y)ba_i,t_i is his repayment of old debts, with period—minus—one debt equal to zero(i.e., b_i,t.0 for all t); et is the exchange rate; and e't are the age—independent nominal taxes or transfers. We also assume in (1) that money is not used for store of value purposes, which is guaranteed when the nominal effective interest rate is positive. In addition we need to impose the solvency (terminal) condition:
tb goes to zero as T goes to infinity. (la) (R/y a+T,t+T
We assume that the government has no real spending. In a freely floating exchange rate regime the government injects and withdraws money from the economy via the taxes and transfers . Hence, if mt is the per—capita stock of money in period t, then:
mt mt-1 - 8t •
7 On the other hand, with positive nominal interest rates all domestic money is
spent on domestic goods (see Helpman (1981)), implying:
mt. e ty(pt)
Taken together the last two equations imply:
(2) [et-1y(Pt-1) — WO/et = Y(Pt)
Using (1) and (2) it is clear that in a pure floating exchange rate
regime monetary injections and withdrawals via e't have no real effects.
Put differently, in this system the time pattern of consumption and real debt
(individual as well as aggregate), and the real exchange rate 11t'( d
not depend on the time pattern of monetary injections. This result is in line
with models in which there are no overlapping generations and individuals live
to the end of the economy's horizon (see Helpman (1981)).
We use this case as a benchmark of comparisons with exchange rate
management policies. It should though be pointed out that neutrality of the
above described Monetary policy need not hold in the presence of a
labor—leisure choice or externally—financed investment. It also need not hold
if the buyer's currency is used for transactions instead of the seller's
currency (see Helpman and Razin (1984)). Moreover, a special feature of the
current formulation of overlapping generations is that the neutrality result
also depends on the assumption of an equal division of period t-1 proceeds
among all living individuals at the beginning of period t. It can, for
example, be shown that if this is not so, and individuals can take loans using
current period output as collateral (in case they. do not survive to the next
period), then monetary policy will have real effects. We do not pursue this
line here in order to avoid sidetracking. 8
3. INTERTEMPORAL CONSTRAINTS ON EXCHANGE RATE MANAGEMENT
Suppose that in the benchmark case considered in the previous section we
obtain the following solution for per—capita consumption and debt:
Et = (1—Y) 1:=0YaEa,t 5t = (1—Y)1:=0Ya5a,t t =
and the real exchange rate {1/t}. Suppose also that in period t = 0
the government begins to manage the exchange rate. The question we consider
is: what are th.e real consequences of exchange rate management in terms of
from the benchmark we know from deviations of {ct'bt'pt} case? As Helpman (1981), in a model without overlapping generations in which
individual lives extend to the economy's horizon, exchange rate management has
no real effect as long as the government is intertemporally balanced,
independently of the time pattern of taxes. The reason is that in that case
the private sector fully internalizes the government's intertemporal budget
constraint. This, however, cannot be expected in an economy in which
individuals pay future taxes with a probability smeller than one. Therefore,
the time pattern of taxes required in order to manage the exchange rate will
generally have real effects.
Clearly, for every time pattern of exchange rates there exists a time
pattern of taxes and transfers which preserves the benchmark real variables.
However, while in previous models (e.g., Helpman (1981)) there was no constraint on the time pattern of the neutral taxes but only on their present value, here this
pattern is unique. As is clear from (1) and (2), if in period t.0 the real 9
exchange rate remains (150) and per—capita debt does not change, then for
a given pattern of exchange rates (et)t.0 the taxes have to {0t}t.1 satisfy:
W I — e i (5 ) (3) t t——lY t1 — et y(t15 ) ' t 0,1,...
where e1 This policy — —1* generates monetary injections and withdrawals which keep the money supply in line with the nominal value of output implied
by the exchange rate et and the real exchange rate (15t); i.e.,it assures:
mt = mt-1 = e ly(k)
with no deficits or surpluses in the overall balance of payments.
If (3) is satisfied, we have
(4) Let_g(5t_i) — etDets = Y(5t), t
which is the same. as (2), implying no change in real variables. In this case
no reserve movements are required in order to manage the eichange rate.
Observe, however, that even when the exchange rate is maintained constant over
time, varying taxes and transfers are required as long as the real exchange
rate is not constant over time. Hence, exchange rate management without real
consequences requires a well coordinated time—varying policy of monetary
injections and withdrawals. No such policy is required under a free float.
It is clear from this discussion that if a policy that satisfies (3) does
not accompany the exchange rate management programme there will be reserve
movements. Assuming intrerest bearing reserves, reserve movements generate
public debt which has real effects. The time pattern of the external public debt per capita is given by: 10
(5) b = Rb 1 + t eLlY(Pt_i) — etY(Pta) — et], t = 0,1,... with the initial conditions:
kG 0, e 1 n u, IA =" = r 1 = r-1.
We assume that the government repays its debts. Therefore its policy is restricted to satisfy (5) with the terminal condition:
(6) lim Rtb .0.
Equation (5) describes reserve (external interest bearing assets) movements according to the standard balance of payments mechanism. External debt grows at the rate of interest due to rollovers plus periodical additions through deficits in the overall balance of payments, the last component being represented by the terms in the square brackets. The first two terms describe the decline in the overall demand for money [et_ly(pt_i)
Part of this decline is satisfied by negative injections (withdrawals) via taxes W.tI. The rest is attained via foreign exchange purchases by the private sector, which bring about reserve losses. It is clear from (5) that when (3) is satisfied, we obtain the solution G p = p and b = 0 for all t; i.e., there are no reserve movements. t t t
Now, suppose that the exchange rate management policy starts in period zero and the policy rule given in (3) is not followed. Then the effects of reserve movements on individual budget constraints can be seen from the following rewriting of the budget constraint (1), using (5):
ca,t = — (R/y)Ca_ — R4_1) (7) bat 1,t-1 APO 11
In order to see as clearly as possible the real effects of reserve
movements, assume for the moment that all goods are traded; i.e., yN = 0
and APO E Then (1) and (2) imply (using the terminal condition on • a+i,t+T •
(8) 1 1°3T= (Y/R)TCa+T,t+T = /7=0(Y/R)TY (R/Y)ba-1,t-1
while (7) implies (using the terminal condition on and ba+i,t+T (7)): (9) /7=0(Y/R)Tcla+i,t+T = wa,t
where wat is real wealth of an individual of age a at time t and
(10) /7=0(Y/R)1Y1 — Rbt_i wa,t = (R/y)ba-1,t-1 (1-Y) 17=0(Y/R) T44.T. .
It is clear from a comparison of (8) with (10) that reserve movements have
real effects and that these effects depend on the time pattern of reserve
movements. Different time patterns of reserves generate different
redistributions of wealth across generations, thereby effecting the time
pattern of aggregate spending as we will show explicitly in the next section.
Observe also that if we assume that no new cohorts are born and the
probability of survival equals one, then viewed from t=0 constraint (10)
coincides with (8), which implies neutrality of the exchange rate policy.
The redistributional effect embodied in (10) can also be seen in another
way by combining it with (5) in order to obtain:
t+T e (11 w t+T-1 et+T a,t = /7=o(Y/R)T(YTej e /' t+T — (R/y)b a-1,t-1 • 12
It is seen from here that the real wealth of an individual born at time t depends both on the given depreciation rates of the managed exchange rate and on the tax rates. An individual born at t is better off the further away in the future taxes are imposed and the exchange rate is depreciated, and the nearer in the future transfers are given and the exchange rate is appreciated. However, the taxes cannot be divorced from exchange rate movements, because from (5) and (6) they have to satisfy:
—t —t 1 ' (12) oR (etiet) = it.oR e' et-1y(Pt-1) etY(Pd]
_ where p...1. p ..1 and e...1 =with y(pt) E yr in the case of traded goods only. Hence, the larger initial appreciations of the currency the larger the taxes that have to be collected.
Coming back to (11), and the case of traded goods only, observe that from period t.1 onward exchange rates and taxes are fully anticipated. However, at time t.0, when exchange rate management begins, there is an unanticipated change both in the exchange rate and in taxes (and in the real exchange rate whenever there are nontraded goods). It is therefore useful to decompose the contribution of period zero disposable income, inclusive of capital gains on wealth, into anticipated and unanticipated components. Given the discussion of the benchmark case it is clear that the anticipated component of real income is yT, while from (11) total real income is:
— e 0 —1 0 ' YT e 0 0 Therefore, the last two terms represent the unanticipated components, and they can be expressed as: 13
— e 0 —1 (13) 0
where
1, 11 a, (13a) = e0 0 is the unanticipated capital gain on money balances and
(13b) h
is the unanticipated increase in real taxes (in the presence of nontraded
goods there exists also a capital gain due to the unanticipated movement in
the real exchange rate). The definition of the real loss due to taxes is
clear from (13b), while the capital gain on money balances may require an
explanation. Before the change in the exchange rate policy the private sector
held money balances:
1 = e—lYT
The real value of this money was expected to be yTE_If60. As a result of the
unanticipated stabilization of the exchange rate at eo the real value of
this money has become y Hence, (13a) describes the unexpected — 1 T/e0' capital
gain on period minus one money holdings.
Now, using yN = 0 and (13) it is seen from (5) that:
(14) b g = k—h. 0 14
Namely, the initial loss of reserves is equal to the public's unanticipated capital gain on money holdings minus the unanticipated increase in tax obligations. In view of (14), condition (3) for t.0 (which describes the period zero absorption policy that is required for real neutrality of the exchange rate ru, management policy) can be interpreted as follows: The tax rate 00 is chosen so as to make the unanticipated increase in tax liabilities h just equal to the unanticipated capital gain on money balances k. When this holds there are no initial reserve movements.
4. DISINFLATION BY MEANS OF AN EXCHANGE RATE FREEZE
We pointed out in the Introduction that the motivation for this study came from the experience of Argentina, Chile and Israel with the use of a slowdown in the rate of currency depreciation for disinflation purposes. In order to evaluate the macroeconomic effects of this policy we consider in this section the extreme case of an exchange rate freeze (as applied in Chile between June 1979 and June 1982). For concreteness, suppose that the government freezes the exchange rate at the level e from period zero to infinity. In this case real effects are prevented if taxes equal —1 eft, t = 1,2,..., as given in (3). In particular, if there are traded goods only it can be seen that price stability with no real effects is achieved when the government taxes away the period zero capital gains on money holdings and it balances its budget in all future periods by setting taxes equal to zero. If, however, there are nontraded goods in the system, then taxing away the capital gain on money holdings in period zero and setting taxes equal to zero 15 in all future periods will not attain price stability, nor will it prevent real effects. As we have shown in the previous section real neutrality requires the taxes to vary over time in reaction to real exchange rate movements (see (3)). When other real world complications are added as well, such as the dependence of the velocity of circulation on the nominal interest rate, the required policy coordination for real neutrality becomes even more complicated.
Returning to odr case with traded and nontraded goods, we choose to analyze the following policy experiment. Suppose that the exchange rate e is chosen below - ET0 and taxes are not changed in period zero. Starting with period t=1 taxes are imposed according to (3) until period 1-1. This level of taxation is too low to prevent reserve losses. From t=T onwards fixed real taxes e'/e are added to the taxes in (3) in order to pay interest on public foreign debt, so that the government's budget is balanced for t=T,
T+1,... . In this case exchange rate management begins with an overvalued currency; we wish to explore the resulting real effects and their dependence on the timing of •the contractionary policy.
We have selected a particular tax structure to accompany the exchange rate freeze which is both feasible (it satisfies (12)) and simple to understand. Other variates can, of course, also be considered, but it seems to us that the simplicity of the tax structure is an advantage as far as the current illustration is concerned. Our scheme implies that in every period t c (1,2,...,T-1) taxes are just equal to the decline in the demand for money
(see (3)). In this case the consolidated budget deficit (of the government and the Central Bank) is equal to interest payments on public foreign debt.
Hence, from t=1 to t=T-1 public foreign debt grows at a rate that equals the 16 rate of interest R-1. From t.T and on taxes are equal to the decline in the demand for money plus a constant that covers interest payments on public external debt. The result is that from t.T-1 and on public external debt remains constant.
Let g = bg > 0 be the initial public foreign debt that results from the exchange rate freeze. Then under our tax scheme (5) implies:
, 0 < t < T — 1
(15) b
i.e., the government's foreign debt grows at the rate of interest until period 1-1 and remains constant afterwards.
Using (3) and (15) taxes are given by:
for 1 < t < T-1 et Y(Pt-1)—Y(Pt) y( 14g e = Pt-1)—Y(Pt) (R-1)R for t > T
In this case, the individual budget constraint (1) can be written as:
(16) ba,t =(R/y)ba_i,t_i + ca,t — [y(pt) — et] where the effective taxes (including capital gains) are given by:
_g 2 t =0
(17) 0 9 1 <• t < T-1
(R-1)RT—lg t >T
Now, (16) implies the individual budget constraint: 17
co (18) Y/R)T Ca+T,t+T = /7=0 T[Y(Pt+ )—°t+.1 (R/Y)ba_l,t_l E Wa,t T= (Y4R) 1 ]
We assume that individuals maximize expected lifetime utility:
00 T / • T / E, ,d vot+T , c+1 ) = lw (y6) vklat+i,cet,t.4.1. T=u +1 T=o subject to (18), where (-) is the temporal indirect utility function which is derived from a ditect utility function of the form alog cN (1—a)log cT.
In this case:
c a,t = (1—y )wa,t and per capita consumption is:
. a c — t = (1—y6) a=ol a,t (1—y6)(1—y)la=ow y awa,t*
Using the right hand side of (18), we obtain:
(19) ct = (1—Y6)(17.0(YIR)TEY(Pt+T)— t+T — Rbt4}, t 2:0 and by aggregating (16) over all age groups we obtain:
(20) bt = Rb + ct — Ly(p ) — et] , t > 0
with the initial condition b = 1
Finally, we have a clearing equation in the market for nontraded goods. We assume that there exist fixed quantities of traded and nontraded goods; yT and yN, respectively. In this case: 18 (21) ) = YT PA
and the clearing condition in the market for nontraded goods becomes:
(22) act = PtYN
where the left—hand—side represents spending on nontraded goods in terms of traded goods.
The dynamic equations (19)—(20) together with the side conditions
(21)—(22) determine a unique equilibrium path that satisfies the solvency constraint :
—t (23) lim R bt = 0 t—>o)
The competitive equilibrium without intervention is obtained by solving
(19)—(23) for g = 0 which implies et. 0 for all t. It is shown in the Appendix that this solution is:
(24) 5t = B (5-1—B)At+1
(25) Et = C z(5-1—B)lt t = 0,1,2,...
(26) Tt = aEt/YN
where:
(27) B = — y1(1 —
(28) C = _ yT(1—Y,IsT1—Y)R
(29) A = aR(1—y6)(1—y)/y — (1—y6R)(R—y)/y 19 fru.° (30) x = R[p — p — 46]/2 > 0
(31) p= (1—a)(y6 1/y) a(1 6) > 0
2 (1—y6)R (1—xy/R) R[1—(1—a)(1—y6)] — (32) A (1—Ay/R) R[1—a(1—y6)J — Xy a(1—a)(1 — y6) > 0
In order to minimize the number of cases to be investigated assume that
.0• Define also:
(33) — (1—y6R)(R—y) a R(1—y6)(1—y)
Then we have three cases to consider:
Case (i): y6R > 1 .> (6R > 1, a > 0 > _ or y6R < 1, 6R > 1, a > a .> (1 > > 0) _ Case (ii): y6R < 1, 6R > 1, a < a .> (1 > > 0)
Case (iii): 6R < 1 (y6R < 1, & > 1 > a)
Case (i)
In this case B > 0, C < 0, x > 1, implying that the country is a
creditor in all time periods and its foreign asset holdings are rising over
time. .Consequently, its aggregate spending is rising over time, leading to
permanent appreciations of the real exchange rate (15). There exists no steady state.
Case (ii)
In this case B < 0, C > 0, 1 > x > 0, implying that the properties of the dynamic path are the same as in Case (i), except that the economy converges to a steady state with .E = B < 0, .E = C and .-15 = aC/yN. 20
Case (iii)
In this case 13 > 0, C > 0, 1 > x > 0, implying that the country is a debtor in all time periods, its debt is growing over time, its total spending is declining over time and its real exchange rate is depreciating in all time periods. The economy approaches a steady state with 5. = B > 0, and E C and .T aC/yN. The dynamics of Cases (ii) and (iii) are depicted in
Figures 1 and 2, respectively.
[Figures 1, 2]
In order to study the comparative dynamics of an exchange rate freeze we have to compare the solution (Et, Zt, 150 with the solution {bt,ct,p0 that obtains for g > 0. We have not been able to obtain clear—cut comparative dynamics' results from the analytic solution to system (19)—(23) when a > 0. For this reason we proceed in two stages. First, we present analytically the comparative dynamics for the case a = 0; i.e., the case in which consumers do not value nontraded goods, and then we simulate cases in which a > 0.
The properties of the solution for a = 0 is of interest for two reasons. First, continuity implies that the same properties are preserved for a > 0 but small enough. Hence, it provides insight into comparative dynamics of cases in which the share of spending on nontraded goods is small.
Second, our simulations indicate that large spending shares on nontraded goods lead to effects of an exchange rate freeze which are similar to those that we 1 have derived for the case a = 0.
1 The case a. 0 is simpler than the case a > 0 because when nontraded goods are not valued by consumers the dynamic system does not depend on future endogenous variables, and it can therefore be solved by a simple iterative procedure starting at t = 0. However, when a > 0 period t wealth depends on the price of nontraded goods in all periods from t to infinity. In this case the dynamic equations at time t depend on an infinite future sequence of an endogeneous variable; i.e., the real exchange rate, requiring a complicated solution procedure. This difficulty is well known in rational expectations models. 21
Now, solving (19)—(23) for the case a = 0 and g > 0 by means of direct iterations of the dynamic equations we obtain the following solution:
T 11: (y 26)-11(y6ot 1—y6)g[1— tElyT — -Y)Y
(24) ct—Et = 0 < t _< T-1
i_yogEl_VyT 117:141_y)yT 1—( 26) 2 -1 T-1 Y 2 (i 0 ](Y6R) 1—(y 6) t+l—T _ g(1_1,6):1 _y)RT 17.(y6r) (1 , t > T
2 N —t-1 1—(Y 61 + lEy6R)t , 0 < t T-1 27 1-6'2 o) -1 (25) St —bt
t+1 —T )(y6R)t+l—T gy(1_6014r1 RT—1 1 —(y6R) (5 — b1 , t > T-1 -1 1—y6R T
Obviously, in this case pt = 0 for all t. It is clear from this solution that average spending ct is larger than Et for t = 0 and possibly for other smell values of t, and that c < E for t large t t enough. Hence, the exchange rate freeze brings about higher spending levels initially and lower spending levels in the future, as compared to no intervention. On the other hand, when 6R < 1
(Case (iii)) it makes private foreign debt lower in all time periods. 22 When a > 1 private debt is lower until some time after T and higher there— after. Nevertheless, a direct calculation shows that total debt G b + b is larger than 5 in t t t all time periods, which means that public debt increases by more than private debt declines. A comparison of the time
profiles of consumption and debt for Case (iii) is illustrated in Figure 3. [Figure 3]
It is seen from (24) that the initially higher spending level is larger
the later taxes are imposed, and that the eventually lower spending level is
smaller the later taxes are imposed. Thus, the longer the delay in the
required contractionary policy the larger are the real effects of exchange
rate management. Moreover, the contractionary policy cannot be delayed at
will, because given a limit on taxing capacity, say x percent of GNP
(possibly ninety—nine percent), taxes which eventually have to equal g(R-1)RT-1 cannot exceed x percent of yT.
The economics behind these results are as follows. The capital gain from
the unexpected exchange rate freeze is appropriated by the individuals who are
alive in period zero. To them the present value of future tax liabilities is
smaller than the capital gain, and they respond by raising spending in all
periods. All future generations face larger tax liabilities and reduce
spending; the later an individual is born the larger his tax liability in
present value terms (except that all those who are born after 1-1 have the
same tax liability). Over time the population share of individuals who were
alive at t=0 declines and the share of those with heavier tax liabilities increases. Therefore, aggregate spending is initially larger and it becomes smaller far enough in the future. 23
In order to obtain an idea about the economy's response to an exchange rate freeze when consumers value nontraded goods we have simulated the system
(19)—(23) for various parameter values in order to cover all three cases. The qualitative results of the simulations were always the same; aggregate spending increases on impact and stays higher for some time, it falls below the no intervention level at some point in time and remains lower thereafter.
Naturally, this implies a real depreciation on impact, a lower real exchange rate for some time ind a higher one eventually. In addition, private debt declines on impact while public debt increases, resulting in an increase in aggregate foreign debt (or decline in assets): Private debt remains lower for some time, but may eventually become larger than the no intervention level of debt. However, aggregate foreign debt is higher in all time periods. These results are in line with the observed response of private consumption, debt and the real exchange rate to the disinflation attempts in Israel, Chile and Argentina that were discussed in the introduction.
Tables 2 and 3 show two simulations that substantiate our claim. The numbers in Table 2 show the same features as the curves in Figure 3. The numbers in Table 3 tell a similar story for a much higher interest rate. The higher interest rate turns the economy into a foreign asset holder and causes consumption to rise over time instead of declining. However, the comparative dynamics of the exchange rate freeze do not change, except for the fact that private foreign debt becomes higher from period 9 (foreign asset holdings decline). This, however, happens also when consumers do not value nontraded goods.
[Tables 2 and 3 to be inserted here]
t f 24
5. CONCLUDING COMMENTS
Our analysis suggests that it is extremely difficult to disinflate by means of exchange rate management without affecting consumption, debt and the real exchange rate. When an exchange rate freeze (or a slowdown of devaluation) is used without a reduction of private disposable income to low enough levels, the resulting loss of reserves worsens the economy's net asset position vis—a—vis the rest of the world, brings about higher consumption which is paid for with lower consumption of future generations, and brings about a real exchange rate appreciation following the exchange rate freeze.
These predictions, are consistent with the episodes that were described in the
Introduction, despite the fact that in those episodes exchange rate management ended with large devaluations, which seems different from the accompanying policies that we have specified. Observe, however, that an expected devaluation acts in our model as a tax on money balances. This is seen from equation (1) by remembering that e that if et t—g(Pt-1) = mt-1 so is the effective real tax rate it equals to: .
m e t-1 t et = Y(Pt) et et
Hence, a higher exchange rate in period t increases the effective tax rate by depleting the real value of money balances; the explicit real tax rate is Wt/et.
It is clear from this discussion -- and it can be shown in detail — that if, say, in period T the exchange rate freeze is ended with a maxi devaluation, then the implicit tax on money balances per se will reduce the size of the public internal debt (will increase reserves). In this case the structure of effective taxes will not be as we have specified, but it is possible to describe ,every feasible combination of the post freeze exchange 25 rate and tax policy by a suitable sequence of effective tax rates. The crucial element in our specification is that effective tax payments are postponed when the exchange rate freeze is introduced, and this feature seems to fit well the episodes of our concern.
Naturally, we do not claim that our model provides a complete explanation of these episodes, nor do we claim that it is the only explanation. We do, however, believe that our analysis highlights certain intertemporal aspects of exchange rate policies that are important in reality. 26
APPENDIX
In this appendix we derive the solution of (19)—(23) for g = 0; i.e., equations (24)—(26), and the general solution for g > 0. Then we explain the calculation method that was used in Tables 2 and 3,
By substituting (21) and (22) into (19)—(20) we obtain:
T (A.1) b ] PtYN = a(1—Yo)[AY1 /7=0* (Pt+TYN et+T) t-1
(A.2) b =Rio t t-1 +--oa.l t-v N -vT Dvt-N et
Now define
vc (A.3) P = D t = —1,0,1,2,... t L1 0 j1 i t+1+T which implies:
D Y (A.4) t = , Pt = t-1 R
Now, substituting (A.4) into (A.1) and (A.2), we obtain the following system of difference equations:
bt (A.5) b A (Pbt-1 1 (yrI — Dt)a ; t = 0,1,2,... t t-1 where: 27 2 a(1—y0P/y a(1—y411— YYN (A.6) A= (1—a)(1—yOyN R[1—(1—a)(1—y6)]
(_ a(1—y)R YYN (A.7) a.
1 — (1—a)(1 — y6)Id)
.ar.
0 4147=0(k)eT t+T et (A.8) Dt
0 (• where 0t is defined in (17) and I is the 2x2 identity matrix. We also have an initial and a terminal condition. The initial condition is on b -1 and the terminal condition is (23) in the text; i.e.;
(A.9) b .6 -1 -1
—t (A.10) lim R bt= 0 t->03
Now, the no—intervention solution is obtained by choosing g = 0, which implies et. 0 and Dt. 0 for all t. In this case (A.5) is a homogeneous system whose general solution is:
) (A.11) y (I -1 t+1 T — A) a A 1 751—1- ) where 28
a(1—y6)(1—y)R2 (I—A)aTI YY (R—Y) (A.12) N A (:) 1-611 and
(A.13) A = aR(1—yó)(1—y)/y (1—ydR)(R—y)/y
However,
t —1 (A.14) AtA = VA.V
where is a diagonal matrix with eigenvalues of A on the diagonal and V
is a matrix of corresponding eigenvectors. We normalize so that
(x 0 2 A = 01 x 2) (1 )
where:
(A.15) xi = ;fu (-1)10747], i. 1,2
(A.16) p = (1—a)- 1- y6) a(1+6)
Then:
2 x. — — (1—a)(1 — y6)] (A.17) a(1—yOR vi y IyA - , i = N q1—a(1—y(5).11 (1—a)(1—YOYN 1,2
Substitution of (A.12) and (A.14) into (A.11) gives us: 29
(A.18a) PI. [v,,(15- 1-0-v L P + v2-1/1' c. iv2(54-Bnx2 -[vicrY i-P)-viv2(6.4-Bnxi )
(A.18b) St = B +v-2-1([F-1-13-v1(E-1-B)]Ari - [17-14-v2(5-1-B)]xri}
R Now, since p > 1+6 and is increasing in II, then A >4(1+6)41+6)2 2 2 2 -7116].R On the other hand, Ai is declining in II. Therefore xi <
.6R < R. Hence, since vl < 0 and v > 0 the 2 terminal condition
(A.10) is satisfied * (A.18b) if and only if:
(A.19) = P "F. v1(5-1 B)
This determines the initial value of P 1. Substituting A.19) into (A.18) yields:
t+1 (A.20a) 'Ft = P + vl(g_l - 6)),
(A.20b) 5t = B + (5.4 -
where A = xi. Equation (A.20b) is presented in the text as equation (24).
In order to obtain a solution to (Tt,Et) we first use (A.4) and (A.20a) to calculate:
(A.21) 1 T't (1 - v (E-1 -
Then, substituting (A.21) into (22) we obtain:
YN Y O1 AR ct TI-(1 - 1)13 + - (1 ---ME -B)At a -1 Hence
(A.22) C - z(5_1-B)xt 30 1)/a. where C =yN(1—y/R)P/a and z =—yNvi
This is the equation given in (25).
g > 0 observe that: In order to solve the system for the case
T-1 t >T (A.23) Dt = D = (R-1)R gI, for
system for which we can apply Hence, for t > T (A.5) describes a hompgeneous (5t,13). This yields the the same procedure that was used to calculate
counterparts of (A.20ji t—T .P + v (b — B )A • t > T (A.24a) Pt g l T g t—T b B + (b — 13 pt • t > T (A.24b) tgT g
where: a(1—Y0(1—y)R2 YYN(R—Y) T-1 (A.25) "EL- YT (R-1)R = 1 1-6R Bg ) (f
to calculate (PT,bT) as functions Using forward iterations of (A.5) in order t.T, we obtain a system of three of (P...1,g), and (A.24a) evaluated at
(PT, bT, P_1) as functions linear equations which enable us to solve to calculate (Pt, bt) for of g. Having calculated P_.1 we use (A.5) t) for t > T. Having 0 < t < T and (A.24) to calculate (Pt,b
calculated the sequence (Pt,b0 4 we calculate Tables 2 and 3 were computed by fik,c0t=0 using (A.4) and (22). means of this procedure. REFERENCES
Aschauer, David and Greenwood, Jeremy, "A further exploration in the theory
of exchange rate regime," Journal of Political Economy, 91, (October
1983), 868-875.
Barro, Robert J., "Are government bonds net wealth ," Journal of Political
Economy, 82 (November/December 1974), 1095-1117.
Blanchard, Olivier, J., "Debt, deficits and finite horizons," Journal of
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Dornbusch, Rudiger, "External debt, budget deficits, and disequilibrium
exchange rates," in G.W.Smith and J.T.Cuddington (eds.), International
Debt and the Developing Countries (Washington: The World Bank, 1985).
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utility of money," Journal of Monetary Economics, forthcoming.
Frenkel, Jacob A. and Razin, Assaf, "BudgeX deficits and rates of interest
in the world economy," Journal of Political Economy, forthcoming.
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stabilization, liberalization, reform," in Carnegie—Rochester Series on
Public Policy 17 (1982): 115-152.
Helpman, Elhanan, "An exploration in the theory of exchange rate regimes,"
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Helpman, Elhanan and Razin, Assaf, "Towards a consistent comparison of
alternative exchange rate regimes," Canadian Journal of Economics, 12
(August 1979), 394-409.
• Helpman, Elhanan and Razin, Assaf, "The role of saving and investment in
exchange rate determination under alternative monetary mechanisms,"
Journal of Monetary Economies, 13 (May 1984), 307-325. Lucas, Robert, E.Jr., "Interest rates and currency prices in a two—country
world," Journal of Monetary Economies, 10 (November, 1982), 335-360.
Polak, J.J., "Monetary analysis of income formation and payments problems." IMF Staff Papers, 6 (November 1957-58), 1-50. TABLE 1: ARGENTINA
1978 1979 1980 1981
Index of Real Exchange Rate' 100 73 •72 85 Index of Real Private Consumption2 • 100 101 109 107 Trade Balance2 (millions of U.S. dollars) 2,913 1,782 —1,373 712 Reserve Gains2 (millions of U.S. dollars) —2,297 —4,381 2,749 3,437
Sources:
1 Dornbusch (1985) 2 International Financial Statistics
CHILE
1978 1979 1980 1981
Index of Real Exchange Rate 1 100 88 75 Index of real private consumption 2 100 119 122 132 Trade balance2 (millions of U.S. dollars) —426 —355 —764 —2,677 Reserve Gains2 (millions of U.S. dollars) —724 —1,128 —1,402 —77
Sources:
1 Harberger (1982)
2 International Financial Statistics ISRAEL
1981 19821 19831 19841
Index of Real Exchange Rate2 100 96 91 98 Index of Real Pri— vate Consumption3 100 106 115 110 Trade Balance4 (millions of U.S. dollars) —1,371 —1,837 —2,741 —2,130 Reserve Gains5 (millions of U.S. dollars) —2,2806 —1,940 —2,307 —803
1 Length of year defined as quarter of previous year plus the first three quarters of the current year. This is done due to the fact that exchange rate management began in the last quarter of 1982. 2 Computed by means of the implicit price deflators of imports and GDP. These numbers are for calendar years. Therefore for 1982 the number represents an underestimation of the year 81 IV — 82 I — 82 II — 82 III. Source: Israel Central Bureau of Statistics.
3 Source: Israel Central Bureau of Statistics. 4 Current Account Balance minus Interest Payments minus Defense Imports. Source: Israel Central Bureau of Statistics.
5 Reserve gains minus public sector unilateral transfers. Source: Bank of Israel 6 1981 was an election year in which duties and taxes on imported durables waTreduced. TABLE 2
b + G t Pt = act bt bt .1 .1 g=0 g= g=0 g g= .1 (R-1)RT-'L (R-1)RT-
0 3.237 2.687 9.887 10.196 3.370 1 4.957 4.413 5.590 5.734 5.164 2 5.871 5.295 3.308 3.361 .6.121 3 6.356 5.723 2.096 2.098 6.632 4 6.613 5.905 1.452 1.423 6.905 5 6.750 6.050 1.110 1.060 7.050 6 6.823 6.128 .928 .868 7.128 7 6.862 6.168 .831 .766 7.168 8 6.882 6.190 .780 .711 7.190 9 6.893 6.202 .753 .683 7.202 10 6.899 6.208 .738 .667 ...v. 7.208
6.905 6.215 .722 .650 7.215
Y b bG N = YT = ' -1 - -1
R. 1.1, y. .9, 6 = .5, a. .7, T = 5
Case (iii) (6R < 1) TABLE 3
b + bG Pt = dct t t .1 .1 .1 g = 9 = g= g -1)R'-1 g (R (R4-1)RT4 (R.1)RT-1
- .733 - .739 .622 .623 - .733 -1.996 -2.007 1.099 1.099 -1.995 2 -4.169 -4.192 1.919 1.099 -4.167 3 • -7.911 -7.957 3.330 3.331 -7.907 4 -14.353 -14.446 5.760 5.761 -14.346 5 -25.445 -25.530 9.945 9.942 -25.430 6 -44.540 -44.614 17.148 17.141 -44.514 7 -77.416 -77.470 29.550 29.536 -77.370 8 -134.018 -.134.036 50.903 50.875 -133.936 9 -231.465 -399.091 87.664 87,613 -231.324 10 -399.236 -399.091 150,953 150.864 -398.991
CO ema0 Co
yN yT.= 1, b 1 = b!, = 0
R. 2, y. .9, iS = .5, a. .7, =5
212_111 .(ya > 1)
I _J