Policy, Research, and External Affairs
WORKING PAPERS
Macroeconomic Adjustment
and Growth
Country Economics Department
The World Bank
December 1 990
WPS 562
Anticipated
Real Exchange-Rate
Changes
and the Dynamics
of Investment
Luis Serven
Unanticipated changes in the real exchange rate affect invest-
ment through their impact on the desired capital stock, whose
direction depends on a number of factors and is in general
ambiguous. In contrast, anticipated changes can also have an
important effect on the optimal timing of investment, in a
direction that depends on the financial openness of the economy
and on the import content of capital goods. This issue is explored
using a simple macroeconomic model.
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Policy, Research, and External Affairs
Macroeconomic AdJustment
and Growth
WPS 562
This paper- a product of the Macroeconomic Adjustment and Growth Division, Country Economics
Department - is part of a larger effort in PRE to study the response of private investment to
macroeconomic adjustment measures. Copies are available free from the World Bank, 1818 H StreetNW,
Washington DC 20433. Please contact Susheela Jonnakuty, room NI 1-039, extension 39076 (50 pages,
with charts and figures).
The impact of permanent real depreciation on a a boom, since the depreciation amounts to
country's capital stock is uncertain. Whether removing a tax.
total capital stock rises or falls depends on how
depreciation affects aggregate demand, the real Such a pattem could lead the uninformed
interest rate, and especially the import content of observer to conclude that the real depreciation is
capital goods. In the long run, the capital stock "contractionary" in the first case and "expan-
can be expected to rise in traded goods and fall sionary" in the second. In fact, the sharp change
in nontraded goods. in the investment trend could largely reflect the
elimination of the transitory (positive or nega-
Despite this long-run ambiguity, anticipated tive) investment incentive. These speculative
(as opposed to unanticipated) changes in real investment swings will be larger the smaller the
exchange rate have a predictable effect on the adjustment costs associated with capital accu-
dynamics of capital accumulation. They provide mulation.
an incentive for speculative reallocation of
investment over time, so they can greatly distort These results agree broadly with the experi-
the timing of investments. ences of Chile and Uruguay in the late seventies
and early eighties. The exchange-rate-based
In the framework Serven presents, the time disinflation attempted in both countries led to a
profile of investment is related to how finan- real overvaluation and growing expectrtions of
cially open an economy is and to the import real depreciation. Chile - which had a rela-
content of capital goods. tively closed capital account and a high import
content of investment - witnessed an invest-
When a real depreciation is expected, an ment boom. Uruguay, on the other hand, which
investment boom is likely to develop if the is financially fairly open, experienced an
import content of capital goods is high relative to investment slump.
the degree of capital mobility: the anticipated
depreciation promotes flight into foreign goods. Similar results apply to consumers' spend-
Conversely, with high capital mobility, the ing on durable goods. These spending fluctua-
opposite investment pattem is likely to emerge, tions simply reflect changes in the optimal
as the anticipated depreciation promotes flight timing of consumption and investment - but
into foreign assets. they obviously have a strong destabilizing
potential. This suggests the importance of real
In the first case, the investment boom will be exchange rate stability to avoid persistent over-
followed by a slump when the depreciation or undervaluations. When exchange rate action
actually takes place, as it amounts to removing a is justified, it should be undertaken immediately
transitory subsidy to investment. In the second to prevent distortions in the intertemporal
case, the predepreciation slump will give way to allocation of spending.
|he PRE Working Paper Series disserninates the findings of work under way in the Banr's Policy, Research, and Extemal
Affairs Complex . An objective of the series is to get these findings out quickly, even if presentations are less than fully polished.
'Me fimdings, interpretations, and conclusions in these papers do not necessarily represent official Bank policy.
Produced by the PRE Dissemination Center
Anticipated Real Exchange Rate Changes
and the Dynamics of Investment
by
Luis Serven*
Table of Contents
1. Introduction 2
2. Anticipated real exchange rate changes and investment: 4
two stylized cases
3. The model 6
3.1 The long run 12
3.2 Anticipated exchange rate changes and the timing 16
of investment
3.3 The dynamics of an anticipated real depreciation 19
4. Concluding remarks 29
References 32
Charts 34
Figures 36
Appendix A: The dynamic model 44
Appendix B: Solution of the model 45
* I thank Rudiger Dornbusch for helpful comments and suggestions.
Tina Almero and Bilin Neyapti provided research assistance.
1 - Introduction
With real depreciation being a key comnponent of most macroeconomic
adjustment programs, the possibility that it may have an adverse effect on
investment (and hence on growth) has recently attracted some attention. Different
reasons for such anti-investment bias have been pointed out: first, the high
import content of investment goods in most LDCs implies that the real cost of
new capital goods will rise with a real depreciation, thereby discouraging
investment1; second, the adverse real income effect of a real depreciation may
depress aggregate demand and thus reduce firms' desired capacity2; third, without
monetary accomodation, exchange depreciation may result in a liquidity squeeze
that raises interest rates and thus the cost of capital, also depressing
investment.
Obviously, all these arguments are concerned with the impact of a real
depreciation on the desired capital stock, and thus they are subject to the
criticism that the response of the latter will be very different in the tradable
and nontradable sectors, with the effect on aggregate investment being in
principle uncertain3. Moreover, these arguments do not provide any insight on
the dynamics of investment, that is, the path along which the desired capital
stock will be reached. For that purpose, the distinction between anticipated and
unanticipated real depreciations is crucial.
Anticipated real exchange rate changes can have a substantial impact on
1 This has been pointed out by Branson (1986) and Buffie (1986).
2 This follows from the 'contractionary devaluation' literature; see e.g.
Krugman and Taylor (1978). If the private sector is a net debtor in foreign
currency, then a real depreciation would also have an adverse wealth effect,
which could similarly lead to reduced investment ((Easterly, (1989)).
3 This has been emphasized by Lizondo and Montiel (1989).
3
the timing of investment -- quite apart from their effect on the optimal capital
stock. There are two reasons for this. The first one is the well-known fact that
antic;ipated real exchange rate changes will be reflected to some extent in the
real interest rate; for example, pending a perfectly anticipated real
depreciation the real interest rate and the user cost of capital are temporarily
high, and investment must be temporarily low. The secord reason is that
anticipated real exchange rate changes affect the expected time path of the real
cost of new capital goods, again due to their import content; pending a real
depreciation, investment goods imports are transitorily cheap and thus investment
must be transitorily high4. The combination of these two factors determines the
optimal allocation of investment over time. Through this mechanism, anticipated
real exchange rate changes can lead to wide investment swings, whose precise
direction depends on the import content of capital goods and on the degree to
which real interest rates incorporate exchange rate expectations --or, 3n other
words, on the degree of financial openness of the economy.
Hence, the import content of capital goods and the degree of capital
mobility are two key ingredients in determining the effect of anticipated real
exchange rate charges on investment. The third ingredient is of course the
evolution of the optimal capital stock. In this paper we use a simple model to
examine the role of each of these factors in shaping the time path of investment.
The paper is organized as follows. First, in Section 2 we provide an illustration
of the behavior of investment in two historical ep'sodes of transitory real
appreciatio. and anticipated depreciation. In Section 3 we set up the formal
model, and we use it to explore the role of the different determinants of
investmt..nt and to analyze the dynamics of investment under alternative expected
4This argument was first proposed by Dornbusch (1985).
4
real exchange rate trajectories. Finally, Section 4 concludes.
2 - Anticipated real exchange rate changes and investment: two stylized cases
An interesting illustration of the behavior of investment under
expectations of real exchange rate changes can be found in the transitory real
appreciation episodes associated with exchange rate based stabilizations5. In
these policy experiments, the rate of nominal depreciation is redaced to slow
down inflation; since the latter displays substantial inertia in the short run
(due to backward-looking wage indexation, or to the slow adjustment of
expectations), the result is a real appreciation. The latter is very likely to
be perceived as a transitory phenomenon, that will be reversed by the eventual
fall in inflation (if the stabilization succeeds) or by a return to a higher rate
of devaluation (if the stabilization fails). Thus, such experiments represent
clear-cut cases of transitory real appreciation and anticipated depreciation.
Two stylized examples are provided by the stabilization attempts of the
late seventies in Chile and Uruguay. In order to fight inflation, both countries
adopted a policy of preannounced devaluation (the 'Tablita'), according to which
the rate of nominal depreciation was gradually reduced. In Chile, the
preannouncement scheme was introduced in February 1978; in June 1979, the rate
of depreciation was reduced to zero, and thus the nominal exchange rate was left
unchanged until June 1982. As documented by Corbo (1985), the combination of
a fixed nominal exchange rate with wage indexation to lagged inflation led to
a growing real appreciation. By 1981, the cumulative real appreciation was close
to 30 percent (Chart 1), and doubts about the sustainability of the exchange rate
5 This is a particular case of the 'expenditure cycle' associated with
exchange rate based stabilizations, which has been documented by Kiguel and
Liviatan (1989).
5
were widespread.
During this real appreciation stage, an expenditure boom developed. The
major ingredient was the spectacular expansion of private investment, which in
real terms more than doubled in 1978-81, and as a ratio of real GDP rose over
ten percentage points in these years.
In Uruguay, the preannounced depreciation strategy was adopted in October
1978. The regime lasted until November 1982, when the exchange rate was finally
allowed to float. As inflation proved stubborn, the result again was a persistent
real appreciation -- which by late 1982 exceeded 30 percent -- along with
increasing expectations of real depreciation. However, in sharp contrast with
the case of Chile, the overvaluation was accompanied by a private investment
slump: the share of private investment in real GDP rose initially in 1979 and
then fe'l about 4 percentage points in 1980-81 (Chart 2).
Although the performance of private investment in these two episodes
undoubtedly was the result of a number of factors, it seems clear that the
evolution of the real exchange rate must have played an important role6. As
argued above, there arq two main mechanisms (not mutually exclusive) through
which the transitory real appreciation may have affected investment. The first
one emphasizes the 'desired' capital stock as the force driving investment. It
would imply that in Chile the real appreciation contributed to increase the
optimal capital stock, due perhaps to its strong favorable effect on the real
cost of capital goods imports, and maybe also to a favorable aggregate demand
6 The trade liberalization measures adopted by both countries (especially
Chile) in the seventies may be another factor in the observed investment
performance, as the mounting real overvaluation could have raised the expectation
of a reversal of the trade reforms.
6
effect7. However, in Uruguay these factors would have operated in the opposite
direction.
The second mechanism follows from the impact of anticipated real exchange
rate changes an the timing of investment. If the real appreciation is perceived
as transitory, its persistence will lead to increasing expectations of future
real depreciation -- and thus to the anticipation that the real cost of
investment goods imports will rise in the future. At the same time, the ex-ante
real interest rate will also rise to reflect the anticipated depreciation.
Depending on the relative strength of these two factors, their combTned effect
can be an investment boom or a recession. To verify if this argument can
contribute to reconcile the contrasting performances of private investment in
these two historical episodes, we need to define it more precisely -- a task to
which we now turn.
3 - The model
To explore these issues more formally, we use a simpie investment model
which explicitly incorporates the import content of capital goods, and allows
for the effect of real exchange rate expectations on the real interest rate.
First, following the standard cost of adjustment approach (see e.g. Hayashi
(1982)), investment is assumed to depend on the market value of existing capital
relative to its replacement cost:
(1) I = K*9i(V*P/PK) - 1] + 6K >0
7 For the case of Chile, the strong effect on investment of a reduction in
the real cost of new capital goods has been empirically confirmed by Solimano
(1990). His results also indicate that a real appreciation expands output in the
short run, and reduces it over the longer term.
7
where I is gross real investment, K is the capital stock and 6 its rate of
depreciation, V is the real market value in terms of domestic goods of one unit
of installed capital (i.e., the real price of equity), P is the domestic price
level, and PK is the price of new investment goods. The parameter K can be
related to the adjustment cost technology implicit in the investment equation
(1). Broadly speaking, the more rapidly adjustment costs increase with
investment, the lower *.8
The rate of capital accumnalaion is given by
(2) K = I - AK
Hence, net capital accumulation will cease when V=PK/P, that is, when the
market value of installed capital and its replacement cost are equalized; then
I = 6K. In turn, the price of new capital goods is a weighted average of the
prices of domestic goods and imports:
(3) PK = P7'el1'7 0<7<1
where e is the nominal exchar.ge rate (the foreign price level is assumed constant
and equal to one), and 1-7 is the unit import conten'. of capital.
The economy produces one single good, which can be sold domestically or
exported; the level of output is demand determined. We use a semi-reduced form
relating output to the real exchange rate and investment demand:
(4) Y = Y(e/P,I) Yl,Y2>0
8 For investment to be proportional to the capital stock, as in (1), the
adjustment cost function has to be assumed linearly homogeneous in I and K. We
could easily dispense with this assumption.
8
where Y is real output, and elP is the real erchange rate9.
Since monetary considerations are not our main concern here, wK. will
drastically simplify portfolio behavior. We assume that the an.icipated rate of
return on capital r, to which we shall refer as the 'domestic real interest
rate', depends on both domestic and foreign factors:
(5) r = pe(r*+E(eIe-P/P)] + (l-p)*j(Y, VeK) Opgl; Jl'J2kO
where the operator E(Z) denotes the expected value of the variable Z. Equation
(5) can be viewed as the equilibrium condition in the equity market, inverted
to solve for r. The latter is expressed as a wei,`xicd average of the foreign real
interest rate adjusted for anticipated real depreciation, and of 'domestic
conditions' in the equity market, summarized by real output and the outstanding
real equity stock. The respective weights are given by p and 1-p, where p can
be interpreted as a direct measure of the degree of capital mobility: at one
extreme, with perfect capital mobility, p-l, so that the domestic and the
depreciation-adjusted foreign real interest rate must be equal. At the other end,
with a closed capital account, p=O, and the domestic real interest rate depends
only on domestic real output and on the outstanding stock of equity1o; an
9 Equation (4) could be obtained from the goods market equilibrium condition
Y = C(e/P, Y) + I + X(e/P) - (e/P)*[MC(e/P,C)+Hl(e/P,I)]
where C is real consumption, X are exports, and MC and HT are imports of
consumption and investment goods, respectively. Solving for Y, we would get an
expression similar to (4).
1OReduced-form interest rate equations similar to (5) have been widely used
to analyze the implications of alternative degrees of financial openess; see e.g.
Edwards (1986), Blejer and Gil-Diaz (1986). One important difference is that
these authors relate the real interest rate to conditions in the domestic money
market, rather than in the equity market used here; our approach amounts to
assuming that, with a closed capital account, equity market equilibrium can just
be expressed as VK - g(r,Y), with gl>O ,g2<0.
9
increase in either of these variables creates an incipient excess supply in the
market and leads to an increase in the real interest rate.11
An alternative rationalization of equation (5) is provided by the existence
of rationing in the domestic credit market12. Suppose :hat firms can finance
their investment with credit or with foreign indebtedness; assume further that
the interest rate on credit is administratively fixed below the market-clearing
level, and that the total amount of credit available to each firm is subject to
a ceiling. At any given time, the credit ceiling will be binding for some firms,
while others will still have access to additional credit. For the formar group,
the interest rate relevant for investment decisions is given by the depreciation-
adjusted interest rate on foreign debt (which represents the marginal source of
financing), while for the latter group it would equal the interest rate on
credit. In the aggregate, the relevant interest rate would be a weighted average
of these two (with the weights depending on the fraction of firms in each
financial regime), similarly to what is assumed in (5).
The anticipated rate of return on capital is the sum of profits plus
anticipated capital gains on equity
On the other hand, one possible criticism to (5) is that under imperfect
capital mobility it allows domestic and foreign real interest rates to be
different even in the long run. An alternative specification would be to express
the rate of change of the domestic interest rate as a function of its deviation
from interest parity (Edwards and Kahn (1985) 3rowne and McNelis (1990)).
Perfect capital mobility would then amount to an infinite speed of adjustlent
of the domestic interest rate, and in the long run interest parity would hold
regardless of the degree of capital mobility. However, the resulting investment
dynamics would not be qualitatively very different from those in the paper; thus,
we shall ignore this complication here.
11 The implicit rationale for an increase in real output to reduce the
excess demand for equity is that it would raise the transactions demand for more
'liquid' assets.
12 For a more detailed exposition, see Serven (1990).
10
(6) E(V/V) + (F/V) - 6 - r
where F are gross real profits (including depreciation) per unit of capital.
Equation (6) can be integrated forward to express the market value of capital
V as the present discounted value of expected future profits, with the discount
rate equal to r+6. In long run equilibrium, profits and the user cost of capital
must be equal, i.e., F = (r+6)V. In turn, real profits are an increasing
function of the output/capital ratio (or the rate of capacity utilization):
(7) F = F(Y/K) F'>U
It will be useful to denote the real exchanp' rate as X _ e:P . Hence, we
can write the relative price of capital goods in terms of domestic goods as
(8) PK/P = X1-7
Thus the real cost of new capital goods rises with the real exchange rate.
Similarly, we define Tobin's Q as the market value of capital relative to its
replacement cost:
(9) Q _ V*P/PK - V/(X1-7)
where we have used (8). Also, we can define the real interest rate ir terms of
capital goods as
(10) rK E r + E(P/P - 4K'PK) = r - (l-7)-E(Xi/X)
Thus, rK differs from r due to the anticipated change in the relative price of
capital goods, which (from (8)) is proportional to the anticipated rate of real
depreciation; in the long run, with a constant real exchange rate, r-rK.
11
From (8), (9) and (10), it follows that the anticipated rate of change of
Tohin's Q is just
(11) E(Q/Q) = rK + 6 -
In turn, from (1) and (9) the rate of capital accumulation is
(12) K . K*O.[Q-1]
Combining (4), (5), (7), (8), (11) and (12), the model can be reduced to
a system of two dynamic equations in Tobin's Q and the capital stock, with the
real exchange rate and its anticipated rate of change as the forcing variables.
However, to complete the model we need two additional elements. First, we have
to specify how the real exchange rate is determined. Since for our purposes the
precise form in which real exchange rate changes are generated is not directly
relevant, it will be convenient to assume throughout that the real exchange rate
is set exogenously. This can be viewed as resulting from the combination of a
managed nominal exchange rate and some source of nominal rigidity in the economy
(e.g, incomplete wage indexation)13. Hence, we shall not concern ourselves with
the separate determination of domestic prices and the nominal exchange rate.
Finally, we must specify how expectations are formed. We shall assume that
13 For example, the model could be completed with a price equation of the
type
P -s oe
where so is a parameter, W is the nominal wage and s the share of labor in
variable costs. This can be rewritten
X - (e/P) = (1/so)e(W/e)-s
Thus, with such pricing behavior, a real depreciation amounts to a cut in the
real wage in terms of foreign goods. In turn, this could be implemented either
through a nominal wage cut with a given nominal exchange rate or, perhaps more
realistically, through a nominal depreciation accompanied by a less than
proportionate (or zero) nominal wage adjustment.
12
expectations are rational; hence the expected and actual values of the variables
in the model can differ due only to the arrival of unanticipated information -
- that is, at times of unanticipated shocks.
In order to solve the dynamic system under rational expectations, it is
important to note that the capital stock is a predetermined variable, while
Tobin's Q is not. At any given instant, the capital stock is given by past
investment decisions, and cannot jump in response to new information about the
paths of the exogenous variables. In contrast, Q is free to jump instantaneously
in reaction to unanticipated information about the present and/or future values
of the forcing variables.
To facilitate the manipulation of the model, it is convenient to linearize
it around the steady state (see Appendix A). As shown by Buiter (1984), the
linearized system has a unique solution if and only if it possesses saddlepoint
stability. This amounts to the requirement that the two eigenvalues of the
transition matrix have opposite signs. In economic terms, such requirement is
met if and only if an increase in the capital stock raises profits per unit of
capital by less that the user cost of capital. In particular, a sufficient
condition for this to hold is that an increase in the capital stock raise output
less than proportionately, so that the output/capital ratio (and hence unit
profit) falls. Under such condition14, the dynamic system has a unique solution,
which is 'forward looking' in the sense that Tobin's Q will depend on the past
only through its effect on the capital stock.
3.1 - The long run
14 Under perfect capital mobility (p=l), this condition is also necessary.
See Appendix B.
13
To understand the dynamics of investment in this model, we need to examine
first the long-run effects of real exchange rate changes. These are
straightforward: in the long run, the level of the real exchange rate affects
the optimal capital stock directly through its effect on the real cost of new
capital goods, and indirectly through its impact on real output and the real
interest rate.
In the steady state the capital stock, Q, and the real exchange rate are
constant. From (12), Q must equal unity, while from (11) real profits per unit
of capital must equal the user cost of capital. Replacing (5), (7) and (8) into
the long-run version of (11), it follows that
(11') [pr* + (l-p).j(Y(X, l[7-]), 61-7*) + d 21-7)
= F(Y(R, R[(-l])It)
where we have denoted the long-run values of the variables by an overbar.
The steady state is depicted in Figure 1 as the intersection at point A
of the horizontal line drawn for Q=l and the qq line that represents equation
(11'). The latter can be upward or downward sloping depending on whether an
increase in Tobin's Q, given the capital stock, raises real unit profits (the
right-hand side of (11')) by more or by less than the user cost of capital (the
left-hand side). Following Blanchard (1981), we label these alternatives the
'good news' and 'bad news' cases; they are respectively depicted in Figure l(a)
and l(b). In the good news case, a higher Q must be matched by a higher capital
stock, in order to restore the equality between profits per unit of capital and
its real user cost; hence, the qq schedule must be upward sloping. In the bad
news case, the opposite happens. In particular, perfect capital mobility (p-l)
is sufficient for the good news case to obtain.
14
The consequences of a change in the long-run real exchange rate rate can
be easily illustrated. Consider first the case when domestic conditions have no
effect on the real interest rate (p=l); then the real depreciation raises the
real cost of capital only due to its import content. At the same time, it raises
profits through its expansionary effect on output. Hence, the net result is
ambiguous: intuitively, if the import content of capital is small relative to
the impact of the depreciation on output and profits, then a real depreciation
raises the steady-state capital stock. Graphically, the qq schedule shifts to
the right. In the alternative case, it shifts to the left, and the long run
capital stock falls (Figure 2).
Consider now the general case of imperfect capital mobility (pO is the elasticity of output with respect to the real exchange rate
(i.e., aQY,(e/P)/Y); B>0 is the investment multiplier (8%Y2); a>0 is the
elasticity of unit profit with respect to the output/capital ratio
(i.e.,a-(Y/K)F'/F); 1>si>0 is the output share of investment; e and U
respectively denote the semi-elasticities of the real interest rate with respect
15
to output and to the real equity stock (both assumed non-negative); and D is a
parameter combination which is positive if and only if the dynamic model is
saddlepoint stable.
The term in square brackets in this expression captures the three effects
described above. First, the profitability effect is the positive direct impact
on output (via a) and thus on profits (through a) of the real depreciation;
second, the adverse impact on the real cost of capital goods due to their import
content is captured by the term (1-7); third, the interest rate effect is the
combined impact on the equity market of the output increase (through e) and of
the higher value of equity in terms of domestic goods (which raises the interest
rate through 0).
The net impact on the capital stock is therefore uncertain. Clearly, the
larger the import content of capital 1-7, the more likely a reduction in the
capital stock. Note in particular that the ambiguity persists even in the case
of perfect capital mobility, in which the real incerest rate is constant across
steady states. The relevant condition for the long run capital stock to rise
then is that the profitability effect aa exceed the unit import content of
investment 1-7. If the latter is nil, then the capital stock must rise.
It is clear that, even if the long run capital stock falls, long-run output
may rise due to the direct impact of the real exchange rate on demand. The long
run output change is given by
(14) (AY!Y) = a(AXIX)+13s(AK/K)
= (lg D)sav(ele-p)+o(r+6)]-test(1-7)(heo-p)+r+6um(tiXsi)
Thus, if capital goods have zero import content, then output must rise in
16
the long run with a real depreciationl5. The larger the import content of
investment 1-7, the more unlikely a real depreciation is to result in output
expansionl6.
3.2 - Anticipated Exchange rate Changes and The Timing of Investment
The long run analysis above illustrates the effect of the real exchange
rate on the long-run capital stock. However, in the model the anticipated time
path of the real exchange rate also affects the optimal investment path or, in
other words, the time profile of the accumulation process by which the optimal
capital stock will be reached.
This is apparent from equation (11), which expresses the anticipated time
path of Tobin's Q in terms of the real interest rate and the profit rate, both
in terms of capital goods. For a given profit rate, a high (low) rK implies a
rising (falling) path for Tobin's Q and hence also for investment. From (5) and
(10), the effect on rK of a change in the anticipated rate of depreciation is
just
8 rK
(15) E(iX) = p _ (1-7)
which summarizes the two opposing effects described earlier. First, the capital
gain effect 1-7, through which an increase in the anticipated rate of
15 Notice also that if the impact of a real depreciation on noninvestment
demand is contractionary (i.e., ap), the expected depreciation reduces
rK, and investment must rise relative to the future. The depreciation thus
promotes flight into foreign goods, and amounts to a transitory subsidy to
investment. 'rhus, the precise direction in which investment is intertemporally
reallocated depends on institutional features of goods and assets markets.
Notice the contrast with the case of an anticipated future increase in
tariffs on investment goods. It is clear that in such case there is no asset
substitution affect, and the anticipated tariff increase would just amount to
an anticipated capital gain (of magnitude 1-7) on early investment. Hence, it
would unambiguously result in a transitory investment boom.
18
How does this agree with the empirical facts? We can return to the two
episodes of transitory real appreciation and anticipated real depreciation in
Chile and Uruguay that we described earlier. In Chile, the degree of openness
of the capital account of the Balance of Payments in the late seventies and early
eighties was limited; empirical equations simtlar to (5) yield an estimatel7 of
the degree of openness p below 1/4. In contrast, the import content of investment
averaged about 40 percent in 1977-81; in particular, about 90 percent of
machinery and transport equipment was purchased abroad in that periodl8. Thus,
our model suggests that in the case of Chile an anticipated real depreciation
should reduce the ex-ante real interest rate in terms of capital goods and thus
promote a transitory investment boom -- which seems in broad agreement with the
observed patternl9.
In contrast, the financial liberalization of the late seventies had left
Uruguay's capital account very open. Domestic and depreciation-adjusted foreign
interest rates moved closely together in 1978-82; in fact, the corresponding
empirical estimates of the deg-ee of capital mobility p are very close to
inity2 , exceeding the import content of investment by a wide margin. Under such
17 See Edwards (1986).
18 See Banco Central de Chile (1986). These figures refer to total
investment; the import content would probably be much higher in the case of
private investment, since a large portion of public investments take the form
of construction and public works, whose import content is nil.
19Again, the suspicion that the trade liberalization of 1977-79 might be
just a transitory phenomenon and could be followed by tariff increases may have
played also an important role in the investment boom. As noted in the text, an
expected tariff rise would unambiguously reduce rK -- adding also to the
transitory investment boom.
20 The results reported by Blejer and Gil Diaz (1986) yield a value of p
equal to one. Hanson and De Melo (1985) reach the same result for the long run;
however, their short-run estimate of p is only .43 . Nevertheless, even this
latter value appears substantially larger than the import content of aggregate
19
costditions, it follows that the ex-ante real interest rate in terms of capital
must rise when a real depreciation is anticipated; pending the anticipated
depreciation, there should be an investment slump -- which again does not seem
to disagree with the observed investment performance21.
3.3 - The Dynamics of an Anticipated Real Depreciation
This discussion can be formalized solving the model for the time paths of
the capital stock and Tobin's Q, for a given time path of the real exchange rate.
The dynamics of investment will reflect the combination of the two factors
described earlier: the 'desired' capital stock at each instant, and the optimal
timing of investment. Formally, let K(t) denote the capital stock that would
obtain in the long run if the real exchange rate were to equal X(t) forever; in
other words, K(t) is the optimal capital stock associated with the constant real
exchange rate X(t) (thus, in particular, K(U)=R). Then the time path of K can
be written22
(16) K(t) = )X[K(t) - ft0 h(t,r)*Et[K4r)]edT]
+ ($Ip)e(l-7-p)'[ftmh(t,r)Et[(r)]odr]
where XO respectively are the stable and unstable roots of the dynamic
investment, which for 1978-82 averaged about 15? (World Bank (1988)).
21 Obviously, while the observed facts are in line with our analytical
results, we are not trying to imply that the investment performance in Chile or
Uruguay can be explained exclusively by the time path of the real exchange rate;
in both cases, other factors played an important part. However, the real
appreciation undoubtedly had a major role. More complete descriptions of the
macroeconomic events of the late seventies and early eighties in Chile and
Uruguay can be respectively found in Corbo (1985) and Hanson and De Melo (1985).
22 Details are given in Appendix B.
20
system. The first line of (16) is the desired capital stock compcnent; it causes
the capital stock to change in proportion to its deviation from a weighted
average of expected future optimal capital stocks, with the weights given by the
function h(t,'r)23. Loosely speaking, it depends only on the discrepancy between
the actual and optimal capital stocks. The second line in (16) is the speculative
or intertemporal reallocation effect; it relates the rate of change of the
capital stock to a weighted average of future anticipated rates of real
depreciation. In particular, it is completely unrelated to the discrepancy
between the current capital stock and its future optimal value.
To examine in more detail the dynamics of an anticipated permanent real
depreciation, let us consider first the case of a gradual real depreciation.
Specifically, assume that, starting from long run equilibrium at time zero, the
rate of real depreciation becomes positive, and the real exchange rate is
continuously depreciated until time T; from instant T on, the real exchange rate
stays constant. Thu in the interval between 0 and T there is a perfectly
anticipated real depreciation; for simplicity, we further assume that the latter
proceeds at a constant rate.
It may be instructive to separate the two factors determining investment.
Consider first the case of no speculative effect, that is, 7+p=1 (thus the second
line in (16) vanishes). Then the real interest rate in terms of capital goods
is unaffected by the anticipated rate of depreciation, and the dynamics depend
only on the change in the optimal capital stock. This is illustrated in Figure
3, which reflects the case of an expansionary long-run effect on the capital
stock (the contractionary case is analogous). Starting from the long run
23 The weights are given by h(t,T)=jexp{#(t-'r)}; thus they are positive and
(exponentially) declining in r, with ft h(t,'T)dT - 1.
21
equilibrium A at time zero, there is an upward jumr in Q to Q(O), which
immediately raises investment and output. In Appendix B we show that Q(O) is
given by
(17) Q(O) = 1 + H*(l-e-#T)T-l -2.(AR/X)
where H E {(r+6)-[O-(l-7)J - (l-p)-(ae+(1-7)0)) is just the term in square
brackets in (13), and hence it is positive (negative) if and only if the desired
capital stock rises (falls) with a higher real exchange rate; and AR is the long-
run real exchange rate change (thus T-1(AR/R.) approximately equals the
percentage rate of real depreciation in the interval between zero and T). Hence,
given the magnitude of the depreciation and its impact on the long run capital
stock, the initial jump in Q is smaller the longer the time interval T over which
the depreciation takes place, and also the larger the unstable root of the
system.
After the initial jump in Q and investment, two adjustment patterns are
possible. If the increase in Q raises profitability by more than the real
interest rate (i.e., in the good news case, depicted in panel (a) of Figure 3),
then following its initial jump Q must be falling, and capital accumulation is
decelerating. In the bad news case (Figure 3(b)), Q keeps rising (and investment
increasing) for some time, with the length of this expansionary phase increasing
with that of the depreciation stage T; however, Q and investment must start
declining before time T. When the rate of depreciation returns to zero at instant
T, the system must be at point AT on the se schedule in Figure 3a, which
describes the unique trajectory along which the model will converge to the new
long run equilibrium at A'. In both the good news and bad news cases, Q keeps
falling and K rising after instant T towards their long-run values. Hence,
22
throughout the adjustment Q remains above, and K below, the steady state level.
In other words, the adjustment is monotonic, and, in particular, the capital
stock cannot overshoot its long-run level. Obviously, in the absence of any
incentives to the intertemporal reallocation of investment, there is no reason
for overaccumulating capital.
Let us now turn to the more interesting case of no effect on the desired
capital stock, but a non-zero speculative effect. Throughout, the desired capital
stock remains unchanged, and the anticipated depreciation affects only the time
path of investment (i.e., the first line of (16) is zero). Thus, investment will
initially rise or fall depending on the sign of the intertemporal reallocation
effect. The initial value of Q is now
(17') Q(O) = 1 + 11-7-P]-(l-e-T)T(T)-l(AX/X)
Hence, as argued above, if the unit import content of capital 1-7 exceeds (falls
short of) the degree of capital mobility as measured by p, Tobin's Q and
investment must rise (fall) initially. Of course, the reason is that the initial
effect of the anticipated depreciation is to reduce (raise) the real interest
rate in terms of capital goods. From (17'), the jump in Q is proportional to the
magnitude of the intertemporal reallocation term 1-7-p ; again, it is smaller
the longer the depreciation interval T and the larger the unstable root of the
system #.
The two alternatives are depicted in Figure 4(a) and 4(b) respectively.
Since their dynamics are analogous, we focus on Panel (a), which corresponds to
the case of high import content relative to the degree of capital mobility. The
initial rise in Q (to Q(O)) is followed by a gradual decline; net investment
slows down and, eventually, becomes negative before T. Thus, there is a clockwise
23
movement from Ao to AT. At instant T, the system must be at a point such as AT
on the original saddle path, with the capital stock exceeding its initial (and
final) level; the excess capital is then gradually eliminated.
What about the general case of nonzero long-run effect and nonzero
intertemporal effect? It is clear that the dynamics will be a mixture of the two
polar cases just examined. In the long run, the optimal capital stock may rise
or fall with the real depreciation; regardless of this, if the import content
of capital is high (low) relative to the degree of capital mobility, then
investment will be relatively higher before (after) instant T. Formally, the
condition for a transitory investment boom can be expressed in terms of the
initial change in Q, which is given by
(18) Q(0) - 1 + [(H//A) +
Hence, even if the capital stock falls in the long run (H0
where 9 is the (constant) rate of real appreciation. Hence, exchange rate
28 See Appendix B.
27
expectations will evolve as shown in Figure 7. The solid line represents the
expectations prevailing at a given instant to abcut the future path of the rate
of depreciation; the dotted lines correspond to the expectations that will be
held at later instants t2>tl>tO provided the depreciation has not yet taken
place. Notice that the first two schedules reflect an initial stage of
anticipated real appreciation (that is, the anticipated depreciation is initially
negative), followed by depreciation; however, the length of this expected
appreciation stage is shorter for t, than for to, and at a later time t2 no
further appreciation is expected anymore. This follows from the fact that as
time passes and the appreciation goes on, the cumulated real appreciation rises,
so that the real depreciation required to restore the original real exchange rate
grows larger -- eventually becoming the dominant factor. Thus, although initially
investors may expect the ongoing real appreciation to continue for some time,
they eventually will come to expect an increasingly large real depreciation29.
As should be clear from our previous discussion, such real exchange rate
path can generate substantial investment fluctuations. Again, let us focus on
the intertemporal reallocation effect. As before, the initial impact on
investment through this channel depends on the degree of capital mobility
relative to the import content of capital goods. Consider first the low capital
mobility case. Intuitively, at time zero investors anticipate an initial period
(of uncertain duration) of real appreciation; thus, if capital mobility is low
relative to the import content of capital goods, the ex-ante real interest rate
in terms of capital rises; Q and investment will initially jump down. However,
as shown in the previous figure, the anticipated appreciation is followed by
29Observe that this happens despite the fact that the instantaneous
probability of a real depreciation is constant. If, perhaps more realistically,
the latter were increasing over time, then this effect would be reinforced.
28
increasing expected real depreciation, so that immediately after its initial jump
rK is falling and Q must be rising. As time passes and the anticipated
depreciation fails to materialize, expected future real exchange rates are
continuously being revised upward, leading to a growing investment boom and to
an increasing overaccumulation of capital (Figure 8); moreover, the higher the
probability of instantaneous depreciation, the earlier the boom will develop,
and the more rapidly Q and investment will be rising.
Of course, these results are reversed if capital mobility is high. In that
case, there will be an initial investment rise, followed by an increasingly deep
recession as the growing anticipation of real depreciation leads to continuous
increases in the ex-ante real interest rate in terms of capital goods.
The other factor affecting investment is the change in the optimal capital
stock due to the changing level of the real exchange rate. Of course, in the long
run this effect vanishes (as the steady state real exchange rate is unchanged),
but in the short run it affects profits and the real interest rate, and hence
the desired capital stock at each instant is changing. As before, the joint
impact of the intertemporal reallocation effect and the desired capital stock
change on investment is in general ambiguous. Formally, the initial value of
Tobin's Q can be shown to equal
(21) Q(O) - 1 - (#+V) 2./-[((HI) + (l-7-p)].(9/X)
Notice that the larger 9 and the smaller the instantaneous probability of
depreciation r, the greater the size of the initial jump in Q; the reason is that
both factors increase the 'effective' anticipated appreciation rate. The
direction of the jump again depends on the weighted sum of the intertemporal
effect and the optimal capital stock effect.
29
4 - Concluding Remarks
Our results can be easily summarized. We have seen that in general the
impact of a permanent real depreciation on the desired capital stock is
uncertain; whether the aggregate capital stock rises or falls depends on the
effects of the depreciation on aggregate demand and on the real interest rate,
and, in particular, on the import content of capital goods. Moreover, the long-
run capital stock can be expected to rise in the traded goods sector and to fall
in the nontraded goods sector.
In spite of this lo-:g-run ambiguity, we have seen that anticipated real
exchange rate changes have a predictable effect on the dynamics of capital
accumulation. This is so because they provide an incentive for a speculative
reallocation of investment over time -- quite apart from their effects on the
optimal capital stock --, thus introducing potentially large distortions in the
timing of investment.
In our framework, the time profile of investment can be easily related to
the degree of financial opennes0 of the economy and to the import content of
capital goods: when a real depreciation is expected, an investment boom is likely
to develop if the import content of capital goods (measured by the parameter 1-
7 in the model) is high relative to the degree of capital mobility (which in the
model is summarized by the parameter p) -- the anticipated depreciation then
promotes flight into foreign goods; conversely, with high capital mobility the
opposite investment pattern is likely to emerge, as the anticipated depreciation
promotes flight into foreign assets. In the former case, the investment boom will
be followed by a slump when the depreciation actually takes place, as it amounts
to the removal of a transitory subsidy to investment; in the latter case, the
30
pre-depreciation slump will give way to a boom -- since the depreciation amounts
to the removal of a tax. Such pattern could lead the uninformed observer to the
(incorrect) conclusion that the real depreciation is 'contractionary' in the
first case and 'expansionary' in the second -- while in fact the sharp change
in the investment trend could to a large extent reflect the elimination of the
transitory (positive or negative) investment incentive. Also, these speculative
investment swings will be larger the higher the intertemporal substitutability
of investment -- or, in other words, the smaller the adjustment costs associated
with capital accumulation.
These results seem in broad agreement with the experiences of Chile and
Uruguay in the late seventies and early eighties. The exchange rate-based
disinflation attempted in both countries led to a real overvaluation and growing
expectations of real depreciation. In the process, Chile -- which had a
relatively closed capital account and a high import content of investment --
witnessed an investment boom; in contrast, Uruguay, characterized by a high
degree of financial openness, experienced an investment slump.
Although in the paper we have focused on investment, it is clear that
similar results would apply to consumers' expenditure on durable goods. Through
both channels, transitory real exchange rate changes lead to an intertemporal
reallocation of real expenditures and can generate large swings in real
absorption. While these expenditure fluctuations simply reflect changes in the
optimal timing of consumption and investment, they obviously have a strong
destabilizing potential. For example, the unjustified perception that a real
depreciation is imminent can lead to an expenditure boom -- causing a
deterioration of the external accounts that in fact forces the real depreciation
to be undertaken. From the viewpoint of macroeconomic and exchange rate policy,
31
this suggests that a stable real exchange rate path, avoiding persistent over-
or undervaluations, can play a major role in stabilizing expenditure and output.
Our results also support the view that, when the economic fundamentals warrant
exchange rate action, it should be undertoken immediately -- to prevent the
distortionary consequences that expectations of real exchange rate changes may
have on the timing of consumption and investment.
32
References
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Blanchard, 0. (1981): "Output, the Stock Market, and Interest Rates",
American Economic Review 71, p. 132-143.
(1984): "Current and Anticipated Deficits, Interest Rates, and
Economic Activity", European Economic Review 25, 7-27.
Blejer, M., and F.Gil-Diaz (1986): 'Domestic and External Factors in the
Determination of the Real Interest Rate: The Case of Uruguay", Economic
Development and Cultural Change, p.589-606.
Branson, W. (1986): "Stabilization, Stagflation, and Investment Incentives:
The Case of Kenya", in Economic Adjustment and Exchange Rates in Developing
Countries, S. Edwards and L. Ahamed, eds. The University of Chicago Press.
Browne, F. and P. McNelis (1990): "Exchange controls and Interest Rate
Determination with Traded and Nontraded Assets: The Irish-United Kingdom
Experience", Journal of International Money and Finance 9, p. 41-59.
Buffie, E. (1986): "Devaluation, Investment and Growth in LDCs", Journal
of Development Economics 16.
Buiter, W. (1984): "Saddlepoint Problems in Continuous Time Rational
Expectations Models: A General Method and Some Macroeconomic Examples",
Econometrica 52, p.665-680.
Corbo, V. (1985): "Reforms and Macroeconomic Adjustment in Chile during
1974-84", World Development 13, p.893-916.
Dornbusch, R. (1985): 'Overborrowing: Three Case Studies", in International
Debt and the Developing Countries, G. Smith and J. Cuddington, eds. World Bank.
Easterly, W (1989): "Devaluation in a Dollarized Economy", in Structuralist
Computable General Equilibrium Models, L.Taylor, ed. The MIT Press.
Edwards, S. (1986): "Monetarism in Chile, 1973-1983: Some Economic
Puzzles", Economic Development and Cultural Change, p.535-559.
Edwards, S. and M. Kahn (1986): 'Interest Rate Determination in Devloping
Countries", IMF Staff Papers p. 377-403.
Hanson, J. and J. De Melo (1985): "External Shocks, Financial Reform, and
Stabilization Attempts in Uruguay during 1974-83", World Development 13, p. 917-
939.
Hayashi, F. (1982): "Tobin's Marginal q and Average q: A Neoclassical
Interpretation", Econometrica 50, p. 213-224.
Kiguel, M. and N. Liviatan (1989): "The Business Cycle Associated with
33
Exchange Rate Based Stabilization", Mimeo, World Bank.
Krugman, P. and L. Taylor (1978): "The Contractionary Effects of
Devaluation", Journal of International Economics 8, p.445-456.
Lizondo, J. and P. Montiel (1990): wContractionary Devaluation in
Developing Countries: an Analytical Overview", IMF Staff Papers
Serven, L. (1990): "Financial Constraints, the Real Exchange Rate, and
Investment", mimeo, The World Bank.
Solimano, A. (1989): "How Private Investment Reacts to Changing
Macroeconomic Conditions: the Case of Chile", World Bank PPR Working Paper.
CHART I
CHILE: Private Investment (% of GDP)
and Real Exchange Rate (1980 = 100)
% of GDP RER Index
25- -120
20 11999 110
15(96 OF GDP) --9- RER_80
100
10
* ~~~~90
5
1975 1976 1977 1978 1979 1980 1981 1982 1983 1984
-+-( OF GDP) --y RER-..80
CHART 2
URUGUAY: Private Investment (% of GDP)
and Real Exchange Rate (1980 = 100)
% of GDP RER Index
14 160
140
12 - -~~~~3 - 140
120
10 13
110
8-- 1~~~~~s100
~~E~~~io
4 I l , l80
1976 1976 1977 1978 1979 1980 1981 1982 1983 1984
+ (% of GDP) --E-- RER-80
- 36 -
Figure .
The steady state
(a) Good news (b) Bad news
Q Q
q q
A
14+1 1
A
q
q
K K
- 3 -
Fiaure .
Long-run effect of a real depreciation (good news case)
(a) Expansionary (b) Contractionary
Q ~~~~~~~~~Q
q q' q' q
q' q' q
=_ - K
- 38 -
F4iure 3
Anticipated gradual depreciation
(Expansionary case, no intertemporal effect)
(a) Good News (b) Bad news
Q q
~~~~~~~~~tK
AT ~~~~~~~~AT
AO,
A A Al
qt s~~5
K K
- 39 -
Figure 4
Anticipated gradual depreciation
(No capital stock effect)
(a) Low capital Mobility (b) High capital mobility
Q Q
S S
K K
Figure 5
Anticipated gradual depreciation
Negative capital stock effect, low capital mobility
Q
s'
A0
1
K
Figure 6
Anticipated jump depreciation
No capital stock effect
(a) Low capital Mobility (b) High capital mobility
Q Q
I S
AO
",\ AT
K K
Figure 7
Anticipated Rate of Change
of Real Exchange Rate
Rate
of Depreciation t
t2 *,
0~~~~~~
to~~S
Periods Ahead
- _3 -
Figure 8
Transitory real appreciation
No capital stock effect
(a) Low capital Mobility (b) High capital mobility
Q Q
1 1
time time
44
Appendix A
The dynamic model
The dynamics of the capital stock are given by (12) in the text. To obtain
a dynamic equation for Tobin's Q in terms Q, K and the real exchange rate, we
proceed as follows. First, replacing (1) into (4) and using the definition of
Q, we have
(Al) Y - Y(X, K*-4[Q-1]+6K)
and thus profits can be expressed
(A2) F = F(Y(X, K.#-[Q-l1+6K)/K)
Combining these expressions with (5) and (10) in the text, the real interest rate
in terms of capital goods can be rewritten
(A3) rK = (l-p)*j(Y(X, K#[Q-l]+6K), QeX1-7K) - (1-7-p)E(X/X)
Thus the anticipated rate of change of Q (11) can be written
(A4) E(Q) - Q+[6 + pr* + (p+7-l)*E(X/X) + (l-p)*j(Y(X. KO[Q-1]+6K), QKX1-7)]
- F(Y(X, K*[Q-l]+6K)/K)-X7-1
Thus the dynamic system consists of (A4) and (12) in the text. Linearizing
around the long-run equilibrium, we get
K K-K X-X
(A5) E(Qj A* L Be E(+)
where we have defined the matrices
0
A [ K-1((eBu1+O)(1-p)+c(r+8) (1...Bs)] (ebs1It/b+D)(1-p)-(r+U)UBsI9I5 I
71{(EB+o(1-7) (
[-(Ea+G (1-7) (1-p) + (i+6) (1-7-oa) X1-1{p+7-1)
45
Appendix B
Solution of the model
The determinant of the matrix A in (AS) is
(Bl) JAI - -
Hence, s1O, (8X/I8)T
where Al is the change in the real exchange rate between instants 0 and T. Thus,
X(t)-R - T-1*(t-T).A6 for OT
Replacing these expressions into (B2) and (B3), and assuming perfect
foresight, we can write the final form equations for q and K as
(B5a) Q(t)-O - (pT(/A\)i1)Vl|[(l-7-P)[((p_)eXt + XeXt-/pT _ -e/(t-T)
* 0)Y1.*H*(p22(eXt.1) + X2ext(e-PT_l) + Xp(l-eP(t-T))] (A2/X) for tT.
(B6a) K(t)-t - *(pT)-1l[(1-7-p).()l(eXt-l) - (-)-le-#T(e#t-eXt )]
+ H*[i71(T-t) + (eXtl) +p1) l(-X)leT(eteXt
for tT.
47
Letting t-0 in (B5a), we get expression (18) in the text, which, for Hl0
and 1-'y-p-o, reduces to (17') and (17), respectively.
Using (B5) and (B6), we can verify the features of the adjustment path
mentioned in the text. First, when 1-7-p-o, so that no intertemporal reallocation
occurs, it is easy to see from (BSa) that the sign of (Q-0) is the same as that
of H; also, for tO Q declines continuously, as assumed in the diagram;
in the bad news case, it is positive up to instant t*, defined by
-* (pX)1- ln [p-2(2X2)epT_p-2X23
Thus t* is increasing in T. To see that in either case the capital stock cannot
overshoot its long-run level, it is enough to recall that for tT
Using again (B2) and (B3), and the perfect foresight assumption, we can
solve for the trajectories of K and q:
(B7a) Q(t)-Q = (p-X)le T(peit-)eXt).((HIp)+1-7-p].(LIR) for tT.
(B8a) K(t)-R = .[ [l(p -Xlee.I T(eXt-ePt)] (H/l)
+ (-)&le-#T(ePt-eXt)(1l-7-P)] *(fi X) for tT.
Comparing (B7a) and (B7b), it is clear that Q(t) has a discontinuity at
t=T. More precisely, at time T it must um by the amount (-7-p)(IX/I),
reflecting the simultaneous impulse in the rate of depreciation. Of course, this
is not a violation of market efficiency; on the contrary, it results from the
fact that at t=T the real interest rate in terms of capital is unbounded; hence
Q must jump to provide the required rate of return.
Letting t=O in (B7a), we get (19) in the text. Also, from (B7a) it is clear
that between 0 and T, Q-1 cannot change sign, so that the initial expansion (or
49
contraction) must last until T. To see if it may proceed at an ever-accelerating
pace, we can let H-0 in (B7a) and compute
sgn(Q(t)) - sgn( [p2eJ t_2eXt]-(1-7-p)* /R/ } for tX2, so that there will be a continuous
acceleration. In the bad news case, there will be an initial acceleration, that
may be followed by a slowdown starting at time t* if
t _ 2 (p)-1 ln(X/p) < T.
Transitory appreciation and anticipated depreciation
Finally, we examine the case of a gradual real appreciation accompanied
by anticipated depreciation. Assume that if no depreciation has yet taken place,
then the (constant) rate of instantaneous real appreciation is e; hence if no
depreciation has yet occured the actual real exchange rate path is
X(T) = - 9
or X(f) = X - r
In turn, there is an instantaneous probability I of a real depreciation that will
return the real exchange rate to its initial value X. Thus, if at any instant
the depreciation has not yet occured, the probability that it will not occur
within the next r instants is just
Pr [another r instants of appreciation] = e-f
As 7 grows, the probability approaches zero, so that the long run real exchange
rate is known to be unchanged at X. Hence, pending the depreciation, the
anticipated real exchange rate can be expressed
(B9) Et[X(t+7)] = X - 0.(t+r)-e-T for 7->0
and its anticipated rate of change is
(B10) Et[X(t+r)] = 9-e17.(1(t+'r)-1] for r>0
which is (20) in the text. Letting 7*(t)E(lI1)-t, it follows that for 7<7r (t)
there are expectations of real appreciation, while for r>,r*(t) real depreciation
is expected. As t grows, the expectation of real depreciation becomes dominant;
eventually, for t>r-1 only real depreciation would be anticipated.
Proceeding as before, we find that if the real depreciation has not yet
occured at time t, the paths of Q and K are
(Bll) Q(t)-Q = -
[(HP/) (pilre)p(l eXt)] + (1-7-p)((p+ll/eXt+r(leXt)]]
50
(B12) K(t)-f -
e[Ht(1 et _+ +
Letting t=O in (Bll), we get (21) in the text. For (1-7-p)=o, it can be
seen from (Bll) that Q will remain below (above) unity throughout the real
appreciation stage if and only if H is positive (negative); thus the capital
stock will be falling (rising). In turn, for H=O it can be seen that
sgn(Q(t)-l) - sgn (l-7-p)*[r(#+r)(l-eXt)+X/ext
and sgn(Q(t)) = sgn(l-7-p)
Thus with low (high) capital mobility, Q will initially jump down (up) and then
rise (fall) continuously; Q-1 will change sign at time t , given by
t E=
which is a decreasing function of the instantaneous probability of depreciation.
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Stock Changes
WPS543 Development Assistance Gone Donald B. Keesing November 1990 S. Fallon
Wrong: Why Support Services Have Andrew Singer 37947
Failed to Expand Exports
WPS544 How Support Services Can Expand Donald B. Keesing November 1990 S. Fallon
Manufactured Exports: New Andrew Singer 37947
Methods of Assistance
WPS545 Health and Development: What Nancy Birdsall November 1990 L. Mitchell
Can Research Contribute? 38589
WPS546 The Transition to Export-Led Growth Stephan Haggard November 1990 E. Khine
in South Korea, 1954-66 Byung-Kook Kim 39361
Chung-in Moon
WPS547 Does High Technology Matter? An Andrea Boltho November 1990 M. Hileman
Application to Unied States Regional Robert King 31284
Growth
WPS548 Deposit Insurance in Developing Samuel H. Talley November 1990 M. Pomeroy
Countries Ignacio Mas 37666
WPS549 Intertemporal Substitution in a Patricio Arrau December 1990 S. King-Watson
Monetary Framowork: Evidence 31047
from Chile and Mexico
WPS550 Firms' Responses to Relative Price Joh.i L. Newman December 1990 A. Murphy
Changes in C6te d'lvoire: The Victor Lavy 33750
Implications for Export Subsidies Raoul Salomon
and Devaluations Philippe de Vreyer
WPS551 Australias Antidumping Experience Gary Banks December 1990 N. Artis
37947
WPS552 Selected World Bank Poverty Nancy Gillespie December 1990 M. Abiera
Studies: A Summary of Approaches, 31262
Coverage, and Findings
WPS553 Money, Inflation, and Deficit in Egypt Marcelo Giugale December 1990 V. Israel
Hinh T. Dinh 36097
P WE Working Paper Series
Contact
AiQh DAte for paper
WPS554 Korea's Labor Markets Under Dipak Mazumdar December 1990 M. Schreier
Structural Adjustment 36432
WPS555 T'he Macroeconomics of Price Reform Simon Commander December 1990 0. del Cid
in Socialist Countries: A Dynamic Fabrizio Coricelli 39050
Framework
WPS556 Taxing Choices in Deficit Reduction John Baffes December 1990 A. Bhalla
Anwar Shah 37699
WPS557 The New Fiscal Federalism in Brazi' Anwar Shah December 1990 A. Bhalla
37699
WPS558 Alternative Instruments for Kenneth M. Kletzer December 1990 J. Carroll
Smoothing the Consumption of David M. Newbery 33715
Primary Commodity Exporters Brian D. Wright
WPS559 Fiscal Policy and Private Investment Ajay Chhibber December 1990 D. Bilkiss
in Developing Countries: Recent Mansoor Dailami 33768
Evidence on Key Selected Issuas
WPS560 The Persistence of Job Security in Milan Vodopivec December 1990 CECSE
Reforming Socialist Economies 37188
WPS561 The Labor Market and the Transition Milan Vodopivec December 1990 CECSE
of Socialist Economies 37188
WPS562 Anticipated Real Exchange-Rate Luis Serven December 1990 S. Jonnakuty
Changes and the Dynamics of 39076
Investment