Policy, Planning, and Research
WORKING PAPERS
Macroeconomic AdjustmentL
and GrowthCountry Economics Department The World Bank
June 1989 WPS 221
How Does
Uncertainty
About
the Real Exchange
Rate
Affect Exports?
Ricardo J. Caballero
and
Vittorio Corbo
Increased uncertainty about the real exchange rate depresses
ex-ports if firms are sufficiently risk averse. If firms with a fixed
capital stock are risk-neutral, such uncertainty increases exports.
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Under what conditions does inCreased uncer- be negative. This is true only if the degree of tainty about the real exchange rate depress risk aversion is large enough to offset the
expor-.s? positive effect from Jensen's inequality and the
convex curve of the profit function in terrns of For any given level of capital stock, a firm's prices.
marginal return increases as uncertainty rises. In
terms of the real exchange rate, the marginal Caballero and Corbo tested the qualitative profitability of capital is represented by a convex implications of a simple two-period model on curve. The implication: increased uncertainty several developing countries. Their results: raises exports. It turns out that firms that are uncertainty about the real exchange rate showed risk-neutral are better off increasing investmnents a clear, strongly negative effect on export because the cost of being caught with too little performance.
capital is greater than the cost of being caught
with too much. Point estimates indicate that increases as
small as five percentage points in the annual If one allows for risk aversion, however- standard deviation of the real exchange rate can and if aggregate activity is positively correlated shrink the export sector by 2.5 percent (Colom-with innovations in the real exchange rate (or bia) to 30 percent (Thailand and Turkey). The terms of trade) - the relationship between effects are substantially greater in the long run.
exports and an uncertain real exchange rate can
This paper is a product of the Macroeconomic Adjustment and Growth Division, Country Economics Department. Copies are available free from the World Bank, 1818 H Street NW,Washington DC 20433. Please contact Aludia Oropesa, room NI 1-035, extension 61758 (24 pages with tables).
eTh PPR Working Paper Scries disseminates the findings of work under way in the Bank's Pol:cy, Planning, and Research Complex. An objective of the series is to get these findings out quickly. even if presentations are less than fully polished. The findings. interpretations, and conclusions in these papers do not necessarily represent official policy of the Bank.
More than half a decade after the onset of the debt crisis, many
countries are still struggling to achieve a current accnunt situation that
is compatible with reduced external financing and a moderate but
sustain-able rate of output growth. Given the sudden decrease in the availability
of external funds, most of the initial adjustments have involved drastic
reductions in imports and inveqtment and only marginal increases in
exports.
It is now generally understood that a key element of a successful
medium-term strategy of adjustment and growth, is to move resources into
the export sector. If the economy is close to full employment, the
neces-sary reallocation of resources will require restrictive aggregate demand
policies (to reduce domestic demand) and a sustained real effective
depre-tion to make net exports more profitable (Fischer 1986, Khan 1987,
Killick et al., 1984).
Unfortunately, there is no mystery in the fact that this type of
policy, by affecting real balances, usually entails sharp short-run
reces-sions. Finding important non-price variables affecting the export sector
should help us in designing export incentives which have less short and
medium-term costs. The main purpose of this paper is to show that real
exchange rate uncertainty is one of these non-price variables. Reducing
the level of exchange rate uncertainty may lower the size of the real
devaluation r.quired to improve the current account balance while avoiding
a recession.ll
In section I we construct a simple two-period model that
high-lights the different channels through which real exchange rate uncertainty
may affect exports. Hartman (1972) and Abel (1983) showed that competitive
of capital. increase investment when price uncertainty rises. In contrast,
Caballero (1-989) showed that the interaction between imperfect competition
and asymmetric adjustment costs can offset the Jensen's inequality argument
given in Hartman and Abel, generating a negative relationship between
investment and uncertainty. The ultimate outcome of this argument is
irre-versible investment (Pindyck 1986, Bertola 1988). Furthermore, a working
paper version of this paper (Caballero and Corbo, 1988), examines
irrevers-ible investment as the reasoa for the negative relationship between
uncer-tainty and exports. An alternative way to undo Hartman and Abel's result
is to introduce risk aversion. Given its simplicity and the empirical
ori-entation of this paper, we have chosen risk aversion to motivate the
export-real exchange rate uncertainty issue. If the return on export
investment projects ave, on average, positively correlated with aggregate
activity (consumption), and the degree of risk aversion is large enough to
offset the convexity of the profit function with respect to prices, exports
are reduced when there is a sudden increase in real exchange rate
uncertainty.
Section II describes the data and section III estimates the
empi-rical relevance of the issues discussed in section II. We study the cases
of six developing countries Chile, Colombia, Peru, Philippines, Thailand
and Turkey, showing a clear and strong negative effect of real exchange
rate uncertaL1ty on exports. Our estimates suggest that increases as small
as five percentage points in the annual standard deviation of the real
exchange rate, can lead to short-run (one year) shrinkages of the export
sector in the range of 2.5 (Colombia) to 30 percent (Thailand and Turkey).
These effects are substantially magnified in the long run if changes in
-3
I. The Theory
In-this section we present a simple model that considers the
impact of uncertainty on export levels. This model gives theoretical
justification for circumstances under which export levels are an increasing
function of the real exchange rate and a decreasing function of the
vari-ance in the real exchange rate. Given that the main motivation of the
paper is empirical, the model outlined below presents only the minimum
ingredients in order to test the implications of real exchange rate on the
level of exporle.2/
We assume a representative firm in the export sector facing the
following demand curves
Xd(t)fP(t]
(Al 4t) w(t)j
and technology functions
X(t) - A
(t)NaKt1-where Xd and X represent exports demanded and produced, Pw and Px are the
international price and export price indices, I is the (absolute value)
price elasticity of demand, N and K are labor and capital used in
produc-tion, a is the labor share, and Al(t) and A2(t) are arbitrary functions of
time.
Real wages, V(t), and the real exchanego rate, V(t) (both deflated
by the consuer price indez (CPI)), are exogenous to the firm.
We :an now define the (maimlized) operating profits
il(K,t),
as1](K.t) -- maxV(t)P* (t)A1(t)1/7x(t)/A-W(t)N(t)
N(t)
where p _-- represents an
inder
(inverse) of monopoly power.Essentially, there is no major technical difference in the
com-plexity of solving the problem presented below when only the real exchange
rate is uncertain or when there are multiple sources of uncertainty. In
order to make notation less burdensome, let us assume the former case and
summarize all the remaining state variables as a deterministic function of
time (B(t)), so:
*1) 11(K(t),t) - B(t)K(t) OJ(t) 02
where ° 1..iil-a) ' 1 and ° 9 > 1.
1
1-a/A
2
1_0/
It is also useful to write exports as a function of prices and the
capital stock, resembling an export equation:3/
a
(2)
X(t) - D(t)(#P(t)) 1-aK(t)
where D(t) is just a function of time, and P - P=V.
Equation (2) shows that higher moments of V will have a chance to
affect exports (given the realization of the real exchange rate, V(t)) only
if there is some type of capital rigidity.4/ Before discussing this issue
in more detail, it is convenient to establish the real exchange rate
process.
Let us asuam that the logarithm of V(t) is an independently!/ and
identically distributed normal variable, with mean -_212 and variance o2.
The correction _Cf2/2 is standard. Its main purpose is to allow
the separation between the mean and the variance of log normally distrib-uted variables.
Delivery Lag
Let us. first highlight the issues arising from the convexity of
marginal profits. Assume that capital is bought (and predetermined) one
period before it is actually used. In this context, if owners of the firm
are risk neutral, Hartman and Abel's result holds (i.e., uncertainty has a
positive effect on investment and exports), even if the firm is not
per-fectly competitive. The explanation of this result is simple, from
equa-tion (1) it is easy to show that the marginal operating profit function,
11K(K(t,t), is convex in the real exchange rate (°2 > 1). Hence, for any
given level of capital, its expected marginal return increases as
uncer-tainty rises. Therefore, when capital is predetermined and agents are risk
neutral, investment is an increasing function of uncertainty. As a result.
exports will be higher for every real exchange rate realization.
This apparent paradox can be explained by the fact that in a
flex-ible world the firm loses both when the realization of the exchange rate is
unfavorable and when it is favorable. When the exchange rate is
unfavor-able, the firm has too much capital compared with its optimal value.
Con-versely, when the exchange rate is favorable, the firm has a capital stock
that is too low. It turns out that losses due to the latter are higher
than losses due to the former, so a profit maximizing firm would invest
more -- and therefore raise exports -- than in a less
uncertain
world, inorder to re&zce the probability of being caught with too little capital.
So far we have seen that for the case of a predetermined capital
stock, the convexity of the profit function implies that uncertainty in the
real exchange rate increases investment and exports. However, the above
discussion hinted at several ways of obtaining a negative effect of
-5-paper version of this paper, is by truncating the losses of being caught
with too little capital. This can be achieved by allowi..g firms to pay a
premium in order to reduce the investment lag. In this case the problem
becomes very similar to that of irreversible investment. When capital is
irreversible, but not predeterminet it is always possible to invest in the
second period, limiting the losses of having invested too li4tle in the
previous period to possible higher costs of rushing* capital installation
in the second period. At the same time, the losses of being caught with
too much capital are the same as in the case in which capital is
predeter-mined. The net result is that for a broad set of parameters uncertainty
reduces instead of increases exports. A second alternative is by
intro-ducing risk aversion; if the convexity of the utility function is large
enough to offset the convexity of the profit function with respect to
prices, investment, and therefore exports, will be reduced as real exchange
rate uncertainty rises. The next sub-section explores this second
alternative in more detail.
Risk Aversion
Assume that the preferences of the frni's owners can be
character-ized by a representative consumer with a constant relative risk aversion
instantaneous utility functions
U(C(t))
-where C(t) denotes average consumption at time t and
7
is the coefficient of relative risk aversion.The standard Consumption-Capital Asset Pricing Model (C-CAPH) implies that in equilibrium the price of a unit of capital -- here assumed
to be one -- must equal the present value of its return,6/ discounted by
the marginal-rate of substitution between today's and tomorrow's
consump-tion:
(3)
C(t + 1)
'y
11K(t
+l)A
1)
pEt |[ C(t) ) (K(t + l).t + 1)
where p is the subjective discount factor.7/
Solving the stock of capital from (3) yieldss
(4) K(t + 1)-f pB(t + l)Et
[
C(tt +1) V(t + 1)°2If we further assume that the pair (ln
{
C(t))
n V(t + l)) isjoint-normally distributsd with mean8' (7/2, -02/2), variance (l,2) and covariance
pg.
then there is an explicit relationship between the capital stock and realexchange rate uncertainty:
1-
(5) K(t + 1) -
f
pB(t + l)e(G2(02G1)0/2-1792pa)}It is apparent from (5) that as long as there is a positive correlation
between the rate of consumption growth and the real exchange rate
inno-vations (p > 0), there is always a coefficient of relative risk aversion,
'7,
large enough to produce a negative relationship between investment, andtherefore exports, and exchange rate uncertainty. The empirica' evidence
shown in section III suggests that indeed this is the case for the
-3
II. The Data
The information on export prices and volumes (annual) was provided
by the old World Bank's Economic Analysis and Projections Department. Full
description of sources and methodology are given in Moran and Park (1986).
Prices correspond to Paasche indices using unit values as proxies for
individual commodity prices.9/ Moran and Park obtained the basic exports
value data from the World Bank trade data system. Volumes of exports
correspond to values of exports divided by their respective price indices.
Data on consumer price indices, nominal exchange rates and world
demand proxy (industrial country real GDP) were obtained from the DMF's
International Financial Statistics. This information was available on a
quarterly basis. The real exchange rate is defined as the export price
times the nominal exchange rate divided by CPI prices.
To develop a measure of uncertainty we first calculated quarterly
standard deviation estimates of the real exchange rate. Each quarter's
standard deviation was estimated using the real exchange rate realizations
of the current and previous three quarters. The annual uncertainty level
was measured by averaging the standard deviation of the real exchange rate
of the four quarters of each year. This is equivalent to the standard
deviation estimates of a GARCH (generalized autoregressive conditionally
heteroskedastic) model on the exchange rate equation with a very long and
restricted mowing average structure.10/ This is certainly an area which is
III. Empirical Evidence
The theoretical sectio.. of this paper highlighted the relationship
between exports and the first and second moments of the real exchange rate
probability distribution. This section attempts to test these
relation-ships on the time set-es data of six developing countries: Chile.
Colombia, Peru, Philippines, Thailand and Turkey.ll/
The theoretical model was only designed to motivate the
relation-ship between export. and uncertainty. In order to preserve the main
impli-cations of the theoretical model and at the same time provide a simple d
feasible) export equation, we have made the following assumptions.
1. The relationship between the logarithm of capital and the standard
deviation . the real exchange rate is approximately linear.
2. Lagged exports are included in the right-hand side to account for
slow adjustment and learning-by-doing mechanism (i.e., Caballero
and Corbo, 1987).
3. The (inverse) index of monopoly power, p, is linearly related with
world demand.
Of the three assumptions the third one merits a longer defense.
Caballero and Corbo (1986) showed, for the same set of countries used in
this paper, that tying the relative price effect with the effect of world
demand se em d to marginally improve the behavior of export equations.12/
They introduced this restriction by assuming that the inverse of the
mark-up, p. was linearly related to the level of world activity. This
restric-tion was justified in terms of the prt.:ence of customer markets (Bils,
1985). In any event, this restriction is thoroughly tested and the results
without the world demand variable are also reported. All the fundamental
from export equations. Furthermore, the model with flexible mark-up seems
to perform marginally better than the fixed mark-up model, supporting our
specification.
We can now prtceed to expand the 'exports equation shown in (2),
as follows:
(6) x(t) - co + cl (p(t) +
wdMt))
+ c2U(t)
+ c3x(t - 1) + c4a(t) + e(t)where x, p and wd denote the logarithm of exports, real exchange rate and
world demand, respectively,
and
a(t) is just a function of time.Before entering into the econometric issues involved in the
esti-mation of equation (6), it is worth presenting the results of a simple
regression in which no dynamic components are present. Table 1 does
pre-cisely this.
The parameters reported in this table are almost surely
inconsis-tent since important dynamic elements are omitted. Nevertheless, they are
shown as suggestive informal evidence in favor of our central hypothesis.
With the exception of Peru and Colombia, uncertainty seems to have strong
depressive effects on export levels.131
Below we present the results of fully specified equations. In
doing this, we discuss several econometrlc issues that may have the
poten-tial to bias our current as well as previous estimates of export equations.
After these considerations, the results remain supportive of our central
hypothesis.
?The
point estimates alvays have the right sign, although thiscan be supported statistically in only half of the countries considered in
TABLE 1
Export Equations: First Approach
COUNTRY VAI VAR2 Dv R2
Chile 1.86 -5.45 1.14 0.64 (0.29) (2.14) Colombia 1.78 -0.84 1.18 0.64 (0.40) (2.90) Peru 3.97 -1.24 0.27 0.07 (2.25) (5.57) Philippines 3.27 -7.89 0.48 0.57 (0.72) (3.43) Thailand 4.00 -10.90 0.68 0.76 (0.45) (3.24) Turkey 3.91 -5.67 1.87 0.93 (0.30) (2.22)
Notes% VARI Logarithm of the real exchange rate plus log of world demand.
VAR2 Standard deviation of the logarithm of the real exchange rate. For details on its computation see the text.
1. The model was estimated by Instrument Variables.
2. Robust standard devLations are in parenthesis (White 1980).
3. A constant was also included in the regressions.
4. In this case the Durbin Watson (DV) is not a proper statistic.
- 12
-Maln Results and Simultaneity
Table 2 presents OLS (ordinary least squares) and IV (instrumental
variables) estimates of equation (6).14/ The instruments chosen for the IV
estimates are: a constant, the log of industrial countries' CPI divided by
the developing countries' domestic CPI, the log of world demand, the
standard deviation of tue log of the real exchange rate, the log of lagged
exports, and the log of time.
It is apparent from this table that most of the models using the
assumption of predetermined real exchange rate (and therefore use OLS
pro-cedures) are subject to serious downward biases on the estimates of price
elasticity of exports. In fact, once simultaneity is corrected, the price
elasticity estimates increase for every country in our sample.
Further-more, in several countries the price elasticity estimates more than
doubles. The OLS specification error statement is backed by Hausman's
specification testl5/ presented in the last column of Table 2. This
statistic is above the critical level for fJ.ve out of our six countries
(the exception is Peru) at the ten percent significance level. Moreover,
the Lagrangian multiplier test presented in the second to last column in
Table 2 shows that the over-identifying restrictions imposed in the IV
procedure cannot be rejected at any reasonable significance level (with the
exception of Peru that is rejected at the ten percent significance level).
Perhaps even more striking is the fact that when the IV procedure
is used, the estimates of the effects of real exchange rate uncertainty on
exports are always negative, as expected. As said before, this can be
validated statistically for only half of the countries studied (Peru,
Thailana and Turkey). However, the probability that the coefficient of
TlABU 2
Expor Eqmtewa: Floibl- Mmrk-p
OLS ea IV Enatilat
C _o..1 el VADI vAI R(t-I) i IRl LV2 1 at aU mm
Chil, OLS 0.49 -0.611 0.77 2.15 -8.62 1.92 0.91
(0.20) jl.60) (0-09) (0.54) (S.9")
IV 0.02 -1. 0.61 - 2.3 -6.17 1.75 0.09 3.04 4.30
(0.31) (1.30) (0.12) (0.47) (3.55)
Colombia OLS 0.24 -0.67 0.74 - 0.92 U..3 1.34 0.39
(0.23) (1.21) (0.11) (0.63) (4.49) IV o.us -0.4 o.0 - 1.70 -0.91 1.69 0.65 1.61 3.06 (0.87) (1.-) (0.14) (O.50) (3.97) Peru .LS 0.02 -1.13 0.70 2.19 2.C7 -4.70 1.47 0.90 (0.25) (0.40) (0.07) (0.67) (1.35) (2.22) IV 0.67 -1.06 0.76 1.9S 3.91 -4.06 1.74 0.99 5.24 1.22 (0.26) (0.52) (0.06) (0.76) (1.36) (2.89)
Philippinmm OLS O.52 -0.12 0.91 - 5.61 -1.35 2.07 0.90
(0.27) (1.66) (0.04) (1.56) (16.10) IV 0.79 4.30 0.30 - 5.60 -2.16 1.#6 0.97 2.63 3.25 (0.3) (1.35) (0.04) (1.30) (9.74) That lead 0S 0.29 -4.11 0.90 - 2.64 -40.20 2.27 0.96 (0.20) (0.69) (0.06) (1.33) (16.61) IV 1.20 -5.90 0.70 - 3.99 -19.70 1.56 0.96 0.09 3.81 (0.51) (1.22) (0.11) (0.36) (5.50) lurk.1 O.S 3.71 -5.63 - - - 1.76 0.93 0.00 6.32 (0.29) (2.25) IV 3.92 -5.66 - - - - 1.36 0.9 (0.29) (2.22)
U*se: EP Estimtln procedure. LRVI Long-rum atfect of VARI. LRV2 Long-run etfect of VAR2.
LU Ontr-identificatioa statistic (Lagrangian mitiplier). MM1 Hllauasa epecification test.
error, is considerably smaller than the significance level of each
indi-vidual test.- This makes us confident in stating that there is clear
evi-dence of the depressing effect of real exchange rate uncertainty on export
levels.
Not only does real exchange rate uncertainty depress exports, but
it does it by a substantial amount, even in the short run. For example, an
increase of five percentage points in real exchange rate uncertainty in the
Chilean economy leads, according to our estimates, to a total decline in
experts of about ten percentl6/. The example is far more dramatic in the
case of Thailand and Turkey, where similar increases in uncertainty would
lead to a thirty percent decline in exports.
With the exception of Turkey, where adjustment seems to be very
fast, all the effects previously described are magnified in the long run.
Continuing our previous example, the same increase of five percentage
points in real exchange rate uncertainty would lead to a long-run decline in exports of 25 percent in the case of Chile, and almost wipe out
Thailand's export sector.
Constant Ulasticity of Demand
At the outset of this section we argued that allowing for p, the index of monopoly power, to depend linearly on world demand provided an improvement-A the flt of export equations in some countries. In this
sub-section we show that this is indeed the case, but more importantly, we show
- 5
Table 3 is clear evidence of this. Both, the downward bias of OLS
estimates at-well as the depressing effects of real exchange rate
uncer-tainty, are fully carried over to the case in which world demand does not
affect the elasticity of demand faced by export sectors. If anything, the
results are even more favorable to our hypothesis in this case.
Table 4 shows that there is marginal evidence in favor of the
flexible
p
specification. There we present the results of a modifiedJ test.l7/ The results of this test are inconclusive for Chile, Peru,
Philippines and Thailand. whereas it favors the flexible demand elasticity
specification in the case of Colombia and Turkey. This result is backed,
in the case of Colombia, by a high x2 statistic for the Lagrangian
multi-plier test in the constant demand elasticity specification.
Unaticipated Exchange Rate Changes
The derivations in the theoretical section suggested that both the
expected and the realization of the exchange rate should enter the
right-hand side of equation (6). The former should enter through its effect on
the capital stock, whereas the latter through its effect on hiring and
firing of flexible factors. In the empirical section, on the other hand,
we disregarded this difference and proceeded using just the realization of
the exchange rate. This would not be a problem, however, if all the
instruments belonged to the information set at t-l since in that case the
estimation procedure would be unable to distinguish between the realized and expected exchange rate. Unfortunately, some of the instruments used correspond to contemporaneous variables and hence do not belong to the
TAM a
EVott Equtle.: Ceetet ark-up
C"A"Sbrw EP La vmtS a(b-1) lag t 1l1 LMW Ot a Lu mm
Chi I- OLS 0.2 -0.48 0.S7 - *.97 -3.66 1.99 0.91
(0.28) (1.48) (0.07) (1.76) (10.60)
IV 1.1 -1.72 0.77 - 4.94 -7.86 1.73 0.37 0.02 4.40
00.43) (1.60) (0.08) (1.75) (6.17)
Cole li OLS 0.07 -1.03 0.03 - 0.42 -1.76 1.76 O.6
(0.25) (1.14) (0.06) (1-29) (5.73) IV O. -0.96 0.75 - 2.06 -3.97 1.68 0.# 5.10 1.94 (0.84) (1.61) (0.-0) (1.21) (6.11) Per OLS 0.64 -1.11 0.73 2.94 2.6 -4.46 1.46 0.66 (0.27) (0.46) (0.07) (0.69) (1.87) (2.09) IV 0.M -1.08 0.77 8.03 4.81 4.C0 1.62 0.66 3.07 1.43 (0.81) (0.54) (0.C0) (0.U4) (2.01) (2.60) Phllippime OLS 0.56 0.19 0.99 - *6.10 12.50 2.07 0.97 (O.3) (1.66) (45.40) (55.60) (124.50)
IV 1.17 -O.6t 0.07 - 5.3JO -18.70 1.76 0.96 1.76 1.U8
(O.5) (1.43) (0.08) (37.60) (43.50) Tlhlownd OLS 0.17 -8.94 0.9 - 3.57 -4.7 2.26 0.66 (0.24) (1.06) (0.04) (5.84) (72.20) IV 1.64 -7.14 0.99 - 13.90 -8.60 1.U 0. 0.14 8.10 (0.66) (2.19) (0.06) (6.07) (26.10) Turkey (LS 6.06 -9.22 - - - - 1.6 0.J1 (0.78) (3.58) IV 7.27 -9.26 - - - - 1."6 0.7 2.84 6.60 (0.09) (8.45) fkb!s EP Eatibetler procedre.
LEU t.aprit& of the rel excheag rate.
LRE Le-ru edfet ef LUt. LYR1 Les-rur ffect f VMARI. LW!2 Log-rua offect of VAR2.
LU Oor-ldetlficatloe tUtietic (Lagrangiam mItIplier).
MM Ha.. epeciflcation tet. See note for TalM 1.
TABLE 4
Constant vs. Flexible Hark-up
3oaConstant 0i:Variable
COUNTRY Mark-up Mark-up CONCLUSION
Chile -0.13 1.19 Inconclusive
Colombia 2.00 -1.29 Flexible Hark-up
Peru 0.04 -0.04 Inconclusive
Philippines -0.40 0.43 Inconclusive
Thailand 0.55 -0.37 Inconclusive
TL., ey 2.41 0.04 Flexible Mark-up
-
:3
-presented in Table 2 suggests that this did not imply substantial biases.
In order words., the covariance between the *news component of the real
exchange rate and instruments seems to be very small.
That this is so is shown in Table 5. For each country the first
row reproduces the IV results of Table 2. Whereas the second row shows an
alternative set of IV estimates in which the contemporaneous instruments
are lagged one period. The results from both procedures are very close to
each other. It seems safe to conclude that our results are also robust in
the presence of slight mis-measurement of the relevant relative price
variable.
IT. Conclusion
The theoretical section of this paper studied the conditions under
which increases in the degree of uncertainty about the real exchange rate
depresses exports. Existence of a fixed and predetermined factor is not
enough. On the contrary, the convexity of marginal operating profits with
respect to the real exchange rate implies that an increase in uncertainty
raises cxports. The cost of being caught with too little capital outweighs the cost of being caught with too much capital. Therefore, it is optimal
for firms to increase investment in order to reduce the probability of
TABLE 5
Export Equations Complete Model
Another Choice of Instruments
COUNTRY TYPE PRICZ VAil x(t-1) log t
Chile Tab 2 0.92 -1.99 0.61 (0.31) (1.80) (0.12) NCI 0.94 -2.24 0.60 -(0.28) (1.76) (0.11) Colombia Tab 2 0.85 -0.45 0.50 -(0.37) (1.97) (0.14) NCI 0.86 -0.58 0.49 _ (0.37) (1.91) (0.14) Peru Tab 2 0.87 -1.08 0.78 1.95 (0.28) (0.52) (0.08) (0.76) NCI 0.85 -1.19 0.78 1.95 (0.26) (0.50) (0.08) (0.76) Philippines Tab 2 0.79 -0.30 0.86 (0.35) (1.35) (0.04) NCI 0.69 -0.64 0.87 (0.30) (1.47) (0.05) Turkey Tab 2 3.92 -5.66 -(0.29) (2.22) NCI 3.93 -5.11 -(0.30) (2.71) Notes$
Tab2 Results in Table 2.
NCI Mon-Conteuporaneous Instrument See notes to Table 1.
However, if risk aversion is allowed for, and aggregate activity
is positively correlated with real exchange (and/or terms of trade)
innova-tions, it is possible to obtain a negative relationship between exports and
real exchange rate uncertainty. The latter requires the degree of risk
aversion to be large enough to offset the positive effect resulting from
Jensen's inequality and the convexity of the profit function with respect
to prices.
The empirical section tested the main qualitative implications of
the previous model. These tests were applied to six developing countries:
Chile. Colombia, Peru, Philippines, Thailand and Turkey, showing a clear
and strong negative effect of real exchange rate uncertainty. the point
estimates obtained indicated that increases as small as five percentage
points in the annual standard deviation of real exchange rates, can lead to
short-run shrinkages of the exports sector on the range of 2.5 (Colombia)
to 30 percent (Thailand and Turkey). These effecte are substantially
mag-nified in the long run.
Tn obtaining these estimates, simultaneity was carefully treated
and shown to have a substantial impact on the estimates of the price
elas-ticity of exports. Also, the results were shown to be robust to a variety
- 21
-FOOTNOTES
1. Note that the role of uncertainty examined in this paper is different
from that of credibility. The latter is usually thought of as the
lack of confidence that current good policies will continue. In that
context, the main effect of an increase in uncertainty is to lower the
expected exchange rate. In this paper, on the other hand, we worry
about changes in uncertainty given the expected real exchange rate.
2. See the working paper version of this paper (Caballero and Corbo,
1988) for an alternative motivation, based on delivery lags and
irreversible investment.
3. Remember that here prices are not given, therefore the traditional
interpretation of equation (2) ac an export equation does not apply.
4. If there is no capital rigidity, it is possible to optimize equation
(1) with respect to K(t), so X(t) is only a function of t and V(t).
5. Adding serial correlation is a trivial extension. Furthermore, in the
empirical section we carefully consider the possibility of real
exchange rate predictability. See subsection on 'Unanticipated
Exchange Rate Changes' in section III.
6. Remember that this is a two-period model with a delivery lag,
therefore there is only one productive period.
7. Notice-that K(t4l) is known at time t due to the delivery lag.
8. Notice that the assumptions on the mean and variance of the rate of
growth of consumption are only made for notation convenience. None of
the main results are affected by these assumptions.
9. Limitations, advantages and biases are discussed in Moran and Park
- 22
-10. Notice that a GARCH-H (where the H denotes the dependence of the mean
on the-higher moments) model applied directly to the export equation
may not be a good approximation of uncertainty if the econometrician
has less information than the firms themselves.
11. The initial project also included Korea. Even though we did obtain a
negative relationship between uncertainty and the level of exports,
there were clear symptoms of strong specification error. We opted for
excluding these results to avoid distracting the reader with too many
second order arguments.
12. Notice that in strict rigor the flexible mark-up model should also affect the coeffLcient of the uncertainty term, we have omitted thls highly non-linear complexity.
13. Paredes (1988) analyzes the effect of uncertainty in the real exchange
rate on ezport performance.
14. Time and/or lagged exports were excluded when non-significant.
15 Hausman (1978).
16. This is a very conservative example. In fact, the swings in exchange rate regimes of Chile uggests changes on the. uncertainty level far beyond the five percent change used in this ewmple.
17. The modification is designed to take into account the correlation
betweesrecgreesors and disturbances. See MacKlnnon, White and
-
23
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