0,
where c is total consumption expenditure measured in terms of traded
goods. This specification postulates that transactions costs per unit of
consumption are a decreasing function of the stock of money per unit of
consumption, but that the productivity of money in reducing transac-
tions costs is subject to diminishing returns. The accumulation of net
9. Adding an exogenous currency risk premium to this condition would not
affect any of the properties of the model.
DETERMINANTS OF THE LRER 269
worth over time is the sum of household saving and net real capital
gains or losses. It can be expressed in the form of the budget constraint
shown by equation 6.7:
(6.7) ti=y+(i*+E)f -t-(11+r)c-r*a
where t denotes real (lump-sum) taxes, and x* is the rate of increase in
the domestic-currency price of traded goods. The latter, in turn, is the
sum of the rate of depreciation of the domestic currency and the exter-
nal inflation rate, denoted 7r,:
The path of consumption expenditure is determined by the maximi-
zation over an infinite horizon of an additively separable utility func-
tion in which future felicity (that is, the future flow of utility) is dis-
counted at the constant rate of time preference p. Consumption of traded
goods, denoted cT, and of nontraded goods cN, are the only direct sources
of utility for the household. Thus the representative household will seek
to maximize a function of the form:
f u(c,,c,)e-'dt
To make the analysis more tractable, I will give the felicity function u(c,
cN) a specific form. Following Dornbusch (1983), I will assume that the
felicity function is of the constant relative risk aversion (CRRA) type in
total consumption, while the intratemporal elasticity of substitution be-
tween the two types of goods is unity. This means that the felicity func-
tion can be written as equation 6.8:
(6.8) u(cT,c) - N
1-o
The parameter 9 represents the share of traded-goods consumption in
total consumption expenditure (see below), while a is the inverse of the
intertemporal rate of substitution. The Cobb-Douglas specification for
intratemporal substitution between the two types of goods implies that
consumption expenditure is allocated in constant shares between the
two types of consumption goods as shown in equation 6.9:
(6.9) cT-0
c, = (1- 9)ec
270 EXCHANGE RATE MISALIGNMENT
where total consumption expenditure c is given by c = CT + c\,/e. Using
these in equation 6.8 permits us to express the felicity function in the
indirect form in equation 6.10:
(6.10) u(c,c,) = v(e, c) = 1C[e C]
1-a
where ic is a constant. The term in square brackets is the ratio of the
price of traded goods to the "true" consumption price index Po P-
(where PT is the domestic-currency price of traded goods, and PN is the
domestic-currency price of nontraded goods) times total consump-
tion measured in terms of traded goods. Thus this term measures
total consumption in units of the consumption bundle, which is the
direct source of utility for the household.
The household's problem can thus be stated as follows: it chooses
paths for consumption expenditure c and money m so as to maximize:
(6.11) [Kel0 exp(-pt)dt
Jo- 1-C
subject to the flow-budget constraint (equation 6.7) and a transversality
condition. These constraints can conveniently be written as equation
6.12:
a= y - t + ra - im -(1+ - r(m/c))c
(6.12)
lim a exp(- rdt) > 0
where r is the real interest rate earned by domestic residents on their
holdings of foreign bonds, measured in terms of traded goods (r = i -
7t*). This is equivalent to the external nominal interest rate i* faced
by domestic residents, minus the foreign-currency rate of inflation
in the price of traded goods:
r = i - r* = (i* + e) - ( +-e) = i* -r,.
The present-value Hamiltonian for this problem can be written as:
H = (recf + A)exp(-pt)
1-u
where A is the costate variable for the household's financial wealth a,
with economic interpretation as the marginal utility of wealth. The so-
lution of this problem is characterized by the first-order conditions shown
in equations 6.13.a through 6.13.b:
DETERMINANTS OF THE LRER 271
(6.13.a) KCYC - A(1 -r(m/c) -T'(m/c))c
(6.13.b) -'C'(m / c)
(6.13.c) A(p - r) = A
as well as the budget constraint and transversality conditions given in
equation 6.12. These conditions have intuitive interpretations. Equation
6.13.a describes the necessary condition for the level of consumption to
be at its optimal level at each instant, conditional on the marginal utility
of wealth. It states that the marginal utility gain from an extra unit of
consumption must be equal to its marginal utility cost-that is, the loss
arising from forgone saving. The latter is the product of the marginal
utility of wealth A and the reduction in saving associated with an extra
unit of consumption, given by the quantity (1 + T + '), which includes
the transaction costs associated with each extra unit of consumption.
Equation 6.13.b is the necessary condition for the allocation of the house-
hold portfolio between money and bonds to be at its optimal level, con-
ditional on the level of consumption expenditure. It states that the mar-
ginal gain from holding an extra unit of money, in the form of re-
duced transaction costs, must be equal to its marginal cost, in the
form of forgone interest. Finally, equation 6.13.c is necessary for
wealth to be allocated optimally over time. It states that since wealth
should be drawn down more quickly (through increased consump-
tion) when the household is more impatient (that is, when p is large
relative to r), the marginal utility of wealth should rise more rapidly
under those conditions.
These equations can be used to describe the household's demand for
money, the path of its consumption expenditure, and its rate of accumu-
lation of financial assets at each moment in time. Equation 6.13.b im-
plicitly defines a relationship between money and consumption that
resembles a standard money-demand equation, shown in equation
6.14:
(6.14) m = h(i)c, h' < 0.
Thus the demand for money depends in familiar fashion on the interest
rate and the level of transactions. To derive an expression for the path of
consumption expenditure, differentiate equation 6.13.a with respect to
time. Using equations 6.13.b, 6.13.c, and 6.14, we can derive the time
path of consumption. It is given by equation 6.15:
( + ihi ]
272 EXCHANGE RATE MISALIGNMENT
where y = (1 - a)(1 - 0). This represents a generalization of the familiar
Euler equation for the optimal time path of consumption under con-
stant relative risk aversion, to incorporate changing relative prices of
the two consumption goods as well as the role of the transactions tech-
nology. Note that, given the real interest rate measured in terms of traded
goods r:
a. An expected real depreciation makes consumption cheaper in the
future (since it implies a lower relative price of nontraded goods).
This increases the consumption-based real interest rate (the op-
portunity cost of current consumption), which steepens the con-
sumption path (thereby discouraging current consumption), and
b. A steepening of the path of the future nominal interest rate (a posi-
tive value of i) would tend to increase the transactions costs asso-
ciated with future consumption, thus decreasing the consumption-
based real interest rate, which tends to tilt the consumption path
toward the present, making it flatter.
The Consolidated Public Sector
The consolidated public sector includes both the government and the
central bank. The economy operates with a predetermined exchange rate,
administered as a crawling peg in which the domestic currency depreci-
ates continuously at the policy-determined rate e. The central bank's
functions consist of maintaining the parity (by exchanging domestic and
foreign currency for each other on demand in unlimited amounts at the
official exchange rate) and providing credit to the government. The lat-
ter, in addition to credit from the central bank, receives lump-sum taxes
from the private sector and spends by purchasing both traded and
nontraded goods, in the amounts g, and g, respectively. Thus the con-
solidated period-by-period (flow) budget constraint of the public sector
can be expressed as equation 6.16:
(6.16) fc = t + rfc + (th + 7r* m) - (g, + g, /e)
where fc, which may be positive or negative, is the stock of bonds held
by the consolidated public sector. Like the private sector, the govern-
ment has to respect an intertemporal budget constraint, given by limfc
exp(-*r dt)>O.
For concreteness, I shall assume that it does so in a particularly simple
way-by levying taxes in an amount sufficient to keep fc - tih = 0. Notice
that this does not imply a balanced budget, but rather a reliance on the
inflation tax to finance fiscal deficits.
DETERMINANTS OF THE LRER 273
Equilibrium Conditions
The model is closed with two equilibrium conditions. The first is an
arbitrage relationship describing the terms on which the rest of the world
will lend to the domestic economy, and the second characterizes equi-
librium in the market for nontraded goods.
The Supply of Funds
Though the home country is a price taker in the world goods market, its
financial liabilities are not perfect substitutes for those of the rest of the
world, and thus the interest rate at which residents of the country can
borrow abroad reflects a risk premium, which is an increasing function
of the share of the country's liabilities held in world financial portfolios.
This is incorporated in the model in the form of an upward-sloping sup-
ply-of-funds schedule relating the external interest rate confronted by
the country's residents, i*, to the country's net international indebted-
ness, as well as to world financial conditions, measured by the world
interest rate iW. The specific formulation expresses i* as the sum of the
world interest rate and a risk premium p, which is inversely related to
the country's aggregate net creditor position, as expressed by equation 6.17:
(6.17) i* = i + p(f), p(0) > 0, p' < 0.
The supply-of-funds schedule described by equation 6.17 is depicted as
the curve i* in figure 6.1.10 The external interest rate faced by the economy
is determined by the height of this schedule above the relevant value of
the net external asset position f.
Equilibrium in the Market for Nontraded Goods
Finally the equilibrium condition in the market for nontraded goods
can be expressed as equation 6.18:
(6.18) YyeCN +9-
= (1-9O)ec + g_
For future reference, it is worth noting that the specification of equilib-
rium in the nontraded-goods market (equation 6.18) implies that all
10. For a similar specification, see Bhandari, Haque, and Turnovsky (1990).
Agenor (1997) provides more detail on this specification and how it relates to
alternative approaches to modeling international capital market imperfections.
274 EXCHANGE RATE MISALIGNMENT
Figure 6.1 The Supply-of-Funds Schedule
1
0
production of nontraded goods is available for consumption, either by
the households or by the government. This has the consequence that the
transactions costs associated with consumption must absorb traded
goods only. This assumption is not necessary and is discussed further
below.
Equation 6.18 can be solved for the value of the real exchange rate
that clears the nontraded-goods market, conditional on the values of c
and g.. This short-run equilibrium real exchange rate is given by equa-
tion 6.19:
e = e(c,g,)
(6.19) e= (1-O)e/(y' -(1- O)c) <0
e2 =1/(y - (1 -O)c) < 0
The real exchange rate that solves equation 6.19 is a short-run equilib-
rium one in the sense that it clears the market for nontraded goods for a
given value of private consumption expenditure c. Thus, this real ex-
change rate will be sustainable only to the extent that c is itself sustainable.
The Long-Run Equilibrium Real Exchange Rate
As shown in Montiel (1998), the model of the previous section can be
solved to derive the entire dynamic path of the real exchange rate and
other endogenous macroeconomic variables in response to a variety of
DETERMINANTS OF THE LRER 275
macroeconomic shocks, be they transitory or permanent, occurring in
the present, or expected to occur in the future. A key characteristic of the
model is that the economy it describes tends to settle into a steady-state
equilibrium after a shock in which the stock of net international indebt-
edness and the real exchange rate are both unchanging.
This section examines the properties of that equilibrium. Since the
focus is specifically on the determination of the long-run equilibrium
real exchange rate, the solution method chosen in this section is one that
focuses specifically on that variable and links up with the traditional
literature that views the equilibrium real exchange rate as that value of
the real exchange rate that is consistent with the simultaneous attain-
ment of internal and external balance.
To solve the model, we first reduce it to a smaller number of key
relationships. The first step is to consolidate the budget constraints of
the household and public sectors. To do so, we differentiate the house-
hold balance sheet constraint (equation 6.4) and substitute into the flow-
budget constraint (equation 6.12). This permits equation 6.12 to be writ-
ten as equation 6.12':
(6.12') f, = y-t+rf, -(th+n* m)-(1+r(m/c))c.
Adding equations 6.12' and 6.16 together, and using the definitions of y
and c as well as the equilibrium condition in the nontraded-goods mar-
ket (equation 6.18), we have equation 6.20:
(6.20) f = y,(e)+ rf -(8+T(m/c))c- g,.
This is the flow-budget constraint for the economy as a whole. Recalling
that c, = Oc, and that transactions costs are assumed to be incurred in
traded goods, aggregate demand for traded goods is given by (Oc + g,),
and aggregate supply is (y,- c). Thus, aggregate excess supply of traded
goods, equal to the real trade balance surplus, is (YT - zc) - (Oc - gT) = YT -
(T +O)c - gT. Adding the receipt of real interest payments from abroad
(recall that f is the country's international net creditor position) yields
the inflation-adjusted current account surplus, measured in units of
traded goods, which is the right-hand side of equation 6.20. This is
equated to the change in the economy's real net creditor position (f).
This equation thus determines how the real net creditor position evolves
over time.
11. As is common with models of this type, that equilibrium is unique and
saddlepoint stable.
276 EXCHANGE RATE MISALIGNMENT
Private spending, in turn, evolves over time according to the Euler
equation 6.15, reproduced here for convenience:
(6.15) c=. r+ye/e- h+-p c.
1 +-tr(h(i)) + ih(i)
As is evident from equation 6.15, the evolution of private expenditure
over time is itself dependent on the paths of the real exchange rate and
domestic nominal interest rates. These are determined respectively by
the nontraded-goods market equilibrium condition (equation 6.19, re-
produced below for reference) and the arbitrage condition (equation 6.5),
reproduced below as equation 6.5':
(6.19) e= e(c,g,)
(6.5') i= (r + ir, + p(f)) +E-
where equation 6.5 has been modified to take into account the foreign
Fisher relationship and the supply-of-funds schedule (equation 6.17).
To analyze the properties of the long-run equilibrium real exchange
rate, begin by imposing the long-run equilibrium conditions c = e = i in
the Euler equation 6.15. This implies the steady-state condition equa-
tion 6.21:
(6.21) p
= r" + p(f).
Since rw and p are both exogenous, this equation determines the long-
run equilibrium value of the net international creditor position for this
economy, f*.12 Because the premium p is a decreasing function of the net
creditor position f, the equation implies that countries with a high rate
of time preference will be driven to have a smaller stock of net external
claims in long-run equilibrium than those with lower rates of time
preference.
Next, to derive the long-run equilibrium value of the domestic nomi-
nal interest rate, substitute equation 6.21 in 6.5', yielding equation 6.22:
i= (p + Z) + e
(6.22) .
12. This value can be positive or negative, without violating the transversality
conditions on the private and public sectors.
DETERMINANTS OF THE LRER 277
This value of i pins down the long-run values of consumption velocity h
and transactions cost per unit of consumption T, as expressed in equa-
tions 6.23 and 6.24:
(6.23) h*= h(i) = h(p + *)
(6.24) * = Tfh(i)] = T[h(p + x*)].
With these results in hand, the conditions that characterize the long-
run equilibrium real exchange rate in this model can be described. Us-
ing equations 6.22 and 6.24 in 6.21 yields equation 6.25:
(6.25) 0 = YT(e)+ pf -(T[h(p +;,r*)] +6)c - g,.
This is the long-run external balance condition in the model. It states
that for the economy's real external net creditor position to reach an
equilibrium value, the inflation-adjusted current account balance must
be zero. An alternative and more useful formulation, however, focuses
on the conventional (non-inflation-adjusted) current account balance.
Adding the inflation adjustment 7rwf* to both sides, we can write equa-
tion 6.25 as 6.25':
(6.25') ,wf*=y,(e)+(p+rw)f*-(rl h(p+nr +eO+6)c-g,.
Condition 6.25' states that in long-run equilibrium the real current ac-
count balance, which is equal to real national saving, must be equal to
the inflationary erosion of the real value of the country's net claims on
the rest of the world.13 The latter represents the sustainable value of the
country's capital account balance. A net creditor country (with a posi-
tive value of f*) would run a sustainable current account surplus and
capital account deficit that would enable it to acquire claims on the rest
of the world that are sufficient to offset the inflationary erosion of its
existing claims. By contrast, a net debtor country would run a sustain-
able current account deficit and capital account surplus, accumulating
13. The model from which equation 6.25 was derived does not feature growth
of productive capacity. In a growth context-for example, with constant Harrod-
neutral technical change at the rate n-steady-state equilibrium would require
constancy of the country's net international creditor position per effective worker,
so the left-hand side of equation 6.25 would be modified to (n + 2,)f. In a growth
context, a net debtor country would be able to run larger sustainable current
account deficits than in the static case.
278 EXCHANGE RATE MISALIGNMENT
new debt sufficient to offset the effective amortization of its existing debt
through the inflation component of its nominal interest payments.
Since YT is increasing in the real exchange rate e, and since an increase
in consumption expenditure reduces the trade surplus, the set of combi-
nations of e and c that satisfies equation 6.25' is plotted as the positively
sloped external balance locus EB in figure 6.2. Internal balance is, of
course, given by the nontraded-goods market clearing condition 6.19.
As suggested by equation 6.19, the locus traced out by the set of combi-
nations of e and c that are consistent with internal balance (IB) has a
negative slope in figure 6.2. The long-run equilibrium real exchange rate
is that which is simultaneously consistent with external and internal
balances in the long run. It is defined by the intersection of the two loci
at point A in figure 6.2, and is labeled e*.
Long-Run Fundamentals
The response of the long-run equilibrium real exchange rate to its fun-
damental determinants can be established by examining the effects of
permanent changes in the various exogenous variables included in the
Figure 6.2 Determination of the Long-Run Equilibrium Real
Exchange Rate
e
EB
A
e* - - - - - - - - - - - -
II
Ic
C
Note: An upward movement is a depreciation of the real exchange rate.
DETERMINANTS OF THE LRER 279
model on the location of the long-run equilibrium point A. In this sec-
tion, I take up these fundamentals one at a time, identifying individual
fundamentals as well as the qualitative nature of their influence on the
long-run equilibrium real exchange rate.
Fiscal Policy
I begin by considering changes in government spending, holding the
fiscal deficit constant. As is well known, effects on the long-run equilib-
rium real exchange rate depend on the sectoral composition of these
changes."
Changes in Government Spending on Traded Goods
An increase in government spending on traded goods has no effect on
the internal balance locus, but it shifts the external balance locus up-
ward-to EB' in figure 6.3. The increase in government spending cre-
ates an incipient trade deficit, which requires a real depreciation in or-
der to maintain external balance. As indicated in figure 6.3, at the new
long-run equilibrium B, the equilibrium real exchange rate depreciates,
and private consumption of traded goods falls." The reduction in pri-
vate consumption of traded goods is smaller than the increase in gov-
ernment consumption, however, because the real depreciation induces
an increase in the production of traded goods, allowing the accommo-
dation of an increase in total spending on traded goods.
Changes in Government Spending on Nontraded Goods
In contrast to the previous case, the locus affected in this case is the
internal balance locus IB. The increased demand for nontraded goods
requires an increase in their relative price to maintain equilibrium in the
nontraded-goods market, and the IB schedule thus shifts downward, to
14. For earlier work on the effects of the composition of government spend-
ing on the long-run equilibrium real exchange rate see Montiel (1986) and Khan
and Lizondo (1987).
15. In contrast, Penati (1987) finds that an increase in government spending
on traded goods has no effect on the long-run equilibrium real exchange rate.
The aspect of model specification that accounts for this difference is that in the
present model, a steady-state equilibrium is ensured by an endogenous risk pre-
mium, while in Penati's model the same result is achieved by endogenizing the
rate of time preference. This feature makes Penati's model block-recursive and
permits external balance to be restored after an increase in government spend-
ing on traded goods through an increase in the economy's net claims on the rest
of the world, with no repercussions for relative prices.
280 EXCHANGE RATE MISALIGNMENT
Figure 6.3 Effects of Changes in Government Spending on the Long-
Run Equilibrium Real Exchange Rate
e
EB'
EB
B
A
e2 --------------- -- - -
C
IB'
IB
Note: An upward movement is a depreciation of the real exchange rate.
IB' in figure 6.3. The new equilibrium is at point C. As in the previous
case, private consumption expenditure is crowded out in long-run equi-
librium, but in this case the equilibrium real exchange rate appreciates.
The upshot of this exercise and the previous one is that the long-run
equilibrium real exchange rate is a function of the sectoral composition
of government spending.
A Reduction in the Fiscal Deficit
Consider a reduction in the fiscal deficit, in the form of a tax increase.
Since taxes are actually endogenous in the model under the assump-
tions made in the section on the analytical framework, this shock is
equivalent to a reduction in the rate of monetary emission by the central
bank, which in turn is equivalent to a reduction in the rate of crawl of
the nominal exchange rate. The gain from a lower fiscal deficit in this
model comes in the form of a reduction in the distortions associated
with the inflation tax. A reduced rate of depreciation lowers the domes-
tic interest rate, increases the demand for money, and reduces the trans-
actions costs associated with consumption-in other words, T* falls. This
has the effect of increasing the supply of real output. Whether the long-
run equilibrium real exchange rate will appreciate or depreciate depends
DETERMINANTS OF THE LRER 281
on whether transactions costs are borne in the form of traded or
nontraded goods.6 This will determine the form that the increase in real
output takes. As currently specified, the model assumes that these costs
are borne in the form of traded goods. The reduction in r* will thus
increase the supply of such goods, shifting the external balance locus
downward and resulting in a real appreciation, together with an increase
in consumption. On the other hand, if transactions costs are incurred in
nontraded goods, the external balance locus would remain fixed, and
the internal balance locus would shift to the right. In that case, the
equilibrium real exchange rate would depreciate, and consumption
would rise."
It may be worth noting that the effects of a reduction in the fiscal
deficit brought about by changes in spending would simply be a combi-
nation of one of the first two shocks described above with the third. The
effects would depend on whether the reduction in spending fell on traded
or nontraded goods, as well as on the composition of transactions costs.
Changes in the Value of International Transfers
The other demand-side variable that enters the model is the external
real interest rate r,. Before analyzing the effects of changes in external
financial conditions, however, it is useful as a point of reference to con-
sider the effects on the equilibrium real exchange rate of changes in the
level of international transfers received by the domestic economy. These
will provide an interesting contrast with the case of interest rate changes.
As formulated above, the model does not explicitly consider the role of
international transfers. It is straightforward to add them, however. Such
transfers would simply represent an addition to household incomes equal
to the amount of the transfer. They would appear as an additive term in
the household's budget constraint equation 6.7, in the dynamic equa-
tion 6.20 forf, and in the long-run equilibrium condition equation 6.25'. "1
Accordingly, the effect of a permanent increase in the receipt of transfer
income would be to shift the external balance locus to the right-the
16. This property that the long-run equilibrium real exchange rate is affected
by a change in the rate of monetary expansion-that is, the failure of
superneutrality-also characterizes the model of Penati (1987).
17. A change in the foreign inflation rate i, affects the model in exactly the
same way as a change in the rate of depreciation E, since the two variables enter
only in the additive form 7r* = e + tFv in equation 6.25.
18. It makes no difference in this model whether the transfer is received di-
rectly by the private sector or whether it goes to the government, since under the
fiscal regime assumed above, the latter would transfer the proceeds to the pri-
vate sector.
282 EXCHANGE RATE MISALIGNMENT
receipt of additional transfer income permits an expansion of consump-
tion to be consistent with external balance at an unchanged exchange
rate. There are no direct effects on the internal balance locus, so the equi-
librium is at B in figure 6.4, with an equilibrium real appreciation and an
increase in private absorption.
Changes in International Financial Conditions
The analysis of transfers is instructive because many observers' intu-
ition about the effects of changes in capital inflows on the long-run equi-
librium real exchange rate is derived from the corresponding effects of
transfers. Capital inflows and transfers have in common the feature that
they permit an expansion of absorption relative to income in the short
run. However, the two phenomena differ in two important respects. First,
the volume of capital inflows is an endogenous variable that can arise
from a variety of changes in domestic and external economic conditions.
Presumably, the change in the long-run equilibrium real exchange rate
associated with a particular capital-inflow episode depends on the source
of the shock that triggers the inflow. Second, unlike transfers, capital
inflows create repayment obligations in the long run. These also will
affect the long-run equilibrium real exchange rate.19
Consider, then, a particular shock that has been associated with the
emergence of capital inflows: a reduction in world real interest rates.20
Again, this shock directly affects only the external balance locus. To see
in which direction the locus moves, differentiate equation 6.25':
de/dr, + <0.
Thus, the real exchange rate consistent with external equilibrium moves
in a direction opposite to the world interest rate. In this case, when the
world real interest rate falls, the external balance locus thus shifts
19. Such obligations will affect the long-run equilibrium real exchange rate
under the "stock" approach to the definition of external balance described in the
previous chapter, which is the approach adopted here. If the "flow" approach
were adopted instead, the effects of capital inflows on the LRER would resemble
those of transfers, except that the endogenous nature of capital inflows would
cause those effects to depend on the source of the shock triggering the inflows.
20. The view that the capital-inflow episode affecting several large develop-
ing countries during the early 1990s was triggered by a reduction in interest
rates in the United States, first put forward by Calvo, Leiderman, and Reinhart
(1993), is now widely accepted. For a review of this episode, see Fernandez-
Arias and Montiel (1996).
DETERMINANTS OF THE LRER 283
Figure 6.4 Effects of Changes in Foreign Transfers and World Real
Interest Rates on the Long-Run Equilibrium Real Exchange Rate
e EB"
LB
C
e2 - -- -- --- - -- - ---
EB'
A
BL
I I
II
C2 C 01
Note: An upward movement is a depreciation of the real exchange rate.
upward, to a position similar to EB " in figure 6.4, and the equilibrium
real exchange rate, determined at point C, actually depreciates, contrary
to what happens in the case of an increase in the level of transfer receipts.1
Why is this the case? Equation 6.25' suggests that the effect of a change
in world interest rates on the real exchange rate consistent with external
balance depends on the effect of this change on the country's long-run
net interest receipts. Thus, like those of a transfer, the effects of a change
in external interest rates on the long-run equilibrium real exchange rate
depend on their long-run implications for national income. In this model,
however, the implications of a reduction in world interest rates for
21. Notice that deldr~, does not depend onf*. Thus, the direction of the shift in
the external balance locus, and therefore the result that a change in r, causes the
long-run equilibrium value of e to move in the opposite direction, does not de-
pend on whether the economy is initially a net external creditor or debtor. This
result is also derived, with a different approach to modeling imperfect asset sub-
stitutability, by Agenor (1996). However, the dynamics of adjustment to the new
equilibrium do indeed depend on the economy's initial international net credi-
tor position, as shown in Montiel (1998).
284 EXCHANGE RATE MISALIGNMENT
national income are negative in the long run, unlike those of transfers.
This is precisely because of the capital inflows induced by the change in
world financial conditions. In the new long-run equilibrium, the
country's net creditor position with the rest of the world deteriorates,
reflecting the effects of net external borrowing (capital inflows) during
the transition from one long-run equilibrium to the next.2 The change
in the external real interest rate has no other direct effects on the country's
long-run current account balance (equation 6.25'). In particular, the in-
terest rate that the country actually faces in world capital markets is
unchanged from one long-run equilibrium to the next, because changes
in the country's net external creditor position drive that interest rate to
equality with the domestic rate of time preference. A higher risk pre-
mium, associated with a reduced net international creditor position, rec-
onciles the constant effective interest rate faced by domestic residents in
the long run with the lower world interest rate. Since, unlike in the case
of transfers, the borrowing has to be repaid, this is reflected in a reduc-
tion in long-run equilibrium national income.2
The Balassa-Samuelson Effect
To capture the effects of differential productivity growth in the traded-
goods sector, the production function in this sector can be respecified as
shown by equation 6.26:
(6.26) yT =YT(LT,a); Y- > 0, YT2 >0
where a is a productivity parameter. Since the demand for labor in the
traded-goods sector will now be a function of this productivity param-
eter, labor market equilibrium becomes equation 6.27:
(6.27) LT(w,a)+ L,(w)= L
and the equilibrium real wage can be written as equation 6.28:
w=w(e,a), with:
(6.28) LT2
w2 = _> 0.
LTI + LNe
This means that output in the traded- and nontraded-goods sectors are
given respectively by equations 6.29 and 6.30:
22. The transition is described in Montiel (1998).
23. For a more extensive discussion of this issue, see Agenor (1996).
DETERMINANTS OF THE LRER 285
(6.29) YT = yT [LT [w(e, a), a], a]
dy,L L4e L YT2>.
da LT1 +L've
YN = yN[LN[w(e,a)]], with:
(6.30) dy,, I,I
da = y,L,w2 < 0.
Thus, the effect of the productivity shock in the traded-goods sector is
to increase the demand for labor in that sector, thereby increasing the
equilibrium real wage. In turn, this causes the nontraded-goods sector
to release labor, which is absorbed by the traded-goods sector. At a given
real exchange rate, the traded-goods sector expands, while the
nontraded-goods sector contracts.
To examine the effects on the long-run equilibrium real exchange rate,
notice that the productivity shock a enters the internal and external bal-
ance equations 6.19 and 6.25' only through its effects on yN and y, re-
spectively. Since, according to equation 6.30, an increase in a reduces y,
it creates excess demand in the nontraded-goods market, requiring a
real appreciation to restore internal balance. In figure 6.5, the IB locus
shifts downward. At the same time, however, by increasing production
of traded goods (see equation 6.29), the shock gives rise to an incipient
trade surplus, so a real appreciation is also required for the restoration
of external balance. Thus, EB shifts downward as well. Both effects op-
erate in the direction of equilibrium real appreciation, as proposed by
the Balassa-Samuelson analysis. Thus, differential productivity growth
in the traded-goods sector creates an appreciation of the equilibrium
real exchange rate."
Changes in the Terms of Trade
As indicated previously, the model as specified is not suitable for ana-
lyzing changes in the terms of trade, since exportable and importable
goods are not distinguished from each other in the traded-goods sector.
To make the necessary modifications, split up total traded-goods out-
put into output of exportables yx and importables yz, both produced
under conditions described previously for YT, that is, with a fixed
24. It can be shown that the downward shift in EB exceeds that in IB. The
implication is that the favorable productivity shock results in an increase in real
private absorption in equilibrium, as one would expect.
286 EXCHANGE RATE MISALIGNMENT
Figure 6.5 Effects of Differential Productivity Shocks and Terms-of-
Trade Changes on the Long-Run Equilibrium Real Exchange Rate
e A
e* - - --~-- -- ----- -
EB'
e B
IB
I JB'
c* C,
Note: An upward movement is a depreciation of the real exchange rate.
sector-specific factor and mobile labor, with sectoral employment lev-
els Lx and LZ. Let 0 denote the terms of trade, defined as the price of
exportables in terms of importables, and redefine the real exchange rate
e as the relative price of importables in terms of nontraded goods. To keep
the demand side of the model simple, assume that the exportable good
is not consumed at home.
The analysis of the effects of terms-of-trade changes is, as might be
expected, quite similar to that of productivity shocks to the traded-goods
sector. Labor market equilibrium is now given by equation 6.31:
(6.31) Lx(w/) + Lz(w) + L,(we) = L
where w is now the real wage in terms of importables. The real wage
that clears the labor market becomes:
w = w(e, O), with
(6.32) L'w /2
w2 = w > 0.
L/0 + L' + L',e
DETERMINANTS OF THE LRER 287
An improvement in the terms of trade increases the real wage, because
this permits labor to be transferred from the importables and nontraded
sectors to the expanding exportables sector. Sectoral supplies are now
as expressed in equations 6.33, 6.34, and 6.35:
dp
y = y7[Lw(e, )]
(6.34) dy y L W 0
y, = y[L,[w(e,0)e]]
(6.35) dyN = yLQw,e <0.
The internal balance equilibrium condition remains as before, with the
exception that output of nontraded goods is now specified as in equa-
tion 6.35. The external balance condition (equation 6.25'), however, has
to be modified to take into account that traded-goods production now
involves output of both exportables and importables, yielding equa-
tion 6.36:
(6.36) rwf*= yx(e,)+yz(e,o)+(p+ ,)f*-(z *+O)c -gz
As shown above, an improvement in the terms of trade results in a con-
traction in output of nontraded goods. The resulting excess demand in
the nontraded-goods market causes the internal balance schedule to shift
downward. The effects on the external balance schedule depend on
whether the real value of total traded-goods output increases or de-
creases. This effect is given by:
a(0yx +Yz) = yx - Py'IAew,> 0
The value of traded-goods output increases through two channels: a
valuation (income) effect arising from the higher relative price of
exportables and an output effect arising from the absorption in the ex-
portable sector of labor released by the nontraded-goods sector. The
implication is that, as in the case of the favorable productivity shock, the
external balance locus will shift downward-the incipient improvement
288 EXCHANGE RATE MISALIGNMENT
in the trade balance requires a real appreciation to keep the trade bal-
ance at its sustainable level. Thus, the effects of a terms-of-trade im-
provement can also be represented as in figure 6.5.25,26
Commercial Policy
Finally, consider the effects on the long-run real exchange rate of a liber-
alization of commercial policy, modeled as a reduction in export subsi-
dies. This is the simplest case to model in the present context, because it
makes using several of the results derived for the analysis of the effects
of terms-of-trade shocks possible. Consider, in particular, an export sub-
sidy set at the rate (4 - 1). In this case, the internal terms of trade will be
0, and the previous analysis can be repeated, at least on the supply side
of the economy. In particular, an increase in the subsidy would pull la-
bor out of the importable and traded-goods sectors into the exportables
sector, just as would an equivalent favorable terms-of-trade shock. A
direct implication is that effects of subsidy changes on the internal bal-
ance schedule IB are the same as those of an equivalent terms-of-trade
shock. A subsidy increase causes IB to shift downward by creating an
excess demand for nontraded goods, and a subsidy decrease causes it to
shift upward.
Where matters differ is in regard to the effects of export subsidies on
the external balance schedule. Because changes in the internal terms of
trade have the same output effects whether brought about by external
terms-of-trade changes or by subsidy rate changes, an increase in the
subsidy rate would create an expansion in the output of traded goods
and cause an incipient trade balance improvement, just as before. Again,
the reason is because a subsidy increase draws labor from the nontraded
to the exportables sector. However, the income effect is absent in this
case. The reason is that, unlike in the case of an external terms-of-trade
improvement, the increase in the price of exportables brought about by
a subsidy increase has to be financed. In the case of the subsidy, a tax
liability is created for the private sector in an amount equal to the sub-
sidy rate times the output of exportables-that is, in the amount (4 - 1)yx.
When this tax liability is taken into account in equation 6.36, the result is
equation 6.37:
25. Just as before, it can be shown that the downward movement in EB exceeds
that in IB, so the sustainable level of private absorption increases as a result of this
shock.
26. As figure 6.5 suggests, an improvement in the terms of trade is associated
with an appreciation of the long-run importables real exchange rate. Whether
the long-run exportables real exchange rate, given by eo, depreciates or appreci-
ates, however, is ambiguous in the model.
DETERMINANTS OF THE LRER 289
(6.37)
Irwf* =yx(e,0) +yz(e, )+(p + irw)f]* -(0 - 1)yx(e,) - (z +69)c
=yx(e,0)+ yz(e,0)+(p +7,)f *-(r +6)c.
The implication is that a given change in the export subsidy rate would
cause the external balance schedule to shift in the same direction, but by
a smaller amount, than a terms-of-trade change that has an equivalent
impact on the internal terms of trade.
In the case at hand, the issue concerns the effect on the real exchange
rate of liberalization of commercial policy-that is, a reduction in the
export subsidy rate. The results just established imply that a shock of
this type would shift both the internal and external balance schedules
upward, with the implication that commercial liberalization results in a
depreciation of the equilibrium real exchange rate.
Summary and Conclusions
The objective of this chapter has been to analyze the determination of
the long-run equilibrium real exchange rate in the context of a simple
analytical framework that is flexible enough to accommodate a broad
variety of potential influences on the real exchange rate. The long-run
equilibrium real exchange rate was defined as the rate consistent with
the steady-state value of a country's international net creditor position,
given the paths of all relevant policy and exogenous variables.
The determinants of the long-run equilibrium real exchange rate iden-
tified here consisted of the following:
Domestic Supply-Side Factors. The most venerable theory regarding
long-run real exchange rate determination is the Balassa-Samuelson ef-
fect. This was incorporated in the analysis in the form of an asymmetric
productivity shock favoring the traded-goods sector. The equilibrium
real exchange rate appreciates, both because excess demand is created
in the nontraded-goods sector and because the trade balance tends to
improve.
Fiscal Policy. Changes in the composition of government spending
between traded and nontraded goods affect the long-run equilibrium
real exchange rate in different ways. Additional tax-financed spending
on nontraded goods creates incipient excess demand in that market, re-
quiring a real appreciation to restore equilibrium. By contrast, tax-fi-
nanced increases in spending on traded goods put downward pressure
on the trade balance, and require a real depreciation to sustain external
balance. The effects of a tax-based fiscal adjustment depend on the form
in which transactions costs are incurred.
290 EXCHANGE RATE MISALIGNMENT
Changes in the International Economic Environment. The aspects of the
world economic environment analyzed here consisted of the terms of
trade for the domestic economy, the availability of external transfers,
the level of world real interest rates, and the world inflation rate. Im-
provements in the terms of trade and increases in the flow of transfers
received tend to appreciate the equilibrium real exchange rate, the former
both by improving the trade balance and creating excess demand for
nontraded goods, and the latter through positive effects on the current
account. Reductions in world real interest rates and increases in world
inflation, by contrast, cause the long-run equilibrium real exchange rate
to depreciate. Lower world interest rates cause capital inflows, which
reduce the country's net creditor position over time, and the long-run
loss of net interest receipts requires a real depreciation to maintain ex-
ternal balance. Changes in world inflation affect the equilibrium real
exchange rate through effects on transactions costs associated with
changes in real money balances. In the case of an increase in world infla-
tion, the long-run real exchange rate tended to depreciate in this model,
though this conclusion is sensitive to an essentially arbitrary assump-
tion about the form in which transactions costs are incurred.
Commercial Policy. Finally, trade liberalization, analyzed here in the
form of a reduction in export subsidies, is associated with long-run real
depreciation. The effect works by channeling resources into the
nontraded-goods sectors. The emergence of incipient excess supply in
the nontraded-goods market dictates the nature of the adjustment in the
real exchange rate.
Part III
Methodologies for Estimating
the Equilibrium RER:
Empirical Applications
7
Estimating the Equilibrium
RER Empirically:
Operational Approaches
Theodore 0. Ahlers and Lawrence E. Hinkle*
The estimation of long-run equilibrium RERs (LRERs) and measurement
of misalignment have traditionally relied on two approaches with strong
operational advantages: a relative purchasing power parity-based meth-
odology that assumes a stationary LRER and a target resource balance
methodology that employs trade equations or elasticities.' In addition,
in cases of split or multiple exchange rates, the parallel market rate has
sometimes been used as an indicator of misalignment.
The two traditional approaches are still widely used in operational
applications in both industrial and developing countries, particularly
when the data or time required for implementing more complex
methodologies are not available. Even when it is feasible to employ the
general-equilibrium methodologies discussed in the subsequent chap-
ters in Part III of this volume, the traditional operational approaches
still provide good starting points for the analysis, and transparent refer-
ence points for cross-checking the plausibility, of the results from the more
complex methodologies. Most of the input data required to implement
* Ms. Ingrid Ivins provided research and computational assistance in the prepa-
ration of this chapter. The authors are grateful to Peter Montiel, Fabien
Nsengiyumva, and three anonymous readers for very helpful comments on ear-
lier drafts.
1. The term resource balance is used in this chapter to refer to the difference
between exports of goods and nonfactor services, and imports of goods and
nonfactor services. The resource balance equals the current account balance ex-
clusive of net interest and other factor service payments.
293
294 EXCHANGE RATE MISALIGNMENT
the two operational approaches are needed for the other methodologies
in any case.
When the RER is stationary in a time-series sense, long-run equilib-
rium exchange rates may be estimated on the basis of relative purchas-
ing power parity (PPP) by using either a base-year or a trend approach.
The base-year approach first establishes a base period in which the ob-
served RER is believed to be at its equilibrium level. Misalignment is
then measured as the difference between the observed RER and its base-
period value, on the implicit PPP assumption that the LRER has remained
at its base level. The utility of this PPP-based methodology is limited
because of its inability to allow for permanent changes in the LRER that
would cause the RER to be nonstationary. The methodology is, how-
ever, still useful for analyzing situations where the LRER is believed to
have remained unchanged, such as when shocks to the economy have
primarily affected nominal variables or when shocks to the "real" fun-
damentals have been transitory In both cases, relative PPP would hold
during the sample period. Alternatively, the LRER may be estimated as
the trend or mean value to which the RER tends to return in the long
term under PPP theory; and misalignment is then measured as the de-
viation from this trend or mean value.
Since all the other methodologies for measuring misalignment, in-
cluding the trade-equations approach, are much more time-consuming
to implement than the above relative PPP-based approaches, these are
often the only feasible methodologies for multicountry studies in which
the amount of time that can be devoted to individual country cases is
limited. For the same reason, PPP-based graphical analysis is also widely
used for making initial diagnoses of individual countries and for identi-
fying hypotheses for analysis using more sophisticated techniques.
The trade equations-elasticities methodology is the second of the stan-
dard operational approaches for estimating the LRER. Although there
are a number of variations of this methodology, the key quantitative
relationships in each are relatively straightforward and transparent. Each
of the variants of this methodology involves the same three basic ana-
lytical tasks. First, trade equations or trade elasticities are used to estab-
lish a quantitative relationship between the RER, imports, exports, and,
hence, the resource balance. Second, a target, norm, or equilibrium re-
source balance is determined using independent projections of the sav-
ing-investment balance or of sustainable capital flows. And, third, the
actual resource balance in the initial year is adjusted for changes in cy-
clical, exogenous, and policy variables that affect it in order to estimate
the underlying structural balance and provide an appropriate basis for
computing the change required in the initial RER. The quantitative rela-
tionship between the RER and the resource balance established in the
ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 295
first step is then used to calculate the appreciation or depreciation in the
initial RER required to move the resource balance from its adjusted level
in the initial year to the target level, everything else remaining the same.
The estimated long-run equilibrium RER is the one that corresponds to
the target or equilibrium resource balance.
The trade-equations-elasticities methodology permits taking into ac-
count permanent changes in some of the fundamental determinants of
the RER. The methodology can directly address the relative price effects
of changes in the terms of trade and tariff rates, and cover, at least in a
back-of-the-envelope fashion, permanent changes in most of the other
fundamental exogenous and policy variables in which one may be in-
terested. Like the relative-PPP-based approach, the trade-equations meth-
odology can also provide useful inputs for more complex ones. For ex-
ample, adjusting the initial resource balance, determining a target re-
source balance, and projecting exogenous variables are steps common
to many of the approaches used for estimating equilibrium real exchange
rates. The analytical techniques for carrying out these steps, which are
set out in this chapter, are used both with the trade-equations method-
ology and with some of the other methodologies discussed in the subse-
quent chapters of Part III of this book.
As noted above, a parallel exchange rate has sometimes been used as
an additional indicator of distortions in the foreign exchange market
and potential misalignment. However, because exchange rate misalign-
ment does not necessarily lead to the development of a parallel market
and parallel rates are much less common than they were a decade ago,
opportunities to apply this approach are limited. Moreover, the approach
turns out to be fraught with analytical difficulties. For both reasons, the
existence of a parallel foreign exchange market is considered as a spe-
cial case in Part IV of this volume. There the chapter by Ghei and Kamin
examines the relationship between the parallel and the unified equilib-
rium exchange rates and considers the usefulness of the parallel rate as
a guide for determining a unified exchange rate.
This chapter discusses the two standard operational approaches for
estimating the LRER. The structure of the chapter is as follows. The fol-
lowing section first sets the PPP-based approach in the context of recent
theoretical and empirical work on the determination of equilibrium RERs
and then discusses the interpretation and usefulness of PPP-based esti-
mates of misalignment. The remainder of the chapter goes on to con-
sider alternative ways of carrying out the three basic analytical tasks
involved in implementing the trade-equations methodology. Since the
trade-equations methodology is more complex than the PPP-based ap-
proach, the rest of the chapter is considerably longer than the discussion
in the following section on the PPP-based approach. The first section on
296 EXCHANGE RATE MISALIGNMENT
the trade-equations approach discusses the use of trade equations and
trade elasticities to establish quantitative relationships between the RER
and the resource balance. It also presents a specific example of a trade-
elasticities methodology employing a three-good framework (with ex-
ports, imports, and domestic goods) that is suitable for use in low-in-
come countries with minimal data in which changes in the terms of trade
and commercial policy are important considerations. Then come two
sections on the resource balance. The first of these examines alternative
methods of determining a target resource balance using saving-invest-
ment balance and sustainable capital flows approaches. The second then
considers techniques for adjusting the initial resource balance to reflect
changes in cyclical, exogenous, and policy variables affecting it in order
to estimate the underlying structural balance. The final section concludes
with a brief discussion of the advantages and limitations of the trade-
equations methodology. The various analytical techniques are illustrated
with empirical examples for C6te d'Ivoire at the time of the devaluation
of the CFA francs in 1994.
The Relative PPP-Based Approach to RER
Misalignment
As noted above, the simplest methods of estimating the long-run equi-
librium RER are based on relative PPP. Although more sophisticated
methodologies that take into account variations in the fundamentals
determining the LRER have been developed, the PPP-based approaches
are still widely used in both graphical analyses of individual countries
and in econometric analyses of large multicountry samples because of
the relative ease with which these can be implemented.
The use of a relative-PPP-based methodology can be justified in ei-
ther of two ways. On the one hand, the analyst may simply adopt ex
ante the traditional relative-PPP view on the determination of the long-
run equilibrium real exchange rate, which essentially takes the LRER to
be a constant. On the other hand, the analyst may view the LRER as
being determined by a broad set of fundamentals, which may turn out
ex post to be stationary in a time-series sense for the specific country
concerned. In the first case, the decision to apply the PPP approach would
be made without considering the data. In the second case, the PPP ap-
proach would be adapted only after the RER for the country concerned
passes a test of stationarity.
Whichever justification for using relative PPP is adopted in a specific
case, theoretical and empirical work on PPP has suggested that the equi-
librium RER may be estimated in two ways-using either a base-year or
a long-term trend value. This section gives an updated presentation of
ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 297
these two standard techniques for estimating the LRER and then dis-
cusses the interpretation of such PPP-based analyses.
Base-Year Estimates of the Equilibrium RER
When relative PPP is assumed to hold ex ante, measuring the equilib-
rium real exchange rate essentially involves removing the effects of
nonsytematic transitory shocks. In practice, these are eliminated by iden-
tifying a base period in which such shocks are believed, on the basis of
independent evidence, to have been negligible-a procedure that en-
sures that the actual RER coincided with its equilibrium-PPP value in
the base period. Thus the actual RER in the base period represents the
estimate of the equilibrium rate, and the nominal exchange rate consis-
tent with the LRER from that moment on can be calculated by simply
adjusting the nominal exchange rate for the cumulative difference be-
tween domestic and foreign inflation.
The alternative case is that the LRER is interpreted as subject to change
in response to changes in underlying fundamentals but turns out em-
pirically to be stationary for a particular country. In this case, the
stationarity of the RER forces the analyst to take the position that its
fundamental determinants are either individually stationary-that is,
their "permanent" values have not changed during the sample period
although the fundamentals may have been subject to transitory varia-
tions-or that any nonstationary fundamentals must be cointegrated
among themselves. In either situation, the LRER can still be measured
using a base-year value, although the identification of a suitable base
year is more complicated under their interpretation. In this case, the
base-year method for estimating the equilibrium RER involves analyz-
ing the movements in the fundamental variables determining the LRER
to identify a base year in which, on average, these fundamentals, and
hence the RER, were at sustainable levels. If the fundamental variables
do not change after the base year, or return to their level in that year,
then the LRER should also remain at the base-year level. Misalignment
is then measured as the difference between the actual RER in the current
year and its (unchanged) equilibrium value in the base year.2 Note that
the expenditure-PPP version of the external RER (usually computed with
CPIs) should be used both in the base-year analysis and in the trend
analysis discussed below since this RER concept is the one employed in
relative-PPP theory.
2. Appreciations, depreciations, and misalignment may be expressed in ei-
ther domestic- or foreign-currency terms. Formulas for converting from one to
the other are given in appendix C.
298 EXCHANGE RATE MISALIGNMENT
The base-year approach is most useful in cases in which all move-
ments after the base year result from either nominal shocks (which tem-
porarily cause the actual RER to diverge from its equilibrium level) or
from transitory movements in the fundamentals. However, if the fun-
damentals change permanently after the base year, so too will the LRERW
In this case, the base-year approach will provide little guidance on the
RER's new equilibrium value until a new base year has been established.
In the base-year approach everything thus depends upon the identifica-
tion of a suitable base year.
The definition of the long-run equilibrium RER in Part II suggests
the criteria for selecting a representative base or equilibrium year. Re-
call that this definition requires that the current account deficit can be
financed by a "sustainable" level of capital flows and that the market
for nontraded (or domestic) goods also be in a sustainable equilibrium
for given values of the predetermined, exogenous, and policy variables
that influence these objectives. As mentioned above, the procedure for
choosing the base year also depends upon whether the rationale under-
lying the procedure is a simple ex ante relative-PPP-based one or a more
sophisticated one in which the real exchange rate is driven by stationary
fundamentals. In the simple PPP case, the "independent evidence" of
equilibrium referred to previously is likely to concern the behavior of a
particular outcome variable, such as the resource balance.
In contrast, from the "stationary fundamentals" perspective, the base
year chosen should be a recent year in which the actual exchange rate is
believed to have been close to its equilibrium value because all the fun-
damentals were close to their sustainable values. As explained in the
survey of empirical estimation in Chapter 5, the set of fundamentals to
be considered in choosing a base year may include both exogenous and
policy variables. In practice, when selecting base years, one usually fo-
cuses first on the external balance criteria, typically interpreted as choos-
ing a year with a reasonable or normal current account (or resource)
deficit for the country concerned. For assessing the sustainability of ex-
ogenous variables, the analyst looks for terms of trade that are reason-
ably close to their likely long-term trend levels and capital flows that
are consistent in amount and terms both with the likely longer-term
availability of capital and with the country's debt-servicing capacity. For
assessing the sustainability and desirability of policy or objective vari-
ables, one looks at growth, investment, employment, and inflation per-
formance and compares these to the country's long-run policy targets.
3. In addition, if the law of one price does not hold or only holds loosely, the
return to a base-year value could be quite slow even after a purely nominal shock
to the exchange rate, as domestic prices may be quite sticky and the actual RER
will tend to follow the nominal RER.
ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 299
Other things being equal, it is also desirable to select as recent a base
year as possible to minimize the changes in the economy's structure
taking place between the base year and the current year. Because a year
that is appropriate as a base for a particular country may not be appro-
priate for another, country-specific rather than standardized base years
should be used when measuring misalignment relative to a base year.'
The Devarajan-Lewis-Robinson (DLR) constant-elasticities model, the
econometric model, and the reduced-form econometric methodology
presented in Chapters 8, 9, and 10, respectively, also employ base peri-
ods, like those used here, in which the observed RER equals the equilib-
rium RER. The criteria for selecting these base periods are essentially
the same under these methodologies so that the base period used for the
relative-PPP-based analysis may also be used with the more sophisti-
cated methodologies.
A common problem in determining an appropriate base year is that,
because of policy shortcomings and external constraints, years in which
exogenous variables are at sustainable levels are not always years in
which policy variables were at desirable levels. For example, histori-
cally, desirable growth and investment levels have sometimes been at-
tained only when the terms of trade have been temporarily inflated or
capital flows have been unsustainable. Conversely, sustainable terms of
trade and capital flows have often been associated with undesirable
growth and investment outcomes. Hence, in determining when the RER
was near its long-run equilibrium value and selecting a corresponding
base year, one is often forced to make tradeoffs between sustainability
and desirability and to take these tradeoffs into account in an ad hoc
way in subsequent qualitative analysis. Moreover, in both historical and
forward-looking analysis, some care is needed in analyzing the move-
ments of the fundamentals to identify shifts in these or breaks in time
series that could indicate that a change in the base year is needed. As a
result, the choice of a base year may be subjective; and reasonable alter-
natives should be considered when they are available.
For the C6te d'Ivoire examples shown in the graphs in this section,
the RER was nonstationary, as explained in Chapter 10, and 1985 was
chosen as the base or equilibrium year for analytical purposes. This was
the most recent year before the devaluation year of 1994, in which both
the terms of trade and capital flows were at broadly sustainable levels
and there was reasonable growth and low inflation. This choice, however,
4. The standard procedure is to select the RER for the base year as its equilib-
rium value. However, because of lags in the effects of the RER on the economy,
one could also argue that the RER for the preceding year or a three-year moving
average centered on the preceding year would be a more accurate estimate of
the rate that actually generated the base-year equilibrium.
300 EXCHANGE RATE MISALIGNMENT
has elements of both unsustainability and undesirability. The situation
in 1985 was unsustainable in that the debt service burden was too heavy
for the long term and the terms of trade were more favorable than their
historical trend. It was also undesirable in that the investment level was
too low to support the desired long-term growth rate and trade policy
was too restrictive to promote accelerated export and productivity
growth. Hence, even in 1985 the actual RER was probably overvalued
relative to the equilibrium RER in normative terms and even somewhat
overvalued in positive terms. Furthermore, as a result of the sharp de-
cline in the terms of trade in subsequent years, the equilibrium RER
probably depreciated in the 1986-93 period rather than remaining con-
stant at the 1985 base-year level as assumed in the PPP-based analysis.
The effect that choosing different base years can have on PPP-based
analysis is illustrated in figure 7.1. In the long debate over the overvalu-
ation of the CFA franc, most of those arguing for a devaluation chose
1985 as the best available base year. This choice indicated that on the eve
of the devaluation in 1993 Cte d'Ivoire's actual real effective exchange
rate (REER) had appreciated by 37 percent relative to the equilibrium
base year. In contrast, some of those arguing for maintaining the exist-
ing parity chose 1980 as a base year, a choice which showed that C6te
d'Ivoire's actual REER in 1993 was close to its base-year level. Note, in
addition, that the use of either year as a base assumes that the equilib-
rium RER remained constant at the level of that year. If, however, as
discussed in the preceding paragraph, the sustainable values of the terms
of trade or other fundamentals in fact deteriorated after the base year,
the equilibrium RER would depreciate. The use of either base year would
thus give an underestimate of the misalignment.
Means for Short Base Periods
For sustainability of predetermined variables, theoretically it would be
desirable to have an equilibrium period, rather than just a single equi-
librium year, so that the predetermined variables have time to approach
their steady-state values. In addition, in practice all of the fundamentals
will not necessarily be at sustainable levels in precisely the same year.
One way of dealing with these problems is to use the average value of
the RER over a short equilibrium period as a base. However, the utility
of this alternative empirically depends very much on the situation in
the particular country concerned. In some circumstances, particularly
when an appropriate choice of base year is not obvious or when a coun-
try has a market-determined exchange rate that fluctuates significantly
year to year, a mean for a short time period may be a more representa-
tive indicator of the equilibrium value of the RER than a single base-
year estimate. In other cases, equilibrium periods may be limited to little
ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 301
Figure 7.1 The REER for C6te d'Ivoire, 1970-95 (Base Years 1985= 100
and 1980=100)
140-
I
130
120 REER with Base
Year 1985
110-
100 .
90 *U .*.
80 REER with Base
---. :Year 1980
70 --
6 0I I I I I I I I
70 71 72 73 74 75 76 77 78 79 80 81 82 83 S4 85 86 87 88 89 90 91 92 93 94 95
--*--REERwith Base Year 1980 ----REER with Base Year 1985
Note: The REER has been calculated using CPIs, weighted average parallel and official ex-
change rates, and adjusted IFS country weights. An upward movement is an appreciation
of the REER.
Source: Computed from World Bank data.
more than a year or two by the volatility of the terms of trade, capital
flows, or other fundamentals. In Cte d'lvoire, for example, the longest
period in the 1980s that might reasonably have been used as a base was
1985-86. If this two-year period had been used as a base together with a
one-year lag in the RER, the results would have been similar to those
from using 1985 because the average RER for 1984-85 was almost equal
to that in 1985. However, when, as in this case, some exogenous or policy
variables diverge in the same direction from sustainable levels for the
entire period, the mean value of the RER for the period may not reflect
the sustainable values of these variables any better than does the RER
for a single year.
Long-Period Mean and Trend PPP Estimates of the
Equilibrium RER
One way of dealing with fluctuations in the fundamentals during the
sample period is to estimate their sustainable values on the basis of their
sample means or, in the trend-stationary case, as their trend values within
the sample. In effect, this procedure amounts to estimating the LRER as
the sample mean or the trend value of the RER within the sample, rather
than as the particular value of the RER in a specified base year. Hence,
302 EXCHANGE RATE MISALIGNMENT
instead of trying to identify a particular year or short span of years in
which the RER is believed to be at its equilibrium level, one tries to
identify the long-term trend value toward which the actual RER tends.
Thus, the LRER could be estimated as being the mean value of the RER
over a long period of time or as evolving along a deterministic or sto-
chastic trend. Justification for both procedures can be found in the
literature.
However, as discussed in the survey of empirical research on PPP in
Chapter 5, the evidence supporting relative PPP is not that strong; and,
hence, some care is needed in using this procedure. For example, ac-
cording to Clark and others (1994): "Empirical evidence suggests that
PPP-based indicators may be useful to explain long-run movements in
exchange rates among industrial countries, but less so to explain move-
ments of these exchange rates in the short run, or of exchange rates be-
tween industrial and developing countries, either in the long or the short
run." Hence, before deciding whether to use a long-period mean or a
trend as a base for a particular developing country, time-series data for
its RER should be analyzed to determine, if possible, whether its RER
has been stationary for the sample period as illustrated for C6te d'Ivoire
and Burkina Faso in Chapter 10 on the single-equation methodology.
Unfortunately, sometimes the short time period for which RER data are
available and the weak power of unit-root tests will make it impossible
to determine whether the RER is stationary or nonstationary for the
sample period. Both possibilities should then be considered.
Means for Long Time Periods.
The long-run referred to in the above citation for which relative PPP has
been found to hold for a few industrial countries is in fact very long-
specifically, periods of 70 to 100 years, over which both nominal and
real shocks to the external RER may prove transitory. In addition, ultra-
long-term relative PPP has been shown to hold only for a small group of
industrial countries with fairly similar income levels. The long-term
behavior of RERs between developing and industrial countries at quite
different income levels, which is our primary interest here, could be
equally different. If a sufficiently long data series is available for a par-
ticular developing country, the equilibrium value of the RER in the very
long term could be determined as its mean; and RER misalignment could
be measured accordingly However, data for 70 to 100 years are only
rarely available for developing countries. Data for even 20 to 30 years
are hard to come by for many low-income and transition economies.
Since PPP theory permits extended periods of misalignment during
which the actual RER diverges from its long-term equilibrium value and
empirical studies of PPP have found substantial volatility in RERs and
ESTIMATING THE EQU[LIBRIUM RER EMPIRICALLY 303
only very slow convergence toward the mean, the significance of a mean
for anything other than a very long period is not clear. Despite the weak-
ness of the theoretical and empirical support for PPP, it is entirely pos-
sible that, as in the Burkina Faso case in Chapter 10, the RER for a par-
ticular country will be stationary for a given sample period. In this case,
the mean value of the RER for the sample period will be the best esti-
mate of its equilibrium value. However, when available time-series data
are long enough neither for determining with any accuracy whether the
RER for a particular country is stationary or nonstationary nor for com-
puting a meaningful long-term mean, a base-year estimate of the equi-
librium RER is likely to be preferable.
Trend Estimates of the Equilibrium RER
As discussed in the chapter on the two-good internal RER and the sur-
vey of empirical research, the Balassa-Samuelson effect provides theo-
retical justification for observing persistent long-term trends in the equi-
librium RER. Countries experiencing significantly higher or lower pro-
ductivity growth than their trading partners should show a statistically
significant long-term trend appreciation or depreciation in their exter-
nal RER. Demand factors (for example, a high-income elasticity of de-
mand for services and other nontraded goods) or long-term trends in
other fundamentals (for example, a sustained deterioration in the terms
of trade) can also generate trends in the RER. In samples for which the
RER is nonstationary, such trends are more meaningful measures of the
equilibrium RER than the mean; and misalignment should be measured
relative to the trend value of the RER rather than relative to its mean.
Such time trends can be either deterministic or stochastic. Figure 7.2
shows the time trends in the RER for C6te d'Ivoire and compares these
to the mean and 1985 base-year values of the equilibrium RER. Since
empirically it is very hard to distinguish between deterministic and sto-
chastic time trends with short noisy time-series data, deterministic trends
have been used in figure 7.2 for simplicity.
Interpretation of PPP-Based Analyses
Five points concerning the interpretation of analyses based on relative
PPP are worth noting: (a) the alternative of measuring competitiveness
only in terms of goods that are internationally traded, (b) the relation-
ship between the expenditure-PPP external RER and the internal RER,
(c) the effects of structural breaks in the RER series, (d) statistical indica-
tors of misalignment from multicountry studies, and (e) measures of
misalignment based on data for standardized baskets of goods from the
International Comparison Programme (ICP).
304 EXCHANGE RATE MISALIGNMENT
Figure 7.2 C6te dIvoire: The REER-Actual Values, Average Values,
and Time Trends, 1967-85 and 1986-93 (1985=100)
160
150-
140-
130-
120-
11011---------------- - ---- ---------
100-
90
80 1
67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
-*-Actual Values 1967-95 ------ Average Value 1967-85
--- Time Trend 1967-85 -*- Time Trend 1986-93
--- Average Value 1986-93
Note: The time trend value was computed as an OLS regression of the logarithm of the
REER and a time trend. The annual growth rate is 0.3 percent in 1967-85 and 1.0 percent in
1986-93. The REER was computed using CPIs, adjusted country weights, and weighted aver-
age official and parallel exchange rates. An upward movement of the REER is an appreciation.
Source: Computed from World Bank data.
Competitiveness in Internationally Traded Goods: An Alternative
Approach
The base-year and trend approaches for measuring RER misalignment
were originally developed for use with the expenditure-PPP version of
external RER. However, they can be used equally well with the external
RER for traded goods since relative PPP can be applied to traded goods
as an interpretation of the law of one price. As discussed in the chapter
on the external RER, it can, in fact, be quite reasonably argued that the
entire foregoing analysis should be in terms of the external RER for traded
goods rather than the expenditure-PPP version using CPJs.
Theoretically, somewhat different behavior should be expected in the
prices of homogeneous and differentiated traded goods, with the exter-
nal RER for homogeneous traded goods obeying relative PPP more
closely than the RER for differentiated traded goods. Unfortunately,
5. Although the theoretical basis for expecting relative PPP to hold for inter-
nationally traded goods is stronger than for all goods (both traded and nontraded),
Isard and Faruquee (1998) note that the hypothesis that the relative price of traded
ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 305
data on the relative prices of internationally traded goods are only avail-
able for recent years for industrial countries and often not available at
all for developing countries. Because of the shortage of data, relatively
little empirical research has been done for industrial countries, and even
less research for developing countries, on whether relative PPP holds
for traded goods.
When the required data are available, it is useful to examine the be-
havior of the external RERs for both homogeneous and differentiated
traded goods. Unfortunately, only limited data are available for the prices
of traded goods in C6te d'Ivoire. Since these data have already been
presented in figures 2.12 and 2.13 in Chapter 2 on the external RER and
the application of the techniques presented above to traded goods is
straightforward, the external RER for traded goods is not shown here.
Relationship to the Internal RER
Because of the Belassa-Samuelson effect and highly income-elastic de-
mand for nontraded goods, all countries in which productivity grows
faster in the traded-goods sector than in the nontraded-goods sector,
the common experience, should experience a sustained trend apprecia-
tion in the equilibrium internal RER. This pattern is in fact what has
been observed in studies of the internal RER in industrial countries. De
Gregorio, Giovannini, and Wolf (1994), for example, find that for 14 in-
dustrial countries the internal RER appreciated almost uniformly at an
average rate of more than 1 percent per year in the period 1970-85. Fur-
thermore, as explained in earlier chapters, it is entirely possible and con-
sistent for the external RER for all goods, the external RER for traded
goods, and the internal RERs to follow different trends. The typical pat-
tern for a country experiencing more rapid productivity growth than its
trading partners is a rapidly appreciating internal RER, a more slowly
goods should remain constant over time can still be questioned on the following
grounds: "(1) the composition of tradable goods across countries can change
over time; (2) changes over time in the relative prices of different tradables can
contribute to deviations from PPP insofar as the weights of different categories
of tradable goods in national price or cost indices differ across countries; and (3)
the scope for arbitraging price or cost differentials across countries can be af-
fected by the liberalization of trade and foreign exchange restrictions, reduc-
tions in transportation costs, or changes in other components of the costs of mar-
ket penetration." But they conclude that "these limitations notwithstanding, cal-
culations of different measures of international price and cost competitiveness
can often be helpful when judging whether exchange rates are reasonably close
to medium-run equilibrium levels."
306 EXCHANGE RATE MISALIGNMENT
appreciating external RER for all goods, and a constant or depreciating
external RER for traded goods. The internal RER is, in addition, gener-
ally more useful than the external RER in assessing the magnitude of
real shocks.
Although relative PPP is not directly applicable to the internal RERs,
analytically it is still useful to know how the internal RERs have be-
haved both relative to trend and to their values in the last equilibrium
(base) year. Figures 7.3 and 7.4 thus look separately at the internal RERs
for imports and exports for C8te d'Jvoire. Figure 7.3 indicates that the
internal RER for imports behaved in a similar fashion to the expendi-
ture-PPP external RER, jumping upward by 20 percent during 1985-86
because of the appreciation of the nominal effective exchange rate (NEER)
and then remaining relatively stable until the 1994 devaluation. As fig-
ure 7.4 shows, the export sector was more severely affected than the
import competing sector. Because of the sustained decline in the prices
of its major export commodities (primarily coffee and cocoa) and de-
valuations by competing developing-country exporters, C6te d'Ivoire's
internal RER for exports appreciated strongly throughout the entire pe-
riod, rising by almost 80 percent during 1986-93, four times the appre-
ciation in the RER for imports.
Structural Breaks
Large external shocks and major regime shifts can cause structural breaks
in the RER data for developing countries and create significant prob-
lems in interpreting these. Such structural breaks can cause
nonstationarity in the RER and lead to significant shifts in means, trends,
and base years.
The data for C6te d'Ivoire provide a good example of the possible
effects of structural breaks. The combination of the large drop in C6te
d'Ivoire's terms of trade after 1985 and the strong appreciation in its
NEER shown in figure 7.5 caused a marked change in the external envi-
ronment that the country faced, and its RER was nonstationary as dis-
cussed in Chapter 10. Since figure 7.5 shows that the NEER and the terms
of trade behaved in significantly different ways in the periods 1967-85
and 1986-93, figures 7.2-7.4 take 1985 as the dividing point between
two different time periods and give the means and time trend values
separately for the 1967-85 and the 1986-93 periods. During 1967-85, the
average value of the expenditure-PPP external RER was 10 percent more
appreciated than the 1985 base-year level but showed little trend move-
ment over the period. In the 1986-93 period, in contrast, the external
RER appreciated strongly and was, on average, nearly 30 percent more
appreciated than in the 1985 base year.
Figure 7.3 C6te d'Ivoire: The REER and the Internal RER for Imports-Actual Values, Average Values, and Time Trends,
1970-85 and 1986-93 (1985=100)
140 ---
,* -RI . .-*r a.-
130 - - ,II
120 9-
100,
'0 ~ I
I '
10 - -- - - - - - ---
90 '
80 I
70I I I I I I I I I I l i l l I 1 1 1 1 11I
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
-U- Internal RER for Imports: Actual Values 1970-95 0 Internal RER for Imports: Time Trend 1970-85
--- Internal RER for Imports: Time Trend 1986-93 ------ Internal RER for Imports: Average Value 1970-85
- - - Internal RER for Imports: Average Value 1986-93 - - * - - REER
Note: The time trend value was computed as an OLS regression of the logarithm of the RER and a time trend. The annual growth rate is 0.4
percent in 1970-85 and -0.5 percent in 1986-93. The REER was computed using CPIs, adjusted country weights, and weighted average
official and parallel exchange rates. An upward movement is an appreciation.
Source: Computed from World Bank data.
Figure 7.4 C6te d1voire: The REER and the Internal RER for Exports-Actual Values, Average Values, and Time Trends,
1970-85 and 1986--93 (1985=100)
200 --
180
160
14 - e-- -- - - - --.- -
140
120
80 -
60
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
- Internal RER for Exports: Actual Values 1970-95 ------ Internal RER for Exports: Average Value 1970-85
- - - Internal RER for Exports: Average Value 1986-93 ----- Internal RER for Exports: Time Trend 1970-85
---- Internal RER for Exports: Time Trend 1986-93 - - * - - REER
Note: The time trend value was computed as an OLS regression of the logarithm of the RER and a time trend. The annual growth rate is 31
percent in 1970-85 and 7.9 percent in 1986-93. The REER was computed using CPlx, ad3usted country weights, and weighted average official
and parallel exchange rates. An upward movement is an appreciation.
Source: Computed from World Bank data.
ESTIMATING THE EQU1LIBRIUM RER EMPIRICALLY 309
Statistical Indicators of RER Misalignment
Because of the availability of CPIs for calculating the expenditure-PPP
version of the RER in most developing countries and the relative ease of
computing PPP-based measures of misalignment, these measures have
been used in numerous multicountry econometric studies. These stud-
ies have noted some empirical regularities that are useful in assessing
RER misalignment in individual countries. Since selection of appropri-
ate base years requires detailed knowledge of individual countries and
can be criticized as subjective, most large multicountry studies have
measured misalignment of the RER relative to its long-term mean or
trend value; and hence their insights apply to misalignment measured
in this way. In Chapter 12, for example, in analyzing parallel market
exchange rates for a sample of 24 developing countries, Ghei and Kamin
use a simple relative PPP-based measure for the equilibrium unified
RER-the average of the official real exchange over long periods of time
during which a county's exchange markets were unified.
Large appreciations of the actual RER relative to its trend value, which
are easily detectable in a PPP-based analysis, are often warning signs of
serious exchange rate misalignment and potential currency crises. For
Figure 7.5 C6te d'Ivoire: The Real Effective Exchange Rate (REER), the
NEER, and the Terms of Trade, 1970-95 (1985=100)
180
170- - NEER
160 -
150
140..*. 4 4
130 .
120 -.-
110 - REER
90
80 Teqs
70 ofTrade
60
5 0 l I l l I I I I I I I I I 1 1 I I
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
-a- NEER using Adjusted Country Weights and Weighted Average
Official and Parallel Exchange Rates
--+-- REER using CPIs, Adjusted Country Weights, and Weighted
Average Official and Parallel Exchange Rates
-+-- Terms of Trade
Note: An upward movement is an appreciation of the REER.
Source: Computed from World Bank data.
310 EXCHANGE RATE MISALIGNMENT
example, Milesi-Ferretti and Razin (1996, 1998) use the degree of appre-
ciation of the RER relative to its 25-year average (median) as a bench-
mark for assessing the sustainability of current account deficits and find
that even this crude measure of misalignment is a useful predictor of
currency crises. Kaminsky, Lizondo, and Reinhart (1997) find that sub-
stantial appreciation of the RER above its trend value is a warning sign
of a future devaluation and that the 10 percent of RER observations that
are the farthest from the trend are accurate leading indicators of a cur-
rency crisis within the next 24 months. Similarly, Goldfajn and Valdes
(1996, 1997) analyze a large set of RER appreciations for 93 countries
from 1960 to 1994 and find that for large real appreciations of 15 percent
to 35 percent relative to trend the probability of a subsequent devalua-
tion ranged from 68 percent for real appreciations of 15 percent or more
to 100 percent for appreciations exceeding 35 percent. Hence, even if
there is some uncertainty about the precise level of the equilibrium RER,
large appreciations in a short period of time are a warning sign of mis-
alignment. Finally, volatility of the real exchange rate, which is readily
measurable, implies that the RER spends more time farther away from
its equilibrium level. Volatility is, as noted in Chapter 11 on the effect of
the RER on trade flows, a deterrent to export growth; and, as Razin and
Collins (1997) have observed, volatility has served in effect as a reason-
able proxy for misalignment in some multicountry studies.
Measures of Misalignment Based on International Comparison
Program Data
Equilibrium exchange rates can be based on absolute as well as relative
PPP. As explained in the chapter on the external RER, measurement of
absolute PPP requires the use of standardized baskets of goods. For ex-
ample, the "Big Mac Index" is a simple one-good absolute-PPP exchange
rate, which The Economist uses as an informal indicator of the equilib-
rium nominal exchange rate. It is simply the ratio of the domestic-currency
price of a Big Mac in the home country to its price in the numeraire
country.' However, data for more comprehensive measures of absolute
PPP have been hard to come by.
Because relative-PPP-based measures of misalignment have various
theoretical shortcomings and estimating equilibrium exchange rates
using the more sophisticated methodologies discussed later in this vol-
6. See The Economist (1995, August 26) and (1996, April 27). In a lighter vein,
Cumby (1996) analyzes data for 14 countries for the "Big Mac Index" and finds
that their exchange rates converge to "Big Mac parity" twice as fast as to relative
PPP.
ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 311
ume is quite time-consuming, researchers have long sought a method-
ology simple enough to use in measuring misalignment for panel data
for a large number of countries. Until recently, the lack of price data for
representative standardized baskets of goods had inhibited the empiri-
cal use of absolute PPP for this purpose. Hence, as the Summers-Heston
data for standardized baskets of goods has become available for 90 or so
countries from the International Comparison Programme (ICP) described
in appendix A to Chapter 2, some researchers have utilized these to de-
velop alternative simplified procedures for estimating equilibrium ex-
change rates.
Aggregate ICP exchange rates have themselves occasionally been used
to analyze trade distortions and exchange rate misalignment. Nominal
exchange rates for developing countries derived from the ICP data are
generally lower (less appreciated) than nominal market exchange rates
with the U.S. dollar because of the Balassa-Samuelson effect discussed
in Chapters 3, 5, and 6. Figure 7.6, which compares the aggregate ICP
dollar exchange rate for GDP for C6te d'lvoire with the official rate,
illustrates this point. The magnitude of the differences between aggre-
gate ICP exchange rates and nominal exchange rates also tends to vary
inversely with per capita income.
A predictable tendency in the ICP data for the relative price levels of
countries to vary positively with their relative income levels as a result
of the Balassa-Samuelson effect has been exploited by a number of re-
searchers to derive estimates of the equilibrium RER. Dollar (1992) re-
gresses the relative price levels of the standardized baskets of goods
from the ICP data on relative per capita GDP. This regression gives him
a norm that he considers as the equilibrium relationship between the
free trade RER and per capita income. Deviations from this norm give a
measure of the combined effects of trade and exchange rate policy on
outward orientation. Bosworth, Collins, and Chen (1996) employ a pro-
cedure similar to Dollar's to derive a measure of exchange rate mis-
alignment that they then use in analyzing the factors affecting growth
in an 88-country sample. Razin and Collins (1997) use data on the rela-
tive international price of the standardized basket of consumption goods
and services in different countries as a measure of the real exchange
rate. This measure is then regressed on the fundamental variables deter-
mining the RER using panel data, and the fitted values are used as an
estimate of the equilibrium RER.
7. See, for example, Rogoff (1996) for data and regression results document-
ing these stylized facts.
312 EXCHANGE RATE MISALIGNMENT
Figure 7.6 CMte d'Ivoire: The International Comparison Programme
and Official Exchange Rates with the U.S. Dollar
0.0095
0.008511-m'. V,M. K- : International Comparison
0.0075-- . Program US$ Exchange Rate
0.0065-- orA
0.0055--
0.004-- Wit
0.0035-
Official US$
0.0025-. Ex change Rate..
0.0015-
60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96
-*--Official US$ Exchange Rate
- - a - - International Comparison Program US$ Exchange Rate
Note: An upward movement is an appreciation.
Source: Computed from World Bank data.
Such statistical analyses of ICP exchange rates may give broad indi-
cations of misalignment suitable for use in general multicountry studies
and provide country-specific information that is useful in particular
cases. However, more research is needed on the relationship between
these general measures of misalignment and those from the methodolo-
gies discussed elsewhere in this volume before basing policy recom-
mendations for individual countries on ICP exchange rates.
Conclusion: Advantages and Limitations of the
Relative-PPP-Based Approach
The relative-PPP-based approach set out above has a number of practi-
cal advantages in estimating the equilibrium RER in low-income devel-
oping countries. Its data requirements are limited. The methodology is
both straightforward and transparent. With simple computer spread-
sheets it is easy to run extensive sensitivity analyses of the results as-
suming different base years or means. A number of multicountry statis-
tical analyses of misalignment are also available for comparative pur-
poses. These are significant practical advantages for balance-of-payments
management in a developing country in which data and professional
manpower may both be limited. Relative-PPP-based measures of mis-
ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 313
alignment can also be quite useful in high-inflation countries where
shocks to the external RER are primarily nominal ones. Thus, for ex-
ample, the implementation of real exchange rate targeting has often re-
lied on simple relative-PPP-based rules.
The PPP-based approach does have some major limitations, however.
In developing countries, lack of data on the prices of internationally
traded goods usually forces one to use the external RER for all goods
(computed with CPIs) rather than the theoretically preferable external
RER for traded goods. The PPP-based analysis also relies on relatively
simple base-year or mean-trend estimates of the equilibrium RER. If there
are structural breaks in the time-series data for the RER or permanent
changes in the fundamentals and hence in the equilibrium RER, base-
period or mean estimates of misalignment may no longer be relevant,
and PPP analysis is of little help in determining the new equilibrium
RER. Moreover, real exchange rates can be quite volatile-and conver-
gence to the mean, if it occurs at all, is typically quite slow. Hence, the
RER may diverge from a PPP-based equilibrium for long periods, and it
may be of little practical use for policy purposes.
However, all of the other methodologies for measuring misalignment,
including the trade-equations approach discussed below, are much more
time-consuming to implement than the relative-PPP-based approaches.
Thus the relative-PPP-based approaches are often the only feasible meth-
odologies for multicountry studies in which the amount of time that
can be devoted to individual country cases is limited. For the same rea-
son, PPP-based analysis is also widely used for making initial diagnoses
of individual countries and for identifying hypotheses for analysis us-
ing more sophisticated techniques. A comparison of the movements of
the fundamentals with movements of the RER since the last equilib-
rium may also be useful for detecting cases of possible misalignment.
The PPP-based methodology thus provides a starting point-it may be
used alone, when nothing else is available, or as a reference point when
more sophisticated methodologies are also used.
The Trade-Equations Approach: Establishing the
Quantitative Relationship between the RER and
the Resource Balance
The second of the established operational methodologies for measuring
exchange rate misalignment is the trade-equations approach. The
8. See, for example, Calvo, Reinhart, and Vegh (1995).
314 EXCHANGE RATE MISALIGNMENT
general rubric "trade-equations approach" is used here to cover a
group of similar methodologies, all of which involve three basic ana-
lytical tasks:
a. Using trade equations or trade elasticities to establish a quantita-
tive relationship between the RER, imports, exports, and, hence,
the resource balance;
b. Independently determining a target, norm, or equilibrium resource
balance using projections of the saving-investment balance or sus-
tainable capital flows; and
c. Estimating the underlying or structural resource balance by ad-
justing the actual resource balance in the initial year for cyclical,
exogenous, and policy changes that affect it.
The quantitative relationship between the RER and the resource bal-
ance established in task (a) is then used to calculate the appreciation or
depreciation in the initial RER required to move the resource balance
from its adjusted level in the initial year to its target level, everything
else remaining the same. The estimated long-run equilibrium RER is the
one that corresponds to the target or equilibrium resource balance. The
following section of this chapter discusses task (a). Tasks (b) and (c) are
taken up in the subsequent two sections.
Because of the different structures of industrial and low-income de-
veloping economies and the greater availability of data in the former,
trade is usually modeled in somewhat different fashions for the two
groups. In industrial countries, trade equations based on the Mundell-
Fleming production structure, the subject of the first part of this section,
are usually used. In developing countries, in contrast, a trade-elastici-
ties approach based on a three-good production structure, the subject of
the last part of this section, is often employed.
The Mundell-Fleming Framework-Industrial
Countries
The general analytical framework used in the trade-equations method-
ology in industrial countries usually employs equations 7.1 through 7.3:
(7.1) logM =E logRER +r, logYD + f(Z,)
(7.2) logX logRER+ qx logY, +g(Zx)
(7.3) ARB = AX - AM
where M and X are the quantities of imports and exports, YD and Y, are
ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 315
domestic and foreign real income, Zm arid Zx are vectors of whatever
predetermined or exogenous variables (for example, lagged values of
the RER, the terms of trade, commercial policy) are relevant in a particu-
lar case, and the resource balance (RB) is expressed in real terms. The
two trade equations are usually estimated econometrically to obtain
values for eM and Ex, the price elasticities of import and export demand,
and for T, and rx, the income elasticities of import and export demand.
To solve the above system of three equations, domestic and foreign
income are determined exogenously by setting them at full employment
or some other desired level. The change in the resource balance is also
set exogenously as the difference between the target and the adjusted
resource balances, which are determined separately in tasks (b) and (c).
One is thus left with three variables-M, X, and RER-to be determined
endogenously; and the three equations are solved for these.
A number of general points about the application of the trade-equa-
tions approach to industrial economies are worth noting. First, the ana-
lytical framework used for industrial countries is usually based on the
Mundell-Fleming production structure. In this framework, complete spe-
cialization of both the domestic and foreign economies in producing
one composite good (their own GDPs) makes export supply functions
perfectly elastic, while the domestic and foreign goods are taken to be
imperfect substitutes in demand. Export and import quantities are thus
demand-determined. The RER exerts its effect on the trade balance
through the price elasticities of domestic demand for imports and of
foreign demand for exports. Second, since industrial-country trade mod-
els focus primarily on competitiveness in the domestic and foreign mar-
kets for differentiated traded goods, the traded-goods version of the ex-
ternal RER (computed using relative wholesale prices or unit labor costs
in the traded-goods sector) is commonly used in equations 7.2 and 7.3.
Third, the estimated equilibrium exchange rates for large industrial coun-
tries like the G-7 that account for large shares of world trade need to be
mutually consistent since one country's economy can have important
income and relative price effects on the others', a fact that considerably
complicates the estimation of equilibrium exchange rates for large in-
dustrial economies. Fourth, if the RER is quite volatile and subject to
large random fluctuations, these could be reflected either in similar vola-
tility in the resource balance or in significant statistical noise in the em-
pirical relationship between the RER and the resource balance, either of
which could complicate empirical analysis and policy making.'
9. See Knight and Scacciavillani (1998).
316 EXCHANGE RATE MISALIGNMENT
Both the International Monetary Fund (IMF) and the Institute for In-
ternational Economics (IIE) employ the trade-equations approach for
estimating equilibrium exchange rates for the G-7 countries. Major pa-
pers by Wren-Lewis and Driver (1998) for the IE and Isard and Faruqee
(1998) for the IMF documenting their approaches have been published
within the last year. Since both of these papers have already been re-
viewed in the survey of empirical research in Chapter 5, they are not
discussed further here. The reader is referred, instead, to the previous
survey for a review of the papers and to the papers themselves for de-
tailed presentations of industrial-country applications of the trade-equa-
tions methodology.
The Three-Good Framework-Developing Countries
The General Analytical Framework
An alternative analytical framework is usually adopted for small devel-
oping countries whose production structures are less flexible and whose
exports are dominated by undifferentiated primary products. For these
countries, imports could still reasonably be modeled by equation 7.1, in
which the demand for imports depends upon the domestic price and
income elasticities of demand. However, equation 7.2 for exports is more
problematic in a developing-country context. For a small open develop-
ing economy that accounts for a tiny fraction of world trade, it is more
appropriate to consider export demand as being infinitely price-elastic
and to drop foreign income from the export equation but to allow for a
finite elasticity of export supply.0 Then the quantity of exports is deter-
mined by the elasticity of export supply. Hence, export supply elasticities
are conventionally employed in modeling developing countries rather
than export demand elasticities used in equation 7.2.
For example, Wren-Lewis and Driver (1998) follow the Mundell-
Fleming tradition of modeling trade in industrial countries in terms of
differentiated products that are imperfect substitutes. They estimate price
elasticities of demand for exports ranging from -0.23 for Canada to
-1.36 for Japan, with a median of -0.96. In contrast, the empirical evi-
dence on RERs and trade flows in developing countries cited by Ghei
and Pritchett in Chapter 11 suggests that the standard assumption of an
infinite price elasticity of demand for developing-country exports is rea-
sonable. Conversely, Wren-Lewis and Driver assume an infinite price
elasticity of export supply for the G-7 countries rather than supply
10. Conceptually, this approach also implies supposing that the home coun-
try produces at least one other type of good besides the exportable good and,
hence, requires adopting a three-good framework.
ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 317
elasticities in the 1.0-2.0 range suggested for developing countries by
Ghei and Pritchett.
The differences in approach to modeling trade in industrial and de-
veloping economies also lead to differences in view about the relevance
of the Marshall-Lerner condition. This condition for a real depreciation
to improve the resource balance measured in domestic currency terms,
starting from a zero balance, requires that the sum of the absolute val-
ues of the price elasticities of demand for imports and exports exceed
unity.n The Marshall-Lerner condition is satisfied for industrial coun-
tries by the average values of the price elasticities of demand for im-
ports (-0.9) from Ghei and Pritchett and of the demand for exports
(-1.0) from Wren-Lewis and Driver (1998). Although the Marshall-Lemer
condition would also be satisfied by the representative values of de-
mand elasticities for developing countries, it is not directly applicable
to them for two reasons. First, the condition assumes an infinite price
elasticity of export supply, whereas the empirical evidence suggests a
supply elasticity of 1.0 to 2.0 for developing countries. Second, many
developing countries are capital importers and start from a resource
deficit rather than from the balanced position assumed in deriving the
simplest version of the Marshall-Lerner condition.
Because trade models of developing countries focus on domestic re-
source allocation incentives, the internal RER rather than the external
RER for traded goods is usually the appropriate RER measure for them.
The use of the internal RER also has the advantage that the effects of
changes in some fundamentals on the equilibrium RER that are difficult
to handle in the Mundell-Fleming framework can easily be handled in a
three-good framework with importables, exportables, and domestic
goods. Because of its assumed production structure, the Mundell-
Fleming framework cannot distinguish between the terms of trade and
the RER. Thus, it cannot be used to analyze the impact of changes in the
terms of trade and commercial policy whereas these can be readily in-
corporated in a three-good framework.
Finally, for analyzing small economies it is not necessary to deter-
mine a set of mutually consistent multicountry RERs as is done in mod-
eling the G-7 economies. Rather, a simpler partial-equilibrium approach
that ignores the impact of a developing country's RER and trade flows
on the rest of the world can be used. Because of the relative ease with
which it can be implemented and the availability of estimated elastici-
ties from the large amount of empirical work on trade reviewed in
11. The resource balance measured in foreign-currency terms will almost al-
ways improve for reasons explained in footnote 40 in Chapter 11 on trade flows
and the RER.
318 EXCHANGE RATE MISALIGNMENT
Chapter 11, the trade-elasticities approach has been widely used in op-
erational applications in developing countries. This chapter and the sub-
sequent one on the DLR model give two examples of trade-elasticity
methodologies. Both chapters utilize three-good frameworks with ex-
ports, imports, and domestic goods and constant-elasticities assump-
tions. In this chapter, the relationship between the three goods is in terms
of constant price elasticities of the supply of exports and of the demand
for imports. The DLR model also assumes constant elasticities-but in
this case they are elasticities of transformation in production between
exports and domestic goods and of substitution in consumption between
imports and domestic goods.12
A Specific Three-Good Methodology
The remainder of this section presents a specific trade-elasticities meth-
odology that is suitable for use in low-income countries in which only
limited data are available. The relationship between the resource bal-
ance, trade elasticities, and the internal RER is set in an explicit three-
good framework. This formulation allows for different RERs for imports
and exports and facilitates the analysis of the relative price effects of
changes in the terms of trade and commercial policy.3 Essentially, the
approach involves using the definitions of the price elasticities of de-
mand for imports and the supply of exports to replace the trade equa-
tions 7.1 and 7.2 above for imports and exports." The procedure for cal-
culating the equilibrium RER is otherwise the same as that set out above
for the trade-equations approach.
Appendix A gives the detailed derivation of the basic RER, trade-
elasticities, resource balance equation in a three-good framework. As shown
there, the RER for imports (RERM) may be expressed as in equation 7.4:
(AITT
(7.4) ARERM A ITT
RERM x- X-e 1). These properties
can readily be revealed using standard tests for the presence of a unit
root.20 The appropriate unit-root tests are well known; in our applica-
tions we use the Dickey-Fuller (DF), augmented Dickey-Fuller (ADF),
and Phillips-Perron (PP) tests. Although there are concerns about the
low power of these tests against stationary but persistent alternatives,
the ADF test appears to perform satisfactorily on this score even when
(as in our case) the number of observations is small (Hamilton 1994). We
also supplement the unit-root tests with variance ratio tests (Cochrane
1988); these tests exploit the fact that the variances of conditional fore-
casts explode for nonstationary series and converge for stationary series
as the forecast horizon grows.
20. Hamilton (1994) emphasizes the difficulty of distinguishing truly
nonstationary processes from processes that are stationary but persistent. The
problem is that the finite-sample autocovariances of any nonstationary series
can be reproduced arbitrarily closely by those of a suitably persistent stationary
series. The usual tradeoff between consistency and efficiency is therefore present
even at this preliminary stage. If we correctly characterize the order of integra-
tion, we gain efficiency in estimation and inference by applying the appropriate
estimation technique; but a misclassification typically means that these techniques
will deliver inconsistent estimates or standard errors. Unfortunately the alterna-
tives are non-nested and we see no generally robust way of proceeding in mar-
ginal cases. Hamilton (p. 447) suggests comparing estimates obtained under al-
ternative classifications; if they differ widely the investigator may sometimes
see ancillary statistical or other grounds for preferring one over the other.
428 EXCHANGE RATE MISALIGNMENT
Table 10.1 Stationarity Statistics-Levels without and with Time Trend
C6te d'Ivoire Burkina Faso
DF ADF PP DF ADF PP
Levels without Time Trend
log(REER) -0.59 -1.26 -1.89 -2.25 -4.25 -2.25
log(TOT) -1.42 -1.54 -1.78 -1.95 -1.82 -1.87
RESGDP -2.11 -2.57 -2.25 -3.84 -2.22 -4.07
log(OPEN1) -1.06 -1.39 -1.42 -4.02 -3.04 -4.30
log(OPEN2) -2.35 -1.99 -2.48 -3.23 -3.02 -3.35
log(OPEN3) -2.52 -2.16 -2.69 -3.63 -2.99 -3.82
log(HBS3) n.a. n.a. n.a. -1.21 -2.05 -1.67
log(ISHARE) -1.01 -0.78 -0.68 n.a. n.a. n.a.
Levels with Time Trend
log(REER) -1.83 -2.46 -2.09 -4.89 -2.76 -5.35
log(TOT) -1.51 -1.56 -1.69 -2.30 -2.08 -2.34
RESGDP -2.05 -2.50 -2.24 -4.27 -2.69 -4.64
log(OPEN1) -1.02 -1.32 -1.29 -3.84 -2.94 -4.20
log(OPEN2) -2.81 -2.30 -3.02 -3.12 -2.95 -3.31
log(OPEN3) -2.47 -1.99 -2.72 -3.47 -2.91 -3.75
log(HBS3) n.a. n.a. n.a. -3.65 -3.75 -3.68
log(ISHARE) -2.42 -2.19 -2.42 n.a. n.a. n.a.
Note: DF, ADF, and PP refer to Dickey-Fuller, augmented Dickey-Fuller, and Phillips-Per-
ron stationaritv statistics. The number of observations is 29 for C6te d'Ivoire and 24 for
Burkina Faso. The variables are defined in appendix B (ISHARE is not available for Burkina
Faso).
Source: Computed from data from sources listed in appendix B.
Table 10.1 shows the results of unit-root tests for all stochastic vari-
ables. C6te d'Ivoire and Burkina Faso represent two extremes. For C6te
d'Ivoire, all three tests indicate nonstationarity for all variables. More-
over, we can reject the unit-root hypothesis for the first difference of the
variables (not reported), so we conclude that these are I(1) variables. For
Burkina Faso, all variables appear to be trend-stationary, with the pos-
sible exception of the terms of trade, which is bordering on
nonstationarity. Figures 10.3 and 10.4 provide some additional informa-
tion in the form of variance ratio tests.2" These tests corroborate the unit-root
21. This ratio is defined as (1/k)Var (X,- X,_)/Var (X, - X,_), where X, is the
variable of interest and k is the lag length (Cochrane, 1988).
SINGLE-EQUATION ESTIMATION OF THE LRER 429
Figure 10.3 Variance Ratio Tests for CMte D'Ivoire
log(TOT) RESGDP
1.80 1.80
1.50 150
Z
q 1.20 1.20
0.90 0.90
0.90
0.60 0.60
0.30 0.30
0.00 i ii i i I 0.00 I I~ 1 I
1 3 5 7 9 11 13 15 1 3 5 7 9 11213115
loglOPENI) log(REER)
2.10 1.80
0 00
1.50 L
1.20
S0.90
0.90
S0.60
0.60
0.30 0.30
~~0.00 il 1 1 1 1 1 00
1 3 5 7 9 1113 15 123456 7 8 9 10 11 12 13 14 15
log(REER)
1.80
1.50
Zj 1.20
S0.90
r 0.60
0.30
0.00 I
1 2 3 4 5 6 7 8 9 10 11121314 15
Source: Computed from data from sources listed in appendix B.
tests, and for Burkina Faso's terms of trade the variance ratios decline at
longer horizons, consistent with a persistent but stationary variable. We
therefore proceed under the assumption that the terms of trade are sta-
tionary. In principle, of course, the vector [ln e,Fj, sj']' may contain an
arbitrary combination of 1(0) and I(1)-or even 1(2)-variables. We focus
our exposition, however, on the two cases represented by our examples.,
22. Methods have recently been developed that allow consistent estimation
and inference in regressions that involve mixtures of integrated processes. See
Phillips (1995) and Phillips and Chang (1995).
430 EXCHANGE RATE MISALIGNMENT
Figure 10.4 Variance Ratio Tests for Burkina Faso
log(TOT) RESGDP
1.80 1.80
150 1.50
1.20 - 120
0.90 0.90
0.30 0.30
0.00 0.00
1 3 5 7 9 11 13 15 1 3 3 7 9 11 13 15
log(OPEN1) log(REER)
1.80 1.80
11.80
II0 1.50
1.2 1.20
0.90 00.90
.0 60
0.30 0.30
0.00 1L iii 0.00
1 3 5 7 9 1 1 3 15 1 3 5 7 9 11 13 15
log(HBS3)
1.80
1.50
S1.20
S0.90
S060
3T 5 7 9 11 13 15
Source: Computed from data from sources listed in appendix B.
The 1(1) Case
When the variables are all I(1), as for Cte d'Ivoire, stationarity of the
residual 1 case is the "struc-
tural error correction model" of Boswijk (1995; discussed in Ericsson 1995), which
is obtained by premultiplying equation 10.14 by a square matrix and then im-
posing a set of restrictions.
432 EXCHANGE RATE MISALIGNMENT
Determining the Cointegrating Rank
The cointegrating rank is a property of the full system, and a system
estimator is required to test for it. Table 10.2 reports the results of
Johansen's likelihood ratio tests for the cointegrating rank in COte
d'Ivoire. We use a lag length of one for the underlying VAR system; this
is very restrictive even for annual data, but longer lag length leaves us
with very few degrees of freedom. The null hypothesis for these tests is
that the number of cointegrating vectors relating the n nonstationary
variables is less than or equal to r (where r < n). Comparing the esti-
mated likelihood ratios in column 2 to the asymptotic critical values in
column 3, we see (row 1) that the hypothesis of no cointegration (r = 0)
can be rejected in favor of at most one cointegrating vector. In row 2, the
hypothesis of one