W P's _     O0
POLICY RESEARCH WORKING PAPER   1800
Single-Equation  Estimation                              An econometic methodology
for estimating both the
of the  Equilibrium    Real                              equilibrium real exchange
Exchange  Rate                                           rate and the degree of
exchange-rate misalignment.
John Baffes
Ibrahim A. Elbadawi
Stephen A. O'Connell
The World Bank
Development Research Group
August 1997



| POLICY RESEARCH WORKING PAPER 1800
Summary findings
Estimating the degree of exchange-rate misalignment                A recent strand of the empirical literature exploits
remains one of the most challenging empirical problems          these observations to develop a single-equation approach
in an open economy. The basic problem is that the value         to estimating the equilibrium real exchange rate.
of the real exchange rate is not observable.                       Drawing on that earlier work, Baffes, Elbadawi, and
Standard theory tells us, however, that the equilibrium       O'Connell outline an econometric methodology for
real exchange rate is a function of observable                  estimating both the equilibrium  real exchange rate and
macroeconomic variables and that the actual real                the degree of exchange-rate misalignment.
exchange rate approaches the equilibrium rate over                They illustrate the methodology using annual data
time.                                                           from C6te d'lvoire and Burkina Faso.
This paper - a product of the Development Research Group - is part of a larger effort in the group to investigate the
determinants of the real exchange rate. Copies of the paper are available free from the World Bank, 1818 H Street NW,
Washington, DC 20433. Please contact Pauline Kokila, room N5-030, telephone 202-473-3716, fax 202-522-3564,
Internet address pkokila@worldbank.org. August 1997. (51 pages)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about
development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The
papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this
paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the
countries they represent.
Produced by the Policy Research Dissemination Center



Single-Equation Estimation of the Equilibrium Real
Exchange Rate
JOHN BAFFES
IBRAHIM A. ELBADAWI
STEPHEN A. O'CONNELL
We are grateful to Chris Adam, Neil Ericsson, Philip Jefferson, and Luis Serven for helpful advice,
to Peter Montiel for very thorough comments on an earlier draft, and to Ingrid Ivins for assistance
with data. Larry Hinkle provided invaluable comments and advice throughout and constructed the
counterfactual simulations for Cote d'Ivoire and Burkina Faso.






Contents
1. Introduction
2. The equilibrium real exchange rate
2.1 Rationing of foreign credit
2.2 The terms of trade and trade policy
2.3 Nominal rigidities and short-run dynamics
2.4 Real exchange rate misalignment
3. Estimating the equilibrium real exchange rate: introduction
3.1 Specifying an empirical model
3.2 Small samples, limited information, and the single-equation approach
3.3 Sustainable fundamentals and exogeneity requirements
3.4 Relationship to the PPP approach
4. The econometric methodology
4.1 Step 2: Estimation of
4.1.1 The I(1) case: cointegration
4.1.2 The I(1) case: estimation
4.1.3 The I(0) case: estimation
4.2 Step 3: Calculating the equilibrium real exchange rate
4.2.1 Sustainable fundamentals: time-series-based estimates
4.2.2 Sustainable fundamentals: counterfactual estimates
4.2.3 Estimating the degree of misalignment
5. Estimation results
5. 1 Unit root tests
5.2 Tests of cointegration: CMte d'Ivoire
5.3 Long-run parameters and adjustment speed: Cote d'Ivoire and Burkina Faso
5.4 Short-run dynamics: CMte d'Ivoire and Burkina Faso
5.5 The equilibrium real exchange rate and misalignment
6. Conclusions
Endnotes
References
Appendix 1: Conditioning and weak exogeneity
Appendix 2: Data description
Appendix 3: Counterfactual simulations: CMte d'Ivoire and Burkina Faso
A3.l Time-series measures: TOT and LPFOR
A3.2 Counterfactual simulations: RESGDP
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A3.3 Counterfactual simulations: ISHARE and OPEN 1
A3.4 Concluding caveat
Figure 1: Internal and external balance
Figure 2: Adjustment to an increase in rw (under a binding credit constraint)
Figure 3: Variance ratio tests for CMte d'Ivoire
Figure 4: Variance ration test for Burkina Faso
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1.   Introduction
Estimating the degree of exchange rate misalignment remains one of the most challenging empirical
problems in open-economy macroeconomics (Edwards (1989), Williamson (1994), Hinkle and
others (1995)). A fundamental difficulty is that the equilibrium value of the real exchange rate is not
observable. Standard theory tells us, however, that the equilibrium real exchange rate is a function
of observable macroeconomic variables, and that the actual real exchange rate approaches the
equilibrium rate over time (Edwards (1989), Devarajan, Lewis and Robinson (1993), Montiel
(1997)). A recent strand of the empirical literature exploits these observations to develop a single-
equation approach to estimating the equilibrium real exchange rate (Edwards (1989), Elbadawi and
O'Connell (1990), Elbadawi (1994), Elbadawi and Soto (1994, 1995)). Drawing on this earlier
work, we outline an econometric methodology for estimating both the equilibrium real exchange
rate and the degree of misalignment and illustrate the methodology using annual data from CMte
d'Ivoire and Burkina Faso.
The procedure involves three steps. In the first step, the investigator examines the time-
series characteristics of the real exchange rate and the fundamentals. This, in turn, determines the
estimation technique to be used in the second step to uncover the parameters of the long-run
relationship between the real exchange rate and its fundamentals. In the third step, the investigator
uses the long-run parameters to calculate the equilibrium rate and the degree of misalignment under
alternative assumptions regarding the sustainability of the fundamentals.
The paper is organized as follows. In section 2 we define the real exchange rate and derive
the equilibrium relationship between the real exchange rate and macroeconomic "fundamentals"
such as government spending patterns and the terms of trade. We present the comparative statics
and discuss the sources of short-run misalignment and dynamic adjustment. Section 3 draws on the
theory to develop a single-equation econometric model of the real exchange rate. In Section 4 we
outline our methodology, and in Section 5 we apply the methodology to CMte d'lvoire and Burkina
Faso. Section 6 concludes with an assessment of the practical value of the single-equation
econometric approach to the equilibrium real exchange rate.
2.    The Equilibrium Real Exchange Rate
The concept of the real exchange rate (RER) that has been most heavily used in analyses of external



adjustment by developing countries is the domestic relative price of traded to nontraded goods (e.g.,
Dornbusch (1984)):'
RER_e_ EPT
PN
Although the foreign price of traded goods, PT*, is exogenous for a small country, the domestic
price of nontraded goods is endogenous except over short periods of wage/price rigidity. The RER
is therefore endogenous even under a predetermined nominal exchange rate. In this section we use a
simplified model to illustrate the determination of the real exchange rate and derive an expression
for its long-run equilibrium value. Since the relevant theory is well covered by Montiel, we use his
model as a basis for the discussion (see also Edwards (1989) and Rodriguez (1994)).
The literature defines the long-run equilibrium real exchange rate as the rate that prevails
when the economy is in internal and external balance for sustainable values of policy and exogenous
variables. Internal balance holds when the markets for labor and nontraded goods clear. This occurs
when
YN (e)=CN + gN= (1-O)ec + gN,       YN < 0            (2)
where yN is the supply of nontraded goods under full employment, c is total private spending
(measured in traded goods), O is the share of this spending devoted to traded goods, and gN is
government spending on nontraded goods. Equation 2 is shown as the schedule IB in Figure 1.
Starting in a position of internal balance, a rise in private spending creates an excess demand for
nontraded goods at the original real exchange rate. Restoration of equilibrium requires a real
appreciation that switches supply towards nontraded goods and demand towards traded goods. A
rise in government spending on nontraded goods shifts the IB schedule downwards.
To define external balance, we begin with the current account surplus, which is given by
f=b+z+rf =YT(e)-gT-(O+r)c+z+rf                   (3)
wherefis total net foreign assets, b is the trade balance, z is net foreign aid received by the
government, and r is the real yield on foreign assets, measured in traded goods. The trade balance is
the difference between domestic production of traded goods, Yr and the sum of government (gT)
and private spending on these goods. The equation is standard except for the term zw which
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measures the transactions costs associated with private spending. In Montiel's model of optimizing
households, these costs motivate the holding of domestic money, which would otherwise be
dominated in rate of return by foreign assets.2 They are assumed to be incurred in the form of traded
goods (at the rate rper unit of spending) and therefore appear as an outflow in the trade balance.
External balance has been defined in various ways in the literature. The most useful
approach for our purposes is that of Montiel (see also Khan and Lizondo (1987), Edwards (1989),
and Rodriguez (1994)), who defines external balance as holding when the country's net creditor
position in world financial markets has reached a steady state equilibrium. We can solve for the
combinations of private spending and the real exchange rate that are consistent with this notion of
external balance by holdingfat its steady-state level and setting the right-hand side of equation (3)
to zero. This traces out a second relationship between the real exchange rate and private spending,
labeled EB in Figure 1. Starting at any point on this schedule, a rise in private spending generates a
current account deficit at the original real exchange rate. To restore external balance, the real
exchange rate must depreciate, switching demand towards nontraded goods and supply towards
traded goods.
The equilibrium real exchange rate, e *, is given by the intersection of the IB and EB curves,
which occurs at point I in the diagram. Setting the right-hand-side of equation (3) to zero and
combining this with equation (2), we obtain
e = e (g,g, r*f* + z, r*),      el<O, e2>0, e3<0, e4>0.   (4)
where "*" superscripts denote steady-state values of endogenous variables. The signs of the partial
derivatives in (4) are easily verified either graphically or algebraically using equations (2) and (3).
Montiel solves for the steady-state service account r*f* by assuming that the country faces
an upward-sloping supply curve of net external funds and that households optimize over an infinite
horizon.3 Transactions costs per unit, r, are also endogenous; they depend on the ratio of money
holdings to private spending and therefore on the nominal interest rate, which is the opportunity cost
of holding domestic money. Since the nominal interest rate is tied down in the long run by the time
preference rate and the domestic inflation rate, the final expression for the equilibrium real exchange
rate in the Montiel model takes the form
e = e(g9Ng'TZrW;rT),    e]  O,e2 > O,e3 <O,e5 > 0.       (5)
3



where rw is the world real interest rate and )TT is the rate of inflation in the domestic price of traded
goods.4 Note that the nominal exchange rate does not appear among the fundamentals in equation
(5). This is because the underlying behavioral relationships are all homogenous of degree zero in
nominal variables. A nominal devaluation therefore has at most a transitory effect on the real
exchange rate.
Equation (5) emphasizes that the real exchange rate consistent with internal and external
balance is a function of a set of exogenous and policy variables. In practical applications, this
relationship between e* and its macroeconomic "'fundamentals" differentiates the modern approach
to equilibrium real exchange rates from the earlier PPP (Purchasing Power Parity) approach. Under
PPP, the analyst would identify a reference period of internal and external balance and use the real
exchange rate that prevailed during that period as an estimate of the equilibrium for other periods.
Equation (5) implies that this is only legitimate if the fundamentals did not change between the
reference and comparison periods. This criticism of the PPP approach is now widely accepted.5
The analysis underlying equation (5) can be readily modified to accommodate features that
are important in particular applications. For our purposes, important extensions involve rationing of
foreign credit, changes in the domestic relative price of traded goods, and short-run rigidities in
domestic wages and prices. We discuss these extensions briefly in what follows.
2.1 Rationing offoreign credit
Equation (6) is derived under the assumption that the country faces an upward-sloping supply curve
of external loans. The current account and trade balance are therefore endogenously determined at
each moment by the saving and portfolio decisions of households. An extreme version of this view,
more relevant for countries without access to commercial international borrowing on the margin, is
that the country faces a binding credit ceiling (or equivalently, a floor on its international net
creditor position). In this case, the trade surplus becomes exogenous, both in the short run and in the
long run, provided that the credit ceiling remains binding.6 Equation (4) then takes the simpler form
e =e (9N ,gT,b,r*)               e, <O,e2 > O,e3 <O,e4 > 0.  (6)
In our empirical work below, we treat the trade surplus b = rf + z as one of the fundamentals,
consistent with this interpretation.
4



2.2   The terms of trade and trade policy
The domestic relative price of exports and imports is given by
PM   71          PM           / + [''l                    (7)
where 0 is the external terms of trade and 77 is a parameter summarizing the stance of domestic
trade policy. If either i or q change over time, the analysis must be disaggregated to accommodate
different real exchange rates for imports and exports. The equilibrium real exchange rates for
imports and exports can then be written as functions of the set of fundamentals identified above,
along with 0 and i1. Since the real exchange rate for tradables is itself a function of these two, it will
depend on the same set of fundamentals, with elasticities depending on the relative weight (a) of
imported goods in the tradables price index. Equation (6) then becomes
e = e*(gNI, gb 0, 77 r*),      el, e3, e , <O; e 2 e6>0; e X ?   (8)
An improvement in the terms of trade increases national income measured in imported goods; this
exerts a pure spending effect that raises the demand for all goods and appreciates the real exchange
rate. This effect can be overcome by substitution effects on the demand and supply sides, leading to
an overall real depreciation, but the spending effect has proved dominant in most empirical
applications. A tightening of trade policy, appreciates the real exchange rate in the long run.
2.3 Nominal rigidities and short-run dynamics
In Montiel's model, domestic wages and prices are perfectly flexible and internal balance prevails
continuously. If we consider the case of a binding credit ceiling, so that the trade balance is
exogenous, we conclude that as long as changes in the fundamentals are permanent, the actual real
exchange rate never deviates from its long-run equilibrium. This is apparent from inspection of the
internal and external balance schedules: with b tied down exogenously, e and c are free to adjust
immediately to their new long-run equilibrium values when one of the fundamentals changes. This
is illustrated in Figure 2, where we show the adjustment to an increase in the world real interest rate
by a net debtor country facing a binding credit ceiling. The rise in rw increases the required trade
surplus, shifting EB to the left (to EB') and depreciating the equilibrium real exchange rate. The
5



adjustment from point 1 to point 2 is immediate; with a predetermined path for the nominal
exchange rate it takes place through a fall in domestic prices and wages. The binding credit
constraint removes the model's only source of internal dynamics, so that the only possible sources of
a divergence between the actual real exchange rate and its long-run equilibrium is a temporary
change in one of the fundamentals.
If domestic wages and prices are sticky in the short run, a second important source of
internal dynamics comes from disequilibrium in the labor market and the market for nontraded
goods. As long these markets eventually clear, the equilibrium real exchange rate is unaffected by
the short-run nominal rigidity. But any shock that alters the equilibrium real exchange rate will now
give rise to an adjustment process during which the actual real exchange rate will deviate from its
new equilibrium. In Figure 2, sticky wages and prices prevent the real exchange rate from moving to
point 2 in the short run, so that output and spending take the burden of the external adjustment. The
short-run equilibrium is at point 3, where unemployment and inventory accumulation gradually
push nominal wages and the prices of nontraded goods down relative to the prices of traded goods.
The real exchange rate depreciates over time, bringing the economy to point 3 in the long run. The
process illustrated in Figure 2 is often viewed as providing the primary role of nominal devaluation
in macroeconomic adjustment (that of speeding an otherwise excessively slow and contractionary
adjustment to an adverse external shock (Corden (1989)).
An advantage of the econometric methodology below is that it does not require a structural
specification of the short-run dynamics. The long-run equilibrium is consistent with a variety of
sources and patterns of short-run dynamics, including price stickiness, costs of labor mobility, and
other features not present in the model above.
2.4 Real exchange rate misalignment
In the analysis below, we follow Edwards (1989) and Montiel in using the term "misalignment" to
denote the gap between e and e *. Two important differences between this descriptive use of the
term misalignment and its more normative use in most policy discussions must be emphasized. The
first is illustrated by our discussion of nominal rigidities. Without such rigidities, deviations
*
between e and e are market-clearing responses to temporary movements in the fundamentals or to
permanent movements that alter the long-run equilibrium level of net foreign assets. In these cases,
6



there is no obvious role for policy interventions designed to alter the path of the real exchange rate.
The second difference stems from the observation that the real exchange rate may well be
misaligned from a normative perspective even when the economic is in a steady-state equilibrium.
Dollar (1993), for example, argues that African real exchange rates were systematically overvalued
in the 1970s and 1980s, as a result of highly inward-looking trade regimes. In the theory developed
here, the equilibrium real exchange rate is conditional on trade policies and other government
interventions. Given these policy settings (whether socially optimal or not ) misalignment is
necessarily a temporary phenomenon, generated by short-run macroeconomic forces that prevent an
immediate movement to the long-run equilibrium.
3.    Estimating the equilibrium real exchange rate
The theory developed in the previous section delivers a steady-state, or long-run relationship
between the real exchange rate and a set of macroeconomic "fundamentals." The equilibrium real
exchange rate is then defined as the steady-state real exchange rate conditional on a vector of
permanent values for the fundamentals. Given this structure, our task is to construct a time series for
the equilibrium real exchange rate - within sample and potentially out of sample - using data on the
actual real exchange rate and fundamentals.
As a first step we assume that the long-run relationship delivered by theory is linear in
simple transformations (e.g., logs) of the variables. Thus equation (5) becomes
lneT = F,                                   (9)
where e * is the equilibrium real exchange rate, FP is the vector of permnanent values for the
fundamentals. At a conceptual level, the task of estimating the equilibrium real exchange rate
breaks into two pieces. The first is to estimate the vector ,f of long-run "parameters of interest"; the
second is to choose a set of "permanent" values for the fundamentals appropriate to period t.
3.1 Specifying an empirical model
Estimation of /3 requires the specification of an empirical model that is consistent with (9) but
relates observable variables. We obtain such a model by translating into stochastic terms two
straightforward and general features of the theory. The first is that equation (9) comes from a steady
state relationship between actual values of the real exchange rate and fundamentals. To capture this
7



relationship we assume that the disturbance nt in the equation
lne, =  ', + n,,                                       (10)
has finite conditional variance and expected value zero at sufficiently distant horizons (i.e., the limit
of E(nt+k11t[J) as k goes to infinity is 0).7 We will in fact impose the stronger condition that nt is a
mean zero, stationary random variable. Note that equation (9) follows directly from (10) if Ine * and
FP are interpreted as long-run conditional expectations of the relevant variables.
The second general feature of the theory is that the steady state is dynamically stable.8
Shocks that cause the exchange rate to diverge from its (possibly new) equilibrium in the short run
should produce eventual convergence to the relationship in (9) in the absence of new shocks (or
equivalently, in conditional expectation). A specification that captures this notion while retaining
consistency with both (9) and (10) is the general error-correction model
P             P
Alne, =a(lnet,l -, '>F1 )+ E HujAlne,j + E yjAFt-j +v,,              (11)
j=I           j=O
where Ft = [gN g7, b, q,, rt]' is the vector of fundamentals, and vt iS an i.i.d., mean-zero,
stationary random variable. Assuming that all variables are either stationary or I(1) (see below),
equation (11) implies equation (10); and for a < 0, the corresponding long-run equilibrium is
stable.
Equation (11) embodies the central insight of the single-equation approach: that the
equilibrium real exchange rate can be identified econometrically as that unobservedfunction of the
fundamentals towards which the actual real exchange rate gravitates over time (Kaminsky (1988),
Elbadawi (1994), Elbadawi and Soto (1994, 1995)). Note that in contrast to the long-run
relationship, the short-run dynamics are not heavily restricted since (11) is a simple re-
parameterization of the unrestricted pth-order autoregressive distributed lag (ADL) representation of
lnet,
p            p
Ine, = a*Ine,j +            ±iF, +v,,                  (12)
j=1          j=0
under the stability restriction j= 1,pu  < I and the assumption that the real exchange rate enters
the long-run relationship.9 For different parameter values, the unrestricted error-correction
8



representation (11) encompasses a wide variety of commonly used dynamic models (Hendry, Pagan
and Sargan (1984), Ericsson, Campos and Tran (1991)). This flexibility is an advantage, because
although the dynamic structure of any particular theoretical model may place restrictions on the
parameters in (9), these restrictions will depend on the nature of nominal and real rigidities, on
whether households optimize or use rules of thumb, and on other model-dependent features that
have little or no effect on the set of variables that enter the long-run equilibrium. With unrestricted
dynamics, we allow the data maximum scope for determining their actual pattern, while retaining
consistency with the long-run specification.
Much of our econometric work will take place in versions of equation (11). It is
straightforward to incorporate variables that in theory do not belong among the long-run
fundamentals, but that may affect the short-run dynamics; an example is the nominal exchange rate.
Denoting such variables by z, we would capture long-term effects by adding the term S'z inside the
parentheses in (11) (allowing a test of the hypothesis 6 = 0) and short-term dynamics by adding
1j=o,pq7jAz1. to the right-hand side. Equation (11) can also accommodate an intercept or
deterministic trend; and we can readily include dummy variables for potentially important
exogenous events (e.g., the Sahel drought of the early 1980s).
3.2 Small samples, limited information and the single-equation approach
A fundamental difficulty in estimating the parameters of equation (11) is that sample sizes are likely
to be very small. This is partly because the historical reach of developing country data is typically
limited, and partly because models of the type considered here call for national accounts and/or
fiscal data that are available only annually. For C6te d'Ivoire, we have 29 annual observations, and
for Burkina Faso, 24. A general implication of small sample size is that the statistical properties of
estimators may be poor and that testing procedures are likely to have low power. Existing Monte
Carlo evidence can in some cases help discriminate between alternative choices of estimator, but we
will often have to make informal judgments about robustness to sample size. On the positive side,
the shocks to developing country data often appear to have high variance, thereby generating
substantial variation over time; and temporal length of sample has the same effect when the real
exchange rate and its fundamentals are nonstationary. A relatively small sample may therefore
contain substantial information, particularly regarding the long-run parameter space.10
9



A second and more definitive effect of small samples in our case is to limit the scope for
systems-based estimation. The number of unknown parameters in the full joint autoregressive
distribution of the real exchange rate and its fundamentals rises roughly geometrically with the
number of fundamentals and the lag length. With 3 or 4 variables among the fundamentals and
fewer than 30 observations, this "curse of dimensionality" tends rapidly to overwhelm any attempt
to estimate the full joint distribution. We will see below that the dimensionality problem is
somewhat alleviated if the variables are nonstationary and cointegrated (and only the long-run
parameters are of direct interest), but that even here the small sample size exerts a serious limitation
on systems estimation. Our analysis will therefore generally take place in a single-equation context,
where we implicitly condition on the current values of at least a subset of the fundamnentals and the
lagged values of all variables.
Conditioning is at some potential cost, because efficient statistical inference regarding the
parameters of interest - which may go beyond / to include the adjustment speed a and the short-run
parameters Aj and , - generally requires analysis of the full joint distribution of In et, Ft and zt. As
shown by Engle, Hendry and Richard (1983), however, fully efficient estimation and inference can
take place conditional on the fundamentals if these variables are weakly exogenous for the
parameters of interest. As outlined more fully in Appendix 1, weak exogeneity holds when the
parameters of interest can be directly recovered from the distribution of the real exchange rate
conditional on the fundamentals (and the past), and there are no cross-equation restrictions linking
the parameters of this conditional model with those of the marginal model for the fundamentals. In
this case the marginal distribution of the fundamentals holds no information of use to estimating the
parameters of interest. Failure of weak exogeneity limits the scope for fully efficient conditional
inference but may not undermine the ability to perform valid (though not fully efficient) inference in
an essentially single-equation context; in the stationary case, for example, limited-information
approaches like two-stage least squares are available subject to sufficient identifying restrictions."1
For Cote d'Ivoire and Burkina Faso, the "small country" assumption suggests that variables
like the terms of trade and the foreign price level are determined outside the country.12 The same is
true for the trade-weighted nominal exchange rate, since the CFA franc was pegged to the French
franc at an unchanged parity throughout the sample; and the trade balance is in this category if
borrowing constraints are exogenous and binding. Weak exogeneity seems a reasonable assumption
10



for these variables. Unfortunately, it is not guaranteed; if behavior is affected by conditional
expectations of these variables, for example, forecast errors will be jointly determined with the real
exchange rate, potentially violating weak exogeneity. Variables like government spending and the
investment share may also be jointly determined with the contemporaneous real exchange rate.
Weak exogeneity is testable, though generally at the cost of moving to systems estimation. Below
we report some partial tests for the CMte d'lvoire case.
3.3 Sustainable fundamentals and exogeneity requirements
If we begin with equation (10), the equilibrium real exchange rate in equation (9) has a natural
interpretation as the limit of a k-period-ahead conditional forecast of the real exchange rate. This
suggests two broadly alternative ways of tying down the permanent values of the fundamentals: the
first is to use the sample information to generate long-run forecasts of the fundamentals conditional
on information available in period t (or in some earlier period if t is out-of-sample); the second is to
combine theory and a priori information into a counterfactual simulation for the fundamentals.
These correspond closely to the use of a single equation for conditional forecasting and "policy
analysis". We argue below that the investigator will generally want to consider both alternatives.
Here we briefly comment on the relevant exogeneity requirements (see Engle, Hendry and Richard
(1983)).
The requirements for valid single-equation forecasting and simulation generally go beyond
those for valid estimation and inference. When using conditional forecasts of the fundamentals, the
implicit assumption is that there is no feedback from the real exchange rate to the fundamentals. The
appropriate concept is strong exogeneity, which combines weak exogeneity with lack of Granger
causality from the real exchange rate to the fundamentals. Given weak exogeneity, strong
exogeneity can be readily tested by determining whether lagged values of the real exchange rate
enter the marginal model for the fundamentals.
When using counterfactual simulations of the fundamentals, the relevant issue is whether/f
can be treated as a constant in the face of shifts in the marginal distribution of the fundamentals. The
problem here is the Lucas critique of econometric policy analysis: the counterfactual exercise
implicitly alters the joint distribution of the fundamentals and the real exchange rate, thereby
invalidating the original parameter estimates unless the corresponding parameters are invariant to
11



the class of distributional shifts being considered. The appropriate concept in this case is super
exogeneity which combines weak exogeneity with invariance of the parameters of interest to the
class of distributional shifts under consideration. The invariance property is sensitive to the
particular class of interventions under study and we will treat it as a maintained hypothesis rather
than attempting formal testing. 13
3.4 Relationship to the PPP approach
A hallmark of the PPP approach to equilibrium exchange rates was the choice of a single
equilibrium rate for all periods, without reference to movements in the fundamentals. The standard
theory-based criticism, as embodied in our theoretical model, was that notion of equilibrium
delivers a relationship between the real exchange rate and the fundamentals, not a single value for
the real exchange rate. Since the fundamentals are themselves time-varying, this criticism has often
been summarized in the claim that the equilibrium real exchange rate should move over time.
The above discussion suggests, however, that this way of stating the criticism misses the
fundamental distinction between the PPP and econometric approaches. Consider the case in which
the real exchange rate itself is stationary. Stationary variables have time-invariant means, implying
that all movements away from the mean are ultimately temporary. In such a situation the best
sample-based estimate of the equilibrium real exchange rate for any period is simply the sample
mean. To put this another way, the quantity a3Ft in equation (10) is the difference between two
stationary variables and is therefore stationary, so that while the individual fundamentals may have
permanent movements (i.e., may be nonstationary), the relevantfinction of the fundamentals - in
our case, the long-run forecast of a linear combination of these fundamentals - never moves
permanently. When forecasted at successively distant horizons, 8YF,+k simply reverts to the mean of
Inet.14 An equilibrium relationship between the real exchange rate and other macroeconomic
variables is therefore consistent with a time-invariant equilibrium real exchange rate.
The more fundamental distinction between the two approaches resides in their contrasting
use of sample and a priori information. The PPP approach requires a set ofjudgments that are
informed both by theory and data but that remain largely implicit and a priori from an econometric
perspective. The econometric approach, in contrast, uses theory sparingly but powerfully to extract
information about the equilibrium real exchange rate from the entire data sample. A priori
12



information becomes relevant when the analyst is interested in counterfactual simulations for the
fundamentals, but such information is combined with the sample information (used to estimate the
parameters) in a restricted and transparent manner.
The econometric approach has clear advantages in reasonably large samples, where the high
quality of the sample information should outweigh the loss of potentially sophisticated but implicit
judgments central to the PPP approach. To give the PPP approach its due, however, we consider a
problem that is peculiar to samples that are not necessarily small but are short in duration. We have
just pointed out that in the stationary case, the sample mean provides a natural estimator of the long-
run equilibrium real exchange rate. This implies, however, that the average misalignment within the
sample is constrained to be zero. A similar though not identical outcome will tend to prevail in the
nonstationary case: although the equilibrium rate itself is time-varying in this case, an important test
of empirical success is that the equilibrium error is stationary. The resulting estimates of
misalignment will then also tend to have a mean near zero if data-based forecasts for the
fundamentals are used.
In other words, the econometric methodology tends by construction - except when
counterfactual simulations of the fundamentals are used - to deliver an average misalignment of
zero within the sample. This is in strong contrast to the PPP approach which embodies no such
restriction. In large samples, the restriction of a near-zero average misalignment is an unambiguous
virtue, since it imposes the structure required to uncover the long-run parameters. But there may be
severe problems in small samples, particularly if adjustment speeds are slow. Cote d'lvoire's real
exchange rate, for example, is thought by some to have been substantially overvalued for much of
the post-WWII period. Our methodology, when applied using data-based permanent values for the
fundamentals, is essentially incapable of reproducing this finding.
One response to this short-sample difficulty is to "re-base" the fitted equilibrium real
exchange rates ex post by simply shifting their mean; this preserves their rates of change while
altering the estimated degrees of misalignment. Despite its obvious appeal, however, rebasing has
two important shortcomings. First, it leans very heavily on loosely structured a priori information, a
feature of the PPP approach that the present approach is trying to avoid. Second, it embodies an
implicit assumption of super-exogeneity with respect to potentially substantial and largely implicit
interventions in the marginal distribution of the fundamentals. Our use of counterfactual simulations
13



for the individual fundamentals is a close cousin to the rebasing approach, but has the advantages of
greater structure and transparency and, in particular, of exploiting the maintained super-exogeneity
assumption more fully.
Viewed in this light, the PPP approach can be reinterpreted not primarily as an assumption
that the equilibrium rate is a constant, but rather as an assumption that when samples are short and
super exogeneityfails, loosely structured a priori information (e.g., "the economy was in internal
and external balance in 1985") is of greater value to the policy analyst than the information
contained in the sample distribution of the real exchange rate and fundamentals, even when the
latter is combined with structured a priori information about the fundamentals.
4.    The econometric methodology
Given the structure just outlined, we suggest a three-step procedure for estimating the equilibrium
real exchange rate. Step 1 is to determine the order of integration of the individual data series.
Macroeconomic data often appear to possess a stochastic trend that can be removed by differencing
once. Such variables are integrated of order one, or I(l); they are nonstationary in levels and
stationary after differencing. This pattern can readily be revealed using standard tests for the
presence of a unit root. Other variables may prove stationary (I(0)) or trend-stationary (i.e., I(0) after
removing a deterministic trend component). The appropriate unit root tests are well known; in our
applications we use the Dickey-Fuller (DF), augmented Dickey-Fuller (ADF), and Phillips-Perron
(PP) tests. Although there are concerns about the low power of the unit root tests against stationary
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)) that exploit the fact that the variances of conditional forecasts
explode for nonstationary series and converge for stationary series as the forecast horizon grows.
Steps 2 and 3 involve estimation of the long-run parameters and calculation of the
equilibrium real exchange rate. Both steps are affected by the univariate time series properties of the
data as revealed in step 1. In principle, the vector [In et, wt,J /may contain an arbitrary combination
of I(0) and I(l) (or even I(2)) variables. The examples studied here, however, fall into two extreme
cases: in C6te d'Ivoire, we find that all variables are I(1); in Burkina Faso, all variables are
stationary in levels. We therefore restrict attention to these cases.'5
14



4.1   Step 2: Estimation of J
When the variables are all I(l), as in CMte d'Ivoire, stationarity of the residual nt in equation (10)
implies that the real exchange rate and its fundamentals are cointegrated (Granger (1981)). This
property is extremely useful econometrically, and a massive literature has developed in the wake of
Engle and Granger (1987).
4.1.1 The I(]) case: cointegration
As shown by Johansen (1988), cointegration is a restriction on the reduced form or VAR
representation of the joint distribution of the real exchange rate and its fundamentals. This reduced
form can be written as
p
Ax,= Tx1, + ZAjAxi, +E,                     (13)
j=1
where xt = [In et, Ft', zt']' is the nxl vector of variables and et is the vector of reduced-form
innovations (see Appendix 1). If the number of linearly independent stationary combinations of the
variables is r (0 <r < n), then the matrix Fin equation (A2) is of reduced rank r < n. We can then
write F=ab, where a and b are two nxr matrices of rank r.16 The columns of b span the
"cointegrating space" of stationary combinations of the xit; the rows of a give the weights with
which these combinations enter the individual equations of the reduced form. Equation (13)
becomes
p
Ax, = ab'x,-, +    AjAx,_j + s,,                  (14)
j=1
Since the cointegrating vectors are identified only up to a normalization, we are free to impose r
restrictions on the b matrix; for example, we might choose the normalization bi = 1, i = 1, ..., r. We
will restrict attention in this paper to the case in which r = 1, so that there is a single cointegrating
vector. The normalization on lnet l (which assumes only that lnet 1 actually enters the long-run
relationship) then exactly identifies the adjustment speed and the remaining components A, of the
cointegrating vector.'7 With a single cointegration vector, then, a and b are nxl vectors of the formn
a = [a,, a2] and b = [1, 3].
15



We emphasized above that weak exogeneity is important both for fully efficient inference in
a single-equation context and as a building block for the exogeneity concepts invoked in calculating
the equilibrium real exchange rate. Urbain (1992) and Johansen (1992) show that the fundamentals
are weakly exogenous for the long-run parameters and adjustment speed if the cointegration vector
does not enter the marginal model for the fundamentals: a2 = 0. This condition is equivalent to F2=
0 in equations (A3a) and (A3b) of Appendix 1; notice that it removes the cross-equation restriction
that would otherwise have prevented the recovery of T, from the conditional model (A3a) alone.
Although we have been focusing on the long-run parameters, the investigator will typically
be interested in the short-run dynamics as well. For example, policymakers confronting an
overvaluation might want to know the short-run effects of a nominal devaluation. It is clear from
equations (A3a) and (A3b) of Appendix 1 that the same condition that guarantees weak exogeneity
with respect to the long-run parameters also guarantees weak exogeneity with respect to the short-
run parameters of the conditional model itself In reality, however, at least the long-run specification
in (11) was derived not from conditioning but from a theoretical model. If we think of the short-run
parameters of (1 1) as having similar structural interpretations, then the condition for weak
exogeneity are more demanding. A set of sufficient condition is that a2 = 0 and c = 0, where o) is
the vector of covariances between the disturbance in equation (I 1) and the vector of disturbances
from the marginal model (A3b) (Urbain (1992)).18
4.1.2 The I(]) case: estimation
There are a number of potential approaches to estimating the cointegrating parameters. The
simplest and earliest is the Engle-Granger (1987) "two-step" method, which applies OLS to a static
regression relating the levels of the real exchange rate and its fundamentals (equation (10)).
Cointegration implies that the residuals from this regression are stationary, and this restriction
provides a test for cointegration. Because of the dominance of the common stochastic trend, the
estimates of , from the static regression are super-consistent, approaching the true parameters at a
rate proportional to the sample size rather than the square root of the sample size; and they remain
so even in the absence of weak exogeneity. In the second step, lagged residuals from the static
regression are used in place of the equilibrium errors on the right-hand side of a reduced-form error-
correction equation. Again OLS provides consistent estimates, this time of the adjustment speed
16



and short-run parameters of the reduced-form error-correction specification.'9
While the Engle-Granger method is extremely simple to implement, the estimates of the
cointegration vector are biased in small samples. The degree of bias depends on the degree of
persistence in the residual, suggesting that superior estimates might be obtained by accounting for
the short-run dynamics (Banerjee, et al (1993)). We therefore also report OLS estimates of /j taken
directly from the error-correction specification (9). These control for the short-run dynamics -
which may be of interest themselves - and, like the static regression estimates, remain consistent
even with a failure of weak exogeneity.20 Moreover, in line with our earlier discussion, a second and
potentially decisive advantage emerges under weak exogeneity: estimates of , taken from the
conditional error-correction model are equivalent to full-information maximum-likelihood
estimates. They are therefore asymptotically efficient, and the t-ratios generated by OLS are
asymptotically normal, allowing standard inference. This is in contrast to the static regression case,
where the t-ratios have non-standard distributions even asymptotically.
A third natural alternative is the Johansen (1988) procedure, which is a systems approach
based on estimation of the full VAR in equation (13). The "curse of dimensionality" is a serious
limitation here, however. Monte Carlo evidence suggests that the Johansen procedure deteriorates
dramatically in small samples, generating estimates with "fat tails" (i.e., frequent outliers) and
sometimes substantial mean bias; moreover, it is less robust than the single-equation alternatives to
misspecification of system parameters like lag length and to practical features like serial correlation
in the equilibrium error (Hargreaves (1994)). Because of these small-sample limitations, we use the
Johansen procedure to determine the number of cointegration vectors (i.e., to test for the rank of r
in equation (13)) and to test for weak exogeneity - both of which are features of the entire system of
equations - but otherwise restrict attention to the single-equation methods.
4.1.3 The I(O) case: estimation
In the case of Burkina Faso, we find that all variables are stationary in levels. We pointed out above
that in this case, the long-run "equilibrium" value of lnet, like that of any stationary variable, is
simply its mean. A consistent and efficient estimator of the equilibrium real exchange rate is
therefore the sample mean, corrected for any deterministic trend. This implies that the long-run
parameters need not be estimated for the purpose of tying down the long-run equilibrium. If the
17



fundamentals are super exogenous with respect to these parameters, however, a structural shift in
the marginal process generating the fundamentals (for example, a shift in the mean of Ft) will
produce a corresponding change in the mean of lnet, with the slope of the effect given by the
associated long-run parameter. Moreover, the long-run parameters and the short-run dynamics may
be of theoretical interest even in the absence of super exogeneity; and the investigator may have a
practical interest in generating short-to-medium-term conditional forecasts of the real exchange rate.
For all of these reasons, we proceed with estimation in the stationary case even though it is not
strictly necessary for assessment of the long-run equilibrium.
The theory of specification and estimation in the stationary case is well developed and we
will not review it here; see Hendry (1995). What is clear is that the existence of a long-run
relationship no longer exerts the kind of statistical leverage that it does when the variables are
individually nonstationary. This is apparent in equation (10) since all the dynamics have been
pushed into the residual nt, which is therefore likely to be correlated with the right-hand side
variables. OLS estimates of the static regression are therefore inconsistent in the 1(0) case, even
though (as emphasized above) they are super-consistent when the variables are nonstationary and
cointegrated.21 The error-correction model corrects this problem to some degree by incorporating
dynamics; but the contemporaneous values of the fundamentals till raise issues of
predeterminedness. Lacking identifying information on (11), one way to obtain consistent estimates
of the parameters in that equation is to use higher lags of the fundamentals as instruments.22
The lack of a clear statistical distinction between the individual and joint variation of the
variables carries over to the conditions for weak exogeneity, which now make no general distinction
between the short and long-run parameters. A sufficient condition in the present limited information
context (i.e., where identifying restrictions on the marginal model are not available) is that equation
(11) and the marginal model form a block-recursive system (which also obviates the need for
instrumental variables and guarantees predeterninedness). We do not formally test for weak
exogeneity in the I(0) case (Burkina Faso), treating it instead as a maintained hypothesis where
necessary (see Monfort and Rabemanajara (1990)).
4.2   Step 3: Calculating the equilibrium  real exchange rate
Above we distinguished conditional forecasts and counterfactual simulations as two alternative
18



approaches to constructing sustainable values for the fundamentals. Here we broaden the first of
these alternatives to consider various alternatives based on the time series behavior of the data. For
policy purposes, concern often centers around the current or prospective situation rather than the
historical episodes that make up the data sample. While our discussion focuses on within-sample
estimates or simulations, the considerations outlined below apply equally to the construction of
projected sustainable values for the fundamentals.
4.2.1 Sustainablefundamentals: time-series-based estimates
When the fundamentals are stationary, their movements are inherently temporary. We pointed out
above that in this case the conditional long-run forecast is simply the sample mean (as corrected for
any deterministic trend). At the other extreme all movements in the fundamentals are permanent. In
this case, the fundamentals are individually random walks and the equilibrium real exchange rate in
period t is simply Ft
In practice, the fundamentals are likely to include both transitory and permanent
components. This is clear for nonstationary fundamentals, where the permanent component
corresponds to the underlying stochastic trend. The Beveridge-Nelson method, which we use below
in the C6te d'Ivoire case, assumes that the fundamentals each follow a univariate ARIMA(p, I,q)
process, with the autoregressive and moving average parts generating stationary fluctuations around
an underlying random walk (Beveridge and Nelson (1981)). Movements generated by the unit root
part are permanent and are extracted to construct Fpt, the permanent component of Ft. The
equilibrium rate is then given by F"t. This will tend to be a somewhat smoother series than Ft,
reflecting the elimination of transitory shocks to the fundamentals.23
We will also calculate sustainable values using centered moving averages of the
fundamentals in both the stationary and nonstationary cases. This approach can be defended by
appealing to the judgmental nature of the decomposition exercise and the disadvantages imposed by
small samples. Moving averages mechanically smooth the data, to a greater degree the larger the
number of periods used. In the nonstationary case, even a narrow moving average typically smooths
the individual series more substantially than a B-N decomposition and may therefore yield results
that are more appealing economically. The B-N approach is particularly problematic in small
samples, where the results can be highly sensitive to the underlying ARIMA specification and can
19



often exacerbate turning points in economically implausible ways. This problem can affect the
resulting equilibrium rate even more dramatically: if the fundamentals are all smoothed with a
moving average, the resulting equilibrium rate is simply the corresponding moving average of Ft.
The weighted sum of permanent components, in contrast, can easily be substantially more variable
than Ft itself (as in our C6te d'Ivoire example below). Small samples also increase the possibility
that stationary but persistent series are misidentified as nonstationary, in which case the B-N
decomposition presumes a permanent component that in fact is not present.
In the stationary case, the moving average approach provides a way of acknowledging that
even stationary fundamentals may have long-lasting movements. When a stationary variable is
highly persistent, its conditional expectation at policy-relevant horizons can easily be relatively far
from its unconditional mean. Using a moving average allows the long-run equilibrium rate to move
in response to the current values of the fundamentals, even though these movements are thought
ultimately to be temporary.
4.2.2 Sustainable fundamentals: counterfactual estimates
Ex-ante modeling of the permanent components of the fundamentals provides an important
alternative to ex-post approaches that rely on the underlying data-generating processes of the
fundamentals. There are two important reasons for pursuing this extension. The first is that in a
small sample it may be virtually impossible, using time-series decomposition methods or moving
averages, to distinguish persistent but unsustainable changes in the fundamentals from genuinely
sustainable changes. The accumulation of international arrears by Cote d'Ivoire starting in the early
1980s provides an example: by this indicator, trade balances in that country appear to have been
unsustainably large for over a decade. The second reason is that counterfactual simulations are
needed to address the "what if' questions that are of central interest to policymakers, particularly
when the fundamentals include variables potentially under policy control. Again using the Cote
d'Ivoire case, policymakers might want to know the implications for the real exchange rate of a
trade liberalization or change in government spending patterns. Preserving the relative simplicity of
the single-equation approach, one way of handling these concerns is to construct counterfactual
simulations of sustainable values for selected fundamentals. A potentially important side-effect of
such simulations is to break the restriction implicit in the methodology that the average degree of
20



misalignment be near zero within sample.
In Appendix 2 we construct counterfactual simulations for the resource balance, openness,
and investment share variables for both CMte d'Ivoire and Burkina Faso. For Cote d'Ivoire, these
simulations incorporate the following judgments:
the actual resource balance was unsustainably low after 1979.
trade policy was unsustainably restrictive, particularly after 1979.
* the investment to GDP ratio was unsustainably low, particularly after 1979.
For Burkina Faso, the key judgments are (the investment to GDP ratio does not enter the model):
* the resource balance is determined by the volume of concessional inflows, and
drought-year levels are unsustainable.
* trade policy was unsustainably restrictive throughout the sample.
Details of these calculations appear in Appendix 2.
4.2.3 Estimating the degree of misalignment
The estimated degree of misalignment, m, is simply the percentage difference between the real
exchange rate and its computed equilibrium value:
m, = Ine, = [Ine, -f8'Fp] --,8'(F - F;P)                (15)
For within-sample estimates, et is simply the actual real exchange rate. For out-of-sample estimates,
et can be forecasted using a dynamic simulation that feeds projected paths for the fundamentals
through the estimated short-run parameters of the model.
The degree of misalignment is decomposed mechanically in equation (15) into an error-
correction term that captures the deviation of the exchange rate from the "fitted" real exchange rate
using long-run parameters (the term in square brackets) and a term that captures the deviation of the
current fundamentals from sustainable values. Expressing m this way brings out the role of
sustainability calculations for the fundamentals. Suppose, for example, that the long-run parameter
for the real exchange rate is negative, implying that a sustained terms of trade improvement
appreciates the real exchange rate. If most movements in the terms of trade are temporary, however,
and households optimize without borrowing constraints, then the short-run impact of a change in the
terms of trade should be substantially below the estimated long-run impact (as in our theoretical
model). A temporary improvement in the terms of trade would then produce offsetting changes in
21



the components of mt: the second component would be large and negative, reflecting the temporary
nature of the terms of trade boom; the first would be large and positive, reflecting the very modest
response to the actual real exchange rate to the substantial short-run movement in Ft. Misalignment
calculated using the actual rather than sustainable value of the terms of trade (i.e., setting FPt = Ft)
would pick up only the second of these effects, producing the mistaken impression of a badly
undervalued real exchange rate.
What the decomposition cannot do, is to identify the source of misalignment relative to
plausible values for FP. As discussed earlier, el may differ from FPt for reasons of real or nominal
rigidities or, equivalently, equilibrium or disequilibrium dynamics; or it may be pushed by random
shocks.
5.    Estimation Results
In this section we illustrate the methodology using annual data for Cote d'Ivoire and Burkina Faso.
We begin by noting that data limitations force two compromises in the estimation. The first is that
we are unable to separate government spending into traded and nontraded goods. Data are available,
however, for the shares of government consumption spending and total investment spending in
potential GDP, and we use these to proxy for the level and composition of spending. A rise in
government spending appreciates the real exchange rate if government spending is more intensive in
domestic goods than is private spending; a rise in the investment share of GDP is likely to shift
spending towards traded goods, other things equal, given the high import content of investment, and
therefore to depreciate the real exchange rate. The second compromise is that in lieu of direct
measures of the stance of trade policy, we must construct proxies for this variable. It is common in
this literature to use various ratios of trade to GDP, on the argument that a more liberal trade
regime, ceteris paribus, means higher trade volumes. We experimented with three such proxies: the
ratio of current imports to current GDP, the ratio of constant-price imports to constant-price GDP,
and the ratio of total trade (imports plus exports) to constant-price GDP. All three performed
adequately for Burkina Faso, but in Cote d'Ivoire the ratio of current imports to current GDP was
clearly superior to the other proxies. We therefore retain only this proxy in the analysis reported
here. For the case of Cote d'lvoire we also include a drought dummy variable that takes the value I
for 1983 and 1984 and zero otherwise.
22



5.1    Unit Root Tests
As a first step we test all variables (except the drought dummy variable) for unit roots, to determine
whether they can be represented more appropriately as stationary, difference-stationary, or trend-
stationary processes. The results appear in Table 1. For C6te d'Ivoire, all three tests indicate
nonstationarity for all variables. Moreover, 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 possible exception of the terms of trade,
which is bordering on nonstationarity. Figures 3 and 4 provide some additional information in the
form of variance ratio tests.24 These tests corroborate the unit root 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 it is stationary.
Based on the above tests, we proceed to step two, in which we estimate the long- and short-
run relationships between the real exchange rate and its fundamentals.
5.2    Tests of Cointegration: C6te d'Ivoire
Once it is confirmed that the variables behave as integrated processes, tests for cointegration can be
undertaken to establish a long-run relationship between the RER and its fundamentals.25 Table 2
reports the results of Johansen's likelihood ratio tests for the cointegrating rank of the system. We
use a lag length of 1 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 estimated 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 vector cannot be rejected
in favor of more than one. The asymptotic tests therefore indicate one cointegrating vector.
Likelihood ratio tests of cointegration are known to be sensitive to small-sample bias,
tending to reject low values of r too often. In column 4 we show a set of critical values that adjust
for small-sample bias using a method suggested by Cheung and Lai (1993). Using these critical
values it is difficult to distinguish between 0 and 1 cointegrating vector. We will proceed under the
assumption that there is one vector, although we are marginally unable to reject the hypothesis of
23



zero at the 10% level using the adjusted critical values.
5.3   Long-run parameters and adjustment speed. Cote d'Ivoire and Burkina Faso
For Cote d'Ivoire we estimate the long run parameters using both the static regression, equation
(10), and the error-correction model (ECM), equation (11).26 We emphasized earlier the difficulties
of system estimation in small samples, and the signs and magnitudes of the estimates obtained using
the Johansen approach are less in line with the theory. We therefore confine attention to the results
in Table 3. For Burkina Faso the long-run parameters are obtained from the ECM and appear in
Table 6.
Columns 1 to 3 of Table 3 give static regression estimates for CMte d'Ivoire using alternative
versions of the trade policy variable while column 4 shows the corresponding parameter estimates
from an unrestricted ECM (recall that this is equivalent to the unrestricted ADL; the short-run
parameters from this regression are presented in Table 4). As discussed earlier, both the static
regression and the ECM deliver super-consistent estimates of long-run multipliers when
cointegration is present. The estimates in columns 1 and 4 (which use the same openness variable)
are reasonably close, providing some further support for the existence of a cointegrating relationship
between the variables. In the static regression cases, we corroborate the existence of cointegration
by applying unit-root tests to the estimated residuals (the critical values are more demanding than
with a single variable, since the OLS estimation tends to induce stationarity in the residual); in each
case the calculated values rejects nonstationarity in favor of stationarity at standard levels. Since the
OPEN1 results are generally strongest, we use this variable in what follows.
As discussed earlier, weak exogeneity holds with respect to the long-run parameters if the
cointegrating vector does not enter the marginal model for the fundamentals. Engle and Granger
(1987) suggest testing for weak exogeneity by introducing the error-correction term (the lagged
residual from the static regression) into the equations of the marginal model and applying
asymptotic t-tests to the hypothesis that the coefficients are zero. Using this test we are not able to
reject weak exogeneity of the variables individually at reasonable significance levels, with the
exception of ISHARE where we reject at the 5% level. Rejection for ISHARE suggests problems
with inference in the error-correction specification: the long-run parameter estimates remain super-
consistent, but standard errors are biased and inconsistent. To handle this we re-estimate the ECM
24



via instrumental variables, using lagged differences in the other fundamentals as instruments for
ISHARE. These results appear in column 5 of Table 3 (the full ECM is column 3 of table 4).
Inference can proceed from the IV version of the ECM, conditional on legitimacy of the chosen
instruments.27
For both countries, the estimated long-run parameters strongly corroborate the theoretical
model. Estimated coefficients for the resource balance/GDP ratio are negative for both countries, as
expected, suggesting that a rise in capital flows raises domestic absorption and shifts the
composition of potential output towards nontraded goods. The implied elasticities of the real
exchange rate with respect to the resource balance (-0.26 for C6te d'Ivoire and -1.50 for Burkina)
are comparable in magnitude to those obtained in Elbadawi and Soto (1995) for C6te d'Ivoire and
Mali.
The effects of shocks to the terms of trade (TOT), as remarked in Section 2, are theoretically
ambiguous. However, consistent with the bulk of the empirical literature, the results here indicate
that an improvement in the terms of trade appreciates the real exchange rate, suggesting that the
spending effects of this variable dominate substitution effects. Again the terms of trade elasticity
estimates are plausible as compared to other estimates in the literature. Perhaps the most interesting
point is that despite the differences in the economic structure of the two countries, the extent of the
effect appears to be the same for both countries (a 10% terms of trade improvement appreciates the
real exchange rate by 4% in C6te d'Ivoire and by 3.5% in Burkina Faso).
In both countries a negative parameter estimate supports the notion that trade-liberalizing
reforms are consistent with a more depreciated real exchange rate. The size of the elasticity differs:
it is roughly -I for C6te d'Ivoire and -0.47 for Burkina Faso. While these elasticities are not
precisely estimated, they are consistent with evidence obtained by M'Bet and Madeleine (1995) and
Elbadawi and Soto (1995) suggesting that the effects are stronger in the larger CFA countries.
For C6te d'Ivoire, a 10% increase in the share of investment in GDP (ISHARE) depreciates
the real exchange rate by at least 2.7%, consistent with the view that this shifts the composition of
spending toward traded goods. This evidence is consistent with that of Edwards (1989), but reveals
an effect substantially lower than those estimates, which are in the range of 7% for a group of 12
LDCs. For Burkina Faso, the trend effect is significant, albeit with a very small coefficient, further
corroborating the strong static trending effects revealed by the univariate unit-root tests.
25



To test the long-run homogeneity property - that the foreign price level, converted to CFA
francs using the nominal exchange rate, does not affect the equilibrium real exchange rate - we
included LPFOR in the specification and tested the null hypothesis of zero long-run coefficient. We
use the dynamic regression results for this test since the t-statistics from the static regression have
non-standard distributions even under weak exogeneity. For Burkina Faso, homogeneity cannot be
rejected at any reasonable level of significance (Table 6). For C6te d'Ivoire, however, inclusion of
the change in LPFOR (or just the change in the nominal exchange rate) in the ECM, causes marked
detarioration of the results. Thus, while long-run homogeneity cannot be rejected, the remaining
results are unsatisfactory. For the purposes of subsequent calculations, we treat long-run
homogeneity as a maintained hypothesis.
5.4   Short-run Dynamics: C6te d'Ivoire and Burkina Faso
Tables 4 and 6 show the short-run parameters from the estimated ECMs for Cote d'Ivoire and
Burkina Faso. For CMte d'Ivoire (Table 4) we show two alternatives, corresponding to the long-run
parameters in columns 1 and 4 of Table 3. Column I uses the lagged residual from the static
regression in column 1 of Table 3, so that the short-run parameters are estimated conditional on the
cointegration vector from the static regression.28 In column 2 we estimate the short-run parameters
jointly with the long-run parameters using the unrestricted ECM. Columns 3 and 4 estimate these
regressions using lagged differences of the other right-hand-side variables as instruments for
ISHARE.
For the case of CMte d'lvoire the short-run effects of the fundamentals are generally
appreciable in size, statistically significant, and in the same direction as the long-run effects. For the
case of Burkina Faso, the short-run impact effects are generally less than half the size of their
corresponding long-run coefficients, and in most cases are statistically insignificant.
The short-run estimates provide direct evidence on the short-run effects of nominal
devaluations on the real exchange rate. Under long-run homogeneity, nominal devaluations have at
most a transitional role to play in macroeconomic adjustment. If domestic wages and prices are
sticky, however, shocks that depreciate the equilibrium real exchange rate (e.g., a fall in sustainable
capital flows, a persistent deterioration in the terms of trade deterioration, or a trade liberalization)
will generate a contractionary adjustment under fixed exchange rates. Nominal devaluation can then
26



be an important part of efficient macroeconomic adjustment (e.g., Corden (1989)), provided that
their short-run effects on the real exchange rate are not neutralized by domestic inflation. The results
of the error-correction model corroborate this view for both countries. The estimated short-run
elasticities are statistically significant, fairly substantial, and virtually identical across the two
countries: these results suggest that a 50% devaluation (such as the one effected in 1994) will
depreciate the real exchange rate by 15% in the short-run.29
A crucial parameter in the estimation of these short-run dynamic models is the coefficient of
the error-correction term which measures the speed of adjustment of the RER to its equilibrium
level. The adjustment speed estimated for Cote d'Ivoire in Table 4 is lower (at -0.30 and -0.45,
respectively, in the unrestricted and 2-step ECM) than the corresponding estimate for Burkina Faso
in Table 6 (at -0.54). The adjustment speed for Cote d'Ivoire is somewhat higher than that obtained
for Cote d'Ivoire by Elbadawi and Soto (1995) using a similar framework. From these estimates the
number of years required to eliminate a given misalignment can be derived.30 For example,
eliminating 95% of a shock to the real exchange rate would take slightly more than 3 years in
Burkina Faso and could take as long as 8 years in Cote d'lvoire. Elbadawi and Soto (1995) find a
similar difference in adjustment speed for Mali. This finding suggests that smaller economies in the
zone are more adaptive to shocks than the larger ones. This conclusion appears consistent with the
widely held view that the latter group of countries has experienced much higher degree of
overvaluation during the 1986-94 period than the former one. One reason for this may be a greater
prevalence of nominal rigidities in the larger economies, with their larger manufacturing sectors and
a greater proportion of production for the domestic market.
Adjustment speeds for both countries, however, are substantially larger than the -0.19
obtained by Edwards (1989) for a group of developing countries using a partial adjustment model.
To the degree that these adjustment speeds can be legitimately compared, they may provide some
support for the view that membership in a monetary union produces greater flexibility of nominal
wage settlements in the private sector by increasing the credibility of monetary policy (Rodrik
(1994)).
5.5   The equilibrium real exchange rate and misalignment
Tables 5 and 7 show alternative measures of the equilibrium real exchange rate. For Cote d'Ivoire,
27



we use the long-run parameters derived from the static regression in column (1) of Table 3. For
Burkina Faso, we use the long-run parameters from the unrestricted ECM in column 1 of Table 6.
For Cote d'Ivoire we report four measures of the "equilibrium" real exchange rate: the fitted
RER, its corresponding 5-year moving average, an equilibrium rate based on Beveridge-Nelson
decompositions of the fundamentals, and one based on the counterfactual simulations (Appendix 3).
For Burkina Faso, we replace the B-N decomposition with the fitted trend for the real exchange rate;
as discussed earlier, this represents the most natural long-run forecast for a trend-stationary variable.
Recall that when we generate long-run "forecasts" of the real exchange rate using time-
series-based estimates of the "permanent" fundamentals, we require not only adequate estimates of
the long-run parameters but also a lack of Granger causality from the real exchange rate to the
fundamentals. With a lag length of 1, weak and strong exogeneity coincide and the partial tests
reported earlier for Cote d'Ivoire therefore provide some support for these calculations. As an
additional check, we tested the multivariate generalization of Granger non-causality from the real
exchange rate to the fundamentals and were unable to reject non-causality at any reasonable levels,
using a lag length of either I or 2. As argued earlier, the use of counterfactual simulations for the
fundamentals involves an assumption that the long-run parameters are invariant to the interventions
being constructed; we treat this as a maintained hypothesis.
The last columns of Tables 5 and 7 show the percentage gap between the observed and
equilibrium real exchange rates, using the counterfactual simulations for the equilibrium rate. The
gap between these two series provides a measure of real exchange rate misalignment. The figures
show a remarkable success on the part of the computed index in reproducing well-known
overvaluation (and undervaluation) episodes in the recent macroeconomic history of these countries
and the CFA zone more generally. In particular, note that C8te d'Ivoire managed to reverse
substantial real overvaluation by the end of the first half of the 1980s. While some of this was
generated by contractionary macroeconomic policies that fell heavily on investment, a substantial
contribution came from the steady depreciation of the French franc against the US dollar and other
major currencies. When the French franc moved in the reverse direction following 1986, the fiscal
laxity and structural rigidities that characterized the Ivoirian economy all along were fully exposed;
our calculations imply that during the 1987-93 period the real exchange rate was overvalued by 34%
on average. By 1994 a set of corrective measures, including a zone-wide 50% devaluation, were
28



effected. Using a CGE approach, Devarajan (1997) estimates the degree of overvaluation in C6te
d'Ivoire for 1993 at 36%, a figure close to our estimates based on counterfactual simulations of the
fundamentals.
For Burkina Faso, in contrast, our results for 1980-93 do not indicate any major
overvaluation. Indeed, according to our estimates, Burkina Faso's real exchange rate was
undervalued by 1% on average between 1980 and 86 and by nearly 14% during 1987-93. The
estimated undervaluation may be on the high side for the latter period.31 Burkina Faso is generally
regarded, however, as having adjusted successfully to the adverse shocks that affected the entire
zone after 1986, especially in comparison with the larger CFA countries (Devarajan and Hinkle
(1995)). Substantially milder overvaluation (or even undervaluation) is one measure of this success;
another is the absence in Burkina Faso of the deep recession experienced by C6te d'Ivoire
experienced during the 1980s and early 1990s. Both observations suggest a more flexible domestic
wage and price structure in the smaller of the two countries, and therefore significantly milder
nominal rigidities.
Conclusions
The decision to devalue depends fundamentally on degree of misalignment of the real exchange rate
and the speed with which internal adjustment mechanisms are likely to restore macroeconomic
balance. Measuring the degree of misalignment is difficult, however, given that the equilibrium real
exchange rate is unobservable whenever the economy is not in internal and external balance. The
standard PPP approach is to identify a period in which the economy is judged to have been in
balance, and to take the real exchange rate of that period as the equilibrium rate for all years. But
this fails to account for the effect of changes in the fundamentals on the equilibrium real exchange
rate.
Once the endogeneity of the equilibrium real exchange rate is recognized, however, a second
problem arises: restricting attention to plausible candidates for years of macroeconomic balance,
there will rarely be enough observations to estimate the elasticities of the equilibrium rate with
respect to even a small list of fundamentals. In this paper, we addressed these problems by imposing
the relatively mild (and testable) restriction, drawn from standard theories of the equilibrium real
exchange rate, that the distance between the actual and equilibrium real exchange rates is a
29



stationary random variable. When the variables are 1(1), this leads naturally to the use of
cointegration methods for estimating the long-run relationship between the real exchange rate and
its fundamentals. When the variables are stationary, standard procedures of dynamic specification
and estimation apply. We illustrated the methodology using annual data for CMte d'Ivoire and
Burkina Faso.
How useful an addition is this methodology to the standard toolbox for assessing the
equilibrium real exchange rate and the degree of misalignment? Our view is that this methodology
belongs in the analyst's toolkit as a clear advance over PPP and a useful complement to other
methods. There are three fundamental reasons for this.
* First and foremost, this approach provides a natural way of incorporating the reality
that the fundamentals will sometimes move permanently. In such a case our approach
extracts maximal leverage from the theoretical proposition that the real exchange rate
will not stray indefinitely from a function of the fundamentals.
Second, estimating the equilibrium real exchange rate is typically motivated by policy
concerns. The analyst may therefore be particularly interested in the relationship
between the equilibrium real exchange rate and hypothetical changes in individual
fundamentals. For out-of-sample exercises, interest would center on how changes in
the fundamentals would alter both the actual and the equilibrium rates, and thereby
the degree of misaligmnent. Under super exogeneity of the fundamentals, our
approach delivers a set of parameters that can be used for such policy analysis in a
transparent and straightforward manner.
* Third, this approach takes a partial step towards imbedding the determination of the
long-run relationship in the overall dynamic relationship between the real exchange
rate and its fundamentals. Under weak exogeneity with respect to the short-run
parameters, fully efficient estimation and inference on these parameters can take place
conditional on the current and lagged fundamentals. The resulting information on
short-run dynamics may be of interest in its own right and if Granger non-causality
also holds, can be used to generate short-term forecasts of the real exchange rate and
degree of misalignment.
From the general viewpoint of dynamic specification, there are various directions in which
the approach advocated here might be extended. One is to allow both 1(0) and I(1) variables in the
long-run relationship. In this case the theory still implies cointegration among the I(1) variables, but
the Engle-Granger two-step method will produce inconsistent estimates of the long-run parameters
on the stationary variables. We are therefore pushed towards allowing explicitly for the short-run
dynamics, whether via the error-correction model, the Johansen procedure, or some alternative. A
30



second extension would be to allow multiple long-run relationships between the variables. Such a
case might arise, for example, from the existence of a reaction function relating fiscal policy to the
trade balance and/or the real exchange rate; moreover, since most of our variables are already
measured in ratios (the real exchange rate, the openness variable, etc.), we may already be reducing
the order of integration of underlying nonstationary variables (like the domestic price level). The
structural error-correction model of Boswijk (1995) represents the closest counterpart to our
analysis in the case of multiple cointegrating relationships. Finally, we have chosen not to impose
any theoretical structure on the short-run dynamics. In cases where particular sources of short-run
dynamics are of interest, there may be a substantial return to developing a theoretical structure to
capture these dynamics, and imposing the resulting identifying restrictions; for an interesting
attempt to incorporate rigidity of domestic prices, see Kaminsky (1 988). An interesting challenge
along these lines is that of separating misalignments due to price rigidities from those due to internal
real dynamics or temporary movements in the fundamentals.
Naturally, most of these extensions will bring out a tension between maintaining the
simplicity of a single-equation approach - an important feature if this approach is to be used
intensively "in the field" - and allowing the overall dynamic relationship(s) to emerge from the
data. Here we identify three particular cautions regarding the use of this methodology in the policy
arena.
First, the econometric approach is data-intensive and inherits all the limitations of
developing country data. Our empirical findings for CMte d'Ivoire and Burkina Faso are broadly
consistent with the empirical literature on equilibrium real exchange rates in developing countries,
and they line up well with estimates obtained by other methods. But they are not robust. We noted
above that the econometric results were quite sensitive to the choice of proxies for the fundamentals
and to and the estimation procedure. The choice of real exchange rate index also made a difference
empirically, and although changes in long-run elasticities are to be expected, we found that the
overall statistical performance was highly sensitive to whether an internal or external real exchange
rate concept was employed (see Hinkle et al.) and whether the nominal exchange rate was adjusted
for black market transactions. While such conditions define the art of econometric practice, they
may be particularly acute when the notion of long-run equilibrium in short samples is required to
carry so much weight in short samples.
31



The reality of short samples brings out a second potential weakness in this approach, even
relative to the PPP approach. In effect, the single-equation methodology assumes that the economy
was in internal and external balance on average over the sample period. This avoids the need for a
priori and possibly ad hoc claims about macroeconomic balance in any particular year, providing
instead a systematic way of bringing the whole sample to bear in determining the path of the
equilibrium rate. But it implies that unless the analyst is prepared to undertake counterfactual
simulations for the fundamentals, the average degree of misalignment in the sample will tend, by
construction, to be small. There will be little scope for uncovering episodes of over- or under-
valuation that last more than a few years. In the CFA zone, where the real exchange rate was widely
thought to be overvalued for most of the period between 1978 and 1994, the implicit "balance on
average" assumption may be seriously misleading. The PPP approach, of course, does not require
such an assumption; the result is that the real exchange rate can in principle be overvalued (or
undervalued) in every other period than the benchmark one. We suggested that a natural way of
handling this within our methodology was to construct counterfactual simulations for the
fundamentals. In our counterfactuals for Cote d'Ivoire, freer trade, higher domestic investment, and
smaller trade deficits all produced a depreciation of the equilibrium rate and therefore tended to
increase the estimated degree of misalignment.
Finally, the methodology relies on concepts of equilibrium and misalignment that are
conditional on policies or structural features that can reasonably be treated as predetermined,
whether or not those policies or features generate welfare losses. In this view, short-run
misalignments may well reflect market-clearing responses to shocks, and long-run movements in
the real exchange rate may well reflect highly suboptimal macroeconomic policy choices. For both
reasons the misalignments most readily identified using single-equation time-series methods may
not be the most interesting from a policy perspective.
32



Endnotes
1l This is what Hinkle et al. call the "internal" real exchange rate.
2. Montiel assumes that transactions costs are a decreasing function of the ratio of money holdings to
spending: r = r(m/c), r' < 0.
3. The latter feature ties the domestic real interest rate to the time-preference rate in any steady state. Given
r, the value off* is then determined uniquely by the external supply function.
4. Sincep. =p +e, wherep wis the world inflation rate, we can think of the world rate of inflation and the
domestic rate of crawl of the exchange rate as among the fundamentals. Also, we have suppressed the time
preference rate in writing equation (5).
5. Williamson (1994), for example, writes that "PPP comparisons are indispensable for comparing living
standards, but they are the wrong basis on which to calculate equilibrium real exchange rates. They are
wrong conceptually, and they provide seriously misleading advice. For that purpose they should be
abandoned, once and for all." (p. 191). In section 3 below we discuss further the distinction between the PPP
approach and our approach.
6. The domestic real interest rate, in contrast, becomes endogenous. Movements in the domestic real
interest rate reconcile private spending decisions with the exogenous credit constraint, with the spread
between the domestic and foreign real interest rates capturing the shadow price of the credit constraint.
7. By finite conditional variance we mean that Var(nt+kIItl) is finite, where the information set
/t-I contains all values of In e and F dated t-l or earlier.
8. This does not rule out theoretical models that exhibit instability in certain directions (e.g., rational
expectations models); the key assumption is that the economy chooses" a convergent path for given values
of the fundamentals.
9. In terms of the ADL parameters, the adjustment speed and long-run parameters i in the error-correction
representation are given by a =(E=1,p,U*j (so that the stability restriction implies a < 0) and ,8i'  -
10. In the end, this high variability is useful only if it can be parameterized in a sufficiently parsimonious
manner. With so few data we are virtually forced into assuming that the parameters are constant over the
sample. This rules out structural changes that may in fact be important over the sample period and, if
incorrect, can produce misleading inferences about the nonstationarity of the data and the values of the
parameters.
11. In the stationary case, specifying a dynamic simultaneous model or even a just-identified structural
VAR' along the lines of Bemanke (1986) would require more identifying information than we are willing to
impose ex ante. Moreover, systems-based estimates that exploit this information are known to be less robust
to misspecification than limited-information approaches that ignore identifying information outside of the
equation being estimated.
12. C6te d'Ivoire may well be large enough in the world cocoa market to affect its terms of trade.
33



13. See Hendry (1995). Not surprisingly, tests for super exogeneity generally require intensive study of the
relationship between the estimated equation and the associated reduced form for the fundamentals. One
natural test (given weak exogeneity) is to establish parameter constancy in the estimated model given a
sample break in the associated reduced form for the fundamentals.
14. Estimation of long-run parameters appears superfluous in this case. The investigator will typically be
interested, however, not only in a good conditional forecast of the real exchange rate, but also in various
characteristics of the short-run dynamics. Uncovering the relevant parameter estimates requires estimation
even in the stationary case. Moreover, estimates of,8 are also required to apply counterfactual simulations
for the fundamentals.
15. 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).
16. Since each of the variables in x is either I(0) or /1(), all of the first differences in (14) are stationary.
Stationarity of St then implies that each row ofFxt-I must also be stationary (since it is a linear combination
of stationary variables) although the individual xit's are all nonstationary. This is accomplished if the rows of
Finduce linear combinations of stationary linear combinations of the nonstationary variables xt: hence the
decomposition of F. Note that if there are n stationary combinations, then the individual xit's must all be
stationary.
17. If there are multiple cointegrating relationships, normalization alone is insufficient to relate the long-run
parameters uniquely to their counterparts in any particular economic theory - i.e., to obtain interpretable"
parameter estimates - and we require further identifying restrictions (see, for example, Johansen and
Juselius (1994)). In this case the single-equation approach is likely to pick up a weighted combination of the
cointegration vectors (Johansen, 1992). This lack of identification may not be highly damaging for
forecasting purposes, but it raises a variety of issues that go beyond the scope of single-equation approaches.
The closest counterpart to our approach in the r > I case is the structural error correction model" of Boswijk
(1995) (discussed in Ericsson (1995)), which is obtained by premultiplying (14) by a square matrix and then
imposing a set of restrictions.
18. Under these conditions case equation (11) and the unrestricted reduced forms (A3b) form a block-
recursive system.
19. Engle and Granger (1987) demonstrated an equivalence between cointegration and error correction for
nonstationary variables. In the nonstationary case, therefore, equation (10), which implies cointegration, also
implies that the real exchange rate has a reduced-form error-correction representation, i.e., one that is similar
to ( 11) but with contemporaneous values of the fundamentals excluded. It is this reduced-form error-
correction equation that is estimated in the second step of the Engle-Granger method.
20. A failure of weak exogeneity, however, means small-sample bias and invalid inference regarding the
long-run parameters. Recall also that the conditions for weak exogeneity with respect to short-run parameters
are stronger.
21. The standard sufficient condition for consistency of OLS in the stationary case is that the right-hand
side variables are predetermined, i.e., that the residual is uncorrelated with contemporaneous and lagged
right-hand side variables. In equation (10) the condition is Cov(nt, xt_k) = Cov(nt, wt) = 0. In the stationary
case, predeterminedness corresponds closely (but not exactly) to weak exogeneity (Engle, Hendry and
Richard (1983), Monfort and Rabemanajara (1990)).
34



22. See Monfort and Rabemanajara (1990) for development of exogeneity concepts and tests in the
stationary context.
23. Any set of cointegrated variables has a common trend representation; this could be the basis of a joint
decomposition of the real exchange rate and fundamentals into a stochastic trend component and a stationary
(moving average) component (see Banerjee, et al (1993)). The B-N approach approximates this by treating
the variables one by one.
24. This ratio is defined as (J/k)var(Xt-XtIk)/Var(Xt-Xt l), where Xt is the variable of interest and k is the
lag length (Cochrane, 1988).
25. We include the drought variable in the long-run relationship, on the grounds that it picks up a supply
shock that is highly asymmetric between traded and nontraded goods. Unfortunately, the critical values of
Dickey-Fuller tests and the many of the tests used in the Johansen procedure are sensitive to the exact
specification of deterministic variables in the cointegrating relationship. We do not attempt the Monte Carlo
simulations that would be required to establish critical values for our case.
26. We apply instrumental variables (IV) to the Bewley transform of equation (14), using the ADL
variables as instruments. This gives numerically equivalent results to using OLS on the ADL representation.
The advantage of the Bewley transform is that the long-run parameters and their standard errors can be read
directly from the equation. See Banerjee, et al, pp. 55-64.
27. Although these results are encouraging, weak exogeneity may be a more serious problem than is
indicated by our variable-by-variable tests. Using Johansen's system-based chi-squared test, we strongly
reject joint weak exogeneity for the fundamentals taken together.
28. Note that this is not the same as the error-correction representation referred to in the Granger
Representation Theorem (Engle and Granger, 1987). The latter is a reduced-form equation that omits
contemporaneous changes of the fundamentals.
29. The calculation for C6te d'Ivoire relies on the second-stage ECM estimates. As discussed earlier, the
dynamic regression estimates are unsatisfactory when LPFOR is included.
30. The time required to dissipate x% of a shock is determined according to: (Ji)t=(J-x), where t is the
number of years and/, is the absolute value of the speed of adjustment parameter.
31. For example Elbadawi and Soto (1995), using a similar methodology, estimate that the RER in Mali
was virtually in equilibrium (on average) during the 1987-94 period, while the CGE estimates of Devarajan
(1997) suggest that the RER in Burkina Faso was overvalued by about 9% in 1993.
35



TABLE 1: Stationarity Statistics - Levels without and with Time Trend
C8te 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
log0(TO7)       -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(OPENI)     -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 (ISHA RE)   -1.01     -0.78      -0.68
Levels with Time Trend
log(REER)       -1.83     -2.46      -2.09       -4.89       -2.76       -5.35
l0og (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(OPENl)     -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 (ISHARE)    -2.42     -2.19      -2.42
NOTES: DF, ADF, and PP refer to Dickey-Fuller, augmented Dickey-Fuller, and Phillips-Perron
stationarity statistics. The number of observations is 29 for CMe d'Ivoire and 24 for Burkina Faso. The
variables are defined in Appendix 2 (ISHARE is not available for Burkina Faso).
36



Table 2: Johansen's Maximum Likelihood Test of Cointegration Rank for Cote d'Ivoire
10% critical value             5% critical value
L-Max        unadjusted       adjusted       unadjusted       adjusted
With the dummy
r = 0              45.01           36.35           48.34           39.43          52.44
r < 1              30.05           30.84           41.02           33.32          44.31
Without the dummy
r = 0              32.65           30.84           39.17           33.32          42.32
r< 1               18.63           24.78           31.47           27.14          34.47
NOTES: The first row (r = 0) tests the null hypothesis of no cointegration; the second (r < 1) tests the
null hypothesis of at most one cointegration vector. The first column (L-Max) gives the estimated Johansen
likelihood value in each case. The second and fourth columns give the 10% and 5% critical values taken
from Osterwald-Lenum (1992, Table 1.1). The third and fifth columns give the small-sample-adjusted
critical values. The adjustment factor is calculated as T/(T-nk), where T is the number of observations
(28), n is the number of variables including the intercept and drought dummy variable (7), and k is the
number of lags (1). When the dummy is included (upper panel), the adjustment factor is 1.33; when it is
excluded, this becomes 1.27. See Cheung and Lai (1993) for discussion of the adjustment factor.
37



TABLE 3: Long Run Parameter Estimates for Cote d'Ivoire. Dependent Variable is
log(REER).
OPENI            OPEN2            OPEN3         OLS-ECM         IV-ECM
Constant            3.61              4.29            4.30            1.72           1.35
(16.71)          (22.01)          (12.22)        (2.22)          (1.42)
log(TOT)            0.40              0.16            0.15           0.80            0.75
(3.03)           (1.06)           (0.94)         (2.07)         (2.21)
RESGDP              -2.67             -1.47           -1.45          -0.89           -1.53
(-5.49)          (-3.25)         (-3.71)         (-0.49)        (-1.04)
log(OPEN)           -0.78            -0.08            -0.03          -0.28           -0.46
(-3.68)          (-0.34)          (-0.12)        (-0.42)        (-0.82)
log(ISHARE)         -0.27            -0.31            -0.30          -0.47           -0.43
(-5.83)          (4.63)          (-5.15)         (-3.24)        (-3.56)
D83-85              -0.22            -0.30            -0.30          -0.52           -0.44
(-3.01)          (-3.43)         (-3.49)         (-2.35)        (-2.51)
R2-Bar               0.72             0.56            0.56            0.42           0.36
Q                   14.32            13.80            14.21          7.16            4.68
(0.05)           (0.05)          (0.05)          (0.31)         (0.59)
DW                   1.16             1.14             1.15           2.22           2.15
DF                  -3.55            -3.31            -3.31
ADF                 -3.54            -3.84            -3.89
PP                  -3.61            -3.30            -3.29
NOTES: The numbers in parentheses are t-ratios (note that these have non-standard distributions even
asymptotically in columns 1-3). The static cointegration regressions in columns 1-3 use the three alternative
openness variables discussed in Appendix 2. The last column reports the long-run parameters of the
unrestricted ECM (equation (11) in the text; equivalent to the unrestricted ADL), using OPEN 1 as the
openness variable. The long-run parameters and associated standard errors are obtained by estimating the
Bewley transform of the ECM; see Banerjee, et al (1993) for details. The full set of parameters for this
regression appear in column 1 of Table 4.
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TABLE 4: ECM Parameter Estimates for C6te dIlvoire. Dependent Variable is log(REER).
2-step ECM                            Unrestricted ECM
OLS                     IV                 OLS                IV
Constant                             3.61                   3.53                1.72              1.35
(16.71)                (15.68)              (2.22)            (1.42)
Adjustment Speed
log (REERt-1 or Error,-,            -0.30                   -0.39               -0.45             -0.37
(-1.85)                (-2.09)             (-2.32)           (-1.63)
Long-Run Parameters
log(I'OTt1)                          0.40                   0.49                0.80              0.75
(3.03)                 (3.29)              (2.07)            (2.21)
RESGDP,-]                           -2.67                   -2.81               -0.89             -1.53
(-5.49)                (-5.58)             (-0.49)           (-1.04)
log(OPEN,.1)                        -0.78                   -0.81               -0.28             -0.46
(-3.68)                (-3.71)             (-0.42)           (-0.82)
log (ISHARE,_1)                     -0.27                   -0.30               -0.47             -0.43
(-5.83)                (-5.27)             (-3.24)           (-3.56)
D83-85 t-I                ~~-0.22                  -0.22               -0.52             -0.44
(-3.01)                (-3.03)             (-2.35)           (-2.51)
Short-Run Parameters
Alog (TOTd                           0.38                   0.43                 0.37             0.33
(2.86)                 (2.97)              (1.78)            (1.44)
ARES GDPt                           -1.47                   -1.86               -0.95             -0.76
(-3.29)                (-3.72)             (-1.27)           (-0.90)
Alog (OPENd                         -0.38                   -0.49               -0.29             -0.28
(-1.99)                (-2.59)             (-0.95)           (-0.87)
Alog (ISHA4REd                      -0.10                   -0.10               -0.18             -0.11
(-1.72)                (-1.40)             (-2.37)           (-0.96)
Alog (PFOR,-.4                      -0.30                   -0.14               -0.29             -0.14
(2.39)                 (-1.06)             (-0.97)           (-0.58)
AD83-85                             -0.05                   -0.05               -0.07             -0.04
(-1.04)                 (1. 01)            (-0.97)           (-0.43)
Q                                   14.32                   7.17                7.16              4.68
(0.05)                 (0.31)              (0.31)            (0.59)
R2-Bar                               0.49                   0.74                0.42              0.36
D W                                  1.11                    1.12               2.22              2.15
NOTES: The numbers in parentheses are t-ratios. The period of estimation is 1965-93. In columns I and 3, the
long-run parameters and associated standard errors are obtained by estimating the Bewley transform of the ECM. In
columns 1 and 2 we use the lagged residual from the static regression as the error-correction term. Colum-ns 2 and 2
are instrumental variable estimates, using two lags of all right-side-variables as instruments for ISHARE.
39



TABLE 5: Observed and Equilibrium RER Indexes for CMte d'Ivoire - 1980 to 1993
Equilibrium RER
Year     Observed       Fitted      S-year MA       B-N       "Sustainable"    Overvaluation
1980        139          130           137          136            92              34
1981        121          121           120          124            94              22
1982        109          109           112          116            99              9
1983        104          104           108          121           107              -3
1984        100          100           103          121           131             -31
1985        100          100           103          104           112             -12
1986        126          116           128          115           118               6
1987        149          149           149          121           102              31
1988        149          149           149          132            97              35
1989        143          143           144          186           108              24
1990        152          152           149          185           121              20
1991        151          151           145          165           110              27
1992        164          164           153          168           108              34
1993        166          166           154          156           118              29
NOTES: The observed RER is the one used in the econometric analysis. The long-run parameter vector is
taken from the static regression in column 1 of Table 3. "Fitted" values are obtained directly from that
regression; "5-year MA" refers to five-year moving averages for all fundamentals; "B-N" refers to Beveridge-
Nelson decompositions of all fundamentals; and the "sustainable" RER is defined as the fitted RER with all
fundamentals replaced by counterfactual sustainable values, as determined in Appendix 3. Overvaluation is
defined as 100*(observed RER - sustainable RER)/(sustainable RER).
40



TABLE 6: Error Correction Model Parameter Estimates for Burkina Faso. Dependent
Variable is Alog(REER)
Unrestricted                      Restricted
wl Trend        w/o Trend          wl Trend         wlo Trend
Constant               0.92             1.21               1.59             2.78
(0.64)          (1.16)             (1.36)            (2.31)
Trend                  0.01                                0.01
(0.30)                             (1.06)
Adjustment Speed
log(REERt-1)          -0.50            -0.51              -0.54            -0.60
(-2.76)         (-2.87)            (-2.81)          (-3.20)
Long-Run Parameters
log(fOT,1)             0.79             0.81               0.45             0.03
(1.20)          (1.28)             (1.37)            (0.13)
log(OPEN,1)           -1.02            -0.78              -0.78            -0.06
(-0.92)         (-1.15)            (-1.37)          (-0.20)
RESGDP,.I             -7.69            -6.87              -5.69            -2.20
(-1.62)         (-1.97)            (-2.15)          (-1.88)
log(PFORt-I)           0.10            0.17
(0.48)          (1.28)
Short-Run Parameters
Alog(TOTd             0.17             0.17
(0.74)          (0.74)
Alog(OPENd            -0.13            -0.08
(-0.42)         (-0.32)
ARESGDP,              -3.20            -2.99              4.42             -2.24
(-2.75)         (-3.33)            (-2.66)          (-5.32)
Alog(PFORd            -0.30            -0.30
(-1.31)         (-1.42)
R2-Bar                 0.73             0.75               0.72             0.72
Q                      8.76             9.51              7.44              3.99
(0.12)          (0.09)             (0.19)            (0.55)
DW                     2.24             2.20               1.99             2.01
NOTES: Numbers in parentheses are t-ratios. The period of estimation is 1970-93. The unrestricted ECM
corresponds to equation (11) in the text. The long-run parameters and associated standard errors are obtained by
estimating the Bewley transform of the ECM.
41



TABLE 7: Observed and Equilibrium RER Indexes for Burkina Faso - 1980 to 1993
Equilibrium RER
Year    Observed      Fitted     Trend      5-year MA     "Sustainable"    Overvaluation
1980       115         92         106           93              87              31
1981       102         92         105           93              90              14
1982       104         94         105           91             100               4
1983        99          93        105           92             122             -18
1984        96          83        104           95             138             -16
1985       100         99         104           95             119              -6
1986       102         106        103           96             109              -2
1987        99          95        103           100            101              -4
1988        99          99        103           98             103             -16
1989        95          99        102           97             114             -11
1990        95          90        102           99             107             -13
1991        93         102        102           100            108             -12
1992        92         104        101           100            104             -12
1993        91         103        101           103            103             -27
NOTES: The observed RER is the one used in the econometric analysis. The fitted RER is the one estimated
from the cointegration regression (Table 6). "Trend" refers to fitted linear trend for the RER. "5-year MA" refers
to 5-year moving averages. The sustainable RER is the fitted RER where the fundamentals (i.e. RESGDP and
OPEN) have been replaced by their sustainable counterparts as outlined in Appendix 3. Overvaluation is defmed as
100*(observed RER - sustainable RER)/ (sustainable RER).
42



Figure 1
Internal and external balance
e
EB
IB
C                           C
The EB schedule is drawn for steady-state values of
the service account and transactions costs.
A rise in e is a real depreciation.



Figure 2
Adjustment to an increase in r,
(under a binding credit constraint)
e                                   EB
EB
2                                  17~
e .  .. X...........................
e ;  ......    ............... ...:.......
IB
c
*        *         *C
C3       C2        Cl
A rise in rw shifts EB downwards to EB./ With flexible
wages and prices, adjustment to the new long-run
equilibrium at point 2 is immediate. With nominal
rigidities, the economy jumps to point 3 and then
converges gradually to point 2 along EB.



FIGURE 3: VARIANCE RATIO TESTS FOR COTE D'IVOIRE
log(TOT)                                                                  RESGDP
1.80                                                                     1. 80 
1.60                                                                     1.60
1.40                                                                     1.40
120 W                                                                    1.20
K. 00                                                                     10
0 080 - -0.80 
J. 0.60                                   ~0.60--
0.40                                                                     0.40 --
0.20 --0.20+
0.00-I   I   I                      I                                              I   III                       I              
1 2 34567891011121314 15                                                 12 3 4  567891091112213 14 15
log(OPENI)                                                                 log(REER)
1.80                                                                      1.80 
1.60                                                                      1.601
1.40 -1.40-
1.20 -1.20
1.00 -                                                                    1.00 
~080                                                                       0 080±
0.60 - -0.60
0.40                                                                      0.40
0.20                                                                      0.20T
1 2 345678910911121213 14 15                                              12 3 4  567891091112213 14 15
logISEARE)
1.80
1.60
1.40
1.20
K. 00 
0.80 
~.0.60-
0.40-
0.20-
0.00                                                       I
1  2 3   4   5 6 7   8   91011  121314  15



FIGURE 4: VARIANCE RATIO TESTS FOR BURKINA FASO
log(TOT)                                                                      RESGDP
1.80                                                                         1.80
1,60                                                                         1.60-
1.40                                                                         1.40
1.20                                                                     .~1.20
1.00 -10 
0.80 -08 
tr 0.60 -06
0.40 -0.40
0.20 --0.2014
1  2   3 4 5   6 7   8   910  11  1213  1415                                 1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
log(OPEN1)                                                                     log(REER)
1.80                                                                          1.80 
1.60                                                                          1.60
1.40                                                                          1.40
N 1.00                                                                        N ~.00   
.%3.80                                     ~8
Z.60                                      ~360
0.40                                                                          0.40
0.20                                                                          0.20
0.00                                                                          0.00                                               I I I I
123456789101112131415                                                         123456789101112131415



References
Banerjee, A., J. Dolado, J. W. Galbraith and D. F. Hendry (1993), Co-Integration, Error-
Correction, and the Econometric Analysis of Non-Stationary Data, Oxford University Press,
U.K.
Bernanke, B. (1986), "Alternative Explanations of the Money-Income Correlation", Carnegie-
Rochester Conference Series in Public Policy 25, 49-99.
Beveridge, S. and C. R. Nelson (1981), "A New Approach to Decomposition of Economic Time
Series into Permanent and Transitory Components with Particular Attention to Measurement
of the Business Cycle", Journal of Monetary Economics 7, 15 1-174.
Boswijk, H. (1995), "Efficient Inference on Cointegration Parameters in Structural Error
Correction Models", Journal of Econometrics 69, 113-158.
Cheung, Y-W. and K. Lai (1993), "Finite Sample Sizes of Johansen's Likelihood Ratio Tests for
Cointegration", Oxford Bulletin of Economics and Statistics 55, 313-28.
Cochrane, J. H. (1988), "How Big Is the random Walk in GNP?" Journal of Political Economy
96, 893-920.
Corden, W. M. (1989), "Macroeconomic Adjustment in Developing Countries", World Bank
Research Observer 4, 51-64.
Devarajan, S. (1997), "How Overvalued was the CFA? Estimates of Real Exchange Rate
Misalignment with a Simple General Equilibrium Model", Mimeo, The World Bank.
Devarajan, S. and L. Hinkle (1995), "The CFA Franc Parity Change: An Opportunity to Restore
Growth and Reduce Poverty," Mimeo, The World Bank.
Devarajan, S., J. Lewis and S. Robinson (1993), "External Shocks, Purchasing Power Parity, and
the Equilibrium Real Exchange Rate", World Bank Economic Review 7(1): 45-63.
Dollar, D. (1992), "Outward-Oriented Developing Economies Really Do Grow More Rapidly",
Economic Development and Cultural Change 40(3), April: 545-66.
Dornbusch, R. (1984), Open Economy Macroeconomics, New York: Basic Books.
Edwards, S. (1989), Real Exchange Rates, Devaluation and Adjustment. Exchange Rate Policy in
Developing Countries, MIT Press, Cambridge, Massachusetts.
Elbadawi, I. (1994), "Estimating Long-run Equilibrium Real Exchange Rates," in Estimating
Equilibrium Exchange Rates, J. Williamson, ed, Institute for International Economics,
Wshington, DC.
Elbadawi, I. and R. Soto (1994), "Capital Flows and Equilibrium Real Exchange Rates in Chile,"
Policy Research Working Paper 1306, The World Bank, Washington DC.
Elbadawi, I. and R. Soto (1995), "Real Exchange Rate and Maccroeconomic Adjustment in Sub-
Saharan africa and Other Developing Countries," (forthcoming) in Elbadawi and Soto, eds,
Foreign Exchange Market and Exchnage Rate Policies in Sub-Saharan Africa, a special
issue of Journal of African Economies.
43



Engle, R. and C. Granger (1987), "Co-Integration and Error-Correction: Representation,
Estimation, and Testing", Econometrica 55, 251-76.
Engle, R. F., D. F. Hendry and J-F Richard (1983), "Exogeneity", Econometrica 51, 277-304.
Ericsson, N. R. (1995) "Conditional and Structural Error Correction Models", Journal of
Econometrics 69, 159-71.
Ericsson, N. R. (1992) "Cointegration, Exogeneity, and Policy Analysis: An Overview", Journal
of Policy Modeling 14, 251-80.
Ericsson, N. R., J. Campos and H-A. Tran (1991), "PC-Give and David Hendry's Econometric
Methodology", International Finance Discussion Papers No. 406, Board of Governors of
the Federal Reserve System, Washington DC.
Granger, C. W. J. (1981) "Some Properties of Time Series Data and Their Use in Econometric
Model Specification", Journal of Econometrics 16, 213-28.
Hamilton, J. (1994), Time Series Analysis, Princeton University Press, N.J.
Hargreaves, C. (1994), "A Review of Methods of Estimating Cointegrating Relationships",
Chapter 4 in C. Hargreaves, ed, Nonstationary Time Series Analysis and Cointegration,
Oxford: Oxford University Press.
Hendry, D. F. (1995), Dynamic Econometrics, Oxford: Oxford University Press.
Hendry, D., F., A. R. Pagan and J. D. Sargan (1984), "Dynamic Specification", Chapter 18 in Z.
Griliches and Michael D. Intriligator, eds, Handbook of Econometrics, Vol 2, Amsterdam:
North-Holland: 1023-92.
Hinkle, L. E. and F. Nsengiyumva (1997), "The Relationship Between the External and Internal
Real Exchange Rates: Competitiveness, Productivity, and the Terms of Trade," Mimeo, The
World Bank.
Johansen, S. (1988), "Statistical Analysis of Cointegration Vectors", Journal of Economic
Dynamics and Control, 12, 231-54.
Johansen, S. (1992), "Cointegration in Partial Systems and Efficiency of Single-Equation
Analysis," Journal of Econometrics 52, 389-402.
Johansen, S. and K. Juselius (1994), "Identification of the Long-Run and the Short-Run Structure:
An Application to the ISLM Model", Journal of Econometrics 63, 7-36.
Kaminsky, G. (1987), "The Real Exchange Rate in the Short Run and in the Long Run",
Discussion Paper, Department of Economics, University of California at San Diego,
December.
Khan, M. S. and J. S. Lizondo (1987), "Devaluation, Fiscal Deficits, and the Real Exchange Rate
in Developing Countries", World Bank Economic Review 1, 357-74.
M'Bet, A. and N. Madeleine (1994), "External Shocks, Macroeconomic Adjustment and Behavior
of the CFA Economies Under a Flexible CFA Pegging Scenario: The Cases of C6te d'Ivoire
and Burkina Faso," Revised Report Presented at the AERC Workshop, Nairobi, Kenya.
44



Monfort, A. and R. Rabemanajara (1990), "From a VAR Model to a Structural Model: With an
Application to the Wage-Price Spiral", Journal ofApplied Econometrics 5, 203-27.
Montiel, P. (1997), "The Theory of the Long-Run Equilibrium Real Exchange Rate," Mimeo, The
World Bank.
Phillips, P. C. B. (1995), "Fully Modified Least Squares and Vector Autoregression",
Econometrica 63, 1023-78.
Phillips, P. C. B. and Y. Chang (1995), "Time Series Regression with Mixtures of Integrated
Processes", Econometric Theory 11.
Rodriguez, C. A. (1994), "The External Effects of Public Sector Deficits", Chapter 2 in W.
Easterly, C. A. Rodriguez, and K. Schmidt-Hebbel, eds, Public Sector Deficits and
Macroeconomic Performance, Oxford: Oxford University Press.
Rodrik, D. (1993), "Trade Liberalization in Disinflation", CEPR Discussion Paper No. 832,
London: Centre for Economic Policy Research, August.
Serven, L. (1996), "Does Public Capital Crowd Out Private Capital? Evidence from India," Policy
Research Working Paper 1613, World Bank, Washington DC.
Urbain, J.-P. (1992), "On Weak Exogeneity in Error-Correction Models", Oxford Bulletin of
Economics and Statistics 54, 187-207.
Williamson, J., ed, (1994), Estimating Equilibrium Exchange Rates, Institute for International
Economics, Washington, DC.
World Bank (1989), Sub-Saharan Africa: From Crisis to Sustainable Growth: A Long-Term
Perspective Study, Washington, D.C.
45



Appendix 1: Conditioning and weak exogeneity
Weak exogeneity is a property of the joint distribution of the real exchange rate and the
fundamentals. In this appendix we introduce the concept of conditional and marginal models and
explore the relationship between the single-equation model (I 1) and the full distribution of the (nxl)
vector [In et, Ft, zt ', conditional on its own past (see also Ericsson (1992)). With reasonable
generality we can describe this distribution as the p-th-order Gaussian vector autoregression (VAR)
p
x, = E njxt,  + El,      -P - IN(O, c72),                  (A 1 )
j=J
where the 17) are (nxn) matrices of reduced-form coefficients and is the nxn symmetric and positive
definite matrix of contemporaneous covariances between the innovations sit Equation (Al) can be
written equivalently as
p
Ax, = Tx,_ +    AjAx,, + E,,                               (A2)
j=J
where F=[(Ej=1,pJll)-I] and A1 =17 The first row of (A2) is a reduced-form error-
correction model for Alnet; it is similar to (I 1) but excludes contemporaneous values of F and z. To
obtain the distribution of lnet conditional on lagged xt and contemporaneous F and z, we first
partition the vector xt into xt = [In et, w t]', where wt = [F't, z 't1 is the vector of macroeconomic
determinants of the real exchange rate. Without loss of generality, we can then factorize the joint
distribution represented by (A2) into the distribution of Alnet conditional on contemporaneous wt's
(and lagged xt's) and and the associated marginal distribution of the wt's (given lagged xt's). Under
normality of et, the conditional and marginal models take the form
p
Aw =J>2X,  + E A2Ax, 1 +±2j                         (A3b)
Ji=1
where the numerical subscripts refer to the blocks of appropriately partitioned matrices. By
construction, the disturbance term in (A3a), , =22, - £,2(2222-%'21 is uncorrelated with all of the
46



variables on the right-hand side of that equation. Equation (A3) follows the standard regression
relationship between two jointly normal scalar random variables y and z, i.e., the conditional
distribution of yt is given by yt =,ul + (f12/q2)(zt -,u) + vt, where the pi's are means and the aj's
are covariances; and the disturbance vt has the properties E(vt I zJ = 0 and Var(vt I z) = a I -
(a92 2/-2. That this representation is simply a re-parameterization of (A2) can be confirmed by pre-
multiplying (A2) by the nxn nonsingular matrix
B   =   11£2 (E22 ) 
which results in (A3).
Equation (A3a) is a single-equation conditional error-correction model whose general form
mimics that of equation (11). Although it is often assumed in writing an equation like (11) that the
disturbance is uncorrelated with the right-hand side variables, this is true by construction for
equation (A3a). To the degree that the parameterizations differ, therefore, OLS estimation of ( 1)
will tend to uncover the parameters of (A3a) (in which orthogonality holds by construction),
yielding inconsistent estimates of the parameters of (1 1). Moreover, even if the parameters of (1 1)
can be recovered from those of (A3a), the latter are potentially complicated functions of the
underlying VAR parameters. There may therefore be cross-equation restrictions linking these
parameters to those of the marginal model (A3b). In such a case efficient estimation of the
conditional model requires that these restrictions be imposed; and failure to impose them may
produce inconsistent standard errors, invalidating inference.
These considerations motivate a search for conditions under which estimation and inference
regarding particular parameters of ( 1) can proceed successfully in the conditional model alone (i.e.,
without analyzing the full system). In such cases the sub-vector wt is said to be weakly exogenous
for the parameters of interest (Engle, Hendry and Richard (1983)). In the context of the above
discussion, weak exogeneity requires (a) that the parameters of interest can be directly recovered
from those of the conditional model; and (b) that there be no cross-equation restrictions linking
these parameters to those of the marginal model.
47



Appendix 2: Data Description
The data were taken from three sources: (1) IMF, International Financial Statistics, (2) UNCTAD,
and (3) the World Bank's Unified Survey. The variables were constructed as follows:
Real Exchange Rate (RER). Ratio of the domestic consumer price index (CPI) to the trade-
weighted foreign wholesale price index (WPI), multiplied by the trade-weighted nominal exchange
rate (NER): RER = (CPI/WPI)*NER.
Terms of Trade (TOT). Ratio of export price index (Px) to import price index (PM) (expressed in
dollars, taken from UNCTAD): TOT = PX/PM.
Openness (OPEN). OPEN 1 is the import to GDP ratio (IMPGDP), and is defined as the value of
imports at current prices (IMPCP) over GDP at currrent prices (GDPKP): OPEN 1 = IMPCP/
GDPCP. OPEN2 is the ratio of the value of imports at constant prices (IMPKP) plus exports at
constant prices (EXPKP) to GDP at constant prices (GDPKP): OPEN2 = (IMPKP +
EXPKP)/GDPKP. OPEN3 is the ratio of imports at constant prices to domestic absorbtion at
constant prices: OPEN3 = IMPKP/(GDPKP - (EXPKP - IMPKP)).
Resource Balance to GDP Ratio (RESGDP). Value of exports at constant prices (EXPKP) minus
value of imports at constant prices (IMPKP), divided by GDP at constant prices (GDPKP). EXPKP
has been adjusted by the domestic terms of trade (TOTD) which are defined as the ratio of export to
import deflator. Thus RESGDP = (EXPKP*TOTD - IMPKP)/GDPKP.
Investment Share (ISHARE). Ratio of gross investment at constant prices (IGROSS) to the sum of
private consumption (PCONK), government consumption (GCONK), and gross investment, all at
constant prices: ISHARE = IGROSS/(PCONK+GCONK + IGROSSK).
Foreign Price Level (PFOR). Domestic consumer price index (CPI) divided by the real effective
exchange rate (RER): PFOR = CPI/RER.
48



Appendix 3: Sustainable Fundamentals
A3.1 Time-series measures: TOTandLPFOR
Both Burkina Faso and Cote d'Ivoire are very small economies by world standards and are therefore
price takers in the markets for both their exports and imports. Moreover, the nominal exchange rate
for the CFA francs was fixed throughout the 1970-93 sample period and could not be changed by
individual CFA countries. The terms of trade (TOT) and the foreign price level converted to CFA
francs (LPFOR) are therefore exogenous variables. While these variables fluctuate substantially
from year to year, we have no basis on which to question the sustainability" of their longer-run
movements. We therefore use 5-year centered moving averages as the sustainable values of these
variables (extrapolating out of sample using the first and last-year values). We also generate
alternative sustainable values for Burkina Faso and Cote d'Ivoire using sample means and
Beveridge-Nelson decompositions, respectively.
A3.2 Counterfactual simulations: RESGDP
RESGDP is the ratio of the resource balance to GDP, both in constant prices. Since Burkina Faso
relied heavily on concessional aid flows in 1970-93, determining a sustainable resource balance is
essentially a problem of determining sustainable levels of financial inflows. These inflows can be
divided into net factor income, net transfers, and net capital flows. We used 5-year moving averages
for the first two (interest payments were small and changed very slowly over the sample, so we
ignored the feedback from borrowings to interest payments). We then divided net capital flows into
its dominant component - net long-term concessional borrowing - and "other" flows (net direct
investment, net portfolio investment, net short term borrowing, net errors and omissions), using 5-
year moving averages for the latter. The government of Burkina Faso attempted to maximize net
concessional borrowing during the sample period, so this component was ultimately determined by
the foreign donors. To smooth out year-to-year fluctuations in net concessional borrowing, we used
the smaller of the 5-year moving average of the actuals or 3.5% of GDP (the highest level reached
except in drought years). The sustainable resource balance is then the sum of these sustainable
components. Note that the Bank's debt stock and flow data are not consistent with the national
accounts and balance of payments data for Burkina Faso and Cote d'Ivoire. Since the balance of
payments and national accounts data are consistent with each other and essential for the analysis, we
used balance of payments data when there were conflicts between these and Bank's debt data.
49



The C6te d'Ivoire case is both more complicated and more representative of the problems
likely to emerge in developing country applications. C6te d'Ivoire avoided balance of payments and
debt problems in the 1970s. We therefore treated actual flows as essentially sustainable during the
1965-79 period, using 5-year moving averages to smooth out temporary fluctuations. After 1980, it
was unable to meet its debt service payments. Moving averages therefore seem unlikely to capture
sustainable movements in net borrowing and interest payments after 1980, and we cannot ignore the
feedback from higher debt levels to higher interest payments. For 1980-93 we proceed as follows.
To proxy the sustainable level of borrowing, we used zero net repayments and net
disbursements after 1979 (i.e., no change in the debt stock other than through write-downs). C6te
d'Ivoire's debt ratio jumped from 47% in 1979 to 62% in 1980, then climbed to 115% in 1985 after
which the country defaulted. The Mastricht Treaty, after which the fiscal guidelines for the West
African Monetary Union are modelled, sets 60% of GDP as the maximum desirable debt level for
the EU countries. A developing country might be able to target a somewhat higher debt level than
60% depending upon its rate of growth and its access to financing on concessional terms; so 1979 is
by these criteria the last year of sustainable debt levels.
We calculate sustainable direct and portfolio investment as assumed percentages of total
sustainable investment as determined below; together with the sustainable borrowing figures, these
yield a sustainable level of total capital inflows.
To proxy sustainable interest payments, we use 4% of GDP. This represents a kind of
compromise between a normative scenario in which interest payments are capped at 2.5% of GDP
and a positive scenario (essentially feasibility calculation) that caps them at 5%. For comparison,
the Mastricht debt ceiling, with an inflation rate of 3% and a real interest rate of 3% implies interest
payments of 1.8% of GDP for the EU countries. Cote d'Ivoire was unable to sustain the service
payments on its debt after interest payments reached 3.5 and 5.2% of GDP in 198 land 82.
The sustainable resource deficit for 1980-1993 is then calculated as the sum of net transfers,
net factor income, and net capital inflows, using 5-year moving averages of the actuals for transfers
and factor income flows other than interest payments.
A3.3 Counterfactual simulations: ISHARE and OPEN]
ISHARE is the ratio of investment to GDP in constant prices; OPEN 1 is the ratio of imports to
absorption in current prices. The sustainability criterion we use for these variables is consistency
50



with a 3% long run growth rate of GDP per capita.
With population growth estimated at about 3% for both countries over the sample, GDP
growth of 6% is required to achieve 3% growth in GDP per capita. Using ICORs of 4 for COte
d'Ivoire and 5 for Burkina Faso, this would in turn require investment ratios of about 25% and 30%
of GDP, respectively. The 25% ratio is in line with those actually achieved during 1960s and 70s in
COte d'Ivoire; it is also the target that the World Bank has suggested as a guideline for Africa as a
whole (World Bank (1989)). For Cote d'Ivoire, thererfore, we use a moving average of the actual
investment levels for 1965 to 1981, which were reasonably close to 25%, and 20% for 1982-93
when investment was depressed far below this level. For Burkina Faso, where the investment/GDP
ratio is used only as an input to calculate the target import/absorption ratio (see below), we assume a
sustainable investment ratio of 25%.
For both countries we assume that increases in the import to GDP ratio were required to
deliver the import content of additional investment and also support a more liberal trade regime. We
estimate an import content of investment of roughly 0.6 for both countries. To incorporate trade
liberalization, we assume increases in the import ratio of 3% and 2%, respectively, for Cote d'Ivoire
and Burkina Faso. The target import ratio is then estimated as the actual import ratio plus 3% of
GDP plus 0.6 times the difference between the target investment ratio and the actual investment
ratio. This target import/absorption ratio is used for the entire sample period as a more open trade
policy would have been desirable throughout.
A3.4 A caveat
As the above discussion suggests, determining target values for particular countries requires considerable
country specific knowledge and a number of assumptions based on partial information and analysis.
These assumptions are open to question, and different ones - regarding either the key parameters or the
underlying notion of sustainability - would yield different results. It may therefore be important in
specific cases to consider alternative plausible assumptions and to compare the results of the various
alternatives to those from using moving averages for the target variables.
51






Policy Research Working Paper Series
Contact
Title                             Author                    Date               for paper
WPS1773 The Costs and Benefits of            J Luis Guasch            June 1997           J Troncoso
Regulation Implications for       Robert W  Hahn                                38606
Developing Countries
WPS1774 The Demand for Base Money            Valeriano F Garcia       June 1997           J Forgues
and the Sustainabity of Public                                                 39774
Debt
WPS1775 Can -tlch-Inflation Developing       Martin Ravallion         June 1997           P Sader
Count; es F-'ape Absoclut- Poventy-/                                            33902
VVPS1 776 From Prices to ricories Agricultural John Baffes            June 1997           P Kokila
Subsidization Vlithoiit Protect<,n-    uacob Meerman                            33716
WPS1777 Aid, Policies, and Gtowth           Craig Burnside            June 1997           K. Labrie
David Dollar                                 31001
WPS1778 How Government PolI-ies Aftect       Szczepan Figiel          June 1997           J Jacobson
the Relationsh!p between Pclisi    Tom Scott                                    33710
and World Vheat Pr,ces            Parios Varangis
WPS1779 Water Allocation Mecnariasns        Ariei Dinar               June 1997           M. Rigaud
Principles and Exanipies          Mark W  Rosegrant                             30344
Rutr Meinzen-D,ck
WPS1780 High-Level Rent-Seekirng ana         Jacqueline Coolidge      June 1997           N. Busjeet
Corruption in African Regmimes    Susan Rose-Ackerman                           33997
Theory and Cases
WPS1781 Technology Accumuiation oiri         Pier Carlo Padoan        June 1997           J Ngaine
Diffusion Is There a F& c;cn3l                                                  37947
Dimension'-
WPS 1782 Regional lnreyration anc thi - ;:ices   L Alan Winters       June 1997           J Ngaine
of Imports An                     VV011i  Vvoi CIhang                           37947
Investigation
WPS1783 Trade Policy ODPtions for the        Glenn W  Harrison        June 1997           J Ngaine
Chilean Government A Quantitative  Thomas F Rutherfoid                          37947
Evaluation                        David G Tarr
WPS1784 Analyzing the Sustainabil:ty of Fiscal John T Cud(iington     June 1997           S King-Watson
Deficits in Deveiopirg Cour,tries                                               31047
WPS1785 The Causes of Governmi,nt arnd the  Simon Commande?           june '997           E Witte
Consequences tor Growtr and       Hamic, R Davoc.i                              85637
Weli-Beiu                              .J Lee
WPS1786 The Economics of Custtms Unions   Corstant;ne MichalocoIos June I997             M Patena
in the Commonwealth o'            Dahld Ta'r                                    39515
Independent St-tes



Policy Research Working Paper Series
Contact
Title                             Author                   Date              for paper
WPS1 787 Trading Arrangements and           Diego Puga               June 1997          J Ngaine
Industrial Development            Anthony J Venaoles                          37947
WPS1788 An Economic Analysis of Woodfuel   Kenneth M. Chomitz        June 1997          A. Maranon
Management in the Sahel The Case  Charles Griffiths                            39074
of Chad
WPS1789 Competition Law in Bulgaria After    Bernard Hoekman         June 1997           J Ngaine
Central Planning                  Dimeon Djankov                               37947
WPS1 790 Interpreting the Coefficient of    Barry R Chiswick         June 1997           P Singh
Schooling tn the Humarn Capital                                               85631
Earnings Function
WPS1791 Toward Better Regulation of Private  Hemant Shah             June 1997           N. Johl
Pension Funds                                                                 38613
WPS1792 Tradeoffs from Hedging Oil Price    Sudhakar Satyanarayan   June 1997            E. Somensatto
Risk in Ecuador                   Eduardo Somensatto                           30128
WPS1793 Wage and Pension Pressure           Alain de Crombrugghe     June 1997           M Jandu
on the Polish Budget                                                           33103
WPS1794 Ownership Structure Corporate       Xiaonian Xu              July 1997           J Chinsen
Governance, and Corporate         Yan Wan                                      34022
Performance: The Case of Chinese
Stock Companies
WPS1795 What Educational Production         Lant Pritchett           July 1997           S. Fallon
Functions Really Show A Positive    Deon Filmer                               38009
Theory of Educatiorn Spending
WPS1796 Cents and Sociability Household     Deepa Narayan            July 1997           S. Fallon
Income and Social Capital in Rural   Lant Pritchett                           38009
Tanzania
WPS1797 FormaI and inforiTIaI Regulation    Sheoli Pargal            July 1997           E de Castro
of Industrial Pollution           Hemamala Hettige                            89121
Comparative Evidence from         Manjula Singh
Indonesia and the United States   David Wheeler
WPS1798 Poor Areas, Or Only Poor People?    Martin Ravallion         July 1997           P Sader
Quentin Wodon                               33902
WPS1 799 More for the Poor Is Less for the  Jonath B Gelbach         July 1997           S Fallon
Poor The Politics of Targeting    Lant H Pritchett                             38009