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
ii
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
iii
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
2
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*), el0, 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 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,e3 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 , 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 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.
38
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