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Applied Economics, 1999, 31, 661–671

The real exchange rate in Colombia: ananalysis using multivariate cointegration

JESUÂ S G. OTERO

Department of Economics, University of W arwick, Coventry CV 4 7AL UK

Johansen’s analysis of cointegrated systems is used to build a model of the Colombianreal exchange rate (RER). One cointegrating vector is found, which can be thought ofas a long-run RER equation. The deviations of the RER from its long-run equilibriumrelationship, after correcting for short-run dynamics, are interpreted as a measure ofRER misalignment. The simulation performance of the model during the period ofestimation and three years into the future is particularly good, with the simulatedRER reproducing the long-run behaviour of the actual series.

I. INTRODUCTION

Economists generally agree that the real exchange rate(RER) is a key relative price in the economic system.Through its changes, the RER a� ects the ¯ ows of foreigntrade, the current account balance, the level and composi-tion of production and consumption, the allocation of re-sources, and employment. Being a relative price, and unlikethe nominal exchange rate that in some countries consti-tutes a policy instrument, the RER is an endogenous vari-able that responds to exogenous shocks and policy-induceddisturbances. In this sense, it is particularly relevant tomodel the behaviour of the RER, in order to understandhow it is determined in the short and long run.

A branch of the macroeconomic literature identi® es vari-ations in the terms of trade as one of the major determinantsof the RER (Dornbusch, 1980; Neary, 1988; Ostry, 1988;Edwards, 1989). This literature has been developed mainlyto understand the process of determination of the RER indeveloping countries, which have been historically subjectedto substantial changes in the prices of the goods they exportand import. The changes in the terms of trade can beexpected to have sectoral resource reallocation e� ects on thesupply side of the economy; also, because terms of tradechanges a� ect a country’s real income, they can be expectedto have demand-side e� ects. Among these models, the Ed-wards model is perhaps the most comprehensive. Indeed,according to this theoretical framework, real factors (re-ferred to as fundamentals’) and macroeconomic policiesa� ect the RER in the short run, but in the long run only realfactors a� ect the sustainable equilibrium level of the RER.

In this paper, we build an RER determination model forColombia based on the Edwards model. The implications ofthis theoretical framework have been tested by Edwards(1989) and Elbadawi (1994): Edwards in the context ofa partial adjustment model, using pooled data for a group of12 developing countries including Colombia, and Elbadawiusing cointegration analysis for the cases of Chile, Ghanaand India.

In contrast to Edwards, we follow Elbadawi’s use ofcointegration analysis, and interpret the deviations of theRER from its long-run equilibrium relationship, after cor-recting for the short-run dynamics, as a measure of RERmisalignment. Elbadawi, however, uses Engle and Gran-ger’s two step procedure, and in doing so implicitly assumesthat there is only one cointegrating vector and that allvariables, except the RER, are weakly exogenous for theestimation of the parameters of the long-run RER equilib-rium relationship. Under this approach, if the assumption ofweak exogeneity does not hold for some of the variables,then a single-equation RER model is no longer appropriate,and we require to model the set of variables as a system ofequations. We therefore use Johansen’s (1988) maximumlikelihood analysis of cointegrated systems which, ina multivariate context, allows us to determine and estimateall possible cointegrating vectors, and test for weakexogeneity (see also Johansen and Juselius, 1990).

In the second place, unlike Edwards and Elbadawi, weuse neither moving averages nor the Beveridge–Nelson de-composition to correct for the short-run dynamics, becausethe ® rst method involves the loss of observations and thesecond one cannot always be applied. Instead, we use an

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1 The same correspondence applies when the shock is either anticipated or permanent.2 Edwards points out that the removal of the only distortion in the economy, generates a positive welfare e� ect that reinforces the RERappreciation.

alternative method that is already contained within Johan-sen’s estimation procedure, and which will be described infurther detail later on. Another interesting aspect of ourmodelling exercise is that the performance of the estimatedmodel is evaluated with a simulation for the period of estima-tion, and with a simulation three years into the future. Like-wise, we perform a policy experiment in order to examinewhat might have taken place as a result of alternative policies.

The outline of the paper is as follows: Section II states theEdwards model, which constitutes our theoretical frame-work. Section III develops an RER determination model forColombia using Johansen’s analysis of cointegrated sys-tems. Concluding remarks are o� ered in Section IV.

II . A MODEL OF THE REAL EXCHANGERATE

Edwards (1989) develops an intertemporal (two-period) gen-eral equilibrium model for a small open economy, withmicroeconomic foundations, to analyse the process of deter-mination of the equilibrium RER, and to show how it reactsto disturbances such as terms of trade shocks, imposition ofimport tari� s and changes in government expenditure,among others. The concept of equilibrium RER used byEdwards is closely related to that of fundamental equilib-rium exchange rate’ (FEER) proposed by Williamson (1983).In particular, the equilibrium RER in a particular period isde® ned as that relative price of tradables to nontradablesthat, for given sustainable (equilibrium) values of other vari-ables, such as taxes, international prices, and technology, equi-librates simultaneously the internal and external sectors. Next,we summarize the main predictions of the Edwards model.

Firstly, assuming that at the initial equilibrium there areno tari� s in either period (so that we can concentrate onsubstitution e� ects ruling out ® rst-order income e� ects), theimposition of an anticipated import tari� will appreciate theRER. The intuition behind this result is that the impositionof the tari� makes future consumption of importables moreexpensive; this, in turn, makes consumers substitute awayfrom these goods into nontradables, in the present and thefuture, leading to an incipient excess demand for non-tradables. Consequently, there will be an increase in therelative price of nontradables in both periods in order toclear that market. Regarding the imposition of either a tem-porary or a permanent import tari� , it is also possible toshow that they appreciate the RER, provided the assump-tion of intertemporal substitution in consumption holds. If,on the other hand, the changes in tari� s are accomplishedwhen the tari� s are initially greater than zero, then theassociated ® rst-order income e� ects may compensate the

substitution e� ects; thus, a temporary increase in importtari� s may result in an equilibrium RER depreciation.

Secondly, the e� ect of a terms of trade deterioration (thatcan be either temporary, anticipated or permanent) on theequilibrium RERs, can be decomposed into substitutionand income e� ects. For instance, a temporary terms of tradeworsening has a positive substitution e� ect on the equilib-rium RERs, which is identical to that of imposing a tempor-ary import tari� .1 The reason is that the terms-of-tradeworsening can be viewed as an increase in the domestic priceof imports (due to an increase in their world price), which inturn makes consumers alter their consumption. On theother hand, the temporary terms of trade worsening also hasa negative income e� ect on the equilibrium RERs, which inturn generates downward pressure on the price of all goods,including nontradables. It is not possible to determinea priori which of the two e� ects dominates; nonetheless,assuming that the income e� ect is stronger than the substi-tution e� ect, a terms of trade worsening decreases the priceof nontradables relative to exportables in periods 1 and 2,that is a RER depreciation.

Thirdly, an increase in the government’s consumption ofnontradables in period 1, generates an upward pressure onthe price of these goods, that in turn appreciates the RER inthat period. However, given that the government has toincrease taxes in period 2 in order to satisfy its intertem-poral budget constraint, there will be a negative incomee� ect that reduces the demand for nontradables in bothperiods. The ® nal result on the equilibrium RER in period 1will depend upon which of the two e� ects dominates; assum-ing that the substitution e� ect dominates, then an RERappreciation will occur in period 1. On the other hand, if the® scal policy consists of an increase in the government’sconsumption of tradables in period 1, then the RER willunambiguously depreciate in the current and future periodsbecause of the negative income e� ect already described.

Fourthly, the model also investigates the e� ects of capitalcontrols on the path of equilibrium RERs; capital controlsare modelled as a tax on foreign borrowing, so that thedomestic real interest rate exceeds the world real interestrate. Within this framework, a liberalization of the capitalaccount that reduces the extent to which foreign borrowingis taxed, causes an RER appreciation in the current period.The rationale for this result is that the reduction in the taxon foreign borrowing increases the domestic discountfactor, which in turn makes consumers care less aboutfuture consumption relative to current consumption. Asconsumers increase their ® rst-period consumption in allgoods, including nontradables, there will be an incipientexcess demand for nontradables and a subsequent increasein their relative price, that is, an RER appreciation.2 Lastly,

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3 See Balassa (1964) for an alternative explanation of the e� ects of technological progress.4 The model is for a small open economy that produces and consumes tradables and nontradables.5 During the adjustment path foreign reserves decline because agents reduce their excess real balances. Once the economy is back at theinitial equilibrium, the stock of real balances is the same as before the monetary disturbance, but its composition has changed in favour ofdomestic credit. The adjustment process implicitly assumes that there is a su� cient level of foreign reserves; if, on the contrary, these areinsu� cient, then agents will anticipate a balance of payments crisis.

technological progress appreciates the equilibrium RERs,since any productivity shock has a positive income e� ect,that in turn generates a demand pressure on the non-tradables market in periods 1 and 2.3

So far, we have been concerned with the process of deter-mination of the equilibrium RER, and how it responds toreal disturbances. The existence of an equilibrium RER,however, does not imply that the actual exchange rate is atits equilibrium level at all times, as the actual rate maydepart form the implied equilibrium rate in the short andmedium run. In this sense, sustained discrepancies betweenthe actual and equilibrium RERs are referred to as situ-ations of RER misalignment.

Edwards (1989) constructs a dual nominal exchange ratemodel in order to analyse the interactions between RERmisalignment and macroeconomic policies.4 In particular,he investigates the e� ects of monetary disturbances on thelong-run equilibrium RER, in the form of a once-and-for-allunanticipated increase in real balances caused by an in-crease in the stock of domestic credit. The model predictsthat the RER initially appreciates in comparison to itslong-run equilibrium level, although this is only a tempor-ary result as the dynamics of the system moves the economyback towards its initial long-run equilibrium.5 Interestingly,the duration of the adjustment process may be accelerated ifthe government adopts an unanticipated discrete nominaldevaluation’ (such policy measure reduces the stock of realbalances). If, on the other hand, the devaluation policy isadopted when the economy is at its long-run equilibrium,then it will cause a temporary RER depreciation. The im-portant point to notice is that monetary disturbances haveshort-lived e� ects on the equilibrium long-run RER; incontrast, policy measures a� ecting fundamentals, such asthose mentioned above, will a� ect the equilibrium RER.

III. A REAL EXCHANGE RATE MODELFOR COLOMBIA

Since the mid-1980s there has been a growing interest inidentifying the main determinants of the RER in Colombia(Carkovic, 1986; Herrera, 1989; Wunder, 1991; Echavarr õ  aand Gaviria, 1992; Langebaek, 1993; Caldero n, 1995). Inthese models, the RER is assumed to depend upon a set ofrelevant variables, which are then analysed in terms of theirsigni ® cance and expected sign. The performance of themodels is typically assessed during the estimation period interms of R2 s, and by looking at misspeci ® cation tests such

as the DW statistic; Echavarrõ Â a and Gaviria (1992), forexample, is the only work that departs from this traditionalapproach by presenting the CUSUM test for testing modelinstability. Also, few empirical applications examine thetime series properties of the series under review; neglectingthis aspect could have led some authors to deal with unbal-anced equations (e.g. Langebaek, 1993). Lastly, it is ratherunfortunate that the predictive ability of the models, eitherduring the estimation period or beyond it, has never beenassessed.

In this section, we build an RER determination model forColombia based on the Edwards model. We use quarterlydata for the period 1970–1992. The modelling exerciseincludes (a) the formulation of a model to ® nd the determi-nants of the RER in the short and long run; (b) the estima-tion of a measure of exchange rate misalignment; and (c) theevaluation of the performance of the model, in terms of itsability to predict the behaviour of the RER during theperiod of estimation, and three years into the future.

Data description and sources

The model described previously states that in the long runonly real factors a� ect the sustainable equilibrium level ofthe RER, whereas in the short run real factors and macro-economic policies a� ect the RER. The set of real factorsincludes variables such as the terms of trade, import tari� s,government expenditure, capital controls and technologicalprogress; with reference to macroeconomic policies, thesecomprise the e� ects of monetary, ® scal and exchange ratepolicies. Next, we describe the variables to be used as well astheir sources.

To begin with, we construct an empirical counterpart tothe concept of RER in the tradition of the dependent econ-omy de ® nition; that is, the RER is de ® ned as the relativeprice between traded and nontraded goods, so that anincrease (decrease) in this ratio denotes an RER deprecia-tion (appreciation). In order to calculate the RER we as-sume, following Edwards (1989) and Helmers (1991), thatthe foreign country’s WPI is a suitable proxy for the worldprice of tradables, and that the domestic country’s CPI isa suitable proxy for the price of nontradables. Both WPIsand CPIs were selected on the grounds that the former areheavily weighted with traded goods, while the latter containa large proportion of nontradable goods. An additionalreason is that our modelling exercise is performed usingquarterly data, and these two indexes are available on thatbasis in almost every country; for the calculations, we use

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6 The order of the underlying VAR (i.e. two lags) was selected using a general-to-speci® c procedure.7 From 1980 to 1992, 24% of total imports took place during the ® rst quarter, whereas 25%, 26% and 25% took place during the second,third and fourth quarters, respectively (calculations based on Cubillos and Valderrama, 1993).8 The results are practically the same had we set any of the other quarters equal to the import tari� of the whole year.9 This series exhibits outliers in 1979 : 3, 1981 : 2, 1982 : 4 and 1983 : 1, which correspond to dates of substantial variation in the stock offoreign debt.1 0 The revenue side of the ® scal balance excludes revenues from the Cuenta Especial de Cambios.1 1 These revenues may not have a considerable e� ect on the aggregate demand, but have modi® ed the relative prices of land, buildings andlivestock; see Wunder (1991) and the references therein.

a basket of 14 countries that accounted for approximately80% of Colombia’s foreign trade during the period1970–1992 (see the Appendix).

We use the price of co� ee to capture the terms of trade, asthis commodity has historically constituted Colombia’smajor export. In this sense, one would except that changesin the price of co� ee lead to changes in the country’s termsof trade, which can be formally tested by means of Granger’scausality tests. In particular, using quarterly data for theperiod 1970–1995, we ® nd that changes in the price of co� eeGranger-cause changes in the terms of trade (F2 , 9 6 = 4.36),and that changes in the latter variable do not Granger-causechanges in the former (F2 , 9 6 = 1.47).6 The (logarithm of the)price of co� ee is denoted L CP, and is expressed in 1986dollars to account for the erosion of co� ee purchasingpower due to US in¯ ation, as measured by this country’sCPI; the source of L CP is Banco de la Repu blica (1993) andfor the CPI of the US we use data from the InternationalFinancial Statistics of the IMF.

Regarding import tari� s, we ® rst calculate an implicitimport tari� (de® ned as the ratio of tari� revenues to totalimports) using annual data from national accounts. Then,we assume that tari� revenues are equally distributedthroughout the year,7 so that the import tari� of any quar-ter can be set equal to that of the year as a whole. For ourpurposes, we set the import tari� of the second quarterequal to that estimated for the year as a whole, and then weinterpolate in order to obtain a quarterly series of importtari� s, which is denoted TAR.8 It is worth bearing in mind,as argued by Edwards (1989), that TAR does not constitutea perfect measure of existing trade controls in the economy,since it ignores the role of nontari� barriers such as importquotas.

With reference to government expenditure, it is worthrecalling that the theoretical model distinguished betweengovernment consumption on nontradable and tradablegoods. Given that in practice such data are not available, weassume that central government’s current and capital ex-penditures provide suitable proxies for government con-sumption on nontradable and tradable goods, respectively.On this basis, we calculate the variable GCOMP as the ratioof central government’s current expenditure to total expen-diture, so that an increase in GCOMP re¯ ects an increase inthe share of government expenditure on nontradables, andconsequently a decrease in the share of government expen-

diture on tradables. The data were obtained from variousissues of the Revista del Banco de la Repu blica for the period1970–1979, and from Ramos and Rodrõ  guez (1995) for theperiod 1980–1992. Naturally, we are aware that GCOMP isnot a comprehensive measure of the expenditure of thepublic sector, as it includes only central government.

Regarding a proxy for the capital controls existing in theeconomy, we follow Herrera (1989) who uses the stock offoreign debt of the private sector. In this sense, a relaxationof the impediments to free borrowing and lending will beassociated with an increase in the private sector’s stock offoreign debt, which in turn allows private agents to increasetheir expenditure on tradable and nontradable goods. The(logarithm of the) stock of foreign debt of the private sectoris denoted LPFD, and is expressed in 1986 dollars using theUS CPI; the data on LPFD were obtained from variousissues of the Revista del Banco de la Repu blica.9 Lastly,technological progress is measured as a time trend, althoughthis variable is not signi ® cant.

Turning to the macroeconomic policies that might a� ectthe behaviour of the RER in the short run, we consider therole of monetary, ® scal and exchange rate policies. In thecase of monetary policy, we use a measure of money marketdisequilibrium (denoted EMS) that corresponds to the re-siduals of a money demand cointegrating relation, assumingthat money supply is given; in this sense, positive (negative)residuals denote excess money supply (demand). Concern-ing ® scal policy, we use the ® scal surplus of the centralgovernment as a proportion of GDP, which we denote FS;the data were obtained from various issues of the Revista delBanco de la Repu blica for the period 1970–1979, and fromRamos and Rodrõ  guez (1995) for the period 1980–1992.1 0

Exchange rate policy is denoted D L NER and correspondsto the rate of nominal devaluation; the data were obtainedfrom Banco de la Repu blica (1993).

Lastly, we are aware that over the period 1970–1992revenues from illegal drug exports could have a� ected thebehaviour of the RER. Nonetheless, the share of drug-related revenues that is repatriated is not likely to havea considerable e� ect on the aggregate demand, becausethese revenues have commonly been used to buy durableimported goods, livestock, lands, and (luxurious) urban andrural properties.1 1 For our purposes, incorporating theseillegal activities is beyond the scope of the analysis becausethe required data are not available.

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1 2 The data series and the results of the ADF tests are available from the author upon request.1 3 In a variant of the model we included a RER index constructed in the tradition of the PPP theory, with WPIs as proxies for both foreignand domestic price levels. The results of this alternative model are not reported since they suggest that L CP has been determined by thevariables in the VAR (i.e. L CP is not weakly exogenous), which is unlikely to occur in reality.1 4 The test of normality in the equation for L CP is failed at the 5% signi® cance level, but not at the 1%.1 5 See Doornik and Hendry (1994a., 1994b.) for details about these tests.1 6 These results are available from the author upon request.1 7 It should be remembered that the theoretical model predicted that if the changes in tari� s are accomplished when the tari� s are initiallygreater than zero, then the associated ® rst-order income e� ects may compensate the substitution e� ects, conducting to a RER depreciation.Echavarr õ Â a and Gaviria (1992) also obtain that import tari� s a� ect positively the RER in Colombia.1 8 We also estimated variants of the model including terms of trade and a trend term (the latter as proxy for technological progress), butthese variables were not signi® cant. It is also worth noting that in the speci ® cation with the terms of trade, we found a long-run relationshipbetween this variable and L CP.

T esting for nonstationarity

The order of integratedness of the series, except EMS whichwe already know is I(0), is investigated with the use ofgraphical and correlogram evidence, and with augmentedDickey–Fuller (ADF) tests. Inspection of the plots andcorrelogram of L RER, L CP, TAR and L PFD suggest thatthey may be nonstationary in levels, while GCOMP, FS andD L NER appear to be stationary. These ® ndings are alsosupported by the ADF tests.1 2

Cointegration analysis

We consider a three-dimensional VAR model for the vari-able set {L RER, L CP, L PFD}. There is also a set of non-modelled variables, which comprises TAR, GCOMP,D L NER, EMS and FS. Based on the theoretical model,TAR and GCOMP are assumed to enter in levels in thecointegrating space, which implies that they are regarded asexogenous to the system; this assumption allows us toreduce the dimension of the VAR enabling estimation. Con-cerning D L NER, EMS and FS, they are included only inthe short-run dynamics, along with a dummy variable thataims at removing the e� ects of the dates of substantialaccumulation of foreign debt by the private sector; thisdummy variable takes the value of one in 1979 : 3, 1981 : 2,1982 : 4 and 1983 : 1, and zero otherwise.1 3 The reducedform vector error correction (VEC) representation of theVAR model is:

D yt = G 1 D yt ± 1 + ¼ + G k D yt ± k+ 1 + P y4 t ± 1 + C Xt + e t

(1)

where yt = [L RERt , L CPt , L PFDt],y4 t = [yt , TARt, GCOMPt], andXt = [D L NERt ± 1 , EMSt , EMSt ± 1 , FSt , FSt ± 1 ,

Dummy].

The model is estimated for lag lengths of 4 and 3, usingthe same sample period, and then we test whether the fourthlag is redundant, which is accepted (F9 , 1 5 5 = 1.593). Table 1shows single-equation misspeci® cation test statistics whenthe VAR is estimated using three lags; all equations pass the

LM[4] test for residual serial correlation, Engle’s LM[4]test for ARCH, White’s test for heteroscedasticity, and thetest for normality.1 4 The stability of the model is analysedby means of the one-step residuals test, and sequences of1-step (1­ ), break point (N ) and forecast (N ­ ) F-tests,calculated from a recursive estimation of the model.1 5 Re-sults not reported here indicate that the equations forL RER, L CP and L PFD are relatively constant during theperiod of estimation, as in very few occasions the F-statisticsare rejected at the 1% signi ® cance level.1 6

We proceed with cointegration analysis which, in terms ofmodel Equation 1, involves testing the hypothesis of re-duced rank in the matrix of coe� cients P . The determina-tion of the number of cointegrating vectors is based on themaximal eigenvalue and trace tests, the interpretability ofthe results, and the graphs of the cointegrating relations.The cointegration tests in Table 1 suggest the presence oftwo cointegrating vectors. The ® rst one can be thought of asa long-run RER equation: The RER appreciates when thereis an increase in L CP, L PFD and GCOMP, and depreciateswhen there is an increase in TAR.1 7 The second cointe-grating vector does not have a clear economic interpreta-tion. The graphs of the cointegrating relations (notpresented here) suggest the presence of one cointegratingvector. Taking these aspects into consideration, thesubsequent analysis is based on the assumption of onecointegrating vector, since the test statistics, the graphicalanalysis and the economic interpretation of the results sup-port this choice.

Having determined the number of cointegrating relations,we continue with the formulation and testing of hypothesesabout the cointegration vectors and the adjustment coe� -cients. Regarding the ® rst type of hypotheses, we testwhether each individual variable can be excluded from thelong-run relation. The null hypothesis of long-run exclusionis rejected for all variables, except GCOMP (see Table 1). Inother words, the ratio of central government’s current ex-penditure to total expenditure is not needed in the cointe-gration space; later on it will be shown that GCOMP isnonetheless signi® cant for modelling the short-run dy-namics.1 8 With reference to the tests on the adjustmentcoe� cients, we test whether the set of variables are weakly

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Table 1. Cointegration analysis

Model diagnostic testsL RER L PFD L CP

LM[4] 0.163 1.073 0.787Normality 2.751 1.491 6.626*ARCH[4] 0.714 0.993 0.575Heteroscedasticity 0.556 1.158 0.618

Cointegration analysisMaximal eigenvalue testNull hypothesis r = 0 r < 1 r < 2Alternative hypothesis r = 1 r = 2 r = 3Test value 37.410** 20.900** 3.100

Trace testNull hypothesis r = 0 r < 1 r < 2Alternative hypothesis r > 1 r > 2 r = 3Test value 61.410** 24.000** 3.100

b 9 eigenvectors L RER L PFD L CP GCOMP TAR(standardized) 1.000 0.284 0.389 0.099 - 4.109

- 0.663 1.000 0.390 0.264 - 3.328

Standardized a coe� cientsL RER - 0.117 0.049L PFD - 0.193 - 0.041L CP - 0.176 - 0.156

Testing long-run exclusion L RER L PFD L CP GCOMP TAR(Test distributed as x 2

1 ) 15.367** 5.489* 13.609** 0.125 14.392**Testing weak exogeneity 5.549* 10.808** 0.934(Test distributed as x 2

1 )

Restricted b 9 eigenvector 1.000 0.222 0.358 Ð - 3.813Restricted a coe� cients

L RER - 0.139L PFD - 0.178L CP Ð

Notes:* denotes signi ® cance at the 5% level, but not at the 1%. **denotes signi® cance at the 1% level. The number of cointegrating vectors isdenoted by r. Critical values for the maximal eigenvalue and trace tests are reported in Osterwald-Lenum (1992).

Fig. 1. Restricted cointegrating relation

exogenous for the estimation of the parameters of thelong-run RER equation (see Johansen, 1992). The results inTable 1 indicate that the hypothesis of weak exogeneity isaccepted for L CP, but not for L RER and L PFD.

Lastly, we test the joint hypothesis that GCOMP can beexcluded from the cointegration space, and that L CP isweakly exogenous for the estimation of the parameters ofthe long-run RER equation. The test statistic of this jointhypothesis is x 2

2 = 1.048, which is accepted. The restrictedcointegrating vector and adjustment coe� cients are re-ported in the last panel of Table 1, and in Fig. 1 we plot therestricted cointegrating relation.

Real exchange rate misalignment

We derive a measure of RER misalignment that corres-ponds to the deviations of the RER from its long-run equi-librium relationship. At ® rst glance, it appears that thecointegrating relation depicted in Fig. 1, that is the linear

combination b 9 y4 t , can be interpreted as a measure of RERmisalignment; however, the limitation of b 9 y4 t is that it is notcorrected for the short-run dynamics of the model. In con-trast to Elbadawi (1994), we use neither moving averages

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Fig. 2. Restricted cointegrating relation (Correcting for the short-run dynamics)

nor the Beveridge–Nelson decomposition to correct for theshort-run dynamics, because the ® rst method involves theloss of observations and the second one cannot always beapplied. Instead, we follow Johansen and Juselius (1992),who recommend calculating the cointegrating relations asb 9 r1 t , where r1 t are the residuals from regressing y4 t ± 1 on theshort-run dynamics ( D yt ± 1 , ¼ , D yt ± k+ 1 ) and the set of non-modelled variables entering in the short run (Xt). In otherwords, we use the linear combination b 9 r1 t as a more precisemeasure of RER misalignment, with positive (negative) re-siduals denoting undervaluation (overvaluation) of theRER.

Figure 2 plots the cointegrating relation corrected for theshort-run dynamics (i.e. b 9 r1 t). As can be seen, the linearcombination b 9 r1 t is markedly di� erent from b 9 y4 t , sugges-ting that short-run e� ects play a signi ® cant role in our RERmodel. Further inspection of the graph reveals that themagnitude of the misalignment ¯ uctuates within a range ofapproximately 6 20%.

The behaviour of the indicator illustrates that from 1970to around 1977 the RER passes from being overvalued tobeing undervalued. After this year and up to around 1985negative residuals are predominant, suggesting overvalu-ation of the RER; during this period, the country experi-enced a co� ee price boom, accumulation of foreign debt,and a signi ® cant expansion of the public sector. In 1986,after a period where ® scal imbalances and the deteriorationof the foreign sector led the government to adopt an adjust-ment programme that included, among other reforms, ® scalausterity and acceleration of the rate of crawl of the nominalexchange rate, our measure of misalignment suggests thatthe RER was undervalued; in the following year, the RERappears to be overvalued once again. From 1988 to 1992our estimates indicate a period of RER undervaluation, asmost of the residuals are positive; the magnitude of themisalignment in 1992 is less than that observed in theprevious two years.

Short-run dynamics

Once we have found evidence of a cointegrating relation-ship, we estimate the VAR in error correction form. But,before doing this, it is worth recalling from the outcome ofthe test of hypotheses about the adjustment coe� cients, thatonly LCP can be regarded as weakly exogenous for theestimation of the parameters of interest. Given that D L PFDt

is not weakly exogenous, a one-equation model for D L RERt

conditioning upon it and the remaining variables is notvalid; instead, we need to model D L RERt and D L PFDt

jointly.We thus proceed by conditioning upon the price of co� ee,

so that D L CPt is included as a regressor in the reduced formerror correction models (ECMs). The lag length of theECMs is equal to two because we included three lags in theVAR model of the variables in levels. Least-squares esti-mates for the ECMs are reported in Table 2 along with theassociated standard errors. As expected, the two equationsare initially overparametrized, so that a more parsimoniousrepresentation could be obtained by excluding some of theregressors based on Wald tests for zero restrictions. Thecoe� cient on the error correction term is negative andstatistically di� erent from zero in the two equations. It alsoappears that the ECMs are well speci ® ed as none of thediagnostic tests is failed.

On the basis of the reduced form ECMs, we formulatea system of simultaneous equations to model D L RERt andD L PFDt . To de ® ne a structural equation for D L RERt weinclude D L PFDt as explanatory variable, and excludeD L RERt ± 1 , D L PFDt ± 1 , D L PFDt ± 2 , D L CPt ± 1 , D L CPt ± 2 ,D T ARt ± 1 , GCOMPt , EMSt , EMSt ± 1 , FSt and the dummyvariable. These restrictions are based on the theoreticalmodel, and the signi® cance of the coe� cients in the reducedform ECMs. With regard to the equation for D L PFD,we exclude, based on the signi ® cance of the estimatedcoe� cients, D L RERt ± 1 , D L RERt ± 2 , D L PFDt ± 2 , D L CPt ± 1 ,D L CPt ± 2 , D T ARt , D T ARt ± 1 , GCOMPt , GCOMPt ± 1 ,EMSt , EMSt ± 1 , FSt , FSt ± 1 and D L NERt ± 1 . Two-stageleast-squares estimation of the resulting equations, using asinstruments the explanatory variables of the reduced formECMs, yields the results reported in Table 2.

In the ® rst equation the estimated coe� cients on D L PFDt

and D L CPt have the expected negative sign, although thesecond one is not signi® cant, and the coe� cient on D T ARt

is positive. The public sector a� ects the RER throughchanges in the composition of government expenditure andchanges in the ® scal surplus; in particular, the RER appreci-ates when GCOMP increases and FS decreases. Hence, evenwhen the government ® nancial balance is equal to zero, theRER may appreciate or depreciate as a result of changes inthe composition of government expenditure. The coe� cienton D L NERt ± 1 is positive and relatively large, so that in theshort run a policy of nominal devaluation causes a deprecia-tion of the RER. On the contrary, variations in the RER do

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Table 2. Estimates of the ECMs conditioning upon D L CP

Ordinary least squares Two stages least squares

D L RER D L PFD D L RER D L PFDStd. Std. Std. Std.

Variables Coe� . Error Coe� . Error Coe� . Error Coe� . Error

Constant 0.685 0.240 0.788 0.284 0.515 0.166 0.49 0.167D L RERt ± 1 0.151 0.130 - 0.069 0.154D L RERt ± 2 - 0.193 0.109 - 0.119 0.129 - 0.167 0.098

D L PFDt - 0.097 0.069D L PFDt ± 1 - 0.129 0.063 0.129 0.074 0.174 0.065D L PFDt ± 2 - 0.002 0.064 - 0.068 0.076

D L CPt - 0.026 0.026 0.055 0.030 - 0.022 0.022 0.066 0.027D L CPt ± 1 - 0.003 0.031 0.060 0.036D L CPt ± 2 0.036 0.029 - 0.004 0.034

D T ARt 0.646 1.220 - 0.130 1.446 1.753 0.609D T ARt ± 1 1.024 1.263 1.841 1.497

GCOMPt 0.037 0.073 - 0.020 0.087GCOMPt ± 1 - 0.152 0.075 0.029 0.088 - 0.138 0.054

EMSt - 0.036 0.134 - 0.176 0.159EMSt ± 1 0.036 0.128 0.164 0.152

FSt 0.172 0.226 0.236 0.268FSt ± 1 0.662 0.242 0.068 0.287 0.664 0.212

D L NERt ± 1 0.610 0.188 - 0.165 0.223 0.71 0.146

Cvectort ± 1 - 0.112 0.043 - 0.143 0.051 - 0.08 0.03 - 0.09 0.03

Dummy - 0.010 0.020 0.239 0.024 0.247 0.023

Diagnostic testsLM[4] 0.039 1.627 2.096 5.434**ARCH[4] 0.155 1.652 0.868 0.611Normality 4.231 1.522 2.875 4.514Heteroscedasticity 0.433 0.550 0.478 0.753

Notes:The LM[4], ARCH[4] and heteroscedasticy tests are reported in their F versions. The test for normality is distributed as x 2

2 . **denotessigni ® cance at the 1% level.

1 9 Dornbusch (1985) stresses that for some Latin American countries overvalued exchange rates were often important causes of excessiveforeign borrowing.

not depend upon monetary disequilibria, as the coe� cientson current and lagged values of EMS are not statisticallydi� erent from zero. Lastly, it appears that the regression forD L RERt is well speci ® ed as none of the diagnostic tests isfailed.

Turning to the second equation, the main economicdeterminants of D L PFDt are D L CPt and CV ectort ± 1 .Although we are not particularly concerned with this equa-tion, it is of some interest to notice that changes in L PFDrespond negatively to deviations of the RER from its im-plied long-run relationship (lagged once); put another way,the stock of foreign debt held by the private sector wouldincrease when the actual value of the RER is below its

equilibrium level, and vice versa.1 9 The equation passes thetests for ARCH[4], normality and heteroscedasticity, butnot the LM[4] test for residual serial correlation. Despitethis, we proceed the analysis with the estimated system ofequations as the vector error autocorrelation test of up tofourth order, that is the multivariate equivalent of the singleequation LM[4] test, is easily accepted (F1 6 , 1 4 0 = 1.216).

Solution of the model and policy analysis

The next important aspect is to simulate (or solve) thesystem of simultaneous equations, in order to obtain thepredictions of the system for the values of its endogenous

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Fig. 3. Ex-post simulation of L RER: ( Ð Ð ) actual, (- - - - -)simulated

Fig. 4. Ex-post forecast of L RER: ( Ð Ð ) actual, (- - - - -) ex-postforecast

2 0 Historical data show that GCOMP increases from an average of 66% during 1970–1992, to 74% during 1993–1995. On the other hand,from 1970 to 1992 the ® scal balance of the central government was on average close to zero; in 1993 and 1995 the de ® cit amounted to 0.8%and 2.7% of GDP, respectively, and in 1994 the ® scal balance showed a surplus of 0.7% of GDP.

variables , that is D L RERt , D L PFDt , L RERt and L PFDt .The simulation of the model begins in 1972 and runs for-ward until 1995. Actual values in year 1971 are supplied asinitial conditions for the endogenous variables, and histori-cal series beginning in 1971 and ending in 1995 are used forthe non-modelled variables. For the period up to 1992, thatis the period of estimation, the simulation corresponds to anex-post’ or historical ’ simulation, while for the period1993–1995 the simulation corresponds to an ex-post’ fore-cast. It is also worth noting that the predictions of the modelconstitute true multiperiod forecasts’ because prior to the® rst period of the simulation we use actual values for laggedendogenous variables , and thereafter the values forecastedby the model itself.

In Fig. 3 we compare actual values of L RER with thepredictions obtained from the ex-post simulation over theperiod of estimation. Inspection of the graph shows thatthe simulation performance of the model is particularlygood, with the simulated series of L RER reproducing thelong-run behaviour of the actual series. Interestingly, thesimulated series predicts the main turning points in thehistorical data, and tracks the historical data closely sincethe mid-1980s.

The ability of the model to predict beyond the estimationperiod is evaluated with an ex-post forecast in which themodel is simulated forward starting in year 1993 andcontinuing as long as historical data of the non-modelledvariables are available , that is 1995 (see Fig. 4). The ® rstimportant aspect to be noticed is that the plots of thesimulated and actual series are reasonably coincident, withthe former reproducing the downward trend that the latterhas been exhibiting since the early 1990s. Between 1993 and1994 the decline predicted by the model is less accentuatedthan that which actually occurred. In 1995, the ex-postforecast of the index of the RER is on average 83.91, which isvery close to the actual value (i.e. 85.06).

Lastly, it is of some interest to change the time path ofsome non-modelled policy variables, in order to examinewhat might have taken place as a result of alternativepolicies. In particular, since the public sector a� ects thebehaviour of the RER through changes in GCOMP and FS,we examine the economic consequences that would haveresulted had these ® scal variables followed a di� erent timepath. We thus perform a simulation experiment for theperiod 1993–1995, in which we assume that GCOMP andFS remain at the average levels observed over the period1970–1992.2 0 The results indicate that if the two ® scalvariables had followed the alternative time paths, the RERwould have appreciated less than actually occurred; morespeci ® cally, the model predicts an average RER of 98.18 and91.94 in 1994 and 1995, respectively, compared to ex-postforecasts for the same years of 95.16 and 83.91 (see Fig. 5).

IV. CONCLUDING REMARKS

We use Johansen’s analysis of cointegrated systems to builda model of the Colombian RER based on the Edwardsmodel. In general terms our results match up with theEdwards model. We ® nd one cointegrating vector, whichcan be thought of as a long-run RER equation. The RERappreciates as a result of increases in the price of co� ee andin the stock of foreign debt held by the private sector; also, itdepreciates as a result of increases in import tari� s. Theratio of central government’s current expenditure to totalexpenditure is not needed in the cointegration space, but itis nonetheless signi® cant for modelling the short-run dy-namics. Technological progress, proxied by a time trend, isnot signi ® cant.

The modelling of the RER short-run dynamics is basedon a system of two equations, given that the stock of foreigndebt held by the private sector is not weakly exogenous.

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Fig. 5. Policy analysis L RER: ( Ð Ð ) ex-post forecast, (- - - - -)experiment 1

Estimation of the system indicates that (a) the set of realfactors a� ect the short-run behaviour of the RER; (b) theRER appreciates when the ratio of central government’scurrent expenditure to total expenditure increases, andwhen the ® scal surplus as a percentage of GDP decreases;(c) in the short run a policy of nominal devaluation causesa depreciation of the RER; and (d) variations in the RER donot depend upon monetary disequilibria.

We interpret the deviations of the RER from its long-runequilibrium relationship, after correcting for the short-rundynamics, as a measure of RER misalignment. The actualmethod to estimate such measure is already contained with-in Johansen’s estimation procedure, and does not requirethe use of either moving averages or the Beveridge–Nelsondecomposition to correct for the short-run dynamics. Thederived measure of exchange rate misalignment ¯ uctuateswithin a range of approximately 6 20% during the period1970–1992.

Finally, we solve the system of simultaneous equations, inorder to obtain predictions for the RER. The simulationperformance of the model during the period of estimation isparticularly good, with the simulated series of the RERreproducing the long-run behaviour of the actual series.More importantly, the simulation of the model beyond theestimation period is also successful, with the simulated seriesreproducing the downward trend that the actual series hasbeen exhibiting since the early 1990s. A policy analysisexperiment indicates that during the period 1993–1995 theRER would have appreciated less than actually occurred, ifthe ® scal de® cit and the ratio of central government’s cur-rent expenditure to total expenditure had remained at theiraverage levels for the period 1970–1992.

ACKNOWLEDGEMENTS

The author would like to thank Jeremy Smith, MichaelClements, Ana Marõ Â a Iregui and participants in theDevelopment Economics Workshop at the University ofWarwick for helpful comments and suggestions. Financial

support from the Fundacio n para el Futuro de Colombia– Colfuturo, the British Council and the Banco de la Repu b-lica is gratefully acknowledged. All remaining errors aremine.

REFERENCES

Banco de la Repu blica (1993) Principales indicadores econo micos1923–1992, Banco de la Repu blica, Bogota .

Balassa, B. (1964) The purchasing power parity doctrine: a re-appraisal, Journal of Political Economy, 72, 584–96.

Caldero n, A. (1995) La tasa de cambio real en Colombia: Mitosy realidades, Coyuntura Econo mica, 25, 101–18.

Carkovic, M. (1986) The real exchange rate determination andoptimal exchange rate policy: The case of co� ee in Colombia,PhD Thesis, University of California, Los Angeles.

Cubillos, R. and Valderrama, F. (1993) Estimacio n del PIB trimes-tral segu n los components del gasto, Archivos de macro-econom õ  a documento 13, DNP, Bogota .

Doornik, J. and Hendry, D. (1994a) PCFIML 8.0: InteractiveEconometric Modelling of Dynamic Systems, InternationalThomson Publishing, London.

Doornik, J. and Hendry, D. (1994b) PCGIV E 8.0: An InteractiveEconometric Modelling System, International Thomson Pub-lishing, London.

Dornbusch, R. (1980) Open Economy Macroeconomics, BasicBooks, New York.

Dornbusch, R. (1985) External debt, de ® cits, and disequilibriumexchange rates, in International Debt and the DevelopingCountries, G. Smith and J. Cuddington (eds), The WorldBank, Washington, pp. 213–35.

Echavarr õ  a, J. and Gaviria, A. (1992) Los determinantes de la tasade cambio y la coyuntura actual en Colombia, CoyunturaEcono mica, 22, 101–12.

Edwards, S. (1989) Real Exchange Rates, Devaluation, and Adjust-ment: Exchange Rate Policy in Developing Countries, MITPress, Cambridge, MA.

Elbadawi, I. (1994) Estimating long-run equilibrium real exchangerates, in Estimating Equilibrium Exchange Rates J. William-son (ed.), Institute for International Economics, Washington,pp. 93–131.

Helmers, L. (1991) The real exchange rate, in T he Open Economy:T ools for Policymakers in Developing Countries, R. Dorn-busch and L. Helmers (eds), Oxford University Press, NewYork, pp. 10–33.

Herrera, S. (1989) Determinantes de la trayectoria del tipo decambio real en Colombia, Ensayos Sobre Pol õ  tica Econo mica,15, 5–23.

Johansen, S. (1988) Statistical analysis of cointegration vectors,Journal of Economic Dynamics and Control, 12, 231–54.

Johansen, S. (1992) Testing weak exogeneity and the order ofcointegration in UK money demand data, Journal of PolicyModeling, 14, 313–34.

Johansen, S. and Juselius, K. (1990) Maximum likelihood estima-tion and inference on cointegration – with applications to thedemand for money, Oxford Bulletin of Economics and Statis-tics, 52, 169–210.

Johansen, S. and Juselius, K. (1992) Testing structural hypothesesin a multivariate cointegration analysis of the PPP and theUIP for UK, Journal of Econometrics, 53, 211–44.

Langebaek, A. (1993) Tasa de cambio real y tasa de cambio deequilibrio, Archivos de macroeconomõ  a documento 19, DNP,Bogota .

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Ramos, J. and Rodrõ  guez, N. (1995) De ® cit ® scal y tasa de intere sen Colombia. Borradores Semanales de Economõ  a No. 19,Banco de la Repu blica, Bogota .

Williamson, J. (1983) T he Exchange Rate System, MIT Press,Washington.

Wunder, S. (1991) Dutch disease theory and the case of Colombia,PhD Thesis, Institute of Economics, University of Copen-hagen.

APPENDIX. CONSTRUCTION OF THEREAL EXCHANGE RATE INDEX

The RER is de ® ned as RERt = ( + kj = 1 a j , tEj , tW PI*j , t)/CPIt ,

where a j , t is the share of country j in Colombia’s trade;although the trade weights have the subscript t, in practicethey are kept constant during the periods 1970–1974,1975–1979, 1980–1984, 1985–1989 and 1990–1992; Ej , t isan index of the nominal exchange rate between country

j and Colombia in period t; W PI*j , t is the wholesale priceindex of country j in period t; and CPIt is the consumer priceindex of Colombia in period t. The base year is 1986 so thatthe RER is equal to 100 in that year.

The trade weights are calculated with data from theDirections of Trade Statistics of the IMF. The ® gures inparentheses are percentages of average trade weights, beforenormalization, for the periods 1970–1974, 1975–1979,1980–1984, 1985–1989 and 1990–1992; US (39.6, 34.6, 32.1,36.3 and 39.2); Germany (11.4, 13.2, 10.9, 10.5 and 7.9);Venezuela (1.3, 5.6, 7.1, 3.8 and 5.9); Japan (5.4, 5.9, 7.8, 7.0and 5.6); Netherlands (3.1, 3.7, 2.7, 3.5 and 2.7); Spain (4.4,3.0, 2.7, 2.4 and 2.0); France (2.4, 3.1, 2.8, 3.0 and 2.7); UK(3.2, 2.6, 2.1, 2.4 and 2.6); Ecuador (1.9, 2.1, 1.9, 1.2 and 1.4);Italy (2.0, 2.0, 2.9, 1.8 and 1.7); Canada (2.2, 2.0, 2.7, 2.4 and1.9); Sweden (2.2, 2.6, 1.9, 1.6 and 0.9); Switzerland (1.9, 1.3,1.2, 1.3 and 1.5); and Mexico (1.2, 1.0, 1.2, 1.7 and 1.6). Thetrade weights of these 14 countries add up 82.2%, 82.7%,79.8%, 79.0% and 77.8%.

The nominal exchange rates and the WPIs of the 14countries listed above were obtained from the InternationalFinancial Statistics of the IMF; it is worth mentioning thatfor France and Ecuador we use their respective CPIs, as theWPIs were not available. The source of Colombia’s CPI isBanco de la Repu blica (1993).

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