SAJEMS NS Vol 3 (2000) No I The Economics of Exchange Rates: A South African Model S Brink and R Koekemoer Department of Economics. University of Pretoria ABSTRACT 19 This paper attempts to capture the determination of the South African exchange rate in a theoretically plausible model with reliable forecasting ability. A sticky- price, Dornbusch-type monetary model of the rand/dollar exchange rate is proposed. The three-step Engle and Yoo cointegration procedure is applied and the test results indicate that the nominal exchange rate is cointegrated with relative real output, the relative money supplies and the inflation differential. An error correction model is estimated and shocks are applied to each of the long-run variables. Some policy implications are derived from these sensitivity tests. Finally, a fundamental equilibrium exchange rate (FEER) for the rand/dollar rate is defined and the FEER values are estimated until the year 2000. JEL C 51, F 31 1 INTRODUCTION The South African currency unit (the rand) has for some years been sensitized both politically and with respect to other fundamentals. As a result, fluctuations tend to be more than moderate and, in some cases, in an unexpected direction. The openness of the economy is one of the vehicles of growth, employment and an equitable distribution of income and wealth in the much-publicized macroeconomic strategy of the government, where a stable exchange rate, or at least a less unpredictable one, is a prerequisite for a successful outward policy. In short, it is essential to make sense of the propellants of the exchange rate. Attempts to model the South African exchange rate have, despite its importance for the outcome of the above-mentioned macroeconomic strategy and unlike its major counterparts (e.g. the dollar/pound rate or the Deutsche mark/pound rate), been surprisingly few and generally not very successful. In this paper, a model of the rand/dollar exchange rate is proposed. It conforms to the sticky-price Dornbusch version of the monetary model, and therefore belongs to the asset- approach class of models. R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 20 SAJEMS NS V crl 3 (2000) No'l The validity of the monetary approach to exchange rate determination has been frequently questioned, due to the lack of empirical support reported by most researchers in the field. Irrespective of whether the monetary model's empirical failure stems from inadequate statistical techniques or fundamentally flawed theoretical content, its application to the South African exchange rate model requires some justification. In an effort to provide this, the asset-market approach to exchange rate determination, to which the monetary approach belongs, is briefly recapitulated below to illustrate the absence of clear alternatives. Some perspectives on the empirical status of the monetary model and an elaboration of the version used in the rand/dollar model then follow. After that, the rand/dollar exchange rate is modelled, using the three-step Engle and Y 00 cointegration technique and reporting the results thereof. Finally, some relevant policy implications are considered and a fundamental equilibrium exchange rate (FEER) is proposed, given certain criteria for internal and external equilibrium. 2 SELECTING THE THEORETICAL FOUNDATION: THE ASSET APPROACH RECAPPED Markets for foreign exchange came to be viewed as asset markets during the latter half of the 1970s. The asset approach may be contrasted with the traditional flow approaches, in the sense that the latter allows shocks to affect trade flows via shifts in the terms of trade or an altered relationship between domestic absorption and output. An expansionary monetary or fiscal policy, for example, will therefore raise the demand for imports and consequently for the foreign currency, depreciating the domestic currency. Conversely, an improvement in the current account in the flow model signifies an appreciation of the exchange rate. The contrasting "asset" models do not assign adjustments in the relative prices of goods more than a fairly minor supporting role. The asset approach models commonly view the exchange rate as the foreign currency price that equilibrates the net stock demands for financial assets denominated in different currencies (Frankel, 1980: I). In principle, the two modelling strategies can be synthesized. The exchange rate would then be viewed as equilibrating the total demand for and supply of foreign currency, with complete integration of the current and capital accounts of the balance of payments. In this case, flows should be consistent with the corresponding asset stock requirements. Most research has, however, emphasized one approach at the expense of the other, and since the advent of the 1973 float the asset-market view has become dominant. Asset-market models have occupied most of what has been written on exchange rates for the past 25 years. Rather than elaborating on the contrast between the R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 3 (2000) No 1 21 traditional flow models and the asset approach models, distinguishing between the different asset-market models may prove useful for the purpose of this study. The monetary approach to exchange rate determination ranks prominently among the latter class of models: Virtually all the considerable number of models developed since 1973 to clarify the volatility of floating rates, feature an adjustment process that assigns the equilibration of national money markets a prominent role. The monetary approach undoubtedly falls short of an adequate explanation of the observed volatility in major currencies. However, consensus suggests that better results would not be obtained by disregarding financial market implications. Stress should primarily fall on an improved specification of asset-market models (Boughton, 1988: 2). Non-monetary asset models are collectively referred to as portfolio-balance models. All the asset-market (i.e. monetary and non-monetary) models share the perfect capital mobility assumption. That is, the absence of substantial transactions costs, capital controls, or any other constraints on the flow of capital between countries is implied. Exchange rates thus adjust instantly, with the empirical implication that they may exhibit a degree of variability exceeding that of their underlying determinants (Frankel, 1980: 1). The taxonomy of asset-market models establishes a particular dichotomy according to which the monetary and portfolio balance models are distinguished: If domestic and foreign bonds are regarded as perfect substitutes, portfolio shares become infinitely sensitive to expected rates of return and bond supplies become irrelevant. Determination of the exchange rate then shifts towards the money markets (op. cit.: 4). In the non-monetary or portfolio balance class of asset-market models, the perfect substitutability assumption is relaxed and asset holders allocate their portfolios across shares that are well-defined functions of expected rates of return (op. cit.: 4). The perfect mobility of capital assumption is retained and a distinction between perfect mobility and perfect substitutability can evidently be drawn: The first implies the absence of impediments to capital flows whereas the second is the much stronger assumption that asset holders are indifferent as to the composition of their bond portfolios, provided that the expected rate of return on the two countries' bonds is identical when converted to a common numeraire (op. cit.: 2). The portfolio balance model is considered to be the most general model of exchange rate determination. Its empirical validity is, however, flawed on two counts: A test of the complete model is close to impossible given the R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 22 SAJEMS NS Vol 3 (2000) No 1 unavailability of appropriate data and, in truncated fonn, it generates poor results, even for the early period of the 1973 float. Although there can be I ittle doubt that a suitable exchange rate model should reflect the asset-market approach as opposed to the traditional flow approaches, the portfolio balance model is not a natural choice on account of data considerations. In early versions of the rand/dollar model presented in this paper, first, a portfolio balance approach and, later, a hybrid model of the monetary and portfolio balance approaches were followed. In both cases, substantial difficulty was encountered in assembling the data, and the test results were unsatisfactory. Instead, a simple monetary model is proposed for and adapted to South African circumstances. Given the empirical shortcomings of the monetary model, the selection of the monetary approach as a basis for the rand/dollar rate needs some justification: The monetary model is generally regarded as the "standard work- horse" in intemational finance (Frankel & Rose, 1994: 3). In addition, the monetary model provides a useful tool for exchange rate analysis because it, firstly, clearly defines the role of speculation among the exchange rate detenninants and, secondly, gives a simple definition of the equilibrium exchange rate. Moreover, it directly relates the equilibrium rate to the underlying instruments of monetary policy (Bilson, 1978: 48). Most importantly, an obvious altemative is clearly lacking. The sticky-price Dombusch model of the rand/dollar rate yielded unexpectedly good results for the sample period. The rand/dollar model, which closely resembles the "standard workhorse" variant of the monetary model, was adjusted in earlier attempts to improve empirical results. Current account data was introduced to obtain a variant similar to the Hooper-Morton model. Also, attempts were made to capture Driskill's imperfect substitutability assumption or, alternatively, to specify a hybrid monetary-portfolio balance model. Finally, variables similar to those proposed by Throop (1993) were introduced - without success. These variables included the budget deficit, the price of oil and a gold price/oil price tenns-of-trade type of variable. All the attempts to find a better model proved fruitless or were prematurely frustrated by the unavailability of data. As a result, the "standard workhorse" variant of the monetary model was retained. Ideally, a truly sophisticated exchange rate model should accommodate forward- looking expectations. Rational expectations with time-in variate parameters as embodied in the efficient market hypothesis, may be introduced. The rand/dollar model implicitly contains rational expectations in the sense that expected future values are assumed to materialize. Expected future values therefore equal actual future values. Altematively. expectations with time-variate parameters, as embodied in the learning models, may be introduced. Although plausible, a R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 3 (2000) No 1 23 learning model was not simulated in this study due to technical constraints, but will be pursued in future research. Regrettably, an intertemporal optimizing model was also excluded from the empirical work, as it requires an approach with strong micro foundations, which is beyond the scope of this study. The focus of this study is mainly on a simple, structural long-run macro-model. As with learning, intertemporal optimization will undoubtedly receive the attention it deserves in future empirical work on the South African exchange rate. 3 EMPIRICAL STATUS OF THE MONETARY MODEL Friedman (1953: 158) in his argument for flexible exchange rates, stated that: "The ultimate objective is a world in which exchange rates, while free to vary, are in fact highly stable: Instability of exchange rates is a symptom of instability in the underlying economic structure". The monetary model, as part of the asset approach, was induced by the failure of the traditional trade-flow models, to define the elements of the "underlying economic structure" that have been responsible for the erratic exchange rate movements. It may be said that the monetary approach has for the past two decades become the standard point of departure for the literature on exchange rate determination. Admittedly, the monetary approach fails to provide an adequate explanation of the movements in major currency values during the floating-rate period that commenced in 1973. The causes of this failure will be subsequently examined. After initial claims of success (the so-called first-period tests for the present float prior to 1978), the empirical failure of a simple monetary model with flexible prices became apparent (Frankel and Rose, 1994: 5). The coefficient estimates and empirical fit of such models were less than reassuring, with the possible exception of hyperinflation conditions. In addition, the observed volatility of real exchange rates and the highly positive correlation of nominal and real exchange rates became obvious enough to warrant explicit treatment (op. cit.: 6). Moreover, the models forecasted poorly out-of-sample. The apparent contradiction of the assumption of flexible prices emerging from these [mdings, naturally led to the assumption of sticky prices. The essence of the sticky-price overshooting, or Dornbusch model is captured in a simple, yet strong, statement that proportionality exists between the real exchange rate and the contemporaneous real interest differential (op. cit.: 8). Early tests of the overshooting model focussed on more complete models than the simple proportionality between the real exchange rate and the real interest differential. Such· tests of exchange rate models with sticky prices met with initial success, but eventually fell apart both in and out-of-sample (op. cit.: 11). The emphasis has subsequently shifted to subjecting the simple testable result of R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 24 SAJEMS NS Vol 3 (2000) No I the model relating the real exchange rate to the contemporaneous real interest differential to increasingly sophisticated time-series econometrics. Meese and Rogoff (1988) applied the Engle-Granger test for cointegration and found no evidence of such a relationship. Similarly. Campbell and Clarida (1987) reported a lack of supporting evidence. It has been noted that the poor results could be attributed either to the existence of a missing variable or, alternatively, the weak power in the tests (Frankel and Rose, 1994: 11). Subsequent studies employed increasingly powerful econo- metric procedures (such as the Johansen procedure) and included other variables. For example, evidence of cointegration between the real exchange rate and real interest differential was reported after the incorporation of a measure of the cumulated current account (op. cit.: 12). Strong results were reported in a subsequent study by Throop (1993), after allowance for several other variables has been made: A lagged effect of the real interest differential, the budget deficit, the real price of oil and a measure of the relative price of non-traded goods. 4 DEVELOPING THE MONETARY EQUATION A general statement of the monetary approach comprises five hypotheses: I. Purchasing power parity (PPP) holds over some time horizon. 2. Uncovered interest parity (UIP) holds at all times. 3. The demand for real money balances is a stable function of a small set of real variables. 4. The supply of money is determined by a stable process. 5. Expectations are (in some sense) rational (Boughton, 1988:4). The joint hypotheses of PPP in the long run and UIP at all times call for some remarks. The relative version of PPP can be written in its ex' ante expectational form as: with e(de) the log of the expected depreciation in the domestic currency, e(dp) the log of the the expected domestic inflation rate and t(dpI the log of the expected foreign inflation rate. Equation (I) states that the expected exchange rate depreciation equals the expected inflation differential. UIP states that the expected depreciation is equal to the interest differential: e(de) = i-if (I) (2) R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 3 (2000) No 1 25 Equations (1) and (2) can now be rewritten and combined to establish ex ante real interest parity (RIP): I.ir -l.irf = [i -&(dp)}- [i,- &( dp I)] with r denoting the real interest rate. Equation (3) states that RIP holds if both PPP and UIP hold. The joint hypothesis of PPP and UIP therefore also imply the rather strong hypothesis of RIP. As deviations from PPP are assumed not to occur in the long run and such deviations are generally caused by exchange rate or inflation forecast errors, such errors are assumed not to exist. In addition, deviations from UIP caused by risk premia or exchange rate forecast errors are assumed to be absent. The first two hypotheses in the list above should therefore be recognized as the stringent assumptions that they are: Simultaneous PPP, UIP and RIP are implied and all sources of deviation from any of these parity conditions are assumed not to exist (Marston, 1997: 289). The fundamental equation in the monetary approach is a conventional money demand function: m= p+¢Y-Ai where m = the log of the domestic money supply, p = the log of the domestic price level, y = the log of domestic real income, i = the nominal domestic short term interest rate, ¢ = the income elasticity of the demand for money and A, = the interest rate semi-elasticity of the demand for money. A similar money demand function is formulated for the foreign country: (3) (4) m,= p,+¢y,-Ji, (5) A relative money demand function is obtained by subtracting equation (5) from equation (4): Uncovered interest parity is implied by the perfect substitutability or single-bond assumption: i -i, = &(de) where e(de) represents the expected depreciation of the do",!estic currency. The relative price level can be obtained by rewriting equation (6): (P - Pf) = (m - m,)- ¢(y- y,)+ J(t - if), Equations (7) and (8) are subsequently combined: (p - p,) = (m - m, ) - ¢(y - y,) + A.&( de) (6) (7) (8) (9) R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 26 SAJEMS NS Vol 3 (2000) No I Equation (9) states that relative prices are determined by the domestic money supply relative to the foreign money supply, domestic income relative to foreign income and also by the expected depreciation in the domestic currency. A long-run version ofPPP is now introduced: (10) with the bars over the variables signifying long-run relationships and e == the log of the spot exchange rate, reflecting the domestic price of foreign currency. Equation (9) can be combined with (10) and rewritten as: (11 ) In its expectational form, PPP equals the expected depreciation to the expected inflation differential: (12) A long-run version of exchange rate determination can now be obtained by combining equations (11) and (12): ---- e = (m - mf)- ¢( Y- Yf)+ Jl( E(dp}- E( dpf} (13) Equation (13) states that, in the long run, the exchange rate as the relative price of currency, is determined by the relative supply of and demand for money. If the domestic money supply expands, a proportionate depreciation results. Similarly, an increase in domestic income or a decline in the expected inflation rate, stimulates the demand for domestic money and results in an appreciation. It is assumed that expectations are rational, that the system is stable, that income growth is exogenous (or random with mean zero) and, finally, that monetary growth follows a random walk as a benchmark specification. The expected inflation rates, domestic and foreign, are consequently replaced by the actual rates, to render the final form of the exchange rate equation: e = (m- mf)- ¢(Y- Y f}+Jl(n - nf) (14) with n denoting the actual inflation rate. The long-run exchange rate is therefore determined by relative money supplies, relative income levels and relative inflation rates. Short-term deviations from PPP may occur, resulting in deviations from RlP. A real interest differential (RlD) could arise as follows: R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 3 (2000) No 1 27 Short-run adjustments (depreciation) towards the long-run equilibrium exchange rate are assumed to take place at a rate 0: &(de) = -(}(e - e) while the long-run depreciation is reflected by relative PPP: &(de) = (Il-Il j ) (15) (16) Combining equation (15) with (7), UIP, and then with equation (16) results in a rate of adjustment proportional to the real interest differential: - J e-e --o[(i-Il}-(;j"Il j )] (17) It is important to note that a real interest differential could only arise from deviations from either PPP or UIP or both. Deviations from VIP over any time horizon are ruled out by the hypotheses; while deviations from PPP are provided for only in the short run. It therefore follows that the only deviation from these parity conditions accommodated in this model, is a short-run deviation from PPP which will result in a short-run deviation from RIP. Equation (17) may then be said to capture the short-run deviations from parity conditions and thus the short- run overshooting of the exchange rate. A general equation of exchange rate determination may be expressed as: e = (m- mj)- ¢(Y- Y j)+ l(Il- II I }-~{(j. Il}-(;j" Ill)] (18) with the last term, RID, signifying short-term overshooting. In the long run, however, all of PPP, VIP and RIP are observed and this term will become zero, indicating that overshooting in the long run is ruled out. 5 THE STICKY-PRICE, DORNBUSCH MODEL OF THE RANDIDOLLAR EXCHANGE RATE 5.1 The theoretical model The theoretical model of the rand/dollar exchange rate is representative of the Dornbusch, sticky-price class of models. The specification includes the following variables: EXCH = f(M3, GOP, !NFL) (+ + ) with EXCH = LN(the spot exchange rate in rand/dollar) R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 28 SAJEMS NS Vol 3 (2000) No I M3 = LN[(SA M3 money supply)/(USA M3 money supply)] GOP LN[(SA real GOP)/(USA real GOP)] INFL SA inflation rate - USA inflation rate. The specification corresponds to the long-run version of the Dornbusch model (equation (13) above), except that the inflation differential is substituted for the differential between the expected rates of price changes. The spot rand/dollar exchange rate therefore depreciates (EXCH increases) if South Africa's monetary discipline becomes slack in comparison to monetary discipline in the US. Likewise, if the increase in the CPI accelerates domestic prices compared to the US, EXCH rises, signalling a depreciation in the dollar value of the rand. Economic growth may again effect an exchange rate appreciation, provided the domestic expansion of the GDP exceeds that of its foreign counterpart. 5.2 The data All South African data were taken from the Quarterly Bulletin of the South African Reserve Bank. The Consumer Price Index (CPI) was used to calculate the inflation rate. The 3-month bankers' acceptance rate was considered the representative short-term interest rate, which was deflated and subsequently featured in the error correction model (ECM), to be discussed below. The International Financial Statistics of the International Monetary Fund was the source for data on the United States. The 3-month Treasury Bill Rate represents the short-term US interest rate and appears in the ECM, after the US inflation rate was deducted, as the real short-term interest rate. The sample period commences in 1979, despite the ready availability of earlier data, and is decidedly shorter than what would be ideal. The reason for this is that South Africa maintained some form of fixed exchange rate system even after the demise of the Bretton Woods system until 1979. It was only from 1979 onwards that the exchange rate was permitted to float. A structural break thus manifested itselfin 1979, and it appeared meaningful to restrict the sample period to the era of floating. Although all relevant data for 1996 were available, 1995 was taken as the cut-off date of the sample period. It appears that 1996 was by no means an ordinary year for South Africa's foreign exchange markets. Unsubstantiated rumours of an overvalued currency triggered speCUlative sales resulting in a capital outflow and a sharp depreciation in the rand during February 1996. In addition, a mild subsequent recovery during March was rapidly reversed into a second run on the R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 3 (2000) No 1 29 rand in April, when balance of payments difficulties became apparent. As a result, the rand lost 20,6 per cent of its dollar value during the first four months of 1996. An exchange rate model comprising the fundamentals of exchange rate determination loses most of its explanatory power on such occasions as the 1996 currency crisis, when negative psychology prevails. The years 1997 and 1998 were no more normal in the sense that the exchange rate failed to stabilize and continued to be dominated by non-fundamentals. It is hoped that in future, with the benefit of hindsight, sense can be made of this interlude. An explanatory list of all the variables included in the long-run co integration relationship and the ECM is presented in Table 1: Table 1 List of variables EXCH LN(Spot rand/dollar exchange rate) M3 LN(Relative M3 money supply) GOP LN(Relative real GOP) !NFL Inflation differential RS Real short-term interest differential DUM Dummy variable 1 in 1990, 1991 and 1992 Tests for stationarity were subsequently performed. Data plots for EXCH, GOP, M3, INFL and RS respectively (see Figure 1) indicate that EXCH and M3 show defmite upward trends. A similar trend in INFL is less conspicuous, although the Augmented Dickey-Fuller test results (see Table 2) unambiguously indicate that it is integrated of order I. The variable RS tests potentially stationary. Inspection of its data plot reveals a slightly upward trend, with what appears to be a structural break in 1986. Incidentally, a similar break is observed in the !NFL series in 1986. . R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 30 SAJEMS NS Vol 3 (2000) No I Figure 1 Data plots for EXeH, GDP, MJ, INFL and RS: 1979 - 1995 1.6 1.2 0,8 0,4 0.0 -0,4 80 82 84 86 88 90 92 94 80 82 84 86 88 90 92 94 EXCHI -2.8 20..-------------------------, -3,0 -3,2 15 -3.4 -3.6 10 -3.8 -4.0 5 -4.2 -4.4 O~~~~~ __ ~~ __ ~~~ 80 82 84 86 88 90 92 94 80 82 84 86 88 90 92 94 I M31 I INFL! 4~--------------------~ o -12 80 82 84 86 88 90 92 94 R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 3 (2000) No 1 31 The results of the Augmented Dickey-Fuller tests for non-stationarity are reported in Tables 2 and 3. All variables appear to be integrated of order one, except for the variable RS which is stationary. Table 2 Series EXCH GDP M3 INFL RS Augmented Dickey-Fuller tests for non-stationarity, levels; 1979 -1995 Model Lags TT,T".TO $),$,0 Trend and intercept 0 -1,49 1,29 Intercept 2 -1,88 2,66 None 3 0,03 Trend and intercept I -3,06 4,17 Intercept 0 -0,44 0,19 None 3 2,65 Trend and intercept I -2,25 3,18 Intercept 0 0,66 0,44 None I -1,84 Trend and intercept 0 -1,56 2,32 Intercept 0 -2,06 4,27 None ° -0,49 Trend and intercept 1 -3,32 3,68 Intercept 0 -1,98 3,93 None 0 -2,03* *(**) Slgmficant at a 5(1)% level. Table 3 Series EXCH GDP Augmented Dickey-Fuller tests for non-stationarity, first differenced; 1979 -1995 Model Lags TT,T",TO $J.$,O Trend and intercept 1 -4,22* 6,18* Intercept : None Trend and intercept 0 -3,01 6,13* Intercept 2 -4,23** None R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . 32 SAJEMS NS Vol 3 (2000) No I Table 3 continued Series Model Lags TT.Tp.TO $J.$IO M3 Trend and intercept ° -2,23 2,49 Intercept ° -2,23 4,95* None INFL Trend and intercept 1 -5,01 ** 8,97** Intercept None RS Trend and intercept 0 -3,37 5,67* Intercept 0 -3,5* 12,27** None *(**) SIgnificant at a 5( 1)% level. 5.3 The estimation results of the cointegration model The Engle and Yoo (1991) three-step estimation technique was employed, whose first step tests whether the set of variables specified in the cointegration equation is co integrated, that is whether the particular combination of variables is in fact consistent with a long-run equilibrium relationship. The cointegration results for the first step are reported in Tab Ie 4. Table 4 First step estimation results, dependant variable: EXCHt Variable Coefficient Std. Error t-Statistic Probability M3, 0,842896 0,059393 14,19182 0,0000 GDP, -1,107141 0,078135 -14,16952 0,0000 INFL, 0,041884 0,007885 5,312114 0,0001 R-squared 0,951247 F-statistic 136,5808 Adjusted R-squared 0,944282 Prob(F -statistic) 0,000000 Figure 2 compares the actual values with the fitted values generated by the cointegration equation: R ep ro du ce d by S ab in et G at ew ay u nd er li ce nc e gr an te d by th e P ub lis he r (d at ed 2 00 9) . SAJEMS NS Vol 3 (2000) No 1 33 Figure:Z The cointegration equation: actual, fitted and residual values 0.5 0.3 0.2 0.0 0.1 0.0 ,-----l -0.5 -0.1 -0.2 -0.3 80 82 84 86 88 90 92 94 The cointegration regression augmented Dickey-Fuller test statistic was -2,86. This test consists of a unit root test on the residuals of the co integration equation. Critical values for the relevant response surfaces can be found in MacKinnon (1991). The response surface for any number of regressors, excluding any constant and trend components, 1~6, can be calculated as C(P) ~