Forthcoming: Applied Financial Economics 2000/01. On the equilibrium value of the peseta

Transcription

1 Forthcoming: Applied Financial Economics 2000/01 On the equilibrium value of the peseta I. Paya a, A. Duarte b and K. Holden c a Cardiff Business School, University of Wales College of Cardiff, UK b Department of Applied Economics and Economic Policy, University of Alicante, Spain. c Liverpool Business School, Liverpool John Moores University, UK Abstract This paper empirically analyses the equilibrium value of the peseta in the light of recent contributions in this field of study. Following MacDonald (1997), the approach to the long-run relationship between the real effective exchange rate of the peseta and its fundamental determinants focus on the reasons that keep the actual value of the peseta away from that predicted by the theory of PPP. The cointegration method is used to estimate the reduced form of a multilateral model for Spain for the period As a result, the estimated long-run exchange rate appreciates with positive shocks to differences in productivity, terms of trade and net foreign assets, and depreciates when price differentials increases. The equilibrium correction model helps to explain short-run deviations of the actual from equilibrium exchange rate and to forecast the peseta real effective exchange rate up to the fourth-quarter of Running title: On the equilibrium value of the peseta Keywords: Equilibrium Exchange Rate, Cointegration, Forecasts, Spain JEL Classifications: C32, F31 Corresponding Author: Professor Ken Holden, Liverpool Business School, 98, Mount Pleasant, Liverpool L3 5UZ

2 I. INTRODUCTION The study of the equilibrium value of the exchange rate has a long tradition in economics 1. Currently, this topic is of special interest in Spain. Having met the convergence criteria for participation in the Economic and Monetary Union (EMU), the parity of the peseta was set in December 1998 at 1 Euro = pesetas with effect from January In this context, the central purpose of this paper is to examine the consistency of the actual market value of the peseta exchange rate with its long-run equilibrium path. In other words, we shall explore if the exchange rate of the peseta against its main commercial partners is consistent with the evolution shown by the major fundamental variables. This will be particularly useful in assessing if the actual exchange rate of the peseta is undervalued or overvalued with regard to the other EMU currencies. At the same time, it is expected to throw some light on whether changes will be needed in the Spanish economy in order to cope with the new situation; that is, with the loss of the exchange rate as an instrument of macroeconomic policy. Within this new context adjustments will be required in other areas of the economy, such as prices, wages and competitiveness, if the current market value of the peseta is different from its equilibrium value or the one dictated by fundamental macroeconomic variables. Modelling the long-run behaviour of the exchange rate is not a simple task from a theoretical or from an empirical point of view. The theory of purchasing power parity (PPP) is one of the most common approaches to the analysis of the equilibrium real exchange rates. However, the empirical evidence about the validity of this theory, in its different versions, offers mixed results. On the one hand, a growing amount of evidence demonstrates that, in industrialised countries, PPP represents a reasonable characterisation of long-run movements of nominal exchange rates and traded goods 3. On the other hand, Frenkel (1978) and Krugman (1978) have found evidence that PPP 2

3 does not explain the short-term dynamics of exchange rates. To this evidence should also be added the lack of agreement amongst econometricians on the most appropriate approach and technique for modelling long-run equilibrium relations 4.In this paper, after a brief review of the current literature on this topic, the equilibrium value of the peseta will be explored in the light of recent contributions in this field of study 5. In particular, our approach to the long-run relationship between the real effective exchange rate of the peseta and its fundamental determinants will focus on what keeps the actual value of the peseta away from that predicted by the theory of PPP. The cointegration method will be used to estimate the reduced form of a multilateral model of the real effective exchange rate of the peseta. The paper is organised in the following way. In section II some key concepts in alternative approaches to assessing the equilibrium value of an exchange rate will be discussed, along with a brief account of the selected econometric methodology. In section III the data sources and definitions will be presented, as well as estimates of the long-run exchange rate and the short-run dynamic model. The model is estimated for the sample period 1977: Q1 1997: Q1, and used to generate forecasts up to 1998: Q4. Finally, the conclusions are summarised in section IV. II. THEORETICAL APPROACHES AND ECONOMETRIC METHODOLOGY. The background The theory of PPP is one of the approaches traditionally employed to determine the equilibrium value of exchange rates. According to this theory, the evolution of the equilibrium value of the real exchange rate (that is, the nominal exchange rate adjusted by some index of prices), is relatively constant and, therefore, fluctuations of the nominal exchange rate cancel out fluctuations of relative prices. The versions of PPP traditionally 3

4 mentioned in the literature are: the law of one price, which relates exchange rates to prices of individual, homogeneous goods in different countries; absolute PPP, which relates exchange rates to overall price levels; and relative PPP, which relates exchange rates to changes in inflation rates. 6 This latter version, also called strong form PPP, is highly controversial in empirical research. In this paper we shall concentrate on this strong form version of PPP and will use recent developments to model the long-run behaviour of the real effective exchange rate of the peseta. Another approach to determining the equilibrium exchange rate is the well-known macroeconomic balance approach. This is related to the concept of fundamental equilibrium exchange rates (FEER), and has been extensively developed by Williamson (1985, 1994), following the line of research initially proposed by Swan (1963). Currently this approach is being use by the staff of the International Monetary Found (IMF)(e.g. Clark, Bayoumi and Symansky, 1994, and MacDonald, 1995) and the equilibrium exchange rate is defined as the value that is consistent with an internal and external balance over the medium term. Internal balance is defined as achieving the underlying level of potential output and external balance is defined as achieving an equilibrium position in the current and capital accounts. In applied work, internal balance is usually related to the concept of macroeconomic stability, and in particular with the level of unemployment consistent with a nonaccelerating rate of inflation (NAIRU). In fact, NAIRU is the level of unemployment consistent with a situation of nominal stability, since at this rate it is assumed that there is no pressure for inflation to rise or fall. Following this line of analysis, potential output can be defined as the level of real output consistent with the NAIRU. However, the specification of the external balance is not so clear. Broadly speaking it can be defined as the net flow of international capital that corresponds to the equilibrium level of national 4

5 saving and investment. Although the FEER is an appealing approach to examining the evolution of the current and equilibrium exchange rates, it has some limitations. One of them rests in the difficulties in specifying a complete multilateral structural model, with the additional problem that it does not provide an empirical link between the real exchange rate and its determinants (MacDonald, 1997). Another difficulty is related to the normative choice of the model to be used, and particularly in setting the target for the current account of the balance of payments (Black, 1994). An alternative approach, which to a great extent will be followed in this paper, consists of studying the forces that make the nominal exchange rate deviate from its corresponding value of PPP. MacDonald and Marsh (1997), have demonstrated it can establish a sensible long-run relationship for single currencies during the period of the recent float, and the econometric methodology associated with it has revealed important forecasting advantages over other well-known techniques. There are four major reasons that explain departures of the nominal exchange rate from its corresponding PPP value (Clark, et al, 1994): (1). Hysteresis effects. These are due to adjustment costs in international trade 7. In the short run, trade cannot fully respond to (possibly temporary) changes in the exchange rate because of the presence of adjustment costs. These costs include introducing new products, changing distribution channels and varying the level of production. By their very nature, these costs justify the slow response in the short run on the part of exporters to changes in the exchange rate. However, the gap between the current exchange rate and its PPP value eventually becomes so large that action to correct the relative price 5

6 change is inevitable. (2). Price rigidities in terms of the currencies in which the goods are sold. This explanation was given in the seminal paper written by Dornbusch (1976). Overshooting of the exchange rate relative to its equilibrium value results from differences in the speed of adjustment between the financial and the goods markets. The evidence suggests that exogenous shocks tend to lead to more rapid adjustment in financial markets than in goods markets. (3). Imperfect substitution between traded goods. This effect is due to the existence of product differentiation between countries and, therefore, to the influence that different rates of growth and income elasticity have on the long run trend of exchange rates (Krugman, 1989). Associated with this argument there is also the question of how to distinguish between changes in the real exchange rates that are due to changes in demand and to structural changes that affect the equilibrium exchange rate. (4). Different rates of technological change in the traded and nontraded sectors. This effect refers to the differential evolution shown by prices and productivity between these two sectors (Balassa, 1964). Prices of tradable goods are determined on a worldwide basis while prices of nontradables depend on conditions in the domestic market. As a result, tradable goods (mainly manufacturing) face higher competition than nontradable (notably services) and consequently major advances in productivity tend to concentrate in the tradable goods sectors. This explains two important and related questions: on the one hand, that the relative price of tradable goods tends to rise at a lower pace in sectors where productivity is high. On the other hand, this also explains the secular long-run 6

7 trend towards the appreciation of the currency when measured by some deflator (GDP) or price index (CPI) which includes both types of goods, that is, traded and nontraded. In what follows we shall postulate a simple model to explore the actual behaviour of the exchange rate in terms of relevant economic variables. The aim of the model is to define an equilibrium condition to assess whether the current exchange rate is overvalued, undervalued or in equilibrium. Equilibrium is defined, in a behavioural sense, as the value given by a set of relevant economic variables that explain movements in the actual real exchange rate in a well-define statistical sense 8. As will be seen, this equilibrium condition includes two major components. One is the long-run component of the real exchange rate and the other is the short-run component. While the long-run component is determined by some of the above listed causes of persistent departure of the exchange rate from its equilibrium value, the short-run component relies on the linkage between the uncovered interest parity condition and the real exchange rate. A clear advantage of this approach is that departures of the actual real exchange rate from its corresponding equilibrium value are related no only to economic fundamentals but also to transitory factors and random disturbances. Furthermore, an attempt will be made to adapt existing theory to key features of the Spanish economy during the period under analysis. Finally, the usefulness of this model will be assessed by its ability to replicate relevant historical episodes of misalignments in Spain as pointed out by some analysts and also by its ability to forecast subsequent real exchange rate movements. The model Having mentioned the major factors that keep an exchange rate away from equilibrium, 7

8 we now turn to set out the basic features of the model to be used to estimate the equilibrium value of the peseta. From the above discussion it is clear that the underlying equilibrium exchange rate can be altered not only by relative prices, as is the case in the competitiveness model, but also by other real and nominal factors. In turn, these factors can be associated with developments in the international and domestic financial markets, commodities shocks, changes in trade policy, etc. We start with a definition of the real exchange components to determine the equilibrium value of the real exchange rate. The real exchange rate (q t ), taking as reference the consumer price index (p t ), can be defined as: (1) q t = s t p t * + p t where s t denotes the nominal spot exchange rate, defined as the foreign currency price of a unit of home currency. Lower case letters indicate logarithms of the variable and an asterisk denotes a foreign country. A similar relationship may be defined for the price of traded goods as (2) q t T = s t p t T* + p t T where the T superscript indicates that the variable is defined for traded goods. The general price index entering (1) may be decomposed into traded and non-traded components as: (3) p t = (1 α t )p T NT t + α t p t (3 ) p * t = (1 α * t )p T* t + α * NT* t p t where the α s denote the shares of nontradable goods sectors in the economy, and NT denotes a non-traded good. 8

9 Substituting expressions (3), (3 ) and (2) in (1), a general expression for the long-run equilibrium real exchange rate, q t, may be obtained as (4) q t q T t + α t (p NT t - p T t ) α * t (p NT* t - p T t ) As can be seen from the right hand in expression (4), two different components help to explain the long-run evolution of the real exchange rate: first, the real exchange rate for tradables q T t, that is the relative price of tradable goods at home and abroad expressed in a common currency, and second, the differential evolution of sectoral prices between countries weighted by the corresponding share of non-tradables in the economy α t (p NT t - p T t ) α * t (p NT* t - p T t ) 9. To examine the influence of each of these components on the equilibrium value of the exchange rate we focus on four major forces that may drive movements in the real exchange rate 10 : differential productivity growth, terms of trade, net foreign assets, and price differentials. Differential productivity growth, as is now widely known, systematically affects the relative price of home and traded goods. As was previously mentioned, a traditional argument is the Balasa-Samuelson hypothesis, which provides a clear explanation to the fact that long-run movement in the real exchange rate is driven largely by differential productivity growth in the traded and non-traded sectors. The terms of trade may change as a consequence of changes in trade patterns. In this respect, Trefler (1995) has shown that home bias in consumption is required to explain trade patterns and volumes, and therefore this is a potential argument to explain the appreciating effect of an improvement in a country s terms of trade. In fact, this effect can occur for two major reasons. One is because domestic tradables might enter with a greater weight in the domestic consumer price index that in the consumer price index of 9

10 the benchmark country. The other reason depends on the extent that demand factors can explain persistent and often large deviation from PPP (Genberg, 1978). In this particular case, an improvement in the terms of trade (i.e. the ratio of domestic export unit value to import unit value), could appreciate the real exchange rate via a wealth effect on the demand for non-traded goods. Thus, assuming without loss of generality that α t = α * t, the effects of the second term on the right hand side of expression (4), can be summarised as follows: (5) (p NT t - p T t ) (p NT* t - p T t ) = f(prdt, tt) where, prdt is a measure of productivity differentials and tt represents the terms of trade. As noted above, an increase in any of these variables will result in anappreciation of the general real exchange rate. The relationship between fiscal policy and exchange rates has recently been addressed in a number of studies 11. While the experience suggests that the impact of changes in fiscal policy on nominal and real exchange rates in the short run is ambiguous, the theoretical direction of the longer-run effects appears to be clearer (Clark and Laxton, 1995). These authors have shown that under conditions of high international capital mobility, the longrun effect of a sustained reduction in the government budget deficit that raises national saving and reduces the ratio of government debt to GDP will eventually lead to a real exchange rate appreciation. A country that saves more than its trading partners will accumulate more foreign assets and its currency will strengthen relative to other currencies. Finally, the effect of price differential on the real exchange rate for tradables as a result of 10

11 asymmetrical adjustment speeds in goods and asset markets (Dornbusch, 1987). This result is of particular relevance within the context of the Spanish economy, characterised by rigidities in the labour market (Viñals and Jimeno, 1996). In the world market for products, as is known, the relative price of domestic and foreign variants of the product is ultimately determined by relative unit labour costs measured in a common currency. In this context, given sluggish wages for contract reasons or institutional factors, exchange rate movements are reflected in changes in the real exchange rate. Therefore, the factors affecting the real exchange rate for tradable goods can be represented by the following expression. T (6) q t = g(pdn, nfa) Where pdn represents price differentials and nfa is net foreign assets. Again from the above discussion the expected impact on the real exchange rate of pdn is negative while in the case of nfa it is positive. Combining (5) and (6), the long-run equilibrium real rate can be expressed in terms of the following functional form (7) q t = f (prdt, tt, pdn, nfa) The above discussion has been limited to the discussion of key determinants of the longrun equilibrium exchange rate. Now we shall concentrate on the mechanisms of adjustment from the short run to the long run of the actual exchange rate. For this purpose we start with the familiar open economy Fisher equation that shows the link between the nominal interest rates and the expected rate of depreciation. Assuming perfect international mobility of capital and risk neutral speculation this linkage is: 11

12 (8) i t * = i t + s e t+k where i and i* are the nominal interest rates at home and abroad, is the first difference operator and the superscript e stands for the expectation operator. Subtracting from both sides of equation (8), the expected rate of inflation differential ( p* e t+k - p e t+k ) - yields an equation in terms of real interest rates: (9) r t * = r t + q e t+k According to (9) real interest parity prevails when the real interest differential (r t * - r t ) equals the expected rate of real appreciation q e t+k. Assuming that the actual real exchange rate adjusts gradually to the equilibrium level: (10) q e t+k = 1/γ (q t q t ) where 1/γ is the speed of adjustment. Combining (9) and (10), the equilibrium condition for the real exchange rate is: (11) q t = q t + γ ( r t r t *) This result shows that the real exchange rate is composed by two components: the longrun component of the real exchange rate which, in turn, is determine by factors already discussed (such as productivity differentials, terms of trade, net foreign assets, and price differentials), and the real interest rates differentials. The implications of this model are quite obvious. When real interest rates at home exceed those abroad the real exchange rate will appreciate relative to its trend value. For example, a rise in interest rates following a restrictive stance of monetary policy would bring about a transitory real appreciation. But also as argued above, structural disturbances such as productivity differential growth will have a systematic impact on relative non-traded goods prices and therefore on real interest rate differentials. 12

13 In the next section we shall explore in detail the dynamic process of adjustment of the static equilibrium condition for the real exchange rate derived in equation (11). It will be shown that the technique of cointegration provides a suitable framework to explain the equilibrating mechanism between movements of the actual real exchange rate and its economic determinants. In what follows we shall postulate a simple reduced form equation model that relates the above listed causes of departure of the exchange rate from its equilibrium value to some specific explanatory variables. Econometric methodology In this section we shall concentrate on the process of identification and estimation of the long-run relationship between the effective real exchange rate and its fundamental determinants. Furthermore, we shall also examine the dynamic adjustment to the longrun path taking into account the long-run implications in the short-run analysis. Long-run analysis The cointegration technique provides a suitable framework for examining long-term comovements between a set of time-series variables. The economic interpretation of cointegration is that if two or more variables are linked to form a long-run (or equilibrium) relationship, then even though the series may be non-stationary (or contain stochastic trends) they will move closely together over time and the difference between them will be stable or stationary. In other words, the presence of cointegration implies the existence of a long-run equilibrium to which the economic system converges over time. Johansen (1988, 1991) and Johansen and Juselius (1990) have proposed a full- 13

14 information maximum likelihood method for estimating cointegrated relationships and this will be used to determine the long-run relationship between the real effective exchange rate and the fundamentals for the peseta. Briefly speaking, given a group of non-stationary series, we are interested in determining whether the series are cointegrated, and if they are, in identifying the cointegrating (long-run equilibrium) relationships. Specifically, if the k variables in equation (1) are integrated of order one I(1) and are cointegrated, and are represented by the vector y, and assuming that y has a vector autoregressive (VAR) representation of order p then: (2) y t = A 1 y t A p y t-p + B x t + ε t, where x t is a d vector of deterministic variables, and ε t, is a vector of innovations. Equation (2) can be written in vector equilibrium correction model (VECM) form as: (3) y t = Π y t-1 + ΣΓ i y t-i + Bx t + ε t, where: Π = Σ A i I, Γ i = -Σ A j. The Granger representation theorem asserts that if the coefficient matrix Π has reduced rank r < k, then there exist k x r matrices α and β each with rank r such that Π = α β and β y t is stationary 12. Thus, r is the number of cointegrating relations (the cointegrating rank) and each column of β is the cointegrating vector. In terms of our model, this means that if the exchange rate and the variables that are considered to be fundamentals form an equilibrium relationship, then they should not deviate from each other too much for too long. This is achieved when the error term ε t is stationary. Furthermore, the exchange rate that is predicted from this equation is the long-run equilibrium rate that is defined by the fundamentals at each time period t. The elements of α are known as adjustment parameters in the vector error correction 14

15 model and indicate the speed with which the system responds to last period's deviation from the equilibrium level of the exchange rate. In our model, this means that if the exchange rate in the last period was overvalued relative to the fundamentals, in the current period the exchange rate corrects itself by a proportion α of the deviation. In summary, Johansen's method provides a framework for estimating the Π matrix in an unrestricted form, and then testing whether we can reject the restrictions implied by the reduced rank of Π. Overall, to implement the Johansen method requires: testing the order of integration of each variable that enters the multivariate model; setting the appropriate lag-length of the VAR in order to ensure Gaussian error terms in the VECM, and determining whether the system should be conditioned on any predetermined I(0) variables; testing for reduced rank; identifying whether there are trends in the data; testing for weak exogeneity. Short-run analysis When there is one cointegrating vector in our specification we shall introduce the equilibrium correction model (ECM) in the short-run analysis. The model is constructed following the spirit of a general-to-specific approach, and therefore our initial model is specified with enough lags in all variables until the residuals are white noise. The general short-run model can be expressed as: (4) zepta t = a(b) zepta t-1 + b(b) z t + α(zepta t-1 - βz t-1 ) + ε t where B is the lag operator, the vector z contains explanatory variables from (1) and the residual, ε, is white noise. The term, α(zepta t-1 - βx t-1 ), is the equilibrium correction term and β is the vector of cointegrating parameters. The final model is completed after 15

16 removing the statistically insignificant variables. III. EMPIRICAL RESULTS The data All variables, except the rates of interest, have been transformed using the natural logarithmic operator. To measure the real effective exchange rate we use the multilateral CPI-based real effective exchange rate for Spain relative to its partner countries (LREERCP) 13. The sample period is 1977:Q1 to 1997:Q1. By construction, a rise in LREERCP implies an appreciation of the real effective exchange rate. Figure 1 shows the evolution of this variable during the sample period. To capture the influence of the explanatory variables as noted in the previous section we use the following variables (see Figure 2). The proxy for productivity is LDIFPRDT, which is the ratio of the domestic consumer price index (CPI) to the producer price index (PPI), relative to the equivalent foreign (trade weighted) ratio 14. Price rigidities due to frictions in the labour and the goods markets have been captured by the price differential LPDN between Spain and its trading partners; in particular, LPDN is equal to the ratio of the Spanish Producer Price Index relative to the equivalent trade-weighted foreign index. The terms of trade, LTT, is constructed as the ratio of domestic export unit value to import unit value. Finally, LNFA is the ratio of net foreign exchange reserves to the Spanish GDP. The variables used to model the short-run dynamics consistent with the long-run equilibrium are: the real price of oil, LROILPP, defined as the ratio of the nominal price of oil (pesetas/ton) to the Spanish Producer Price Index. To measure the world interest 16

17 rate we use RLTIRGM, which is the real long term interest rate of Germany. The influence of policy intervention has been capture by DUMSHOCKS and DUMDEV; the latter contains the following devaluations: 2/76, 7/77, 6/12/82, 17/9/92, 23/11/92, 14/5/93, and 6/3/95. Additional information on data definitions and sources can be found in Appendix A. Unit root tests The data are quarterly and in seasonally unadjusted form to avoid distortion of the underlying properties. The test for unit roots (seasonal and nonseasonal) is the one proposed by Hylleberg et al. (1990) (HEGY). For a series {x t }, this test involves various t and F tests of the coefficients of the regression (5) (1 B 4 )Y t = π 1 Y 1t-1 + π 2 Y 2t-1 + π 3 Y 3t-2 + π 4 Y 3t-1 + ε t where ε t is white noise, and Y 1t = (1+B+B 2 +B 3 ) x t, Y 2t = -(1-B+B 2 -B 3 ) x t, Y 3t = -(1-B 2 ) x t, in which B is the lag operator. We use four different deterministic components. These are (i) an intercept, seasonal dummies and a time trend. (ii) an intercept and a time trend, (iii) an intercept and seasonal dummies (iv) an intercept, and (v) none of them. The component F- and t-tests need the disturbances of (5) to be uncorrelated. We check this using the Lagrange multiplier test for autocorrelation and add lagged values of Y t when required in order to remove autocorrelation. Table 1 presents the results of the HEGY test. Overall the results support the hypothesis that each of the series does indeed contain a unit root at the zero frequency but none at the seasonal frequencies. In the particular case of the variable DIFPRDT, even though π 3 = 0 can be accepted, implying a four-quarter (annual) seasonal unit root, the test on π 4 17

18 and the joint F-test reject the null hypothesis of seasonal unit root. However, the variable PDN shows signs of seasonal unit root when seasonal dummies are included in the model at two-quarter (half year) and at four-quarter (annual) frequency. Therefore, we conclude that all the variables are I(1). Model estimation First the unrestricted VARs were estimated with the real exchange rate (LREERCP) and the fundamental variables: productivity differentials (LDIFPRDT), price differentials (LPDN), net foreign assets (LNFA), and the terms of trade (LTT). Each of these variables is regressed on its own lagged values and lagged values of the other four variables. A constant term and two dummy variables are also included. One dummy variable is (DUMDEV) which, as defined above, takes into account some specific devaluations of the peseta. The second dummy variable (DUMSHOCKS) was found necessary to take account of outliers in the data. For all variables, lag length selection has been done starting with the longest lag. To select the lag length, the multivariate generalisation of the Akaike Information Criterion (AIC) and the Schwarz Criterion (SC) have been used; the latter criterion, as an alternative to the AIC, imposes a larger penalty for additional coefficients. The lag length for the VAR is set at three (k=3), and the model evaluation diagnostic tests are provided in Table 2. According to this table, the residuals can generally be considered to be Gaussian. The only system problem is the rejection of normality in LTT, due to excess kurtosis and skewness problems. LNFA also shows problems of heteroscedasticity. Figure 3 plots recursive estimates of the residuals for each equation. This confirms that the performance of the VARs is generally satisfactory. 18

19 The results of the cointegration tests are shown in Tables 3. In this table, the eigenvalues are presented in the first column, while the second column gives the Likelihood Ratio (LR): Qr = - T Σ log (1 - λ) For r = 0,1,...,k-1, and λ is the i-th largest eigenvalue. Qr is the trace statistic and is the test of H1(r) against H1(k). In the case of LREERCP, the LR test rejects the hypothesis of no cointegration but not the hypothesis of at most 2 cointegration equations at 5% significance level. 15 Below the results of the cointegration rank test, estimates of the unnormalized and normalised cointegrating coefficients are provided. The numbers in parentheses under the estimated coefficients are the asymptotic standard errors, and as can be seen, all the estimated coefficients are not only significant but also have the expected signs. The effective real exchange rate appreciates in the long run if the terms of trade improve (LTT), or the domestic country s net foreign asset position relative to GDP (LNFA), or the productivity differential (LDIFPRDT) increases. This outcome indicates that the variables included in the cointegrating equations can be considered as fundamentals. Finally, the price differential (LPDN) is another coefficient of interest; its negative sign indicates that an increase in price differential leads to a depreciation of the peseta. The results presented above do not indicate whether the long-run relationship we have found reflects the endogeneity of the fundamentals, or the determination of the exchange rate or both. An understanding of the causal links between these variables is not only interesting in its own right but also it would imply that exchange rates changes are 19

20 forecastable. Our first step in testing for exogeneity, or more accurately, whether any of our variables in the right-hand side of the reduced form equation are weakly exogenous with respect to the parameters of the system (α, β), is to test for the presence of all zeros in row i of α ij, for i = 2, 3, 4, 5, and j = 1, indicating that the cointegrating vectors in β do not enter in the equation determining these variables. The results reported in Table 4 imply that the vector of fundamentals, with the exception of the variable price differentials 16, are weakly exogenous in the sense of Engle et.al (1983). In other words, this means that when estimating the parameters of the model (i.e. Π, α, β), there is no loss of information from not modelling the determinants of y it, for i=2, 3, 4 and 5. These variables are weakly exogenous to the system and can enter on the right-hand side of the VECM. Next we test for more general Granger-causality using standard tests on the vector autoregression level representation of our system. As demonstrated in Sims et.al. (1990), standard inference procedures are valid in this case under the maintained hypothesis of one cointegrating vector and provided that we test the exclusion restrictions on one variable at a time. Based on the results reported in Table 5 we can not reject the null hypothesis that the real exchange rate does not Granger-cause the vector of fundamentals. Therefore it appears that Granger causality runs one-way from the vector of fundamentals to real exchange rate and not the other way. Figure 4 shows the impulse response functions between the real effective exchange rates and fundamentals. In this figure, following a one standard deviation shock to the fundamentals, the REER takes some time to reach its equilibrium value. Clearly, this behaviour of the REER might be reflecting some rigidities in the domestic market, which 20

21 was not liberalised until the mid 80s. The short run adjustment mechanism is modelled as an equilibrium correction model (ECM). The cointegrating vector from the Johansen procedure is used in the ECM, along with current and past differences in the fundamentals and other variables that affect the real effective exchange rate in the short-run. Excluding non-significant variables, the model with general lags reduces to the results shown in Table 6. The results suggest that the model capture appropriately the information in the data. The coefficient of the equilibrium correction term (ZDEVI t-1 ) is statistically significant and negative, implying that the model is converging to the long-run path. The model contains one lagged exchange rate that is positively correlated with the current rate; in other words, this outcome may be consistent with the view of some analysts who tend to predict the future rate in relation to past movements of rates. Also, short run exchange rate fluctuations are explained by changes in the price of oil (LROILPP) 17, changes in the real long-term interest rate in Germany (RLTIRGM), and two dummy variables (DUMDEV) and (DUMSHOCKS) to capture policy interventions measures 18 Implications Figure 5(a) plots the CPI-based real effective exchange rate (LREERCP) against its long-term equilibrium value (ZEPTA) as calculated from the cointegrating vector estimated above. Movements of the estimated long-run Spanish effective exchange rate combine the individual effects of each of the fundamentals. Below, Figure 5(b) shows the evolution of misalignments (ZDEVI) that is, the deviation of the actual exchange rate from the estimated long-run equilibrium exchange rate and measured as the difference between them (ZDEVI = LREERCP ZEPTA) 19. Let us examine the implications of 21

22 each of these. In 1977, the decline of the estimated long-run Spanish effective exchange rate was partially restored during 1978 and 1979, by the joint influence of productivity differentials, the terms of trade and the accumulation of international reserves. From 1980 until 1983, the equilibrium exchange rate depreciated sharply as the terms of trade deteriorated and price differentials grew above trend. Since this latter year, and particularly, after 1986, the equilibrium value of the peseta started to recover due to the better performance shown by productivity differentials, the terms of trade and net foreign assets. Such improvement, however, was partially offset by the negative effect of the rate of growth of price differentials. The upward trend shown by price differentials can be seen as a sign of substantial friction in the labour and the good markets. In mid-1985, as part of a policy intended to facilitate Spain s transition into full membership in the EC, the Spanish authorities implemented a number of policy measures in the area of external liberalisation. The substantial relaxation of the rules governing foreign direct investment was followed by a massive inflow of foreign capital as reflected by the sharp increase in the accumulation of international reserves. This pattern lasted until 1992, when most currencies from the EMS suffered strong speculative attacks and the peseta had to be devalued in September and November 1992, and in May According to the ECM, short-run deviations are explained primarily by the contemporaneous first difference in the price of oil and by the first difference in real long-term interest rates in Germany lagged two periods. In addition, the adjustment coefficient that captures deviations from equilibrium is rather small indicating a long 22

23 period of time for adjustment to take place. It is also worth mentioning that even though the long-run specification affects the final short-run specification, none of the differenced fundamentals by itself have a significant effect in explaining short-run deviations. From Figure 5(b), it is apparent that the actual exchange rate deviated from the estimated equilibrium value for long periods. Overall it was undervalued until mid-1986, the year of Spain s accession to the European Community (EC). Until 1986, the peseta had been managed flexibly for a number of years, with the Bank of Spain intervening in the foreign exchange markets to prevent undesirable fluctuations and to ensure the maintenance of competitiveness for Spanish exports. It should be remembered, however, that during the second half of the seventies and the early years of the eighties the exchange rate policy developed in an adverse environment. This environment was characterised by the impact of the second energy crisis, the international economic recession and the change of stance in monetary and exchange rate policy in the U.S.A. During this period three devaluations were carried out (February, 1976, July, 1977, and December, 1982), in order to compensate for the loss of competitiveness due to the high level of domestic inflation relative to Spain s competitors. Furthermore, can be considered a period of adjustment and preparation for liberalisation, while was a period of external openness with the elimination of exchange rate controls. After 1986, the evolution of the actual exchange rate is more in line with fundamentals, reflecting the changing view of the monetary authorities as far as exchange rate policy is concerned 20. Finally, pressures from an overvalued peseta (1990: Q1-1993: Q1) in the context of rising interest rates and speculative attacks forced the authorities to devalue the currency 21. At the end of the sample period, 1997: Q1, the position of the peseta, as 23

24 predicted by the ECM, is slightly undervalued (0.7 percent). An assessment of this position from January 1999 onwards is important for an obvious reason. With the creation of the Euro as a new currency in circulation, the exchange rate as an instrument of economic policy no longer exists and the economy will be strictly dependent on the evolution dictated by economic fundamentals. To this end, in the next section we shall concentrate in forecasting the equilibrium value of the peseta. Forecasts The estimated ECM was used to generate forecasts for the quarterly equilibrium value of the real effective exchange rate during the post-sample period 1997:Q1 1998Q4. To test the forecasting ability of the model we used out-of sample forecasts 22 of the log real effective exchange rates over 1996:Q1-1997:Q4 23. Table 7 reports the static one-period ahead forecasts. The Root Mean Square Error criterion (RMSE) was used to assess the performance of alternative models, namely, our model, a Random Walk and an ARIMA (0, 1, 1). Actually, our model outperforms both the Random Walk model and the ARIMA model from the fourth quarter onwards. In Table 8, the forecasting ability of the model is shown using a dynamic out-of sample forecast of the log real effective exchange rate from one to eight quarters ahead. Again, the model is capable of forecasting the exchange rate one-year ahead more accurately than the Random Walk or the ARIMA model as measure by the RMSE or the Percentage Absolute Error (PAE). Next a sequence of one-step-ahead forecasts was calculated using actual rather than forecasted values for lagged dependent variable. The forecast has been made using all available information at the time of the forecast 24. Figure 6 shows the within-sample predictive performance of the model and figure 7 the out-of-sample forecasted values. 24

25 According to Table 9, the equilibrium value of the peseta at 1998:Q4 would be This outcome, though taken with caution, means that the Spanish Peseta Real Effective Exchange Rate in January 1999 was roughly equal to its equilibrium value. IV. CONCLUSIONS Since January 1999 Spain has faced new challenges as a full partner in a more economically integrated Europe. Monetary and exchange rate policies are tied to decisions taken within the new European Central Bank and this means that Spain has to put some additional effort into coping with domestic macroeconomic imbalances. This situation still leaves open the question as to whether the peseta exchange rate is actually reflecting its corresponding equilibrium value. This potential problem has been addressed in this paper. In particular, this paper empirically analyses the Spanish peseta real effective exchange rate in a long-run context, and the outcome from a reduced form multilateral model was then compared with the actual values. To a great extent, our results reflect the change in view of the Monetary Authorities after 1986, the year of Spain s accession to the EC. Since then, the actual value of the peseta real effective exchange rate has not departed too far from the equilibrium value. The exception was the time of the speculative attacks on some currencies within the EMS in late 1992, when the pound sterling and the Italian lira decided to withdraw from the system. However, our forecast value for the peseta real effective exchange rate for the fourth-quarter 1998 is almost equal to the expected actual value. Therefore, no major changes to the Spanish economy are needed at present on account of the rate at which Spain joined the Euro. This result, however, should be taken with caution because it clearly depends on the methodology applied in this paper and on the forecasted values of 25

26 major exogenous variables. 26

27 Table 1. Seasonal Unit Root Tests π 1 = 0 VARIABLES π 2 = 0 π 3 =0 π 4 =0 π 3 =π 4 = 0 SSRU SSRR LM(4Lags) LAGS Nº OBS K REERCP I, SD, Trend * * -5.74* * I, SD, * -4.66* -5.82* * I, Trend * -4.76* -5.84* * I * -4.73* -5.91* 45.07* None * -4.34* -6.23* 43.64* * DIFPRDT I, SD, Trend * * 29.59* I, SD, * * 29.54* I, Trend * -2.42* -3.04* 8.37* * I * -2.44* -3.06* 8.49* None * -2.39* -3.14* 8.62* PDN I, SD, Trend * I, SD, * I, Trend * -2.29* -2.20* 5.42* I * -2.22* -2.25* 5.37* None * -2.24* -2.28* 5.49* TT I, SD, Trend * -4.35* -2.63* 15.39* * I, SD, * -4.28* -2.73* 15.32* * I, Trend * -4.31* -2.45* 14.15* I * -4.23* -2.57* 14.11* None * -4.14* -2.62* 13.85* NFA I, SD, Trend * -3.85* -6.47* 41.80* I, SD, * * 40.16* I, Trend * -4.18* -6.73* 49.02* I * -3.65* -7.15* 47.18* None * -3.53* -7.34* 47.72*

28 ROILPP I, SD, Trend * -3.85* -4.57* 25.24* 3.01E E I, SD, * -3.89* -4.60* 24.02* 3.10E E I, Trend * -3.90* -4.60* 23.70* 3.18E E I * -3.94* -4.62* 24.26* 3.18E E None * -3.68* -4.81* 23.69* 3.38E E * RLTIRGM I, SD, Trend * * 28.24* I, SD, * * 28.56* I, Trend * -3.43* -5.75* 29.42* I * -3.40* -5.84* 29.75* None * -2.84* -6.23* 28.88* Notes. Columns 3 to 7 report t-values on the π i, where i = 1,...4, derived from estimates of equation (4). The tests for a unit root at frequency 0, and ½, are based on the t- statistics of π 1 and π 2 respectively. Testing for a unit root at the annual frequency involves t statistics on π 3 if π 4 =0 because it has a complex root (+i, -i), or a joint F test for π 3 =π 4 =0. The formula is ( SSRR SSRU ) * ( N º OBS K) F = SSRU * Q where Q is the number of restrictions, in this case the restrictions are two. SSRU is the sum of square residuals of the unrestricted equation for the unit root test. SSRR is the sum of square residuals of the restricted equation for the unit root test, namely, without Y 3t-2 and Y 3t-1. The lag length used in the regression was chosen using both the Akaike and the Schwarz selection criterion. (*) denotes that the null hypothesis is rejected at the 5% significant level. Critical values for seasonal unit roots at the 5% of significant level and with a sample of 100 are from Hylleberg et al (1990). Deterministic components are: intercept (I), seasonal dummy (SD), trend or none of them. In column 10, the LM test, an asterisk denotes rejection of the null hypothesis of no serial correlation with 4 lags at the 5% significant level. CRITICAL VALUES π 1 =0 π 2 =0 π 3 =0 π 4 =0 π 3 =π 4 =0 I, SD, Trend I, SD I, Trend I None

29 Table 2: Residual Misspecification test Sample period: 1977: Q1 1997: Q1 LREERCP LDIFPRDT LPDN LNFA LTT Std. Dev Skewness Kurtosis Jarque-Bera 2.03 (0.36) 1.64 (0.44) 1.72 (0.42) 2.10 (0.35) 129.4** (0.00) LM - F (3,78) 0.13 (0,94) 1.35 (0.27) 2.32 (0,08) 0.57 (0.64) 2.3 (0.09) ARCH F (3,77) 0.60 (0.61) 0.70 (0,55) 0.33 (0.80) 0.33 (0,79) 0.04 (0.98) Het. χ 2 (33) (0.41) (0.47) (0.19) ** (0.00) (0.41) ** Denotes rejection at the 1 percent significance level; * denotes rejection at the 5 per cent significant level. P- values between brackets. 29

30 Table 3. Johansen Cointegration Tests: Trace Statistics Likelihood 5 Percent 1 Percent Hypothesized Eigenvalue Ratio Critical Value Critical Value No. of CE(s) None ** At most 1 * At most At most At most 4 *(**) denotes rejection of the hypothesis at 5% (1%) significance level. L.R. test indicates 2 cointegrating equations at 5% significance level. Critical values based on Osterwald-Lenum (1992). Unnormalized Cointegrating Coefficients: LREERCP LDIFPRDT LPDN LTT LNFA C Normalized Cointegrating Coefficients: LREERCP LDIFPRDT LPDN LTT LNFA C (0.416) (0.058) (0.0427) (0.030) (0.156) The numbers in brackets under the estimated coefficients are the asymptotic standard errors. Restricted Estimates, in other words, the equilibrium real exchange rate (ZEPTA) is determined as follows: ZEPTA = LDIFPRDT LPDN LTT LNFA Estimation involved a VAR with three lags and a restricted constant in the cointegrating vector. 30