61. During most of its recent history, Norway has attempted to maintain a stable nominal exchange rate. This has in part reflected the desire for real stability: to moderate the response of the real exchange rate to developments in the oil sector in order to reduce “Dutch disease” effects. More recently an exchange rate targeting framework has been adopted within which monetary policy has been assigned the task of ensuring exchange rate stability. Exchange rate targeting, as a framework for monetary policy, is preferred by the authorities to monetary targeting, (which they consider to be infeasible because of the apparent lack of a stable demand for money function), and to inflation targeting (which is thought to run the risks of excessive fluctuations in the exchange rate and weakening the credibility of the incomes policy framework).22

Abstract

61. During most of its recent history, Norway has attempted to maintain a stable nominal exchange rate. This has in part reflected the desire for real stability: to moderate the response of the real exchange rate to developments in the oil sector in order to reduce “Dutch disease” effects. More recently an exchange rate targeting framework has been adopted within which monetary policy has been assigned the task of ensuring exchange rate stability. Exchange rate targeting, as a framework for monetary policy, is preferred by the authorities to monetary targeting, (which they consider to be infeasible because of the apparent lack of a stable demand for money function), and to inflation targeting (which is thought to run the risks of excessive fluctuations in the exchange rate and weakening the credibility of the incomes policy framework).22

III. DETERMINANTS OF THE REAL EXCHANGE RATE IN NORWAY: DOES POLICY MATTER?21

A. Introduction

61. During most of its recent history, Norway has attempted to maintain a stable nominal exchange rate. This has in part reflected the desire for real stability: to moderate the response of the real exchange rate to developments in the oil sector in order to reduce “Dutch disease” effects. More recently an exchange rate targeting framework has been adopted within which monetary policy has been assigned the task of ensuring exchange rate stability. Exchange rate targeting, as a framework for monetary policy, is preferred by the authorities to monetary targeting, (which they consider to be infeasible because of the apparent lack of a stable demand for money function), and to inflation targeting (which is thought to run the risks of excessive fluctuations in the exchange rate and weakening the credibility of the incomes policy framework).22

62. The appropriateness of the present monetary and exchange rate policy framework, and the validity of the arguments in favor of it, depend significantly on what determines the real exchange rate. It has, for example, been argued that if higher oil wealth and the accumulation of foreign assets put upward pressures on the real exchange rate, a policy that attempts to control the real rate by keeping the nominal rate stable will be ineffective in the long run because it causes higher inflation. A necessary condition for the framework to work, therefore, is that policy has a well-defined, significant, and dependable role in the determination of the real exchange rate. This is a more basic issue than assessing the system’s other possible shortcomings—such as that, by tying monetary policy to that of European countries, it has a tendency to make policy procyclical, since stronger activity relative to Europe tends to appreciate the exchange rate and thus result in lower interest rates.

63. This chapter focuses on the short- and long-term determinants of the real exchange rate and its principal components, the nominal rate and relative prices, with a view to assessing the relative importance of policy-related variables vis-à-vis cyclical factors and long-term wealth variables. Section B describes the theoretical framework. Section C discusses estimation issues and presents the results. Section D concludes.

B. The Framework

64. The simple purchasing-power hypothesis suggests that the real exchange rate should be constant over time. Clearly, there is little support for this hypothesis in its simple form. Indeed, a number of factors are likely to cause systematic fluctuations in the real exchange rate. We examine the role of policy variables, cyclical factors, and other factors such as oil wealth and accumulation of assets.

Determinants of the real exchange rate

Policy variables

65. Interest rates could potentially influence the real exchange rate by affecting both components of the real exchange rate. The effect on the nominal exchange rate operates both directly and through expectations. Higher interest rates relative to trading partners attract capital flows that strengthen the value of the domestic currency. Such an interest rate differential also indicates an expectation of future weakening in the currency, through the interest rate parity condition. For given expectations of the future evolution of the nominal exchange rate, therefore, higher interest rates will mean a higher current exchange rate. There could also be reverse causation depending on how monetary policy is conducted: an actual or expected appreciation in the nominal exchange rate could cause a policy response in the form of lower interest rates. This suggests that the two variables are likely to have a two-way relationship. The effect of the interest rate on the relative price component of the real exchange rate is also likely to generate an inverse relationship between the two because higher interest rates would tend to lower price inflation through their effect on domestic demand. The predicted sign of the interest rate in the real exchange rate equation is, therefore, ambiguous.

66. The relationship between fiscal policy and the exchange rate is not any less clear-cut. One possible relationship is through the interest rate: higher deficits by putting pressure on resources lead to higher interest rates and, therefore, a higher exchange rate. Higher expenditure could also, for a given stock of money, force the price of the currency up or lead to higher domestic prices, again leading to a higher real exchange rate. The effect, however, also depends on the composition of expenditure: higher expenditure out of imported goods or tradables could have the opposite effect on the exchange rate. In any event, data on the two types of fiscal expenditure are not readily available.

67. Fiscal policy in Norway, as in other major oil-exporting countries, has also had a role to play in influencing the expenditure of oil revenues. Higher oil prices or discovery of new oil reserves could put pressure on resources in the nontradable sector and cause an appreciation of the real exchange rate, a phenomenon referred to as the “Dutch disease”. It has been suggested that the domestic economy and the real exchange rate could be immune from these effects, if at any point in time only permanent revenue from oil was spent and the rest was invested abroad. Following this policy would prevent the real exchange from being significantly influenced by movements in oil wealth or the accumulation of foreign assets (discussed below).

Cyclical factors

68. The real exchange rate is likely to respond to cyclical factors. The relative strength of the krone over the past year, like that of the U.S. dollar and pound sterling, could in part be explained by the stronger cyclical position of these countries relative to continental Europe. Higher activity puts pressure on domestic prices, or for a given stock of money, on the nominal exchange rate and the interest rate, pushing up the real exchange rate as a result. While stronger activity relative to partner countries might lead to a higher real exchange rate, an exchange rate appreciation could also lower activity through its effect on net external demand. Therefore, economic activity and the real exchange rate are likely to have a two-way relationship.

Other factors

69. Over longer periods improvements in the foreign asset position could put upward pressure on the exchange rate: a permanently higher level of net foreign assets (and, therefore, higher flow of income from abroad) requires an appreciation in the real exchange rate (and a worsening trade balance) in the steady state in order to preserve external equilibrium. To the extent that the foreign exchange market is efficient and market participants are rational, it will be the unexpected component of movements in foreign assets that will influence the exchange rate. The net foreign asset position is in turn likely to be affected by the exchange rate, which appears in the definition of the net foreign asset position through the trade balance, causing simultaneity in the system.23

70. In the case of Norway, oil discovery and oil price movements, or oil wealth, may also affect the real exchange rate and the non-oil economy through the “Dutch disease” effect. Higher oil wealth is likely to put upward pressure on the real exchange rate.

71. Productivity is likely to be another important determinant of the real exchange. Higher productivity growth in the traded sector relative to that in the non-traded sector could, along the Balassa-Samuelson lines, lead to higher real exchange rate defined as the ratio of the price non-tradables to that of tradables. Higher economy-wide productivity growth relative to trading partners, however, could have the opposite effect if productivity growth is concentrated in the non-tradable sector.

72. Finally, movements in the terms of trade could also affect the exchange rate by creating excess demand or supply in the non-traded sector. In the case of Norway, movements in the terms of trade largely reflect those in the relative price of oil and are, therefore, incorporated in the oil wealth variable discussed above. A separate terms of trade variable is not included in the following analysis.24

The model

73. The real exchange, ret, is defined as the product of the nominal exchange rate, et and the Norwegian price level relative to that in its trading partners, pt (The nominal exchange rate is the price of domestic currency so that a rise in the exchange rate means an appreciation). We estimate a model of the real exchange as a function of the interest rate differential with respect to trading partners, it, GDP relative to trading partners, yt, net foreign asset position as ratio to GDP, ft, government consumption as ratio to GDP, xt, estimated oil wealth as ratio to GDP, wt, and productivity relative to trading partners, prt:

ret=f(it,yt,ft,xt,wt,prt),(1)

Since the components of the real exchange rate may respond differently, especially in the short run, to movements in the right–hand side variables, and we also estimate separately equations for the two components of the real exchange rate, i.e. the nominal exchange rate and relative prices, in order to obtain a better idea of the relationships involved.

Data definitions and sources

74. To examine the determinants of the exchange rate in Norway, in particular the role that oil wealth may have played, it is important that the data cover a sufficiently long period that includes the early 1970s, when oil production began. Moreover, quarterly data, although less readily available than annual data, have the advantage of allowing a more thorough examination of the role of policy variables and cyclical factors. It was necessary, to rely on a number of different sources to obtain complete and consistent quarterly series for the variables for Norway and its trading partners for the period 1970–1995. These include the OECD Analytical Database, IMF International Financial Statistics, the World Economic Outlook Database, and data provided by the authorities. The trading partners selected for the exercise are the 14 countries with the share of trade larger than 1 percent of the total in the IMF World Economic Outlook Database.25

75. The nominal exchange rate used in the estimation is the effective rate and the real exchange rate is the CPI based real effective rate, both as measured in the IMF World Economic Outlook Database. Quarterly GDP levels in Norway and in its trading partners are obtained from the OECD, aggregated for the latter using the above weights (essentially the same weights as in calculating the effective exchange rate). The interest rate differential is calculated as short–term interest rate minus that in trading partners. The fiscal variable is government consumption in nominal terms relative to nominal GDP. The productivity variable is constructed as the ratio of the productivity index to that in trading partners. Annual series on oil wealth and net foreign asset position as ratios to GDP were obtained from the authorities. Quarterly numbers are obtained for the latter two series using cubic spline. This means that the estimated short–run coefficients associated with these two variables may not necessarily be meaningful. Estimates of oil wealth start in 1973, and the variable is set equal to zero in the period prior to that. Other variables are from the OECD Analytical Database. Some interest rate figures for the 1970–75 period are obtained from IMF International Financial Statistics.

C. Estimation Methodology and Results

76. In the presence of series that are likely to contain unit roots it is customary to use the Johansen maximum-likelihood procedure to test for and estimate long-run relationships. We use a modified version of this procedure that allows for the presence of exogenous non-stationary variables.26 At the same time, given the number of variables involved in the exercise, it is useful also to examine the relationship between the variables using other, more transparent methodologies in order to get a clearer idea of the nature of the interactions involved. Accordingly, before applying the maximum-likelihood method, we propose to use the autoregressive distributed lag (ADL) approach, which involves using the OLS to estimate cointegrating relationships.27 Using two different procedures is also intended to enhance confidence in the empirical analysis. In each case we obtain both the long–run cointegrating relationship and the short–run error–correction specification. This distinction is important in the present context because it allows a distinction between short–run cyclical and long-run actors, such as oil wealth and the foreign asset position.

Testing for unit roots

77. The Augmented Dicky-Fuller unit root tests are reported in Table 9. The order of the lag structure is determined using the Schwarz Bayesian Criterion. The variables used in the study all have unit roots in levels but are stationary in their first differences.28 This warrants the examination of cointegration among the level variables.

Table 9.

Norway: Augmented Dicky-Fuller Unit Root Tests 1/

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See text for data definitions and sources. An asterisk denotes rejection of a unit root at the 5 percent level. The order of lags is chosen such that the Schwarz Bayesian Criterion is maximized.

Estimating cointegrating relationships using the ADL approach

78. This methodology derives short- and long-run estimates of the coefficients based on estimating the traditional autoregressive distributed lag model, with the order of the dynamic structure chosen by maximizing the Schwarz Bayesian Criterion. Strictly speaking the ADL approach followed here assumes that only one cointegrating vector exists between the variables under consideration. Moreover, the approach does not distinguish between exogenous and endogenous variables, and therefore is not equivalent to the maximum-likelihood approach followed below. However, on the positive side, apart from simplicity, it has the advantage of not requiring that all variables in the cointegrating relationship to be of the same order of integration and the results can help in choosing the variables to use in the Johansen’s procedure.

79. The results of estimating this model for the real exchange rate are reported in Tables 10 and 11. These indicate that in the long run oil wealth positively affects the real exchange rate (at the 5 percent level) while the productivity differential has a negative effect (at the 10 percent level). Both variables are also significant (at the 5 percent level) in the short run, together with the net foreign asset position variable, which, however, appears with a negative sign. This could be because of how the quarterly foreign asset data was constructed (see Section B), or more likely it could indicate the reverse effect of the exchange rate on the valuation of net foreign asset position (see further discussion below). Other variables do not seem to influence the real exchange rate. In particular, we do not seem to find a significant link between the interest rate (monetary policy) or government consumption (fiscal policy) and the exchange rate.

Table 10.

Norway: Estimating the Cointegrating Relationship for the Real Exchange Rate using the Autoregressive Distributed Lag Approach 1/

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Dependent variable is the real exchange rate ret; the lag structure is selected using Schwarz Bayesian Criterion; sample period is 1970q3-1995q4; and single and double asterisks, respectively, denote significance at the 5 and 10 percent levels.

Table 11.

Norway: Estimating the Error-Correction Relationship for the Real Exchange Rate using the Autoregressive Distributed Lag Approach 1/

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Dependent variable is change in the real exchange rate Δret; ecmt-1 is the error-correction term obtained from the long-run relationship in Table 2; sample period is 1970q3-1995q4; and single and double asterisks, respectively, denote significance at the 5 and 10 percent levels.

80. Although examining the determinants of the real exchange rate directly is useful, it could be argued that it would be more appropriate to decompose the exchange rate into its two principal components: the nominal exchange rate and relative prices. This is in particular useful given that the dynamic response of the nominal rate and relative prices to shocks may be quite different, with the former likely to respond much faster than the latter.

81. The results for the nominal exchange rate are reported in Tables 12 and 13. As in the case of the real exchange rate, oil wealth is a significant determinant of the nominal rate both in the short and in the long runs, but now the interest rate is also significant, appearing, however, with a negative coefficient in the long-run relationship. This could indicate the dominance of the reverse effect, namely rising (falling) interest rates resulting from an actual or expected weakening (strengthening) in the exchange rate.

Table 12.

Norway: Estimating the Cointegrating Relationship for the Nominal Exchange Rate using the Autoregressive Distributed Lag Approach 1/

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Dependent variable is the nomial exchange rate et; the lag structure is selected using Schwarz Bayesian Criterion; sample period is 1970q3-1995q4; and single and double asterisks, respectively, denote significance at the 5 and 10 percent levels.

Table 13.

Norway: Estimating the Error-Correction Relationship for the Nominal Exchange Rate using the Autoregressive Distributed Lag Approach 1/

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Dependent variable is change in the nominal exchange rate Δet; ecmt-1 is the error-correction term obtained from the long-run relationship in Table 4; sample period is 1970q3-1995q4; and single and double asterisks, respectively, denote significance at the 5 and 10 percent levels.

82. Relative prices seem to behave quite differently (Tables 14 and 15). Over the long run only productivity differential is significant (at the 10 percent level), while in the short run, apart from this variable, the differential in activity and fiscal expenditure also seem to affect relative prices. This suggests that cyclical factors and fiscal policy affect the relative price component of the real exchange rate, but only in the short run.

Table 14.

Norway: Estimating the Cointegrating Relationship for Relative Prices using the Autoregressive Distributed Lag Approach 1/

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Dependent variable is the Norewegian price level relative to its trading partners pt; the lag structure is selected using Schwarz Bayesian Criterion; sample period is 1970q3-1995q4; and single and double asterisks, respectively, denote significance at the 5 and 10 percent levels.

Table 15.

Norway: Estimating the Error-Correction Relationship for Relative Prices using the Autoregressive Distributed Lag Approach 1/

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Dependent variable is change in the Norwegina price level relative to its trading partners Δpt; ecmt-1 is the error-correction term obtained from the long-run relationship in Table 6; sample period is 1970q3-1995q4; and single and double asterisks, respectively, denote significance at the 5 and 10 percent levels.

Cointegration with exogenous variables

83. The standard Johansen procedure for estimating long-run relationships assumes that all the included variables are endogenous to the system. As a result it could give rise to a large number of statistically acceptable estimated cointegrating vectors, some of which would not make sense theoretically. In some applications, as in the present one, it would make sense to assume that some variables are exogenous. This reduces the number of possible estimated cointegrating vectors and, by giving a more theoretical structure to the system, mitigates the need to rely solely on the data, or other arbitrary post–estimation procedures, to choose among the estimated vectors.

84. Among the right-hand side variables, as argued in Section B, the interest rate differential, it GDP relative to trading partners, yt, and the net foreign asset position, ft, are likely to be influenced by the exchange rate, and are unlikely to be exogenous. Thus, in the following analysis we treat ert, et, pt, it, yt, and ft as endogenous I(1) variables and xt, wt, and prt, as exogenous I(1) variables.29

85. We use the ADL results to choose variables for the Johansen’s procedure. Accordingly, each equation is estimated using all the variables that are significant in either the long–run or the short-run ADL relationships. The included variables are then separated into exogenous and endogenous using the above classification. This methodology requires that the first differences of the exogenous variables be included as I(0) variables in the cointegrating equation. The order of lags in the cointegrating VAR is set equal to 2, consistent with the lag structure optimally chosen in the ADL approach above.

86. The results of the maximum-likelihood estimation of the cointegrating VAR for the real exchange rate are presented in Tables 1618. Table 16 supports the hypothesis of one cointegrating relationship between the variables included in the model, and Table 17, reporting x2 exclusion tests for all the variables, suggests that the cointegrating relationship is between the real exchange rate, oil wealth, and productivity differential; the net foreign asset position does not appear to belong to the long–run relationship. These results are similar to those obtained using the ADL approach. However, unlike the ADL model, the error–correction results (Table 18)—which are obtained as a byproduct of estimating the cointegrating VAR relationship—suggest that the real exchange rate in the short-run only responds to lagged net foreign assets (with a negative sign) and the error–correction term.

Table 16.

Norway: Cointegration Likelihood Ratio Tests for the Real Exchange Rate Equation 1/

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Based on a cointegrating VAR of order 2, with unrestricted intercepts and restricted trend, which includes ret and ft as endogenous I(1) variables, wt and prt as exogenous I(1) variables, and first differences of the latter variables as I(0) exogenous variables. Sample period is 1970q3-1995q4.

Table 17.

Norway: Estimated Coefficients in the Cointegrating VAR(2) for the Real Exchange Rate Using the Maximum-Likelihood Method and Likelihood Ratio Tests of Exclusions

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The sample period is 1970q3-1995q4. x2 statistic in each case tests the restriction that the coefficient is equal to zero in the cointegrating relationship; an asterisk denotes significance at the 5 percent level, and a double asterisk at the 10 percent level.

Table 18.

Norway: Estimated Error-Correction Model for the Real Exchange Rate Based on the Cointegrating VAR(2) in Table 17 1/

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Dependent variable is Δret; sample period is 1970q3-1995q4; and an asterisk denotes significance at the 5 percent level.

87. The results for the nominal exchange rate, reported in Tables 1921, suggest that the variables included are cointegrated when the maximal eigenvalue test is used; the trace test marginally rejects cointegration. The fact that the error-correction term is significant in the short-run equation (Table 21), however, provides further evidence in favor of cointegration. The estimation results are similar to those obtained before in that oil wealth and the interest rate differential appear to affect the nominal exchange rate with positive and negative coefficients, respectively. But they also indicate that the net foreign asset position negatively influences the nominal exchange rate in the long run, as well as in the short run.

Table 19.

Norway: Cointegration Likelihood Ratio Tests for the Nominal Exchange Rate Equation 1/

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Based on a cointegrating VAR of order 2, with unrestricted intercepts and restricted trend, which includes et, it, and ft as endogenous I(1) variables, wt as exogenous I(1) variables, and first difference of the latter variable as I(0) exogenous variable. Sample period is 1970q3-1995q4.

Table 20.

Norway: Estimated Coefficients in the Cointegrating VAR(2) for the Nominal Exchange Rate Using the Maximum-Likelihood Method and Likelihood Ratio Tests of Exclusions

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The sample period is 1970q3-1995q4. x2 statistic in each case tests the restriction that the coefficient is equal to zero in the cointegrating relationship; an asterisk denotes significance at the 5 percent level, and a double asterisk at the 10 percent level.

Table 21.

Norway: Estimated Error-Correction Model for the Nominal Exchange Rate Based on the Cointegrating VAR(2) in Table 20 1/

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Dependent variable is Δet; sample period is 1970q3-1995q4; and an asterisk denotes significance at the 5 percent level.

88. Finally, Tables 2224 present the results for the relative price variable. Cointegration tests (Table 22) indicate the presence of two cointegrating relationships, which violates the assumption behind using the ADL approach. However, the signs of the coefficients are the same in both relationships (Table 23), implying that using either vector would yield the same conclusions as far as the direction of the effect of a variable is concerned. The long-run results suggest that, unlike in the ADL case, GDP relative to trading partners, the foreign asset position, and fiscal expenditure all positively influence relative prices in the long run, while the productivity differential, as before, enters with a negative sign. Foreign assets and fiscal expenditure appear to have an influence in the short run as well (Table 24).

Table 22.

Norway: Cointegration Likelihood Ratio Tests for the Relative Price Equation 1/

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Based on a cointegrating VAR of order 2, with unrestricted intercepts and restricted trend, which includes pt, yt, and ft as endogenous I(1) variables, xt and wt as exogenous I(1) variables, and first differences of the latter variables as I(0) exogenous variables. Sample period is 1970q3-1995q4.

Table 23.

Norway: Estimated Coefficients in the Cointegrating VAR(2) for the Relative Price using the Maximum-Likelihood Method and Likelihood Ratio Tests of Exclusions

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The sample period is 1970q3-1995q4. x2 statistic in each case tests the restriction that the coefficient is equal to zero in both cointegrating relationships; an asterisk denotes significance at the 5 percent level, and a double asterisk at the 10 percent level.

Table 24.

Norway: Estimated Error-Correction Model for the Relative Price Based on the Cointegrating VAR(2) in Table 23 1/

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Dependent variable is Δpt; sample period is 1970q3-1995q4; and an asterisk denotes significance at the 5 percent level.

D. Conclusion

89. The estimation results reported in this Chapter indicate a role for policy variables in the determination of the real exchange rate in Norway, but not one that is particularly dependable. The interest rate appears to have a negative relationship with the nominal exchange rate, suggesting a reverse causation: monetary policy appears to respond to actual or expected movements in the exchange rate rather than the other way around. Fiscal policy appears to have an independent effect on the relative price component of the real exchange rate, but the evidence is mixed as to whether this effect extends beyond the short term. Overall, the results do not suggest that the real exchange rate can successfully and directly be controlled by macroeconomic policy. The observed link between policy variables and the exchange rate, of course, may have been weakened by frequent changes in the exchange rate policy framework during the estimation period.

90. The results, however, provide support for the hypothesis that oil wealth is an important determinant of movements in the nominal and real exchange rates. Higher estimated oil wealth, other things being equal, leads to a higher real exchange rate by causing a nominal appreciation. The productivity differential relative to trading partners also influences the real exchange rate inversely through its relative price component. There is little support for the hypothesized positive effect of the net foreign asset position on the exchange rate, while there is some evidence that the cyclical position of the economy influences the real exchange rate through relative prices.

21

Prepared by Hossein Samiei.

22

See the articles in Choosing A Monetary Policy Target (ed. Ann Berit Christiansen and Jan Fredrik Qvigstad), 1997, Scandinavian University Press, for a discussion of issues involved.

23

See, among others, H. Faruqee, “Long-Run Determinants of the Real Exchange Rate: A Stock-Flow Perspective,” IMF Staff Papers, Vol 42 (March 1995); T. Feyzioglu, “Estimating The Equilibrium Exchange Rate: An Application to Finland,”, IMF Working Paper, WP/97/109, for a discussion of the determinants of the real exchange rate.

24

This procedure was also justified by the empirical results: the terms of trade, when included in the regressions, did not have a significant effect on the exchange rate.

25

These are in order of importance: Germany (19.8 percent), Sweden (18.0 percent), United Kingdom (12.9 percent), United States (9.4 percent), Denmark (6.5 percent), France (6.3 percent), Japan (5.3 percent), Netherlands (5.0 percent), Italy (5.0), Finland (4.0 percent), Belgium (2.8 percent), Switzerland (1.9 percent), Spain (1.8 percent), and Austria (1.3 percent).

26

See I. Harboe, S. Johansen, B. Nielsen, and A. Rahbek (1995), “Test for Cointegration Ranks in Partial Systems,” Preprint No. 5, Institute of Mathematical Statistics, University of Copenhagen; and M. H. Pesaran, Y. Shin, and R. J. Smith, “Structural Analysis of Vector Error Correction Models with Exogenous I(1) Variables,”, mimeo., University of Cambridge February 1997, for a description of how exogenous variables may be introduced in Johansen’s procedure.

27

See M. H. Pesaran and Y. Shin, “An Autoregressive Distributed Lag Modelling Approach to Cointegration Analysis,” mimeo., University of Cambridge, January 1997, for a discussion of this approach.

28

All estimations and testings were carried out using Microfit 4.0 for Windows.

29

In principle it is possible to test whether these restrictions are supported by the data. Given the relatively strong case for the restrictions, however, this is not attempted here.