This Selected Issues paper analyzes the current account performance of Denmark in 1993–98. The paper presents a brief review of structural features of the external current account. It looks at the decline in export market share and concludes that it reflects primarily cyclical factors and the unwinding of an unsustainable export market gain immediately after the German unification. The paper also examines implications for fiscal policy of Denmark’s decision to remain for the time being outside the European Monetary Union.


This Selected Issues paper analyzes the current account performance of Denmark in 1993–98. The paper presents a brief review of structural features of the external current account. It looks at the decline in export market share and concludes that it reflects primarily cyclical factors and the unwinding of an unsustainable export market gain immediately after the German unification. The paper also examines implications for fiscal policy of Denmark’s decision to remain for the time being outside the European Monetary Union.

III. Sovereign Asset and Liability Management in Denmark43

A. Introduction and Summary

75. The Kingdom of Denmark maintains one of the most sophisticated sovereign debt management offices in the world. Changes instituted in the 1990s have lowered costs and improved the management of the DKr 745 billion of government debt outstanding at the end of 1998. Such changes include: (1) the transfer of debt management from Ministry of Finance to the independent Danmarks Nationalbank in order to conduct a more active policy in which exchange rate risk can be managed in coordination with the reserves; (2) the establishment of a benchmark for the risk and return characteristics of foreign debt; and (3) general limitations and other policies with regard to debt management. These changes have allowed the debt management office to better accomplish its stated goals of achieving the lowest possible costs for the debt in the long run.

76. Some of the impetus for the recent changes in debt management policy has arisen from the desire to lower the level of outstanding government debt and reduce the burden of interest payments within the central government budget. This goal is a laudable one, particularly so because demographic trends in Denmark, like in many industrial countries, show that the costs of maintaining the existing level of government-provided social services and transfer payments are expected to increase as the population ages and there will be fewer entrants to the labor force from younger cohorts to support these fiscal expenditures through tax revenues. The authorities in Denmark are attempting to ready themselves by reducing the interest rate burden by lowering the level of outstanding government debt well in advance of the expected pressures on fiscal accounts. As currently stated in the Medium-Term Economic Survey,44 the goal is to lower public debt to approximately 35 percent of GDP by 2005. Although the eventual elimination of all government debt may be desirable to completely remove the interest rate burden imposed upon the fiscal accounts, government debt often takes on an auxiliary goal of providing a benchmark yield curve for pricing other domestic securities. Indeed, the Danish authorities have stated that “in the long term government debt policy must be planned to take account of the overall requirement to build up a well-functioning, effective Danish capital market.”45 Thus, it is not presently planned to completely eliminate all government debt.

77. The amount of net foreign debt in the Danish economy also has been the subject of concern in the past. During the mid-1980s, net foreign debt increased to more than 40 percent of GDP, one of the highest rates in the OECD, following more than a quarter century of current account deficits. The financing of the debt required annual interest payments abroad of about 4 percent of GDP.46 For several years now, the government has attached high priority to lowering the net external debt of the economy. As can be seen in Table III-1, the recent sequence of years with current account and central government surpluses have permitted the reduction of net foreign debt (final column) to 24 percent of GDP in 1998. This process slowed with the current account deficit incurred in 1998, but the government has maintained its longer-term goal for a reduction. While the initial goal called for elimination of the net foreign-denominated debt by 2005, this goal has been scaled down in view of the recent and projected current account deficits over the next two years, to a level of net foreign debt amounting to 15 percent of GDP by 2005, with total elimination to take place sometime in the future.

Table III-1.

Denmark: External Assets and Liabilities

(In DKr billion)

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Source: Danmarks Nationalbank.

78. While taking the goal of lowering the burden of interest payments as a well-reasoned one, and acknowledging that the management of Danish sovereign debt is done in an efficient manner, this paper attempts to step back and ask a very basic question: are there sound economic reasons for maintaining some positive amount of external net foreign debt? As is well-known, the need to finance continuous current account deficits by providing claims on domestic capital to foreigners can become onerous if such deficits appear unsustainably large or the terms on which they are financed make countries vulnerable to monetary or exchange rate instability. Despite the maintenance of a fixed exchange rate regime and the recent dip of the current account into negative territory, it does not appear that the current account deficit is unsustainable nor does the current level of the net foreign debt appear overly burdensome. Denmark does not appear to be in a situation which would call for the immediate decline in foreign debt to maintain the safety or soundness of the monetary and financial system. The decision regarding the level of foreign indebtedness is thus a voluntary one and a potentially positive role for external foreign debt remains.

79. The rationale for government issued foreign-denominated debt is usually expressed as either (1) an inability of the private sector to tap financial markets to finance the current account (or a desire to lower the cost of such borrowing to the economy by having the government be the intermediary) or (2) provide the central bank with borrowed reserves or a combination of the two. According to the Nationalbank’s publication, Danish Government Borrowing and Debt, the primary purpose of the central government’s borrowing in foreign currencies is to maintain an adequate foreign-exchange reserve.47 An additional reason relies on the interaction between hedging and incentive considerations. This role for foreign-denominated debt, though not completely divorced from the above considerations, is seldom cited in official documents and does not feature in the Nationalbank’s publications.

80. The hedging rationale for foreign-denominated debt suggests that it may be desirable for an open economy that is subject to shocks to output to maintain a positive amount of foreign debt to act as a macroeconomic hedge. This argument basically derives from a basic portfolio analysis in a general equilibrium setting. The intuition is that uncertainty in net wealth and consumption can be reduced by the issuance of foreign or domestic currency debt to foreigners who take on some of the risk of fluctuations in the issuing countries’ output. The degree to which domestic or foreign debt, or some combination of them, can act as a hedge depends on whether domestic output is negatively correlated with domestic and foreign inflation. When a negative correlation exists, low output growth is associated with high inflation which lowers the real value of nominal debt. Holders of nominal debt thus “share” in the states of nature in which there is low output. Alternatively, when output growth is high, inflation is low and holders of debt maintain high real values of their debt, “sharing” in good times as well. If domestic output is relatively more negatively correlated with foreign inflation, then foreign-denominated debt will be favored over domestic debt for the same reason.

81. A second argument often used in favor of foreign debt relates to the government’s ability to “inflate away” the value of domestic liabilities through its ability to manipulate the domestic price level. When such an incentive exists, potential debt holders may insist on high nominal interest rates in the domestic currency and the government may “solve” the incentive problem by issuing foreign-denominated debt. The government is implicitly assumed to be unable to influence foreign inflation and thus cannot repudiate the debt in this way. Of course, some governments have explicitly defaulted on their foreign debt by not repaying either interest or principle on time. Their ability to borrow abroad is usually curtailed after such events, or the risk premiums investors insist upon often preclude borrowing. A risk premium on foreign debt may also arise if the government has difficulty committing to domestic price stability. This may influence the likelihood of nonpayment if it is viewed as a signal of other macroeconomic weaknesses. Since the credibility of the Danish authorities in maintaining the real value of assets is well established, this second argument is not applicable for a country like Denmark where the credit rating agencies have rated Denmark’s foreign currency debt slightly below the AAA rating on the domestically-denominated debt and the authorities have never used rapid inflation as a method to repudiate the debt.

82. To examine whether the foreign debt can play a role in hedging output risk in Denmark, an examination of the characteristics of the Danish economy relative to its trading partners is performed. The use of foreign debt as a hedge for output risk has been analyzed theoretically, but little empirical evidence has been brought to bear on the issue. This paper represents an initial attempt to examine this potential role for foreign-denominated debt. Even though it has not been an explicit reason for the use of foreign-denominated debt, it fits into the Danish authorities’ argumentation for a reduction of the net external debt in that it relates explicitly to the macroeconomic risks of excessive and costly foreign debt and is thus appealing in a macroeconomic context.

83. The major trading partners in this analysis are Germany, Sweden, and the United Kingdom and the 11 EMU countries. The conditions under which a positive amount of foreign currency debt would be optimal are taken from Bohn (1996). In this paper, a model of a small open economy is presented and the desirability of foreign currency debt depends on the structure of macroeconomic disturbances.

84. The results of the exercise presented in sections III and IV show that using foreign-denominated debt to hedge output risk is not advisable for Denmark. Although the results would marginally encourage the use of euro-denominated debt to hedge output fluctuations with the Euro-11 countries, the results appear to be statistically insignificant. The intuition behind the results is that shocks to Danish real output are not highly correlated with their trading partners relative to the shocks to their respective monetary sectors.

B. Facts about Danish Sovereign Assets and Liabilities

85. To provide a context for the discussion, consider some general characteristics regarding the external debt of Denmark and, more specifically, the government debt48 As shown in Table III-1 most of the net external debt (DKr 371 billion) is comprised of central government liabilities owned by foreigners,49 both foreign-denominated debt and domestically-denominated debt. Less than a third (DKr 101 billion) of the net central government liability was offset by foreign exchange reserve assets held by the Danmarks Nationalbank in 1998. The private sector has much smaller net foreign debt, with banks holding more foreign assets than liabilities and other private sector entities holding the reverse, more liabilities than assets. On net, the private sector has a net liability position relative to foreigners of about DKr 24 billion. Thus, although the policy goal is to lower net foreign liabilities (final column in Table III-1) to 15 percent of GDP by 2005, the goal is likely to require the public sector to lower its net external liability position rather than rely exclusively on an alteration of the private sector asset and liability positions.

86. Examining the characteristics of the sovereign debt component of net foreign debt provides the background for a discussion of the usefullness of foreign-denominated debt. The nominal amounts outstanding of Danish government debt have grown substantially since the early 1980s, leveling off in the late eighties and again in the late nineties. There are various methods of measuring the level of public sector debt with some countries calculating it in gross terms and others netting the debt with other types of assets to arrive at net debt. Simply examining the central government’s gross nominal debt, Figure III-1 shows the growth in Danish gross debt since 1988 along with the amounts of government issued foreign debt. Although the amount of outstanding gross debt has leveled off close to 800 billion kroner in recent years, as a percentage of GDP gross debt has been falling. Since 1988, gross total debt (domestic and foreign) reached a high of just over 80 percent of GDP in 1993 and as of end-1998 was below 70 percent of GDP. Using the EMU definition of debt, the proportion of EMU debt to GDP has been reduced to less than 60 percent, below the cut-off level for entry into the EMU.50

Figure III-1.
Figure III-1.

Real Domestic and Foreign Debt

Citation: IMF Staff Country Reports 1999, 107; 10.5089/9781451811070.002.A003

87. The distribution between domestic and foreign sovereign debt is determined by the “central government borrowing norm” which is agreed between the government and Danmarks Nationalbank. The agreement is composed of two parts, one determining the domestic borrowing and another for the foreign borrowing. The domestic borrowing norm states that the issuance of domestic krone-denominated securities within a year shall match the gross central government borrowing requirements, including the redemption of domestic debt. The foreign borrowing norm states that the central government’s redemption on foreign debt, including securities bought back from the market and early redemptions, are normally refinanced by foreign borrowing. These requirements provide a division between fiscal and monetary policy by ensuring that domestic liquidity is not affected by the government’s borrowing policies.51 However, in situations in which foreign currency is needed for intervention purposes or there is excess foreign currency in the reserve account, the foreign borrowing norm may be waived (as long as the government account does not fall below zero). The government may issue foreign currency bonds to raise additional funds for reserve purposes or, alternatively, excess reserves can be used to redeem foreign borrowings lowering outstanding foreign debt.52 As noted above, recent policy pronouncements have indicated a desire to lower net external debt over the next several years which could mean waivers from the foreign borrowing norm if the foreign-denominated portion of external government debt is to be reduced appreciably.

88. Table III-2 shows the components of the net and gross financing requirement over the last several years. Central government receipts less expenditures equal the net financing requirement as a result of the government’s financial balance for the year. The redemptions of domestic and foreign debt within the year are then added to the financial balance to result in the gross financing requirement. Since 1994 there has been an improvement in the government’s financial balance which has substantially reduced the gross financing requirements of the central government.

Table III-2.

Central Governments Financing Requirement

(In billions of DKr)

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Sources: Finansiel Statistik, April 1999; Danmarks Nationalbank.

89. The composition of the Danish sovereign foreign debt by the major currencies used for issuance is presented in Figure III-2. Since 1988 there has been a pronounced trend toward the use of core European currencies rather than the U.S. dollar or Japanese yen for issuance. As of 1998 over three-quarters of the debt was formally denominated in German mark with the next largest proportion denominated in what is now euro. Even this breakdown may be slightly deceiving since currency swaps are used to alter the currency composition of the foreign debt. As of end-1998 over 90 percent of the foreign debt was effectively denominated in euro. The stated purpose for denominating much of the portfolio in German marks (pre-1999) and euro (post-1998) is to lower nominal exchange rate risk. This is a result of the monetary policy objective of maintaining a stable krone rate against the major EMS currencies prior to 1999 and now relative to the euro.

Figure III-2.
Figure III-2.

Currency Composition of Foreign Debt

Citation: IMF Staff Country Reports 1999, 107; 10.5089/9781451811070.002.A003

90. The issuance maturities of the government debt range from nine months to 30 years. The maturities are generally divided into three categories: short term with initial maturities up to three years; medium term with initial maturities up to five years; and long term with initial maturities of as much as 30 years. Most issuance maturities, however, are chosen so as to provide relatively liquid series and to ensure the effective maturity (duration) remains around a desired four years for the domestic bonds and around a desired 2.5 years for the foreign bonds. The effective maturity, measured by the Macaulay duration53 in Denmark, can also be managed using interest rate swaps, as well as strategically issuing securities of various maturities, and the Danish authorities actively use both techniques. Figures III-3a and III-3b provide the maturity structure of the domestic and foreign debt separately. Notice that the bulk of the debt has a term to maturity exceeding two years and that the foreign debt has a larger proportion of short-term securities than does the domestic debt component. This conforms to the stated durations which were 4.4 years for the domestic denominated debt and 2.0 for foreign-denominated debt in 1998.

Figure III-3a.
Figure III-3a.

Maturity Structure of Domestic Debt

Citation: IMF Staff Country Reports 1999, 107; 10.5089/9781451811070.002.A003

Figure III-3b.
Figure III-3b.

Maturity Structure of Foreign Debt

Citation: IMF Staff Country Reports 1999, 107; 10.5089/9781451811070.002.A003

91. Another way of analyzing the government debt is to examine its terms by type of interest payment as this also has an implication for duration and interest rate risk management (Figure III-4). The vast majority of the domestic government debt is issued as fixed-rate debt. Fixed-rate issues are supplemented by short-term Treasury bills issued as zero-coupon securities with opening maturities of up to nine 9 months. These securities are kept open until 3 months before maturity. Floating-rate securities are no longer being issued although there remain some outstanding issues. Just as the currency risk of a foreign-denominated bond can be altered with a currency swap, so too can the interest rate risk be altered with an interest rate swap. Use of interest rate swaps, introduced in 1998, means that the target duration can be maintained without disturbing the issuance of a regular series of bonds. Thus, the goal of maintaining large liquid issues in order to lower outright borrowing costs and to support capital market development can be accomplished alongside better management of interest rate risk.

Figure III-4.
Figure III-4.

Debt by Type of Interest Payments

(In billions of DKr)

Citation: IMF Staff Country Reports 1999, 107; 10.5089/9781451811070.002.A003

92. In terms of the subsequent discussion regarding the optimal amount of foreign debt, several observations can be usefully recalled. First, the domestic and foreign borrowing norms suggest that the need for domestic and foreign debt mechanically appears to arise from refinancing the existing debt and the central government yearly financial budget balance. While the amount of outstanding sovereign debt thus appears to be a residual outcome of other policy decisions, it is important to recognize that the budgetary process determining government receipts and expenditures takes as an input the desired level of government debt and its expected cost. The projected budget surpluses over the next five years, for instance, are intended to be used to reduce total government debt. Second, the amount and proportion of foreign debt compared to domestic debt is not such that questions of sustainability are relevant. However, the amount is large enough that its reduction would have a nontrivial budgetary effect from a reduction in interest payments. Also by lowering the deficit of the investment income account, debt repayment would also decrease the drag on the current account, allowing surpluses to be more easily accomplished. Lastly, the currency composition of the foreign debt is heavily influenced by the desire to minimize nominal exchange rate risk but does not appear to be related to hedging output risk.

C. The Underpinnings for a Positive Theory for Foreign Debt

93. The goal of the model is to show how the value of nominal domestic and foreign debt relate to output uncertainty and how debt policy can improve social welfare. The analysis begins with some standard macroeconomic modeling assumptions; a small economy with identical, infinitely-lived, risk-averse individuals. Each individual maximizes the utility of a stream of future (discounted) consumption and receives a stochastic endowment of output. The government acts on behalf of individuals to maximize social welfare, that is, the expected utility of the representative individual.54 Individuals are thus assumed not to borrow directly, but only indirectly though the government as intermediary. In Denmark’s open capital markets, individuals and corporations are permitted to borrow abroad. The model should thus be interpreted broadly whereby the government represents all potential domestic borrowers. As noted above, public sector borrowing overwhelms the private sector borrowing that has maintained net liabilities of less than 10 percent of the total net investment position of Denmark.

94. The government decides how to interact with risk-neutral, foreign lenders who extend to the country nominal domestic or foreign currency-denominated debt.55 Since the government is assumed not to be able to sell off output to the foreigners directly, non-indexed debt may provide an indirect way of hedging against output risk. The notion is that if nominal and/or foreign currency debt is outstanding, the country gains from unexpected inflation in the corresponding country. The value of real debt falls at the same time as consumption falls due to low output growth. Money is introduced in the model so as to study usefulness of nominal bonds. However, since the correlation of inflation and real growth is crucial for the results, Bohn introduces money in a way that does not guarantee a perfect negative correlation between these two variables. In particular, a basic cash-in-advance constraint with unit velocity would imply a perfect negative correlation and thus agents are assumed to experience a technical delay in clearing money balances forcing them to hold money into the next period. In this way, velocity will be less than one and the negative correlation between inflation and output growth is not assumed a priori Money supply is determined before the shocks to output and velocity are realized so that the government cannot perfectly control inflation. Thus, for a given money supply, realizations of the shocks to output and velocity determine that period’s price level and thus the real value of debt.

95. With regard to the foreign economy in the model, it is assumed to be identical to the domestic one except that the agents are risk-neutral.56 The domestic government takes the foreign money supply as exogenous. The issue of changes in relative prices is ignored by assuming that one unit of the foreign goods is equivalent to one unit of domestic goods so that purchasing power parity holds. This also implies that the effects of real exchange rate changes on output are absent from the model.

96. Given this setup, the problem is one in which the government chooses foreign debt and domestic debt so as to maximize the utility of its citizens subject to a national budget constraint which incorporates the notion that old government debt to foreigners is financed by new debt, taxes, or money balances. The optimal debt policy is then given by the first-order conditions of the constrained optimization problem. These conditions imply that optimal risk-sharing requires that bonds be issued (or purchased, if debt is negative) until the covariance of taxpayers’ marginal utility with unexpected returns (represented by an inflation innovation) on the debt is zero. From this set of conditions, Bohn (1996) finds that the optimal supply of nominal, N, and foreign currency, F, debt satisfies the following system of linear equations.
0 and Y0 is the initial level of output, y is the growth rate of output with y representing its mean, π and π* are the domestic and foreign inflation rates, respectively, and r is the real return on both domestic and foreign bonds (also the rate of time preference of the risk-neutral lender).

97. Note that unless the inflation rates in both countries are perfectly correlated, in which case one of the securities is redundant, the system results in a unique solution for the amount of both domestic and foreign bonds that provide an optimal hedge against output fluctuations. Bohn (1996) goes further and assumes that shocks to output and inverse velocity,57 the two stochastic components in the model, can be decomposed into a country-specific shock and a common shock. Output shocks, both country-specific and common, are assumed to move output growth away from y while inverse velocity shocks move inverse velocity growth away from zero.


Where Ψ and V represent the country-specific components and μ and η denote common worldwide components to the shocks to output and (inverse) velocity. These random variables, Ψ, Ψ*, v, v*, μ, and η are independent and white-noise with mean zero and finite moments. With the imposition of these assumptions regarding the shocks to output and inverse velocity, the optimal quantities of nominal and foreign currency debt are as follows:


98. These equations imply that a government should always issue nominal debt. However, the quantity depends on the variances. In this setup, if there were only real shocks in the domestic economy (i.e. no shocks to velocity) then inflation and output would be perfectly (negatively) correlated and nominal debt would provide a perfect hedge against output fluctuations.58 If the variance of domestic money demand shocks is large relative to the variance of output shocks, nominal debt becomes less desirable.

99. With respect to foreign currency debt, the optimal amount may be positive or negative depending on the configuration of shocks. If the common component of the shock to output is large (that is, output growth between the domestic and foreign country is closely related) and domestic monetary disturbances have a relatively larger idiosyncratic component, then foreign currency debt has an advantage over domestic debt as a hedge. This corresponds to the case when foreign and domestic output are closely related and the common component of the two country’s monetary shocks is small. Another way of interpreting this result is that foreign currency debt is most appropriate for a country with a relatively unstable monetary system and that is highly vulnerable to shocks from abroad. In fact, in the model, any time output is negatively correlated with foreign inflation, foreign currency debt can play a role in hedging domestic output fluctuations.

100. The results above rely on the negative correlation between output and inflation. However, recent data suggest that the correlation between Danish output and inflation is positive. Bohn anticipates this issue and, in an earlier version of the paper, shows that in a macroeconomic setting with a Phillips curve economy, the optimal nominal debt is reduced. With positively correlated inflation rates, nominal and foreign currency debt are substitutes so that the lower nominal debt is offset by higher foreign currency debt and the optimal foreign currency debt remain unchanged.59

101. Although some elements of Bohn’s model are not realistic (e.g., the purchasing power parity assumption that sidesteps issues of real exchange rate changes), it is one of the few papers to present a positive (risk-sharing) role for foreign-denominated debt based on hedging the real output of the economy. It considers a small, open economy operating within a global economy subject to worldwide shocks to output. The arguments favoring foreign debt do not rely on the lack of credibility of the government (although Bohn notes that this increases the optimal amount of foreign debt as long as actual default probabilities remain small)60 nor are they related to the maintenance of reserves for intervention purposes. Since Denmark has maintained a credible monetary policy and has not attempted to repudiate its debt through inflation, the underlying structure of model accords fairly well with the circumstances of a small, open developed country considering its optimal debt policy. Danish debt policy is now considered in light of this model.

D. Empirical Analysis of a Positive Theory for Foreign Currency Debt

102. Before attempting to distinguish the relative variance of country specific and common shocks to output and inverse velocity and its implications for domestic and foreign debt, consider some basic information about the macroeconomic environment in which Denmark and its trading partners operate.

103. In Table III-3, first differenced logged real GDP and a first differenced logged velocity are evaluated for Denmark and three of its trading partners, Germany, Sweden, and the United Kingdom using quarterly data ranging from first quarter 1981 to fourth quarter 1998.

Table III-3.

Standard Deviations and Correlations Between Selected Variables; Denmark, Germany, Sweden, United Kingdom, and the EU11

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Sources: IFS and OECD quarterly data 1981Q1 to 1998Q4 for all except EU11. EU11 uses Eurostat data from 1990Q1 to 1998Q4.

Standard deviations of first differences of logged output.

Velocity = Nominal GDP/Broad Money. Standard deviations of first differences of logged inverse velocity.

Data for the EU11 is also used, but is only available from first quarter 1991 to fourth quarter 1998. For Germany, the country to which Denmark has traditionally pegged its exchange rate and its largest trading partner, the results supporting the use of foreign debt denominated in deutsche marks is weak. First, note that correlation of output changes between the two countries is basically nil—only about 0.04 over this time period.

104. Low correlation between the output measures is also supported when examined relative to a larger sample of trading partners. Table III-4 shows that, except for Norway and Japan, Denmark has the lowest correlation between its output and its trading partners’ output (weighted by their trade in goods with Denmark) of about 0.25 between 1984 and 1997. The 16 countries in Table III-4 together represent 95 percent of Denmark’s trade. The average correlation of their own GDP with those of the trading partners is about 0.57 for the 1984-1997 period.

Table III-4.

Various Indicators of Output Correlation

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Sources: OECD, Economic Outlook, December 1997; and IMF, World Economic Outlook databank.

Based on data for countries that together account for at least 95 percent of Denmark’s trade. Their weights are based on trade in goods with Denmark

West Germany.

105. An examination of the movements in velocity, simply defined as nominal GDP divided by broad money, also suggests that foreign debt denominated in deutsche marks may not help hedge against output fluctuations. As noted above, foreign debt is useful when the domestic economy is characterized by a more unstable monetary system (higher variance of money demand shocks) than the foreign country and the two countries are hit by common output shocks. Yet, these velocity statistics suggest a weak relationship here as well. First, the standard deviation of the changes in the logarithm of velocity in Denmark is only marginally above that in Germany, 0.052 versus 0.031, and the correlation coefficient between the measures of velocity is 0.12, much higher than that for output growth. Again this suggests that the use of foreign debt to hedge output fluctuations is not likely to be successful.

106. Looking at the United Kingdom as the foreign country in the model shows that issuing debt denominated in British pounds would be even less helpful in hedging output shocks in Denmark if the correlation of output differences and velocity differences are any indication. Output measures between the United Kingdom and Denmark are negatively correlated and the standard deviation of velocity, instead of being higher in Denmark, is lower. Although these are admittedly crude estimates, it appears that there is likely to be more uncertainty in the monetary system in the United Kingdom than Denmark and shocks to output are not coincident.

107. Of the three trading partners, Sweden is the most promising country for which the issuance of foreign currency denominated debt might help counter Danish output fluctuations. The correlation of GDP growth rates, while not high, is about 0.2 and the standard deviation of the velocity measure is slightly higher in Denmark than in Sweden. This corresponds to a configuration of economic conditions that would marginally favor a positive amount of foreign debt denominated in Swedish krona.

108. The results for the EU11 show a negative correlation of output over the last nine years and slightly higher velocity variation: also not particularly promising.61 However, given the possible positive outcome for Sweden and the fact that the foreign debt was denominated predominantly in deutsche mark and is now denominated almost exclusively in euro, these three sets of data will be used for the subsequent analysis.

109. Of course, the examination of correlations of these output and velocity measures does not truly correspond to the model which relates the relative size and sign of shocks to output and velocity. Thus, the next step is to get some notion as to the relation between the country specific and common shocks to output and velocity. This is done in a two-step process. First, for each trading partner, a vector autoregression (VAR) is fit using real output and velocity data from each of the two countries, Denmark and one of its trading partners. This VAR provides white noise residuals representing “shocks” to output and (inverse) velocity.62 However, these residuals will represent all that is unpredictable about output and velocity dependent on lagged values of these variables from both countries. To obtain the country-specific and common components of these residuals, a simple factor model is assumed in which the residuals have one “common” factor and an orthogonal error term. The factor loading (or coefficient on the common factor) represents the weight of the common shock in the total shock and the error term represents the idiosyncratic portion, or the country specific component. This deconstruction will allow the calculation of the relative variances of the shocks included in the equation above.

110. Consider the country which is most favorable for the hypothesis—Sweden. Before beginning to specify the appropriate time-series Vector Autoregression, unit root tests are run on natural logarithms of the underlying data series of real output and inverse velocity for Denmark and Sweden to determine whether the data series, in levels, are stationary. Using a standard Dickey-Fuller test both series reject the hypothesis of no unit root at less than a 5 percent significance level. An augmented Dickey-Fuller test is then used to determine the number, s, of lagged differences of the series, Δyt and Δαt, that make the error terms white noise. Even though these tests are run on each of the four series separately, the exercise provides an initial estimate of the number of lagged variables to be used in the vector autoregression. For each series, an ADF test shows that four lags of Δyt and Δαt for both Denmark and Sweden are jointly statistically significant and that the resulting residuals satisfy the characteristics of white noise. Thus, the VAR model estimated for Δyt separately involves the joint estimation of the following two equations.


111. As well, a similar two equations are estimated for inverse velocity, Δyt, for Denmark and Sweden. Tables 5 and 6 show the parameter estimates and a set of test statistics, testing the adequacy of the VAR representation. For inverse velocity only the first and fourth lags in each equation are necessary to obtain white noise residuals. Recall that the purpose of the VAR is to obtain residuals which represent the (total) shocks to the two series so as to decompose the shocks into a common and idiosyncratic component. Thus, the focus is on tests that assure that the residuals are random, exhibit no autocorrelation, and that the variance of the residuals also exhibit no autocorrelation (i.e., there is no autoregressive conditional heteroscedasticity (ARCH) present). As can be seen from Tables III-5 and III-6, the residuals satisfy these criteria. The only potential issue is whether the residuals are normally distributed since the residuals from the Danish real GDP equation fail that test.63 This could be an issue since both techniques used below to perform the factor analysis assume that each pair of data series are bivariate normally distributed (principal factors technique) or are multivariate normally distributed (maximum likelihood technique). Though the numerical results are somewhat sensitive to the technique, the two techniques give qualitatively similar results.

112. The next step is to use the residuals from the VAR and decompose them into a common and idiosyncratic component. This is done through factor analysis on the residuals of all four equations.


where i represents the four residual series, Danish output, Swedish output, Danish inverse velocity, and Swedish inverse velocity. The factor “loading,” £,-, in the equation above represents the correlation of the residual from the ith equation with the common (single) factor. From the estimates of bf and the (random) factor, F, underlying the processes generating the residuals, the variance of the common component can be calculated as var(bi F) and the variance of residuals from the factor equation, var(ei), represent the idiosyncratic shocks. Table III-7, panel A, shows the variance of the common component and idiosyncratic component for the Danish and Swedish case.

Table III-5. Denmark: VAR Results for Denmark and Sweden

Equation for Real Denmark GDP

Note: sigma = 0,02043; KSS = 0.02419.

Equation for Real Sweden GDP

Note: sigma = 0.01412; RSS = 0.01157.

Table III-6. Denmark: VAR Results for Denmark and Sweden

Equation for Inverse Velocity Denmark

Note: sigma = 0.03669; RSS= 0.08345.

Equation for Inverse Velocity Sweden

Note: sigma - 0.03525; RSS = 0.07704.
Table III-7.

Denmark: Variances of Common and Idiosyncratic Shocks

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Source: Staff estimates.

113. Using these estimates representing the common and idiosyncratic shocks to output and inverse velocity, equation (2) above can be use to determine whether the use of foreign debt denominated in Swedish krona would provide an optimal hedge for output risk. From equation (2), the issuance of foreign debt would be optimal if the term in brackets is positive and lending in the foreign currency would be the appropriate policy if the term is negative. Using the estimates in Table III-6 results in a negative number for this term, -0.00544, indicating that issuing foreign debt in Swedish kroner would not be optimal and, in fact, lending Swedish kroner would be preferred. Using the principal factors technique, which does not impose a multinominal distributional assumption, results in the number -0.00521 for the term from equation (2). These results derive from the Danish economy being relatively more sensitive to common shocks in velocity and idiosyncratic shocks to output rather than the reverse.

Selected Tests

F-test on all regressors except constant: F(16,114) = 121.81 [0.0000] **

Denmark GDP AR(l-5): F(5,53)=0.6935 [0.6306]

Sweden GDP AR(l-5); F(5,53)=0..8835 [0.4987]

Denmark GDP ARCH(4): F(4,50)=0.3100 [0.8700]

Sweden GDP ARCH(4): F(4,50)=0.9814 [0.4262]

Denmark GDP Normality: ChiA2(2) = 27.755 [0.0000]**

Sweden GDP Normality: ChiA2(2)=0.59753 [0.7417]

Vector AR (1-5): F(20,94)=0.7536 [0.7604]

Vector normality: ChiA2(4)= 28.988 [0.0000]**

Selected Tests

F-test on all regressors except constant: F(8,122) = 21.294 [0.0000] **

Denmark inverse velocity AR(l-5): F(5,57)=1.7751 [0.1326]

Swedish inverse velocity AR(l-5): F(5,57)=0.5657 [0.7258]

Denmark inverse velocity ARCH(4): F(4>54)=1.8537 [0.1320]

Swedish inverse velocity ARCH(4): F(4,54)=0.1.8182 [0.1387]

Denmark inverse velocity Normality: ChiA2(2) 0.8285 [0.6608]

Swedish inverse velocity Normality: ChiA2(2)=0.4407 [0.8022]

Vector AR (1-5): F(20,102)=0.8811 [0.6106]

Vector normality: ChiA2(4)= 1,3081 [0.8600]

114. A similar exercise is performed for the EU11. Quarterly data for real output and the components of velocity are available from first quarter 1990 from Eurostat Using the Euro area data for the logarithm of output and inverse velocity shows that both series have unit roots. An augmented Dickey-Fuller test is used to detect an initial estimate of the number of lagged variables to include in the VAR analysis. Unlike the Swedish data, only one lag of output is found to be marginally significant in these tests and is used to estimate VARs of output. For the inverse velocity equation four lags were used although a more parsimonious model appears sufficient to generate white noise error terms. Estimates of the parameters of the VAR and standard test statistics are included in Tables III-8 and III-9.

Table III-8. Denmark: VAR Results for Denmark and EU11

Equation for Real Denmark GDP

Note: sigma =0.01427; RSS= 0.005093

Equation for Real EU11 GDP

Note: sigma = 0.004377; RSS=0.0004788

Table III-9. Denmark: VAR Results for Denmark and EU11

Equation for Denmark Inverse Velocity

Note: sigma=0.02905; RSS=0.01857

Equation for EU11 inverse velocity

Note: sigma=0.008939; RSS=0.001758

115. The residuals from the estimated VAR are then used in the factor analysis to decompose the total shock into a common component and an idiosyncratic component. These results are included in Table III-7, panel B. The configuration of the variances of the shocks in equation (2) shows that foreign debt denominated in euro would aid in hedging output fluctuations vis-a-vis the euro area. That is, the term within brackets in equation (2) is positive, though very small (0.00023) implying that an outstanding foreign debt of about 1 percent of GDP would be optimal. It is interesting to note that the factor loading on the residuals from the VAR equation for Danish inverse velocity is close to zero suggesting that shocks to velocity are unrelated to the underlying factor driving the shock processes for the other variables. Using the principal components technique, the bracketed term is slightly larger and negative, -0.00176, suggesting that, as in the case of Sweden, issuing foreign debt would not be useful.

116. Lastly, the same exercise is complete for Germany, with the VAR results in Tables III-10 and III-11 and the construction of the relevant variables in Panel C of Table III-7. Again, the constructed variable of interest (the bracketed term in equation 2) is negative suggesting that using foreign debt as an output hedge relative to Germany is not advisable. The magnitude of the derived variable is smaller than for Sweden, as the initial analysis would have also suggested. The maximum likelihood technique and the principal factors technique give numbers that are both negative and the same order of magnitude, although they would imply that Denmark should lend in deutsche marks to Germany in an amount varying from 14 percent of GDP to 22 percent of GDP, i.e., have net assets denominated in deutsche mark to hedge output risk.

Table III-10. Denmark: VAR Results for Denmark and Germany

Equation for Real Denmark GDP

Note: sigma = 0.02161; RSS - 0.02616.

Equation for Real Germany GDP

Note: sigma = 0.009580; RSS = 0.005140.

Table III-11. Denmark: VAR Results for Denmark and Germany

Equation for Denmark Inverse Velocity

Note: sigma = 0.03567; RSS = 0.07508.

Equation for Germany Inverse Velocity

Note: Sigma = 0.02953; RSS = 0.05146.

Selected Tests

F-test on all regressors except constant: F(10,48) = 10.182 [0.0000] **

Denmark GDP AR(l-3): F(3,22)=0.3368 [0.7989]

EU11 GDP AR(l-3): F(3,22)=0.5263 [0.6688]

Denmark GDP ARCH(3): F(3,19)=0.3476 [0.7913]

EU11 GDP ARCH(3): F(3,19)=0.5286 [0.6680]

Denmark GDP Normality: ChiA2(2) = 1.5443 [0.4630]

EU11 GDP Normality: ChiA2(2)=5.0694 [0.0793]

Vector AR (1-3): F(30,35)=0.7468 [0.7910]

Vector normality: ChiA2(4)= 8.6359 [0.0709]

Selected Tests

F-test on all regressors except constant: F(16,42) = 2.2786 [0.0167] **

Denmark inverse velocity AR(l-3): F(3,19)=2.7321 [0.0724]

EU11 inverse velocity AR(l-3): F(3,19)=2.0449 [0.1417]

Denmark inverse velocity ARCH(3): F(3,16)=0.7397 [0.5437]

EU11 inverse velocity ARCH(3): F(3,16)=0.1001 [0.9588]

Denmark inverse velocity Normality: ChiA2(2)= 1.5667 [0.4569]

EU11 inverse velocity Normality: ChiA2(2)=8.5357 [0.0140]*

Vector AR (1-3): F(12,30)=3.5604 [0.0023]**

Vector normality: ChiA2(4)= 10.042 [0.0397]*

Selected Tests

F-test on all regressors except constant: F(16,110) = 7.6944 [0.0000] **

Denmark GDP AR(l-5): F(5,51) = 0.7154 [0.6148]

Germany GDP AR(l-5): F(5,51) = 0.5672 [0.7247]

Denmark GDP ARCH(4): F(4,48) = 0.2111 [0.9311]

Germany GDP ARCH(4): F(4,48) = 0.8581 [0.4959]

Denmark GDP Normality: ChiA2(2) = 25.47 [0.0000] **

Germany GDP Normality: ChiA2(2) ?= 6.6941 [0.0352]

Vector AR (1-5): F(20,90) - 0.8228 [0.6804]

Vector normality: ChiA2(4) - 32.641 [0.0000] **

Selected Tests

F-test on all regressors except constant: F(12,116) = 6.3844 [0.0000] **

Denmark inverse velocity AR(l-5): F(5,54) = 1.8038 [0.1276]

Germany inverse velocity AR(l-5): F(5,54) = 0.8639 [0.5114]

Denmark inverse velocity ARCH(4): F(4,51) = 1.6591 [0.1739]

Germany inverse velocity ARCH(4): F(4,51) = 2.4951 [0.0543]

Denmark inverse velocity Normality: ChiA2(2) = 0.9633 [0.6178]

Germany inverse velocity Normality: ChiA2(2) = 21.301 [0.0000] **

Vector AR (1-5): F(20,96) = 0.9438 [0.5351]

Vector normality: ChiA2(4) = 22.613 [0.0002] **

117. Perhaps the best way of interpreting the results is to view them as circumstantial evidence against using foreign-denominated debt to hedge output fluctuations. Only in one case, for the euro, would one conclude that the use of foreign debt may be marginally useful for Denmark as a hedge to output fluctuations—and even then the use would be economically insignificant. The relative magnitudes of common and idiosyncratic components of output and inverse velocity shocks with respect to Sweden and Germany show that use of foreign debt denominated in either Swedish kroner or deutsche marks would not help to hedge output variations. However, it is important to exercise caution in interpreting these results because the magnitudes of the bracketed numbers are very close to zero and they are constructed using econometric estimates, which are themselves subject to estimation error (particularly given the relatively small samples). Thus, these numerical outcomes may not be statistically significantly different from zero.

118. Having examined the underlying correlations of output and velocity, however, one might have suspected, a priori, that using foreign-denominated debt may not be particularly useful for hedging output risk. Thus, the numerical results are not surprising since they embody the intuition that Denmark’s output shocks are not correlated with those of its trading partners and its monetary system is relatively more stable than that of these same trading partners (the domestic money demand shocks are relatively smaller than those in the trading partner countries). These results lead to the conclusion that, from the perspective of hedging output risk with foreign debt, the elimination of foreign debt planned by the Danish government is a sensible goal. Thus, although the policy debate has centered on other reasons for the elimination of foreign debt, the analysis presented here adds yet another reason—one in which the potentially positive effects of foreign debt on the real economy are taken into consideration.


  • Bohn, Henning, 1990, “A Positive Theory of Foreign Currency Debt,” Journal of International Economics, No. 29, pp. 273292.

  • Danmarks Nationalbank, 1999, “Danish Government Borrowing and Debt 1998,” (Copenhagen, Denmark).

  • Danmarks Nationalbank, “Danmark’s External Debt 1998,” Statistisk Afdeling, No. 24–8 March 1999, Table 2, (Copenhagen, Denmark).

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  • OECD, 1991, Economic Surveys, Denmark 1990/1991, pp. 2526 (Paris: Organization for Economic Cooperation and Development).


Prepared by Laura Kodres.


The Danish Economy: Medium-Term Economic Survey, March 1999, p. 54.


From the Act, passed December 22, 1993, setting out the legislative basis for government borrowing.


OECD Economic Surveys, Denmark, 1990/1991, (p. 25-26.)


Danmarks Nationalbank, “Danish Government Borrowing and Debt” 1998, p. 57.


The source of much of the information in this section comes from “Danish Government Borrowing and Debt” published by Danmarks Nationalbank, 1998, and other publications of the Nationalbank.


Other public sector entities had net foreign assets of about DKr 14 billion at the end of 1998.


The EMU debt includes the liabilities of both the central and local governments but also allows the public sector’s claims on itself, i.e., holdings of government securities held by the Social Pension Fund and other social funds, to be deducted.


When the central government issues foreign-denominated debt, the proceeds are added to foreign exchange reserves and the balance in the central government’s account at the central bank increases. Article 104 of the Maastricht treaty, which prohibits monetary financing, imposes the constraint that the balance of the central government’s account with the Nationalbank must be positive at all times.


This occurred in 1998 when Tele Danmark, a partially government-owned entity, was fully privatized by a sale of stock to foreigners. The proceeds from the sale were used to reduce the central government’s foreign liabilities.


This measure of duration is a weighted discounted present value of the coupon payments and final par value where the weights are the time in years from the present for each of the cash flows. Duration provides a more precise measure of the potential interest rate risk of a portfolio of bonds than the average of stated maturities by accounting for the effect that the different timing of the cash flows has on the portfolio’s price sensitivity to interest rate changes.


The model does not include the goal of maintaining a liquid government securities market for capital market development nor the notion that continual debt issuance may make it easier to access debt markets in times of distress.


The term “nominal” debt will refer to domestically-denominated government debt that is not indexed.


Actually, all that is necessary is that foreign investors are sufficiently less risk averse than the domestic ones that they are willing to provide the “insurance” represented by government debt. If foreigners are not risk neutral, then they would also want to hedge their own countries’ output risk, complicating the solution of the model by requiring four types of debt. Bohn argues that international investors are likely to be more diversified and less risk averse than the typical taxpayer.


The model is specified in terms of inverse velocity instead of velocity since the money balances are determined in the model as inverse velocity times the price level times output.


Inflation is negatively correlated with output given a fixed money supply growth rate (that is, the government cannot manipulate inflation), exogenous output, and the equation determining inflation, where a is the change in inverse velocity.


See Bohn, p. 284.


Bohn explicitly assumes actual default is not available only the “excusable” default of a decrease in the real value through inflation.


The EU11 includes Germany so the results cannot be viewed as unrelated to those of Germany.


Recall the model is in terms of inverse velocity as is the empirical work in this section.


The endogeneous variable, the difference of logged real Danish GDP, does not reject the normality test.

Denmark: Selected Issues
Author: International Monetary Fund