The Effective Krone Rate and Trade in Services

Erik Haller Pedersen, Economics

INTRODUCTION AND CONCLUSIONS

Danmarks Nationalbank calculates and publishes the effective krone rate, which is an index indicating the strength of the krone vis-à-vis a basket of currencies. The weights for the calculation of the effective krone rate are based on trade in manufactured goods, and are updated from time to time on the basis of an international data set, a " trade matrix" . This article applies a method for quick and easy approximate updating of the weights, based solely on trade data from Statistics Denmark. In addition, the significance of including trade in services in the calculation of weights is assessed.

The conclusion is that the effective krone rate is a fair representation. It is relatively robust to the choice of base year, as well as to the exclusion of trade in services. Inclusion of trade in services, which has a wider geographical spread than trade in manufactured goods, makes the index slightly more exposed to fluctuations in the dollar than the traditional krone-rate index.

CALCULATION OF THE EFFECTIVE KRONE RATE – TRADITIONAL METHOD

The value of the krone vis-à-vis another currency is represented by the bilateral exchange rate, e.g. Danish kroner per euro. In a nominal effective krone-rate index, the strength of the krone is measured against a basket of currencies. In order to calculate this index, it is necessary to determine the weight of each currency in the index, and in practice also to limit the number of currencies included.

The way the weights are calculated depends on the intended use of the krone-rate index. Usually it is sought to measure the effect of exchange-rate fluctuations on foreign trade, i.e. a measure of competitiveness. The weights must therefore reflect the relative importance of Denmark's trading partners in terms of overall trade. The more exposed Danish manufacturers are to competition from a given country's products, the greater should be the weight of that country's currency.

Today 27 countries are included in the set of weights for calculating the nominal effective krone rate. The weights are based on trade in manufactured goods in 2002. The final weights are achieved by weighting together a set of bilateral import weights and a set of double-weighted export weights. Danish business enterprises compete with e.g. German manufacturers in the Danish market (captured in the import weight), but also in the German market and third markets (summed up in the double-weighted export weight). This calculation requires an international data set and cannot be performed using data from Statistics Denmark only. Calculation of the nominal effective krone rate is documented by Ølgaard (1992) and by Pedersen (1998) and (2004).

Competitiveness is influenced not only by the bilateral exchange rate, but also by differences in wage developments in Denmark and abroad. This is reflected in the real effective krone-rate index, measuring the relative development in wages expressed in the same currency, cf. Pedersen (1996). The real effective krone rate illustrates the development over time in Denmark's competitiveness vis-à-vis its major trading partners. The weights used for calculating a real effective rate are identical to those used for calculating a nominal effective rate.

ALTERNATIVE CALCULATION OF WEIGHTS FOR THE EFFECTIVE KRONE RATE

The Appendix describes an alternative method for calculating the weights in the krone-rate index. This method differs from the traditional method, but only slightly. In the outlined alternative method, the import weight is determined in the usual way, while the export weight is explicitly broken down into a bilateral export weight, e.g. competition with German products in the domestic German market, and a weight indicating competition in third markets, e.g. with Germany in markets outside Germany, cf. Box 1. The traditional method applies a single, double-weighted export weight, cf. above.

In itself, this methodological change has only a small impact on the weights. The most significant difference between the new method outlined in the Appendix and the traditional method is that exports have been given a greater weighting, cf. the Appendix.

An advantage of the outlined alternative calculation method is that, assuming a relatively stable global trade structure, the weights can be updated on the basis of national data only, unlike the traditional method, which requires an international data set. This can be used to assess the robustness of the krone-rate index to ongoing changes in trade flows.

The approximation approach, which assumes that some sub-components in the calculations of weights remain unchanged, can also be used to estimate the significance of including trade in services in the calculations. International statistics for trade in services still leave much to be desired, and it is difficult to set up a full international trade matrix that includes trade in both manufactured goods and services. Application of the bilateral export and import weights calculated on the basis of national data makes it possible to estimate the significance of trade in services, a steadily increasing sector that now accounts for close to 25 per cent of global trade. There are, however, various methodological issues related to including trade in services, cf. below.

CALCULATIONS BASED ON DANISH DATA

In Table 1, the effective krone rate has been calculated using the 2002 weights and the calculation method outlined in the Appendix, i.e. TCW (Total Country Weights). This enables comparison with the traditional method since trade flows in 2002 are also used for calculating the weights for the effective krone rate, shown in the last column in the Table.

As described in the Appendix, the weights on the export side are higher in the TCW calculations than in the traditional calculations. Consequently, the aggregate weight of the euro area is a little greater, primarily on account of Germany. German business enterprises are major competitors of Danish enterprises, especially in third markets, and are given a greater weighting in the alternative calculation. In contrast, the weights of several other euro area member states have been reduced.

The greater weighting of the euro area is offset by the lower weighting of the " dollar area" , i.e. the USA, China and Hong Kong. It is important to emphasise that Denmark predominantly competes with neighbouring countries. Total trade with Asia, including China and Japan, and the whole of Eastern Europe, is still lower than trade with Sweden.

When calculated as described in the Appendix, the set of weights changes only marginally, and the overall development in the krone-rate index since 1997 is almost the same, irrespective of the weighting method applied, cf. Chart 1. The alternative method therefore seems to be applicable as an approximation of the traditional calculation method. Below it is used to assess the quality of the 2002 weights compared with a more current set of weights, and also to assess the significance of including trade in services in the calculation.

In Table 2, the alternative method is used to calculate sets of weights on the basis of trade in manufactured goods in 2002 and 2006, respectively. The purpose is to assess the robustness of the krone-rate index in terms of the base year. Since 2002 the weights of particularly Germany and the UK have declined, while those of Sweden and China have increased. China's weight has increased by more than 50 per cent, but the overall changes are so small that the effective krone rate based on 2002 weights must be assessed to give a true and fair view of the development, cf. Chart 1.

The last column in Table 2 shows a set of weights calculated using the method outlined in the Appendix, but now including trade in services. In this case, the changes in relation to the traditional index are somewhat greater.

Danish trade in services has a wider geographical spread than trade in manufactured goods. While the 27 countries in the krone-rate index account for approximately 90 per cent of Denmark's aggregate trade in manufactured goods, their share of trade in services is only 75 per cent. The more diverse trade is also reflected in a lower weight for the euro area, whereas that of the " dollar area" , i.e. the USA, China and Hong Kong increases – from 11.6 per cent to 14.4 per cent. The greater exposure to the dollar rate is illustrated in Chart 1, where the krone-rate index including trade in services shows a steeper downward trend during the period from 1998 to 2001 (dollar strengthening), but also increases more after 2001 (dollar weakening), compared with the traditional index, cf. also the decomposition in Table 3. Overall, the difference from the traditional krone-rate index is, however, not great. Including trade in services in the krone-rate index has no material impact on the overall development in the index over time, and thus on the assessment of Denmark's competitiveness.

METHODOLOGICAL ISSUES WHEN INCLUDING TRADE IN SERVICES

Denmark's considerable agricultural exports are excluded when weights are calculated on the basis of manufactured goods. The reason for this has traditionally been that price formation is not fully market-based due to the many subsidy schemes and trade restrictions in this area. For a large proportion of Danish exports, e.g. pork, this is likely to be of lesser importance, but it has been decided to apply the calculation method most frequently used internationally.

The increasing international trade in services, which now accounts for almost one quarter of global trade, is typically excluded too^[1]. This is mainly attributable to data availability problems in that international statistics for trade in services are far less comprehensive than foreign-trade statistics for goods. In addition, there are a number of fundamental methodological problems.

When calculating the weights, it is sought to determine where the underlying economic activity took place. The invoicing currency is of less significance. What matters is competition experienced by Danish enterprises from enterprises based in a given country. Exports from e.g. Sweden to Denmark invoiced in dollars should not affect the weighting of the USA. Local costs in Sweden, not the invoicing currency, will ultimately determine the degree of competition from Sweden.

Attempting to capture the location of the economic activity behind a transaction in the krone-rate index poses special problems in relation to services such as sea freight. If a Swedish company employs a Danish shipping company to sail goods from China to the USA, this is registered as export of a service from Denmark to Sweden, even though the activity, i.e. the actual service, takes place between China and the USA. In reality, Denmark is more likely to be competing with other seafaring nations such as Greece. Moreover, the service typically includes very little Danish output and few Danish costs, since most input – bunkering, crew, etc. – tends to be foreign. Thus it is more likely to reflect Danish ownership of foreign output. It is sought to include only trade based on Danish output in the weighting, and therefore this activity should not be fully included.

Another case in point is a Swiss business enterprise which holds the copyright to the works of some of the world's best-selling authors. When one of them publishes a new book, Swiss exports of services to Denmark increase, despite the fact that the actual " production" seldom takes place in Switzerland.

These examples serve to illustrate some of the fundamental problems related to including services in an effective krone-rate index, and, viewed in isolation, they support continued exclusion of services in the calculations. Indeed, this is typically the case in most national calculations of effective exchange rates, including the indices calculated by the ECB. There are no plans to change the traditional calculation method, or, for that matter, to include services when the weights for calculation of the effective krone rate are updated again in a few years.

LITERATURE

Alsterlind, Jan (2006), " Effective exchange rates – theory and practice" , Sveriges Riksbank, Economic Review, 2006:1.

Bayoumi, Tamim, Jaewoo Lee and Sarma Jayanthi (2005), " New Rates from New Weights" , IMF, Working Paper no. 99.

Lynch, Birone and Simon Whitaker (2004), " The new sterling ERI" , Bank of England, Quarterly Bulletin, Winter.

Pedersen, Erik Haller (1996), " Real Effective Exchange Rates" , Danmarks Nationalbank, Monetary Review, 2nd Quarter.

Pedersen, Erik Haller (1998), " Revision of the Weights for Calculation of the Nationalbank's Effective Krone Rate Index" , Danmarks Nationalbank, Monetary Review, 2nd Quarter.

Pedersen, Erik Haller (2004), " Revision of the Weights for Calculation of Danmarks Nationalbank’s Effective Krone-Rate Index" , Danmarks Nationalbank, Monetary Review, 4th Quarter.

Zanello, Alessandro and Dominique Desruelle (1997), " A Primer on the IMF's Information Notice System" , IMF, Working Paper no. 71.

Ølgaard, Christian (1992), " The Effective Krone Rate and Competitiveness" , Danmarks Nationalbank, Monetary Review, February.

APPENDIX

The alternative weighting method presented in this article is described in Zanello and Desruelle (1997) and applied by Lynch and Whitaker (2004) and Bayoumi et al. (2005), among others. See also Alsterlind (2006).

The point of departure is a matrix, i.e. a table describing output and trade flows between, in this case, 28 countries: Denmark and 27 export markets. If the first country in the matrix is Denmark, the top row, first cell, shows Danish output sold in the domestic market, followed by Danish exports to the 27 export markets. The second country could be Germany, so that the second row, first cell, shows German exports to Denmark, i.e. Danish imports from Germany. Cell two shows German output for the domestic German market, and the rest of the row shows German exports to other countries than Denmark. Similarly, each of the remaining countries has a row with output for the domestic market and exports broken down by recipient country. 

The first column of the matrix shows Danish output for the domestic market at the top, followed by Danish imports by country, so that the first column shows the Danish market broken down by supplier countries. Column two is Germany, and so forth.

A value-added and trade matrix like this is used as the starting point for calculating weights for effective exchange-rate indices. The matrix can be standardised horizontally or vertically to obtain shares, cf. the two share matrices below. Standardisation by imports and domestic demand for domestic output is called " s" (supply matrix), and standardisation by exports and output intended for the domestic market is called " w" (application matrix). Since the standardisation basis is not the same, the diagonal elements of the two matrices usually differ.

To calculate the weights for the effective krone rate, we need the Danish row of ws, i.e. the first row in the w matrix, and all the ss. If the first row of the w matrix is multiplied by each row of the s matrix, and the result is entered into a new matrix, v₁, we obtain a total breakdown by country of the competition met by Danish exporters, cf. Zanello and Desruelle (1997). The new matrix is a product of the s matrix and a matrix with the first row of the w matrix as the diagonal, surrounded by zeros.

The sum of the matrix elements is 1, but the first row of the new matrix indicates the share of Danish output. The first-row elements are therefore not included in the effective krone-rate index, while the remaining elements are included. Thus, the element in row j column k describes the share of country k of the market in country j. These weight contributions to the krone rate must be rescaled to add up to 1.

In the above expression of country k's share in country j, k and j are also used in the sum signs, where k counts up all 28 countries, while j counts up the 27 export markets, i.e. the 28 countries excluding Denmark.

We have thus described the weights for the effective krone-rate index. The 27 row sums in the v₁ matrix illustrate the 27 country weights. For example, the total weight for Germany is the sum of row 2.

The set-up in the v₁ matrix can also inspire a decomposition of the index across countries, cf. Lynch and Whitaker (2004). The red first column of the matrix shows the contribution from imports. The blue diagonal shows the bilateral contribution from exports, i.e. the contribution from German competition in the German market, British competition in the UK market, etc. The rest, in green, shows the third-market contribution from exports, i.e. the contribution from German competition in the UK market, British competition in the German market, etc. While there are only 27 bilateral import contributions and 27 bilateral export contributions, there are many third-market contributions, cf. the number of green elements in the v₁ matrix.

The aggregate weight contribution from imports, the share of red fields, can be expressed as:

The formulae are written with 1 for Denmark. If 1 is replaced by i, full accordance is achieved between the notation in the references showing the calculation of effective exchange rates for all countries in the matrix.

The aggregate contribution from bilateral exports, the share of blue fields, is:

The total weight of country j in the aggregate krone-rate index can now be expressed as a sum of three components: the contributions from imports, bilateral exports and third-market exports:

This formula has been used to set up Table 1 in the text. The formula has also been used for the calculations in Table 2 with all quantities unchanged except bilateral imports and exports, i.e. MW_1j and BXS_1j, which can be calculated using data from Statistics Denmark only. This corresponds to the updating technique used by the Bank of England for calculating the sterling ERI, cf. Lynch and Whitaker (2004), which, however, also updates the third-market contribution on the basis of the most recent data for the countries' aggregate trade. The significance of not updating the third-market contribution is assessed to be minimal in the short run and consequently updates have been omitted here. This also makes the updating process more operational.

The calculation method outlined in this Appendix deviates only slightly from the method used for calculating the traditional effective krone rate. The difference can be illustrated on the basis of the above matrices. The alternative method inserts zeros in row 1 in the v₁ matrix and rescales the remainder of the elements in the matrix by the same factor so that they add up to 1. The traditional method, on the other hand, sets row 1 in the s matrix at 0 and scales the rest of the elements in the s matrix columns so that each column adds up to 1. With this converted s matrix, the v₁ matrix has inherent zeros in the first row and its elements include the weight contributions to the traditional calculations of the country weights for the krone-rate index. The resulting country weights differ only slightly under the two methods. The major difference is that in the alternative calculation we also choose to change w¹₁ in the w matrix, which in these calculations takes added value as its point of departure rather than output value as hitherto, cf. the method description in Pedersen (1998). Consequently, the export side is given a greater weight under the alternative calculation method than under the traditional method – 69.3 per cent and 54.4 per cent, respectively. Others often simply weight the import and export sides together with a weight of 0.5 each. This is the case for e.g. the effective exchange rate index calculated by the European Central Bank, ECB.