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Appendix

Danish companies face competition from companies abroad on both the domestic and export markets. The breakdown of this competition by country cannot be determined precisely, but when effective exchange rates are calculated it is normally assumed that competition on individual export markets and on the domestic market is directly proportional to each country's market share. The starting point is thus trade flows, whereas normally which currency the trade is invoiced in is without significance.

As a starting point two sets of weights are calculated, one representing the distribution of competition on export markets (double-weighted export weights) and one for the domestic market (bilateral import weights).

Double-weighted export weights

Calculation of a set of double-weighted export weights assumes that each country's market share is known, including its domestic market share, i.e. the diagonal in the matrix. The calculation is based on a trade matrix for manufactures (SITC 5-9), as illustrated below.

a_i,j indicates the export share of manufactures from country "i" to country "j". The basis is thus the export statistics, which are normally considered to be more correct than the import statistics.

The diagonal elements in the matrix indicate total deliveries to the domestic market from country "i"'s industry in relation to the total inflow of manufactures to country "i", i.e. including imports from other countries:

PV_i = Production value in manufacturing sector in country "i"

X_i = Value of manufactured exports from country "i"

M_i = Value of manufactured imports to country "i"

One of many problems with regard to the layout of the matrix is that national accounts and foreign-trade statistics must be collocated.

It should be noted that there is no row for "Rest of World" (RoW). The underlying assumption is that where RoW includes industry it does not compete with industry in Denmark or the other 25 countries, for example because it manufactures other categories of goods which are not close substitutes for products from industrialized countries. This is a simplified assumption for calculation purposes.

On the other hand, there is a column for RoW comprising the 25 countries' export shares to RoW. Here the assumption is that Danish manufacturers' exports to RoW compete solely with exports from the 25 countries, but not with industry in RoW.

The aforementioned assumptions are, as stated, necessary for the calculation, but at the same time do have a certain relevance. The greater the divergence between the stages of industrial development of the countries included, the more difficult it becomes to interpret changes in the effective exchange rate as reflecting any change in competitiveness, since often there is no close substitution between the manufactured goods. This problem is inter alia discussed in the OECD (1994)¹⁾ and emphasizes that an effective exchange-rate index will not necessarily be "better" simply because many countries are included in the calculation. Nonetheless, the international development is towards including new countries in the calculation of weights, as more and more newly industrialized countries become players in the world market for manufactured goods. The Southeast-Asian countries' share of world trade in manufactured goods has thus doubled from 1985 to 1995, and now constitutes almost 25 per cent. However, this is partly offset by a decrease in the share of other non-OECD countries, so that the OECD countries' total share of world trade has declined only moderately during the period.

The matrix of market shares describes the extent to which Danish manufactured exports compete with the 25 other countries in the 26 markets where RoW is considered as one. To gain an overall impression of competition with each country the shares on the individual markets must be weighted together. This is based on the collocation of Danish manufactured exports distributed by country, i.e. using bilateral export weights (b_j).

The double-weighted export weight for country "i" (W_i^x) is generated as follows:

If "i" is e.g. Germany, the double-weighted export weight is Germany's share of the US market multiplied by the share of Danish exports to the USA, plus Germany's share of the Japanese market multiplied by the share of Danish exports to Japan ....., plus Germany's domestic-market share multiplied by the share of Danish exports to Germany, plus Germany's share of the market in RoW multiplied by the share of Danish exports to RoW.

Since industry's production value in country "i", PV_i , to a certain extent comprises output sold to the domestic market but in real terms does not compete with imports from other countries (a case in point is newspapers), in practice the domestic-market share is overestimated. In other words, the double-weighted export weights entail a bias towards bilateral export weights not subject to simple adjustment.

Bilateral import weights

Danish industry's domestic-market sales take place in competition with foreign companies, as is the case for the export markets. Equivalent to the treatment on the export side, competition on the domestic market from each country is assumed to be directly proportional to that country's share of Danish manufactured imports. The impact of foreign competition on the domestic market is therefore represented by a set of bilateral import weights (W_i^m). RoW is not included in the set of weights on the import side due to the assumption that industry in RoW does not compete with either Danish enterprises or enterprises in the other 25 countries.

Overall set of weights

In order to obtain an overall set of weights the double-weighted export weights (W_i^x) and the bilateral import weights (W_i^m) must be weighted together. The method is not determined beforehand. The Nationalbank has chosen to weight the export side with the proportion of the value of manufactured output which is exported. As a consequence of the greater international division of work this proportion has been increasing in historical terms, but with fluctuations over time, inter alia as a consequence of varying cyclical development in Denmark and abroad. The actual trend, cf. Chart 3, is therefore used. It might be argued that a similar adjustment should be made on calculating the market-share matrix and the bilateral

sets of weights. However, it is the assessment that the greater uncertainty this will entail for the calculation exceeds the advantages.

The total set of weights for country "i" is now:

where a^e is the trend-determined export share in the base year, i.e. 1995. This is estimated at 60.3 per cent. The resulting set of weights is shown in Table 1.

Calculation of the effective krone-rate index

Given the set of weights as calculated above, the nominal effective krone-rate index (NEER) is now:

and S_i( ) is the bilateral krone rate vis-à-vis currency "i" compiled as foreign currency per krone to time t and basis time t₀.

In other words the effective krone-rate index is calculated by weighting indices for the value of one krone vis-à-vis the various currencies using the calculated weights. An effective exchange rate is therefore born as an index and has no meaning in absolute terms at any given time, since only the development over time can be subject to interpretation. An increase in the effective krone-rate index reflects a strengthening of the krone. It will be seen that a geometrical weighting is used. The advantages of this are described in the Box.

The index is linked to the old index as of May 30, 1997, when the value was 100.563246, so that 1980 is still equal to 100. Effective krone rates from before June 2, 1997 are thus unchanged.

The real effective exchange rate (REER) is as follows:

and P_DK is a price index for Denmark, and P_i equivalently a price index for country "i".

The consequences of not double weighting the export weights

While calculation of an effective krone rate based on bilateral weights can apply Danish data exclusively, double weighting requires detailed statistics from all countries involved, which makes it more difficult to involve many countries and to construct up-to-date weights. On the other hand the advantage is that the theoretical basis for double-weighted export weights

is considerably stronger than for the bilateral weights, but the latter can very well be used as a supplement in certain situations.

Chart 4 shows the result of omitting double weighting for the period 1990 to 1998. 89 weights are used, but the 95 set of weights would give an equivalent result. Although the overall development is the same there are deviations of up to 1.50 index points between the two indices over the period considered. The deviations become particularly significant in periods of strong fluctuation in the Swedish krona or Jananese yen, the two currencies accounting for the greatest difference between the bilateral and double-weighted export weights.

Footnotes