Grubel-Lloyd Index

Grubel-Lloyd indices of various countries over the course of 5 years according to Part 7 of SITC Rev.4 (this includes, among other things, prime movers, metalworking machines, office machines, electrical machines, road vehicles and other means of transport).

The Grubel-Lloyd Index is the measure of an economy that specifically deals with international trade . The index provides information about whether a nation tends more towards inter-industrial trade (value 0) or intra-industrial trade (value 1). Inter-industrial trade is understood to mean the exchange of different products (or between different industries), whereas intra-industrial trade describes the exchange of similar products. It is named after the German-Canadian economist Herbert Grubel (* 1934) and the New Zealand economist Peter Lloyd , who first published it in 1975.

Calculation and interpretation

The Grubel-Lloyd Index can be calculated for a specific product or a specific product group using the following formula: ${\displaystyle i}$

${\displaystyle GL_{i}={\frac {(EX_{i}+IM_{i})-|EX_{i}-IM_{i}|}{(EX_{i}+IM_{i})}}=1-{\dfrac {\left|EX_{i}-IM_{i}\right|}{EX_{i}+IM_{i}}}\ ;\ \ 0\leq GL_{i}\leq 1.}$

It stands for the export volume in terms of value or quantity, and the volume of import in terms of value or quantity of the respective product . The sum of exports and imports of a product group corresponds to the total trade volume of this product group. The trade balance , i.e. the amount of exports of the said product group minus the imports of the product group, is subtracted from this trade volume . Finally, this term is divided in the numerator by the total trading volume of the product group. ${\displaystyle EX_{i}}$ ${\displaystyle IM_{i}}$ ${\displaystyle i}$ ${\displaystyle i}$ ${\displaystyle i}$

Differentiation of extreme cases:

• ${\displaystyle GL=1}$: In the event that the exports correspond to the imports, the difference within the amount bars would disappear and the entire index would then assume the value 1. So there is only intra-industrial trade with regard to the product group . As a result, this trade concept deviates from the idea of ​​the comparative cost advantage according to David Ricardo , since these are very similar goods and the national economies have therefore not specialized in a certain product group . ${\displaystyle i}$ ${\displaystyle i}$
• ${\displaystyle GL=0}$: If, on the other hand, the product group is only exported or only imported, the difference between the trading volume and the trading balance of the respective product group approaches zero and the entire index takes on the value 0. In this case there is only interindustrial trade and trade with this product group only takes place in one direction. The trading concept is based on the idea of ​​a comparative cost advantage . The economy or industry consequently specializes in a certain product group , which it can produce to its advantage due to different factors. This aspect is based on the assumption of the Heckscher-Ohlin theorem . ${\displaystyle i}$ ${\displaystyle i}$

The amount bars are necessary because exports do not necessarily have to be higher than imports. If the amount bars did not exist, an index value above 1 could result in an import surplus. After all, values ​​would no longer be comparable with each other when the Grubel-Lloyd index was recorded across several product groups.

Examples of calculation

Grubel-Lloyd indices of different countries, according to part 0 (food and live animals) and part 7 (mechanical engineering products and vehicles) of SITC Rev. 4, from 2014

The index is explained below using examples. The values ​​from the graphic in this section are used for this.

example 1

In 2014, Australia exported around US $ 13 billion in the area of ​​“mechanical engineering products and vehicles” according to SITC Rev. 4, but imported around US $ 84 billion in this product category. The Grubel-Lloyd-Index is calculated as follows:

${\displaystyle GL_{\text{Maschine}}^{\text{Australien}}=1-{\dfrac {\left|13-84\right|}{13+84}}\ =0{,}268}$.

The trade in mechanical engineering products and vehicles in Australia therefore tends towards inter-industrial trade.

Example 2

Spain, on the other hand, exported in the product category of mechanical engineering products in terms of value with around 101.6 billion US $, almost as many products as were imported (96 billion US $). The Grubel-Lloyd index is therefore close to one, which indicates intra-industrial trade:

${\displaystyle GL_{\text{Maschine}}^{\text{Spanien}}=1-{\dfrac {\left|101{,}6-96\right|}{101{,}6+96}}\ =0{,}972}$.

Average of the Grubel-Lloyd index

In order to make the Grubel-Lloyd index comparable for different countries, it has to be averaged over many (all) product groups in a country. This can be done in two ways.

Unweighted mean

Goods groups can be averaged arithmetically, which is also referred to as the unweighted mean (see arithmetic mean ). This results in the following formula:

${\displaystyle GL_{\text{ung}}={\frac {1}{n}}\sum _{i=1}^{n}{\frac {(EX_{i}+IM_{i})-|EX_{i}-IM_{i}|}{(EX_{i}+IM_{i})}}}$.

Weighted mean

If different product groups are to be assessed together, a weighting with regard to the trading volume of the individual product group values ​​must be carried out in order to avoid a distorted result through simple addition. In this way, much traded products can be given greater consideration than products that have an insignificant share in trade (cf. weighted arithmetic mean ). The following formula is used as a basis:

${\displaystyle GL=\sum _{i=1}^{n}w_{i}GL_{i}=\sum _{i=1}^{n}\left({\frac {EX_{i}+IM_{i}}{\sum _{i=1}^{n}(EX_{i}+IM_{i})}}\right)GL_{i}=1-{\frac {\sum _{i=1}^{n}|EX_{i}-IM_{i}|}{\sum _{i=1}^{n}(EX_{i}+IM_{i})}}}$.

It is the weighting factor for each GL values of each product category. The weighting factor represents the ratio of the trading volume of the goods group to the total trading volume. ${\displaystyle w_{i}}$

Importance and evaluation

For older theories such as the comparative cost advantage , it is difficult to explain the increasing intra-industrial trade. Large trading partners like Europe and the USA actually trade many similar products with one another.

This contradiction can partly be triggered by examining the equality of the products more closely. Intra-industrial trade is “simultaneous export and import of products that are very close substitutes in consumption or in terms of factor input”. The goods fulfill the same function or were manufactured using the same technologies, but are not completely identical.

Grubel and Lloyd tried to approach the definition problem of equality by typifying goods. They introduced the degree of substitutability as a distinguishing criterion:

• Type I of goods: close substitutes in production, not in consumption.
• Type of goods II: close substitutes in consumption, not in production.
• Type III of goods: Substitutes with regard to the production and consumption process.
• Type IV goods: Different in production and consumption.

If traded goods have a high degree of substitution, intra-industrial trade tends to take place. Otherwise trade will be more of an inter-industrial nature.

The share of intra- industrial trade in the total trade of the respective country gives an indication of the similarity of business cycles within an industrial sector. One example is the comparability of the automotive industry with other countries in the euro area . The higher the index, the more specific shocks spread across all the countries under consideration and thus work towards a synchronicity (parallel course) of the business cycle.

Problems arise if emerging countries are compared with industrialized countries. Above-average growth in the developing economy distorts the key figure based on absolute values. Domestic differences such as potential contradictions between urban centers and rural regions can also lead to distortions.

Requirements for undistorted GL values

The concept of the Grubel-Lloyd Index as an indicator of intra-industrial trade is subject to certain limits in its application. Therefore, several requirements should be observed in order to obtain values ​​that are as undistorted as possible.

The question arises as to which and how many different products total trade is broken down into. The classification and the level of aggregation of the products are decisive for the best possible mapping of a particular sector. Goods are grouped together, whereby information about export and import values ​​is lost. It can be determined that the higher the level of aggregation within a product classification, the higher the intra-industrial trade. This is because if you have a broad product sector, more products fall into the sector than if you interpret it more narrowly. If many products are now recorded in one sector, the probability is higher that these will be both imported and exported. The reverse is also true. A suitable theoretical concept for the specific purpose of the investigation should be decisive for the choice of the aggregation level. The most common form is to take the goods classification from the International Trade Classification (SITC), so that a uniform and transparent classification is possible. The SITC is structured as follows:

• 10 parts
• 67 sections
• 262 groups
• 1023 subgroups
• 2970 smallest structural units (so-called five-digit)

Another aspect that must be taken into account when interpreting the unweighted Grubel-Lloyd index is the trading volume of the product category under consideration. The volume is completely neglected in the calculation, but product categories with a high trading volume are more important than those with the same GL value but lower volume. To solve this problem, an additional measure is proposed which shows the importance of the product category of the country under consideration (e.g. ratio of trade volume to GDP ).

If the Grubel-Lloyd Index is used to assess changes in the structures of an industry due to changes in certain trade flows, it should be noted that this is only calculated for a fixed period of time . As a result, possible changes during this time are not taken into account, which can lead to misinterpretations.

Furthermore, the different degrees of development of the economies under consideration as well as internal differences (urban centers / rural regions) should be taken into account in the calculation in order to avoid distortions.

Correction of the Grubel-Lloyd index

The Grubel-Lloyd index is intended to be a measure of how strongly intra-industrial trade is carried out in relation to total trade. For this it is calculated across all goods groups with the volume share of the respective goods groups ( ) in the total trade volume ${\displaystyle EX_{i}+IM_{i}}$

${\displaystyle \sum _{i=1}^{n}(EX_{i}+IM_{i})}$

weighted (see above). The results are only precise here if the country's trade balance is balanced and structural equality exists. A trade balance is balanced when imports and exports are balanced. Structural equality exists if either a trade balance surplus or a trade balance deficit was generated uniformly across all goods groups. As soon as one group of goods deviates from the others, structural equality can no longer exist. However, since trade balances are only seldom balanced and structures are the same, this approach leads to a distorted result.

For this reason, Grubel and Lloyd undertook a “global adjustment” of the trade balance in their formula, across all product groups under their weighted index. Here, the intra-industrial “trade of all groups of goods is related to the trade volume adjusted for the imbalance [...] instead of the total trade volume”.

${\displaystyle GL_{\text{korr}}={\frac {\sum _{i=1}^{n}(EX_{i}+IM_{i})-\sum _{i=1}^{n}|EX_{i}-IM_{i}|}{\sum _{i=1}^{n}(EX_{i}+IM_{i})-|\sum _{i=1}^{n}EX_{i}-\sum _{i=1}^{n}IM_{i}|}}}$

Nevertheless, it makes sense to look at both the corrected and the uncorrected Grubel-Lloyd index for an analysis. In the event that exports exceed imports or imports exceed exports across all product groups, the corrected index assumes the value 1. So there is structural equality. The actual values ​​of the respective export or import surpluses are irrelevant. This means that the corrected Grubel-Lloyd index is no longer meaningful, but the prerequisite for the uncorrected Grubel-Lloyd index is given.

Alternatives to the Grubel-Lloyd Index

In the following section, alternatives to the Grubel-Lloyd index are discussed, which were the basis for the findings of Grubel and Lloyd. Although these different indices served as the basis for the Grubel-Lloyd index, their different content means that they are still important today.

In 1960 Verdoorn tried the intensity of inter- or intra-industrial trade, as the ratio

${\displaystyle U_{i}={\frac {EX_{i}}{IM_{i}}}}$

in every three-digit class of goods . The more intra-industrial trade is carried out, the closer the calculated value is to 1. The other way round applies: the further away from 1, the more intensive inter-industrial trade takes place. It is disadvantageous that the measure for an import surplus is in an interval [0.1], for an export surplus it is (1, ). A meaningful aggregation is therefore not possible, which means that no interpretable index value can result if one wants to summarize the values ​​of individual product groups into an overall value. The only comparable case is if , namely if . ${\displaystyle i}$ ${\displaystyle U}$ ${\displaystyle \infty }$ ${\displaystyle EX=IM}$ ${\displaystyle U_{i}=1}$

Also Kojima and Grubel hired in 1964 and 1967 respectively, similar considerations. However, they chose the ratio of exports and imports in such a way that either values ​​between 0 and 1 or greater than 1 always result. In this case, sat Kojima export and import as each other into consideration that the higher of the two values in the denominator and in the numerator is the lower of:

${\displaystyle U_{i}^{\text{Kojima}}={\frac {\min(EX_{i};IM_{i})}{\max(EX_{i};IM_{i}}}}$

with . This results in a number in the interval [0.1], which is to be assessed analogously to the Grubel-Lloyd index, but only for a single group of goods. Grubel carried out this calculation in reverse: ${\displaystyle 0\leq U_{i}\leq 1}$

${\displaystyle U_{i}^{\text{Grubel}}={\frac {\max(EX_{i};IM_{i})}{\min(EX_{i};IM_{i}}}}$with . ${\displaystyle 1\leq U_{i}\leq \infty }$

Here, too, it should be mentioned: the closer the result comes to 1, the higher the level of intra-industrial trade. According to Grubel and Lloyd, however, these considerations are not an optimal measure for intra-industrial trade across all goods groups.

Balassa sets the net trade of a goods class (amount from the difference between exports minus imports) in relation to the trade volume of a goods class (sum of exports and imports). A statement is made about “the share of intra-industrial trade in total trade” in this class of goods. Balassa continues to offset group indices unweighted as an arithmetic mean in order to obtain a statement about the entire intra-industrial trade:

${\displaystyle {\overline {D}}_{i}={\frac {1}{n}}\sum _{i=1}^{n}{\frac {|EX_{i}-IM_{i}|}{EX_{i}+IM_{i}}}}$.

But here too there are disadvantages. This includes that individual groups of goods are not weighted according to their share in total trade. In addition, it cannot be taken into account that in some groups of goods there is a surplus of exports over imports, while in others imports outweigh exports.

One way of taking into account the imbalance in the trade balance is to use the calculation method developed by Michaely in 1962. This calculated an index by subtracting the import shares of the respective goods groups from the total imports of all goods groups from the export shares of the respective goods group from the total exports of all goods groups:

${\displaystyle {\overline {E}}_{i}=\sum _{i=1}^{n}\left|{\frac {EX_{i}}{\sum _{i=1}^{n}EX_{i}}}-{\frac {IM_{i}}{\sum _{i=1}^{n}IM_{i}}}\right|}$ .

Since this calculation yields values ​​between 0 and 2, with 0 being completely intra-industrial trade and 2 completely inter-industrial trade, the results can be better compared by multiplying them by and then subtracting from 1: ${\displaystyle {\tfrac {1}{2}}}$

${\displaystyle {\overline {F}}_{i}=1-{\frac {1}{2}}\sum _{i=1}^{n}\left|{\frac {EX_{i}}{\sum _{i=1}^{n}EX_{i}}}-{\frac {IM_{i}}{\sum _{i=1}^{n}IM_{i}}}\right|}$.

This means that the indices are between 0 and 1, which are to be assessed analogously to the Grubel-Lloyd index, and at the same time allow the imbalance in the trade balance to be taken into account.

Structural differences can be used as a further alternative measured variable . A predominantly intra-industrial foreign trade is characterized by the fact that exports and imports run in similar structures, whereas inter-industrial trade shows recognizable differences in the structure of the goods groups. Differences in the structure indicate specializations, which in turn means that goods of a group that are exported are not imported and vice versa.

literature

• Matteo Aepli: Economic Importance and Competitiveness of the Swiss Food Industry. Mast.-Arb., ETH Zurich, Agricultural, Food and Environmental Economics Group, Institute for Environmental Decisions, 2011, pp. 52–56.
• Andreas Behr : Germany's intra-industrial foreign trade / by Andreas Behr. Dissertation Frankfurt (Main). In: Die Deutsche Bibliothek (Hrsg.): CIP-Einheitsaufnahme (= Volkswirtschaftliche Schriften. H. 485). Dunker and Humblot, Berlin 1998, ISBN 3-428-09533-2 , pp. 4–46.
• Herbert G. Grubel, Peter J. Lloyd. Intra-Industry Trade: The Theory and Measurement of International Trade in Differentiated Products. Wiley, New York 1975
• Paul R. Krugman, Maurice Obstfeld: International Economy: Theory and Politics of Foreign Trade Pearson, Munich 2006, ISBN 978-3-8273-7199-7
• Heidrun Lederbogen: Product differentiation in international trade. A contribution to the analysis of foreign trade structures / Heidrun Lederbogen. Dissertation Bochum. In: Die Deutsche Bibliothek (Ed.): CIP-Einheitsaufnahme (= contributions to quantitative economics. Number 12). Universitätsverlag Brockmeyer, Bochum 1991, ISBN 3-88339-906-X , pp. 8-18.
• Klaus von Stackelberg: International competitiveness with increasing intra-industrial trade relations with emerging countries. Analysis of the trade of the Federal Republic of Germany, Lower Saxony and Japan with the emerging countries of East / Southeast Asia / by Klaus von Stackelberg. Diss. Hanover. In: The German Library (Ed.): CIP-Einheitsaufnahme (= contributions to applied economic research. Volume 23). Dunker and Humblot, Berlin 1991, ISBN 3-428-07189-1 , pp. 32-90.

Individual evidence

1. ↑ Herbert Grubel, Peter J. Lloyd: Intra-industry trade: the theory and measurement of international trade in differentiated products. In: The Economic Journal . 85 (1975).
2. ↑ Stefan Di Bitonto: Intra-Industrial Trade in the Enlarged EU, 2009, p. 10.
3. ↑ Stefan Di Bitonto: Intra-Industrial Trade in the Enlarged EU , 2009, p. 10.
4. ↑ data from the UN Comtrade Database were processed; http://comtrade.un.org/ ; Retrieved on May 20, 2015 at 5:00 p.m.
5. ^ Andreas Behr: The intra-industrial foreign trade of Germany. 1998, p. 11f.
6. ^ Matteo Aepli: Economic importance and competitiveness of the Swiss food industry. (No longer available online.) ETH Zurich Institute for Environmental Decisions, 2011, archived from the original on June 12, 2015 ; accessed on May 29, 2015 .  (PDF 5.5 MB) p. 52.
7. ^ Matteo Aepli: Economic importance and competitiveness of the Swiss food industry. (No longer available online.) ETH Zurich Institute for Environmental Decisions, 2011, archived from the original on June 12, 2015 ; accessed on May 29, 2015 .  (PDF 5.5 MB) p. 52.
8. ↑ Grubel, Herbert G .: The theory of intra-industry trade. In: McDougall, IA and Snape RH: Studies in International Economics - Monash Conference Papers , North-Holland Publishing Company, Amsterdam, 1970, pp. 35-51.
9. ↑ Jochen Meyer: The importance and causes of the intra-industry trade in agricultural products. April 14, 2005, accessed January 9, 2015 .  (PDF 382 kB) p. 4.
10. ^ Andreas Behr: The intra-industrial foreign trade of Germany. 1998.
11. ↑ Lederbogen Heldrun, Product Differentiation in International Trade: A Contribution to the Analysis of Foreign Trade Structures 1991
12. ↑ International list of goods for foreign trade. Federal Statistical Office, accessed on May 29, 2015 . 
13. ^ Matteo Aepli: Intra-industrial trade and competitiveness of the Swiss food industry . In: Journal of Socio-Economics in Agriculture 2011, pp. 245–267, accessed on June 11, 2015 (PDF 568 kB)
14. ↑ Heidrun Lederbogen: Product differentiation in international trade. 1991, p. 17.
15. ^ Andreas Behr: The intra-industrial foreign trade of Germany. 1998, p. 20.
16. ^ Andreas Behr: The intra-industrial foreign trade of Germany. 1998, p. 20.
17. ↑ See Herbert G. Grubel, Peter J. Lloyd. Intra-Industry Trade: The Theory and Measurement of International Trade in Differentiated Products. John Wiley & Sons, New York 1975, p. 27.
18. ↑ See Herbert G. Grubel, Peter J. Lloyd. Intra-Industry Trade: The Theory and Measurement of International Trade in Differentiated Products. John Wiley & Sons, New York 1975, p. 24.
19. ^ Andreas Behr: The intra-industrial foreign trade of Germany. 1998, p. 8 f.
20. ↑ See Herbert G. Grubel, Peter J. Lloyd. Intra-Industry Trade: The Theory and Measurement of International Trade in Differentiated Products. John Wiley & Sons, New York 1975, pp. 24f.
21. ^ Andreas Behr: The intra-industrial foreign trade of Germany. 1998, p. 9 f.
22. ↑ See Herbert G. Grubel, Peter J. Lloyd. Intra-Industry Trade: The Theory and Measurement of International Trade in Differentiated Products. John Wiley & Sons, New York 1975, p. 25.
23. ^ Andreas Behr: The intra-industrial foreign trade of Germany. 1998, p. 10.
24. ↑ See Herbert G. Grubel, Peter J. Lloyd. Intra-Industry Trade: The Theory and Measurement of International Trade in Differentiated Products. John Wiley & Sons, New York 1975, p. 26.
25. ^ Andreas Behr: The intra-industrial foreign trade of Germany. 1998, p. 10.
26. ↑ See Herbert G. Grubel, Peter J. Lloyd. Intra-Industry Trade: The Theory and Measurement of International Trade in Differentiated Products. John Wiley & Sons, New York 1975, p. 26.
27. ↑ See Herbert G. Grubel, Peter J. Lloyd. Intra-Industry Trade: The Theory and Measurement of International Trade in Differentiated Products. John Wiley & Sons, New York 1975, p. 26.
28. ↑ See Herbert G. Grubel, Peter J. Lloyd. Intra-Industry Trade: The Theory and Measurement of International Trade in Differentiated Products. John Wiley & Sons, New York 1975, p. 27.
29. ↑ See Herbert G. Grubel, Peter J. Lloyd. Intra-Industry Trade: The Theory and Measurement of International Trade in Differentiated Products. John Wiley & Sons, New York 1975, pp. 26f.
30. ^ Andreas Behr: The intra-industrial foreign trade of Germany. 1998, p. 14f.