Gravitational model (foreign trade theory)

In foreign trade theory , gravitational models are economic models that describe the bilateral trade flows between two countries based on Newton's law of gravitation in physics. It was first applied to economics by Jan Tinbergen in 1962. The traditional economic gravity model is based on the assumption that trade between two countries depends on the size of the market and the distance between the partner countries.

Scientific background and history

The gravitational model from economics is derived from Newton's gravitational model from natural science. The law of gravitation is a law of classical physics, according to which every mass point acts on every other mass point with an attractive gravitational force. It was first formulated in 1687 in the work Philosophiae Naturalis Principia Mathematica by Isaac Newton (1643-1727). It says that the gravitational attraction between two bodies is directly proportional to the product of the masses and the two bodies and indirectly proportional to the square of their distance  : ${\displaystyle F}$ ${\displaystyle m_{1}}$ ${\displaystyle m_{2}}$ ${\displaystyle r}$

${\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}}$

with the gravitational constant . ${\displaystyle G}$

The gravity model was applied to different areas as early as the 1940s. For example, in the context of migration research, it came to the conclusion that the further two places are apart, the fewer members of a population set out on the path.

In the sixties the physical concept of gravity was transferred to the economy. The special use for explaining international trade flows was first formulated by Jan Tinbergen (1962) and Pentti Pöyhönen (1963), transferred to problems of foreign trade theory and resulted in further contributions by James E. Anderson (1979), Bergstrand (1985) and Alan V. Deardorff (1998) into the “gravitational model of world trade” shown below.

It was not until around 1995 that the gravitational model was established in mainstream trade theory.

The economic gravity model

The gravitational model of world trade is essentially based on the assumption that, ceteris paribus with regard to other influencing factors, the foreign trade activities of a country will change

• (A ) behave positively proportional to its gross domestic product (GDP) as well
• (B) an increasing geographic distance has a negative effect.

The assumption (A) is based on the consideration that when the gross domestic product increases, more will be exported and imported in absolute terms. It follows that the higher the domestic income, the more it can be imported in absolute terms, and the more it is produced domestically, the more it can be exported in absolute terms. The GDP of the two countries therefore represents the supply and demand strength of the countries. The reason for (B) lies in the increase in transaction costs for trading activities with increasing geographical distance, which have an inhibiting effect on them. The distance variable can thus be interpreted as a measure of the cost of overcoming space in foreign trade. The basic statements of the model can be summarized in the following formula:

${\displaystyle Ex_{i->j}=A{\frac {BIP_{i}BIP_{j}}{D_{i->j}}}}$

Here referred to the foreign trade turnover between two countries as the sum of of of exported and of imported goods and services. and describe the respective gross domestic product of and and depict the geographical distance between the two countries. The size represents a constant. ${\displaystyle Ex_{i->j}}$ ${\displaystyle i}$ ${\displaystyle j}$ ${\displaystyle i}$ ${\displaystyle j}$ ${\displaystyle BIP_{i}}$ ${\displaystyle BIP_{j}}$ ${\displaystyle i}$ ${\displaystyle j}$ ${\displaystyle D_{i,j}}$ ${\displaystyle A}$

Trade policy influencing factors

Inhibiting influencing factors :

• trade policy determinants, for example tariffs , quotas , subsidies
• Strangeness between countries or regions
• cultural differences between countries
• historical determinants, for example war
• political situation

Supporting influencing factors :

• bilateral and multilateral trade agreements
• Existence of trade organizations, for example EFTA , NAFTA , WTO
• Similarity between countries or regions, for example same mother tongue of the trading partner
• political order (the more economically liberal the countries, the more intensive trade is carried out)

The various external factors influencing the practical application of the gravitational model show that the model should not be viewed as given, but only after critical analysis of individual factors, in order to achieve useful empirical results.

calculation

In shown below equation indicates exports from country to country , , the gross domestic products of the considered economies and is a distance factor. The parameters α, β and γ are constants which are subject to empirical estimates. These weight the variables according to their influence. The larger the parameters, the greater the influence of the variables. Values ​​between 0.7 and 1.1 are often found for the parameters α and β. A value of 1 means that trade is proportional to the size of the country's GDP. γ weights the distance factor. It fluctuates strongly in different empirical studies. According to an extensive meta study, the average value is 0.9. ${\displaystyle Ex_{i->j}}$ ${\displaystyle i}$ ${\displaystyle j}$ ${\displaystyle BIP_{i}}$ ${\displaystyle BIP_{j}}$ ${\displaystyle D_{i->j}}$

${\displaystyle Ex_{i->j}=A{\frac {{BIP_{i}}^{\alpha }{BIP_{j}}^{\beta }}{{D_{i->j}}^{\gamma }}}}$

The least squares method is usually used to estimate the parameters . A linear relationship between the variables and the parameters is assumed. To establish the linear relationship, the formula is logarithmized:

${\displaystyle \ln Ex_{i->j}=\ln A+\alpha \cdot \ln BIP_{i}+\beta \cdot \ln BIP_{j}-\gamma \cdot \ln D_{i->j}}$

To increase the informative value, the formula can be combined with additional influencing factors such as B. Membership in a free trade area, existence of common borders and a common language can be expanded. An econometric estimate of the gravitational equation lists the following parameters:

${\displaystyle \ln Ex_{i->j}=\ln A+0,54\cdot \ln BIP_{i}+0,81\cdot \ln BIP_{j}-0,89\cdot \ln D_{i->j}+0,26\cdot Grenze+0,61\cdot Sprache+1,06\cdot Freihandelszone}$.

Common border, language and free trade area are so-called dummy variables. H. if they are present they take the value 1. If they are not present, they are 0. Positive estimates indicate a positive, negative ones indicate a negative relationship.

Application examples of the economic gravity model

In economics today, the gravity model is used in particular as an instrument for analyzing international trade flows, as well as an analytical instrument for measuring interregional and international flows, for example in the areas of tourism and immigration statistics. Furthermore, trading potentials can be estimated and the effects of integration can be measured. Current political examples for the use of the approach are estimates of the potential for foreign direct investment as well as problems that the EU enlargement could cause with its progressive integration. The data required for a gravitational analysis are easily accessible, for example via the Bundesbank or Eurostat. Data on the commonly used variables may be included. a. Provided by the database of the world (World Development Indicators). In various business dictionaries, the term regional analysis is associated with the gravitational model.

Individual evidence

1. ^ Morasch & Bartholomae: International Economy - Trade and Competition on Global Markets. UVK Verlagsgesellschaft mbH (Konstanz) with UVK / Lucius (Munich), p. 33.
2. ↑ Tinbergen, JJ (1962). Shaping the world economy; suggestions for an international economic policy.
3. ^ Head, K., & Mayer, T. (2014). Gravity equations: Workhorse, toolkit, and cookbook. In Handbook of international economics (Vol. 4, pp. 131-195). Elsevier. P. 134.
4. ↑ Archive link ( Memento of the original from November 18, 2007 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.  ; Country dossier Norway WS 07/08  
5. ↑ http://www.statoek.vwl.uni-mainz.de/Dateien/Arbeitspapier_Nr_34_Gravitationsmodell.pdf
6. ^ Lorz & Siebert: Foreign trade. 9. Completely revised edition, UVK Verlagsgesellschaft mbH (Konstanz) with UVK / Lucius (Munich) p. 133.
7. ^ Lorz & Siebert: Foreign trade. 9. Completely revised edition, UVK Verlagsgesellschaft mbH (Konstanz) with UVK / Lucius (Munich) p. 133.

literature

• Horst Siebert: Foreign trade. 7th edition, Stuttgart: Lucius & Lucius, 2000, p. 88.
• Geigant, Haslinger, Sobotka, Westphal: Lexicon of economics. 6th edition, Landsberg am Lech, 1983, pp. 775-777.
• Morasch & Bartholomae: International Economy - Trade and Competition in Global Markets. UVK Verlagsgesellschaft mbH (Konstanz) with UVK / Lucius (Munich), p. 33.
• Morasch & Bartholomae: International Economy - Trade and Competition in Global Markets. UVK Verlagsgesellschaft mbH (Konstanz) with UVK / Lucius (Munich), p. 28.
• Lorz & Siebert: Außenwirtschaft, 9th completely revised edition. UVK Verlagsgesellschaft mbH (Konstanz) with UVK / Lucius (Munich) p. 133.

Web links

• For the analysis of Rhineland-Palatinate exports using a gravitational model - Working Paper No. 34 (Oct. 2006) (PDF file; 319 kB)
• Trading costs and gravitation model - book chapter from Morasch, K., & Bartholomae, F. (2017). Trade and competition in global markets. Springer Gabler.
• Head, K., & Mayer, T. (2014). Gravity equations: Workhorse, toolkit, and cookbook. In Handbook of international economics (Vol. 4, pp. 131-195). Elsevier. - Book chapters freely available from Thierry Mayer