Origin of the ‘Gravity Model’ in the study of international trade

‘Laws of Universal Gravitation’ or, briefly, ‘Laws of Gravity’ came into existence in the

16th Century. Natural phenomena in which objects with mass attract one another were considered to be more than coincidental occurrences. Isaac Newton proved that these incidents occur systematically via interactions of mass, distance and gravitational forces. Since then, ‘Newton’s Laws of Gravity’ have been applied to other disciplines.

The very first ‘Gravity Model’ of social sciences was brought into the field by Carey in the 1860s, using the metaphor of Newtonian physics to define gravitational interactions of social incidents, in order to explain human behaviours, in particular. Carey (1858) remarked on his observations concerning social gravitation that:

“Gravitation is here, as everywhere else in the material world, in the direct ratio of the mass and in the inverse one of the distance”(Carey ,1858, p. 644).

Even so, it was not until the 1950s that the so-called ‘Gravity Framework’ came into practice in the subject of international trade. Walter Isard48 noticed that the ‘Gravity

Model’ applied in the social sciences could plausibly be modified to explain trade flows

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among countries. Nevertheless, this was examined as a part of the ‘Location Theory’49 and the ‘Regional Analysis’50 during that period. Following ‘Newton’s Laws of Gravity’, trade flows between countries are hypothetically related to their respective sizes and the distance between them. The traditional setting of the ‘Gravity Model’ of trade was thus of the form:

(2.1)

From the equation above, Xij represents trade flows between countries i and j and Dij denotes the distance between them. Yiand Yjsignify countries’ sizes which are written in the form of national incomesand γ is given as the constant term. In addition,α and β are and λ are parameters to be estimated. While α, β are imposed to capture income elasticity of country i and country j respectively, λis imposed to indicated a distance elasticity. As is evident, bilateral trades were assumed to be positively related to size and negatively obstructed by distance between trade-pairs.

What made the ‘Gravity Model’ stand out? This is certainly an interesting question to ask. The answer, in fact, lies amidst contradictions between trade theories and the empirical evidence found. As far as empirical evidence was concerned, it was, to a large extent, observed that countries did engage in the type of ‘Intra-Industry Trade’ in which (differentiated) products under the same industry are traded. At that period, such

49

The subject is concerned with the geographic location of economic activity. Later, it became a part of economic geography.

50 _{It is commonly known as ‘Regional Sciences’. It is a field in the Social Sciences that are generally}

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findings undoubtedly challenged the classical views underlined by the factor abundance theory51. Further investigations as well as alternative theories were called for, as many agreed that considering only factor endowments as a way of quantifying a country’s comparative advantage and as a key economic reason to trade was deemed too contracted a way to explain the reality of international trade. This is where the ‘Gravity

Model’ was employed formally as an innovative empirical tool to assess international

trade flows. As a result, bilateral trade relationships, as well as global trading patterns were made evident for the first time.

In this regard, Nobel laureate Tinbergen is considered the first to have conducted empirical research applying the ‘Gravity Model’ (it was then regarded as the gravity equation) to the study of international trade flows. Aiming to provide a report determining normal patterns of international trade in the absence of trade impediments, the gravity equation was estimated on 18 countries’ trade flows in the year 195852. In addition to the basic gravity variables: countries’ sizes and bilateral distance, dummy variables were also employed to capture effects of preferential trade agreements53. Basically, each preferential dummy variable was given the value of 1 if particular trade-

51 _{The classical Heckscher-Ohlin (H-O) model is one of the fundamental theoretical trade models that}

build on Ricardo’s theory of comparative advantage. It assumes that countries are completely specialized and only trade (export) products in which their factors of production are abundant. In such a setting, input costs are perceived as a key factor determining a country’s profitability. This further implies that production output is of a constant return to scale type where the same levels of technological developments are also restricted. In conclusion, such strong restrictions allow no room for (different types of) firm to exist, as production functions consequently have to be identical for all countries. It can be said that, as long as these assumptions hold, this type of intra-industry trade would not be allowed to occur in the H-O world.

52 _{They are Brazil, Venezuela, South Africa, Japan, Canada, USA, Austria, BLEU, Denmark, France,}

Western Germany, Italy, The Netherlands, Norway, Sweden, Switzerland, UK and Australia. The study was also extended to include 42 countries’ trade flows in 1959 as a robustness check.

53 _{The dummy variables were imposed to capture preferential treatment of the British Commonwealth and}

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pairs belonged to the same trade agreement: otherwise, the value would be 0. Tinbergen (1962)’s model was: (2.2)

where G is a constant term, the first and second terms of the numerator capture countries’ incomes written in the form of income per capita times population. Dij represents physical distance between particular trade-pairs.

The above model was extended further to capture preferential effects in the following form: (2.3)

where G is a constant, N denotes a set of dummy variables posted to capture neighbouring countries. The PRC dummy variable was posted to account for any trade effects from the Commonwealth preference. PRB was, in the same manner, posted to capture the Benelux preference on trade.

Almost concurrently but independently, PÖyhonen (1963) used the gravity concept to examine the exchange of goods between 10 European countries in 195854. The strength

54 _{They are Belgium, Denmark, Finland, Western Germany, Italy, Netherlands, Norway, Portugal,}

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of the ‘Gravity Model’ was notably acknowledged as Pullianen (1963) extended this same data set, testing the validity of the model on a larger scale with 62 (non- communist) countries over the period of 1948-1960. The results showed that the pattern of trade flows in these 62 countries did not alter much over the period of study. This then implied that trade flows were rather consistent over a period of years and the 1958’s estimate was therefore concluded as a reliable outcome. In that period, Leamer and Stern (1970) also acknowledged the use of the ‘Gravity Model’ in studying international trade flows in their book: ‘Quantitative International Economics’. Provided with the consensus of these empirical studies the ‘Gravity Model’ has been a subject of study ever since.

Notwithstanding its empiric origin, the ‘Gravity Model’ became widely known after it was used to test trade theories of interest in various applications. In general, the empirical success of the ‘Gravity Model’ was deemed to be in support of the monopolistic competition explanation of intra-industry trade55. Even so, formal associations between theories and empirical work were criticized as absent. It can be said that while, on the one hand, the ‘Gravity Model’ has been employed to test trade theories of interest, on the other hand the model itself was searching for its own backbone.

Despite the doubt concerning similarities between physical gravitation and trading relationships, Linneman (1966), nonetheless, derived the ‘Gravity Model’ to explain

55 _{In the world in which intra-industry trade exists, each country is assumed to specialize in different}

product varieties. The firms in different countries may produce the same product varieties in Autarky, but because it is also assumed that, with trade, they can choose to produce a variety that is profit maximizing, it ends up that there is trade in these product varieties. See, Helpman (1987) and Hummel and Levinsohn (1995), for examples.

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international trade flows. As a result, his account was the earliest attempt that provided theoretical explanations for the ‘Gravity Model’ in the international trade arena. In his setting, gravitational relationships were linked with international trade flows under a quasi-Walrasian general equilibrium framework. Countries’ incomes were proxied as the level of demand in the importing country and the level of supply in the exporting one. The basic reason for countries to trade was assumed to be the mismatch between levels of demand and supply in each country. In addition, countries were perceived to be different in terms of comparative advantages, which could be explained by economies of scale and levels of technological development. Linneman (1966) basically asserted that the ‘Gravity Model’ was a reduced form of a (four equations) partial equilibrium model of export supply and import demand functions. Distance was used as a proxy for transport cost as its impacts could drive demand and supply away from an equilibrium. The price terms were treated as endogenous and thus implicit as they were adjusted to equate supply and demand in this setting. In the same vein as Tinbergen (1962), a set of trade-preferential dummy variables were employed to capture any positive effects of trade agreements on membership trading partners. Although Linneman (1966)’s framework was an eye-opening contribution, it was still considered too simple to explain the reality in cross-country trade relationships.