Adam Smith s Discovery of Trade Gravity

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1 Adam Smith s Discovery of Trade Gravity Bruce Elmslie University of New Hampshire University of Canterbury Economics Seminar February 2018

2 First: Where is New Hampshire?

3 The Paper in a Nutshell The gravity equation is a current workhorse of empirical trade theory It was first created in its modern form by Jan Tinbergen in 1962, but was limited in its acceptance as part of the core of the discipline due to its lack of a theoretical foundation until Anderson (1979), Helpman (1987) and others I show that a gravity explanation of trade volume was first developed by Adam Smith in the Wealth of Nations Smith s gravity was an extension of his theory of differential capital productivity and Hume s theory of the gains from trade Smith also developed an explanation for the size of borders and a gravity theory of trade restrictions

4 Newton s Gravity Equation Newton first developed his theory of a proportional relation between force, the product of two masses, and a concomitant inverse proportional relation between force and distance in his Mathematical Principles of Natural Philosophy in Written as : FF = GG mmmmmm ddd

5 Trade Gravity Basics The gravity equation as applied to the determinants of international trade flows between countries has been called one of the most empirically successful in economics. It relates bilateral trade flows to GDP, distance, and other factors that affect trade barriers (Anderson and van Wincoop, 2003, 170). In its original form, Tinbergen (1962) wrote the following: E ij = α 0 Y i α 1Yj α 2Dij α 3 where Eij, Y i, Y j, and D ij are Exports of country i to country j, GNP of country i, GNP of country j, and distance between i and j, respectively. The alphas are constants to be determined in a regression analysis.

6 Smith s Trade Gravity Smith relates bilateral trade volume to size and distance in Chapter II, Book IV, Part II of the Wealth. While buried in the far reaches of the Wealth, here Smith gives his most memorable and penetrating critiques of the balance of trade doctrine, which he dubbed absurd. The biggest danger posed by the doctrine was that it served as the linchpin for almost all other restraints of commerce and generally taught nations that their interests consisted in beggaring all their neighbours. Smith s gravity discussion comes in the context of comparing the trade between England and France relative to their respective colonies in a system of natural liberty with the actual policy-driven extent of trade, where mutual restraints have put an end to almost all [trade]. Trade volume was about 100 times larger between England and its North American Colonies than between England and France.

7 Smith s Trade Gravity Continued [T]he commerce of France might be more advantageous to Great Britain than that of any other country, and for the same reason that of Great Britain to France. France is the nearest neighbour to Great Britain.. France, besides, is supposed to contain twentyfour millions of inhabitants. Our North American colonies were never supposed to contain more than three millions: And France is a much richer country than North America.... France therefore could afford a market at least eight times more extensive The trade of Great Britain would be just as advantageous to France, and, in proportion to the wealth, population and proximity of the respective countries.... [624 25; emphasis added]

8 A Few Notes Note that the discussion is in terms of the gains from trade rather than merely the extent of trade. However, a few pages before this statement, Smith explicitly links the two: the mutually afforded [gains] will be greater or smaller in proportion to the extent of their [each countries bilateral] dealings (616). Smith does not state that he had Newton s gravity model in mind here, but his description of Newton s theory, which Smith called the greatest discovery that ever was made by man is extremely similar: The power of attraction [that] each body possesses, is in proportion to the quantity of matter contained in that body. Allow his principle, the universality of gravity, and that it decreases as the squares of the distance increase, and all the appearances, which he joins together by it, necessarily follow. [Essays on Philosophical Subjects: ] Fits Smith s theory of scientific progress.

9 Gravity Components, Mass and Distance: Distance First Smith links proximity to the number of times capital can be turned over per year: With trade between England and France the returns might be expected four, five, or six times in the year. The capital, therefore, employed in this trade, could in each of the two countries keep in motion four, five, or six times the quantity of industry, and afford employment and subsistence to four, five, or six times the number of people, which an equal capital could do in the greater part of the other branches of foreign trade. (624) And Generally: the quantity of productive labour which any capital employed in the foreign trade of consumption can maintain, is exactly in proportion to the frequency of its returns A foreign trade of consumption carried on with a neighbouring [country], is, upon this account, in general, more advantageous than one carried on with a distant country. [763]

10 Smith and Differential Capital Productivity The previous statements represent a straight forward application of Smith s general argument from Book II linking the productivity of capital employed in different sectors of the economy. For Smith capital employed in agriculture employs the most productive labor and the carrying international trade employs the least. And, importantly, the whole annual produce [is] the effect of productive labour. Smith makes his argument in terms of the number of times capital can be turned over per year. [a] capital employed in the home-trade will sometimes make twelve operations, or be sent out and returned twelve times, before a capital employed in the foreign trade of equal consumption has made one. If the capitals are equal, therefore, the one will give four and twenty times more encouragement and support to the industry of the country than the other. [469 70]

11 What about Self Interest? Stating that trading with more proximate countries is more socially beneficial is not necessarily stating that capitalists will trade in a manner that is most beneficial to the country. As Smith states, consideration of his own private profit, is the sole motive which determines the owner of any capital to employ it [the social benefits] never enter into his thoughts (476 77). However, since capitalists prefer more security to less, they will naturally prefer to employ their capital closer to home given near equal profits. In a system of natural liberty, the mercantile stock of every country naturally courts the near and shuns the distant employment.it naturally courts [that which is]most advantageous, and shuns that which is least advantageous to that country. (798)

12 Mass: Wealth and Population Smith follows Hume s Cosmopolitanism In his 1758 essay, Of the Jealousy of Trade David Hume argued that rather than fearing the wealth and commerce of neighbouring countries, increasing in such wealth actually helps the home country. Just as a person cannot be industrious when surrounded by idle neighbours, a country cannot be industrious when surrounded by ignorance, sloth, and barbarism. (331) Smith merely reproduces this argument, and language, rich and civilized nations can always exchange to a much greater value with one another, than with savages and barbarians. (564)

13 Summing Up In creating his own version of what became the gravity equation of trade volume, Smith applied two aspects of his overall theory of the determinants of the wealth of nations. Namely, he employed his theory of the differing productivity of capital along with his invisible hand that connects the national benefits of trading more with neighbors than with distant countries to the selfinterests of merchants in doing so. Second, he drew on Hume s argument that the volume or value of trade will be positively related the size of the markets of one s neighboring states to complete the argument that trade is positively related in proportion to mass and proximity. There is absolutely nothing ad hoc in Smith s development of this relation.

14 A Gravity Theory of Trade Restrictions In describing his original methodology, Tinbergen (1962, 262) stated that he assumed that the free trade pattern coincides with the average pattern actually prevailing; this means that we assume the impediments to be of a stochastic nature. Smith presumed the opposite: trade restrictions are proportional to a competitor s size and proximity.: the very same circumstances which would have rendered an open and free commerce between the two countries [France and Great Britain] so advantageous to both, have occasioned the principle obstructions to that commerce (625). Where the national gains from trade are the greatest, the mercantile interests made the loudest calls for protection. Thus gravity giveth and gravity taketh away!

15 Smith s Selection of Countries Using England and France was a bold move. Merchants feared the competition coming from France and used national animosity in their favor. Mercantile jealousy is excited, and both inflames, and is itself inflamed, by the violence of national animosity: And the traders of both countries have announced, with all the passionate confidence of interested falsehood, the certain ruin of each, in consequence of that unfavorable balance of trade, which, they pretend, would be the infallible effect of an unrestrained commerce with the other. [625]

16 How Wide is the Border? One of the most anomalous results from the modern gravity estimates is that the borders between countries are surprisingly wide (McCullum 1996). Anderson and Van Wincoop (2013) find that the borders decrease trade by an average of 29% for the industrialized countries. Smith also believed that, after controlling for trade barriers that borders matter. Moreover, he thought that the width of the border was positively associated with the differences in wealth as merchants in poor countries are always understocked and run in arrear to their correspondents. Determinants of the border effect: uncertain elements of human folly and injustice, risks due to the winds and waves, and if a contract comes to be disputed, a lack of understanding of the laws of the country.

17 Gravity and Borders In making his arguments, Smith employs a direct gravity metaphor, [h]ome is in this manner the center round which the capitals of the inhabitants of every country are continually circulating, and towards which they are always tending, though by particular causes they may sometimes be driven off and repelled from it towards more distant employments (571). Thus, controlling for differences in profit, the home trade is preferred to foreign.

18 Conclusions The importance of theory: Smith argued that, upon seeing the trade that existed between Great Britain and it s the North American colonies, the untrained eye will look upon the great commerce of America and the dazzling splendour of the object and see only the immense greatness of the commerce. But it is the theory of what is unseen, the theory of natural trade, that demonstrates the opportunity cost of these actual trade flows. It is the purpose of theory to allow us to look beyond the undiscerning eye of giddy ambition [and the] confused scramble of politics and war (797). For Smith it was the elements of gravity, namely proximity and size, that formed the core of this theory of trade when it was allowed to follow the path cut by natural liberty. Smith used his notion of trade gravity to give an account of the volume or extent of trade that could occur between nations if his system of natural liberty prevailed.

19 Conclusions Continued Evaluations of Smith as a trade theorist not too good or nothing new Ricardo gains at variance with all his general doctrines J.S. Mill ditto Bastable no special contribution Viner all important elements prior to the Wealth of Nations Bloomfield Smith was not a great trade theorist Smith s discovery of trade gravity as the determinant of the extent of natural trade and the potential gains trade, as well as his use of gravity to understand the politics of trade restrictions should at least give some pause before these negative evaluations are set in the stone of the history of economics.