The laws of economic gravity

As the debate over the costs of Brexit continues to rage, it is worth taking a look at the different approaches which have been used to try and quantify the impacts. There are two main types of analysis: (i) gravity models and (ii) computable general equilibrium (CGE) models, both of which have strengths and weaknesses. Gravity models have long been used in the literature and are the economic analogue of Newton’s law of gravitation which states that the attractive force between two objects is the product of their mass proportional to the (squared) distance between them. In 1962, the economist Jan Tinbergen proposed that a similar model could be applied to international trade with the basic relationship shown below:

In other words, the trade flow (F) between two countries (i and j) depends positively on the respective size of the economies and inversely with the distance between them. In broad terms we can think of distance as a proxy for trade costs, which can have a significant impact on cross-border flows. If we take the logarithm of this equation we have a linear expression which can be estimated using standard regression techniques (in reality, the estimation methods are today quite complex but we will leave this aside). Over the years, the basic equation has been augmented with variables to take account of factors such as shared borders, common language, colonial links and whether they share some form of trade agreement (partly to explain why trade flows between countries such as the UK and US are so large), but the basic idea still holds: Large countries which are located relatively close to each other are likely to have significant trade flows. (Here for much more detail on gravity models, including a paper by Keith Head and Thierry Mayer covering all you ever wanted to know and much that you did not).

I looked at data for goods and services exports from the UK to 33 countries, representing 86% of total UK exports, over the period 1999 to 2016. If we fit a trend relationship between them, the slope of the line is negative – as theory predicts (see chart). But it is interesting that the line is less steep today than at the turn of the century. This reflects the notion often put forward by proponents of Brexit that rapidly growing markets such as China have become significantly more important for UK trade. Indeed UK exports to China rose from 0.3% of the total in 1999 to 3.1% by 2016. Over the past 20 years many commentators have suggested that distance is increasingly no barrier to trade, reflecting technological advances which have led to improved inventory management techniques and the like. But although the curve may have flattened, it is not flat, nor is it likely to be at any point in the foreseeable future. Rumours of the death of distance have been greatly exaggerated.

CGE models are much more computationally onerous but they do try to account for all the linkages between the various sectors of the economy to examine how a disturbance in one area feeds throughout the rest of the economy. They rest on the idea that there is a circular flow of income between sectors and also assume optimising behaviour by economic agents (subject to certain constraints). A CGE model of trade, looking at various sectors of the economy across a range of countries, involves a huge amount of data and one of the criticisms is that such models are often based on calibrations which may not necessarily be validated by the data (in contrast to gravity models which are estimated and therefore data coherent). But they are a useful way to understand how shocks percolate throughout the system and to that end are a valuable tool in trying to quantify Brexit shocks.

It is notable that the analysis of Gretton and Vines, which I cited in this post,  is based on a CGE model and as I noted, the welfare losses they report are significantly lower than other estimates I have seen. But the pro-Brexit group Economists for Free Trade, led by Patrick Minford, stretched the limits of CGE-based modelling too far in their latest paper by claiming that Brexit will actually lead to welfare gains. Their analysis is based on some highly dubious assumptions (which Chris Giles in the FT skewers here). I will return to the details of the Minford et al paper another time in order to look more closely at why this is a case of “garbage in-garbage out,” but aside from any issues regarding the basic assumptions, CGE analysis allows no role for economic gravitational effects. No serious analysis of trade can ignore this factor.

As the WTO put it, “the numbers that come out of [CGE] simulations should only be used to give a sense of the order of magnitude that a change in policy can mean for economic welfare or trade. But much more can be done to create confidence in the results.” This is not to say that gravity models are perfect either. But so long as the lines in our chart have a negative slope, we should never dismiss what they have to say.