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.

Trading places

I spent this evening at a seminar organised by the National Institute of Economic and Social Economic Research (NIESR) at which they outlined their latest economic view and some of the associated research topics. One of the presentations, by Monique Ebell, looked at NIESR's ongoing research into Free Trade Agreements and how the UK is likely to fare post-Brexit.

The worrying conclusion was that leaving the European Single Market (ESM) is going to impose significant costs, irrespective of whatever deal the UK signs with other countries. This is due to the fact that the ESM is a deep and comprehensive trade agreement which is designed to reduce non-tariff barriers, whereas conventional FTAs do little to tackle this problem. And because they are generally aimed at trade in goods, they do little to stimulate services trade which is an important issue for the UK.

NIESR used conventional gravity models to estimate the impact of post-Brexit trade flows. Such models approximate bilateral trade flows between two countries by employing the ‘gravity equation’, derived from Newton’s theory of gravitation. The idea is that just as planets are attracted to each other in proportion to their sizes and proximity, so too are countries. Relative size is determined by GDP, and economic proximity is determined by trade costs – the more economically ‘distant’ the greater the trade costs. Gravity models suggest that relative economic size attracts countries to trade with each other while greater distances weaken the attractiveness.

The empirical results suggest that if the UK were to leave the ESM and impose WTO rules, as Theresa May has threatened, this would lead to a long-term reduction of around 60% in UK trade with the EU compared to what would otherwise take place. Swapping ESM rules for an FTA used by the EU in trade with third party countries would produce a smaller, but still significant, reduction of 45% in UK-EU trade. There would be a modest offset if the UK could replace WTO rules with some form of FTA with the BRICS or Anglophone countries, but it would in no way be enough to fully compensate for the losses.

As it currently stands, leaving the ESM will make the UK significantly less well off. Indeed, NIESR's calculations indicate that swapping the current EU trading arrangements for WTO rules will cut GDP by around 2.3% over the longer term (5-10 years). This is rather smaller than the numbers suggested by the Treasury prior to the referendum, but it is likely there would be significant second round effects which I reckon could produce a long-term decline somewhere in the region of 5%.

We should, of course, be careful of the spurious precision attached to such estimates. But they support the view that leaving the safety of the ESM, which is one of the most integrated international trading markets in the world, will leave the UK poorer than it needs to be. And it is for this reason I continue to believe that the gamble taken by David Cameron in holding the referendum in the first place, and the comments made by Theresa May in her speech two weeks ago, represent steps which are not in the UK's national interest.

If conventional FTAs suggest that the gains from trade with third countries will be outweighed by the losses resulting from a loss of access to the ESM, might it be possible to devise ways to narrow the losses? Obviously, one way would be to replicate the features of the ESM which make it so successful, by reducing non-tariff barriers. But this would involve efforts to improve economic integration in any new trade deals, which in turn would require greater regulatory harmonisation, though this is precisely one of the things which the electorate (narrowly) rejected last June.

Ironically, on a day when the proportion of MPs voting in favour of the Article 50 bill (81.4%) was greater than the proportion of the electorate voting for Brexit (51.9%), the government has still given us no indication that it understands the risks which it is taking with the UK's economic future. Moreover, the fact that the EU is expected to present the UK with a significant exit bill, likely to be in the region of £40-60 bn, suggests that it will take at least five years to recover from the initial financial hit (so much for saving money by leaving, eh Nigel?). Thus, even if Brexit does not cause the damage that is feared, in order to come out ahead the new arrangements would require the UK to get a bigger growth boost than the current arrangements can deliver. Let's just say I am not hopeful.