Free trade benefits of Brexit

Patrick Minford is Professor of Applied Economics at Cardiff University

I was astonished during late 2015 to discover that most economists in the UK favoured staying in the EU on the basis of what appeared to be neo-protectionist arguments derived from recent ‘gravity-related’ trade thinking.

In late additions to the second edition of my book Should the UK leave the EU? Minford et al (2015) I pointed out that the gravity modelling was of a partial equilibrium nature (ie. did not include the full effects of Brexit) and that attempts hitherto made to turn it into general equilibrium (the full effects) were misconceived.

It soon became apparent that my professional colleagues were not going to take any notice of these points; and indeed the Treasury economists promptly enlisted help from the LSE’s gravity trade group in developing the gravity-based case for retaining existing trade links with the EU regardless of the costs of its well-known protectionism.

I begin this article with some comments on the various rival ‘gravity’ approaches, all of which have had a strong bias against eliminating EU protection to get to free trade, arguing that the gains are trivial while the losses from abandoning protected trade with the EU are large.

I then go on to set out the quantitative analysis I reached on Brexit, using the models I developed with my Cardiff research group, together with realistic Brexit policy assumptions. As we will then see, these models with realistic assumptions find that there are substantial gains from free trade with the rest of the world.

Gravity trade models and Brexit: a review

At the heart of the Brexit debate there is a fundamental disagreement about how trade works and affects the economy. In the last few years debate has raged over whether EU trade arrangements are beneficial, in particular to the UK.

The EU is a customs union and so erects trade barriers around its Single Market where economic activity is regulated according to EU rules. The welfare effects of a customs union have always been controversial.

According to classical trade theory global welfare is reduced compared with free trade as is the average welfare of citizens inside the customs union; however one country’s citizens may gain from the union if it is a net exporter to others in the union, as then its terms of trade gain may offset the losses experienced by its consumers (Meade, 1955).

However, in recent times a new line of reasoning has become popular among trade economists: this ‘gravity model’ (eg. Costinot and Rodriguez-Clare, 2013) regards trade as an outcrop of internal trade, the only difference being that it crosses borders. Otherwise it grows naturally due to the specialisation and division of labour within neighbouring markets.

Viewed through the lens of the gravity model a customs union merely makes official what is already a fact of neighbourly inter-trade. Other sorts of trade, with more distant markets, grows analogously but more weakly, the greater the distance; size of distant markets may make up for their distance to some extent, because they are a ‘neighbourhood’ that naturally leads to inter-trade.

As part of this view of trade as dominated by inter-trade, substitutability between heterogeneous goods and services of different origins is treated as fairly low. ‘Gravity’ in trade creation can be thought of as a function of distance and size.

In this view of trade it makes no sense to put obstacles in the way of trade with close neighbours such as the EU in the hope of boosting trade with distant markets via new trade agreements that lower trade costs.

The disruption from the former will reduce welfare while the gains from the latter will be small, simply because the reduced trade costs will have little effect in switching demand from existing products in the presence of weak and imperfect competition.

Furthermore, protection is seen in a fairly positive light in the gravity model, because low substitutability between countries’ goods implies that there is scope for protection to improve the terms of trade- the ‘optimal tariff’ mechanism; He et al (2017) show that it pushes optimal tariff rates before and after retaliation above 100%- clearly a worrying policy implication, which in itself casts doubt on the model’s realism.

Before we go further into the technicalities of different models and calculations of trade policy effects, it is worth spending a little thought on what light the history and structure of UK trade throw on the matter.

For centuries the UK has been regarded as the archetype of a ‘trading nation’, in that its great trading companies, such as the East India company, sought out trading opportunities around the world and in the process founded the British Empire, with trading links all over the world.

European neighbouring countries had little to do with it, other than the Dutch with whose Indies trading fleets the UK fought several wars, settled by the Treaty of Westminster in 1674.

In recent years UK trade has been dominated by services, whose weightlessness implies a total lack of ‘gravity’; furthermore, the containerisation of goods transport has brought shipping costs down to almost trivial levels. The role of gravity, viz distance x size, seems on the face of it to be small in UK trade.

As for European trade, in spite of high EU tariffs against non-EU suppliers, the share of EU trade (imports plus exports) in UK trade has never gone over 25% of UK GDP. Currently it is running at 20% against around 30% with the non-EU world; so UK trade with the EU is about 40% of all its trade, in spite of massive trade barriers (around 20% in both food and manufactures) against non-EU countries.

It does not look as if gravity has much to do with it all, certainly European gravity. It is perhaps not a surprise that classical trade theory, with its strong relevance to far-flung UK and other Northern European (Swedish/ Dutch) trade, was developed by British and northern European economists such as Ricardo, Heckscher and Ohlin, while the more recent gravity theory has mainly been developed by economists based in the US or continental Europe where distant trade plays a minor role in GDP.

Compare the UK with a country like the Czech Republic with limited trading activity other than with the EU by which it is surrounded; 80% of its trade is with the EU, reflecting its quite different trade opportunities, which are indeed naturally describable by gravity.

It would certainly be unsurprising if our test of UK trade rejected the gravity model; as indeed it does (Minford and Xu 2019; Chen et al 2021).

I next review the various attempts that have been made by different groups of economists, using different approaches, to evaluate the trade effects of Brexit.

‘Gravity model’ estimates of Brexit trade effects

Clearly these two models, the classical and the gravity models, are different and so may well have different welfare implications. However, while trade economists have recently tended to favour the gravity model over the classical, there has been no convincing empirical test of the two models as overall predictors of the data.

Gravity modellers do point to the Tinbergen (1962) gravity regressions as evidence in favour of the gravity model: these are statistical correlations between the size of two counties’ GDPs and their distance from each other on the one hand, and the size of their trade on the other.

However, these regressions have long been familiar to trade economists, and classical trade models too can generate trade data in line with these regressions. Thus we face here an ‘identification’ problem: two models can both generate the same data, at least that would be the claim of their proponents. We need an empirical test that can discriminate powerfully between the two models- we will develop this in the appendix.

Plainly one has to use the underlying model (ie. one in which all the interactions within trade and the economy are allowed for) to calculate policy effects, since these work through all the channels of the model; one surely, so we would say, cannot use the Tinbergen and related regressions, since these are simply correlations and associations generated by the model, and are not causal.

So we would argue that we must uncover the true model- which requires a test.  Not surprisingly, such tests reveal that the gravity model is widely rejected, while the classical model largely fits the facts. Chen et al (2021) sets out the evidence.

According to [the classical] model there are big gains from free trade with the rest of the world and ironically a small gain from UK-EU tariff barriers

The gains from trade – how they are (mis)calculated

The effects of trade policies such as tariffs can be understood with the help of a simple diagram, showing demand and supply of imports. A tariff raises the home price of imports over the world price. Assume for now the world price stays the same. Then the loss of welfare is shown by the shaded area of reduced consumer surplus.

Figure 1. Loss of surplus due to tariff

This shows the loss to consumers from higher prices, causing lower consumption, and also their loss as producer households from over-production, in which the extra output does not cover rising costs.

In effect the tariff revenue, redistributed by the Treasury to households after paying more to producers for uneconomic output expansion, fails to compensate households for their higher costs of purchase.

If the tariff causes world import prices to fall, there is a countervailing gain from better terms of trade, viz lower import/export prices. The size of this gain depends on substitutability between goods, as measured by the ‘elasticity of substitution’ – the lower, the bigger the gain because as demand falls due to tariffs prices must fall further for product import volume to be maintained.

In a classical model, there is only substitutability between different commodity types. So to get a reduction of import prices a tariff-raising country has to reduce demand for the commodity worldwide. The reduction in world prices will be its tariff times 1/the elasticity, times its world market share.

Even though the elasticity is low, so that its reciprocal is high, the import country’s world market share is typically quite low so that the overall effect on prices is small.

However, in the gravity model it is assumed that the substitutability between goods of different origins is quite low. So our diagram above applies to many different imports from differing origins.

We can now compute consumer surplus costs for each country-facing tariff; but also the terms of trade gain for each country-origin import, this being given by the tariff times 1/the elasticity times the import share in that country-origin supply. This import share is typically high, so the terms of trade effect is correspondingly high.

We see therefore that the temptation under gravity models to raise tariffs is high, owing to the low substitutability these models assume between goods of different origins.

On the one hand, there are losses of consumer surplus, but on the other there are terms of trade gains from protection. While all models differ in their exact assumptions, we can discern a pattern in the welfare estimates: gravity models will find a greater gain from the protection given by the EU customs union against the non-EU world, while it will find a consumer surplus loss from this and also from any EU-UK barriers. Because these barriers are mutual terms of trade effects favour the largest importer, namely the EU.

Hence we find that within a gravity model of the Computable General Equilibrium (CGE, ie. a full model that runs on the computer) type, there is a bias towards protectionism.

The latest Treasury calculations after the referendum, in which the Treasury uses the GTAP model,  a gravity model in respect of low assumed origin substitutability, discarding its earlier pre-referendum methodology in response to our and others’ criticism, find that Brexit is damaging in its trade effects.

However, in addition to using this gravity model, it uses policy assumptions about Brexit that we cannot accept as realistic. First and foremost, it assumes that there will be little adoption of free trade with the rest of the world.

Whereas on this GTAP model the full elimination of the 20% EU trade barriers (tariff and non-tariff) on food and manufactures would boost UK GDP by 4%, the Treasury assumes that only 5% of this would be eliminated in practice, so that the gain falls to 0.2%.

Table 1. Assumptions/models: differing estimates of gains/losses (% of GDP)

Second, it assumes that the EU will erect non-tariff barriers both via standards and border difficulties even with a UK-EU Canada+ trade agreement. This causes a loss to the UK of no less than 5.4% of GDP.

Yet this assumption is in fact illegal under WTO rules against discrimination and border inefficiency-so in effect it would not be allowed under the laws recognised by both the UK and the EU.

Thus under the Treasury’s GTAP model, if realistic Brexit assumptions are inputted, then according to that model, there would be a welfare gain to the UK from Brexit due to the trade effects of 2.6% of GDP in an exit under WTO-rules, or 4% in an exit with a Canada-plus EU FTA.

The Treasury assumptions yield losses under WTO rules of 6.6% of GDP and under Canada+ of 4.9% of GDP. So it can be seen that the Treasury’s assumptions add an unwarranted 9% of GDP to the cost of Brexit, even if one accepts the gravity model.

Using the classical model, as estimated in Cardiff research, in place of the gravity one adds a further 9 or 10% of GDP to the calculated gains of Brexit.

If we assume that only 10% of the existing EU 20% protection of food and manufactures is abolished, then the gain to UK GDP is 7%, mainly via higher productivity, while consumer prices fall 6%); if we assume that the full 20% protection is abolished, these numbers double.

This is true both under the WTO-rules exit and the Canada-plus case; the reason these are the same is that once the UK has driven UK prices to world prices via FTAs with the non-EU world, it makes no difference what EU FTA we have.

EU producers, like our own home consumers and producers, can only sell and buy in our markets at world prices; EU trade barriers will simply be passed on to EU consumers, while UK trade barriers must be absorbed by EU suppliers.

Paradoxically, this implies that the UK Treasury can levy tariffs on the EU and gain at EU expense, while the EU can only raise any tariff revenue it gets from UK imports from its own consumers.

It is worth explaining how it is that these results come about. A key effect of agricultural protection is a large rise in the price of agricultural land. This acts as the base price in alternative use for all land that gets planning permission to be used in other sectors.

Hence it raises costs of production across the whole economy, strongly reducing services output. The non-traded sector also contracts, as costs and prices rise. By moving to free trade through a comprehensive set of FTAs, these higher costs of land are swept away and land is supplied as needed to the different sectors as they expand. Consumer prices fall generally as do costs of production; and at the same time the greater competition from falling import prices puts pressure on home producers to raise productivity.

Notice in all this that the gains from free trade come from abolishing our protection on imports, not-as widely suggested in popular writing-from the greater access to foreign markets granted reciprocally in these FTAs.

This greater access does give short run gains to our exporters, which helps to get political support for FTAs; however, in the long run these gains largely get eroded by the downward pressure on our export prices in other markets from other countries’ exports displaced from the markets where we get better access.

We summarise these results in the Table showing the gains/losses in % of GDP under the different model/assumption combinations; we label the assumptions we have argued reasonably represent the policy reality as ‘Real(istic)’, which of course contrast with those used by the Treasury.

As can be seen, the failure to compute sufficient gains in trade from Brexit come about half from poor policy assumptions, half from the gravity modelling mistake. The poverty of the policy assumptions we have already explained.


Economists in the UK and in international organisations, as well as in the British Treasury and civil service, have widely claimed that Brexit would damage the UK economy.

To support these claims they have used trade models in which ‘gravity’ is a major feature; according to this gravity theory trade is caused mainly by size and proximity, not by comparative advantage and there is little substitutability between the products of different countries.

This model favours protectionism because tariffs can force down import prices a lot. Hence it also supports EU protectionism through its customs union. Also it implies that the UK loses a lot from any UK-EU trade barriers and gains little from free trade with the rest of the world.

However, the model does not fit the UK trade facts. The classical model based on comparative advantage does fit them. According to this model there are big gains from free trade with the rest of the world and ironically a small gain from UK-EU tariff barriers, which under WTO rules are the only ones erectable.

The British Treasury, which has strenuously opposed Brexit from the referendum debate onwards, calculates large losses from Brexit; the difference of these from the properly calculated gains comes half from using the wrong gravity-based model and half from using false policy assumptions.


Chen, G, Dong, X, Minford, P, Qiu, G, Xu, Y and Xu, Z (2021)

‘Computable General Equilibrium Models of Trade in the Modern Trade

Policy Debate’, working paper E2021/14, Economics section, Cardiff University,; forthcoming, Open economies Review.

Corong,E, Hertel, T, McDougall, R, Tsigas, M, Menbrugghe, D (2017) The Standard GTAP Model, Version 7, Journal of Global Economic Analysis, [S.l.], v. 2, n. 1, 1-119, June 2017. ISSN 2377-2999.

Costinot, A and Rodríguez-Clare, A, ‘Trade Theory with Numbers: Quantifying the Consequences of Globalization’, chapter 4, Handbook of International Economics, vol.4, eds. Gopinath, G, Helpman, E and Rogoff, K, Elsevier, 2014, pp. 197-261.

He, C, Li, C, Wang, J, and Whalley, J (2017) ‘The Armington assumption and the size of optimal tariffs’. Economic Modelling,66, November 2017, 214-222. See also, NBER Working Paper 21423

Meade, J, 1955. The theory of customs unions, North-Holland, Amsterdam, pp.121.

Minford, P, with Gupta, Le V, Mahambare, V and Xu, Y (2015) Should Britain leave the EU? An economic analysis of a troubled relationship, second edition, December 2015, pp. 197, (Cheltenham, 2015)

Minford, P and Xu, Y (2018) ‘Classical or gravity: which trade model best matches the UK facts?’ Open Economies Review, July 2018, Volume 29(3), pp 579–611

Minford, P (2021) ‘Free trade under Brexit- why its benefits have been widely underestimated’, Cardiff Economics working paper no 2021/18, downloadable at

Tinbergen J (1962) Shaping the world economy: suggestions for an International Economic Policy. The Twentieth Century Fund, New York.

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