Sacre bleu! The furore over the (rumoured) decision to award the contract to produce the new, “iconic” and definitely blue British passports to a Franco-Dutch firm has something for everyone. From headline writers and cartoonists to publicity-seeking politicians to experts in public procurement law, there is no shortage of commentary. And it has brought predictable reactions from the various sides of the Brexit debate.

For Remainers, it is an ideal target for mockery, as what was supposed to be an easy, symbolic victory for the Brexiteers backfires embarrassingly. For some in the press and on the “hard Brexit” wing of the Conservative party, it is an ideal stick with which both to beat the government for its supposed spinelessness and to point to the EU procurement rules which supposedly force us to award this contract to the best value tender.

And for the so-called “Liberal Leavers” – including the small minority of economists who support Brexit – who claim that Brexit will allow the UK to escape the supposedly protectionist EU and forge a “Global Britain” it provides an opportunity to demonstrate their intellectual consistency, by arguing that the UK could and should continue to follow the same “best value” approach after Brexit. For example, Julian Jessop, Chief Economist of the Institute for Economic Affairs, tweeted: “Free trade = buying goods and services from wherever offers best quality and price, even if abroad. Yes, this includes printing of passports.” Few economists, wherever they stand on Brexit, would disagree.

But although it is tempting to dismiss this episode as merely an amusing distraction from the bigger Brexit issues, it illustrates a fundamental problem with Julian’s argument and that of other Liberal Leavers, including the leading Cabinet Brexiteers like Boris Johnson, Liam Fox and Michael Gove. Post-Brexit, for all their rhetoric to the contrary, the UK will be a less rather than more open economy.

The basic point here is that the government faces what economists call a “time-consistency problem”. That is, that while it would like to commit to welfare-improving policies – for example, that government contracts should awarded on merit, with no national preference – it cannot credibly commit to such a policy, because, in some circumstances, it will be rational for the government to renege on its commitment. Knowing this, other economic agents, in particular the private sector, will plan on the basis that the government won’t keep this promise. The end result is that everyone will be worse off.

What’s the relevance to the EU? Well, here’s one I prepared earlier. More than two decades ago, Raquel Fernandez and I wrote about some of the potential advantages of regional trade agreements, like the EU, compared to a “global” trade strategy:

“ [Consider] the case of a country whose optimal policy is to open itself up to foreign investment. Once foreign investment has been made, however, the country has the ability to confiscate it (in practice, confiscation might be through the imposition of a greater regulatory or fiscal burden) … if the country is unable to commit to abstaining from this action, foreign investors, perceiving this time-inconsistency problem, will not invest.”

So, the country can’t in practice implement the policy it knows to be optimal. In a case like this, a regional trade agreement like the EU provides a solution – it’s a credible way for the government to commit to stick to the optimal policy, particularly on competition and trade issues:

“A regional trade agreement, by making the cost of even a small deviation from an agreed trade liberalization large, makes these small temptations that culminate in an overall greatly distorted economy, easier to overcome. Thus, a country in a regional trade agreement will face the cost of either exiting from the agreement, or an agreed upon large punishment from the other members, should it extend protection to some particular sector of its economy.”

Our paper also explains why the EU – a deep but relatively narrow (compared to the world as a whole) trade agreement, with strong and credible sanctions against countries that break the rules – is likely to be much more effective than wider but shallower arrangements like the World Trade Organisation.

So, what does this mean for Brexit? By definition, the whole point of “sovereignty” – as defined by the Prime Minister and the Leave campaign – is to rule out commitment devices based on permanently binding international commitments, at least ones that are as strong and credible as EU membership. Does anyone imagine that if we were not an EU member, but merely signed up to a broader and weaker set of international commitments on public procurement, that the government would not come under irresistible pressure to award the passport contract to a British company after all?

And, importantly, this argument still holds even if UK politicians, and UK voters, are no more protectionist after Brexit than they have been in the past. All that is required is that politicians, once the constraints of EU membership are removed, are more able to act – perfectly rationally – in the accordance with the short-term incentives that they face. Indeed, Matt Hancock – close to George Osborne, and supposedly an economic liberal – crumbled almost immediately on the Today programme, suggesting that procurement rules could be changed after Brexit. Remainers outside government – for example Frances O’Grady, the TUC General Secretary, a strong supporter of Single Market membership – demonstrated an equal lack of consistency.

Are these arguments just academic? I doubt it. The time-inconsistency argument, although it started as an economic theory, quickly became translated into practice when it provided the intellectual underpinning for central bank independence, as a way for governments to “tie their hands” when it came to interest rates. Does anyone really doubt that if the UK were to legislate to bring interest rates back under the direct control of the Chancellor that the result would be (on average and over time) higher inflation – even if individual Chancellors started off with no intention of manipulating interest rates for political purposes?

Similarly, with removing the disciplines of EU membership. Whatever the theoretical merits of “Global Britain”, Brexit is likely to make us a less open economy, even if that’s not what we (collectively) actually want.