It follows that the EU makes the UK better connected with its European neighbours, which boosts productivity, which helps living standards. It also follows, according to the paper, that the UK’s withdrawal from the EU would undermine trade with the remaining EU members, which would depress productivity, which would damage living standards. In the White Paper’s words, “the key transmission channel through to the economy in the long term comes from the impact of reduced openness, both from trade and foreign direct investment, on productivity. This is the main driver in the estimates of the long-term effects of EU membership on the economy.”

The estimates need of course to be linked to facts and data, and organised in a model which is able to identify the relative power of different forces. The analytical tool at hand is what the Treasury calls “the widely adopted gravity modelling approach”, pioneered in a 1962 paper by Jan Tinbergen. (Tinbergen, a Dutchman, was one of the first two Nobel economics laureates. In 1969 he shared the prize with the Norwegian, Ragnar Frisch.) In the gravity modelling approach, openness — measured by the ratio of trade between two or more countries to their national outputs — is related to certain relevant variables, such as the distance between the countries and the extent of any colonial ties. Of course, the trade-output ratio is likely to be higher the closer are two countries geographically and politically. That is just common sense. The subtlety of Tinbergen’s method is that it enables analysts to obtain numbers on the size and reliability of the effects.

How, then, do economists assess the importance of trade agreements (read: the WTO, the EU, the European Free Trade Area) relative to such factors as distance and colonial ties? The answer is that they use a statistical technique in which a major trade agreement is treated as “a dummy variable” in the dataset from which the equations are estimated. As the Treasury explains in the White Paper (page 159 for those who are interested), the relevant dummy variable here is set equal to one if both countries in the estimation exercise are EU members and at nil otherwise. By this device, the period before 1973 in which the UK was not an EU (or European Economic Community) member can be distinguished from the period after it. The results of the exercise measure by various well-known statistical tests whether any change in the UK economy’s openness after 1973 was significant, and so — presumably — worthwhile for productivity and living standards.

I realise that I may have lost readers in the last few paragraphs. Let it be said straightaway that the introduction of dummy variables is a commonplace method in statistics and is perfectly legitimate, even if it sounds like gobbledygook. Let it also be said that — superficially — the Treasury has been careful and rigorous in its work, with the pages bedizened by regression coefficients, references to “omitted variable effects” and such like, and numerous citations of academic articles.

Now let me explain why, despite all the effort invested in this project by possibly a dozen or so officials over many months, it remains a contemptible dodgy dossier. First, if the Treasury genuinely believes that openness in the sense of EU membership affects productivity, it is not necessary to involve Tinbergen’s gravity model at all. For a few decades the UK’s main statistical agency, now known as the Office for National Statistics, has prepared data on the productivity of our economy. All that needs to be done is to check whether EU/EEC membership had any positive effect on productivity growth, going directly to the time series in official publications.