Gravity, Gobbledygook, and Government Reports

Mark Reckless is an idiot. Now, if I stopped there, it wouldn’t make much of a blog post (although it would, as usual, be factually accurate). So, you might be asking, “Why is Mark Reckless an idiot?” But that is the wrong question. Instead, what you should be asking is “How has Mark Reckless demonstrated his idiocy this time?” And that would be a very good question indeed.

The answer to that question rests in the tweet below. This was Reckless’ comment regarding a description of one part of the methodology that the Treasury used to estimate the costs of Brexit – the equation in question was contained in a technical annex (i.e. where one would expect to find a detailed explanation of the approach used).

Reckless appears to be claiming that the equation in the picture he posted is equivalent to the fraudulent claims of a fortune teller. That could not be further from the truth.

Instead, the equation posted by Reckless is an algebraic representation of the “Gravity Equation” as applied to international trade. Emanating from Newtonian physics, this equation relates trade between two countries to the relative sizes of those countries (in terms of output and population) and the distance between them, plus some other controls for whether or not the countries in question share a common border / language / colonial history.

This is not a controversial method to estimate the impact of those factors on trade between two countries. In fact, the use of gravity equations is widespread in the assessment of international trade. A priori, one would expect larger countries to trade more with each other, but countries that are further away to trade less with each other and this is indeed reflected in the Treasury’s results.

The main point of this exercise, however, was to estimate the impact of being in the EU on the UK’s trade, and the Treasury does this by including a variable to capture that. The main result is that being in the EU increases trade in goods by about 100% (i.e. leaving the EU would result in a decrease in trade in goods of 53%) and increases trade in services by about 22%. Hence, being in the EU increases trade in goods and services overall by about 75%.

However, although the main approach used by the Treasury is reasonable, there are some areas in which it could be refined further. First, the Treasury’s analysis uses data covering the period 1948-2013, yet does not really try to control for factors that change over time (other than GDP and population). For example, there have been substantial changes to exchange rates and barriers to trade during the period covered by the Treasury’s data, both of which would have had substantial impacts on trade between two countries. The Treasury’s attempt to control for these changes over time consists solely of using dummy variables for each year (that do not vary across countries), which cannot even begin to capture the changes in exchange rates, trade barriers etc that would have occurred over the time period. This means that the estimated impact of being in the EU could well be incorrect.

Second, the Treasury’s approach assumes that the impact of being in the EU is the same for all countries. However, it is possible that the EU has an heterogeneous impact across countries – for some countries the impact of being in the EU might be larger than it is for other countries. By assuming away this possibility, the Treasury is likely to have under or over-estimated the impact of Brexit on trade.

Third, and on a more technical note, the Treasury does not specify what standard errors it has used. If the Treasury has used incorrect standard errors (for example, ones that do not correct for serial correlation or heteroscedasticity), that means that the statistical significance of its estimates is incorrect and, more importantly, that the error bounds (i.e. the upper and lower ends of their estimate) are likely to be incorrect.

Nonetheless, these minor potential refinements of the Treasury’s approach do not detract from the fact that Mark Reckless has been remarkably foolhardy in his response to the Treasury’s assessment of the impact of Brexit.



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