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The Centre for European Reform on 27 January 2019 produced one of their Insights dedicated to the costs of  Brexit to the UK economy to September 2018 [link]. These analyses indicated that the UK economy is 2.3%  smaller than it should have been, which equates to £17 billion per annum or, in ‘side-of-the-bus’ terminology  £320 million per week. These are not the expected costs when the UK is actually leaving, but the costs  already incurred to that date. Real monies, so to speak…  The Centre’s Deputy Director John Springford (@JohnSpringford) conducted analyses in which, because we  cannot really know what would have happened had the UK not done something this dumb (this is called the  counterfactual), he created an artificial counterfactual from a couple of other countries. The reason for  doing this is that there is never one single country to compare the UK economy to: is the UK like the United  States, like Germany, like China, or maybe it is more like Belgium? However, you can use the data from a  number of countries and combine (weigh) them in such a way that they resemble the UK economy. The trick   is that even though individual countries may have there own changes to their respective economies, their  combination is much less affected: in this particular situation all countries were subject to the same events  with respect to the world economy, but only one was foolish enough to vote for Brexit. Because this  happened on a single date (the referendum was on 23 June 2016), we can use the combined estimate that  resembles the UK economy from 2008 to 2016 to project forward to the September 2018 date and compare  this to what actually happened. If there were no other large, structural changes, then the difference  between both time series can be interpreted as the effect of the 2016 referendum (and the shenanigans  thereafter). I am not an economist, but I do know that the above method using the artificial counterfactual is that of a  ‘synthetic control’ (or, in much cooler economic terms, the Doppelganger UK). I know this, because I build  quite a number of those (see for example this page on my blog). John Springford was kind enough to provide  the data he used with the report, and although I could not see his methods (that link didn’t work, and even if  it did I cannot read that programme code) this provided the opportunity to do the analyses using the methods  I am familiar with.   So here we go…  * Below is the figure from the CER Insight as the reference, with the measured growth of real GDP relative to  the 4th quarter of 2008 in blue, and the counterfactual ‘what should have happened without the referendum’  in red. As you can see, the difference equates to 2.3%.  So let’s start there. From the Insight you can read that some form of an automated selection method was  used to select the best countries from a group of 22 advanced economies to build the synthetic control with;  more specifically, these were the US, Germany, Luxembourg, Iceland and Greece, making up 50%, 28%, 11%,  10% and 2% of the synthetic control (ie the doppelganger UK). I used those same countries to do the same  thing, but because I use a different method (Bayesian structural timeseries [link], using the programme’s  defaults) my results are slightly different. This is what I find:  The solid line equates to the blue line in the CER figure above, and the dotted line is my ‘UK doppelganger’  (similarly, the vertical dotted line is the referendum timepoint). In addition however, the blue shades provide  the 95% credible intervals, which can be used to obtain an idea of how certain we can be this is a real effect.  In any case, my analyses give a reduction in the UK economy of 3.1%, and this may well be the result of the  referendum result (i.e. we are 66% certain).   Not too dissimilar, but using the same numbers as CER this equates to £23 billion pounds (I should probably  ask Brian Cox how best to communicate such a large number), or about £430 million a week. This ispretty  close to the CER estimate, and if anything shows that the CER estimate may have been on the lower end of  expectations: in fact we may have well already lost more than Boris Johnson’s ‘£350 million a week’  statement painted on a bus.    So let’s take it from there. The method I use also has a method to select countries, and because these may  well be different than those from the CER, I used this as well. The figure looks pretty much the same, but my  ‘UK doppelganger’ is mainly made up of New Zealand (contributing ~42%), the United States (~40%),  Switzerland (~8%), Australia (~6%), Luxembourgh (3%). The effect of Brexit however, is pretty similar and  indicates a reduction in the UK economy of 2.9% (with a certainty of 64%).  * However, I think there is a better way of building the UK doppelganger.   When you think about it, the countries that have been selected together make up a pretty good  doppelganger, but in order to do so we would have to be sure the trend in their pre-referendum timeseries is  similar to that of the UK. The closer these are aligned, the more confident we can be that these are subject  to the same economic processes, and the more confident we can be that without the referendum these would  have continued in a similar way (especially, remember, when we use a combination of these to create the  doppelganger). If we have a look at this for the 5 countries in the CER report (and we use a scaled  transformation of the data because we are interested in similarities in trends and not absolute differences),  we get the following comparison:  The black line is for the UK, and indeed some of the lines are pretty similar, but some are not. In fact, the  most divergent trends are in Iceland, but especially in Greece; the latter should not be a big surprise given  what has happened in the last decade or so.   There is a methodology to pre-select the best countries to contribute to the doppelganger by calculating the  differences between the pre-referendum (standardised) GDP trend in the UK and those of all other countries,  and which is called dynamic time warping. I applied this method and selected the five most comparable  countries: New Zealand, the United States, Switzerland, Australia and Canada (pretty similar to the five  automatically selected countries from the method I used). As you can see in the figure below, these are very  comparable indeed:  This increases the confidence with which we can say something about the post-referendum effect, as  discussed above. Running the model using these 5 countries to create the doppelganger, indicates that the UK economy is in  fact 4% smaller than it should have been, and we are 71% certain this is due to the Brexit process. That is  quite a lot: we are talking about £30 billion extra borrowing (again, Brian Cox will have to translate the  number to grains of sand on a beach), or about £570 million a week! I cannot remember seeing that on the  side of a bus ?!  * So which number is the right one? I don’t think that really matters, because we will never know for sure. The  main take-home message here is that whichever one of the methods here you believe most, Brexit to date  has cost the UK a considerable amount of money already, and in all likelihood this exceeds the ‘£350 million  per week’ lie painted on the side of that bus. In fact, based on the rationale that informed the last analyses  above, I would say the UK lost almost twice that amount per week(!). And we haven’t even left yet... 
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Doppelgangers and the true costs to the UK economy as a result of Brexit
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