Monday, 23 January 2017

Maths is Fun

One of the arguments behind the Leave campaign was that EU migration is out of control.  They argued that the UK needs to take back control and that needs to start at the border.  Only by leaving the EU would the UK be able to achieve its long-held but entirely arbitrary target of a few tens of thousand per year. The UK Government, of course, has been banging on and on about reducing inwards migration for some years now.  Just the other day David Davis started banging on and on about it all over again.  The Conservative Party has failed and failed and failed yet again to make good on this promise.  Will leaving the EU let them finally achieve their xenophobic dream of an Anglo-Saxon land?  Let's find out together.

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It doesn't take a genius to work out that they will fail one more time.  In fact, it turns out that it takes no more than secondary school algebra, some reasoning and a pocket calculator to work out the effect that leaving the EU will have on migration.  What's that you say? You don't like maths?  Oh dear, we'll never be real friends if that's the case. Alright, go and get your Star Wars costume and we'll pretend we're Vulkans.

Let's start with the maths, shall we?  Let's say that the net increase in non-EU migrants per year is N and the net increase in the number of EU migrants is E.  Just to be clear, N and E represent the number of arrivals minus the number of departures over a calendar year. The total annual increase (M) in the number of migrants in the UK is then

M =  E + N

Let's just pause for a second and remember that the UK Government's intention is that M is a positive value of a few tens of thousand.  Nobody is talking about making M negative, which would mean a reduction in the total  number of  migrants. The economic and demographic forces that lead to inwards migration are so powerful that M has only ever been positive.

Let's pause for just another second because you might have noticed that I didn't include the comings and goings of UK nationals.   Most accounts of migration add in a third term for UK nationals leaving and returning but I've deliberately left that out because nobody who actually cares about migration is remotely bothered about increases or decreases in the abundance of their "own kind".  If migration numbers were a measure of the fullness of Britain it would include births and deaths as a further measure of comings and goings of UK nationals.  Births and deaths are never accounted so I'm left with the impression that migration is not a measure of the fullness of the UK but actually a measure of the number of johnny foreigners at the bus stop.  With that in mind, let's express M in terms of what really matters to anyone who might obsess over  it.

Now, let's imagine that leaving the EU won't reduce N.  We'll come back to this later because leaving the EU might even lead to an increase in N.  For the moment, however, let's be optimistic and assume that N is entirely independent of Article 50.  That just leaves E, the net migration from the EU.  What will happen to that number?  I'd expect that number to fall because the UK Government will likely introduce a system that adds bureaucratic and technical hurdles to employees and employers.  For the purposes of generality let's say that net EU migration after Brexit is γ x E, where γ is somewhere between 0 and 1. The ratio R of pre-Brexit and post-Brexit net migration is simple to write down.

  R = ((γ x E) + N)/(E + N);  0 <= γ< =1

Before I go any further I need to justify why I clamped γ so that it is at least zero and less than one.  First off, we don't expect the rate of inward migration from the EU to rise after Brexit.  For many reasons the UK is likely to become a less attractive destination for most Europeans because of the collapse in Sterling; the general culture of rising xenophobia; and the requirement for registration and visas.  Having said that, people will still want to come because despite everything the UK is actually a good place to live and work. It is also the preferred destination for many people with English as a 2nd language and for those who want to cultivate English as a 2nd language. Will we see a mass exodus of migrant workers?  I don't think so, to be honest, because moving country is a huge hassle and not something done lightly.  The likelihood is that migrants already with a medium-term residency in the UK will opt to stay.  The chances of a net reduction seem slim indeed, notwithstanding the outbreak of civil war or a nasty bout of pestilence.  That clamps the lower bound of γ at 0.
It's time to start estimating that ratio.  We have reliable 2016 figures for N and E already (196,000 and 189,000 respectively) but γ requires a bit of a crystal ball. It seems wildly optimistic that we would instantaneously half the migration figures from the EU.  Let's plug that in to our calculator and see what falls out.
  R = (0.5*189000 + 196000)/(189000 +196000) =0.7545

Oh dear, we are still at 75% of current migration levels even when we half EU migration.  In real numbers that equates to 252,000 extra human beings per year, a long way from tens of thousands.  That is not going to please Migration Watch or UKIP or Tony Parsons. Let's see what happens if we miraculously completely stop all EU migration
  R = N/(E + N) =0.5091

Oh dear, the best outcome for the UK Government still leaves us at 51% of current migration levels, equal to a net migration count of 170,545.  That is not going to please EDL or Britain First or Len McCluskey or Andy Burnham.  Tony Parsons is still going to be as angry as a bag of wasps.

Tony Parsons playing the role of Billy Mitchell in Eastenders.  A long way from his punk days at NME.
I bet you've all spotted the problem by now.  Of course, the problem is that N is actually greater than E;  attacking E doesn't really change anything by much.  If you're a STEM geek like me you'll be jumping up and down yelling "Amdahl's Law, Amdahl's Law".  Don't worry if you've never heard of Amdahl's Law because it merely confirms that you are a happy human with functioning social skills.

There's another problem that we need to discuss and that is a reliable estimate for γ after the UK leaves the EU.  Contrary to popular belief, the UK has strict border controls.  I don't know about you but I need to stand in a queue to have my passport checked every time I return to the UK.  There's even a separate queue for non-EU nationals who require pre-arranged visas.  Acquiring residence and employment rights for non-EU nationals is even more demanding: it requires all sorts of form-filling and can be a very time-consuming process with no guarantee of success.  So complex is the process, there are even legal firms that specialise in helping non-EU nationals navigate their way through the system.  It is fully in the power of the UK Government to reduce non-EU migration to any value they wish.  The idea that the UK has lost control of its borders is completely preposterous. For reasons that aren't clear, however,  manifesto pledges to reduce the number have not been honoured.  Despite having full control over the border for non-EU nationals and strict legal limits on the rights of non-EU nationals to reside, invest and work in the UK, their number just keeps increasing.  Making EU nationals jump through the same post-Brexit hoops as non-EUs do today is no guarantee of any reduction in number.  My guess would be that γ will be much closer to 1 than 0.  Please make sure Tony Parsons is in a safe space with plenty of padding when you tell him this.

In everything above I assumed that N was a fixed number.  That might not turn out to be the case because businesses suffering from reduced E might seek to increase N in order to sate their demand for staff.  Trade agreements with, say, India, might trade market access for a relaxed visa programme.  Yes, we might even see N increase as a consequence of leaving the EU.  The simple truth is that the level of migration is fueled by matching UK employment vacancies with a surplus of available humans from countries with weaker currencies.  Businesses that need humans to work in their enterprises have historically found a way to get what they want.  Leaving the EU isn't going to change that.  It will all be for nothing.

Over and out,


PS I realise that I used loaded language in this post in a way that presented reduced migration as a "good" outcome.  I don't share that view in any way at all but I wanted to go through the sums from the perspective of a civil servant charged with the task of reducing migrant numbers. I'm very mindful that I'm a migrant worker (definitely not an expat) and have benefited greatly from EU migration over the years.  Why stop a good thing?

PPS Switzerland is 25% non-Swiss.  It has one of the highest GDP rates in the world. These two facts are not uncorrelated.

PPPS There is an argument that unemployed UK citizens will step in to take up all the vacancies in the event that migrants leave en masse, thereby maintaining current levels of economic activity.  We need to ask yourselves why migrants were needed in the first place? The standard UKIP answer is that migration depress wages.  If this is true then it means that UK workers have placed their labour at a higher rate than the present offer.  It follows that they'll only go to work for more money, which will push up the cost.  The question, then, is whether their retail product will remain cheaper than European imports made by all that displaced labour.  That would only be the case with significant import duties, something that the UK Government is very much against.  Of course, a weak value of Sterling does a pretty good job too.  I'm going to post on this in more detail.  Exciting times ahead.

PPPPS I left out the comings and goings of UK nationals.   It is safe to assume that fewer UK nationals will leave the UK after Brexit and that more will return.  If you include UK nationals in your migration figures then you have a problem because leaving the EU will push up that component of the total figure.  Somebody start a crowd-funder to get Tony Parsons a defibrillator. 

PPPPPS I said that I didn't imagine a huge surge in EU nationals leaving.  I think that will be about right.  Having said that, some will leave as a direct result of Brexit.  Who is most likely to leave?  That will be anyone who is highly employable and can readily find work in the EU, perhaps even a job that comes with a generous relocation package.   These are the people the UK most want to keep because their economic activity generates an awful lot of tax.  They are also the hardest to replace from the UK population because they are most likely to have specialist skills. If you've ever worked at a failing company you will immediately recognise this situation.  


  1. I quite enjoyed this post, but that's probably because I used to be an economist with an interest in labour markets, so am by definition a bit weird too.

    I've also worked in manufacturing, and your analogy with failing companies getting into a death spiral because their best staff get jobs elsewhere, performance falls, more leave, replacements are inexperienced or poor, and then on down the plug hole, reminds me of one I worked for. It got bought out in a fire sale, asset stripped, and many of those who had hung on got made redundant anyway.

    Could that happen to a country? Maybe not quite in that way, but it's not going to be good for those of us who are left in a deregulate low wage economy with unaffordable health care run by Trump Enterprises and compulsory fruit picking for any remaining benefits even if you are chronically sick. That sounds a bit over dramatic, but it is definitely the direction of travel.

    Without young, energetic immigrants Scotland would be a poorer place. It seems that about two thirds of Scots agree with that, but are they prepared to take the only step that will keep them in the EU? We will see, I suspect, within the next two years.

    It is a bit too early for take forward my usual rigorous research methods for testing public opinion- the pub's not open yet - but the sun is shining, so I'm away for a walk on the beach. I need a bit of cheering up.

  2. As you point out, my analogy with a failing company over-eggs the pudding a bit. A failing company is much easier to spot than a failing economy. Also, moving job is much, much easier than simultaneously moving country and job. Countries also have greater inertia than companies. As a consequence, a failing company has a faster death spiral than a failing country. The direction of travel is definitely something they both have in common.

    There's a really interesting comparison between the German academic system and the UK system. Back in the 90s, permanent academic positions in Germany required first passing a process called "habilitation". Typically, a candidate would complete a PhD, then maybe a couple of years as a post-doc, then 5 years further research and academic duties as a habilitation candidate at a German institution. That last stage made it very difficult for the German university system to recruit from outside because no other country had such a system. Everything was reformed to the point that speaking German is no longer even a requirement for some modern research areas such as computer science. The UK is about to turn in the opposite direction by introducing new hurdles in recruitment. This just sounds regressive to me. Don't we all want a successful economy like Germany?

    Please chip in with corrections. I'm most definitely not an economist so end up thinking about it from a STEM perspective. I would guess that might lead to some naïve conclusions.

    The sun is shining! Wow. I am very jealous. It is bitterly cold here. I have no intention of walking anywhere in these temperatures.

  3. One of my friends is an EU national as described in your PPPPPS - she has 10 days remaining in the UK before relocating to the Netherlands. Brexit was at least 50% of the motivation behind the move...

    The UK government could lower your N (non-EU immigrants) by approximately 30% in one fell swoop if they wished to. And do so by nothing more than a bit of bureaucratic number work as simple as putting a number in one column rather than another. By my (not too rigorous and therefore possibly inaccurate, but none-the-less approximately correct) understanding, there are approximately 650k non-EU immigrants coming to the UK each year. With approximately 325k leaving (not sure if the this includes Brits going abroad) that leaves a net inward migration figure of 325k (give or take).

    There are also approximately 300k non-EU students studying in the UK at the moment. Assuming that most are here for 3 years and leave immediately after their course finishes (the latter part of that assumption is known to be true) then approximately 100k are arriving and leaving each year. This number is included in the figures in the previous paragraph. (The fact that more students are probably attending courses that last 1 year as apposed to 3 is even better if you want to lower immigration figures, but let's keep the worst case scenario.)

    All the UK govt has to do is stop counting these visiting students as immigrants and start counting them alongside tourists as temporary migrants or visitors or something. Most other countries do this already. The opinion polls and academic studies that have looked into this in the UK show that people don't care about foreign students coming here providing they go home again and the scare stories that suggest that they don't are inaccurate at best.

    So there you go, the UK govt could show that it has controlled its borders and cut immigration by one simple accounting trick but it chooses not to do so. One has to wonder why. To me it is obvious that the Tories do not care one way or another about immigration (not really) but they are happy to use the issue as a way of gaining and retaining power.

    As a bonus, do you realise that the UK actually doesn't know how many people emigrate (or return to their country of origin) each year? The figures we do have are from 'passenger surveys', i.e. samples of the passengers leaving the UK by plane or ferry with an extrapolation of these figures to provide an overall figure. I'm not even sure if the authorities actually monitor exactly who leaves when, even if that information can be gleaned from passenger manifestos and possibly passport control. But if you a Brit on EU citizen emigrating (as opposed to going on holiday) there is no 'I am leaving the country for good' formality to go through and you simply stop paying your taxes (etc.). As for the non-EU nationals leaving, they may well be counted out the door but immigration authorities have no interest in them unless they try coming back into the country again.

    The whole immigration thing is a farce.


    1. That's a really interesting point about student numbers. The Government could do that and "fix" the problem but they've already said that they won't do this

      The Government are under pressure from groups like Migration Watch who are adamant that students are counted in the official statistics

      This is driven by pure xenophobia. They just don't want foreigners in the UK, no matter how much sophistry they apply to their arguments. The Government have made it clear that they are now listening to these groups.

      I got my stats from the UK Government. As you said, they're not really clear about how they gather the data. That would just never happen in Switzerland but I can't see the UK implementing the level of bureaucracy required to know who lives where.

      The stats I had were about 370k net incomers (half EU and half non-EU) but 50k net UK citizens leaving. That tallies with your 320k figure. I ignored the movements of UK nationals in my numbers. That makes the figures look worse today but I think it will make the figures in 5 years look better than they really are due to the number of returning pensioners from Spain (or lower numbers going there).

      I would imagine economically active EU returners could be counted from their absent tax forms. When I left the UK I filled out a form declaring I was no longer tax resident.

      Sorry to hear about friend going back to the Netherlands. The impact on individual humans is the worst aspect of Brexit and something that is often forgotten.

    2. I got my figures via a quick Google search & from my partner who has the rather challenging job of recruiting non-eu students to come & study at the university she works for. The gist is correct even if someone can squabble over the exact numbers.

      These non-democratic 'watch dog' organisations are able to exert far too much influence over government policy. I honestly wonder of we are watching the start of the 4th Reich developing & can only hope that enough Scots can see this clearly enough or I'm going to have to come & join you in Switzerland.

      My friend is doing fine. The job she is going to is a better one & her decision was only half motivated by brexit. But the UK has lost a very clever brain & she is not alone. I have every faith that she will come back to an independent Scotland as this country has become her home.

    3. Your partner has a tough job right now.

      I do wonder if something quite dark is stirring in the UK right now. And in France and in the US. It is quite worrying. It is also quite exasperating to see student political groups wield their policy of "no platforming". Argument needs to be defeated rather than silenced. Maybe Brexit was the result of some kind of pressure build-up of unpleasant views that were never allowed to be voiced.

      Let's hope your friend can live in a land with a plentiful supply of porridge some time soon.

  4. The reason the UK doesn't know the exact numbers is that the UK has no ID card system in the way that other countries do. Every time one is mooted, complete hysteria breaks out. Funny that. As far as I know most of Europe has some kind of ID card for citizens and residents, and the sky has not fallen in.
    I wonder why.

    1. The difference is in the relationship between the state and the individual. The former Napoleonic countries all have ID cards but also have a fixed constitution laying out the obligations placed on the state and the individual. The scope of use of an ID card is governed by those constitutions. The state can only do what it is allowed to with the information on the card. Changing those permissions is impossible without a formal change to the constitution. None of that is true in the UK. They could share it with any insurance business they choose at the drop of a hat, or decide to link your GP's notes with your driving license.

      I have an ID card here and I had one when I lived in Germany. I've never worried about this because they were in countries where electricity bills quoted the constitution. The UK is quite a different story altogether.

    2. A quick example of the power of the constitution is the recent vote in Switzerland to limit EU migration. That required a change to the constitution. The referendum question was actually worded with the legal text that would be applied the constitution. Compare that to the half-arsed attempt that was the EU referendum. I guess I'm saying that through a combination of incompetence and mendacity I don't trust the UK Government with my data!

    3. As an ex police officer who could have welcomed the punters having a means available to identify themselves to me, I am completely opposed to ID cards in the UK context for the reasons outlined above. But beyond that I'm not sure they are safe because constitutions can always be changed (look at Nazi Germany) & they also allow future unscrupulous or evil organisations (think Nazis again) to use the information current governments hold in good faith. When the Nazis invaded the Netherlands they found it relatively easy to round up the Jews because the Dutch kept excellent records. They had a much harder time in Denmark because those records simply didn't exist. I have no particular fears for the future but I don't trust future generations in the slightest.

    4. I don't mind that the state here has good records as long as they can't join it all up. That's the bit that is worrying. I mean, the state should have good records. They should know who lives where because they need to collect tax. I just don't want my GP knowing my income, or my health insurer knowing my religion. The UK ID card system had no long-term protections at all to stop the complete integration of all the various databases. There are still constant calls for ID cards to be presented at GP surgeries and for the chip on the card to hold criminal records. That is already conflating several different issues in an dangerous way. There is nothing like that here. My ID card has no chip in it, for example. It is just a photograph and a number. I don't even carry it around and only ever needed it to join the library because it proved I lived in Canton Zurich.

      I take your point about constitutions being changed. That can happen.

  5. With regard to you PPPPPS, I've heard that some medical staff have already left, or are planning to leave, since Hunt announced at the Tory conference that, just as soon as he had any native doctors trained, foreign ones would be sacked.

    I guess they decided not to hang around waiting for that fine day. But not to worry because the NHS in England under Jeremy is doing so well that the odd doctor leaving here or there isn't going to make a massive difference. People will still spend a maximum of 4 days on a trolley in a corridor.

    Greg Clark (who he, I hear you ask) is saying that there is a lack of skills, presumably in England, where he is skills minister. He hopes to ape the system in China and Singapore where they seem to do better.

    Good luck with that, Greg matey. Most people here need to work when they are at university or college. I'm not sure how they'd cope with an increased number of hours of "facetime". (We used to call it lectures and tutorials.)

    I'm wondering, too, where all the extra lecturers/tutors will come from. Still I'm sure the estimable Greg has it all under control, a bit like SIR Fallon has the Trident rockets sorted, well sort of!

    As an after thought I imagine that quite a few really good researching university staff will we taking flight given the massive reduction that will come about in EU grants to universities.

    Projects will go elsewhere, and along with them the best minds.

    Oh well, Scotland has a way out of this.

    1. The totally weird thing is that the government first said they would sack foreign NHS staff and then a few months later started an EU-wide recruitment campaign for NHS staff just as they made it clear that rights to work in the UK would be repealed. I don't understand how they can be so disorganised.

      That's a great link. Someone should try to tackle this problem but that interview was just empty words. There were no costings at all. We all know this won't happen.

      We've mentioned this before: that the EU is far better at distributing money than the UK, especially in long-term projects. Universities are first in line to see how big that difference really is. I would guess farmers are second in that queue.


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