Bayes says "no" to no-deal

One of the questions most frequently asked of me is what are the chances of a no-deal Brexit? In common with most analysts I tend to give an answer couched in subjective probability terms. This has the advantage that it is my view – nobody can say it is definitively wrong. Others may not agree with it, but they have the right to apply their own subjective assessments. However, this does strike me as a bit imprecise and led me to wonder whether it might be possible to derive a more accurate data-driven assessment of the odds of no deal.

One way to approach the problem is in terms of Bayesian statistics. In simple terms, Bayesian statistics assesses probability in terms of the degree of belief in an event. This contrasts with the more traditional frequentist school of statistics which represents probability as the number of times an event will occur based on an infinite number of representations of the process (I looked at this issue in more detail here). Bayesian statistics has always struck me as a sensible way to approach problems like Brexit where belief plays a big role and where the frequentist approach, which is based on the assumption that an event can be repeated, is unrealistic.

Bayesian statistics is based on Bayes’ Theorem which describes the conditional probability of an event based upon prior beliefs (or information) and which is written thus:

P(A | B) = P(B | A) . P(A)

  P(B)

This says that P(A | B), which is the probability of event A conditional on event B, depends on the probability of the event B given that A is true (the so-called posterior probability), and the prior probabilities of A and B.

To put this into Brexit terms, let us assume that event A is a no-deal Brexit and B is the event Remain. We are interested in the probability of a no-deal Brexit, P(A). We can rewrite this:

P(A) = P(A | B) . P(B)

P(B | A)

or

P(No-deal Brexit) = P(No-deal Brexit | Remain) . P(Remain)

P(Remain | No-deal Brexit)

Using data from the website What UK Thinks, we can use survey data to provide some of the evidence. Based on the question of how people would be likely to vote in a second referendum, we can derive a value for P(Remain) which is currently 44% (or 51% once we strip out those voters who either do not intend to vote or who have reported as “don’t know”). We proxy the value for P(Remain | No deal Brexit) by looking at the survey evidence which asks respondents to choose between no-deal and Remain. Faced with this choice, 44% of respondents indicated that they would vote Remain (54% once we strip out don’t knows). Similarly, we estimate a value for P(No deal | Remain) by looking at the proportion who would vote for no-deal if the alternative is Remain (38%, or 46% after adjusting for “don’t knows”).

Putting these numbers together gives a constrained probability of no-deal of 44% (where the constrained probability is derived by stripping out “don’t knows” and constraining the remaining categories to sum to 100%). The unconstrained probability, where we do not adjust for the “don’t knows”, comes out around 36%. The good news is that however we slice it, the numbers come out at less than 50%; the bad news is that they are higher than my subjective probability of 30%.

To the extent that politicians are looking at the polling numbers to assess whether a no-deal policy makes sense, this Bayesian interpretation of the evidence suggests that there is more support for a no-deal Brexit than is often supposed. However, it is not high enough to push through with it in the event that it proves to be economically disastrous, since more than 50% of voters do not support it and the backlash from the disaffected half is likely to be severe. One caveat is that some of the surveys have not been updated for a few weeks and therefore do not reflect any possible change of stance since Boris Johnson became prime minister. Moreover, Bayesian probabilities change as more information becomes available, so these are not set in stone by any means.

Bayesian statistics are the big thing these days but as the pollster Nate Silver pointed out, “under Bayes' theorem, no theory is perfect. Rather, it is a work in progress, always subject to further refinement and testing.” The prime minister’s new chief adviser, Dominic Cummings, pointed out in a blog post in 2017 “Rationality is more than ‘Bayesian updating’”. But cold hard statistics do catch up with you eventually and the evidence suggests that support for a no-deal Brexit is limited. If I were a politician it would not be the ground on which I would want to fight a battle – irrespective of what the prime minister says these days.

Right-ho!

The ascent of Boris Johnson to the top of British politics has energised and enraged in equal measure but his cabinet appointments indicate a major shift in the direction of British politics, and not one that is universally welcomed. There were a record 17 changes to the cabinet in what was described as the most brutal purge in modern British political history, with all of them required to commit to taking Britain out of the EU by 31 October. There is a widespread belief that the composition of this cabinet is one of the most right-wing in British history. Whilst we can argue about that, it is undeniable that although the current government goes under the name of Conservative, it is anything but. 

A few weeks ago, The Economist published a thoughtful article on the global crisis in conservatism. One of the key arguments made in this article is that in the Anglo Saxon world, the creed of conservatism arose as a response to the radicalism triggered by the French revolution of 1789. It has historically acted as a brake on some of the more radical economic and social ideas of the last 200 years. Arguably it is one of the reasons why the UK enjoyed relative social stability during the nineteenth and twentieth centuries when many other European countries experienced significant upheaval. Conservatism has also traditionally championed individual property rights and entrepreneurship, and in the last 40 years has blazed a trail towards reducing the role of the state. But something has flipped. As The Economist put it “the new right is not an evolution of conservatism, but a repudiation of it. The usurpers are aggrieved and discontent. They are pessimists and reactionaries.”

The centre-right Republican Party in the US has been hijacked by the Tea Party movement which espouses a low tax, pro-business agenda, but is increasingly defined by a nationalist agenda that puts American interests first. Donald Trump’s recent comments inviting female politicians of colour to “go back” to “their countries” portends a much uglier turn of events. To quote The Economist once again, “the right is changing what it means to belong. In Hungary and Poland  the right exults in blood-and-soil nationalism, which excludes and discriminates.” It goes on to point out that “Hungary’s prime minister, Viktor Orban, paints himself as a low-tax economic conservative, but undermines the rule of law on which business depends.” And here is the nub of the problem: business interests are increasingly coming a distant second to the ideological requirements of the movement. 

It is in this light that we have to see Brexit. The warnings by business regarding the damage that a no-deal Brexit will cause can be ignored, so long as the small coterie of true believers on which the Conservative Party leader depends is satisfied. After all, the man who is now PM is widely reported as having said “f*** business” when challenged about business claims that a hard Brexit will lead to a loss of jobs and a reduction in investment. Despite his recent attempt to convince business leaders that he will be the “most pro-business PM” ever, the business community cannot afford to take him on trust. This is not the form of British conservatism that Margaret Thatcher would recognise. 

A closer look at Johnson’s cabinet illustrates the extent to which the nature of the domestic debate has changed. Two of those appointed (Home Secretary Priti Patel and Education Secretary Gavin Williamson) were fired by Theresa May for disloyalty to the government in acts that in times past might have been regarded as treasonous. Patel is particularly controversial for the nature of some of her political beliefs, including having in the recent past advocated the return of the death penalty. Everyone is allowed to change their opinions, as indeed Patel is reported as having done, but the worrying thing is that her view was no youthful indiscretion – it was espoused whilst she was an MP – which raises the question as to whether it is a Damascene conversion or merely one of convenience.

To further add to the controversy Johnson has appointed Dominic Cummings, campaign director of Vote Leave, as his special adviser. Cummings is regarded as intelligent, effective, albeit abrasive and one whose relationship with the truth is as strained as that of his boss. He has in the past been deeply scathing of government and is on record as suggesting that the May government’s approach to triggering Article 50 was a huge mistake. Whatever else he may be, Cummings is the antithesis of conservatism: He is a radical. Consequently, it is widely believed to be only a matter of time before Cummings is involved in a spectacular falling out with his boss – who is not a true radical. He was also recently ruled to be in contempt of parliament after failing to appear before a parliamentary committee investigating fake news. We therefore have two ministers in cabinet who undermined their previous boss and a special adviser who has been held in contempt. It’s not a good look. As an aside, the next time your employer reminds you of the ethical standards to which you are expected to adhere, you might want to point out that fish rots from the head.

The last few days have also sent a signal that UK politics has changed irrevocably. There is no obvious sign that a centrist such as Tony Blair or David Cameron is about to come riding over the hill to save us. This may change if Brexit turns out to be the disaster that is widely feared, but that won’t be any time soon. The rest of Europe should take note: The AfD is running neck-and-neck with the SPD in German opinion polls; the radical Lega is part of the Italian governing coalition and even in Sweden, the right wing populist Sweden Democrats are now the third largest parliamentary party.

In many ways, the rise of the radical right reflects the failure of the moderate centre to address the concerns of the electorate in the wake of the recession of 2008-09. Precisely because the “old politics” has been seen to fail, electorates are ready to listen to more radical solutions whether from the left or the right. In truth, the shock of 2008 was so great that it was always going to take a long time to recover, and it is more accurate to say that the policies implemented a decade ago were either not given long enough to succeed or were poorly implemented (certainly true of fiscal austerity). But the damage has now been done and the moderates may struggle to make their voices heard in the near future. Unfortunately, it may require the spectacular failure triggered by populist policies to force a change of tack. The economic costs in the meantime could be very severe.

If Johnson is the answer, what is the question?

It seems such a long time ago but it is in fact only three years since Theresa May entered Downing Street, giving a speech which raised hopes that many of the social injustices which had characterised the recent past were about to be rectified. We were sadly disappointed. Now her race is run, and we await the confirmation of Boris Johnson as the 55^th person to hold the position of UK Prime Minister. The political temperature is even hotter than the weather, as we bask in the hottest day of the year so far, but the outlook is far less clear than it was on that sunny July day in 2016 when Theresa May took the reins.

My views on the suitability of Johnson for the highest office have been well documented on this blog over the past three years. That said, I have underestimated him. After he quit his role as Foreign Secretary in July 2018, having turned out to be one of the most disastrous incumbents of that office, I thought he was due a long spell on the backbenches.  I never quite believed his political career was over but his inability to deal with the detail required of a front-line national politician, let alone maintain high level relationships with other governments, demonstrated his unsuitability for the top job. It is a sad indictment of the other candidates that the Tories voted 2:1 in favour of handing the party leadership to Johnson just 12 months after he walked out, claiming that he could not sign up to the type of Brexit proposed by the May government. It is true that the likes of Jeremy Hunt are pretty colourless characters but sometimes you need adults guarding the liquor cabinet. Johnson is akin to the alcoholic who has just been given the keys to a brewery and I fear it will not end well. 

He is an antidote to the caution of the May era and whilst this is welcome in many ways, he does not seem to understand the constraints under which she operated. In the course of his victory speech today, Johnson promised “we are going to get Brexit done on 31 October, we are going to take advantage of all the opportunities that it will bring in a new spirit of can-do. And we are once again going to believe in ourselves and what we can do and like some slumbering giant we are going to rise and ping off the guy ropes of self-doubt and negativity.” You cannot fault the optimism but in many ways these few sentences illustrate all we need to know. It is all about what he didn't say: He didn't explain how “we are going to get Brexit done” nor what are “the opportunities that it will bring.” And if you want to extend his boxing metaphor, Muhammad Ali was an expert at coming back off the ropes but look what happened to him within a few short years. 

As for delivering Brexit on 31 October, it can be done. The question is, at what cost? A no-deal Brexit would fulfil the mandate, but there are sufficient concerns regarding the economic impact that MPs are likely to do all they can to prevent it. Last week’s Fiscal Risks Report from the OBR provided a timely reminder of the potential costs of a no-deal Brexit. Based on the IMF’s relatively benign growth scenario, which reckons on a 4% loss of output relative to baseline over a three year horizon, this “adds around £30 billion a year to borrowing from 2020-21 onwards and around 12 per cent of GDP to net debt by 2023-24.” This may prove to be overly pessimistic, of course, but why would any responsible politician want to take the risk?

As for “all the opportunities that it will bring” we have been through this so many times that it has become boring, but I am professionally bound to ask “what opportunities?”  What exactly is it that the EU prevents the UK from doing today that would make it better off? And don’t say negotiate better trade deals with third countries. Just don’t go there! The UK is already one of the most deregulated economies in the EU and as I pointed out in 2016: “Not in the single currency nor party to the Schengen Agreement, it broadly worked for us.”

In many ways the fact-free nature of the Brexit debate has intensified over the past three years making it even more difficult for the next government to deliver. As a minister who was capable of extreme disingenuousness towards the previous prime minister even as he sat in her government, Johnson cannot rely on the loyalty of those Tory MPs who oppose his vision of Brexit. At some point, fantasy and reality are going to collide. It is one thing to convince your electorate but the Tory debate has been conducted in plain sight and the rest of the world has been looking on in amazement as the Tories attempted to outdo each other’s hard Brexit credentials. Moreover, Brexit is not just about the UK – the EU also has a big say. And why should the EU reopen negotiations with the UK when it has already made the least-worst offer that will satisfy the conflicting requirements of both sides? Nor should we be under any illusions about how widely reviled Johnson is in the rest of the EU. He is the last person to whom Emmanuel Macron will be prepared to offer any concessions.

It is profoundly depressing to think that a country that prides itself on its pragmatism has now elected a person who is more remembered for their appearances on a light-hearted topical news quiz (here or here for example, but there is lots more) than for their tenure as Mayor of London. There again, Johnson is not the only comedian who has achieved high political office recently: Beppe Grillo in Italy and Volodymyr Zelensky in Ukraine spring immediately to mind. And Donald Trump’s previous gig was as host of the TV series The Apprentice.

There is, of course, a deeper issue here: It is all about how the message is delivered, not the content of the message itself, and what better way to do this than employ an engaging frontman (or woman)? Johnson is not a dyed-in-the-wool Brexiteer but he has been well paid for delivering this message by people that are. Nor does Trump have any strong political views but he is a great frontman for those with a message to peddle.

To finish on a lighter note in these dark times, a few days ago, a colleague sent me a copy of The Ladybird Book of Brexit which takes a sideways look at the issue. I was particularly taken with the satirical paragraph which pointed out that ”Montmorency De Douchelord Ponsonby-Fring and his friend Sir William Du Flournay were glad the public voted Leave. Like so many land-owners, newspaper barons, hedge fund managers, firebrand back-bench MPs, ex-pat billionaires and Russian oligarchs, they thought it was high time the ordinary people of Britain got a chance to send a message to an out-of-touch-elite.” And what better person to represent the ordinary people than defender-of-the-common man Boris Johnson?

Telling it straight

Last week I was fortunate enough to attend a speech given by MPC member Gertjan Vlieghe in which he argued quite forcefully that the BoE’s method of communicating with the market is flawed and that there are better ways to deliver a clear message on interest rates. This issue is particularly topical given the concerns expressed about the BoE’s recent attempt to convince markets there is still scope to raise interest rates, despite the apparent change in global monetary conditions which argues against such a move.

We should, of course, recognise that central banks have come a long way since they told us nothing about their intentions (I am indeed old enough to remember when the Fed first started publishing its interest rate announcements in 1994). Even if the BoE’s communications are imperfect, they are a considerable improvement on where we were just over two decades ago. In Vlieghe’s view, however, the BoE should move away from a process of  communicating the path of interest rates by showing “a forecast of what will happen if we do something else” to explicitly telling us its preferred path for rates. It is recognised by a number of policymakers that there is a problem with the current communications policy because it is impossible to derive a unique path for interest rates “simply by observing how far the inflation forecast is above or below target at the end of the forecast period.” In effect, the MPC is “asking outside observers to solve a complex reverse-engineering problem that cannot be uniquely solved.” 

A number of other central banks have adopted a policy of publishing a preferred path for interest rates in a bid to improve policy transparency with most of the evidence suggesting that they are more satisfied with this approach than with the partial transparency adopted by the BoE. I have argued previously that one of the arguments against this idea is that it could be interpreted as a commitment rather than a forecast – a criticism that Vlieghe accepts. But in his view, “none of the central banks that have made the change, have reported this type of systematic misinterpretation between forecasts and promises … They have taken active steps to ensure public understanding of the uncertain nature of the interest rate forecasts, often by publishing uncertainty bands or fan charts rather than only a central path, and always by emphasising the uncertain nature of the path and its data-dependence.”

But the BoE has gone to great lengths to do much the same thing – indeed it was a pioneer of using fan charts – and that has still not prevented large parts of the commentariat from criticising the BoE for the inaccuracy of its forecasts. My own concern is that in an environment where central banking is becoming increasingly politicised, it would be extremely unwise for the BoE to create a hostage to fortune by publishing a preferred interest rate path. Recall the criticism levied at BoE Governor Carney by MP Pat McFadden that he was like an “unreliable boyfriend” due to the hints of interest rate hikes that never materialised (“one day hot, one day cold, and the people on the other side of the message are left not really knowing where they stand”). Imagine how much worse that criticism would be if the BoE produced a path for interest rates that was not subsequently adopted.

I do increasingly wonder whether giving ever more information to markets under the guise of improving transparency might in any case be counterproductive. It always helps to have a little something extra up one’s sleeve in case of need, and an unanticipated burst of monetary tightening would certainly be a good way to fire a warning shot across the bows of the market. Not that central banks appear to believe they have a duty to take the punchbowl away these days, but there is a strong argument that they should be doing more at a time when expectations of further easing have helped to drive equity markets to record highs, even though there are few good fundamental reasons for this. Moreover, it is slightly ironic that central bankers should even be talking about publishing interest rate paths when rates have barely moved in the past decade. If anyone had published a path for European rates in 2009 that showed them at similar levels – or lower – 10 years on, they would have been laughed out of court.

Whilst I do take Vlieghe’s point, and I have a lot of time for his analysis, I do wonder whether he may be somewhat missing the point about communications. It seems that the more central banks communicate, the more markets want. Sometimes it might be better to give them a little fright every now and then.

A battle in a bigger culture war

I have tried over the last six years to look at the Brexit question mainly in terms of economics and deal with the politics only in so far as it distorts economic decision-making. However, it is becoming increasingly clear that Brexit is merely another front in what can broadly be termed a global culture war, defined as a conflict between conservative and liberal values. Perhaps the reason why I did not originally recognise Brexit in these terms is that we have never experienced such a phenomenon in the UK. Maybe the Thatcher era in the 1980s can be classified as a culture war but it always felt more of an economic than a social project, which is how I view it even thirty years on.

The election of Trump and the ongoing Brexit debate are merely the two most obvious manifestations of this clash. But it is happening elsewhere, too. In the course of this afternoon, I happened to read two German language newspaper articles within minutes of each other.  The Frankfurter Allgemeine Zeitung led with a story about how the AfD in Germany “demands a "strong military" with "relentless" soldiers and a leading role in Europe. Their plans for the Bundeswehr are reminiscent of old times.” The subtext of the story was the appeal of the AfD to those wishing to relive past glories – something that the majority of Germans reject. Meanwhile in Switzerland, the Neue Zürcher Zeitung pointed out that not everyone holding views associated with right-wing politics are necessarily extremists (“to be against the "right" has developed into a kind of national  sport, particularly in Germany”). The warning from the NZZ was that we should beware the temptation to generalise, for in doing so we end up talking past each other and hardening attitudes rather than resolving our differences.

However, it is difficult to take such a stance when it has become apparent just how much damage is being inflicted on long-standing institutions in the pursuit of victory in the culture war. The office of President of the United States, to which large parts of the western world looks in order to provide moral and political leadership, is being used as a bully pulpit by a man not fit to occupy the Oval Office. The premiership of the UK is about to be handed to a man who has routinely lied in order to serve his own interests and is about to inherit a country whose institutions have been assailed as never before. Boris Johnson is one of the last people in politics to provide the sort of healing that his country needs.

Those promoting Brexit campaigned three years ago for a UK parliament to oversee UK laws (never mind the fact that it already did). Yet this did not prevent the government from trying to sideline it in a bid to deliver Brexit, and last year the government was found in contempt of parliament after refusing to publish the legal advice underpinning its Brexit decisions. Meanwhile the independent judiciary was characterised as enemies of the people whilst large parts of the press parrot politicians’ fact-free agenda, with one organ in particular paying a considerable sum to the man likely to be the UK’s next PM. The civil service has also come into the line of fire, with Sir Ivan Rogers,former Permanent Secretary to the EU, resigning in January 2017 when it became clear that ministers did not want to hear what he had to say. 

But the resignation of Sir Kim Darroch, the UK’s Ambassador to Washington, following the leaking of confidential diplomatic information to the press, represents a new and sinister turn of events. We do not know who leaked the information and we can only speculate on the reasons. But the Ambassador’s position was totally undermined once Donald Trump refused to negotiate with him (and in the process confirmed Darroch’s views). By politicising diplomacy in this way, a line has been crossed. In effect, the US President has exercised his authority to determine who represents the UK in Washington. Where will it end? So far, the politicisation of central banking happening elsewhere has yet to infect the UK, but with the successor to Mark Carney to be chosen by the new government it is something to look out for.

It is all very well for the revolutionaries to want to overthrow the status quo but what do they propose to replace it with? To quote the late British politician Tony Benn – a firebrand member of the hard left in his day – there are five questions that should be posed to those seeking power: “What power do you have; where did you get it; in whose interests do you exercise it; to whom are you accountable; and how can we get rid of you?” These are questions that apply just as much to the defenders of the status quo as those who wish to overturn it, but what concerns me most is that the rebels cannot provide good answers to the third and fourth of these.

Any Leave supporters reading this will no doubt dismiss the arguments as more scare-mongering on the part of one who will not accept the democratic will of the people to leave the EU. But this is a much bigger issue than that. Whether or not the UK remains in the EU is far less important than maintaining the institutional framework around which the economy (and indeed the whole country) is organised. In the words of the economist Douglass C. North, “Institutions are the rules of the game in a society, the humanly devised constraints that shape human interaction … They structure incentives in human exchange, whether political, social or economic.” Whether you are a Leaver or a Remainer; a liberal or a conservative; a supporter of the political left or the right, a country’s political and economic health is determined by the quality of its institutions. It is vital that they are not undermined.

Productivity: It's a gas

Last November I experienced a leak in my gas supply which required the replacement of a pipe. All seemed to be well until last week when I again smelled gas. Having tried to call the original engineer to rectify the problem – to no avail – I contacted a different local engineer. He discovered that the person responsible for installing the replacement pipe had allowed soldering flux to drip onto it, despite the fact that the instructions for fitting such pipes advised covering it to avoid any contact with flux, with the result that it had started to corrode and required replacing. Away went the gas engineer to get a new pipe, only for him to find that the one he obtained did not fit which necessitated a second trip to the wholesale supplier.

In the end the job was successfully completed, but what should have been a simple one hour job last November turned out to require four hours of work spread over 8 months due to the shoddy initial job and the failure of the second engineer to measure the pipe before purchasing a replacement. This got me thinking about productivity and the reasons why it is so low.

Compared with the rest of the G7, UK productivity lags behind. On data to 2016, output per head in real terms across the other G7 countries was almost 6% higher than in the UK with German output per head 4% above UK levels and the US 7.4% higher. A study conducted by NIESR for the Department for Business, Innovation and Skills in 2015 concluded that although the UK performs well in an international context on the basis of the contribution of higher skills (i.e. university education) to productivity, “the UK’s intermediate (practical, technical and occupational) skills are of more concern.” This would accord with my own anecdotal experience in which an apparent lack of training resulted in poor basic skills with the result that fairly simple jobs take longer to complete than necessary (not to mention costing more money).

But it is not just a British problem. Policymakers have been exercised in recent years by the weakness of productivity growth, which has been one of the marked features of the recovery from the global financial crisis of 2008-09. Only 6 out of 36 OECD countries recorded faster productivity growth over the period 2010 to 2018 compared with the years 2002 to 2007. Across the OECD as a whole, labour productivity has averaged growth of 1% per year since 2010 versus 1.7% between 2002 and 2007. In the euro zone, where productivity growth was not especially rapid before the GFC, it has slowed from an average of 1.1% per year to 0.8% whilst in the US the slowdown has been much more pronounced (from 2.1% to 0.9%). The slowdown in the UK has been almost as severe, leaving the rate of productivity growth at a paltry post-GFC average of 0.6% per annum versus 1.7% in the five years prior to the recession.

Aside from impact on wasted time and higher outlays, why do we care? In the first instance, productivity is the key driver of living standards. In an economy where labour is paid roughly according to the amount of value added it generates, there is a strong link between (real) wage growth and output per worker. Thus, if productivity growth slows, so too will real wage growth and over the period 2008 to 2014 real wages in the UK fell by 9%. The “puzzle” in all of this is that the sustained general pattern of productivity stagnation contrasts with the pattern following previous economic downturns, when productivity initially fell but subsequently recovered towards the previous trend growth rate. Something has clearly changed but we cannot be sure what it is.

Chart 1, 2 and 3 show UK GDP, productivity (output per worker) and employment trends (respectively) in the current cycle compared to  the three major recessions since the 1970s (click to enlarge). The current GDP upswing broadly matches that of the 1970s and early-1980s but lags the 1980s and 1990s. But employment growth has far outstripped previous recovery phases whilst productivity has lagged. To the extent that output is a function of labour input, capital investment and technological progress, it appears that British companies have increased output by expanding labour input rather than capital investment or technological improvements. If these workers are lacking in the appropriate training, it is likely they will take time to get used to the systems and processes required to enable them to do their jobs efficiently with consequent adverse effects on productivity.

It also appears to be the case that there is a widening gap between the performance of firms in the upper quartile of the productivity distribution and those lower down. One reason for this is perhaps that the best educated workers tend to gravitate towards the best paying firms who then improve the company’s productivity performance and are then rewarded for their efforts. In other words, there is a self-reinforcing spiral which rewards those who already have the requisite skills. What is thus required is a more efficient transfer of skills throughout the economy. This is a problem which has long been recognised and the government’s apprenticeship scheme is a way to help give decent vocational training to younger workers (though changes to the Apprenticeship Levy in 2017 may be hampering the operation of this market).

However, there is no quick fix for poor productivity. In any case, measuring it is particularly difficult in an economy in which services account for an increasing share of output. Last December the OECD had a closer look at the way in which it measures productivity and concluded that once we account for differences in the way we measure labour input, particularly with regard to the way in which holidays are treated in the data, the UK’s international productivity does not lag quite as much we had previously thought. Ironically, if my original gas engineer had been on holiday when I called him last year, maybe I would have been spared the result of a lack of training. There again, I would have missed out on a learning experience.