Saturday, 5 August 2017

Barnett Formula: Keeping it Simple

My last (long and complicated) blog attempted to explain how the Barnett Formula affects the devolved nation's Block Grant funding over time. In particular it looked at the impact of different relative population growth rates and how the Barnett Formula has been applied in practice as opposed to how it was expected to work. So if you're interested in the how and the why of these dynamics, please read Calling Time on the Barnett Formula.

Free from the burden of explaining quite why all of these things happen, I wanted to take the opportunity to now write a simpler blog which simply demonstrates what happens under various circumstances in a way which I hope will be easier for the casual reader to digest.

My medium of choice will, of course, be the graph.

Simply put: annual application of the Barnett Formula increases each devolved nation's Block Grant by an amount calculated to give the same per capita increase to the devolved budget as that applied to England's comparable spend1.

To achieve this the formula therefore depends fundamentally on the relative population sizes and how they change over time - so to understand the Barnett dynamics we need to understand how these population proportions (devolved nation vs England) have changed over time.

This graph shows us that since Barnett was implemented in 1978 Scotland's population proportion has been consistently falling (because Scotland's population has been growing more slowly than England's) . Wales' proportion was stable through the 80s and early 90s and has only recently started to decline. Northern Ireland's actually grew slightly through the 80s and 90s and has stabilised more recently. These relative population growth differences entirely explain the differences we're about to see between the devolved nations when we model the impact of the Barnett formula over this period.

The next factor we need to consider is the actual nominal growth in spending in England in those areas where comparable spend is devolved. This is a hard number to get precisely right over such a long time period2 but for illustration purposes we'll use the actual annual growth rates for all public spending in "rUK" (where rUK = UK - Scotland)3. This matters because higher nominal growth accelerates convergence (and there were some high inflation years in this time-frame and nominal growth has clearly slowed dramatically in recent years).

The only other assumption we need is how much higher the (illustrative) devolved category spend per capita was for the devolved nation in 1978 when this all started. For illustration purposes I've chosen to use a fairly representative figure of 20%4.

So based on actual population changes and assuming the above nominal spend increases, we can now see how application of Barnett would affect that 20% premium in spend per capita over time for each of the devolved nations. Here's the graph:

The blue dashed line shows how "true" application of Barnett would have caused Scotland's spend per capita premium to have converged towards England's. Note that the uptick in recent years shows the premium is actually growing: this happens when absolute nominal spend/capita increases in England are small (as they have been) and Scotland's population proportion continues to fall5.

The solid blue line shows the benefit that Scotland achieved because "until 1992, the 1976 population estimates were used for the Barnett Formula"6, so "as applied" the Barnett Squeeze (which causes convergence in Spend per Capita between nations) was partially alleviated. As I said in my last blog on this topic: imagine the howls of grievance we'd hear if failure to apply the Barnett Formula as agreed had resulted in a 2.2% detriment to the Block Grant instead of a 2.2% benefit7.

The red lines show Wales. Because the population proportion didn't materially change between 1978 and 1992 the "true" vs "applied" Barnett Formula issue makes no material difference. What is clear is that simply because of the different trend in population proportion, Wales has seen a far more marked squeeze in Spending than Scotland.

The green lines show Northern Ireland. Because NI's population share was actually growing between 1978 and 1992 the impact of Barnett as applies (vs "true" Barnett) was to exacerbate the Barnett Squeeze. The Barnett Squeeze for NI is worse overall purely because of the different trend in NI population proportion vs Scotland or Wales.

So there we have it. The Barnett Formula was never intended as a long-term solution8 and - as I explored in my previous blog - there are strong arguments for changing to a system which is a) fairer between the devolved nations and b) fairer to the devolved nations insofar as there is a sound needs-based argument for maintaining per capita spend premia in some departments.

As I also argued last time: the easiest way to ensure spend is distributed based on need is not to devolve that spend so that e.g. social protection spend is allocated to individuals based on their need, not where they live.


1. This is a simplification; if you care for the more complicated detail see > Calling Time on the Barnett Formula

2. As the House of Commons briefing paper succinctly puts it: "it is hard to verify the extent to which the Barnett Squeeze is happening, largely due to a lack of comparable data". My previous blog Calling Time on the Barnett Formula provides a more detailed explanation of the complexities

3. This is mainly because I have these figures to hand and they're suitable for a realistic illustration. If one was so inclined one could dig out the England only figures, but that still wouldn't be giving us the spend just on departments which are devolved (which changes over time anyway) - this assumption is fine for illustrative purposes as it captures macro trends of inflation and general public spending policies. My rUK data series only goes back to 1981 (SNAP data), so for 1979 and 1980 only I simply assume inflation growth (inflation was high then: 13.4% and 18.0%).

4. In 1998/99 (the earliest year that GERS breaks spend out to this level) Scottish spend per capita on (the predominantly devolved areas) of [health + education + transport] was 20.1% higher than rUK.

5. Imagine the increase is zero: in this case neither England nor Scotland's absolute spend would increase, but because Scotland's poulation grows less quickly than England's, our spend per capita relatively increases

6. As per the House of Commons Briefing Paper, page 11 [and discussed in more detail in Calling Time on the Barnett Formula]

7. That being the impact of not updating the population proportions up to 1992

8. Because of my last blog and some happy happenstance, I have recently spoken with some people who were there and involved when the Barnett Formula was put in place. I think it's a fair sumary to say it was only ever intended as a short-term fix to avoid what were perceived as tedious department by department negotiations between the Scotland Office and the Treasury; the assumption was always that something better would be put in place within a handful of years.

For those who care about the spreadsheet mechanics, here's a snapshot of the "true" Barnett model

Bikes, Maths and The Big Pig

This morning I posted a question on Twitter to test how easily people get confused when thinking of averages. Within a few hours I had over a thousand answers, enough to confirm my hypothesis that the answer is "pretty easily".

[You can check the current live result here; the thread below is fun if you like that sort of thing]

Here's where I'd normally say something like "the correct answer is of course that it's impossible". That's the point of this test though - it's not obviously impossible because the majority of people intuitively went for the wrong answer.

I think the reason why this happens is interesting, but let's first quickly explain why the correct answer is that it's impossible.

The easiest way to explain is by illustration. In fact the reason I posed the question in the way I did was because I once actually experienced precisely this scenario when cycling on Majorca. I recognise this seems almost too good to be true, so for the doubters out there here's the Strava map of that ride and route profile.

The peak itself is known as "Puig Major" - I'm sure I'm not the only cyclist to have ground my way up there thinking Puig Major must mean "Big Pig" in Spanish1.

As you can see from the chart above it's precisely 10 miles up the hill. So if  - as in fact I did, back when I used to be fitter than I am now - you average 10 mph on the way up, it takes 1 hour to reach the summit.

At this point the impossibility of the challenge hopefully does become obvious. The total journey up and back down again is 20 miles, so to achieve a 20 mph average you'd clearly have to do the whole journey in an hour ... but you've already used all that hour just to get to the top of the hill.


The answer is of course2 true independent of the actual distance involved. It's easy enough3 to prove algebraically that it's impossible to double your average speed after you've covered half the distance of your journey (because you'd need to complete the second half of your journey in zero time):


I think part of the reason why most people instinctively get this wrong is explained in Kahneman's "Thinking, Fast and Slow" - we have a tendency to intuitively use the data that's closest to hand rather than taking the time to think if it's the right data.

So in this example we easily know it's the same distance up as it is down, so we instinctively calculate the total average as being the distance-weighted average of the two speeds (i.e. "half at 10 mph + half at 30 mph = all at 20 mph").

The problem is that we can't calculate average speed by weighting the two "halves" by distance, we have to weight them by time spent. So it would be correct to say "half the time at 10mph + half the time at 30 mph = all the time at 20mph" - but if you were to spend as long at 30 mph as you did at 10 mph, you'd travel 3x as far on the journey down!

The generic rule here - well worth remembering when sanity checking analyses - is you weight averages by the denominator not the numerator. Speed = Distance / Time, so to average two speeds you weight the total by the time spent at each speed, not the distance traveled


Having come this far I can't resist a little physics addition to this problem: why is it harder to achieve the same average speed on a hilly course than a flat one?

The potential energy you invest in to go up a hill you get back coming down, so you might think it should be just as easy to achieve the same average speed on a hilly course (that ends where it starts) as you could on a flat one. Cyclists will know this simply ain't so.

The answer is (at least in part4) to do with wind resistance being a function of the square of your speed: if you go twice as fast you incur four times the drag.

Let's imagine we went up our hill at 10 mph and down it at 30mph. We now know how to calculate our average speed: we spend 60 minutes at 10 mph and 20 minutes at 30 mph, so our average speed is 15 mph (10 x 60/80 + 30 x 20/80 = 7.5 + 7.5 = 15).

Now let's compare the wind-resistance work involved in doing a flat 20 miles at a constant 15mph with our up-and-down-the-hill alternative.

Work = Force x Distance

Distance is the same in both cases, Force is proportional to the square of speed.

The average square of speed in the flat scenario is easy = 15^2 = 225

The average (correctly weighted by time) square of speed in our hilly scenario = 100 x 60/80 + 900 x 20/80 = 75 + 225 = 300

We do 33% more wind-resistance work on our hilly ride.


OK, enough - I'm off to find somewhere flat to ride my bike5.

1. disappointingly it in fact just means "big hill"
2. here I go again
3. and again

4. there will be other moving-part speed-related friction factors which the existence of gears makes complicated
5. I live in East Lothian, that's not going to happen

Thursday, 3 August 2017

Calling Time on the Barnett Formula

The "fiscal framework" which governs how funds are allocated across the four nations of the UK (often simply referred to as the Barnett Formula, which underpins it) has never quite worked as intended and is frankly well past its sell-by date.

If we're to have a sensible discussion about how the fiscal framework could be improved, we first have to understand what happens currently and why.

It's hard to explain this in a way that doesn't quickly become mind-achingly complicated or simply too dull to hold the attention of all but the most obsessively curious. With that in mind, I'll try to separate the core arguments from the explanations, use illustrative examples with realistic figures and put stuff the analytically minded might want to understand into separate, smaller notes.

Note: this is a bit of a beast of a blog post: if you want the simple version with clear graphs, try the later post Barnett Formula: Keeping it Simple

The Barnett Formula & The Fiscal Framework

  1. The Barnett Formula (used to calculate the Block Grant) was designed to cause convergence of per capita spending between the four nations of the UK, an effect known colloquially as the "Barnett Squeeze"

  2. The fact that Scottish population growth has been slower than English population growth has to some extent dampened the expected Barnett Squeeze - but it's still happening

  3. In the years from 1978 to 1992 the formula was applied "incorrectly" in a way which was materially to Scotland's advantage

  4. In pure spend per head terms, Scotland has benefited from the fact that Social Protection has remained predominantly reserved (and therefore continues to be allocated based on need rather than subject to the Barnett Squeeze)

  5. Wales has suffered a worse Barnett Squeeze than Scotland due to the fact that its population growth has not lagged as far behind England's

  6. The retention of Barnett in the current Fiscal Framework (as recommended by the Smith Commission) means this tendency to converge per capita spending is "baked in" to the current system

  7. This is a problem if one believes that spending should be based on need rather than judged to be "fair" simply if  public spending per head converges across the four nations


1. The Barnett Formula (used to calculate the Block Grant) was designed to cause convergence of per capita spending between the four nations of the UK, an effect known colloquially as the "Barnett Squeeze"

There's an excellent House of Commons Briefing Paper which describes how the Barnett Formula works which explains:
The majority of the devolved administrations’ spending is funded by grants from the UK Government – the block grant being the largest. Since the late 1970s the non-statutory Barnett formula has determined annual changes in the block grant. The formula doesn’t determine the total amount of the block grant, just the yearly change.
When there is a change in funding for comparable services in England, the Barnett formula aims to give each country the same pounds-per-person change in funding. In general, if a service is devolved it is considered to be comparable. 
When a change is made to a UK Government department’s budget (normally at a spending review) the Barnett formula takes the budget change, considers how comparable the services provided by the department are to those provided by the devolved administration, and applies a population proportion, as shown below. This calculation is carried out for all UK departments and the results are added to the devolved administrations’ block grants2.

[Change to UK gov department’s budget]
[Comparability percentage]3
[Appropriate population proportion]

Note 2: These amounts are generally referred to as "Barnett Consequentials"
Note 3: The “comparability percentage” is a function of how much of those budgets are devolved, as shown by this handy table:
This needn't distract us when it comes to understanding the fundamental dynamics of the Barnett Formula, but is often a source of heated negotiation in practice (e.g. whether spending on the Olympics or HS2 are deemed "comparable" for the purposes of calculating these Barnett Consequentials). As the Briefing Paper explains: “Each programme area, or service, is given a comparability of either 100% or 0%. A service is 0% comparable if: other arrangements are in place to determine each devolved administration’s share of a budget; expenditure is incurred on behalf of the UK as a whole by the UK department; or, the service is deemed unique at a UK level, such as the Channel Tunnel Rail link.”

Obviously if more spending powers are devolved the comparability percentage goes up, but if we're considering the underlying dynamics of the Barnett Formula it makes sense to consider an area where this doesn't change (if you like, think of a fully devolved area like Education where the comparability percentage is simply 100%).

For most departments (where spend is devolved to all four nations) the "Appropriate population proportion" for Scotland is simply [Scottish population] / [English population]. To understand the Barnett Squeeze let's first consider what happens if this proportion doesn't change (i.e. English and Scottish population growth rates are the same).

We can run the numbers with a simple spreadsheet using actual English population figures and covering the 38 year period since the Barnett Formulas was introduced in 1978. Over that period rUK has seen average annual public spending increasing at about 5.3% pa (a combination of inflation and real growth) so we'll use that assumption for this illustrative department's spending growth in England. Our last assumption is that this is a department where in 1978 Scottish  spend per head was 20% higher than England.

The snapshot of the spreadsheet below shows how the mechanics work: key modelling assumptions are in yellow and the "answer" - the amount by which Spending per head in Scotland exceeds that in England - is in green.

So under these realistic assumptions: if the starting point for the Block Grant in 1978 was a 20.0% higher spend per capita in Scotland than England, after 38 years the application of Barnett would have now reduced that to being only 2.8% higher (if Scotland's population grew at the same rate as England's and there was no "Formula bypass" or other Barnett exceptions5")

Note 4: This makes intuitive sense: 5.3% cumulated over 38 years is more than a 7-fold increase, so by 2015 over 80% of the Block Grant has been determined by the Block Grant Adjustments which are on the same per capita basis, less than 20% is at accounted for by the "base" at the 20% higher rate.
Note 5: as the House of Commons Briefing Paper explains: "The majority of changes in the devolved administrations’ DELs are determined by the Barnett formula. However, there are some items in DEL for which the population based Barnett formula is not appropriate. DEL items outside of Barnett, often known as non-assigned items, are ring-fenced and specific to their particular spending priority. Such items, including depreciation, are determined separately between the devolved administration and UK Government. The population-based approach of the Barnett formula is not appropriate for determining changes in AME grants, because of their demand-led nature, so these are determined periodically between the devolved administration and UK Government." and "Although the Barnett formula represents normal procedure, changes to the block grant can be made outside it - a process often referred to as ‘formula bypass’"

2. The fact that Scottish population growth has been slower than English population growth has to some extent dampened the expected Barnett Squeeze - but it's still happening

Now we have this simple model, it's easy to see what happens if instead of assuming Scotland's Population grows at the same rate as England's, we use the actual population figures6.

The effect of applying the actual (relatively slower) population growth in Scotland is to significantly slow the Barnett Squeeze: instead of the spend/capita premium being reduced from 20.0% to 2.8%, our model now shows it still at 9.3% in 20167.

Note 6: the proportion actually used is the prior-year population proportion, as this is the only data available when the calculations are made in real life
Note 7: this is less easy to intuit than one might expect. The "base" part of the block grant remains static in absolute terms so becomes significantly higher relative to England on a per capita basis - the same effect applies to prior years' Block Grant Adjustments which will have been calculated on a relatively higher proportion. In addition, the fact that prior-year proportions are necessarily used means there is an addition "built in" squeeze dampening affect as long as the Scottish population proportion is declining.

3. In the years from 1978 to 1992 the formula was applied "incorrectly" in a way which was materially to Scotland's advantage

There's an extraordinary throw-away line in the House of Commons Briefing Paper (page 11) which reads (highlighting mine):
".. if population proportions are not regularly updated convergence can be affected. For instance until 1992, the 1976 population estimates were used for the Barnett formula. During this time Scotland’s population was falling relative to England’s, which would have worked against the Barnett squeeze." 
We've got the model so it's easy to scale what effect this would have. To improve modelling accuracy I've applied a nominal spending growth rate of 7.6% pa until 1992 and 5.0% subsequently (reflecting actual growth rates in UK spending over those periods) and then looked at what the 20% premium would reduce to if Barnett were "correctly" applied vs. if 1976 proportions were used until 1992 (as actually happened).

"Correctly" applied the Barnett Squeeze would have reduced the 20% premium to 11.1% by 1992 (note the differential growth assumptions now used over the two periods has reduced the 2016 premium to 8.7%)

As actually applied, the premium only reduced to 13.3% by 1992 (and the 8.7% in 2016 has improved to 9.5%)

So this failure to update the population proportions between 1978 and 1992 benefited Scotland's Block Grant amount by about 2.2% - a significant impact and one which is still implicitly reflected in our Block Grant today (albeit now diluted to just a 0.8% impact).

Pause for a moment: I want you to imagine the howls of grievance we'd hear if failure to apply the Barnett Formula as agreed had resulted in a 2.2% detriment to the Block Grant instead of a 2.2% benefit. OK, now carry on.

If you're struggling to get your head around this, you're not alone. That House of Common's Briefing Paper is at best confusing when it states "During this time Scotland’s population was falling relative to England’s, which would have worked against the Barnett squeeze". The implication that updating the population proportions would have accelerated the Barnett squeeze is wrong: the correct Block Grant Adjustment would have required a lower population proportion to be applied than that actually used, reducing the Block Grant adjustment and accelerating the Barnett squeeze8.

Note 8: the error in the briefing paper is perhaps understandable. If the population proportion had remained the same the squeeze would have been greater, but by keeping the population proportion the same in the calculation that doesn't offset the fact that the actual population figure (the denominator in the per capita calculation) does relatively decline

4. In pure spend per head terms, Scotland has benefited from the fact that Social Protection has remained predominantly reserved (and therefore continues to be allocated based on need rather than subject to the Barnett Squeeze)

Because Social Protection is broken out as a category in Scottish Government GERS figures back to 1998, we can use our model to see what (in purely arithmetic terms) would have happened if in 1999 we'd devolved Social Protection (SP) spend and used the Barnett Formula to calculate Scotland's SP Budget (given what we know actually happened to SP spend in rUK). We can of course compare that to what happened to the actual, predominantly reserved Scottish SP spend per GERS.

What we can see is that on average over this 17 year period Scotland has received £54/capita more Social Protection spending than if it had been simply devolved and subject to the Barnett Formula9. Multiply that figure by Scotland's population and you get a £288m average annual benefit.

To put that figure in the context of a standard SNP grievance: their decision to centralise Police Scotland and incur VAT costs us just £25m pa.

Note 9: of course had this been money from the Block Grant adjusted by Barnett then the Scottish Government would be free to spend the money elsewhere instead

There's a lot going on behind these figures and I've had to hide some columns for display purposes. The graph below simply charts the "Barnett Effect" (the last row of the spreadsheet above), where the bar below the line means the alternative of using the Barnett formula would have led to less per capita spending in Scotland

In the early 2000s the benefit of retaining Social Protection as a reserved department allocating funds UK-wide based on need (vs. our notional alternative of devolving in 1992) was often greater than £100/capita. The fact that the gap closed in recent years is presumably something to do with Westminster policies that shifted Social Protection spending in a way which negatively impacted Scotland more than rUK ... or it could be to do with the dynamics of decelerating growth in cash spend and the relative population growth figures ... but to be honest I think I've reached the limit of my capacity to try and unravel the figures at this point.

5. Wales has suffered a worse Barnett squeeze than Scotland due to the fact that its population growth has not lagged as far behind England's

Applying the Welsh population figures to our model shows how a 20% per capita spending premium in 1978 would have reduced to a 7.4% premium in 1992 (cf Scotland's 13.3%) and 6.0% by 2016 (cf Scotland's 9.5%).

If we look at the relative population growth trends this finding is not surprising: Wales was exposed to a fairly "pure" Barnett Squeeze until the early 1990s as its population growth  pretty much matched England's

6. The retention of Barnett in the current Fiscal Framework (as recommended by the Smith Commission) means this intention to converge per capita spending is to some extent "baked in" to the system

The current Fiscal Framework is designed to satisfy the Smith Commission recommendations, in particular clause 95 (1) which states that "...the block grant from the UK government to Scotland will continue to be determined by the Barnett Formula". 

Devolved revenue raising powers adds a layer of complexity to this debate because the Block Grant (calculated using Barnett) is reduced by an amount to adjust for revenue devolved. The nature of that Block Grant Adjustment (BGA) was the source of much debate during the Fiscal Framework negotiations, in particular how one indexes the BGA in future years to satisfy (and interpret) the Smith Commission requirement of "no detriment".

As the IFS highlighted at the time: " it is impossible to design a block grant adjustment system that satisfies the spirit of the ‘no detriment from the decision to devolve’ principle at the same time as fully achieving the ‘taxpayer fairness’ principle: at least while the Barnett Formula remains in place"

7. This is a problem if one believes that spending should be based on need rather than judged to be "fair" simply if spend per head converges across the four nations

I'd hazard a guess that most voters in the UK buy into the principle of pooling & sharing resources: we spend money on public services based on need, we don't just aim to spend the same amount per person.

Aside: There is an alternative view which is that the constituent nations of the UK should "stand on their own feet" and be fully fiscally autonomous. As this blog has previously explained in detail (> Full Fiscal Autonomy For Dummies) that way madness lies. From a Scottish perspective that could only make sense when oil was generating upwards of £9bn pa of tax revenues - without those oil revenues Scotland would have to find that £9bn pa from some combination of tax rises or spending cuts to be fully fiscally autonomous and satisfy the fiscal constraints that would come with currency sharing. There's a reason we don't hear the SNP calling for Full Fiscal Autonomy anymore.

As an example: need based allocation would make more sense than equalising spend per capita where population densities differ significantly. It costs more to get basic services to people the more geographically dispersed they are - and the four nations clearly have very different population densities

Scotland's population is 6x more dispersed than England's - is it "fair" to expect the same per capita amount to be spent on Transport or Education?

The demographic challenges differ by nation as well with different proportions of the population economically productive versus those dependent on the state. This is crudely measured by the percentage of the population who are of working age (a measure on which Wales fares particularly badly)

There are of course many other factors to consider when it comes to defining need (healthy life expectancy, unemployment rates, areas of deprivation, etc.) but this blog-post is already too long to start exploring them further.

What we can say is that the arguments for a needs based spending allocation formula seem pretty compelling: as the House of Commons Briefing Paper points out, pretty much everybody who has looked at this question has reached the same conclusion
The change in population is the only consideration of ‘need’ in the Barnett formula. However, the cost of providing public services is influenced by a range of other factors including, but not limited to, characteristics of the population, deprivation and population density.
There have been frequent calls for the Barnett formula to take greater account of need, or to be replaced with a needs-based formula. In 2010 the Holtham Commission, which considered funding for devolved government in Wales, recommended that a need-based formula should determine the block grant. After considering devolution in Scotland, the Calman Commission recommended in 2009 that the block grant should be justified by an assessment of need. Lords Committees in 2009 and 2015 recommended replacing the Barnett formula with a needs-based formula. Similar recommendations were put forward by the House of Commons Justice Committee in 2009 and by other Parliamentary committees in the past.
There's an interesting point to be made here relating to "more powers". 

We've shown above that if (say) Social Protection were devolved and subject to Barnett, it would become subject to the Barnett Squeeze. Unless our population were to decline in absolute terms, the act of devolving spending in an area where we currently experience a higher per capita spend than England would inevitably see a decline in the premium given to spend in Scotland (irrespective of actual need). Were Scotland's population growth to accelerate (or the UK's decline) that squeeze would accelerate. Why would anybody in Scotland think that a good idea?

Of course one could argue that the best way to deliver Social Protection based on need is to apply the same policies nationwide and have the same criteria and needs assessments in place irrespective of which constituent UK nation you happen to live in.

Those continually complaining about spending powers that remain reserved to Westminster should maybe take a moment to consider: fairness may best be delivered by keeping spending areas like Social Protection (or Work & Pensions as defined in the departmental allocation table above) largely reserved.

Personally I'd argue against any further devolution of either spending or revenue raising powers until these fundamental issues related to the Barnett Formula are addressed.

Wednesday, 2 August 2017

How Brexit Affected SNP GE Vote Share

A very quick and dirty blog, but I saw this analysis today [A Tale of Two Referendums - the 2017 Election in Scotland] and I couldn't keep my hands off it.

The analysis looks at four cohorts based on indyref and EUref vote (Yes/Remain, Yes/Leave, No/Remain and No/Leave) and tracks how General Election voting moved between 2015 and 2017 within those cohorts. I recommend reading it.

The analysis is excellent and clear but the "visual thinker" in me wanted to see the four cohorts shown in correct relative scale so I did this crude bit of image manipulation (and a few simple sums based on SNP share of those cohorts in 2015 and 2017).

 It may be too much in one picture and I've had to estimate share of cohort figures from the printed graphs but the numbers are good enough to tell the story (working down the cohorts above):

  • The SNP lost share in all cohorts
  • The SNP saw a 2% total vote share decline among Yes/Remain voters (who largely switched to Labour)
  • The biggest source of loss for the SNP was Yes/Leave voters who were responsible for a 5% total vote share decline for them
  • The SNP of course hoped to pick up No/Remain voters - but in fact they lost another 1% total vote share through this cohort, with those No voters who'd lent their votes to the SNP in 2015 largely switching to the Lib Dems
  • No/Leave voters largely switched to the Conservatives - and the few No/Leave voters who had lent their votes to the SNP in 2015 largely switched to Labour, losing the SNP another 1% of total vote share.

Sunday, 23 July 2017

The Emotional Case for Union: Articulating an Implicit Moral Contract

Whether you’re still mourning the result of the EU referendum or are one of those who sees Brexit as some brave new dawn (I know you’re out there), if you’d rather not see the break up of the UK then take a moment to consider this: Brexit is an illustration of the price we pay if we neglect to counter relentless grievance-mongering against a long-standing Union.

Alternatively, if you’re against Brexit but in favour of Scottish independence based on some emotional or “democratic deficit” based argument, I hope what follows may at least give you some pause for thought.

If however you’re in favour both of Brexit and Scotland leaving the UK ... well I’m afraid I can’t help you, best you stop reading now.


It’s probably fair to suggest that what we saw with the EU referendum was the rational economic arguments against Brexit losing out to the emotional “taking back control” arguments in favour. Conversely, the Scottish Independence referendum was won by many voting No because their head was convinced by the economic arguments against, despite their heart being tempted by the emotional case for.

That’s partly because the economic arguments against Scottish Independence were an order of magnitude more compelling that those against Brexit: however bad you think Brexit is for the UK, exiting the UK would be so much worse for Scotland.

But what I want to focus on here is the nature of the emotional arguments in favour of Union, and the fact that far from being distinct or conflicting, the economic and emotional cases are inextricably intertwined. The economic case only exists because of the emotional case, it’s just that the emotional case is so deeply ingrained in most of us that we struggle to articulate it.

This debate matters and it matters now. If we wait until the imminent threat of another referendum before bothering to make the positive emotional case for the UK, we risk seeing Scotland’s relationship with the UK following the same path as the UK’s with the EU. Relationships suffer if emotions are neglected; a good marriage needs to be worked at.


Let’s start by looking at the SNP’s core - and superficially compelling - emotional argument:
"The SNP believes that decisions about Scotland’s future – about our economy and society – are best taken by the people of Scotland: the more powers we have in Scotland the more we can achieve for the people who live here" - SNP 2015 Manifesto
In part this formulation simply relies on the reader’s sense of identity meaning that “we” and “Scotland” are emotionally synonymous. Of course those who are happy to think of “we” as the people of the UK can simply substitute “the UK” for “Scotland” in the phrase above and - if you’re so minded - this phrase then becomes an articulation of why we should leave the EU. There’s an obvious irony to the fact that the SNP’s core argument for independence is effectively the same as UKIP’s “take back control” argument for the Brexit the SNP so vehemently oppose.

But what of those who intuitively have a primarily Scottish sense of identity? For those people, the fundamental issue should be that the implied logical connection between the SNP’s statement and the conclusion that Scotland should be independent doesn’t actually exist; you can agree that “decisions about Scotland’s future should be taken by the people of Scotland” without concluding that Scotland should be an independent country.

Representative democracy allows us to decide how best to define which group of “us” should make what decisions. We decide that some issues make sense controlled at local council level, some by nation-states within the UK, some by the UK as a whole. Of course many also believe that some are better taken at an EU level or by the United Nations. So what some lazily term a “democratic deficit” others see as simply the result of deciding to participate in a democratic hierarchy that allows some decisions to be taken as part of a larger whole for a wider common good.

The biggest weakness in the SNP’s argument is of course the fact that the 2014 independence referendum took place and that the result was so clear. That vote wasn’t just about self-determination, it was self-determination. It was the purest possible demonstration of the people of Scotland making a decision about Scotland’s future – and we decided that our economy and society would be best served by remaining part of a wider democratic union. Just because the SNP don’t like that answer doesn’t make it not so.

The SNP would of course be quick to point out that no decision can be permanent and since the indyref there has been “material change” with the EU referendum vote threatening to see Scotland “dragged out of the EU against our will”.

Of course there have been other “material changes”, not least those to the economic case for independence. The oil revenue forecasts used by the SNP to underpin their fiscal projections are now known to have been recklessly optimistic and the SNP have accepted that they need a more credible answer to the currency question than simply saying “we’ll keep the pound” (but have yet to find one). The deafening silence from the “SNP Growth Commission” suggests they’re struggling to find a palatable strategy for maintaining an independent Scotland’s fiscal sustainability without slashing public services and while also finding the capacity to invest to grow the Scottish economy faster that the rest of the UK. They may be finding that it’s a lot easier to complain about how things are than it is to outline a credible alternative for how things should be.

The Nationalist’s biggest economic problem though is Brexit itself. Their previous assertion that Scotland’s trade with the rest of the UK would be unaffected by independence has gone from being at best dubious to now completely indefensible. If Brexit means the UK becomes subject to trade barriers with the EU, then a decision about Scottish independence becomes in part a decision about which trading block we favour: we would have to choose between the UK and the EU (or quite possibly risk ending up in neither). The fact that we export four times more to the rest of the UK than we do to the rest of the EU is now a pretty compelling economic argument against Scottish independence.

So the economic case remains the Nationalists Achilles’ heel, and they know it. In the press this week Ian Blackford MP (Leader of the SNP in the House of Commons) was quoted as saying that the SNP must convince Scots voters that their “economic future is better as an independent country”. Given they’ve demonstrably failed to do so to date, you’d think the SNP might at least consider the possibility that they’ll need to convince people that having a worse economic future is a price worth paying for independence


But just as the Nationalists need to work on their economic case, so those of us who intuitively feel that the Union is “a good thing” need to find better ways to articulate and communicate our emotional case. One blog certainly won’t do it, but let me make a tentative start.

The people of the UK are bound together by much more than a common language and the economic self-interest of a shared currency and the UK-wide single market. We have a long history of common endeavour and a shared a sense of responsibility to look after all of those who live on these islands.

This results in what we might term an implicit moral contract that most of us accept without ever really considering it. This assumed contract means that wherever you live in the UK, whatever your background, class or economic circumstances, we will pool together to look after you.

There are standards of education you should receive, healthcare you should access, public services you should be able to rely on, a sense of security you should feel and a standard of living you should be able to maintain which should exist wherever you live within the UK. These things should not be based on the economic contribution you individually (or your region collectively) make. As a matter of principle we pool and share resources to ensure that basic standards are guaranteed - and over time raised - for all of “us” in the UK.

Needless to say, politicians will make their own cases for how best to fairly go about it and we can argue the merits of their different strategies all day long - but I’d hazard that few of them would disagree that their aim is to deliver against this contract, that it transcends party politics.

This moral contract lies at the heart of the emotional case for maintaining the Union and fairly obviously underpins the economic one. If you accept this implicit moral contract, questions like “why should we share our oil?” or “why should Scotland need fiscal transfers from the rest of the UK?” just seem daft: pooling and sharing happens because it’s the morally decent thing to do.

Similarly the flaw in the thinking which suggests “full fiscal autonomy” for any constituent part of the UK is some kind of ideal end-game becomes clear: if we economically ring-fence any geographic area of the UK we necessarily break this contract. Fiscal transfers are not a symptom of regional economic failings, they're the tangible result of a positive moral choice.

Referendums certainly (and general elections possibly) can offer us the chance to choose to narrow the definition of the “us” that this moral contract applies to.  Just as the EU referendum appears to have shown that many believe “we” shouldn’t include our EU neighbours, so it’s fair that Scottish Nationalists are free to argue that “we” shouldn’t include those with whom we share these islands.

Those committed to breaking up the UK will keep working towards it. Those of us who disagree with them, who believe that more unites than divides us on these islands, who believe that this implicit moral contract is something precious to be cherished - it's time we got to work too.

Sunday, 11 June 2017

General Election 2017: The Scottish Constituencies

A quick crunch of the figures and some throwaway observations:
  • The "unionist" parties (Conservatives, Labour and Lib Dems) had a 62.4 % overall vote share and greater than a 50% vote share in every constituency in Scotland

  • The SNP's 36.9% share in Scotland was lower than Labour's 40.0% vote share across the UK -- but won them 59% of seats

  • With 27% of the vote, Labour won just 12% of seats; the Conservatives with 29% of the vote won 22% of seats, the Lib Dems with 7% of vote won 7% of seats

  • The Scottish Conservatives received just a 1.5% higher vote share than Scottish Labour by dint of getting 5.7% more votes [757k vs 717k]

  • Scottish Labour were second in 24 constituencies, Conservatives in 10 and Lib Dems in 1 (by just 2 votes)

  • The SNP came second in every seat they lost

  • There were four constituencies with winning margins of less than 100 votes -- these were all won by the SNP

  • Across the 6 constituencies which the SNP won with the lowest margin of victory, they cumulatively won by just 619 votes (or an average of 102 votes per constituency) -- a swing of just 310 votes nationwide would have seen the SNP lose their claim to a majority of Scottish seats at Westminster

  • The lowest winning constituency vote share was the SNP's 32.6% in Lanark & Hamilton East where the Tories polled 32.1%, Labour 31.9%

  • The largest winning margin was comfortably Labour's Ian Murray's 15,514 majority in Edinburgh South; with a 54.9% vote share he was 32.4% ahead of  the SNP who polled just 22.5%

  • The only other constituency won with a majority vote share was the Scottish Conservative's John Lamont who won Berwickshire, Roxburgh and Selkirk with 53.9% of the vote, a majority of 11,060 over the SNP who polled 32.8%

  • The SNP's Vote share dropped from 50.0% in 2015 to 36.9% in 2017; their total votes dropped by a third [from 1,454,436 to 977,569]

Here's the raw data in tabular and graph format - if I've made any errors let me know and I will of course correct

Tuesday, 6 June 2017

Scottish Education: A Generation, Failed

A summary of my recent analysis on the data around the SNP's performance on education appeared in today's Daily Record, along with a broader perspective and some caveats (which generally I agree with) by James McEnaney

Unfortunately one graph appeared mislabelled in print (graph 5 is "writing" not "numeracy") and the online version get's a little confused with graphs and sources - so (with some very minor tweaks) the below is the text of the article with full source links, exhibits we didn't have room for in the paper and references to James' caveats.

Judge SNP on Education? They Flunked it

"Let me be clear – I want to be judged on this. If you are not, as First Minister, prepared to put your neck on the line on the education of our young people then what are you prepared to. It really matters."
Nicola Sturgeon, August 2015 
Nicola Sturgeon has asked to be judged on her record on education and the SNP has been in charge of our fully devolved Scottish education system for roughly 10 years now. Responsibility for the educational outcomes we're now seeing must lie with the SNP - and the trend in those outcomes is simply terrible, as Cabinet Secretary for Education and Skills John Swinney has had to admit.

"the statistics also show a drop in writing performance for S2 pupils which is of particular concern [..] the SSLN [literacy and numeracy] statistics are disappointing"
John Swinney, May 2016
"The figures for Scotland do not make comfortable reading [..] compared to 2012, our performance in science and reading has fallen.  In science and maths we are now below the levels at which we performed in 2006, and more countries have outperformed Scotland in all three areas than at any time since PISA began." John Swinney December 2016

The Evidence of Falling Standards

Scotland participates in one international benchmark survey on educational attainment, the three-yearly PISA study1. PISA surveys 15-year-old pupils, so the most recent data (for 2015) was the first chance to see how pupils who had spent significant time in an SNP-run education system were faring, as these pupils had been in the Scottish education system for 7 years under an SNP administration.

Since the SNP came to power, in each of the three main disciplines as measured by PISA (mathematics, reading & science), Scotland's performance has declined significantly. This is true in absolute terms, relative to the whole of the UK and relative to the average for all OECD countries.

In maths and reading, where Scottish pupils used to perform significantly better than UK students overall, latest available data shows we've dropped back to average at best. In science, where Scottish pupils used to perform in line with the UK average, their performance in the most recent survey is very significantly worse. In all three disciplines, we've gone from out-performing the OECD average to being - well - distinctly average.

If were to you look at our performance in international league-table format: in all three subject areas we've dropped below the UK and OECD averages and into the bottom half of the table2.

As the Scottish Government themselves make clear, "PISA is the major international study of pupil performance in which Scotland participates" - it is their chosen method of benchmarking our educational attainment.

In fact, having withdrawn from the other globally recognised assessment body (TIMSS & PIRLS) in 2011, it's now the only data we have to compare our performance on an international basis. This is good quality data and the results are a damning indictment of the SNP's performance as custodians of our education system.

Caveat: James McEnaney argues that PISA data "is certainly not without its problems", concluding "although PISA has done good things for global education [..] it is a very long way way from being perfect data". I don't dispute that the data is far from perfect, but it is the only international benchmark data we have and the trends observed are consistent across all three subject areas and broadly consistent with the directional message from the SSLN data below. I don't think the data can be ignored (and don't think James is suggesting we ignore it).

The other way we have been able to objectively assess the performance over time of the Scottish education system is the Scottish Government run Scottish Survey of Literacy and Numeracy3 (SSLN).

This data provides worrying evidence of declining performance and wide (and in some cases widening) Attainment Gaps between the performance of pupils from the most deprived and least deprived backgrounds.

To illustrate, let's looks at numeracy performance and the Attainment Gap for P4 (7-8 year-old) pupils. The graph clearly shows standards are dropping and the Attainment Gap is growing.

Another striking example is writing performance for S2 (13-14 year-old) pupils. Here the graph shows overall performance is declining dramatically and the Attainment Gap remains disturbingly large.

There’s a lot more in the SSLN data4. For example it also shows not just a worryingly large Attainment Gap, but also that only 40% of S2 pupils are judged to be performing “well” or “very well” in numeracy. Is our education system producing a generation, soon to vote, who aren't great at adding up?

Caveat: James McEnaney rightly points out that the S2 numeracy data is judging pupils against S3 student's benchmarks, so I guess my cheap line on "not great at adding up" is rather harsh. He also flags concerns with the writing assessment methodology. He knows the data (and the subject) better than I do, so I'm in no position to question his judgement on that.

He does however go on to say "problems with some of the information don't change the downward trends. The SSLN data certainly suggests that the gap between the most-deprived and least-deprived children is, at best, not being closed. It also raises real concerns, shared by teachers, about literacy and numeracy in schools". I think that's a fair summary of the point I'm trying to highlight with this analysis. The full set of graphs is listed under note 4 below - so you can judge for yourself.

But there’s no danger of the SNP being embarrassed by the next set of SSLN data, because – incredibly - they’ve simply decided to stop the survey altogether. They justify this by saying that, because it’s survey based, the data doesn’t provide useful information at a school or local authority level. That’s a frankly ridiculous argument, because that was never what the survey was intended to do.

SSLN gives an overall assessment of the quality of literacy and numeracy education in Scotland, and it does that well. The Scottish Government commissioned the OECD to write a report "Improving Schools in Scotland: An OECD Perspective". That report cites the SSLN data fully 27 times and at no point suggests the data is in any way not fit-for-purpose.

It's hard not to conclude that the SNP's decision to stop the SSLN survey is motivated by the fact that it exposes failings on their part - and that they're fearful of what the next ones might show. Do you think they'd scrap it if they thought the upcoming surveys were going to show how successful their reforms have been? To coin a rather poignant phrase in this context: you do the math.

It gets worse. The Scottish Government states "New statistics on literacy and numeracy performance will be available annually from the teacher professional judgement data collection". So not only are we losing the ability to track performance versus prior years on a like-for-like basis, we're moving from largely objective test-based measurements to subjective measures "based on teachers' professional judgements". It's almost as if the SNP are going out of the way to avoid being judged objectively on their performance.

Combine the SSLN findings with the PISA results and a clear picture emerges: on the SNP's watch, overall standards in Scottish education have dropped and pupils from the most deprived areas are the ones suffering the most.

The Case for the Defence

When grilled on this topic by Andrew Neil during a recent BBC interview, Sturgeon offered a master-class in political spin. She brushed off references to the latest available international benchmark data (reflecting 7 years of SNP control) as "from two years ago" and airily dismissed her own Government's regular survey of over 10,000 pupils as somehow irrelevant.

She even went on to argue that "there's real progress been made". To justify this she fired out a barrage of stats on exam passes and “tariff scores”, both crude measures which suffer from obvious weaknesses when used to judge the performance of our education system. There is no robust way to adjust for the issue of “grade-inflation” (lowering pass marks) and the mix of exams taken, but more importantly these are measures of the end of the educational pipeline. If, for example, there are issues with numeracy at P4 (as the SSLN survey suggests), we need to know about it now, not wait until those pupils leave school in 8 or 9 years’ time.

The other measure seized on by Sturgeon is the number of pupils leaving school for "positive destinations”. This basically means not ending up unemployed or in jail - so if your kids leave school for a minimum wage job on a zero-hours contract, our First Minister will celebrate that as having achieved a “positive destination”.

Who's Really to Blame?

The SNP would of course like to blame “Westminster austerity” for these failings, but that doesn’t wash. The PISA scores show this is an issue specific to Scotland.

The reality, as revealed in the Scottish Government’s own GERS figures, is that the SNP have cut spending on education & training in Scotland over the last 9 years by on average 8% more than it's been cut in the rest of the UK. That was a political choice.

Given the education & training budget has to fund expensive flagship policies like free university tuition, it's not surprising that schools have suffered badly over this period. Primary schools have been particularly badly hit5.

Action has only recently been taken to redress the balance, but the SNP’s response is too little, too late for the generation that has been disadvantaged as a result of education spending  being low on the SNP's priority list.

Over the period the SNP have been in power, teacher numbers in Scotland have declined by 8% and class sizes have increased by 6% - but the trend in England is reversed, with both teacher numbers and class sizes improving6.

The data is clear: the SNP - not “Westminster austerity” - are to blame for failures to invest appropriately in our Scottish education system.

Caveat: James McEnaney rightly argues that - while the data is valid - "we mustn't lose sight of the that fact that it is just one part of a very large and almost uniquely complex picture". I don't disagree with that: wider socio-economic issues are certainly a factor, in particular the broader issue of poverty. I agree with James when he says "the big picture of Scottish education is about much more than just the failures of Nicola Sturgeon and Alex Salmond". It's about more than the SNP's bad choices around specific issues relating to education - but those bad choices are a significant factor


There can be few greater responsibilities for a party of government than to ensure its country's children receive the best possible education, to provide the next generation with the best chances to succeed in life. We know that for the SNP, educating our children will never be their top priority because - as Sturgeon herself and the party's constitution make clear - independence transcends all.

Tony Blair swept to power in 1997 promising to make "education, education, education" his top priorities in office; the Scottish education system appears to be suffering the effects of having an SNP government in power with "independence, independence, independence" as theirs.

Unfortunately it's young Scots emerging from education with reduced life-chances who are the ones paying the price for the SNP's failings today. The question is, will the SNP start paying the price themselves at the ballot box tomorrow?



1. Programme for International Student Assessment (PISA)

The global benchmark standard for education is provided by the OECD's PISA:
The Programme for International Student Assessment (PISA) is a triennial international survey which aims to evaluate education systems worldwide by testing the skills and knowledge of 15-year-old students. In 2015 over half a million students, representing 28 million 15-year-olds in 72 countries and economies, took the internationally agreed two-hour test.
As the Scottish Government website explains:
PISA seeks to measure skills which are necessary for participation in society. Accordingly, it assesses how students apply the skills they have gained to the types of problem they may encounter in work or elsewhere. Pupils are assessed at the age of 15 as this is regarded as a reasonable point at which to test the impact of compulsory education throughout the developed world (most PISA 2012 participants in Scotland were attending S4).
I have used the PISA "data explorer" tool to download and play with the data that's available as a consistent time-series. Fortuitously when it comes to judging the SNP's record, this means our data set starts in 2006, the year before the SNP came to power.

The data is survey based and provided as score averages. As with all good statistical analysis, standard error figures are given. This means our graphs can include vertical bars to show the range within which we can be 95% confident the true figure lies.

A minor irritation is that I've not been able to clarify if the UK data includes Scotland - by implication it does, but either way it doesn't change the overall message (in fact at worst if UK does include Scotland then it dampens the severity of the observed relative trend).

More detail on Scotland's PISA results can be found on the Scottish Government website.

2. PISA Rankings

3.. Scottish Survey of Literacy & Numeracy (SSLN)

As the Scottish Government website explains:
The SSLN was a sample-based survey which monitored national performance over time in literacy and numeracy at P4, P7 and S2. It provided a snapshot of Scotland's achievement in literacy and numeracy at a specific point in time and allowed for comparisons over time to be made. The information from the survey informed the development of dedicated resources to facilitate improvements in learning and teaching.
Whilst the data is survey based, it qualifies for National Statistics certification and rigorous statistical techniques are used to to ensure the data is presented with meaningful confidence intervals. As the latest report explains in helpful detail

As in all sample surveys, as the SSLN is based on a sample of pupils rather than on the
whole population, the results shown are estimates. Therefore there is an element of
uncertainty within the results because the pupils sampled may not reflect the population
Uncertainty around the results is estimated using standard errors. Standard errors are a
measure of the variation in the data i.e. how each observation differs from the mean. As
the SSLN sample design is not a simple random sample - pupils at small schools have a
higher probability of being selected than pupils at large schools - this means that standard formulae used to calculate the standard error from a simple random sample would not be appropriate. Standard errors are therefore calculated empirically using the jackknife procedure.

Standard errors are in turn used to produce confidence intervals around the estimates.
Confidence intervals show the range of values within which one can be reasonably
confident that the actual value would lie if all pupils were assessed. Ninety-five per cent confidence intervals for the main national estimates were calculated and were around ± two percentage points. This means that the true value of each estimate is likely to lie within two percentage points either side of the given estimate.
Where appropriate, confidence intervals are represented on charts by error bars to help
demonstrate this level of uncertainty. Where the estimates are different but the error bars
overlap we cannot be sure that the true values of each estimate are statistically
significantly different from each other. Significance tests (t-tests) are used to assess the
statistical significance of comparisons made.

4. Full set of SSLN graphs




5. Data on Spend/Pupil
Spend per pupil is highlighted in the National Benchmarking Overview Report 2015/16:

6. Data on Teacher Numbers

There's an excellent fact-check by Ferret Scotland on this topic which shows teacher numbers in Scotland have declined by 4,000 since the SNP came to power - that's a 7.5% decline.

The most recent stats on school teacher numbers for England only go up to 2015: over the 2007 to 2015 period they show FTE "regular teacher" numbers increasing by 4%, or nearly 16 thousand teachers. The same period in Scotland saw teacher numbers decline by 8%.

Looking at pupil:teacher ratios back to 2007 takes a bit of work. Summary Statistics for Schools in Scotland shows the data from 2010 and shows pupil:teacher ratios increasing (ie getting worse, as we might expect given the scale of the teacher number decline)

It's a bit of a faff to go back to 2007, but I've done the work so here it is:

I've struggled to get fully comparable stats for England, but this data suggest (as we'd expect from the teacher number stats) that pupil:teach ratios (PTR) are decreasing (improving) in England. This table may be hard to read, but it shows
  • LA Maintained Primary PTR decreased from 21.9 in 2007 to 21.0 in 2015
  • LA Maintained Secondary PTR decreased from 16.5 in 2007 to 15.8 in 2015