What do immigration numbers tell us about the Brexit vote?

A couple of weeks ago I tweeted a chart from The Economist which plotted the percentage increase in the foreign-born population in UK local authority areas against the number of Leave votes in that area. I also quoted the accompanying article: ‘Where foreign-born populations increased by more than 200%, a Leave vote followed in 94% of cases.’


This generated lots of responses, many of which rightly pointed out the problems with the causality implied in the quote. These included the following:

  • Using the percentage change in foreign-born population is problematic because this will be highly sensitive to the initial size of population.
  • Majority leave votes also occurred in many areas where the number of migrants had fallen.
  • Much of the result is driven by a relatively small number of outliers while the systemic relationship looks to be flat.
  • The number of points where foreign-born populations had increased by more than 200% were small relative to the total sample: around twenty points out of several hundred.

Al these criticisms are valid. With hindsight, the Economist probably shouldn’t have published the chart and article – and I shouldn’t have tweeted it. But the discussion on Twitter got me interested in whether the geographical data can tell us anything interesting about the Leave vote.

I started by trying to reproduce the Economist’s chart. The time period they use for the change in foreign-born population is 2001-2014. This presumably means they used census data for the 2001 numbers and ONS population estimates for 2014. My attempt to reproduce the graph using these datasets is shown below. The data points are colour-coded by geographical region and the size of the data point represents the size of the foreign-born population in 2014 as a percentage of the total. (The chart is slightly different to the one I previously tweeted, which had some data problems.)


Despite the problems described above, the significance of geography in the vote is clear – this is emphasised in the excellent analysis published recently by the Resolution Foundation and by Geoff Tily at the TUC (see also this in the FT and this in the Guadian).

Of the English and Welsh regions, it is clear that the Remain vote was overwhelmingly driven by London (The chart above excludes Scotland and Northern Ireland, both of which voted to Remain). Other areas which have seen substantial growth in foreign-born populations and also voted to Remain are cities such as Oxford, Cambridge, Bristol, Manchester and Liverpool.

A better way to look at this data is to plot the percentage point change in foreign population instead of the percentage increase. This will prevent small initial foreign-born populations producing large percentage increases. The result is shown below. For this, and rest of the analysis that follows, I’ve used the ONS estimates of the foreign-born population. This reduces the number of years to 2004-2014, but excludes possible errors due to incompatibility between the census data and ONS estimates. It also allows for inclusion of Scottish data (but not data from Northern Ireland). I’ve also flipped the X and Y axes: if we are thinking of the Leave vote as the thing we wish to explain, it makes more sense to follow convention and put it on the Y axis.


There is no statistically significant relationship between the two variables in the chart above. The divergence between London, Scotland and the rest of the UK is clear, however. There also looks to be a positive relationship between the increase in foreign-born population and the Leave vote within London. This can be seen more clearly if the regions are plotted separately.


The only region in which there is statistically significant relationship in a simple regression between the two variables is London. A one percent increase in the foreign-born population is associated with a 1.5 percent increase in the Leave vote (with an R-squared of about 0.4). The chart below shows the London data in isolation.


The net inflow of migrants appears to have been greatest in the outer boroughs of London – and these regions also returned highest Leave votes. There are a number of possible explanations for this. One is that new migrants go to where housing is affordable – which means the outer regions of London. These are also the areas where incomes are likely to be lower. There is some evidence for this, as shown in the chart below: there is a negative relationship – albeit a weak one – between the increase in the foreign-born population and the median wage in the area.


Returning to the UK as a whole (excluding Northern Ireland), the Resolution foundation finds that there is a statistically significant relationship between the percentage point increase in foreign-born population and Leave vote when the size of the foreign-born population is controlled for. This is confirmed in the following simple regression, where FB.PP.Incr is the percentage point increase in the foreign-born population and FB.Pop.Pct is the foreign-born population as a percent of the total.

 Estimate Std. Error t value Pr(>|t|) 
(Intercept) 57.19258 0.71282 80.235 < 2e-16 ***
FB.PP.Incr 0.90665 0.17060 5.314 1.87e-07 ***
FB.Pop.Pct -0.64344 0.05984 -10.752 < 2e-16 ***
Signif. codes: 0 ~***~ 0.001 ~**~ 0.01 ~*~ 0.05 ~.~ 0.1 ~ ~ 1

Residual standard error: 9.002 on 363 degrees of freedom
Multiple R-squared: 0.2475, Adjusted R-squared: 0.2433 
F-statistic: 59.69 on 2 and 363 DF, p-value: < 2.2e-16

It is clear that controlling for the foreign-born population is, in large part, controlling for London. This is illustrated in the chart below which shows the foreign-born population as a percentage of the total for each local authority in 2014, grouped by broad geographical region. The boxplots in the background show the mean and interquartile ranges of foreign-born population share by region. The size of the data points represents the size of the electorate in that local authority.


This highlights a problem with the analysis so far – and for others doing regional analysis on the basis of local authority data. By taking each region as a single data point, statistical analysis misses the significance of differences in the size of electorates. This is important because it means, for example, that the Leave vote of 57% from Richmondshire, North Yorksire with around 27,000 votes cast is given the same weight as the Leave vote of 57% in County Durham, with around 270,000 votes cast.

This can be overcome by constructing an index of referendum voting weighted by the size of the electorate in each area. This index is constructed so that it is equal to zero where the Leave vote was 50%, negative for areas voting Remain, and positive for areas voting Leave. The magnitude of the index represents the strength of the contribution to the overall result. Plotting this index against the percentage point change in the foreign population produces the following chart. Data point sizes represent the number of votes in each area.


Again, there is no statistically significant relationship between the two variables, but as with the unweighted data, when controlling for the foreign population,  a positive relationship does exist between the increase in foreign-born and Leave votes.

The outliers are different to those seen in the unweighted voting data, however – particularly in areas with a strong leave vote. This can be seen more clearly by removing the two areas with the strongest Remain votes: London and Scotland. The data for the rest of England and Wales only are shown below.08-chart-leave-weighted-nss

There is a clear split between the strong Leave outliers and the strong Remain outliers. The latter are Bristol, Brighton, Manchester, Liverpool and Cardiff. When weighted by size of vote, The previous outliers for Leave – Eastern areas such as Boston and South Holland – are replaced by towns and cities in the West Midlands and Yorkshire and with the counties of Cornwall and County Durham.

Overall, while there is a relationship between net migration inflows and Leave votes – at least when controlling for the size of the foreign-born population – it is only a small part of the story. The most compelling discussions I’ve seen of the underlying causes of the Leave vote are those which emphasise the rise in precarity and the loss of social cohesion and identity in the lives of working people, such as John Lanchester’s piece in the London Review of Books (despite the errors), the excellent follow-up piece by blogger Flip-Chart Rick, and this piece by Tony Hockley. As Geoff Tily argues, the geographical distribution of votes strongly suggests economic dissatisfaction was a key driver of the Leave vote, which pitted ‘cosmopolitan cities’ against the rest of the country. This is compatible with the pattern shown above, where the strongest Leave votes are concentrated in ex-industrial areas and the strongest Remain votes in the ‘cosmopolitan cities’.

The chart below shows the weighted Leave vote plotted against median gross weekly pay.09-wages

Scotland as a whole is once again the outlier, while much of the relationship appears to be driven by London, where wages are higher and the majority voted Remain. Removing these two regions gives the following graph.


Aside from the outlier Remain cities, there is a negative relationship between median pay and weighted Leave votes. The statistical strength of this relationship is relatively weak, however.

Putting all the variables together produces the following regression result:

 Estimate Std. Error t value Pr(>|t|) 
(Intercept) 80.98722 12.18838 6.645 1.12e-10 ***
FB.PP.Incr 2.46269 0.57072 4.315 2.06e-05 ***
FB.Pop.Pct -1.61904 0.21781 -7.433 7.72e-13 ***
Median.Wage -0.12539 0.02404 -5.216 3.08e-07 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 29 on 362 degrees of freedom
Multiple R-squared: 0.2977, Adjusted R-squared: 0.2919 
F-statistic: 51.15 on 3 and 362 DF, p-value: < 2.2e-16

Leave votes are negatively associated with the size of the foreign-born population and with the median wage, and positively associated with increases in the foreign-born. The R^2 value of 0.3 suggests this model has some predictive power, but could certainly be improved.

 Estimate Std. Error t value Pr(>|t|) 
(Intercept) 107.61139 13.30665 8.087 9.97e-15 ***
FB.PP.Incr 2.92817 0.49930 5.865 1.04e-08 ***
FB.Pop.Pct -2.34394 0.27140 -8.636 < 2e-16 ***
Median.Wage -0.14360 0.02313 -6.210 1.50e-09 ***
RegionEast Midlands -9.07601 5.44978 -1.665 0.09672 . 
RegionLondon 9.44698 8.34896 1.132 0.25861 
RegionNorth East -4.11112 8.02869 -0.512 0.60893 
RegionNorth West -16.69448 5.51048 -3.030 0.00263 ** 
RegionScotland -61.65217 5.76312 -10.698 < 2e-16 ***
RegionSouth East -4.60717 4.64123 -0.993 0.32156 
RegionSouth West -18.73821 5.55187 -3.375 0.00082 ***
RegionWales -27.65673 6.53577 -4.232 2.96e-05 ***
RegionWest Midlands 4.06613 5.83469 0.697 0.48633 
RegionYorkshire and The Humber 4.72398 6.61676 0.714 0.47574 
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 24 on 352 degrees of freedom
Multiple R-squared: 0.5323, Adjusted R-squared: 0.515 
F-statistic: 30.82 on 13 and 352 DF, p-value: < 2.2e-16

Adding regional dummy variables improves the fit of the model substantially – increasing the value of R^2 to around 0.5. This suggests – unsurprisingly – there are differences between regions which are not captured in the three variables included here.

2015: Private Debt and the UK Housing Market

This report is taken from the EREP’s Review of the UK Economy in 2015.

In his 2015 Autumn Statement, Chancellor George Osborne gave a bravura performance. He congratulated himself on record growth and employment, falling public debt, surging business investment and a narrowing trade deficit. He announced projections of continuous growth and falling public debt over the next parliament.

While much of this was a straightforward misrepresentation of the facts – capital investment has yet to recover from the 2008 crisis and the current account deficit continues to widen – other sound bites came courtesy of the Office for Budget Responsibility. The OBR delivered the Chancellor an early Christmas present in the form of a set of revised projections showing better-than-expected public finances over the next five years.

When, previously, the OBR inconveniently delivered negative revisions, the Chancellor responded by pushing back the date he claims he will achieve a budget surplus. In response to the OBR’s gift, however, he chose instead to spend the windfall.  This is a risky strategy because any negative shock to the economy means he will miss his current fiscal targets – targets he has already missed repeatedly since coming to office.

As it turns out, these negative shocks have materialised rather quickly. Since the Chancellor made his statement a month ago, UK GDP growth has been revised down, the trade deficit has widened and estimates of borrowing for the current year have increased.


In reality, the OBR projections never looked plausible. The UK’s current account deficit – the amount borrowed each year from the rest of the world – is at an all- time high of around 5% of GDP. Every six months for the last three years, the OBR forecast that the deficit would start to close within a year; every time they were proved wrong (see figure above).  Their current assertion – that the trend will be broken in 2016 and the deficit will steadily narrow to around 2% of GDP in 2020 – must be taken with a large pinch of salt.

The current account deficit measures the combined overseas borrowing of the UK public and private sectors. In the unlikely event that George Osborne was to achieve his stated aim of a budget surplus, the whole of this foreign borrowing would be accounted for by the private sector. This is exactly what the OBR is projecting. Specifically, they predict that the household sector will run a deficit of around 2% per year for the next five years. They note that “this persistent and relatively large household deficit would be unprecedented”.

This projection has been the basis of recent stories in the press which have declared that the Chancellor has set the economy on a path to almost-certain financial meltdown within the current parliament. This is too simplistic an analysis. Financial imbalances can persist for a long time. The last UK financial crisis originated not in the UK lending markets but in UK banks’ exposure to overseas lending.

But the Chancellor’s strategy entails serious financial risks. Even though there is no real chance of achieving a surplus by 2020, further cuts to government spending will squeeze spending out of the economy, placing ever more of the burden on household consumption spending to maintain growth.

The figure below shows the annual growth in lending to households. While total credit growth remains subdued, unsecured lending has, in the words of Andy Haldane, chief economist at the Bank of England, been “picking up at a rate of knots”.


Moderate growth in the mortgage market may conceal deeper problems: household debt-to-income ratios have fallen since the crisis but, at around 140% of GDP, remain high both in historical terms and compared to other advanced nations. The majority of new mortgage lending since 2008 has been extended to buy-to-let landlords. These speculative buyers now face the prospect of rising interest rates and tax changes that will take a large chunk out of their property income. Many non-buy-to-let borrowers are badly exposed: a sixth of mortgage debt is held by those who have less than £200 a month left after spending on essentials.

The Financial Policy Committee has noted that these trends “… could pose direct risks to the resilience of the UK banking system, and indirect risks via its impact on economic stability”.

What is often left out of the more apocalyptic visions of a coming credit meltdown is that underlying all this is an unprecedented housing crisis in which an entire generation are locked out of home ownership. Instead of tackling this crisis, Osborne is using the housing market as a casino in the hope of keeping economic growth on track during another five years of austerity. It is a high-risk strategy. His luck may soon run out.

The report’s authors include:

John Weeks on fiscal policy

Ann Pettifor on monetary policy

Richard Murphy on taxation

Özlem Onaran on inequality and wage stagnation

Jeremy Smith on labour productivity

Andrew Simms on climate change and energy

Jo Michell on private debt

The full report is can be downloaded here.

Information on EREP is available here.

Happy Christmas from the Office of Budget Responsibility

Image reproduced from here

The sectoral balances approach to economic forecasting has come under scrutiny recently. It is certainly the case that when used carelessly, projections based on accounting identities have the potential to be either meaningless or misleading. This will be the case if accounting identities are mistakenly taken to imply causal relationships, if projections are presented without a clear statement of the assumptions about what drives the system or if changes taking place in ‘invisible’ variables such as the rate of growth of GDP are not identified (balances are usually presented as percentages of GDP).

Used with care, however (or luck, depending on your perspective), the approach is not without its merits – as I have argued previously. If nothing else, the impossibility of escaping from the fact that in a closed system lending must equal borrowing imposes logical restrictions on the projections that can be made about the future paths of borrowing in a ‘closed’ macroeconomic system.

Which brings us to the Chancellor’s Autumn Statement and the OBR’s rather helpful projections. As Duncan Weldon notes, the OBR are likely to receive a rather warmly written card from the Chancellor’s office this Christmas. While true that the OBR have, in the past, been less than helpful to the Chancellor, one can’t help but wonder about the justification for announcing the OBR projections at the same time as the Chancellors’ statements. Why are the OBR projections not made known to the public at the same time that they are made available to the Chancellor?

But back to sectoral balances. The model used by the OBR produces projections which comply with sectoral balance accounting identities. Four are used: those of the public sector, the household sector, the corporate sector and the rest of the world. The most closely watched is of course the public sector balance. The headline result of the OBR forecasts is that the public sector will run a surplus by 2019. What has so far received less attention (at least since Frances Coppola examined the projections from the March 2015 OBR forecasts) is the implication of this for the other three balances. The most recent OBR projections are shown below.


Since the government is projected to run a small surplus from mid-2019, the other three sectors must collectively run a deficit of equal size. The OBR projects that the current account deficit will fall from its current level of around five per cent of GDP to around two per cent of GDP. The UK private sector must be in deficit. Interesting details lie in both the distribution of this deficit between the household and corporate sectors, and in the changes in figures since the last OBR reports in March and July.

In order to show how the numbers have changed since the previous forecasts, I have collected the data series from all three releases into individual charts.

The OBR series from these three releases for the public sector financial balance are shown below. Other than postponing the date at which the government achieves a surplus (and some revisions to the historical data) there is little difference between the three releases.


Changes to the projections for the current account deficit are more significant. The latest projections include improvements in the projected deficit of between 0.5% and 1% of GDP, compared with the July predictions. With the current account deficit at record levels in excess of 5% of GDP, I think it is fair to say the projections look optimistic. I note that in each of the three OBR series, the deficit starts to close in the first projected quarter. Put another way, the inflection point has been postponed three times out of three.


Things start to get interesting when we turn to the corporate sector. Here the projections have changed rather more significantly. Whereas the previous two data series showed the corporate sector reversing its decade-long surplus in 2014 and finally returning to where many think the corporate sector should be – borrowing to invest – the new series contains significant revisions to the historical data. As it turns out, the corporate sector has remained in surplus, lending one per cent of GDP in Q2 2015. The corporate sector is not now projected to return to deficit until Q3 2018.


Since the net financial balance for any sector is the difference between ex post saving – profits in the case of the corporate sector – and investment, these revisions imply either falling corporate investment, rising profits, or both.

The data series for corporate investment are shown below. The historical data have been revised down significantly. Investment in Q2 2015 is 1% of GDP lower than previously recorded. (This is hard to square with Osborne’s statement that ‘business investment has grown more than twice as fast as consumption’.) The reduction compared to previous forecasts widens in the projection out to 2020. Nonetheless, it is hard to escape the conclusion that the projections are extremely optimistic. By 2020, business investment is expected to reach twelve per cent of GDP, higher than any year back to 1980.


What of business profits? These are shown in the table below, taken from the OBR report. It seems that corporate profit grew at 10% year-on-year in 2014-15, despite GDP growth of around 2.5%. While projected growth rates decline, corporate profit is expected to grow at over 4% annually in every year of the projection out to 2021 (in a context of steady 2.5% GDP growth). There is not much sign of GoodhartNangle in these projections.


So, to recap: by 2020 we have government running a surplus just under 1% of GDP, a current account deficit of 2% of GDP and a corporate sector deficit around 1% of GDP. Those with a facility for mental arithmetic will have already arrived at the punchline – the household sector will be running a deficit of around 2% of GDP. In fact, given data revisions, the household sector appears to be already running a deficit close to 2% of GDP – a deficit which is projected to remain until 2021 (see figure below).

Fig-7-HHAs a comparison, note that in the period preceding the 2008 crisis, the household sector ran a deficit of not much over 1% of GDP, and for a shorter period than currently projected.

The OBR has this to say on its projections:

Recent data revisions have increased the size of the household deficit in 2014 and we expect little change in the household net position over the forecast period, with gradual increases in household saving offset by ongoing growth of household investment. Available historical data suggest that this persistent and relatively large household deficit would be unprecedented. This may be consistent with the unprecedented scale of the ongoing fiscal consolidation and market expectations for monetary policy to remain extremely accommodative over the next five years, but it also illustrates how the adjustment to fiscal consolidation assumed in our central forecast is subject to considerable uncertainty.  (p. 81)

Perhaps there is something to the sectoral balances approach approach after all. One can only wonder what Godley would make of all this.

Jo Michell