Main Results
Table 1 is the full table for the three main regressions summarised in the paper.
Table 2 is the complete set of regressions, showing groups of variables being added progressively.
TABLE 1
Dependent variable: | |||
Voted Yes in Scottish Referendum | Voted Leave in EU Ref | ||
Scotland Only | All GB | Scotland Only | |
(1) | (2) | (3) | |
Log of Household Gross Income (£p.a) | -0.131*** | -0.214*** | -0.124** |
Age | 0.059*** | 0.048*** | 0.034** |
Age Squared | -0.001*** | -0.0004*** | -0.0003 |
Female | -0.207*** | -0.053* | 0.069 |
Highest Education: A Level/Higher Grade | -0.019 | -0.259*** | -0.348*** |
Highest Education: Non-Degree Further | 0.126 | -0.316*** | -0.390*** |
Highest Education: Degree or Equivalent | 0.136 | -0.508*** | -0.701*** |
Ethnic Minority | 0.276 | -0.124* | 0.171 |
Has Children | 0.075 | 0.104*** | 0.215** |
Has a Partner | -0.053 | 0.099*** | 0.015 |
Identifies Conservative | -1.360*** | 0.246*** | 0.271** |
Identifies Libdem | -0.883*** | -0.784*** | -0.829*** |
Identifies Labour | -0.506*** | -0.533*** | -0.478*** |
Identifies Green | 0.789*** | -0.994*** | -0.801*** |
Identifies UKIP | -0.700*** | 2.003*** | 5.625 |
Identifies SNP | 1.890*** | -0.491*** | -0.456*** |
Religion: Catholic | 0.193* | 0.058 | -0.073 |
Religion: Any Protestant | -0.238*** | 0.168*** | 0.289*** |
Big5: Openness | 0.059*** | -0.016** | 0.029 |
North East | 0.034 | ||
North West of England | -0.005 | ||
Yorkshire and Humberside | 0.067 | ||
London | -0.086* | ||
South of England | -0.117*** | ||
Wales | -0.249*** | ||
Scotland | -0.302*** | ||
Constant | -0.313 | 1.213*** | 0.135 |
Observations | 2,256 | 10,540 | 1,553 |
Log Likelihood | -866.535 | -5,934.568 | -855.068 |
Akaike Inf. Crit. | 1,773.070 | 11,923.140 | 1,750.136 |
Note: | *p<0.1; **p<0.05; ***p<0.01 |
TABLE 2
Dependent variable: | |||||||||||||||
Voted Yes in Scottish Referendum | Voted Leave in EU Ref | ||||||||||||||
Scotland Only | All GB | Scotland Only | |||||||||||||
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | (15) | |
Log of Household Gross Income (£p.a) | -0.225*** | -0.135*** | -0.124*** | -0.131*** | -0.128*** | -0.202*** | -0.201*** | -0.215*** | -0.214*** | -0.064 | -0.116** | -0.116** | -0.124** | -0.190*** | -0.170*** |
(0.036) | (0.046) | (0.048) | (0.048) | (0.017) | (0.019) | (0.019) | (0.020) | (0.020) | (0.046) | (0.050) | (0.050) | (0.051) | (0.049) | (0.045) | |
Age | 0.031*** | 0.053*** | 0.059*** | 0.059*** | 0.038*** | 0.049*** | 0.048*** | 0.048*** | 0.048*** | 0.010 | 0.029* | 0.034** | 0.034** | 0.039** | 0.027* |
(0.011) | (0.015) | (0.016) | (0.016) | (0.005) | (0.005) | (0.006) | (0.006) | (0.006) | (0.015) | (0.016) | (0.016) | (0.017) | (0.017) | (0.016) | |
Age Squared | -0.0004*** | -0.001*** | -0.001*** | -0.001*** | -0.0003*** | -0.0004*** | -0.0004*** | -0.0004*** | -0.0004*** | -0.00001 | -0.0002 | -0.0003* | -0.0003 | -0.0003* | -0.0002 |
(0.0001) | (0.0002) | (0.0002) | (0.0002) | (0.00005) | (0.0001) | (0.0001) | (0.0001) | (0.0001) | (0.0001) | (0.0002) | (0.0002) | (0.0002) | (0.0002) | (0.0002) | |
Female | -0.210*** | -0.222*** | -0.193*** | -0.207*** | -0.043* | -0.041 | -0.050* | -0.049* | -0.053* | -0.006 | 0.055 | 0.058 | 0.069 | 0.052 | 0.0002 |
(0.052) | (0.068) | (0.069) | (0.070) | (0.024) | (0.026) | (0.026) | (0.027) | (0.027) | (0.066) | (0.070) | (0.070) | (0.071) | (0.067) | (0.063) | |
Highest Education: A Level/Higher Grade | 0.044 | 0.041 | -0.0003 | -0.019 | -0.352*** | -0.323*** | -0.308*** | -0.277*** | -0.259*** | -0.326*** | -0.410*** | -0.377*** | -0.348*** | -0.349*** | -0.338*** |
(0.081) | (0.106) | (0.110) | (0.110) | (0.037) | (0.040) | (0.040) | (0.042) | (0.042) | (0.096) | (0.102) | (0.103) | (0.105) | (0.103) | (0.097) | |
Highest Education: Non-Degree Further | 0.016 | 0.164 | 0.149 | 0.126 | -0.433*** | -0.372*** | -0.361*** | -0.331*** | -0.316*** | -0.384*** | -0.418*** | -0.397*** | -0.390*** | -0.390*** | -0.415*** |
(0.102) | (0.136) | (0.139) | (0.139) | (0.048) | (0.053) | (0.053) | (0.054) | (0.054) | (0.125) | (0.133) | (0.134) | (0.136) | (0.126) | (0.118) | |
Highest Education: Degree or Equivalent | 0.067 | 0.165* | 0.155* | 0.136 | -0.653*** | -0.573*** | -0.556*** | -0.522*** | -0.508*** | -0.720*** | -0.719*** | -0.698*** | -0.701*** | -0.695*** | -0.728*** |
(0.067) | (0.089) | (0.090) | (0.091) | (0.029) | (0.031) | (0.032) | (0.033) | (0.033) | (0.082) | (0.087) | (0.088) | (0.090) | (0.082) | (0.076) | |
Ethnic Minority | 0.409** | 0.287 | 0.267 | 0.276 | -0.152** | -0.149** | -0.131** | -0.114* | -0.124* | 0.226 | 0.196 | 0.188 | 0.171 | 0.109 | 0.164 |
(0.169) | (0.217) | (0.222) | (0.223) | (0.059) | (0.064) | (0.064) | (0.066) | (0.067) | (0.226) | (0.245) | (0.251) | (0.251) | (0.229) | (0.210) | |
Has Children | 0.020 | 0.076 | 0.067 | 0.075 | 0.110*** | 0.120*** | 0.108*** | 0.103*** | 0.104*** | 0.202** | 0.229** | 0.203** | 0.215** | 0.199** | 0.200** |
(0.066) | (0.083) | (0.086) | (0.087) | (0.031) | (0.034) | (0.034) | (0.035) | (0.035) | (0.086) | (0.091) | (0.092) | (0.094) | (0.092) | (0.086) | |
Has a Partner | 0.034 | -0.025 | -0.060 | -0.053 | 0.081*** | 0.091*** | 0.087*** | 0.107*** | 0.099*** | -0.053 | -0.026 | -0.022 | 0.015 | 0.061 | 0.056 |
(0.060) | (0.078) | (0.080) | (0.081) | (0.028) | (0.031) | (0.031) | (0.032) | (0.032) | (0.076) | (0.081) | (0.082) | (0.084) | (0.078) | (0.074) | |
Identifies Conservative | -1.453*** | -1.373*** | -1.360*** | 0.320*** | 0.291*** | 0.274*** | 0.246*** | 0.320*** | 0.269** | 0.271** | 0.228** | ||||
(0.136) | (0.139) | (0.140) | (0.038) | (0.038) | (0.039) | (0.040) | (0.112) | (0.113) | (0.115) | (0.107) | |||||
Identifies Libdem | -0.901*** | -0.910*** | -0.883*** | -0.737*** | -0.753*** | -0.765*** | -0.784*** | -0.773*** | -0.825*** | -0.829*** | -0.973*** | ||||
(0.170) | (0.174) | (0.176) | (0.056) | (0.057) | (0.058) | (0.058) | (0.179) | (0.180) | (0.181) | (0.183) | |||||
Identifies Labour | -0.497*** | -0.506*** | -0.506*** | -0.498*** | -0.500*** | -0.505*** | -0.533*** | -0.485*** | -0.482*** | -0.478*** | -0.611*** | ||||
(0.087) | (0.089) | (0.090) | (0.037) | (0.037) | (0.038) | (0.039) | (0.106) | (0.107) | (0.109) | (0.102) | |||||
Identifies Green | 0.887*** | 0.803*** | 0.789*** | -1.066*** | -1.033*** | -1.007*** | -0.994*** | -0.792*** | -0.790*** | -0.801*** | -0.860*** | ||||
(0.157) | (0.164) | (0.164) | (0.109) | (0.109) | (0.112) | (0.112) | (0.257) | (0.259) | (0.263) | (0.248) | |||||
Identifies UKIP | -0.700*** | -0.718*** | -0.700*** | 2.005*** | 1.992*** | 2.011*** | 2.003*** | 5.587 | 5.580 | 5.625 | 5.382 | ||||
(0.195) | (0.202) | (0.202) | (0.130) | (0.131) | (0.137) | (0.139) | (58.378) | (58.377) | (58.622) | (58.183) | |||||
Identifies SNP | 1.862*** | 1.895*** | 1.890*** | -0.684*** | -0.680*** | -0.687*** | -0.491*** | -0.445*** | -0.439*** | -0.456*** | -0.506*** | ||||
(0.101) | (0.105) | (0.106) | (0.068) | (0.069) | (0.070) | (0.080) | (0.099) | (0.099) | (0.102) | (0.102) | |||||
Religion: Catholic | 0.170 | 0.193* | 0.080* | 0.069 | 0.058 | -0.008 | -0.073 | 0.151 | |||||||
(0.115) | (0.116) | (0.049) | (0.050) | (0.050) | (0.125) | (0.131) | (0.117) | ||||||||
Religion: Any Protestant | -0.260*** | -0.238*** | 0.180*** | 0.177*** | 0.168*** | 0.263*** | 0.289*** | 0.186** | |||||||
(0.079) | (0.080) | (0.029) | (0.030) | (0.030) | (0.079) | (0.080) | (0.074) | ||||||||
Big5: Openness | 0.059*** | -0.017** | -0.016** | 0.029 | -0.002 | ||||||||||
(0.020) | (0.008) | (0.008) | (0.021) | (0.019) | |||||||||||
North East | 0.034 | ||||||||||||||
(0.070) | |||||||||||||||
North West of England | -0.005 | ||||||||||||||
(0.051) | |||||||||||||||
Yorkshire and Humberside | 0.067 | ||||||||||||||
(0.054) | |||||||||||||||
London | -0.086* | ||||||||||||||
(0.051) | |||||||||||||||
South of England | -0.117*** | ||||||||||||||
(0.041) | |||||||||||||||
Wales | -0.249*** | ||||||||||||||
(0.053) | |||||||||||||||
Scotland | -0.302*** | ||||||||||||||
(0.050) | |||||||||||||||
Voted Yes in IndieRef | -0.036 | -0.281*** | |||||||||||||
(0.092) | (0.063) | ||||||||||||||
Constant | 1.860*** | 0.186 | -0.015 | -0.313 | 0.400** | 0.975*** | 0.943*** | 1.146*** | 1.213*** | 0.181 | 0.415 | 0.254 | 0.135 | 0.882 | 0.866 |
(0.432) | (0.552) | (0.577) | (0.594) | (0.203) | (0.225) | (0.227) | (0.244) | (0.247) | (0.552) | (0.596) | (0.612) | (0.658) | (0.654) | (0.600) | |
Observations | 2,457 | 2,374 | 2,281 | 2,256 | 11,649 | 11,190 | 11,143 | 10,540 | 10,540 | 1,656 | 1,614 | 1,608 | 1,553 | 1,896 | 1,948 |
Log Likelihood | -1,656.315 | -925.873 | -878.954 | -866.535 | -7,499.412 | -6,319.826 | -6,279.390 | -5,968.492 | -5,934.568 | -1,013.896 | -898.282 | -887.847 | -855.068 | -1,020.807 | -1,149.595 |
Akaike Inf. Crit. | 3,334.630 | 1,885.745 | 1,795.908 | 1,773.070 | 15,020.830 | 12,673.650 | 12,596.780 | 11,976.990 | 11,923.140 | 2,049.793 | 1,830.564 | 1,813.694 | 1,750.136 | 2,083.614 | 2,323.190 |
Note: | *p<0.1; **p<0.05; ***p<0.01 |
Equations 1-4 show IndieRef estimates, based on Scottish Subsample, with regressors added progressively: basic regressors (age, sex, education, income), then: politics, religion, psychology.
Equations 5-9 show Brexit estimates on the whole GB sample, using the same regressors, plus (Eqn. 9) regional dummies
Equations 10-13 are the same as 5-8, but for the Scottish subsample only.
Finally, 14 and 15 use vote in Indie Ref as a predictor. With all the other variables in, it’s not a good predictor since the variables we use themselves predict the indieref vote. Using the indieref without the full variable set is a good predictor.
We make the pretty-ish arrows table in the article from Table 1 above using a little Ruby script.
Voted Yes in Scottish Referendum | Voted Leave in EU Ref | |||||
Scotland Only | All GB | Scotland Only | ||||
(1) | (2) | (3) | (4) | (5) | (6) | |
Log of Household Gross Income (£p.a) | 🢃 | 🢃 | 🢃 | 🡳 | 🢃 | 🢃 |
---|---|---|---|---|---|---|
Age | 🢁 | 🢁 | 🢁 | 🡱 | 🡱 | 🡡 |
Age Squared | 🢃 | 🢃 | 🢃 | ● | 🡣 | ● |
Female | 🢃 | 🡣 | 🡣 | ● | ● | ● |
Highest Education: A Level/Higher Grade | ● | 🢃 | 🢃 | 🢃 | 🢃 | 🢃 |
Highest Education: Non-Degree Further | ● | 🢃 | 🢃 | 🢃 | 🢃 | 🢃 |
Highest Education: Degree or Equivalent | ● | 🢃 | 🢃 | 🢃 | 🢃 | 🢃 |
Ethnic Minority | ● | 🡣 | 🡣 | ● | ● | ● |
Has Children | ● | 🢁 | 🢁 | 🡱 | 🡱 | 🡱 |
Has a Partner | ● | 🢁 | 🢁 | ● | ● | ● |
Identifies Conservative | 🢃 | 🢁 | 🢁 | 🡱 | 🡱 | |
Identifies Libdem | 🢃 | 🢃 | 🢃 | 🢃 | 🢃 | |
Identifies Labour | 🢃 | 🢃 | 🢃 | 🢃 | 🢃 | |
Identifies Green | 🢁 | 🢃 | 🢃 | 🢃 | 🢃 | |
Identifies UKIP | 🢃 | 🢁 | 🢁 | ● | ● | |
Identifies SNP | 🢁 | 🢃 | 🢃 | 🢃 | 🢃 | |
Religion: Catholic | 🡡 | ● | ● | ● | ● | |
Religion: Any Protestant | 🢃 | 🢁 | 🢁 | 🢁 | 🡱 | |
Big5: Openness | 🢁 | 🡳 | 🡳 | ● | ● | |
North East | ● | |||||
North West of England | ● | |||||
Yorkshire and Humberside | ● | |||||
London | 🡣 | |||||
South of England | 🢃 | |||||
Wales | 🢃 | |||||
Scotland | 🢃 | |||||
Voted Yes in IndieRef | ● | 🢃 |
Notes To The Article
The Commonspace CMS system unfortunately chopped out the article’s footnotes, so I’ll reproduce them here:
Matthew Goodwin and Oliver Heath Study : The study was completed after the vote but before the edition of the BES with the actual data on the Brexit vote had been released; instead, Goodwin and Heath model intention to vote (6 months before), which is a good though not perfect correlate with actual vote. I’m using the version (9) of the BES with the actual vote in it.
Kauffmann Study: this was carried out even earlier, before the actual Brexit vote: instead of explaining the vote he is modelling the extent to which people disapprove of the EU, which, too, is a good predictor of the final vote.
Paragraph on ‘Main Findings’: We say ‘Great Britain’ rather than ‘United Kingdom’ since Northern Ireland is not in the BES data.
Relationship between age and voting: in the IndieRef case (but not the Brexit vote), this is actually a bit of a simplification - ‘Yes’ is modelled to rise till about age 40 and fall thereafter, whereas ‘Leave’ rises steadily at all ages. This is ‘all else equal’, and of course incomes generally rise between those ages, which may explain why simple tabulations from polling data don’t show quite this pattern. See the Technical Note for more detail.
Political Parties: These are the parties people identify with; they needn’t be members of them.
Strength of statistical relationships : A technical aside: I’m using statistical significance for this (the p-values) rather than, for example, effect size. So I give more weight in that table to a small but certain influence than to a potentially large effect which has more uncertainty attached to it. The American Statistical Association has a good short paper on this
On Modelling Brexit: I report above a version of the model without these regional dummies, showing that adding or removing these variables doesn’t affect our other conclusions in any major way. So model in column (2) is still comparable with the Indie ref one even though it has more variables.
Analysis of Scottish Voters: ‘Scottish’, as is customary, simply means people living (or at least interviewed) in Scotland. Adding country of birth as an explanatory variable would be interesting.
London (non) Effect: The Resolution Foundation study finds this, too.