using XLSX, DataFrames
using Statistics
using HypothesisTests
using CairoMakie
using DoingEconomics
CairoMakie.activate!(type = "svg")
use_doingecon_theme!()Extra 2. The politics of carbon taxation
Why rural voters reject carbon taxes, and a survey experiment that moves the belief
A UK survey of 2,997 respondents on carbon taxation, from Hope, Limberg and Steinebach (2026). It is a survey experiment: half the sample received an information treatment before being asked their views, so the difference between the halves is caused by the information rather than merely correlated with it.
The argument being tested is that rural opposition to carbon taxes is not only about the higher costs rural households face, but about fairness — a sense that the state already treats these communities unequally, and that a carbon tax adds to the injury.
Concepts: Likert scales, dummy variables, conditional means, and an information-provision survey experiment as a way to test a causal claim about beliefs. Book pages: project, R walk-through, solutions.
path = rawpath("14", "carbon-tax-hope.xlsx")
function sheet_frame(p, name)
cells = XLSX.readxlsx(p)[name][:]
return DataFrame([cells[2:end, j] for j in axes(cells, 2)],
Symbol.(string.(cells[1, :])); makeunique = true)
end
survey = sheet_frame(path, "Data")
function num(x)
(x === missing || x === nothing) && return missing
x isa Number && return Float64(x)
parsed = tryparse(Float64, string(x))
return parsed === nothing ? missing : parsed
end
for col in [:age, :treatment, :carbon_tax_support, :unequal_treatment, :carbon_tax_unfairness]
survey[!, col] = num.(survey[!, col])
end
text_col(v) = [x === missing || x === nothing ? missing : string(x) for x in v]
for col in [:neighbourhood, :commute, :partisanship]
survey[!, col] = text_col(survey[!, col])
end
(respondents = nrow(survey), variables = names(survey))(respondents = 2997, variables = ["respondent_id", "age", "neighbourhood", "commute", "partisanship", "treatment", "carbon_tax_support", "unequal_treatment", "carbon_tax_unfairness"])Part 1 — Measuring and explaining support for carbon taxation
Q1. How the question was asked
Both groups are given a short explanation of a carbon tax immediately before being asked their view: how the tax works, that heavier fossil-fuel users pay more, and that it is aimed at climate change.
That explanation is the step taken to improve accuracy. Asking about an unfamiliar policy otherwise measures whatever the respondent imagines the words mean, and “carbon tax” is a phrase many people hold an opinion about without holding a definition. Briefing everyone identically means the answers refer to the same object — and because both arms get it, it is not the experimental treatment.
Q2. Sample sizes
DataFrame(group = ["Treatment", "Control", "Total"],
respondents = [count(==(1.0), survey.treatment),
count(==(0.0), survey.treatment), nrow(survey)])3×2 DataFrame
| Row | group | respondents |
|---|---|---|
| String | Int64 | |
| 1 | Treatment | 1481 |
| 2 | Control | 1516 |
| 3 | Total | 2997 |
2,997 respondents, 1,481 treated and 1,516 control, all three matching the published solution. The split is near-even, as random assignment should produce.
Q3. How the authors recode support, and what it costs
ImportantThe book’s own description of the scale is inverted
The project text says support is measured “on a 5-point scale running from 1 for ‘strongly oppose’ to 5 for ‘strongly support’”. The data dictionary in the spreadsheet says the opposite: 1 is strongly support and 5 is strongly oppose.
The dictionary is right, and the book’s own instructions confirm it — the dummy variable is defined as 1 when carbon_tax_support is 1 or 2, described as “strongly support or support”. That only makes sense if low numbers mean support.
Taking the question text at face value would invert every result on this page while leaving all the arithmetic looking perfectly reasonable. The check is the published frequency table, which this page reproduces below: if the coding were reversed, the counts would attach to the opposite labels.
The authors collapse the five-point scale to a dummy: 1 for support or strong support, 0 otherwise.
- The advantage is interpretability. The mean of a 0/1 variable is the share supporting, so every conditional mean below reads directly as a percentage, and it behaves well in a regression.
- The cost is intensity. Someone who strongly supports and someone who merely supports become identical, as do a neutral respondent and a strong opponent. The variable can no longer detect a change that moves people from “oppose” to “strongly oppose” — a real hardening of opinion that this measure records as nothing at all.
Q4 and Q5. The dummy variables
# Missing stays missing throughout: a respondent who skipped the question is not a zero.
survey.supports = [s === missing ? missing : Float64(s <= 2) for s in survey.carbon_tax_support]
survey.aged_40_plus = [a === missing ? missing : Float64(a >= 40) for a in survey.age]
survey.commutes_by_car = [c === missing ? missing : Float64(c == "Car") for c in survey.commute]
survey.rural = [n === missing ? missing : Float64(n == "Rural") for n in survey.neighbourhood]
survey.high_unequal = [u === missing ? missing : Float64(u >= 8)
for u in survey.unequal_treatment]
const DUMMIES = [:supports, :aged_40_plus, :commutes_by_car, :rural, :high_unequal]
DataFrame(dummy = DUMMIES,
ones = [count(==(1.0), skipmissing(survey[!, d])) for d in DUMMIES],
zeros = [count(==(0.0), skipmissing(survey[!, d])) for d in DUMMIES],
missing_n = [count(ismissing, survey[!, d]) for d in DUMMIES],
mean = [round(mean(skipmissing(survey[!, d])), digits = 4) for d in DUMMIES])5×5 DataFrame
| Row | dummy | ones | zeros | missing_n | mean |
|---|---|---|---|---|---|
| Symbol | Int64 | Int64 | Int64 | Float64 | |
| 1 | supports | 1318 | 1623 | 56 | 0.4481 |
| 2 | aged_40_plus | 1735 | 1064 | 198 | 0.6199 |
| 3 | commutes_by_car | 1124 | 917 | 956 | 0.5507 |
| 4 | rural | 613 | 2384 | 0 | 0.2045 |
| 5 | high_unequal | 1727 | 1270 | 0 | 0.5762 |
Keeping missing as missing matters more than it looks. Coding a non-response as 0 would silently recruit every respondent who skipped the question into the “does not support” camp, which is a different claim from “did not say”.
Q6 to Q10. Baseline support, in the control group only
Everything from here to the end of Part 1 uses the control group, so it measures support uncontaminated by the experimental treatment.
control = survey[survey.treatment .== 0.0, :]
const SCALE = [1 => "Strongly support", 2 => "Support", 3 => "Neither support nor oppose",
4 => "Oppose", 5 => "Strongly oppose"]
answered = count(!ismissing, control.carbon_tax_support)
distribution = DataFrame(
code = first.(SCALE),
response = last.(SCALE),
respondents = [count(==(Float64(k)), skipmissing(control.carbon_tax_support))
for k in first.(SCALE)])
distribution.percentage = round.(100 .* distribution.respondents ./ answered, digits = 1)
distribution5×4 DataFrame
| Row | code | response | respondents | percentage |
|---|---|---|---|---|
| Int64 | String | Int64 | Float64 | |
| 1 | 1 | Strongly support | 131 | 8.8 |
| 2 | 2 | Support | 557 | 37.3 |
| 3 | 3 | Neither support nor oppose | 282 | 18.9 |
| 4 | 4 | Oppose | 317 | 21.2 |
| 5 | 5 | Strongly oppose | 207 | 13.9 |
(control_group = nrow(control), answered = answered,
did_not_answer = nrow(control) - answered)(control_group = 1516, answered = 1494, did_not_answer = 22)All five counts and all five percentages match the published table. Note that 22 of the 1,516 control respondents did not answer, so the percentages are shares of 1,494.
ordered = reverse(distribution)
fig = Figure(size = (820, 480))
ax = Axis(fig[1, 1];
title = "Support outweighs opposition, but a third of the public is opposed",
ylabel = "% of respondents",
xticks = (1:5, ordered.response), xticklabelrotation = pi / 9,
limits = (nothing, (0, 44)))
barplot!(ax, 1:5, ordered.percentage; width = 0.6, color = series_color(1))
for (x, v) in zip(1:5, ordered.percentage)
text!(ax, x, v; text = string(v) * "%", fontsize = 11,
align = (:center, :bottom), offset = (0, 4), color = INK)
end
fig
The modal answer is “Support”, at 37.3%, and only 8.8% strongly support. Adding the two support categories gives 46.1%; the two opposition categories give 35.1%; 18.9% sit in the middle.
(support_share = round(mean(skipmissing(control.supports)), digits = 4),
from_the_table = round((distribution.percentage[1] + distribution.percentage[2]) / 100,
digits = 4))(support_share = 0.4605, from_the_table = 0.461)The dummy’s mean is 0.461, which is exactly the combined “support” plus “strongly support” share from the table — matching the published value. That identity is the whole reason the dummy is convenient: its average is the share.
So is carbon taxation popular in the UK? More people support it than oppose it, by about 11 percentage points. But two features of the distribution matter more than the sign:
- Support is broad and shallow, opposition is narrower and deeper. Only 8.8% strongly support, while 13.9% strongly oppose. The intense minority is on the opposing side, and intensity is what turns opinion into protest — which is what Part 2 is about.
- A third of the public is against it, and 18.9% more are uncommitted. A policy with 46% support is not one a government can treat as settled.
Q11 and Q12. Who supports it
function conditional(col, labels)
out = DataFrame(group = String[], respondents = Int[], support = Float64[])
for (v, label) in labels
sub = control[coalesce.(control[!, col] .== v, false), :]
s = collect(skipmissing(sub.supports))
push!(out, (label, length(s), round(mean(s), digits = 4)))
end
return out
end
vcat(conditional(:aged_40_plus, [0.0 => "Under 40", 1.0 => "40 and over"]),
conditional(:commutes_by_car, [0.0 => "Does not commute by car",
1.0 => "Commutes by car"]),
conditional(:rural, [0.0 => "Non-rural", 1.0 => "Rural"]),
conditional(:high_unequal, [0.0 => "Perceives less unequal treatment (0–7)",
1.0 => "Perceives unequal treatment (8–10)"]))8×3 DataFrame
| Row | group | respondents | support |
|---|---|---|---|
| String | Int64 | Float64 | |
| 1 | Under 40 | 528 | 0.5303 |
| 2 | 40 and over | 867 | 0.4141 |
| 3 | Does not commute by car | 451 | 0.5521 |
| 4 | Commutes by car | 562 | 0.4075 |
| 5 | Non-rural | 1174 | 0.4685 |
| 6 | Rural | 320 | 0.4312 |
| 7 | Perceives less unequal treatment (0–7) | 683 | 0.4949 |
| 8 | Perceives unequal treatment (8–10) | 811 | 0.4316 |
parties = DataFrame(party = String[], respondents = Int[], support = Float64[])
small = Float64[]
for p in sort(unique(skipmissing(control.partisanship)))
s = collect(skipmissing(control[coalesce.(control.partisanship .== p, false), :supports]))
if length(s) < 20
append!(small, s)
else
push!(parties, (p, length(s), round(mean(s), digits = 4)))
end
end
isempty(small) || push!(parties, ("Smaller parties (combined)", length(small),
round(mean(small), digits = 4)))
sort!(parties, :support, rev = true)
parties9×3 DataFrame
| Row | party | respondents | support |
|---|---|---|---|
| String | Int64 | Float64 | |
| 1 | Green Party of England and Wales | 142 | 0.6901 |
| 2 | Scottish National Party | 47 | 0.617 |
| 3 | Labour Party | 500 | 0.552 |
| 4 | Liberal Democrats | 140 | 0.5286 |
| 5 | Other | 44 | 0.5 |
| 6 | Smaller parties (combined) | 18 | 0.4444 |
| 7 | Conservative Party | 265 | 0.3434 |
| 8 | Prefer not to say | 42 | 0.2619 |
| 9 | Reform UK | 108 | 0.1667 |
Party is by far the strongest divide. Green voters support at 0.69 and Reform UK voters at 0.17 — a four-fold gap, and wider than anything else in the data. Labour (0.55), Liberal Democrat (0.53) and SNP (0.62) sit above the average; Conservative (0.34) below.
The demographic splits are real but much smaller:
- Age: under-40s 0.53 against 0.41 for those 40 and over — a 12-point gap.
- Car commuting: 0.55 for non-car commuters against 0.41 for car commuters. This is the cost channel in its most direct form: a carbon tax raises the price of fuel, and people who drive to work pay it.
- Rural: 0.43 against 0.47 non-rural — only about 4 points, which is the surprise.
That small rural gap is the puzzle Part 2 exists to explain. Rural residents are the group whose backlash the article is about, and on this measure they are barely less supportive than everyone else. Whatever drives rural opposition is not visible as a large average difference — it needs the mechanism, not the headline.
The last row points at it. Respondents who feel the state treats people unequally support at 0.43 against 0.49 for those who do not — a gap comparable to the rural gap, on a variable that is not about geography at all.
Two variables absent from this dataset that should matter:
- Income. A carbon tax is regressive relative to income, so willingness to pay for it should fall as income falls. Its absence is the biggest gap here, and it is likely correlated with several variables that are present, including car commuting.
- Home heating type. A household on oil or LPG — common in rural areas off the gas grid — faces a much larger bill from a carbon tax than one on mains gas or a heat pump, and unlike commuting it cannot be changed cheaply.
Either could account for part of what the party and commuting variables are currently absorbing.
Part 2 — Explaining rural backlashes
The argument is that rural opposition runs through perceived unfairness: rural communities believe the state already treats them unequally, and read a carbon tax as more of the same.
unequal_treatment measures agreement that the government treats people equally regardless of where they live, reverse-coded so that high values mean perceiving more unequal treatment. carbon_tax_unfairness measures agreement that a carbon tax is unfair because it falls on people the government has already disadvantaged.
Q1 to Q3. The correlation among rural respondents
rural_control = control[coalesce.(control.rural .== 1.0, false), :]
rural_table = DataFrame(perception = ["Low unequal treatment (0–7)",
"High unequal treatment (8–10)"])
for (col, label) in [(:carbon_tax_unfairness, "mean_unfairness"),
(:supports, "mean_support")]
rural_table[!, label] = [
round(mean(skipmissing(rural_control[coalesce.(rural_control.high_unequal .== v, false),
col])), digits = 4) for v in [0.0, 1.0]]
end
rural_table.respondents = [count(==(v), skipmissing(rural_control.high_unequal))
for v in [0.0, 1.0]]
rural_table2×4 DataFrame
| Row | perception | mean_unfairness | mean_support | respondents |
|---|---|---|---|---|
| String | Float64 | Float64 | Int64 | |
| 1 | Low unequal treatment (0–7) | 5.127 | 0.472 | 126 |
| 2 | High unequal treatment (8–10) | 6.203 | 0.4051 | 197 |
Both published figures reproduce: unfairness 5.1 against 6.2, support 0.47 against 0.41.
ok = .!ismissing.(rural_control.unequal_treatment) .&
.!ismissing.(rural_control.carbon_tax_unfairness)
(rural_control_respondents = nrow(rural_control),
correlation = round(cor(Float64.(rural_control[ok, :unequal_treatment]),
Float64.(rural_control[ok, :carbon_tax_unfairness])), digits = 4),
n = count(ok))(rural_control_respondents = 323, correlation = 0.2029, n = 323)Among rural control respondents, perceiving unequal treatment goes with both finding the tax unfair and opposing it. The unfairness gap is 1.08 points on an 11-point scale; the support gap is 6.7 percentage points.
The correlation between the two continuous measures is 0.20 — positive and clearly present, but modest. That is worth stating plainly, because it is the honest version of the article’s claim: unequal-treatment perceptions are one input into fairness judgements about carbon taxes, not the dominant one.
And none of this is causal. Both variables are attitudes recorded in the same interview from the same person. A respondent generally aggrieved with government would score high on both without either causing the other. That is precisely what the experiment is for.
Q4 to Q6. The information experiment
The treatment provides information about how the state treats different areas. If the article’s mechanism is right, that information should raise perceived unequal treatment, raise perceived unfairness of the tax, and lower support — among rural respondents.
rural_all = survey[coalesce.(survey.rural .== 1.0, false), :]
effects = DataFrame(outcome = String[], treated = Float64[], n_treated = Int[],
control = Float64[], n_control = Int[], difference = Float64[],
lower = Float64[], upper = Float64[], p_value = Float64[])
for (col, label) in [(:unequal_treatment, "Unequal treatment perception (0–10)"),
(:carbon_tax_unfairness, "Carbon tax unfairness (0–10)"),
(:supports, "Supports a carbon tax (0/1)")]
t = Float64.(collect(skipmissing(rural_all[rural_all.treatment .== 1.0, col])))
c = Float64.(collect(skipmissing(rural_all[rural_all.treatment .== 0.0, col])))
test = UnequalVarianceTTest(t, c)
lo, hi = confint(test)
push!(effects, (label, round(mean(t), digits = 4), length(t),
round(mean(c), digits = 4), length(c),
round(mean(t) - mean(c), digits = 4),
round(lo, digits = 4), round(hi, digits = 4),
round(pvalue(test), digits = 4)))
end
effects3×9 DataFrame
| Row | outcome | treated | n_treated | control | n_control | difference | lower | upper | p_value |
|---|---|---|---|---|---|---|---|---|---|
| String | Float64 | Int64 | Float64 | Int64 | Float64 | Float64 | Float64 | Float64 | |
| 1 | Unequal treatment perception (0–10) | 8.0483 | 290 | 7.6904 | 323 | 0.3579 | 0.0487 | 0.667 | 0.0234 |
| 2 | Carbon tax unfairness (0–10) | 6.1276 | 290 | 5.7833 | 323 | 0.3443 | -0.0438 | 0.7324 | 0.082 |
| 3 | Supports a carbon tax (0/1) | 0.3169 | 284 | 0.4312 | 320 | -0.1143 | -0.1913 | -0.0374 | 0.0036 |
All three p-values match the published solutions: 0.023, 0.082 and 0.004.
fig = Figure(size = (960, 420))
for (k, (col, label, limits)) in enumerate([
(:unequal_treatment, "Unequal treatment\nperception (0–10)", (7.0, 8.6)),
(:carbon_tax_unfairness, "Carbon tax\nunfairness (0–10)", (5.2, 6.7)),
(:supports, "Supports a\ncarbon tax", (0.25, 0.50))])
ax = Axis(fig[1, k]; title = label, titlesize = 12,
xticks = (1:2, ["Control", "Treatment"]), limits = (nothing, limits))
for (j, arm) in enumerate([0.0, 1.0])
v = Float64.(collect(skipmissing(rural_all[rural_all.treatment .== arm, col])))
half = 1.96 * std(v) / sqrt(length(v))
barplot!(ax, [j], [mean(v)]; width = 0.45, color = series_color(j),
label = j == 1 ? "Control" : "Treatment")
errorbars!(ax, [j], [mean(v)], [half];
color = INK_SECONDARY, whiskerwidth = 12, linewidth = 2)
end
end
Legend(fig[0, 1:3], fig.content[1]; orientation = :horizontal, framevisible = false)
fig
The experiment supports the mechanism, and the ordering of the three results is the interesting part.
- Unequal treatment perception rises by 0.36 points [0.05, 0.67], p = 0.023. The information did what it was meant to do: it changed the belief the article says is upstream of everything else.
- Carbon tax unfairness rises by 0.34 points [−0.04, 0.73], p = 0.082. Same direction, similar size, but the interval includes zero. On a conventional 5% threshold this is not significant, and it is the middle link in the causal chain.
- Support falls by 11.4 percentage points [−0.19, −0.04], p = 0.004. The largest and most precisely estimated of the three.
Why the middle link being weakest is awkward for the mechanism. The proposed chain runs information → unequal-treatment perception → unfairness perception → lower support. The two ends move clearly and the middle does not quite. If unfairness were the channel carrying the effect through to support, it should be at least as well identified as the outcome it explains.
Two readings, and this design cannot separate them:
- The chain holds and the unfairness measure is noisy. An 11-point agree/disagree scale is a coarse instrument for a specific belief, and measurement error attenuates exactly this kind of intermediate estimate. Its point estimate is the right sign and a comparable size.
- Information affects support through some other route — general grievance with government, or simply priming a rural identity — and unfairness is a correlate rather than the conduit.
Distinguishing them needs a design that manipulates unfairness perceptions directly, or a formal mediation analysis with its own assumptions. What the experiment does establish is the part that matters most for the article’s headline: telling rural respondents about unequal treatment causes them to withdraw support for a carbon tax.
What this establishes, and what it does not
Established. Rural support for carbon taxation is causally sensitive to beliefs about how the state treats rural areas. An 11-point fall from a short information treatment is a large effect for a survey experiment, and it is not explicable by rural respondents differing from urban ones in some fixed way, because the comparison is within rural respondents randomly assigned.
Not established. Three limits worth being explicit about:
- Survey responses are not votes or protests. The Gilets Jaunes did not fill in a Likert scale. Whether a stated 11-point shift corresponds to political behaviour is outside this design.
- The treatment is information a researcher chose to provide. Its effect size depends on that content, and it says how malleable the belief is, not how much of real-world rural opposition the belief currently explains.
- Durability is unknown. The outcome is measured minutes after the treatment. Attitude effects from information provision are known to decay.
What it implies for policy, taking Part 1 together with Part 2: the rural support gap is small on average (about 4 points) but highly responsive to fairness framing. A carbon tax introduced without visible attention to distribution across places has a latent constituency against it that can be activated by a single piece of information. Revenue recycling targeted at the places that pay most is the obvious lever, and it is aimed at exactly the belief this experiment shows is doing the work.
What this project covered
| Concept | Where | In Julia |
|---|---|---|
| A scale coded opposite to its description | Q1 Q3 | check counts against the published table |
| Dummy variables preserving missing | Q1 Q4 | s === missing ? missing : Float64(s <= 2) |
| The mean of a dummy as a share | Q1 Q10 | mean(skipmissing(col)) |
| Conditional means by subgroup | Q1 Q11 | mask, skipmissing, mean |
| Suppressing tiny subgroups | Q1 Q11 | pool categories under 20 respondents |
| Treatment vs control difference | Q2 Q6 | UnequalVarianceTTest, confint, pvalue |
| Error bars on group means | Q2 Q6 | errorbars! with 1.96 * sem |
| Panels for different scales | Q2 Q6 | one Axis per outcome, own limits |
| Reversing a table for display | Q1 Q8 | reverse(df) |
The R → Julia page has the full translation table.