# Empirical project 11 Solutions

These are not model answers. They are provided to help students, including those doing the project outside a formal class, to check their progress while working through the questions using the Excel or R walk-throughs. There are also brief notes for the more interpretive questions. Students taking courses using Doing Economics should follow the guidance of their instructors.

## Part 11.1 Summarizing the data

1. Surveys rely on respondents’ subjective opinions, which are subject to biases. These biases may affect the two types of answers differently. Public awareness of climate change issues has increased significantly over the past few decades, and people may feel morally obligated to conform to social norms and value the environmental costs highly. As a result, for DC surveys, respondents may be inclined to choose the maximum amount. For TWPL surveys, respondents may be inclined to report overly large values, shifting the distribution to the right and leading to large variations in reported values.

There are many other sources of bias for the surveys. For example, the subset of the population that participates in the survey may not be representative of the population. The design of questionnaires may also affect responses. However, for the purpose of comparing the differences between survey types, these biases may not be as significant.

• The solution depends on your software and is not shown.
• The solution depends on your software and is not shown.
1. (a)(c) The solutions depend on your software and are not shown.
• Solution figures 11.1, 11.2, and 11.3 provide solutions for all the indices. Values are rounded to two decimal places.
scepticism_2 scepticism_6 scepticism_7
scepticism_2 1.00
scepticism_6 0.39 1.00
scepticism_7 0.42 0.46 1.00

Correlation table for ‘climate change beliefs’ items.

Solution figure 11.1 Correlation table for ‘climate change beliefs’ items.

cog_1 cog_2 cog_3 cog_4 cog_5 cog_6
cog_1 1.00
cog_2 0.25 1.00
cog_3 0.32 0.12 1.00
cog_4 0.68 0.28 0.33 1.00
cog_5 0.29 0.41 0.02 0.27 1.00
cog_6 0.41 0.08 0.31 0.46 0.10 1.00

Correlation table for ‘preferences for government intervention’ items.

Solution figure 11.2 Correlation table for ‘preferences for government intervention’ items.

PN_1 PN_2 PN_3 PN_4 PN_6 PN_7
PN_1 1.00
PN_2 0.48 1.00
PN_3 0.43 0.63 1.00
PN_4 0.42 0.44 0.46 1.00
PN_6 0.41 0.50 0.52 0.57 1.00
PN_7 0.46 0.65 0.59 0.39 0.46 1.00

Correlation table for ‘personal responsibility for the environment’ items.

Solution figure 11.3 Correlation table for ‘personal responsibility for the environment’ items.

The correlations are all positive and most are moderately strong.

• Cronbach’s alpha assesses the internal reliability or consistency of a set of measures. Cronbach’s alpha ranges between 0 and 1 with 1 indicating maximum reliability. The coefficient values in question are high, suggesting that the indicators within each category measure the same underlying concept.
1. Solution figures 11.4 to 11.9 summarize the distribution of the variables. Values are rounded to two decimal places.
Gender TWPL (%) DC (%)
Female 51.78 52.29
Male 48.22 47.71

Gender of participants, by group.

Solution figure 11.4 Gender of participants, by group.

Age range TWPL (%) DC (%)
18–24 9.49 9.64
25–29 8.30 8.65
30–39 17.79 17.20
40–49 22.33 22.56
50–59 24.11 23.86
60–69 17.98 18.09

Age of participants, by group.

Solution figure 11.5 Age of participants, by group.

Level of Education TWPL (%) DC (%)
1 (In school) 1.19 1.29
2 (Without school degree) 1.98 2.09
3 (Secondary general school) 34.19 32.80
4 (Intermediate general school) 26.28 26.94
5 (Polytechnic school) 6.92 6.86
6 (University preparatory school) 29.45 30.02

Highest educational attainment, by group.

Solution figure 11.6 Highest educational attainment, by group.

Number of children TWPL (%) DC (%)
No children 64.62 65.71
One 20.36 17.59
Two 11.07 12.33
Three 2.96 3.48
Four or more 0.99 0.89

Number of children, by group.

Solution figure 11.7 Number of children, by group.

Membership TWPL (%) DC (%)
No 92.29 91.35
Yes 7.71 8.65

Environmental organization membership, by group.

Solution figure 11.8 Environmental organization membership, by group.

Income range (euros) TWPL (%) DC (%)
Less than 500 2.96 4.17
500–1,100 13.44 14.21
1,100–1,500 14.23 13.22
1,500–2,000 15.02 14.61
2,000–2,600 11.46 14.81
2,600–3,200 10.67 10.74
3,200–4,000 11.07 8.15
4,000–5,000 5.14 4.97
5,000–6,000 2.77 1.69
6,000–7,500 0.79 0.40
7,500 or more 0.40 0.50
Do not want to answer 12.06 12.52

Household net income per month in euros, by group.

Solution figure 11.9 Household net income per month in euros, by group.

These two groups look very similar in terms of demographic characteristics.

1. Solution figures 11.10, 11.11, and 11.12 provide summary tables for the indices.
Mean Std Min Max
Ref 2.37 0.85 1.00 5.00

Summary table for ‘climate change beliefs’ index.

Solution figure 11.10 Summary table for ‘climate change beliefs’ index.

Mean Std Min Max
Ref 3.19 0.66 1.00 5.00

Summary table for ‘preferences for government intervention’ index.

Solution figure 11.11 Summary table for ‘preferences for government intervention’ index.

Mean Std Min Max
Ref 3.01 0.82 1.00 5.00

Summary table for ‘personal responsibility for the environment’ index.

Solution figure 11.12 Summary table for ‘personal responsibility for the environment’ index.

The two groups are quite similar.

## Part 11.2 Comparing willingness to pay across methods and individual characteristics

• Solution figures 11.13 and 11.14 provide column charts for the variables.

Column charts of minimum WTP.

Solution figure 11.13 Column charts of minimum WTP.

Column charts of maximum WTP.

Solution figure 11.14 Column charts of maximum WTP.

The distributions are more left-heavy (higher number of lower values).

• The solution depends on your software and is not shown.
• Mean WTP is 268.53 and median WTP is 132.00 (rounded to two decimal places).
• Solution figure 11.15 provides the correlation between the average WTP and the demographic and attitudinal variables.
Variable Correlation
Education 0.14
Gender 0.04
Belief –0.14
Preferences –0.19
Feelings 0.19

Correlation table of average WTP and other variables.

Solution figure 11.15 Correlation table of average WTP and other variables.

The correlation coefficients are very low, suggesting that average WTP may not be strongly correlated with the variables.

• Solution figure 11.16 shows the table.
Amount (euros) No Yes Abstain Total
48 21 32 12 65
72 30 40 11 81
84 24 45 12 81
108 35 31 7 73
156 31 40 13 84
192 25 25 11 61
252 32 28 9 69
324 41 27 16 84
432 35 29 11 75
540 31 22 9 62
720 39 13 12 64
960 28 15 14 57
1,200 42 21 11 74
1,440 42 15 19 76
Total 456 383 167 1,006

DC format: Responses for each amount.

Solution figure 11.16 DC format: Responses for each amount.

• Solution figure 11.17 shows the percentage of individuals who voted ‘no’ and ‘yes’ for each amount. Values are rounded to two decimal places.
Amount (euros) No Yes
48 50.77 49.23
72 50.62 49.38
84 44.44 55.56
108 57.53 42.47
156 52.38 47.62
192 59.02 40.98
252 59.42 40.58
324 67.86 32.14
432 61.33 38.67
540 64.52 35.48
720 79.69 20.31
960 73.69 26.32
1,200 71.62 28.38
1,440 80.26 19.74

DC format: Reponses (in percentages), with ‘abstain’ counted as ‘no’.

Solution figure 11.17 DC format: Reponses (in percentages), with ‘abstain’ counted as ‘no’.

• Solution figure 11.18 shows the demand curve.

The demand curve is generally downward sloping, with the percentage voting ‘yes’ decreasing as the amount increases, though this relationship is not perfect due to the nature of the survey, with each individual only being asked their willingness to pay for one amount. (This curve therefore does not represent the sum of individuals’ willingness to pay at a given price, so is not a ‘demand curve’ in the strict sense.)

‘Demand curve’ from DC respondents.

Solution figure 11.18 ‘Demand curve’ from DC respondents.

• Solution figure 11.19 shows the percentage of individuals who voted ‘no’ and ‘yes’ with ‘abstain’ excluded. Solution figure 11.20 provides the demand curve.

The results do not appear to change drastically after excluding ‘abstain’ respondents.

Amount (euros) No Yes
48 39.62 60.38
72 42.86 57.14
84 34.78 65.22
108 53.03 46.97
156 43.66 56.34
192 50.00 50.00
252 53.33 46.67
324 60.29 39.71
432 54.69 45.31
540 58.49 41.51
720 75.00 25.00
960 65.12 34.88
1,200 66.67 33.33
1,440 73.68 26.32

DC format: Responses (in percentages), with ‘abstain’ responses excluded.

Solution figure 11.19 DC format: Responses (in percentages), with ‘abstain’ responses excluded.

‘Demand curve’ from DC respondents, under different treatments for ‘abstain’ responses.

Solution figure 11.20 ‘Demand curve’ from DC respondents, under different treatments for ‘abstain’ responses.

• In Solution figure 11.21, the extra row shows the calculated values for the difference in means. Values are rounded to two decimal places.
Format Mean Standard deviation Number of observations
DC 348.19 378.65 383
TWPL 268.54 287.70 348
Diff in means 79.65 475.50 731

Summary table for WTP.

Solution figure 11.21 Summary table for WTP.

• The ‘width’ of the confidence interval is 1.55, so the confidence interval is [79.65 – 1.55, 79.65 + 1.55], which is [78.10, 81.21]. The mean for the DC format is significantly higher (at the 5% level) than the mean for the TWPL format.
• The median for the DC format is 192, which is similar to the median for the TWPL format (132). In contrast, the mean for the DC format is almost double the mean of the TWPL format.
• The median is therefore more robust to changes in question format, and governments may want to use the median instead of mean WTP.