Supplementary materials
Part 1. Decomposition of the effects from the GAM model into main effects and their interaction
While Figure 4 in the main text shows the predicted surface of happiness in terms of age and income, the figure below decomposes the main and interaction effects that combine to make the predictions. In the representation, the main effect of age is rather wiggly with a dip in middle age and a small recovery after. The main effect of income is positive and slightly curvilinear. The interaction surface is complex: for old people, the effect of income (on top of the main one) is flat, for young people it is negative (again, relative the main effect). For poor people, the effect of age is U-shaped, while for rich people it peaks in mid-life (relative to the main effect of age depicted in the top left panel). In this representation, the interaction effect is in sharper focus, while in Figure 4 in the main text, the predicted values of happiness are easier to trace.
Figure A1. Main and interaction effects of age and income on happiness, based on a GAM model with cubic splines for the main effects and tensor product smooths for the interaction
Part 2. Replication with life satisfaction as an outcome variable
The two figures below show the conditional effects of age and income when life satisfaction (also measured on a 0-to-10 scale) is used as the outcome variable instead of self-reported happiness. The inferences about the impact of age and income remain the same.
Figure A2. Effect of age on life satisfaction per income decile.
Figure A3. Effect of income decile on life satisfaction per age group.
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Part 3. Country variation in the unadjusted effects of age and income on happiness
Figure A4. Unadjusted effects of age and income on happiness per country.
Part 4. A 2D representation of the joint effects of age and income on happiness
Figure A5. Effect of age and income on happiness: a two-dimensional representation (equivalent to Figure 4 in the main text).
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Part 5. Effects of age and income decile on happiness, adjusted for socio-demographic predictors
Figure A6. Effect of age on the residuals of happiness, net of socio-demographic predictors
Figure A7. Effect of income on the residuals of happiness, net of socio-demographic predictors
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Part 6. Replication with equivalized income
This part of the Supplementary materials presents a replication of the main results with a version of the measure of income that is adjusted for household size (equivalized income1) (cf. Jebb et al. 2018). The ESS data does not allow for a precise measurement of equivalized income, because the household income is given only as a categorical variable, which tracks membership in one of ten ordered non- overlapping categories, each defined with a lower and upper limit (e.g. the second decile in Austria is defined between 12,600 and 18,100 euro).
Figure A8. Unadjusted effects of income on happiness, with the raw (left) and equivalised (right) measures of relative income
Nevertheless, I calculate a measure of equivalized income that relegates a household to a lower decile with a rising number of members of the household. For households originally placed in deciles 4 to 9, the first additional member of the household leads to a downgrading of 2 steps (e.g. from 9 to 7) and for 1 For the Eurostat definition and measurement of equivalized income, see:
https://ec.europa.eu/eurostat/statistics-explained/index.php?
title=Glossary:Equivalised_income
each additional one with one more step downgrade. These decisions are based on calculations that start with placing a respondent at the middle of the intervals of their respective income category and dividing this income by the size of the household, which is computed by adding 0.5 to the first additional
member and 0.3 thereafter. For deciles 2 and 3, the first additional household member leads to a downgrading of 1 step. For households in income decile 10, which does not have an upper boundary, the downgrade to category 9 starts with the third household member.
Figure A8 shows the unadjusted effects of income on happiness calculated with the raw measure of relative income (on the left) and the equivalized measure (on the right). The shape of the relationship is very similar with both measures. Equivalized income has a slightly less linear relationship with
happiness, with the lines flattening out to a greater extent after the 4th decile. The confidence intervals at the higher deciles are also wider, since fewer respondents are placed there with the equivalized
measure. Also note that the range of the y-axis is smaller in the right panel.
Figure A9. Effect of age on happiness for different equivalized income deciles.
Looking at how age and income interact with the equivalized measure of income leads to the following results presented in figures A9 and A10. The findings are quite comparable to the ones based on the unadjusted measure of income. For income deciles 1 to 3, the pattern is practically the same with just a bit less pronounced uptick in very old age (cf. Figure 2 in the main text and Figure A9). For income deciles 5 to 7, the relationship is flatter than estimated with the unadjusted measure of income. For income decile 10, the relationship with happiness is slightly increasing in a linear way with age.
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Looking at Figure A10 and comparing the patterns with the ones in Figure A3, we note that the shape of the relationships is very similar. Only for the age groups 61-to-70 and 71-80 the effect of equivalized income flattens out more considerably after income decile 5 or so.
Figure A10. Effect of equivalized income deciles on happiness for different age categories.
