Is there a happiness Kuznets curve?

The Kuznets curve is the inverted-U-shaped relationship between inequality and income per capita:

It was proposed by 1971 Nobel Prize winner Simon Kuznets. Kuznets' theoretical explanation for this relationship was that, at low levels of development, inequality was relatively low. Then, as a country developed, the owners of capital would be the first to benefit because of the greater investment opportunities that the economic growth provided. This would lead to an increase in inequality associated with economic growth. Eventually though, at even greater levels of development the taxes paid by the capitalists would increase, leading to developments such as a welfare state, improved education and healthcare, all of which would improve the incomes of the poor. So, at higher levels of development, inequality would decrease with economic growth. There is a fair amount of support for this relationship (for example, see my 2017 post on this topic).

Income per capita is one measure of wellbeing, albeit one that doesn't capture all aspects of wellbeing. An alternative measure that is increasingly being suggested is subjective wellbeing, or happiness. So, given that there is an inverted-U relationship between inequality and income per capita, it is reasonable and important to ask whether there is a similar relationship between happiness and 'inequality in happiness'.

That is the research question that this 2017 article, by Rati Ram (Illinois State University), published in the journal Economic Modelling (sorry I don't see an ungated version online), seeks to answer. Ram uses several sources of data on cross-national averages and standard deviations of happiness, and runs regressions to test for a quadratic relationship (a relationship that would show an inverted-U shape as in the diagram above). The measure of happiness is based on the Cantril Ladder, which measures subjective wellbeing on a 0-10 scale.

Using this country-level data, Ram finds that:

...it is evident that there is clear evidence of a Kuznets-type inverted-U relation between mean happiness and happiness-inequality represented by standard deviation...

The "turning point" implied by the specification... occurs when mean happiness is 4.93.

However, there is a serious problem with this analysis, and it results from the use of standard deviation as a measure of inequality of happiness.

Imagine all of the possible country-level distributions of happiness, measured on a 0-10 scale. On average, say that country-level happiness has an average of about 5.5 (in Ram's study, his three measures range from 5.38 to 5.91). Some of the country-level distributions have a high mean (higher than 5.5), and some have a low mean (lower than 5.5). And in each case, the distribution of each person's happiness is spread around the mean. And that spread can be measured by the standard deviation.

Now, think about the distributions that have a mean that is higher than 5.5. By definition, the highest possible mean is 10. As the mean gets larger, the top half of the distribution becomes closer to the mean (because nobody's happiness can be higher than 10). The result is that the standard deviation becomes smaller.

Similarly, for distributions that have a mean that is lower than 5.5. As the mean gets smaller, the bottom half of the distribution becomes closer to the mean (because nobody's happiness can be lower than 0). The result is that the standard deviation becomes smaller.

Now think about this overall. As the country-level mean happiness moves away from the overall mean value of 5.5, in either direction, the standard deviation will get smaller. This isn't because there is a Kuznets curve relationship; it is simply a mechanical result of the way that standard deviation is related to the mean, when the distribution is truncated at each end.

There may be a Kuznets curve relationship between happiness and inequality in happiness, but this study doesn't tell us anything about whether it exists. Standard deviation is not the right measure to use. A better measure of happiness inequality is required, which doesn't have a mechanical relationship with average happiness. I wonder if a Gini coefficient might work, or a Thiel Index? Both are more usual measures of inequality than the standard deviation. Identifying a better measure, and testing the relationship using the better measure, might make for an interesting Honours or Masters research project for a good student.