How much of the relation between population mortality and unequal distribution of income is a statistical artefact?

British Medical Journal, Jan 31, 1998 by Hugh Gravelle

The absolute income hypothesis--that holding other factors constant, the higher an individual's income the better is their health--is supported by a considerable body of evidence.[1-3] However, according to the more recent relative income hypothesis, an individual's health is also afFected by the distribution of income within society. Someone with a given income would have worse health if he or she lived in a society with greater inequality of income than in a society in which income is more equally distributed.[4] Several recent papers examining the relation between population mortality and income inequality seem to support the relative income hypothesis.[5-11] They suggest that greater inequality is associated with higher population mortality and that this relation persists even when account is taken of the average income of the population.

However, some scepticism has been expressed about the relative income hypothesis.[12] To quote one of the papers cited above, the "mechanisms underlying the association between income distribution and mortality are poorly understood."[7]

A statistical artefact may explain the relation

There may be a very simple explanation for some, or all, of the reported associations between inequality of income and population health used to support the relative income hypothesis. They may be, at least partly, a statistical artefact caused by using population data rather than individual data. A positive correlation between population mortality and income inequality can arise at aggregate level even if inequality has no effect on the individual risk of mortality. Thus, we do not need the relative income hypothesis to explain the observed associations between population health and income inequality--the absolute income hypothesis will serve.

Mortality risk and absolute income

The absolute income explanation can be illustrated with the help of the figure (the mathematical argument is presented in the appendix). In this, the individual risk of mortality depends only on the income of the individual, as shown by the heavy line. As income increases, the risk of mortality falls, but it does so at a declining rate. Thus, an increase in income reduces the risk of mortality by a smaller amount at high incomes than at low incomes. Note that this model assumes that there is no relation between the distribution of income and the health of any member of the population. The risk of mortality depends on the absolute income, not the relative income, of the individual.

Mortality risk and inequality income

Now compare two countries here the average income is the same [bar] y but the distribution of income is different. To avoid cluttering the figure, suppose that in country A half the population has a low income of y,, and a high risk of mortality [m.sub.1A]. The other half has a higher income of [y.sub.2A] and therefore a lower mortality risk of [m.sub.2A]. The population mortality in country A is [m.sub.A] (the average of [m.sub.1A] and [m.sub.2A]). In country B income inequality is greater--half the population has an income of [y.sub.1B] (and a mortality risk of [m.sub.1B]) and the other half an income of [y.sub.2B] (and a mortality risk of [m.sub.2B). Although the difference in incomes between rich and poor is greater in country B, it has the same average income as country A. However, population mortality in country B, [m.sub.B] (the average of [m.sub.1B and [m.sub.2B]), is greater than the population mortality of country A.

Individual mortality and individual risk

The greater population mortality in the country that has a less equal income distribution (country B), results entirely from the shape of the relation between individual income and the individual risk of mortality. The higher income of rich people in country B compared with rich people in country A reduces their risk of mortality by [m.sub.2A] - [m.sub.2B] compared with rich people in country A. However, the lower income of poor people in country B compared with poor people in country A increases their risk of mortality by [m.sub.1B] - [m.sub.1A] compared with poor people in country A. Because the impact of income on mortality is smaller at higher incomes, the reduced mortality of the rich is more than offset by the increased mortality of the poor and population mortality is therefore higher in country B.

If mortality declines with income, but at a decreasing rate, transferring income from the poor to the rich will increase the mortality risk of the poor more than it reduces the mortality risk of the rich. Overall population mortality increases when inequality increases, even though every individual's risk of mortality depends only on their own income level and not on the income level of anyone else.

Aggregate estimates of data may distort individual risk

In a cross sectional study using population data for different countries or areas, the population mortality will be correlated positively with the degree of income inequality, even if income inequality does not affect e risk of mortality for individuals. The spurious or artefactual correlation at population level between population mortality and income dispersion will always occur if the effect of individual income on the individual risk of mortality is smaller at higher incomes than at lower incomes. This will be so even if there is no underlying relation between the distribution of income and the risk of mortality at the level of the individual.