# What do we know about the effect of income inequality on health?

This post briefly surveys some of the methods and results in the literature on health and income inequality, closing with some remarks on problems with the existing literature and where future research may take us. It is not intended as anything resembling a comprehensive survey; Lynch et al (2004) provides a useful review of the empirical literature up to that time.

### The issues.

Following work such as Wilkinson and Pickett’s The Spirit Level, the notion that income inequality causes low health has become popular. For example, Paul Krugman recently noted in a blog post titled “Inequality Kills,”

We have lots of evidence that low socioeconomic status leads to higher mortality — even if you correct for things like availability of health insurance. Some of the effects may come through self-destructive behavior, some through simple increased stress; think about what it feels like in 21st-century America to be a worker without even a high school degree. In any case […] what we’re looking at is a clear demonstration of the fact that high inequality isn’t just unfair, it kills.

Income inequality and poor population health are correlated across counties, lending support to the idea that inequality does indeed kill. For example, the graph to the right, from The Spirit Level, shows a scatterplot of Gini coefficients against an index of health and social problems: more inequality is correlated with more problems. But such graphs, as we will see, are hard to interpret, and we cannot conclude from the type of correlation it displays that inequality per se causes poor health.

Consider the ambiguity in the Krugman’s argument above: is it inequality, as in the title, that leads to poor health, or is it low socioeconomic status, as in the body? These are clearly related mechanisms, but they are different mechanisms.

Suppose societies A and B have identical income distributions up to the 90th percentile, but A’s distribution in the top decile is more “stretched out,” that is, the relatively rich are richer still in society A. If low personal income causes low health, all else equal the bottom 90% of people in A and B will have the same health. If health is socially determined in the sense that relative deprivation matters in addition to absolute deprivation, then the bottom 90% in society A will experience worse health than in B because in society A the bottom 90% are relatively worse off compared to B. And if more income dispersion causes lower health for everyone, then the richest 10% in society A may also experience lower health than in B. For both policy and scientific reasons, it’s important that we discover whether a person’s health is determined by his income alone, or by both his income and the incomes of the other people in his society.

### Conceptualizing the relationship between income and health.

The literature formalizes these issues as three paths from the distribution of income to a person’s health. First, a person’s income may cause that person’s health (the absolute income hypothesis). Health is only socially determined through this mechanism in the sense that every person’s income is socially determined, there is no further social effect holding individual income constant.

Second, a person’s income relative to other people in her reference group may cause her health (the relative income hypothesis). Finally, the dispersion of income in the society in which the person lives may cause her health, holding her income constant (the income inequality hypothesis). These mechanisms can be expressed:

• Absolute income hypothesis: $$h_i = f(y_i)$$
• Relative income hypothesis: $$h_i = g[ y_i – m(y) ]$$
• Income inequality hypothesis: $$h_i = h [ V(y_i) ],$$

where $$i$$ indexes people, $$h$$ is a measure of health, $$y$$ is income, $$f()$$, $$g()$$, and $$h()$$ are unknown functions, $$m(y)$$ is the income of a reference person (such as the median or mean person’s income), and $$V(y)$$ is the variance or other measure of dispersion of $$y$$ across people. All three mechanisms may occur at the same time, they are not exclusive.

### Pragmatic problems with the idea relative income matters.

The relative income and the income inequality hypothesis are less plausible on their face than the absolute income hypothesis: it is easy to think of reasons why your income causes your health (even in the presence of “free” health care), but it is harder to think of reasons why my income causes your health, as in the absolute and relative income hypotheses. Angus Deaton skeptically refers to the relative and inequality hypotheses as “action at a distance.”

Perhaps Deaton is overly skeptical, as animal studies and other evidence do lend support to the idea that low social position causes physiological changes which lead to poor health (e.g., the Whitehall studies, see Marmot et al 2001). More inequality may cause people low in the hierarchy to experience negative emotions such as stress and shame, which may directly cause low health and indirectly cause low health through behaviors such as substance abuse. However, we face a number of problems attempting to operationalize this notion, and in theory anything goes even if we accept assume this mechanism exists. Deaton, for example, asks us to consider these variants on the relative income hypothesis:

1. Your health depends on your rank in the social hierarchy.
2. Your health depends on the difference between your income and the richest person’s income.
3. Your health depends on the difference between your income and the poorest person’s income.

These all seem reasonable ways of modeling the notion that the social hierarchy affects health. Now consider the implications of a policy which reduces inequality without changing the ordering of income across people or changing mean income. Under 1, there is no effect at all on health, as we have not changed anyone’s rank in hierarchy. Under 2, average health goes up because the distance between the richest person’s income and a person’s income falls. And under 3, average health goes down as the distance between the poorest person’s income others’ incomes falls.

Another pragmatic problem is determining appropriate reference groups. Do you compare yourself to other people in your town? Your country? Your occupation, or your age, or your ethnicity, or your friends, or some combination of all of these and many other characteristics? In theory, this is easy—models assume there are groups 1 through $$G$$ and each agent $$i$$ is assigned a group $$g \in { 1, …, G}$$. In practice, reference groups are nebulous, and we will generally get different statistical answers depending on how we define reference groups.

### Aggregate data and the concavity effect.

Many studies attempt to use aggregate data to get at the effect of inequality on health, yielding results such as displayed as in the scatterplot of health and Gini coefficients above. Discovering that countries with more inequality tend to have lower public health is often interpreted as evidence of social causation of health operating through stress, social cohesion, or other psychological consequences of position in the social hierarchy. However, that conclusion does not follow.

One reason we’ll observe inequality and low health move together even if only the absolute income hypothesis holds is called the “concavity effect.” Suppose that the effect of an extra dollar on health is positive but lower than the effect of the previous dollar, that is, that $$f()$$ is concave, as in the graph to the right. Then, holding mean income constant, increasing the dispersion of income in a society mechanically decreases average health. Intuitively, if we take a dollar from a rich person and give it to a poor person, average health goes up if an additional dollar increases a poor person’s health more than a rich person’s health. The concavity effect implies that studies of aggregate data cannot help us disentangle the absolute, relative, and inequality hypotheses.

The concavity effect is sometimes referred to as a statistical artifact because it generates correlation between population health and income inequality that only operates through the absolute income effect. However, it is important to note that this is the effect we have the most evidence on, the evidence mostly agrees, and the evidence tells us that redistribution, so long as it does not destroy too much average wealth, will increase average health. Put another way, we do not have to believe that inequality per se causes stress or other mental or physical health issues to conclude that reducing poverty will increase population health.

### Evidence from disaggregated data.

With data on individuals we can shed some light on the relationship between income inequality and health, holding personal income fixed. Many papers estimate models similar to, or special cases of, specifications such as,

$$h_{ij} = X_{ij}\gamma + f(y_{ij}) + \alpha \bar y_j + \theta \sigma^2_{j} + u_{ij} \>\>\>\>\>\> (*)$$

where $$X_{ij}$$ is a vector of individual and contextual characteristics for person $$i$$ in country, region, or other reference group $$j$$, $$\bar y_j$$ is mean income within reference group, $$\sigma^2_j$$ is the variance or other measure of income dispersion in $$i$$’s reference group, $$f(y_i)$$ is some function of income, $$\gamma, \alpha$$ and $$\theta$$ are parameters to be estimated, and $$u_{ij}$$ is an error term representing other causes of health. Sometimes, $$f(y_i)$$ is assumed to be linear, which means that curvature in the individual–level relationship may appear as a social effect. Usually, it is a quadratic or step function, and rarely no structure is imposed and the model is estimated using semiparametric methods (as in Jones and Wildman 2008). These papers typically use large, individual level cross-sectional or repeated cross-sectional datasets with countries or regions within countries treated as reference groups; infrequently panels are used or reference groups are defined more narrowly, such as age-region cells.

The evidence from estimating such models provides at best weak support for the relative and inequality hypotheses. As opposed to results from aggregate models which robustly find higher inequality is associated with lower population health without controlling for absolute individual income, the signs of the estimated coefficients on inequality measures are very roughly equally negative or positive, and they are commonly statistically and substantively insignificant. These results lead some authors to draw conclusions such as “evidence favouring a negative correlation between income inequality and life expectancy has disappeared” (Mackenbach 2002) and “there seems to be little support for the idea that income inequality is a major, generalizable determinant of population health differences within or between rich countries” (Lynch et al 2004), whereas “the absolute income hypothesis… is still the most likely to explain the frequently observed strong association between population health and income inequality levels” (Wagstaff and Doorslaer 2000).

### VI. Where is the literature headed?

I’ll close by noting some of the remaining difficulties with this literature, challenges to be overcome in future research.

As we’ve seen, the literature to date largely attempts to estimate partial associations between health, personal income, and aspects of the distribution of income. Even ignoring the ambiguities and problems discussed above, we cannot interpret the resulting estimates as plausibly reflecting causal effects.

At the individual level it is very likely that health causes income as well as income causing health. The income–health gradient in part reflects the disadvantages unhealthy people face in the labor market: health and income are simultaneously determined. Further, countless personal and contextual effects may cause both health and income, so models such as those estimated in the literature typically suffer from both simultaneity bias and omitted variables bias (for example, many studies fail to even condition on education, which is an important cause of both health and income). I expect to see more efforts to pin down the effect of individual income on individual health, and to tie such efforts to the burgeoning literature examining health over the life cycle, particularly the long-term effects of childhood development (e.g., Cunha and Heckman 2007). There is some evidence that some of the correlation between absolute health and income is attributable to what is here “reverse” causation from health to income (e.g., Boyce and Oswald 2011, Case and Paxson 2011). It’s difficult to see how we can credibly estimate the effect of unequal societies on health without making further progress on the effect of a person’s income on her health.

Omitted variables at the reference group (usually, regional) level are also a problem. In equation (*) above, the only reference group level variables are the mean and dispersion of income, implying that reference-group level causes of health which are correlated with the distribution of income may generate partial correlations between income distribution and health even if income distribution does not cause health. Deaton and Lubotsky (2003), for example, show that controlling for the proportion of black people at the regional level removes the association between inequality and mortality across U.S. cities. Which other demographic, policy, or institutional differences across regions cause both inequality and low health?

A related issue for future research is opening the black box and figuring out exactly how income inequality affects health. For example, Drabo (2010) argues that his results imply that more unequal incomes reduce demand for environmental quality, lower environmental quality causes lower health, and after netting out this mechanism there is no further effect of inequality on health. More unequal incomes may lead to changes in a variety of prices, access to various goods and services, the type and quality of various public programs, and changes in various notions of social capital. Which regional characteristics mediate the effect of income inequality on health? Is there an additional effect of inequality per se on health after holding constant personal income and all of the social causes of health which may themselves result from more inequality? At the moment, we simply don’t know.

We have much yet to learn about the effects of the distribution of income on health, and even the simpler issue of determining the effects of individual income on health.