A variety of studies have undertaken to prove a connection from inequality to slower growth, but a full reading of the available evidence is that the evidence on this connection is inconclusive. For example, the OECD has recently published a report called "In It Together: Why Less Inequality Benefits All," and Chapter 3, titled "The Effect of Income Inequality on Economic Growth," offers an OECD analysis seeking to connect the two. But before presenting the new study, the OECD report has the honesty and forthrightness to point out that the full body of literature on this subject is inconclusive as whether such a relationship even exists--and if so, in what direction the relationship goes.
The report first points out (pp. 60-61 that as a matter of theory, one can think up arguments why greater inequality might be associated with less growth, or might be associated with more growth. For example, inequality could result less growth if: 1) People become upset about rising inequality and react by demanding regulations and redistributions that slow down the ability of an economy to produce growth; 2) A high degree of persistent inequality will limit the ability and incentives of those in the lower part of the income distribution to obtain more education and job experience; or 3) It may be that development and widespread adoption of new technologies requires demand from a broad middle class, and greater inequality could limit the extent of the middle class.
In passing, it's worth noting that the first reason falls into the category of "frustrated people killing the goose that lays the golden eggs." In other words, finding a correlation between rising inequality and slower growth could be a sign of dysfunctional responses to the rise in inequality.
On the other side, inequality could in theory be associated with faster economic growth if: 1) Higher inequality provides greater incentives for people to get educated, work harder, and take risks, which could lead to innovations that boost growth; 2) Those with high incomes tend to save more, and so an unequal distribution of income will tend to have more high savers, which in turn spurs capital accumulation in the economy. The report doesn't mention a third hypothesis that seems relevant in a number of developing economies, which is that fast growth may first emerge in certain regions or industries, leading to greater inequality for a time, before the gains from that growth diffuse more widely across the economy.
Given the competing theoretical explanations, what does the actual evidence say? The OECD writes
The large empirical literature attempting to summarize the direction in which inequality affects growth is summarised in the literature review in Cingano (2014, Annex II). That survey highlights that there is no consensus on the sign and strength of the relationship; furthermore, few works seek to identify which of the possible theoretical effects is at work. This is partly tradeable to the multiple empirical challenges facing this literature.The report then goes on to discuss issues like: 1) variations in estimation methods, including whether the analyst looks at one country over time, multiple countries at a point in time, or multiple countries over time, along with the statistical tools used; 2) in many countries around the world, the data on income distribution is not measured well, not measured consistently over time, and not measured in ways that are easily comparable to other countries; 3) in empirical studies the already-weak data on inequality is often boiled down into a single number, like a Gini coefficient or a ratio between those in the 90th and 10th income percentiles, a simplification that might miss what is happening; 4) the connections between income inequality and growth might differ across groups of countries (like high-income and low-income countries), and looking at all countries together averages out these various effects; and 5) whether (and how) the researcher should take into account factors like the extent of progressive taxation and redistribution, the extent of financial markets, or the degree of economic and social mobility over time.
There's an old saying that "absence of evidence is not evidence of absence," in other words, the fact that the existing evidence doesn't firmly show a connection from greater inequality to slower growth is not proof that such a connection doesn't exist. But anyone who has looked at economic studies on the determinants of economic growth knows that the problem of finding out what influences growth is very difficult, and the solutions aren't always obvious. For example, the OECD study argues that inequality leads to less investment in human capital at the bottom part of the income distribution. If this result holds up in further study, an obvious answer is not to focus on inequality directly, but instead to focus on additional support for human capital accumulation for those most in need.
There are a few common patterns in economic growth. All high-income countries have near-universal K-12 public education to build up human capital, along with encouragement of higher education. All high-income countries have economies where most jobs are interrelated with private and public capital investment, thus leading to higher productivity and wages. All high-income economies are relatively open to foreign trade. In addition, high-growth economies are societies that are willing to allow and even encourage a reasonable amount of disruption to existing patterns of jobs, consumption, and ownership. After all, economic growth means change.
On the other hand, it's also true that fast-growing countries around the world, either now or in the past, show a wide range of levels and trends of inequality, as well as considerable variation in the extent of government regulation and control, patterns of taxation and redistribution, structure of financial sector, and much more. Consider the pattern of China's fast economic growth in recent decades, with rising inequality and an evolving mixture of private initiative and government control. At least to me, China looks like a situation where growth is causing inequality, not where inequality is slowing growth. It may be that the question of "does inequality slow down economic growth" is too broad and diffuse to be useful. Instead, those of us who care about both the rise in inequality and the slowdown in economic growth should be looking for policies to address both goals, without presuming that substantial overlap will always occur between them.