Both theoretical and empirical research have found conflicting evidence as to what the relationship between economic growth and inequality is. There is some evidence for monotonic, linear positive or negative relationships. And then there is the much more plausible-sounding nonlinear, hump-shaped relationship.

My understanding is that more recent (empirical) evidence supports the nonlinear view. But there are still open questions such as what kind of shape the relationship takes exactly, or where exactly the turning point is.

In general, the problem with estimating a linear or higher order polynomial relationship is that we impose a functional form on the data. While it’s possible to try very high order polynomials, the problem is that these still impose functional forms on the data, which may result in inconsistent parameter estimates. Furthermore, the model might be too sensitive to outliers and produce “blips” in the relationship.

This is why Henderson, Qian and Wang (2015) use a nonparametric model to estimate the relationship between inequality and growth. This basically means that they do not explicitly assume that the relationship follows a specific (e.g. linear or quadratic) functional form.

Their sample covers 82 countries for the 1965-2003 period. They use the Gini coefficient to measure inequality. They estimate the “standard” parametric linear and quadratic models as well as their nonparametric specification. The results are shown in the figure below. The nonparametric curve is in orange.

We can see that if the Gini coefficient drops by more than ~15%, then the GDP growth rate is decreasing in inequality. In other words, dramatic drops in inequality (or equivalently increases in equality) are bad for growth. On the other hand, huge increases in inequality (30+%) are also bad for GDP growth. Between these two extremes, however, we have quite a big plateau where inequality and GDP are not related in an unambiguous way.

We can thus have three main conclusions.

- Extreme inequality is bad for growth.
- Too much equality (i.e. the lack of inequality) is bad for growth.
- Policies that don’t change inequality too much won’t have adverse/positive effects on GDP growth via inequality.

So this is almost consistent with a hump-shaped relationship. The main difference is that small to moderate changes in inequality have no effect on growth, so the hump-shape has a large plateau as seen above.

To finish this post, let us consider why these effects may arise. I think the most obvious is point #2 above. If we have too much equality, then in essence it’s hard to get rich (or poor). This will destroy incentives to work hard, take risks, be entrepreneurial or innovative, etc. Why do these things when returns to success are low, because for instance all your additional earnings will be heavily taxed by the government?

#1 is kind of the opposite of this. People in the middle class for instance might find that downside risks are too high. I.e. they’re afraid that if they make a risky move and fail, then they’ll be very poor because there’s no safety net. Alternatively, it’s possible that with high inequality, the middle class will mostly disappear. And the lower classes just won’t have enough resources to innovate and move upwards, while the upper classes will have a secure position and won’t risk their wealth much.

In both cases #1 and #2, the problem is that there is a lack of innovation, entrepreneurialism, risk taking, etc. Of course, there could be other reasons as well.

I think this nonlinear hump-shaped relationship is quite obvious and believable. What is, however, new and interesting is the big plateau in the relationship. Basically, there is no relationship whatsoever between growth and inequality for a very large region.

Caveats: this is a highly simplistic, correlational study. We can’t make too many inferences from it. And we’d have to see whether a more careful empirical investigation (with controls, instruments, etc.) and/or theoretical research can arrive at the same conclusion.

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