This paper examines the relationship between inequality and growth using non-parametric methods on cross-country data. It shows that changes in inequality (in any direction) are associated with reduced growth in the next period, and that this relationship is robust to variations in control variables and estimation methods. The inverted U-shaped relationship between inequality and growth is consistent with a simple political economy model, although causal interpretation is difficult due to identification problems. The non-linearity in the relationship explains why previous estimates of the relationship between inequality and growth differ. The paper also finds a strong negative relationship between changes in inequality and past inequality, and a negative relationship between growth rates and inequality lagged one period. The paper concludes that the evidence is reasonably consistent with a political economy model, but that the relationship is non-linear and cannot be interpreted causally due to identification issues. The paper also discusses the limitations of the data and the potential for measurement error to explain some findings. The paper finds that the inverted U-shaped relationship between changes in inequality and growth is robust to different specifications and that the relationship is not due to measurement error or reverse causality. The paper concludes that the evidence supports the idea that inequality and growth are related in a non-linear way, and that this relationship is important for understanding economic development.This paper examines the relationship between inequality and growth using non-parametric methods on cross-country data. It shows that changes in inequality (in any direction) are associated with reduced growth in the next period, and that this relationship is robust to variations in control variables and estimation methods. The inverted U-shaped relationship between inequality and growth is consistent with a simple political economy model, although causal interpretation is difficult due to identification problems. The non-linearity in the relationship explains why previous estimates of the relationship between inequality and growth differ. The paper also finds a strong negative relationship between changes in inequality and past inequality, and a negative relationship between growth rates and inequality lagged one period. The paper concludes that the evidence is reasonably consistent with a political economy model, but that the relationship is non-linear and cannot be interpreted causally due to identification issues. The paper also discusses the limitations of the data and the potential for measurement error to explain some findings. The paper finds that the inverted U-shaped relationship between changes in inequality and growth is robust to different specifications and that the relationship is not due to measurement error or reverse causality. The paper concludes that the evidence supports the idea that inequality and growth are related in a non-linear way, and that this relationship is important for understanding economic development.