Using non-parametrics to inform parametric tests of Kuznets' hypothesis

Simon Kuznets hypothesized that inequality in a country's distribution of income worsens in the early stages of its economic development and that the inequality improves as the country reaches higher stages of development (the 'inverted U hypothesis'). Empirical support for the inverted U hypothesis has been mixed. In testing Kuznets hypothesis, analysts have specified a variety of parametric forms for the relationship between inequality and development, including a quadratic form (a second-degree polynomial). Using data on income distributions on Native American reservations in the USA, the present analysis indicates that non-parametric estimates of the relationship can inform a parametric analysis. Specifically, while a regression with a second-degree polynomial finds mixed support for the hypothesis, the non-parametric analysis suggests the presence of such an inverse relationship. Indeed, the non-parametric form suggests that a polynomial of greater degree might better capture the relationship between economic development and income inequality. Hypothesis testing supports estimating a fourth-degree polynomial rather than a second-degree polynomial. All terms in the fourth-degree polynomial are statistically significant and the estimated coefficients support the Kuznets hypothesis. These regression results counsel caution in testing the inverted U hypothesis by estimating only parametric forms which produce strictly concave functions.