Conventional approaches for examining the Kuznets hypothesis often assume a particular parametric (quadratic) specification among variables. In contrast, this study uses a flexible nonlinear inference approach proposed by Hamilton [Econometrica 69 (2001) 537; J. Econom. 113 (2003) 363] to test for the validity of an inverted-U shape of the Kuznets hypothesis. The new framework permits the data to determine whether or not the relation is nonlinear, what the nonlinearity looks like, and whether the relation can be adequately described by a specific parametric model. An empirical application suggests that there is dramatic evidence of nonlinearity and there exists an inverted-U relation between inequality and per capita GDP, confirming the Kuznets hypothesis. Moreover, we also test if the commonly used quadratic regression can adequately capture the nonlinearity and find that the simpler parametric model is able to describe the nonlinear relation suitably.
