The issue of poverty traps is assessed using quantile regression. For that an augmentation of the usual convergence regressions by quadratic and cubic terms is used with emphasis on curve fitting rather than parameter estimation. The results show that the generic mechanism leading to poverty traps predominantly applies to countries with relatively low levels of income per capita or per worker that simultaneously have low growth rates around and below the lowest quintile of the growth rate distribution. The validity of the results is supported by a nonparametric variant of quantile regression.