Acemoglu et al. (American Economic Review 2008; 98: 808–842) find no effect of income on democracy when controlling for fixed effects in a dynamic panel model. Work by Moral-Benito and Bartolucci (Economics Letters 2012; 117: 844–847) and Cervellati et al. (American Economic Review 2014; 104: 707–719) suggests that the original model might have been misspecified and proposes alternative specifications instead. We formally test these parametric specifications by implementing Lee’s (Journal of Econometrics 2014; 178: 146–166) dynamic panel test of linear parametric specifications against a general class of nonlinear alternatives robustly and reject all these specifications. However, using a more flexible model proposed by Cai and Li (Econometric Theory 2008; 24: 1321–1342) we find that the relationship between income and democracy appears to be mediated by education, but results are not statistically significant.