Maybe not. Daron Acemoglu, Simon Johnson, Pierre Robinson, and Pierre Yared report:
We revisit one of the central empirical findings of the political economy literature that higher income per capita causes democracy. Existing studies establish a strong cross-country correlation between income and democracy, but do not typically control for factors that simultaneously affect both variables. We show that controlling for such factors by including country fixed effects removes the statistical association between income per capita and various measures of democracy. We also present instrumental-variables using two different strategies. These estimates also show no causal effect of income on democracy. Furthermore, we reconcile the positive cross-country correlation between income and democracy with the absence of a causal effect of income on democracy by showing that the long-run evolution of income and democracy is related to historical factors. Consistent with this, the positive correlation between income and democracy disappears, even without fixed effects, when we control for the historical determinants of economic and political development in a sample of former European colonies.