That is from a new paper by De Kadt & Wittels. From the conclusions (p. 27):
The method used is complex, but very interesting.How does democracy affect economic prosperity? This paper applies a new empirical approach to answer this long-standing question. Using the synthetic control method and new balanced panel data for the period 1975-2008 we estimate unique treatment effects for every African country that democratized in the late 20th century. Our approach takes some important steps toward resolving the inferential problems that compromise existing country-level, cross-national research on the economic consequences of political regimes.First, we demonstrate with some confidence that democratization does, in fact, matter for economic output. These effects are highly heterogenous across countries: Some states appear to experience a considerable economic boost, while others are estimated to contract as a result of democratic reform. This pattern of effects is consistent with the common finding that democracy has a weakly positive average effect on eco- nomic growth. Further, we present evidence that corroborates some existing theories about the factors that moderate the economic effects of democratization.