We've already looked at one factor in the extension of the Mafia's power in "The Sicilian Mafia and the International Lemon Cartel".
Here we have some more recent research from MIT's Daron Acemoglu along with Giuseppe De Feo and Giacomo De Luca from the Universities of Strathclyde and York respectively.
From the Social Science Research Network, Posted: 7 Dec 2017:
Abstract
We document that the spread of the Mafia in Sicily at the end of the 19th century was in part shaped by the rise of socialist Peasant Fasci organizations. In an environment with weak state presence, this socialist threat triggered landholders, estate managers and local politicians to turn to the Mafia to resist and combat peasant demands. We show that the location of the Peasant Fasci is significantly affected by an exceptionally severe drought in 1893, and using information on rainfall, we establish the causal effect of the Peasant Fasci on the location of the Mafia in 1900. We provide extensive evidence that rainfall before and after this critical period has no effect on the spread of the Mafia or various economic and political outcomes. In the second part of the paper, we use the source of variation in the location of the Mafia in 1900 to estimate its medium-term and long-term effects. We find significant and quantitatively large negative impacts of the Mafia on literacy and various public goods in the 1910s and 20s. We also show a sizable impact of the Mafia on political competition, which could be one of the channels via which it affected local economic outcomes. We document negative effects of the Mafia on longer-term outcomes (in the 1960s, 70s and 80s) as well, but these are in general weaker and often only marginally significant. One exception is its persistent and strong impact on political competition.
If interested, here's the SSRN download page (65 page PDF)