I have a new paper just published that provides more evidence that the effects of social media on political beliefs have tended to be small. Others scholars have published work reaching similar conclusions, but I think that seeing consistent results across a range of methods is useful. This paper uses fixed effects models of panel data collected from large, representative samples during both the 2012 and 2016 elections. The paper is open-access, and is available here:

https://doi.org/10.1371/journal.pone.0213500

UPDATE: Tom Jacobs provides a nice overview of the work at Pacific Standard, and there’s a short write up by Alex Lardieri in US News & World Reports, too.