I'm dubious of empirical analyses (except when they confirm my preexisting priors, of course), but I nevertheless found Michael Klausner's overview very helpful and provocative:
This chapter examines the empirical literature on corporate law and governance in the United States. Four areas of the US corporate governance literature are discussed: (i) state competition to produce corporate law, (ii) independent boards, (iii) takeover defenses, and (iv) the use of corporate governance indices. The chapter concludes that these areas of research reflect varying degrees of success. The literature on state competition has been a major success. We know much more in this area as a result of empirical analysis in this area than we did on the basis of theory alone. At the other extreme is the literature on takeover defenses and the related literature that uses governance indices as measures of governance quality. Those empirical literatures are plagued by misunderstandings of how takeovers and takeover defenses work, and many results are therefore not as informative as they appear to be. In between is the literature on the impact of an independent board. Here, empiricists faced perhaps insurmountable challenges in proving causation, but nonetheless exposed informative associations.
Klausner, Michael, Empirical Studies of Corporate Law and Governance: Some Steps Forward and Some Steps Not (January 2018). Forthcoming Chapter of Oxford Handbook on Corporate Law and Governance (2018); European Corporate Governance Institute (ECGI) - Law Working Paper No. 381/2018. Available at SSRN: https://ssrn.com/abstract=3097568
