That's the topic of The Deterrent Effect of Tort Law: Evidence from Medical Malpractice Reform by profs Zenon Zabinski and Bernard Black. Here is the abstract:
A principal goal of tort law is to deter negligent behavior, but there is limited empirical evidence on whether it does so. We study that question for medical malpractice liability. We examine whether medical malpractice reforms affect in-hospital patient safety, using Patient Safety Indicators (PSIs) – measures of adverse events developed by the Agency for Healthcare Research and Quality – as proxies for overall safety. In Difference-in-Differences analyses of five states that adopt caps on non-economic damages during 2003-2005, we find consistent evidence that patient safety generally falls after the reforms, compared to control states.