Let's suppose I want to measure the impact of M&A in the hospital sector. I have a dataset containing hundreds of hospitals, a quality indicator and the type of ownership for each over a time period of 5 years (2005 - 2010). Some of the hospitals changed their ownership in 2005, some in 2008 and some didn't changed at all. For the hospitals that changed from nonprofit to profit, I want to measure if there was an impact on the quality. So basically, I want to compare the quality before and after the change of ownership and compared to other hospitals, which don't changed their ownership.
I thought about using the difference in difference approach, but I guess there's a problem, because I don't have that one year of intervention I can compare. Instead I have many different years (some hospitals may changed the ownership in 2006, some in 2009).
Could anybody please explain to me, which (regression-)model would be the right to use here?
I appreciate any kind of help!
Thanks in advance.