I am currently writing my Master's thesis in which I aim at two things: 1) I try to find out if there are efficiency differences between public, private and non-profit hospitals 2) If efficiency increased or deceresead after the introduction of a new payment system.
My dataset contains roughly 1500 hospitals for each of the 13 years. The panel is unbalanced. I estimated the efficiency scores using Data Envelopment analysis. Now I would like to do a regression with the efficiency score as the dependent and some external factors (including ownership form but also patient age, case severity, region etc.) as the independent variables.
I am a bit confused about which regression to use, as I am unsure about how to interpret the results of FE regression. Some of the hospitals changed ownership during the period that the data covered, but I am not interested in change of efficiency after the hospitals became public or private (or whatever) but I am, at first, generally interested in finding out about basic efficiency differences. That is why I am leaning towards random effects regression rather than fixed effects (I will use the cluster robust option in STATA). In order to answer the second question, I created dummy variables for the time periods representing the old and the new payment system. Again, I am not sure which type of regression would be the adequate one. I performed the robust Hausman test which spoke for fixed effects regression, however, I am not sure if fixed effects will lead to the answer that I am looking for.
I would very much appreciate some insights on this (sorry if this is a bit confusing, I can elaborate on my intentions, if necessary)! Thank you very much!