I am doing a study on manipulated hospital discharges using a similar methodology as this paper: https://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.20170092. In short, we observe that patients are more likely to be discharged directly after a higher tariff rate has been reached, leading to distribution of discharges such as this:
- I estimate the following probit model:
glm(close ~ time + time^2 + t_at + t_before , family = binomial(link = "probit"), data = mydata)
Where time is the duration of the treatment and the dummies are at the t=0 where the tariff changes and at t=-1, directly before the tariff changes.
- Next I calculate the probability of a discharge at t=0 and at t=-1 and calculate the hazard-ratio by dividing those two. This would indicate the speed at which the probability of discharge changes between those two times.
Instead of the steps in 2., the referees of my paper would rather see average marginal effects at t=0 and t=-1.
Question: If I calculate average marginal effects, can I still calculate their ratios and call that a hazard-ratio? I assume not. But how can I indicate the rate of change between the two times?
Note1: I do something similar to Table 4. in Eliason. I compare different subgroups to test whether certain patient characteristics affect the extent of discharge manipulation. The referee says that hazard-ratio is economically difficult to interpret and instead I should add interaction-terms to my probit model and calculate marginal effects for those. But the “rate of change” effect so nicely captured by Eliason is lost. Or is it not?
Note2: For example, when testing whether women are more likely to be manipulated I would run :
glm(close ~ time + time^2 + t_at + t_b4 + t_at*female + t_b4*female , family = binomial(link = "probit"), data = mydata)