This approach might work sometimes, but I think it is problematic in most cases for the following reason:
Health care spending can only affect health through medical interventions (unless it is possible to extend someone’s life by signalling that you care enough to spend money on health care).
If the study is designed to estimate the effect of some medical intervention, that intervention will be in the regression model. If you want to interpret the coefficient for health care spending causally, you have a major problem in that the primary causal pathway has been blocked by conditioning on whether the patient got the intervention. In such situations, the coefficient of health care spending would be expected to be zero even if it has a causal effect through the intervention.
This approach might work sometimes, but I think it is problematic in most cases for the following reason:
Health care spending can only affect health through medical interventions (unless it is possible to extend someone’s life by signalling that you care enough to spend money on health care).
If the study is designed to estimate the effect of some medical intervention, that intervention will be in the regression model. If you want to interpret the coefficient for health care spending causally, you have a major problem in that the primary causal pathway has been blocked by conditioning on whether the patient got the intervention. In such situations, the coefficient of health care spending would be expected to be zero even if it has a causal effect through the intervention.