Treatment Effects

If we are interested in determining the value of a new drug or a change in policy, then we would like to know the treatment effect. If we are the US Food and Drug Administration (FDA), we may want to know the treatment effect of a new drug on survival probabilities. If the treatment effect is large relative to the side-effects, the FDA approve the drug to be marketed in the United States.

The treatment effect can be defined as the difference in potential outcomes. As such it is not possible to observe the treatment effect for an individual patient or unit (see Identification). Even though we cannot observe treatment effects (the difference in potential outcomes) directly, we may be able to say something about the distribution of treatment effects. Even though for each patient or unit we only observe, at most, one of the potential outcomes, we may still be able to say something about the joint distribution of potential outcomes.

If we don't know the treatment effect but do know its distribution, is that useful?

It depends.

If we must choose between having a health system policy like Obamacare (the Affordable Care Act), and we knew that the average person was "better off" under Obamacare than they were under the previous system, then a total welfare maximizing government may want to institute the policy. I'm not saying they would or should and I'm not saying everyone is better off under Obamacare.

I am saying that if we know that the average person has a higher potential outcome under policy A with respect to policy B and everyone receives the same policy, then total welfare increases if policy A replaces policy B.

Alternatively, we may be able to learn that some positive proportion of the population has a higher potential outcome under treatment A relative to treatment B. Moreover, we may be able to learn that no one has a higher potential outcome under treatment B relative to treatment A. If a new drug helps some people and has no effect on other people, then we may want allow people to take the drug even if we don't know who is helped.