A government is considering making flu vaccines voluntary as part of a public health campaign. Let’s think of making flu vaccines voluntary as the treatment T. Write T = 0 if the government keeps flu vaccines mandatory and T = 1 if the government makes flu vaccines voluntary.
We will think of a binary outcomes from each person: either they stay healthy or they get sick. If person i stays healthy at treatment status T, we write her potential outcome as YTi = 1 and if she gets sick, we write it as YTi = 0. Suppose society is made up of three groups: the always sick, the never sick, and the vaccine responders. The always sick will get sick whether or not they get the flu vaccine. The never sick will always be healthy regardless of whether or not they get the flu vaccine. The vaccine responders will stay healthy if and only if they get the flu vaccine.
(a) Write down, in potential outcomes notation and as a number (0 or 1), each of the two potential outcomes for each of the three groups.
(b) Write down, in both potential outcomes notation and as a number (0 or 1), the causal effect of making flu vaccines mandatory for each of the three groups.
(c) Is there an effect, on average, of making flu vaccines mandatory in this society?