1. The covid-19 vaccine becomes the top choice to prevent the spread of virus. However, different countries conduct their own R&D and have produced different vaccines. Now suppose there are two countries: the USA (produces vaccine A) and China (produces vaccine B). It has been shown that in the lab experiment, these two vaccines have the same effective rate on hospitalization.

Now, these two vaccines have been given in the field. In both countries, the first-round vaccinations are given to 1) doctors, nurses and other health care practitioners, 2) teachers in the education industry, and 3) other industries with relatively high-risk exposure. However, it has been reported that the effective rate on hospitalization of vaccine A is much lower than that of vaccine B.

1. Explain why in the field, the effective rate of vaccine is much lower than that of vaccine B.
2. Suppose you are invited to join the collaboration program between USA and China to conduct a randomized controlled trial to figure out whether there indeed exists a difference between two vaccines in the field.

1. Provide your detailed experiment design
2. List possible assumptions you will use.
3. Can you test these assumptions? If so, how to test?
4. Write the estimation equation. Explain why this estimation equation can provide the causal effect of the treatment. (Which causal effect can you obtain?)