Provide each questions more than five sentences detailed explanation.

The Ministry of Commerce in a large country wants to know the causal effect of membership in a local Chamber of Commerce on firm revenues and profits. Firms pay for their membership and they supposedly benefit from the network of information and contacts that the local Chambers of Commerce offer them. But usually, it is only a small minority of all firms that end up paying for the membership. The Ministry plans to estimate the causal effect of being a member in a local Chamber of Commerce by letting the Ministry's staff estimate the average percentage change in annual firm sales between firms that are members and the rest of the firms that are non-members of their local Chamber of Commerce. A) Write down the OLS regression specification that the Ministry's staff could use to implement their analysis described above. Interpret what the intercept and slope coefficients would capture in such a specification. B) Using notation from the Potential Outcomes Framework, briefly explain the concept of the Average Treatment Effect (ATE) to the Minister, and how what they plan to estimate in A) relates to this definition. C) Referring to the expressions you use in your answer to B), explain why a randomized control trial (RCT) could be useful, and very briefly describe the basics of the RCT design for how the Ministry could set this up. D) The Ministry mentions that it has no legal authority to force firms to become members in their local Chambers of Commerce. Using notation from the Potential Outcomes Framework, explain why this information could be important for the interpretation of the results from the RCT relative to the ATE, and how the Ministry should address this concern in the RCT analysis? E) The Ministry talked to other economists, and now it is worried about spillover effects on the control group. The staff don't fully understand what the concern is, however. Briefly explain to them the intuition behind this concern, and explain how they could potentially address it when designing the RCT.