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Question: Consider the following regression equation:
outcome = α0 + α1*after + α2*iron + δ*after* iron + e,
where outcome denotes earnings, after is equal to 1 after iron supplementation and zero before, iron indicates that the household have received iron pills, after ∗ iron is equal to 1 for households that have received iron pills, after they received them, and e is an error term. Please briefly answer the following questions:
(a) Suppose you were to simply sample people, ask whether they took iron or not, and run the following regression: outcome = α0 + α1*iron + e. What would you need to assume to interpret α1 as a causal estimate? Is this a reasonable assumption?
(b) Suppose that iron pills are given to randomly selected households and you observe household earnings before and after households are given the pills. How would you summarize the main effects of the iron supplementation on earnings.
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