Malaria affects children to a much greater extent than adults and exposure to malaria in childhood can undermine health and educational outcomes later in life. Up until the 1920s, malaria was common in some districts of the United States and non-existent in others. However, during the 1920s, medical advances led to malaria being eradicated in most of the country. Suppose we estimate the following model. For individuali with birth year. income-o+, Post, + Malaria, + (Pont, x Malaria) + u where income, is individual i's income when she is 50 years old, Post, is an indicator for having been born in 1930 (after malaria was eradicated), Malaria, is an indicator for having grown up in an area where there had been malaria prior to eradication, and u is our unobservable term. Assume our data consist of two cohorts, those born in 1930 and those born in 1910. i. What is the interpretation of 8? Include conditional expectations in your answer. (3pts) ii. What is the difference-in-differences estimator in this context? Please write both the relevant 8 (or Bs) as well as the conditional expectations. (4pts) iii. What is the "control" group in this difference-in-differences setup? (3pts) iv. What is the primary assumption we need to be true for our difference-in-differences setup to provide us the right answer? (3pts)