1. In 2013, the parents in Lincoln School District decided to implement an intra-district choice system that allows parents to choose schools through- out the city, not just the one nearest their house. Jefferson School District decided to stick with its neighborhood schools system in which children at- tend schools in their neighborhood and they cannot choose other schools. You want to study the effect of this policy in Lincoln on the percent of students passing a standardized test. You collect data on the passing rates in 2012 and 2015 in each school, and the data is entered below: Lincoln Jefferson 2012 61% 67% 2015 64% 72% (a) What is the di'erence-in-difference estimate of the effect of the im- pact of the policy? (b) Suppose you have student-level data on whether students passed the test at Lincoln and Jefferson in 2012 and 2015. You estimate a linear regression model K3, = a + blLincolns + bgPostt + b3Post, * Lincolna + 31-3, Where the dependent variable is a dummy variable equal to 1 if student 2' in school 3 in year t passes the test, Lincoln, is a dummy variable equal to 1 if the student attends a school in Lincoln, and Post: is a dummy variable equal to 1 if the year is equal to 2015. Relate each of the passing percentages in the table above to the regression coefcients from this model. [Hint: we covered how to do this in class. Note that the sample mean of a dependent variable that is a dummy variable is the fraction of observations for which the dummy variable is equal to 1, which can be converted to a percentage by multiplying by 100]