Indirect least squares In (b), we used only some of the available variation in the INPRES program (in particular, we used only 2 age and 2 regional groups). Now we will use all of the regional variation. First, generate a new data set that contains the mean schooling of the young, mean schooling of the old, mean wage of the young, mean wage of the old, mean number of children in 1971, and mean program intensity, by region. (Hint: Use the collapse command, which was described in question (2)(d) of Problem Set #3. Note that in that question, you were calculating means for high- and low- intensity regions, age-by-age; in this question, you are calculating means for the young and old, region-by-region. Additional hint: your first line of Stata code should say something like generate educ_yng = yeduc if young == 1 ) Next, generate a variable called educ_dif which equals young mean education minus old mean education. Likewise, generate a variable called wage_dif which equals young mean log wage minus old mean log wage. i. The first stage is given by equation (4) in Lecture 8 notes: SYj - SOj = Pj + vj (where S denotes years of schooling; P denotes program intensity; Y and O index young and old; and j indexes the region). The equation is written as though the only right-hand-side variable is program intensity; however, the vj term can be understood to include the error term, the constant term, and any control variables (i.e., other right-hand-side variables). Note that the left-hand side of the equation is just educ_dif. Estimate by regressing educ_dif on program intensity, including the number of children in 1971 as a control variable; report the estimate. ii. The reduced form is given by equation (5): yYj - yOj = Pj + j (where y denotes log hourly wage). Note that the left-hand side of the equation is just wage_dif. Estimate by regressing wage_dif on program intensity, including the number of children in 1971 as a control variable; report the estimate. iii. Recall the wage-setting equation yi = ai + bSi , where y is log hourly wage. Taking means by region and cohort, we have that yYj = aYj + bSYj and yOj = aOj + bSOj . Subtracting the latter from the former, we get yYj - yOj = aYj - aOj + b( SYj - SOj ). Use this equation, along with the first-stage and reduced-form equations, to argue that b = / . iv. Divide the estimate of from the reduced form by the estimate of from the first