In 1999, the Ontario government abolished Grade 13 of its secondary school curriculum. Since then, Ontario students enter university having completed 4 years of high school instead of 5. You want to estimate the effect of an extra year of high school on university performance. Suppose there are only two factors that determine university performance (y,): the number of years of high school (see notation below) and academic ability (hi). You estimate the following model using OLS estimation: ma=a+as+a (D where T,- is equal to 1 if the student had 5 years of high school prior to university (i.e. the student is part of the treatment group) and 0 if the student had 4 years of high school (i.e. the student is part of the c0ntrol group). Note: For this question, you can use the \"Consistency of a Mean of Function\" corollary (p.1042) to compute the plim (i.e. assume the variance of the functions are nite constants). a) If it is possible to randOmly assign students to either the control or treatment group (N4 students will have 4 years of high school and N5 will have 5 years. N4 + N5 = N) and to force students in the treatment group to take 5 years of schooling in high school and the control group to take 4 years, show that the OLS estimator of 31 will be consistent even if we omit h, in equation (1) (i.e. E,- = gh, + 11),). b) If it's not possible to randomly assign students to the treatment or control group, what will happen to the OLS estimator of 51 if cov'}, 11,)