The Job Training Partnership Act (JTPA) is a typical voluntary job training program for the disadvantaged in the US. You want to estimate the effect of JTPA on wages. For this, you observe a random sample of disadvantaged individuals in the US, some of which have participated in JTPA and others have not. To simplify the question, suppose there are only two factors that deter- mine wages (y,): whether you participated in J TPA (see notation below) and aspiration (as). You estimate the following model using OLS estimation: 111% = (31 + 52% + 5?: (5) where J, is equal to 1 if the individual participated in J TPA (i.e. the individ- ual is part of the treatment group) and 0 if the individual did not participate in J TPA (i.e. the individual is part of the control group). a) (5 points) If it were possible to randomly assign the disadvantaged individ- uals to either the control or treatment group (No individuals will be in the control group and N J will participate in J TPA. N0 + N J = N) and to force individuals in the treatment group to complete the J TPA and the control group not to enrol in it, would the OLS estimator of 62 will be consistent even if we omit to include a,- in (5) (i.e. s,- = 33a, + 1.0,)? Show your work. b) (5 points) Now, assume it is not possible to randomly assign individuals to the treatment or control groups, but you have access to an imperfect measure, 3,, of aspiration: 33?: = 010 + (116?: + Us (6) where 0:1 > 0, cov(u,:,w.,) = 0, cov(u,:,a,-) = O, cov(u,:, J,) = O and you run the following regression 111%? = '70 + 52% + 7215?: + \"U1:- Express \"yo, 72 and v,- in terms of the coeicients of equations (5) and (6). Do not forget that the error term in (5) is 5,- : ga, + 10,. c) (10 points) What will be the asymptotic bias (i.e. use plim) of the OLS estimator b2 in this case (i.e., case of subquestion b)) if cov(J,-, (1,) > 0? Hint