Suppose you have access to data on a job training experiment for a group of men. Men could enter the program starting in January 1976 through about mid-1977. The program ended in December 1977. Men who signed up were randomly assigned into treatment and control groups. Men in the treatment group could choose to participate in the job training program while men in the control group could not. You want to test whether participation in the job training program had an effect on employment status in 1978. Specially, you have access to the following variables. unem78: A dummy variable which is 1 if individual I is unemployed all of 1978 and 0 otherwise. train;: A dummy variable which is 1 if individual i was assigned to the training program and 0 otherwise. unem74; and unem75: Dummy variables which are 1 if individual i was unemployed all of 1974 or all of 1975 respectively and 0 otherwise. age: Individual i's age in 1977 educ;: Individual i's years of education in 1977 black: Dummy variable which is 1 if individual I is black and 0 otherwise. hisp: Dummy variable which is 1 if individual i was Hispanic and 0 otherwise married: Dummy variable which is 1 if individual i is married in 1977 and 0 otherwise. You begin your analysis by estimating a regression of whether or not an individual was assigned to job training on your control variables. Below are the results with a couple of pieces of information removed (replaced by ?): -regress train unem74 unem75 age educ black hisp married, robust Linear regression Number of obs = F(7,437) 445 1.60 Prob > F = 0.1334 R-squared 0.0224 Root MSE = .49174 train Coef. Robust Std. Err. t P>|t| [95% Conf. Interval] unem74 0.02088 0.0772497 0.27 0.787 (.1309472) .1727072 unem75 (0.0955711) 0.0722763 (1.32) 0.187 (.2376234) .0464813 age 0.0032057 0.0033869 0.95 0.344 educ 0.0120131 0.0138597 0.87 0.387 (.003451) .0098624 (.0152268) .039253 black (0.0816663) 0.0888047 (0.92) 0.358 (.2562038) .0928712 hisp (0.2000168) 0.1132098 (1.77) 0.078 (.4225202) .0224865 married 0.0372887 0.0650005 0.57 0.566 (.0904638) .1650412 cons 0.3380222 0.1944555 1.74 0.083 (.044162) .7202064 a) (5 points) F-statistics reported by Stata in the top right of the regression table is associated with the null hypothesis that none of the explanatory variables are jointly significant, i.c.,unem74 = Bunem75 ==married = 0. Do you reject the null hypothesis at the 5% level? Why or why not? b) (4 points) What is the economic interpretation of the null hypothesis from part a)? Specifically, what do you conclude about the random assignment of job training to individuals? You next move on to estimating the effect of the job training program on employment status. -regress unem78 train, robust Linear regression Number of obs = 445 F(?,443) 6.50 Prob > F = 0.0111 R-squared = 0.0139 Root MSE = .45941 Robust Std. unem78 Coef. Err. t P>|t| [95% Conf. Interval] train (0.1106029) .0433918 (2.55) 0.011 (0.1958823) (.0253236) cons .3538462 .0297212 11.91 0.000 .295434 .4122583 c) (4 points) What is the economic interpretation of the estimated coefficient on train;? Be as specific as possible. d) (4 points) Even if you are convinced men were randomly assigned to the job training program, why might you still be concerned that you haven't recovered the causal effect of participating in the job training program on employment status? (Hint: Think about the definition of train; in regard to the question you set out to answer). e) (6 points) Suppose your concerns in part d) have convinced you that the OLS estimate from a regression of unem78, on train; does not answer your research question. Explain how you would still consistently estimate the impact of participating in the job training program on employment status using an instrumental variables approach. What other data, if any, would you need? What would your instrument, endogenous variable, and outcome be? Suppose that as a last exercise, you decide to investigate whether there any differences in how the job training program impacted employment across men of different race/ethnicity. Also, assume that traini is uncorrelated with the residual. Let trainblack; = train, * black, and trainhisp;= train; * hisp. You run the following regression. -regress unem78 train trainblack trainhisp black hisp, robust Linear regression Number of obs R-squared 445 = 0.0436 Root MSE = .4545 Robust Std. unem78 Coef. Err. t P>|t| [95% Conf. Interval] train (.0653595) .1192793 (0.55) 0.584 (.2997889) .1690699 trainblack (.0496972) .1290244 (0.39) 0.700 (.3032794) .2038851 trainhisp (.113212) .1397779 (0.81) 0.418 (.3879289) .161505 black .2142271 .098934 2.17 0.031 .0197839 .4086703 hisp .0021008 .1182197 0.02 0.986 (.230246) .2344477 cons .1764706 .0930891 1.90 0.059 (.0064852) .3594263 f) (5 points) What is the economic interpretation of the estimated coefficient on train? Be as specific as possible. g) (6 points) Are the difference in the effect of the job training program by race/ethnicity statistically significant. Explain why these differences are still economically significant.