please answer all the following questions
1. Assume the following union impact equation: W = 0.5CA + 0.004CA x U + 0.003CA + CR - 0.01CA x RLC + other control variables where W is the wage rate in the establishment. CA represents the existence of a collective agreement in the establislunent. U represents the percentage of the industry that is unionized, CR represents industry concentration. and RLC is the ratio of wage labour cost to value added. a. Theoretically justify the use of each of these explanatory variables. b. What sign would you expect for each regression coefficient? 1:. Why are the explanatory variables entered in the equation in that particular fashionthat is, multiplied by CA? 1!. What is the effect on wages of being covered by a collective agreement as opposed to not covered? e. Evaluate this effect at the following mean values of the explanatory variables: U = 40, G? = 7, m = 36. CHAPTER I5: UNION IMPACT ON WAGE AND NON-WAGE OUTCOME-'5 f. Compare this union impact in an establishment with the impact that would occur if the industry in which the firm operated was completely unionized, other things being equal. g. Compare the union impact of (c) with the impact that would occur if the ratio of wage labour cost to value added were only 20 percent as opposed to 36 percent. In. What does such an equation imply about the impact of the control variables on union and non-union workers? 1. How would you relax that implied assumption? 2. Assume you have estimated the following wage equations where W is the mean wage (or benefit), X is a vector of the mean values of the wage-determining characteristics, B is a vector of the estimated coefficients or returns to the characteristics, and the subscripts denote union and non-union status. WU = XuBu for union workers WN = XNBN for nonunion workers a. Illustrate the hypothetical wage, W*u that union workers would receive if they had their own characteristics (i.e., Xu) but were paid according to the nonunion pay structure for those characteristics. b. Show that the difference between this hypothetical wage and the actual wage of union workers is attributable to differences in the endowments of wage-determining characteristics between union and non-union workers, since both are paid according to the same pay structure, in this case the non-union returns, which are taken as the competitive norm. c. Show that the difference between the actual wage of union workers and the hypothetical wage they would earn if they were paid according to the non-union pay structure is attributable to differences in their returns for the same wage-determining characteristics, in this case the union characteristics. d. Add the differences calculated in (a) and (b) above to show that the average wage differential between union and non-union workers can be decomposed into two components: differences in the average value of the wage-determining characteristics, (XU - XN), evaluated according to the non-union returns, BN, and differences in the pay structure between union and non-union workers, (BU - BN), evaluated with the union characteristics, Xu. e. Give an interpretation to each of these two components in terms of union rents or wage premiums and endowments of wage-determining characteristics such as education or experience
