A. Statistical Discrimination Suppose that individuals come from one of two distinguishable groups, J and K. Prospective employers offer wages based on a weighted combination of an individual-level measure of expech productivity, T.- (\"test score\") and the mean test score of the group of which individual 2' is a member, TJ or TK. In particular, the wage offer to an individual i of each group is given by W23] =(1aJ)TJ+aJ WiK = (1 01K)T_K + axTn (1) l r where 0 5 (1;, S 1 and 0 5 0K 5 1 are the weights placed on the group averages. f 1. (4) Assume that try = ox = a > 0. Prove that an individual with any given score T; will be paid more if they come from the group with higher mean test scores. V 2. (4) We nowIalter our assumptions. In particular, assume that the groups have identical mean scores, that is, T) 2' TK = T. However, we now assume that the test is more informative about individuals who are members of group J, that is, aJ > aK. Prove that an individual 2' with test score T,- will be paid more if they are from group J than if they are from group K only if they score higher than the average on the test. NOTE You can illustrate the point by letting a; = 0.4,ax = 0.2, and drawing the wage schedules on a single diagram. B. Oaxaca Wage Decomposition Suppose that individuals come from one of two distinguishable groups, J and K. The mean wage rates in group J and K are equal to W'] = a") + [3.13] (2) WK = 01K + .5]{SK where 5'; and SK are the mean years of schooling among individuals from groups J and K. 1. (4 points) Find the difference in mean wages between groups J and K in terms of a J, _ and SK. Identify the portion of mean wage differences due to differences in skill and the portion of mean wage differences that might be attributable to discrimination. 2. (4 points) Explain briey why ambi guities might arise in intevpretz'ng the proportion of mean wage differences due to discrimination