This question is based on Thursday's breakout room. Suppose employers care about overall productivity Z, which is made up of two components, X and Y, such that Z=X+Y (and employers know this productivity function). Suppose there are two groups (male and female) whose average Zs are the same (i.e. Z_M =Z_F), but X_M < X_F and Y_M > Y_F (and again, employers know these population averages). (Averages are given by bold font.) Researchers decide to run a resume-based audit study where they randomize names based on gender (using typically male or female names) but hold constant Y. They provide no information on X. Now suppose the researchers provide information on both X and Y on the resumes. Which of the following are accurate conclusions?

If call-back rates are different, there is evidence of taste-based discrimination.

If call-back rates are different, there could be statistical discrimination, as employers could be making predictions about productivity based on differences across men and women.