A bank offers a week long management training program to all its loan officers at the end of the second year in their job. Participation in the program is voluntary. The bank is interested in knowing whether participation in the program makes it more likely that a loan officer is promoted to branch manager. You have data on all the bank’s loan officers, their participation in the program, and whether they have been promoted between years three and five of being in their job. You run a regression for the promotion decision on a constant and a dummy for participation in the training program.
(a) Suppose the bank encourages participation in the training program by sending a personal letter from the CEO to selected employees who have been recommended by their supervisor as showing particular potential for a position in management. Would it be useful to use the CEO letter as an instrument for participation in the training program? Write down the instrumental variables model and explain whether using the CEO letter fulfills the validity and relevance conditions of an instrument or not. Explain in detail which condition(s) are violated.
(b) Suppose the bank encourages participation in the training program by sending a personal letter from the CEO to a randomly chosen set of employees. Now compare this CEO letter to the one in (a). Does it fulfill the conditions violated by the letter in (a)?