A retail chain store offers a week long management training program to all its store managers at the end of the second year in their job.

A retail chain store offers a week long management training program to all its store managers at the end of the second year in their job. Participation in the program is voluntary. The central management of the chain store is interested in knowing whether participation in the program makes it more likely that store managers get promoted to more senior management positions. You have data on all the store managers, 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 of a binary variable on the promotion status (Y) on a constant and a dummy for participation in the training program (D).

(a) Suppose that central management encourages participation in the training program by sending a personal letter from the CEO to selected store managers who have been recom- mended by their supervisors as showing particular potential for a position in higher-level management. Would it be useful to use the CEO letter as an instrument for participa- tion 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 instru- ment or not. Explain in detail which condition(s) are violated.

(b) Suppose that central management encourages participation in the training program by sending a personal letter from the CEO to a randomly chosen set of store managers. Now compare this CEO letter to the one in (a). Does it fulfill the conditions violated by the letter in (a)?