Mediation and Conditional Means (Research Design)

Story: You want the causal effect of training on wages. Training increases productivity, and productivity increases wages. So training can raise wages directly and also indirectly by raising productivity. What is the causal effect of training on wages?

Copy the following code into your .do file:

* simulate mediation dgp
	clear		all
	set		seed 13579
	set		obs 50000

* randomized training
	gen		train = (runiform() < 0.5)

* mediator: productivity increases with training
	gen		u_p = rnormal(0, 2)
	gen		productivity = 5 + 1.2*train + u_p

* outcome: wage depends on training directly and indirectly via productivity
	gen		u_w = rnormal(0, 5)
	gen		wage_lat = 25 + 1.0*train + 2.5*productivity + u_w
	gen		wage = max(wage_lat, 0)
	drop		wage_lat

* labels
	lab var		train "training (randomized)"
	lab var		productivity "productivity (mediator)"
	lab var		wage "wage"

	lab def		yesno 0 "no" 1 "yes", replace
	lab val		train yesno

1. What is the true direct causal effect of training on wages?

2. What is the naive difference in mean wages by training status (total effect)?

• Compute the difference in mean wage by train
• Save this value (the difference) as a scalar called total_hat

3. What is the indirect effect of training on wages through productivity?

• Compute the difference in mean productivity by train
• Save this value (the difference) as a scalar called delta_p
• Calculate the indirect effect as 2.5*delta_p (from the DGP)
• Save this value as a scalar called indirect_hat

4. What is the implied true direct effect once you subtract off the indirect effect from the total effect?

• Report the direct effect as direct = total − indirect