Confounding and Conditional Means (Research Design)

Story: You want the causal effect of training on wages. Higher-ability workers are more likely to enroll in training, and ability also raises wages. So trained workers earn more partly because of training and partly because they have higher ability. What is the causal effect of training on wages?

Copy the following code into your .do file:

* simulate confounding dgp
	clear		all
	set		seed 314159
	set		obs 25000

* confounder
	gen		ability = rnormal(0, 1)

* training selection depends on ability (different rule than earlier exercise)
	gen		p_train = invlogit(-0.5 + 0.8*ability)
	gen		train = (runiform() < p_train)

* wage equation with noise (different levels and effect sizes than earlier exercise)
	gen		eps = rnormal(0, 4)
	gen		wage_lat = 20 + 3.5*train + 6*ability + eps
	gen		wage = max(wage_lat, 0)
	drop		wage_lat

* labels
	lab var		ability "ability (confounder)"
	lab var		p_train "p(train=1)"
	lab var		train "training (selected, not randomized)"
	lab var		eps "wage shock"
	lab var		wage "wage"

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

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

2. What is the naive difference in means (confounded)?

• Compute the difference in mean wage by train

3. What is the mean of ability with and without training (show selection)?

• Report mean ability by train

4. What is are the conditional differences in means (conditioning)?

• Create ability_q4 using xtile
• Report the differences in mean wage by train for the 3rd ability quartile