Collider Bias Simulation (Research Design)

Story: You want the causal effect of training on wages. You’ve collected data on people who are employed. Both training and wages affect whether someone is employed. What is the causal effect of training on wages?

Copy the following code into your .do file:

* simulate collider dgp
	clear		all
	set		seed 24684
	set		obs 50000

* train and wage are independent in the population
	gen		train = (runiform() < 0.5)
	gen		wage  = rnormal(0, 1)

* collider: inclusion depends on both train and wage
	gen		emp_lat = -0.3 + 0.7*train + 0.7*wage + rnormal(0, 1)
	gen		employed = (emp_lat > 0)

* labels
	lab var		train "training (randomized)"
	lab var		wage "wage (independent of training in population)"
	lab var		employed "observed in sample (collider)"

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

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

2. What is the naive difference in mean wages by training status among the employed?

• Compute the difference in mean wage by train using only observations with employed == 1

3. What is the mean probability of being employed with and without training (selection on employment)?

• Report the mean of employed by train

4. What is the difference in mean wages by training status in the full sample (unconditional)?

• Report the difference in mean wage by train using the full dataset