[1] 
	wage equation:			wage = 30 + 1.2*train + 1.8*productivity + 2.0*ability
	productivity equation:	productivity = 10 + 1.5*train + 1.0*ability + u_p

	substituting productivity into the wage equation:
	wage = 30 + 1.2*train + 1.8*(10 + 1.5*train + 1.0*ability + u_p) + 2.0*ability
	     = 30 + 1.2*train + 18 + 2.7*train + 1.8*ability + 1.8*u_p + 2.0*ability
	     = 48 + 3.9*train + 3.8*ability + 1.8*u_p

	true direct effect:   1.2   (coefficient on train in the wage equation)
	true indirect effect: 1.8 * 1.5 = 2.7 (productivity slope * train->productivity)
	true total effect:    1.2 + 2.7 = 3.9  (direct + indirect)

[2.1] 6.906

[2.2] -0.334 (no training); 0.428 (training)

[2.3] 3.869 for 3rd quartile (true effect = 3.9) 

[3.1] 6.437

[3.2] 0.893 (no training); 0.984 (training)

[3.3] -0.469

[3.4]
	conditioning on employed (a collider) opens a spurious path between
	training and wage. employed depends on both training and wage, so
	restricting the sample to employed == 1 induces a negative association:
	among the employed, those who trained needed lower wages to be retained,
	and those with high wages were retained even without training. this
	selection distorts the estimated training effect downward relative to
	the full-sample estimate.

[4.1] 6.906

[4.2] 4.050

[4.3] 2.856

[4.4] 1.656