To Include or Not To Include.  That Is the Question.

We will consider a simple case that illustrates the more general problems.  We are interested in β, which is the effect of x on y. 

2-Var Model:  y = α + βx + ε

3-Var Model:  y = α + βx + δz + ε

  Truth:  2-Var Model Truth:  3-Var Model
Estimate:
2-Var Model
   
Estimate:
3-Var Model
   


Left-Out Variables, Irrelevant Variables, Multicollinearity, Testing

Proofs

Return

b = ∑xy / ∑xx