Motivation. What if there are external variables that are related to ? We want to characterize how off we might be if we omitted a variable.

Omitting a Variable from a True 2-var Model

Assume the true model should have the following:

We didn’t take into account , and we mistakenly used the following model:

Then, our estimators and will be different from . We can state precisely how off they will be (=Omitted Variable Bias):

where is from the auxiliary regression

Omitting a Variable from a 3-var Model

  • True model:
  • Omitted model:
  • Estimator relationships:
  • Auxiliary regression:

General Form

For true model:

where is the omitted variable. Our omitted model: