Multiple regression analysis: Estimation and assumptions - Omitted variable bias
3 important questions on Multiple regression analysis: Estimation and assumptions - Omitted variable bias
Provide the definition for Omitted variable bias
Bias that is caused because the error term u contains factors or variables, that influence Y but are not included in the regression model
Why is it relevant to talk about omitted variable bias for estimation?
Because Omitted Variables can cause bias in the (OLS) estimator
Explain the intuition behind the Omitted Variable Bias formula
The difference between beta hat and beta is a ratio that converges in probability to something (lets call it A).
A itself is a product of 2 factors, one of which is the correlation between regressor X and error term u).
If that correlation = 0, then A will be 0 (multiplying by 0 = 0).
Therefore, A, which is difference between betahat and beta converges in probability to 0.
However with OVB, there is correlation between X and u and thus A does not converge to 0 and thus the difference between Betahat and Beta is not zero.
A itself is a product of 2 factors, one of which is the correlation between regressor X and error term u).
If that correlation = 0, then A will be 0 (multiplying by 0 = 0).
Therefore, A, which is difference between betahat and beta converges in probability to 0.
However with OVB, there is correlation between X and u and thus A does not converge to 0 and thus the difference between Betahat and Beta is not zero.
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