Omitted-variable Bias - Effects On Ordinary Least Square

Effects On Ordinary Least Square

Gauss–Markov theorem states that regression models which fulfill the classical linear regression model assumptions provide the best, linear and unbiased estimators. With respect to ordinary least squares, the relevant assumption of the classical linear regression model is that the error term is uncorrelated with the regressors.

The presence of omitted variable bias violates this particular assumption. The violation causes OLS estimator to be biased and inconsistent. The direction of the bias depends on the estimators as well as the covariance between the regressors and the omitted variables. Given a positive estimator, a positive covariance will lead OLS estimator to overestimate the true value of an estimator. This effect can be seen by taking the expectation of the parameter, as shown in the previous section.