Question

Please consider the effects of omitted variable bias, functional form problems, imperfect multicollinearity, and heteroscedasticity on regression results in general (not just this specific regression). Which of these problems is a violation of the classical linear model assumptions?

Answer 1

omitted variable bias

It arises if a relevant variable is excluded from the regression model. Below are the effects:

- Estimators become inconsistent

- Error Variance estimated by a mis-specified model is biased estimator of true population variance

- Confidence Intervals and Hypothesis Testing are likely to give misleading results about the statistical significance of estimated parameters

- Model forecasts and predictions would be unreliable.

Effects of functional form problems:

- If the functional form is incorrect, then both coefficients and standard errors would be unreliable

- Incorrect standard errors gives false result of T and F Tests.

- Usual Confidence Intervals would not be correct

Effects of imperfect multicollinearity:

- Regression coefficients have large standard errors and variance. This leads to fall in precision of OLS estimators

- Wider Confidence Intervals

- Insignificant t-ratios

- High coefficient of determination

Effects of heteroscedasticity:

- OLS estimators are still unbiased and linear but they are no longer BLUE (best linear unbiased estimator).

- Error variance is a biased estimator of population variance

- Hypothesis testing becomes unreliable.

violation of the classical linear model assumptions:

- Incorrect Functional forms would violate the assumption of linearity

- imperfect multicollinearity violate the assumption of no multicollinearity

- Presence of heteroscedasticity violates the assumption of Homoscedasticity