The Classical Assumptions of Ordinary Least Squares Regression

The classical model of econometrics has nothing to do with ancient Greece or even the classical economic thinking of Adam Smith. Instead, the term classical refers to a set of fairly basic assumptions required to hold in order for OLS to be considered the “best” estimator available for regression models. When one or more of these assumptions do not hold, other estimation techniques (such as Generalized Least Squares) may be better than OLS....

The Classical Assumptions

1. The regression model is linear, is correctly specified, and has an additive error term.
2. The error term has a zero population mean.
3. All explanatory variables are uncorrelated with the error term.
4. Observations of the error term are uncorrelated with each other (no serial correlation).
5. The error term has a constant variance (no heteroskedasticity).
6. No explanatory variable is a perfect linear function of any other explanatory variable(s) (no perfect multicollinearity).
7. The error term is normally distributed (this assumption is optional but usually is invoked).

--A.H. Studenmund, Using Econometrics: A Practical Guide, 7th ed. (Boston: Pearson, 2017), 92-93.