36 Statistical Properties Homoskedasticity Assumption

This page introduces homoscedasticity in econometrics as the assumption that the variance of the error term is constant across all values of the independent variable, formally expressed as a constant conditional variance of the errors. It explains the idea intuitively using scatter plots, contrasting a uniform spread of points (homoscedasticity) with a funnel-shaped pattern (heteroscedasticity). The text emphasizes that while homoscedasticity is not required for OLS estimators to be unbiased, it is crucial for obtaining simple variance formulas, for the efficiency result of the Gauss–Markov theorem, and for reliable statistical inference. When the assumption is violated, standard errors, t-tests, and confidence intervals become unreliable. The page also clarifies what homoscedasticity does not imply, such as independence, normality, or causality, and concludes by highlighting its role in inference and suggesting further study of its formal implications.