Glossary

Heteroscedasticity

A condition in which the variance of the error term in a regression model is not constant across observations. When present, OLS estimates remain unbiased but are no longer efficient, and standard errors become unreliable.

Definition

Why It Matters

Ignoring heteroscedasticity can lead researchers to conclude that a coefficient is statistically significant when it is not, or vice versa, because standard errors are misestimated. In cross-sectional studies, heteroscedasticity often arises because larger units have larger variances. In time series, it manifests as volatility clustering. Robust standard errors and GARCH models address these issues, ensuring that statistical inference remains valid.

Example

A regression of Turkish household expenditure on income across 81 provinces shows that the variance of residuals increases with income, violating homoscedasticity. Applying White's robust standard errors increases the standard error of the income coefficient from 0.012 to 0.019, and the coefficient is no longer significant at the 1% level, correctly reflecting the underlying uncertainty.

Related Terms

Software Notes

SPSS: Analyze > Regression > Linear; save standardized residuals and plot against predicted values. Use the STATS WCORR extension for White's robust standard errors.
R: Use lmtest::bptest() for the Breusch-Pagan test. Fit robust standard errors with sandwich::vcovHC(). For weighted least squares, pass weights argument to lm().
Stata: Use estat hettest for the Breusch-Pagan test after regression. For robust standard errors, add , vce(robust) or , vce(hc3) to the estimation command.