Heteroskedastia

Heteroskedasticity refers to a property of a regression model in which the variance of the error term, or the dependent variable, is not constant across observations. The term is most often used in econometrics and statistics; common spellings include heteroskedasticity and heteroscedasticity. Heteroskedastia is a less common variant and may represent a misspelling.

Causes of heteroskedasticity include nonlinearity, omitted variables, model misspecification, or data composition issues such as mixtures of subgroups with different variances, cross-sectional inequality, or time-varying volatility in repeated measures. In practice, heteroskedasticity often arises when the scale of the outcome grows with the level of an explanatory variable or when subpopulations with distinct variances are combined in a single dataset.

Consequences are most significant for inference. Ordinary least squares estimates of coefficients can remain unbiased and consistent in many cases, but the standard errors used for hypothesis tests become biased, leading to unreliable t-tests and confidence intervals. This can cause incorrect conclusions about relationships unless corrective methods are employed.

Detection involves both graphical and formal approaches. Residual plots can reveal patterns of increasing or decreasing spread, while tests such as Breusch-Pagan, White, Goldfeld-Quandt, and Koenker’s variants offer formal assessment. No single test is definitive, and multiple methods are often used alongside visual examination.

Remedies focus on robust inference and appropriate modeling. Using heteroskedasticity-robust standard errors (such as White’s or HC1), transforming the dependent variable (for example, a log or Box-Cox transformation), or applying weighted or generalized least squares can address the issue when the form of heteroskedasticity is known or can be reasonably modeled.