Heteroscedasticity

Heteroscedasticity refers to a situation in statistics and econometrics where the variability of a variable is unequal across the range of values of a second variable that predicts it. In contrast to homoscedasticity, where the variance of the errors is constant, heteroscedasticity is characterized by a change in spread over the levels of the independent variables.

Overview

Heteroscedasticity often arises in the analysis of cross-sectional data in economics, finance, and medicine, where the variability of the dependent variable may increase or decrease in response to changes in the independent variable. For example, in a study of the effect of income on health expenditure, it may be observed that the variability of health expenditure increases as income increases. This is an example of heteroscedasticity.

Detection

Several tests exist for detecting heteroscedasticity. These include the Breusch-Pagan test, the White test, and the Goldfeld-Quandt test. These tests generally involve regressing the squared residuals from a regression model on a set of explanatory variables and testing whether the explanatory variables are statistically significant.

Implications

Heteroscedasticity can lead to inefficient ordinary least squares estimates, though these estimates remain unbiased. It can also lead to incorrect inferences in statistical tests, as standard errors may be underestimated or overestimated in the presence of heteroscedasticity.

Remedies

Several remedies exist for dealing with heteroscedasticity. These include using robust standard errors, transforming the dependent variable (e.g., through logarithmic transformation), or using a heteroscedasticity-consistent covariance matrix estimator.

File:Heteroscedasticity graph.png

A scatter plot displaying the presence of heteroscedasticity.

See also

• Homoscedasticity
• Breusch-Pagan test
• White test
• Goldfeld-Quandt test
• Robust standard errors
• Logarithmic transformation