Heteroscedasticity refers to a situation in which the variability of the errors (residuals) in a regression model is not constant across all levels of the independent variable(s). It refers to the violation of the assumption of homoscedasticity in linear regression models (LRM).
Heteroscedasticity Consequences
A short detail about the Heteroscedasticity Consequences is described below:
- The OLS estimators and regression predictions based on them remain unbiased and consistent.
- The OLS estimators are no longer the BLUE (Best Linear Unbiased Estimators) because they are no longer efficient, so the regression predictions will be inefficient too.
- Because of the inconsistency of the covariance matrix of the estimated regression coefficients, the tests of hypotheses, (t-test, F-test) are no longer valid.
A detailed discussion about the Heteroscedasticity Consequences are:
- Inefficient Estimates: As a result of a violation of the homoscedasticity assumption, the OLS estimates become inefficient, that is, the estimators are not more Best Linear Unbiased Estimators (BLUE) and therefore, could have larger standard errors. The large standard errors may lead to incorrect conclusions about the statistical significance of the regression coefficients.
- Biased Estimates: Heteroscedasticity may lead to biased estimates of regression coefficients. In the case of heteroscedasticity, the ordinary least squares estimators (OLSE) are still unbiased, but they are no longer the most efficient estimators, as estimators may have larger possible variances. The estimated coefficients for the regressors may not accurately reflect the true population parameters.
- Incorrect Standard Errors: The standard errors of the regression coefficients are biased in the presence of heteroscedasticity, which leads to inaccurate inference in hypothesis testing, including incorrect t-test, F-test, and p-values. Researchers may mistakenly conclude that a variable is not statistically significant when it is, or vice versa.
- Invalid Inference: Larger standard errors may also lead to invalid inferences about the population parameters, it is because the confidence intervals and hypothesis tests based on these estimates may be unreliable and become wider to include the population parameter.
- Model Misspecification: Heteroscedasticity may indicate a misspecification of the underlying model. If the assumption of constant variance is violated, it suggests that there may be unaccounted-for factors or omitted variables influencing the variability of the errors. It suggests that the model may not be capturing all the variability in the data adequately.
- Inflated Type I Errors: Heteroscedasticity can lead to inflated Type I errors (false positives) in hypothesis tests. Researchers might mistakenly reject null hypotheses when they should not, leading to incorrect conclusions.
- Suboptimal Forecasting: Models affected by heteroscedasticity may provide suboptimal forecasts since the variability of the errors is not accurately captured. This can impact the model’s ability to make reliable predictions.
- Robustness Issues: Heteroscedasticity can make regression models less robust, meaning that their performance deteriorates when applied to different datasets or when the underlying assumptions are not met.
The Test of heteroscedasticity, such as the Breusch-Pagan test, or the White test of heteroscedasticity, and consider corrective measures like weighted least squares regression or transforming the data.
Learn about Remedial Measures of Heteroscedasticity
