Heteroscedasticity occurs when the variance of errors is not constant across observations from "summary" of Introduction to Econometrics by Christopher Dougherty
Heteroscedasticity occurs when the variance of errors is not constant across observations. This violates one of the key assumptions of classical linear regression analysis, namely that the error terms are homoscedastic. In simpler terms, heteroscedasticity means that the variability of the errors changes as the values of the independent variables change. This can lead to biased and inefficient parameter estimates, as well as misleading inferences about the statistical significance of the estimated coefficients. When heteroscedasticity is present in a regression model, the usual OLS estimators remain unbiased and consistent, but they are no longer efficient. This means that while the estimators are still centered around the true parameter values on average, they are less precise and have larger standard errors. As a result, the estimated standard errors of the coefficients may be underestimated, leading to incorrect conclusions about the statistical significance of the estimated effects. One consequence of heteroscedasticity is that hypothesis tests based on standard OLS standard errors may be unreliable. In the presence of heteroscedasticity, the usual t-statistics and F-statistics may be biased, leading to incorrect conclusions about the significance of the estimated coefficients and the overall fit of the model. This can have serious implications for the validity of the results and the interpretation of the regression analysis. To address the issue of heteroscedasticity, researchers can use robust standard errors or weighted least squares estimation. Robust standard errors provide a way to correct for heteroscedasticity without changing the coefficient estimates, while weighted least squares estimation explicitly accounts for the changing variance of the errors by weighting observations based on their variance. Both methods can help to mitigate the effects of heteroscedasticity and improve the reliability of the regression results. In summary, heteroscedasticity is a common problem in regression analysis that can lead to biased and inefficient parameter estimates. Detecting and correcting for heteroscedasticity is important to ensure the validity and reliability of regression results. By using appropriate techniques to account for heteroscedasticity, researchers can obtain more accurate estimates of the coefficients and make more reliable inferences about the relationships between variables in their models.
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