Heteroskedasticity and Testing Regression Coefficients

Summary

The document asks whether a regression coefficient reported as significant at the 5% level can still be treated as significant when the model has persistent heteroskedasticity. It notes that attempts to address the issue with Box-Cox transformations and feasible generalized least squares have not resolved it. The response cautions that the original significance result alone is not conclusive and points to heteroskedasticity and autocorrelation consistent covariance estimates, such as Newey-West, as a way to obtain standard errors robust to heteroskedasticity.

The discussion is brief and does not provide a derivation, empirical example, or details on choosing a covariance estimator. It also makes a broad claim that feasible generalized least squares is robust to heteroskedasticity, without explaining the assumptions or conditions required. The practical lesson is to reassess inference using an appropriate standard error method rather than relying automatically on conventional regression errors; the specific correction should match the data and model assumptions.

Key ideas

• Conventional significance tests may be unreliable when regression errors are heteroskedastic.
• Robust covariance estimates can adjust standard errors for heteroskedasticity.
• Newey-West standard errors are suggested as one possible inference method.
• The response does not specify conditions for choosing an estimator or establish that feasible generalized least squares is always robust.

Tags

# Heteroskedasticity and significance of parameters


# Heteroskedasticity and significance of parameters












I am doing a regression analysis and my variable of interest turns out to be significant at the 5% level, but the model contains heteroskedasticity which can not be mitigated (using Box-Cox, Feasible generalized least squares).

Can I still conclude that my variable of interest is significant, or should I consider my result to be insignificant because of persistent heteroskedasticity?

Thank you!

## Answer by simmy (score 1)

https://quant.stackexchange.com/a/26029

You can conclude nothing: your parameters can be significant, but also not significant. If your data are heteroskedastic, you can use a correction to the standard error, that is Heteroskedasticity and Autocorrelation Consistent (HAC) covariance matrix of Newey and West: this computes standard errors robust to heteroskedasticity and you can conclude with more certanty about the significance of your parameters. Anyway, I think FGLS method is robust to heteroskedasticity.

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