<p>Read Arellano (1987, Oxford Bulletin of Economics and Statistics)</p>

CC BY-SA 3.0
2016-01-10T01:42:34.207Z
2016-01-10T01:42:34.207Z
none
<p>No. White's robust errors are only robust to errors that vary linearly based on X(t).  If you have a type of serial correlation or clustering you will want to use Hansen method to adjust standard errors.</p>

CC BY-SA 3.0
2015-05-22T02:05:58.067Z
2015-05-22T02:05:58.067Z
Stuart Allan
<p>I want to ask about OLS White's 1980 "robust" standard errors. 
The key assumption, is that regression errors $u_i$ have distinct variances $σ_i^2$. Then the variance matrix is: $$\Sigma = \operatorname{diag}(\sigma_1^2, \ldots, \sigma_n^2)$$ with its White's estimator: $$\hat\sigma_i^2 = \hat u_i^2$$ This is the HCE (heteroscedasticity-consistent estimator). 
 Is the White's robust variance of $\hat{\beta}$ estimated by OLS assuming  independence? For example, assume that there is some $i,j$ such that $$Cov(u_i,u_j)\neq0$$ Because $i,j$ are part of a cluster. In that case $\Sigma$ is not diagonal but has the same diagonal as before. Will the White estimator converge to the diagonal of the true $\Sigma$?  </p>

CC BY-SA 3.0
2015-05-26T13:02:24.587Z
@Soccerman what's your motivation for diluting this post so much ? We should keep notations inline when possible, IMO, while spacing out equations is fine.
VicAche
<econometrics>
Are White's Robust standard errors robust to clustered errors?
user157623
# Are White's Robust standard errors robust to clustered errors?

(Asked by: username_0 on 2015-05-22)

I want to ask about OLS White's 1980 "robust" standard errors.
The key assumption, is that regression errors $u\_i$ have distinct variances $σ\_i^2$. Then the variance matrix is: $$\Sigma = \operatorname{diag}(\sigma\_1^2, \ldots, \sigma\_n^2)$$ with its White's estimator: $$\hat\sigma\_i^2 = \hat u\_i^2$$ This is the HCE (heteroscedasticity-consistent estimator).
Is the White's robust variance of $\hat{\beta}$ estimated by OLS assuming independence? For example, assume that there is some $i,j$ such that $$Cov(u\_i,u\_j)\neq0$$ Because $i,j$ are part of a cluster. In that case $\Sigma$ is not diagonal but has the same diagonal as before. Will the White estimator converge to the diagonal of the true $\Sigma$?

**Tags:** econometrics
> **Comments:**
> **username_1**: @Soccerman what's your motivation for diluting this post so much ? We should keep notations inline when possible, IMO, while spacing out equations is fine.  

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## 2 answers

### Answer by username_3 on 2015-05-22. Score: 4 | Accepted answer

No. White's robust errors are only robust to errors that vary linearly based on X(t). If you have a type of serial correlation or clustering you will want to use Hansen method to adjust standard errors.


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### Answer by username_2 on 2016-01-10. Score: -1

Read Arellano (1987, Oxford Bulletin of Economics and Statistics)


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