<p>I am creating econometrics notes and proved that, with normally distributed errors, homoskedasticity, and no serial correlation, t-stats based on baseline OLS standard errors do in fact follow a t-distribution.</p>
<p>I was trying to prove that, in the heteroskedastic, no serial correlation case with normally distributed errors, that t-stats based on robust standard errors follow a t-distribution. I was really struggling, then remembered that robust standard errors are known to be biased in finite samples (an example of a paper is <a href="https://www.sciencedirect.com/science/article/pii/S016517651200047X" rel="nofollow noreferrer">here</a>).</p>
<p>Is it the case that there is not a general result regarding the distribution of a t-stat created from robust standard errors in a finite sample? Stata reports t-stats rather than z-scores, so I'm not sure.</p>

CC BY-SA 4.0
2023-04-28T00:56:25.543Z
A robust t-stat does not have a t distribution in finite samples.
chan1142
CC BY-SA 4.0
2023-04-28T08:33:31.297Z
Thank you for confirming. That sounds right. Feel free to make this an answer rather than a comment, however for an "answer" they may expect a reference or some more of an explanation.
Michael Gmeiner
<econometrics><heteroskedasticity><hypothesis-testing>
Do t-stats created with robust standard errors follow a t-distribution in finite samples?
Michael Gmeiner
# Do t-stats created with robust standard errors follow a t-distribution in finite samples?

(Asked by: username_0 on 2023-04-27)

I am creating econometrics notes and proved that, with normally distributed errors, homoskedasticity, and no serial correlation, t-stats based on baseline OLS standard errors do in fact follow a t-distribution.

I was trying to prove that, in the heteroskedastic, no serial correlation case with normally distributed errors, that t-stats based on robust standard errors follow a t-distribution. I was really struggling, then remembered that robust standard errors are known to be biased in finite samples (an example of a paper is [here](https://www.sciencedirect.com/science/article/pii/S016517651200047X)).

Is it the case that there is not a general result regarding the distribution of a t-stat created from robust standard errors in a finite sample? Stata reports t-stats rather than z-scores, so I'm not sure.

**Tags:** econometrics, heteroskedasticity, hypothesis-testing

> **Comments:**
> **username_1**: A robust t-stat does not have a t distribution in finite samples.  
> **username_0**: Thank you for confirming. That sounds right. Feel free to make this an answer rather than a comment, however for an "answer" they may expect a reference or some more of an explanation.  

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## 0 answers

