Robust standard errors for cross-sectional data: what is a "large" sample size?

Question

I know that others have asked about robust standard errors (Robust standard errors in econometrics and Always Report Robust (White) Standard Errors?). An answer to the latter question made this reference to Wooldridge (2009):

The robust standard errors and robust t statistics are justified only as the sample size becomes large. With small sample sizes, the robust t statistics can have distributions that are not very close to the t distribution, and that can throw off our inference.

I have a cross-sectional dataset, and if the null hypothesis of the test for heteroskedasticity is rejected, what criteria should I use to determine if my sample size is "large enough" for a t distribution? I know that there have been a few posts that mention that the $n>30$ rule of thumb is flawed.

Note: I was unable to ask this question in the comments of the answer since I have not reacheda 50 reputation yet. My apologies in advance that this question is redundant.

Answer 1

This is more of a long comment, but I don't think such thresholds exist since they seem fairly dependent on the type of heteroskedasticity.

Moreover, there are several finite-sample adjustments that you can make to speed up convergence, such as multiplying the squared residuals by n/(n-k), which some software already does by default. Some of these adjustments are more involved than others.

Angrist and Pischke's book recommends using $\max \{het. robust,conventional\}$ errors (p. 307). This ROT seems to perform well in their simulation. Others recommend reporting both and letting the reader decide. Imbens and Kolesar (2012) offer a readable survey of this literature (including several simulations), though theirs is a more complicated solution.