# Comparing Classical and Robust (Huber-White/sandwich/heteroscedasticity consistent) Standard Errors in Linear Multiple Regression

I'm running a linear multiple regression model of the type

$y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \beta_3 X_{i3} + u_i$.

I came across King and Roberts' 2015 paper called "How Robust Standard Errors Expose Methodological Problems They Do Not Fix, and What to Do About It". The authors state: "In fact, robust and classical standard errors that differ need to be seen as bright red flags that signal compelling evidence of uncorrected model misspecification."

I was planning to use robust standard errors in my model, as I suspect that the data generation process is heteroskedastic. However, I'd like to compare the classical standard errors of my model (not using the robust option after the reg command) with the robust errors (using the robust option after the reg command). Using Stata 13.1, I'd like to know 1) how to obtain measures of both errors after running my "normal" and "robust" models, and 2) whether there is a particular significance test I could use to evaluate if the errors are significantly different.

• "how to obtain measures of both errors after running my 'normal' and 'robust' models" The standard errors are in the output, aren't they? Dec 11 '15 at 15:28
• "2) whether there is a particular significance test " I'm having trouble imagining such a thing. You might argue that if the change in the standard errors doesn't change your conclusions, you don't worry about it. Dec 11 '15 at 15:29
• I don't know the King and Roberts paper, but this is not a new thing to be saying. Robust (heteroscedasticity consistent) standard errors solve heteroscedasticity problems, but heteroscedasticity problems can mean you have misspecified the model, so you might need to add (say) an interaction term. If you didn't measure the variable that needs to be in the interaction, you can't. But that doesn't make you any worse off (IMHO) than any other regression - there might always be interactions with unmeasured variables that you haven't tested. Dec 11 '15 at 15:32
• I agree with all of @Jeremy Miles' comments. Insofar as this is about Stata, it is both off-topic and unclear what you are asking: in particular, the standard errors are shown in output. The underlying statistical question is unclear. It's a standard point that any model might be misspecified and that you should worry a lot about that. Dec 11 '15 at 17:56
• Many thanks for your comments @JeremyMiles and @NickCox! I did assume that there might be a specific measure to reflect the standard errors of the model as comparing the individual standard errors isn't that straightforward if there are several regressors. Dec 11 '15 at 18:24