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I have made a model with several variables, and 8 of them interact with a dummy to find interaction effects. These are added stepwise, resulting in three models. Now, through a Breusch-Pagan test I have determined that my model contains heteroscedasticity.

I have determined that I will use HC4 (Cribari-Neto, 2004) for the HC standard error analysis, but am unsure how to continue. Thus, my question is:

Do I do the coeftest of the HC standard errors on the base model, or also on the models containing interaction effects?

Intuitively I would say that heteroscedasticity concerns the variables themselves and not necessarily their interaction effect, which means I would only do it on the base model. However, I have not been able to find any literature on this topic or situation.

Kind regards, DB

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  • $\begingroup$ There is in general no reason to suppose that heteroskedasticity would only relate to the variables. Consider the classical example of increased variability of earnings ($y$) given increased schooling ($X$). You may interact $X$ with a gender dummy, and it seems quite conceivable that the differential return to schooling for men vs women would also exhibit heteroskedasticity. $\endgroup$ Jul 29 '19 at 11:37
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The heteroscedasticity-robust standard error take into account the whole regressor matrix $X$, in the case of HC4 this is the following "sandwich" formula

$HC4 = (X'X)^{-1} X' \text{diag} \Big[ \frac{e_i^2}{(1-h_{ii})^{\delta_i}}\Big] X(X'X)^{-1}$ with $\delta_i = \text{min} \Big\{4,\frac{nh_{ii}}{1-p}\Big\}$

Source here

Since an interaction term is always also a column of $X$, a heteroscedasticity-robust will take into account also the variance component of the interaction term. Everything else would make no sense, since a model without interaction term is a completely different model with different standard error for the coefficients but also different (higher) residual standard error.

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  • $\begingroup$ First and foremost, thank you very much for your answer. I, sadly, have to say I am not experienced enough to interpret this with a 100% certainty. Do you mean that I should include the interaction effects too? $\endgroup$
    – DBoet
    Jul 30 '19 at 9:23
  • $\begingroup$ If you think that an interaction term is necessary, you can include it and take into account heteroscedasticity by adjusting the standard error as discussed yes. But if you should is an entire different question and depends on the exact research question, the dataset at hand and other information not available in your question / comment. $\endgroup$ Aug 1 '19 at 21:47

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