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Hend:
unless the so called outliers are data entry mistakes, weird observations might simply be a matter of fact.
Be sure that, on the ground of existing literature, your regression model gives a fair and true view of the data generating process instead.
That said, there's another issue with panel data: observations within the same panel are not independent; hence, you should cluster the standard errors on panel identifier. I'm not sure whether non-default standared errors are supported by -mmregress-.
Following the FAQ advice, it is important to underline that - mmregress - is a user-written program, whose authors are Vicenzo Verardi and Christopher Croux.
In fact, I have no experience wih - mmregress - and I believe outliers should be tackled the way Carlo commented in #2.
Now going to your question, there is some information in the abstract of the SSC mmregress
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In regression analysis, the presence of outliers in the data set can strongly distort the classical least squares estimator and lead to unreliable results. To deal with this, several robust-to-outliers methods have been proposed in the statistical literature. In Stata, some of these methods are available through the commands rreg and qreg. Unfortunately, these methods only resist to some specific types of outliers and turn out to be ineffective under alternative scenarios. In this package we present more effective robust estimators that we implemented in Stata. We also present a graphical tool that allows recognizing the type of detected outliers.
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If this information is not enough, you may type - help mmregress - in the command window and check out the information available.
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