Do I need to transform/standardise my dependent variable? Attached are the results and the residual plot for my regression of control variables on CEO compensation (TDC1). When I look at the plot my main concerns are the outliers (which I checked to be correct without sufficient reason to exclude) and heteroskedasticity. Would it be advised to standardise my dependent variable in this case or should I use a different regression method. The data is panel data over the past ten years and the independent variables include firm specific, individual and period effects.
reg TDC1 Male Tenure Age i.Industry Assets NetIncomeLoss Sales i.Year i.nState


reg logCPIAdjTDC1 Male Tenure Age i.Industry L.Assets L.NetIncomeLoss L.Sales i.Year i.nState

xtreg CPIAdjustedTDC1 Male Tenure Age i.Industry L.Assets L.NetIncomeLoss L.Sales i.Year i.nState if TDC1 < 60000


Given that CEO pay is a non-negative financial quantity, it will generally make sense to examine it on a log-scale, as you have done in your second model.  (As some commentators have also pointed out, it is sensible to adjust for CPI to have a stable financial measure, which you appear to also have done in your second model.)  The residual plot for this second model looks mostly okay, but there is some evidence of nonlinearity and there are some clusters of large negative residuals.  In view of this, I would recommend that you examine the added variable plots for the model to see if you can identify any source of nonlinearity, and consider adding one or more higher-order terms for your explanatory variables.  I would also recommend you manually examine the clusters of outliers to see if there is anything they have in common that might suggest a change in your model.
In relation to the clusters of outliers in the residual plot, note that these are not a significant problem in regression analysis so long as you are careful when making predictions on new data.  All these outliers mean is that your stipulated error distribution (the normal distribution) has tails that are too thin, which is not consistent with the evidence in the data.  If you were to generalise your error distribution for the model (e.g., to a generalised normal distribution) then you could accomodate the higher kurtosis exhibited in the residuals.  In order to form prediction intervals with new data you would need to be careful to ensure that your model can accomodate the residual kurtosis (and ideally also residual skew) but this is something that is achievable with some changes to your model.
Overall, I would say that you have quite a good starting point in your second model, with only a few small remaining issues that should be examined and accomodated with model changes.
