# Non-normal residuals - P-values higher or lower?

Background:

I have estimated a model using panel data with the Arellano Bond estimator (see e.g., http://www.fordham.edu/economics/mcleod/Elitz-usingArellano%E2%80%93BondGMMEstimators.pdf) and n=300. As it turns out, the distribution of my residuals is significantly different from the normal wrt. skewness and kurtosis.

Question:

Is it possible/how can I infer whether the calculated p-values should be higher or lower given the information available (dist, sd., kurtosis, skewness, etc.)?

I hope my question is sufficiently clear.