I'm interested in studying the effect of x$x$ on y$y$ using a fixed effects method. The residuals follow a heavy tail distribution, as the normal qQ-qQ plot suggests. For inference, I need a normal distribution of the residuals.
Which strategies can be applied to the model such that the residuals become more normally distributed? I thought about log-log transformations. This made the residuals indeed more normally distributed, but the heavy tails still persist.