Guvenen et al: Earnings
If I understand correctly we have observed earnings first-differences that we decompose into an "expected" part and an "unexpected" part. But f they are unexpected, it means something like

$$y_{t+1} -y_t = h(I_t) + u_{t+1} , \;\;E(u_{t+1}\mid I_t)=0$$

where $I_t$ is the "information set" (in the broad sense) at time $t$. So by construction, the unexpected part will have conditional mean zero. But , this does not imply necessarily that $u_{t+1}$ will also have a symmetric distribution around zero. If as you conjecture, there are "more shocks downwards (negative) rather than downwards", the distribution will have more probability mass in the negative. Then, in order to maintain a zero-mean the distribution will have to have higher values on the positive: more and smaller negative shocks, fewer and higher positive shocks.  Something like a shifted to the left gamma distribution, so as to have zero-mean,



Is this close to what you have in mind?