Guvenen et al: Earnings

Question

Guvenen et al look at earnings shocks over time, and try to argue whether these are compatible with standard career-ladder models with normal shocks.

However, their data is no real shocks, it is time differences in labor earnings. We do not know which part of these were expected. What are things to consider if one tries to take into account for the fact that these income changes are - to some extent - expected ex ante?

My first guess would be that since people expect future rise in income, correcting the "shocks" for that would mean that the unexpected part of the shocks is to the left of their yearly changes in wage income. That is, there are more shocks downwards than upwards.

Answer 1

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?