Job market signals and signs

What happens to job market signaling under two-dimensional asymmetric information? With 2 types of productivity and noise, the equilibrium remains separating if an extended single-crossing condition is satisfied. If not, there are partially pooling equilibria where only extreme types can be distinguished, and supplementary information is needed. On-the-job interaction gives employers private information on productivity, which employment relationships may reveal to the market. While sticky wages lead to public revelation of this private information through dismissals, flexible wages do not, allowing employers to do cream skimming. Beyond the 2x2 case, employment relationships are always a noisy sign, so education is valuable as a life-time job market signal for high-ability workers.