Assortative Learning

Because of sorting, more skilled workers are more productive in higher type firms. They also learn at different rates about their productivity and therefore expect different wage paths across firms. We show that under strict supermodularity there is always Positive Assortative Matching: differential learning is always dominated by the impact of productivity. Surprisingly, this holds even if learning is faster in the low type firm. The key assumption driving this result is that this is a pure Bayesian learning model. We also derive a new equilibrium condition in this class of continuous time models in addition to the common smooth-pasting and value- matching conditions. This no-deviation condition captures sequential rationality and results in a restriction on the second derivative of the value function.