This paper studies the speed at which workers' pre-tax earnings respond to tax changes along the intensive margin. We do so in the context of Germany, where a large discontinuity – or notch – in the tax schedule induces sharp bunching in the earnings distribution. We analyze earnings...

This paper studies the speed at which workers' pre-tax earnings respond to tax changes along the intensive margin. We do so in the context of Germany, where a large discontinuity - or notch - in the tax schedule induces sharp bunching in the earnings distribution. We analyze earnings responses...

Optimal actions of an agent facing a Shannon capacity constraint on the translation of an uncertain signal into an action can easily turn out to be discretely distributed, even when the objective function and the initial distribution of uncertainty contain no discrete elements. We show this...