Dynamic contracting, persistent shocks and optimal taxation

In this paper I develop continuous-time methods for solving dynamic principal-agent problems in which the agent’s privately observed productivity shocks are persistent over time. I characterize the optimal contract as the solution to a system of ordinary differential equations, and show that, under this contract, the agent’s utility converges to its lower bound—immiseration occurs. I also show that, unlike in environments with i.i.d. shocks, the principal would like to renegotiate with the agent when the agent’s productivity is low—it is not renegotiation-proof. I apply the theoretical methods I have developed and numerically solve this (Mirrleesian) dynamic taxation model. I find that it is optimal to allow a wedge between the marginal rate of transformation and individuals’ marginal rate of substitution between consumption and leisure. This wedge is significantly higher than what is found in the i.i.d. case. Thus, using the i.i.d. assumption is not a good approximation quantitatively when there is persistence in productivity shocks.