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Creator: Zhang, Yuzhe Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 639 Abstract:
This paper studies the stability of a stochastic optimal growth economy introduced by Brock and Mirman [J. Econ. Theory 4 (1972)] by utilizing stochastic monotonicity in a dynamic system. The construction of two boundary distributions leads to a new method of studying systems with non-compact state space. The paper shows the existence of a unique invariant distribution. It also shows the equivalence between the stability and the uniqueness of the invariant distribution in this dynamic system.
Palabra clave: Monotonic operator, Stochastic dominance, Stochastic growth, and Global stability Tema: O41 - One, Two, and Multisector Growth Models, C62 - Existence and Stability Conditions of Equilibrium, and C61 - Optimization Techniques; Programming Models; Dynamic Analysis
Creator: Zhang, Yuzhe Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 640 Abstract:
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.
Palabra clave: Principal-agent problem, Persistence, Efficiency lines, and Stochastic control problem Tema: E61 - Policy Objectives; Policy Designs and Consistency; Policy Coordination, D80 - Information, Knowledge, and Uncertainty: General, and D82 - Asymmetric and Private Information; Mechanism Design