Template-Type: ReDIF-Paper 1.0
Author-Name: Philipp Renner
Author-Name-First: Philipp
Author-Name-Last: Renner
Author-Name: Karl Schmedders
Author-Name-First: Karl
Author-Name-Last: Schmedders
Title: Dynamic Principal–Agent Models
Abstract: This paper contributes to the theoretical and numerical analysis of discrete time dynamic principal-agent problems with continuous choice sets. We first provide a new and simplified proof for the recursive reformulation of the sequential dynamic principal-agent relationship. Next we prove the existence of a unique solution for the principal's value function, which solves the dynamic  programming problem in the recursive formulation. By showing that the Bellman operator is a contraction mapping, we also obtain a convergence result for the value function iteration. To compute a solution for the problem, we have to solve a collection of static principal{agent problems at each iteration. Under the assumption that the agent's expected utility is a rational function of his action, we can transform the bi-level optimization problem into a standard nonlinear program. The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal-agent model. We illustrate our solution method by solving variations of two prominent social planning models from the economics literature. 
Creation-Date: 2017
File-URL: http://www.lancaster.ac.uk/media/lancaster-university/content-assets/documents/lums/economics/working-papers/LancasterWP2017_028.pdf
File-Format: application/pdf
Number: 203620456
Classification-JEL: C63, D80, D82
Keywords: Optimal unemployment tax, principal-agent model, repeated moral hazard
Handle: RePEc:lan:wpaper:203620456