Repeated Moral Hazard and Recursive Lagrangeans

I solve a repeated moral hazard model with a fast and flexible numerical algorithm. Instead of applying the traditional Abreu, Pierce and Stacchetti (1990), I extend the Lagrangean techniques developed in Marcet and Marimon (1998) to the principal-agent framework. A numerical procedure is proposed, that is much faster than the traditional algorithms based on the promised utilities approach, and that can easily deal with large state spaces. Given the computational speed, the algorithm is especially suitable for applications with many state variables and for calibration purposes.