Can Cross-Border Financial Markets Create Endogenously Good Collateral in a Crisis?

In this paper, we explore whether markets can create endogenously good collateral in a crisis by analyzing a simple exchange economy where a country-specific catastrophic shock is shared between two countries. To see this possibility, we examine whether the equilibrium achieved by the time-0 complete markets with solvency constraints can be recovered in the dynamically complete markets with collateral constraints. This paper demonstrates that it is possible to recover the time-0 equilibrium outcome in a sequential manner when pricing errors occur randomly in evaluating Lucas trees at a catastrophic event. Such stochastic components may be interpreted as a policy initiative to create good collateral and yield constrained efficient outcomes at crisis periods.Solvency Constraints, Collateral Constraints, Dynamic Optimal Contract, Catastrophic Shocks

Recursive Contracts, Lotteries and Weakly Concave Pareto Sets

Marcet and Marimon (1994, revised 1998) developed a recursive saddle point method which can be used to solve dynamic contracting problems that include participation, enforcement and incentive constraints. Their method uses a recursive multiplier to capture implicit prior promises to the agent(s) that were made in order to satisfy earlier instances of these constraints. As a result, their method relies on the invertibility of the derivative of the Pareto frontier and cannot be applied to problems for which this frontier is not strictly concave. In this paper we show how one can extend their method to a weakly concave Pareto frontier by expanding the state space to include the realizations of an end of period lottery over the extreme points of a .at region of the Pareto frontier. With this expansion the basic insight of Marcet and Marimon goes through .one can make the problem recursive in the Lagrangian multiplier which yields significant computational advantages over the conventional approach of using utility as the state variable. The case of a weakly concave Pareto frontier arises naturally in applications where the principal’s choice set is not convex but where randomization is possible.Recursive Contracting, Recursive Multipliers, Lotteries

Repeated moral hazard and recursive Lagrangeans

This paper shows how to solve dynamic agency models by extending recursive Lagrangean techniques à la Marcet and Marimon (2011) to problems with hidden actions. The method has many advantages with respect to promised utilities approach (Abreu, Pearce and Stacchetti (1990)): it is a significant improvement in terms of simplicity, tractability and computational speed. Solutions can be easily computed for hidden actions models with several endogenous state variables and several agents, while the promised utilities approach becomes extremely difficult and computationally intensive even with just one state variable or two agents. Several numerical examples illustrate how this methodology outperforms the standard approach.repeated moral hazard; collocation method; dynamic models with private information; recursive contracts

Recursive Contracts

We obtain a recursive formulation for a general class of contracting problems involving incentive constraints. These constraints make the corresponding maximization sup problems non-recursive. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle-point (infsup) functional equation (analogous to a Bellman equation) that characterizes the recursive solution to the planner's problem and forward-looking constraints. Our approach has been applied to a large class of dynamic contractual problems, such as contracts with limited enforcement, optimal policy design with implementability constraints, and dynamic political economy models.Recursive methods, dynamic optimization, Ramsey equilibrium, time inconsistency, limited participation, contract default, saddle-points, Lagrangian multipliers.

Recursive Contracts

We obtain a recursive formulation for a general class of contracting problems involving incentive constraints. These constraints make the corresponding maximization (sup) problems non recursive. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle-point (infsup) functional equation (analogous to a Bellman equation) that characterizes the recursive solution to the planner's problem and forward-looking constraints. Our approach has been applied to a large class of dynamic contractual problems, such as contracts with limited enforcement, optimal policy design with implementability constraints, and dynamic political economy models.Transactional relationships, contracts and reputation, recursive formulation,participation constraint

A Negishi Approach to Recursive Contracts

In this paper, we argue that a large class of recursive contracts can be studied by means of the conventional Negishi method. A planner is responsible for prescribing current actions along with a distribution of future utility values to all agents, so as to maximize their weighted sum of utilities. Under convexity, the method yields the exact efficient frontier. Otherwise, the implementation requires contracts be contingent on publicly observable random signals uncorrelated to fundamentals. We also provide operational first-order conditions for the characterization of efficient contracts. Finally, we compare extensively our approach with the dual method established in the literature

Repeated moral hazard and recursive Lagrangeans

This paper shows how to solve dynamic agency models by extending recursive Lagrangean techniques a la Marcet and Marimon (2009) to problems with hidden actions. The method has many advantages with respect to promised utilities approach (Abreu, Pearce and Stacchetti (1990)): it is a significant improvement in terms of simplicity, tractability and computational speed. Solutions can be easily computed for hidden actions models with several endogenous state variables and several agents, while the promised utilities approach becomes extremely difficult and computationally intensive even with just one state variable or two agents. Several numerical examples illustrate how this methodology outperforms the standard approach

On the recursive saddle point method

In this paper we use the recursive saddle point method developed by Marcet and Marimon (1999, 2011) to a simple concave dynamic optimization problem. While the recursive saddle point problem is well dened and delivers the correct value of our optimization problem, it does not generate only optimal policies. Indeed some of the solutions that it produces are either suboptimal or do not even satisfy feasibility. We identify the reasons underlying this failure and discuss its implications for some existing applications