Working Papers
By Year:
Paper #  Author  Title  

10038 
Harold L. Cole Felix Kubler 
“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. Download Paper


07027 
Felix Kubler Karl Schmedders 
"Nonparametric counterfactual analysis in dynamic general equilibrium"  
In this paper we examine nonparametric restrictions on counterfactual analysis in a simple dynamic stochastic general equilibrium model. Under the assumption of timeseparable expected utility and complete markets all equilibria in this model are stationary, the ArrowDebreu prices uniquely reveal the probabilities and discount factor and the equilibrium correspondence defined as the map from endowments to stationary (probabilityfree) state prices, is identical to the equilibrium correspondence in a standard ArrowDebreu exchange economy with additively separable utility. We examine observable restriction on this correspondence and give necessary as well as sufficient conditions on profiles of individual endowments that ensure that associated equilibrium prices cannot be arbitrary. While often there are restrictions on possible price changes we also show that in most cases results from a single agent economy do not carry over to a setting with heterogeneous agents. Download Paper


07013 
Felix Kubler Karl Schmedders 
"Competitive Equilibria in SemiAlgebraic Economies"  
This paper examines the equilibrium correspondence in ArrowDebreu exchange economies with semialgebraic preferences. We show that a generic semialgebraic exchange economy gives rise to a square system of polynomial equations with finitely many solutions. The competitive equilibria form a subset of the solution set and can be identified by verifying finitely many polynomial inequalities. We apply methods from computational algebraic geometry to obtain an equivalent polynomial system of equations that essentially reduces the computation of all equilibria to finding all roots of a univariate polynomial. This polynomial can be used to determine an upper bound on the number of equilibria and to approximate all equilibria numerically. We illustrate our results and computational method with several examples. In particular, we show that in economies with two commodities and two agents with CES utility, the number of competitive equilibria is never larger than three and that multiplicity of equilibria is rare in that it only occurs for a very small fraction of individual endowments and preference parameters. Download Paper
