Thresholds in a Credit Market Model with Multiple Equilibria

The paper studies a credit market model with endogenous credit cost and debt constraints in which multiple candidates for steady state equilibria arise. We use dynamic programming (DP) with flexible grid size to locate thresholds that separate different domains of attraction. More specifically, we employ DP to (1) compute present value borrowing constraints and thus creditworthiness, (2) locate thresholds where the dynamics separate to different domains of attraction, (3) distinguish between optimal and non-optimal steady states and (5) demonstrate how the thresholds change with change of the credit cost function of the debtor and (6) explore the impact of debt ceilings and consumption paths on creditworthiness. The analytics is provided for a general model and some generic results are presented for a one state variable problem. An earlier version of this paper has been prepared for the 1998 North American Winter Meeting of the Econometric Society, January 1998, Chicago. We want to thank Jess Benhabib, Gustav Feichtinger, Gerhard Sorger, Franz Wirl, Michael Woodford, Wolf-Jürgen Beyn and Thorsten Pampel for helpful discussions and comments. We also want to thank participants in a workshop at the University of Technology, Vienna, the Macroeconomic Workshop at Columbia University, and the SCE conference, at Yale University, June 2001. ∗Department of Mathematics, University of Frankfurt, Robert–Mayer–Str. 8-10, 60054 Frankfurt, Germany, e-mail:[email protected] †Center for Empirical Macroeconomics, Bielefeld and New School University, 65 Fifth Ave, New York, NY 10003, e-mail: [email protected] and [email protected] ‡Department of Mathematics, University of Frankfurt, Robert–Mayer–Str. 8-10, 60054 Frankfurt, Germany.