Modelling nominal debt contracts and fixed rate debt

We provide a simple model of sticky nominal debt contracts and fixed rate debt that can easily be embedded in a dynamic general equilibrium framework. Once linearised, the debt process increases the order of autoregressive dynamics in the system by one; thus potentially introducing more complex adjustment processes. Keywords: nominal debt; dynamic general equilibrium. JEL Classifications: E30, E44 ∗Corresponding author: Department of Economics, University of Warwick, Coventry, CV4 7AL, UK; tel: +44 24 7652 8418; email: [email protected] †Department of Economics, Birkbeck College, University of London, Malet Street, London W1E 7HX, UK; tel: +44 20 7631 6448; email: [email protected] This paper presents a simple model of nominal debt contracting that can be readily incorporated into a dynamic general equilibrium framework. Our motivation for so doing is based on the following observations: 1. Collateralized nominal debt contracts are the norm in most countries with reasonably stable in‡ation 2. Adjustments to such contracts are relatively costly, and hence relatively infrequent 3. Many such nominal contracts are written on a "…xed rate" basis Although a number of papers examine dynamic general equilibrium models with nominal debt (e.g. Aoki et al (2002)) very little attention has been paid to the stickiness of such contracts. Yet nominal debt stickiness is arguably easier to understand than product price stickiness. A well-known criticism of the standard model of product price stickiness is that the “menu costs”that ultimately must generate stickiness are unlikely to be large. In the case of debt contracts, in contrast, the costs of adjustment may well be distinctly larger, since typically this will involve re-assessment of collateral or other features of creditworthiness. Of course, if the nature of debt contracts is to have …rst-order e¤ects, some households face (or act as if they face) a binding credit constraint. A comprehensive discussion of this issue can be found in Mankiw (2000). 1 Financial institutions Financial institutions make loans to households based on nominal contracts. We assume that debt contracts are sticky in nominal terms. To capture this in a tractable way, we progress by analogy to Calvo’s (1983) model of the aggregate price level. We assume a constant probability that any given debt contract will be adjusted in the next period, with complete adjustment towards its optimal value if adjustment does take place. The key point is that households facing a binding credit constraint will always accept any new debt that …nancial institutions o¤er them. This means that, at least in some neighborhood of a steady state in which the credit constraint binds, we can model the level of debt as determined by …nancial institutions.