Ebook Credit Constraints and the Yield Curve

Incomplete markets are a potential explanation for the failure of standard asset pricing models based on complete markets (Heaton and Lucas, 1995). When markets are incomplete, agents need to self-insure against uninsurable risks and therefore buy securities in addition to the standard smoothing motives. Uninsurable idiosyncratic risks do not affect uniformly assets with different risks or maturities. In particular, incomplete market models have been used to analyze the yield curve as a simple departure from the standard Cox, Ingersoll, and Ross (1986) complete market model. But due to the heterogeneous agents structure, only few analytical results have been proposed in such frameworks. Seppala (2000) studies an endowment economy with credit constraints and relies heavily on simulations. Heaton and Lucas (1992) who study a three period economy follow another approach.

In this paper, we present a model with a production economy and heterogeneous agents, incomplete markets and credit constraints. In this economy, agents face both an uninsurable employment risk (they switch between an employed and an unemployed status on the labor market) and an aggregate risk, which affect their wages when they are employed. We are able to derive analytical solutions for the zero-coupon bond prices, whatever the maturity, and to investigate the effect of the idiosyncratic risk on the level and the slope of the yield curve. These solutions allow us to exhibit new effects, which have not been put forward in the literature yet. In particular, we show that the volume of titles affect the level and the slope of the yield curve because of credit constraints.

We obtain analytical solutions because we make two assumptions used in the Bewley-Hugget types of models with incomplete markets, which have not been used together yet. These assumptions are useful to decrease the heterogeneity between agents. The first one is that the labor supply is infinitely elastic. Sheinkman and Weiss (1986) make this assumption in a monetary economy. They obtain that all agents for which the credit constraint does not bind, hold the same quantity of titles. The second is made by Kehoe, Levine and Woodford (1991). In their model, agents with low income are credit constrained and sell all their titles. As a consequence, they do not decumulate progressively their assets to smooth consumption. With these two assumptions, we can reduce the heterogeneity of agents to only four different types. This insures tractability and analytical solutions, even when there are an arbitrarily large number of titles of different maturities, which are not perfect substitutes. The contribution of this paper is thus the derivation of this reduced heterogeneous equilibrium and its application to the yield curve.