RDP 2011-04: Assessing Some Models of the Impact of Financial Stress upon Business Cycles 4. Two Models with Financial-Real Linkages

As outlined in the previous section there are many items that might be influenced by credit and many models that might be constructed to elucidate the interaction between credit and business cycles. A large model capturing all the possibilities might be desirable, but in this paper we focus upon examples of two widely used ways of capturing a number of these linkages.

4.1 The Gilchrist et al (2009) (GOZ) Augmentation of the SW Model

The first model we examine, due to Gilchrist et al (2009), adds the impact of financial conditions upon investment using the financial accelerator mechanism described in Bernanke et al (1999) to the SW model. There is no specific role for collateral. To the SW model they add four equations:

where the over-bar indicates a steady state value, Equation is the rate of return on capital, qt is the real price of capital, mpkt is the marginal product of capital, st is the external finance premium, kt is the capital stock, and nt is entrepreneurs' net worth. Of the coefficients, δ is the depreciation rate of capital and θ is the survival rate of entrepreneurs. Equation (4) defines the external finance premium as the difference between the expected rate of return on capital (which is determined by Equation (3)) and the real interest rate. Equation (5) shows how the external finance premium varies with the degree of leverage, which is governed by the parameter χ. The shock Equation captures fluctuations in the supply of credit unrelated to the leverage of the entrepreneurs. The evolution of the net worth of entrepreneurs in given in Equation (6), with the first term reflecting the leveraged return of capital and the second the cost of debt. A certain fraction of wealth disappears as entrepreneurs disappear Equation. The shock Equation represents exogeneous fluctuations to net worth.

4.2 The Iacoviello (2005) Model

The key feature of the Iacoviello model is that the housing asset acts as collateral and, as the loan-to-value ratio is fixed, the amount that can be borrowed is based on the value of housing. This model has been used as the basis for further studies, such as Iacoviello and Neri (2010) and Gerali et al (2010).

There are three types of agents of interest in this model – a patient consumer who lends and two borrowers: an impatient consumer and an entrepreneur. There is a collateral asset (housing) that is in fixed supply. Its services are consumed and also used in production. Because housing is in fixed supply there is no residential investment in aggregate but there is fixed capital investment. Both the impatient consumer and the entrepreneur are credit constrained, with borrowing limited by a loan-to-value ratio which differs between them. Iacoviello estimates these parameters to be 0.89 for entrepreneurs and 0.55 for households. The decisions made by households and firms are much the same as those in the GOZ model except that credit constraints can limit expenditures, and so changes in the value of collateral can potentially have effects on cycles.