RDP 2011-04: Assessing Some Models of the Impact of Financial Stress upon Business Cycles Appendix A: Derivation of Debt Growth Equation

Let leverage be Equation. Then

It immediately follows that

where Equation and Equation since the steady state growth rate of capital will be the same as output (γ). Designating the ratio Equation as RKN,t, and using the fact that Equation, an expression for lt is available from

Now Gilchrist et al (2009) measure variables in percentages so, designating these by a ‘*’, we get

Hence we have