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 . Then

It immediately follows that

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

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

Hence we have