Collateral, Leverage, and the Business Cycle

I construct an infinite-horizon dynamic stochastic general equilibrium model with a collateral constraint and actual default in equilibrium. Entrepreneurs borrow from households through non-recourse debt contracts backed by capital goods. By taking into account the non-linear payoffs of the collateralized debt contracts and the scarcity of collateral, borrowers and lenders adjust their bid and ask schedules, or equivalently, the credit demand and supply surfaces for debt contracts with different interest rates and loan-to-value ratios. The tangent point between the two credit surfaces maximizes the gains from tranching capital using collateralized debt contracts, and pins down the endogenous leverage driven by the ratio of the price of the senior tranche to the price of the junior tranche of collateral. Therefore, leverage is pro-cyclical if there is more downside risk. I solve the global numerical solution of the model using the method of policy function iteration. I find that (i) the occasionally binding collateral constraint leads to regime-switching dynamics between two stochastic steady states, implying bimodal distributions for key variables; (ii) borrowers and lenders endogenously produce and trade "safe assets" that are almost default-free; (iii) counter-cyclical asset price volatility renders higher downside risk and pro-cyclical leverage, which amplifies business fluctuations