Essays on Collateral Constraints

This thesis consists of three self-contained papers. Chapter 1 provides a general introduction. In Chapter 2, I study the impact of collateral constraints on producers and thereby on aggregate output. In a theoretical paper, Kiyotaki and Moore (1997) show that collateral constraints that restrict the investment decisions of producers can strongly amplify and propagate aggregate shocks. However, the subsequent quantitative literature tends to find rather weak and non-robust effects of collateral constraints. I try to improve on this by modeling the interaction between idiosyncratic risk and collateral constraints. To this aim, agents' productivities as workers and entrepreneurs are assumed to evolve stochastically. This leads to a perpetual mismatch between wealth and skills, which is the reason for collateralized borrowing in this economy. The advantage of this modeling strategy is threefold. First, the evolution of skills can be measured empirically. In contrast, the heterogeneity in patience that the previous literature assumes to excite collateralized borrowing is not even intended as a serious micro-foundation. Second, idiosyncratic risk creates a non-degenerate distribution of wealth. As a consequence, the percentage of constrained agents changes as shocks hit the economy. Among other things, this generates recessions that are much sharper than booms. Last but not least, the impact of collateral constraints turns out to be larger and more robust in the setup with idiosyncratic risk compared to models with heterogeneity in patience. In the baseline calibration, an unanticipated shock that reduces total factor productivity (TFP) by one percent for only one year leads to a sharp and persistent drop in both output and the price of capital. In contrast, without financing frictions the model economy is back at the steady state within one year. Thus, collateral constraints have a substantial impact on the aggregate economy. In Chapter 3, which is joint work with Michael Grill, Felix Kubler and Karl Schmedders, we study the impact of collateral constraints on investors and thereby on asset prices. We consider an exchange economy with long-lived assets that pay risky dividends and can be used as collateral for short-term loans. Investors are heterogeneous with respect to risk-aversion. As a consequence, risk-tolerant agents invest in the risky assets and use them as collateral to borrow from the risk-averse. This investment behavior makes the risk-tolerant agents vulnerable to bad shocks in which case binding collateral constraints force them to sell some of their risky assets. The risk-averse buy these assets only after their price has dropped substantially. For this reason, collateral constraints increase the volatility of asset returns by 50 percent as compared to a benchmark where borrowing is not possible. We show that the high volatility does not substantially decrease when we allow for defaultable bonds. We also find that such bonds are only traded if the costs of default are small. The main focus of our analysis is on the case of two risky assets, where the collateral requirement is determined endogenously for one, but exogenously for the other. In particular, we assume that a regulating agency sets an exogenous margin requirement for the second asset. We find that this regulation has a strong impact on the volatility of the first asset. In particular, a tightening of margin requirements for the regulated asset uniformly decreases volatility of the unregulated asset. For the regulated asset, tighter margins initially increase the return volatility, but then decrease it once margins become very large. In Chapter 4, which is joint work with Michael Grill, we propose a method that overcomes the numerical problems caused by collateral constraints or other types of occasionally binding constraints. The method also works when policy functions need to be interpolated over several dimensions. It uses the equilibrium conditions of the model to numerically locate the kinks in policy functions which are induced by the constraints and then adds interpolation nodes exactly there. To handle the resulting non-uniform grid of interpolation nodes, it uses simplicial interpolation, which is piecewise-linear interpolation on efficiently chosen simplices. Therefore, we call this method Adaptive Simplicial Interpolation (ASI). To evaluate its performance, we embed ASI into a time iteration algorithm. We then compute recursive equilibria in an infinite horizon endowment economy where heterogeneous agents trade in a bond and a stock subject to various trading constraints. A careful analysis shows that ASI computes equilibria accurately and outperforms standard interpolation schemes by far.