The real business cycle (RBC) model pioneered by Kydland and Prescott (1982) was a fundamental step to understand business cycles. This literature, in general, claims that aggregate technology shocks are the main ingredient to explain these fluctuations. However, in order to match various stylized facts, it is well known that these exogenous aggregate productivity shocks need to be large and persistent. Kiyotaki and Moore (1997) and Kocherlakota (2000), among others, state that the majority of shocks appear to be either shocks on particular sectors of the economy or shocks on distribution, rather than large and persistent shocks on aggregate productivity itself. In recent years, a number of theoretical models that highlight the role of credit frictions in propagating and amplifying macroeconomic shocks has further cast doubts on aggregate technology shocks as the driving force in business activities. According to this literature, what is missing in RBC models is a powerful propagation mechanism by which the effects of small shocks amplify, persist and spread across sectors. Different forms of credit market frictions have been used to provide for an alternative mechanism of business cycles. One of the most prominent examples is the Kiyotaki-Moore (1997) credit cycles model. There, collateral constraints play a fundamental role generating, at least at the theoretical level, large, persistent fluctuations in output and asset prices. On the other hand, whether this role is quantitatively significant still seems an open question. Moreover, the existing literature on collateral constraints has compared its results to properties of standard RBC models, but this comparison was based on rather different environments. Unfortunately, quantitative implications derived from this kind of approach can be misleading. Our paper tries to fill this gap. We construct a dynamic stochastic general equilibrium (DSGE) model in the tradition of the RBC literature. Within this framework, we impose restrictions on asset trading which follow from the credit constraint structure used by, for example, Kiyotaki and Moore (1997) and Kocherlakota (2000). We introduce a flexible technology to produce new capital goods. There is an idiosyncratic component of shocks that affects relative productivities across types as well as an aggregate component that has the same effect on all individual production possibilities. Except for the trading restrictions imposed by the collateral constraints, we assume that markets are complete and, in particular, we consider a full set of Arrow securities. Very importantly, this asset market structure still allows us to price any security. This framework is particularly relevant because it has been the environment in which the DSGE literature has extensively studied economic fluctuations associated with business cycles and made important contributions. Our main focus is on the quantitative impact of these additional constraints on equilibrium allocations and prices. Therefore, we study amplification and persistence, some asset pricing implications and, finally, the welfare consequences of collateral constraints. That is, to be confident with our results, we need to be sure that they are not inconsistent with the salient facts properly explained by the previous DSGE literature. One crucial aspect of our environment is that collateral constraints are occasionally binding. Hence, the computational strategy differs from that followed in the literature on credit cycles where the traditional exercises is as follows. Assuming away uncertainty initially, the steady state allocation is characterized. Under some assumptions, the collateral constraint will always be binding for the same subset of agents. The exercise then proceeds imposing an unexpected shock to determine how the aggregate variables react in terms of amplification and persistence. In the environment we study, in contrast, collateral constraints are occasionally binding and therefore the computational strategy must differ significantly. We adapt the approach highlighted in Christiano and Fisher (2000) extending their collocation version of the Parameterized Expectations Approach initially developed by Marcet (1988). More precisely, we propose a multidimensional version of their method where we additionally consider prices as endogenous state variables. Our preliminary results can be summarized as follows. With dynamically complete markets, the introduction of collateral constraints does not help too much to explain the large amplification and persistence observed in the data. On the other hand, they may have nontrivial implications in terms of asset pricing. The welfare implications are typically small. Then we relax the assumption regarding market completeness, not allowing the agents to issue securities for those states with idiosyncratic flavor. This allows us to distinguish the implications of collateral constraints as such from those arising from incomplete markets. Very importantly, the interaction between these two frictions in asset trading has interesting implications for all the macroeconomic aspects mentioned before.
