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We consider the effects of central-bank purchases of a risky asset, financed by issuing riskless nominal liabilities (reserves), as an additional dimension of policy alongside "conventional" monetary policy (central-bank control of the riskless nominal interest rate), in a general-equilibrium model of asset pricing and risk sharing with endogenous collateral constraints of the kind proposed by Geanakoplos (1997). When sufficient collateral exists for collateral constraints not to bind for any agents, we show that central-bank asset purchases have no effects on either real or nominal variables, despite the differing risk characteristics of the assets purchased and the ones issued to finance these purchases. At the same time, the existence of collateral constraints allows our model to capture the common view that large enough central-bank purchases would eventually have to effect asset prices. But even when central-bank purchases raise the price of the asset, owing to binding collateral constraints, the effects need not be the ones commonly assumed. We show that under some circumstances, central-bank purchases relax financial constraints, increase aggregate demand, and may even achieve a Pareto improvement; but in other cases, they may tighten financial constraints, reduce aggregate demand, and lower welfare. The latter case is almost certain the one that arises if central-bank purchases are sufficiently large. * We thank Kyle Jurado and Savitar Sundaresan for research assistance, and participants at presentations at IMPA, MIT, and the Cowles Foundation Conference on General Equilibrium and its Applications for helpful comments. We also acknowledge financial support from CAPES-PNPD and IMPA (Schommer), and the NSF under grant SES-0820438 (Woodford).

This article implements an Augmented Lagrangian algorithm to compute equilibria in a general equilibrium model with incomplete markets and default. It is one of the first attempts to solve such a model on a large scale. Convergence is found for various economic parameters. We illustrate the effectiveness of this approach for simulating general equilibrium economies with a default.

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