This paper is concerned with accuracy properties of simulations of approximate solutions for stochastic dynamic models. Our analysis rests upon a continuity property of invariant distributions and a generalized law of large numbers. We then show that the statistics generated by any sufficiently good numerical approximation are arbitrarily close to the set of expected values of the model's invariant distributions. Also, under a contractivity condition on the dynamics we establish error bounds. These results are of further interest for the comparative study of stationary solutions and the estimation of structural dynamic models.

This paper shows that a macro model with segmented financial markets can generate sizable movements in housing prices in response to changes in credit conditions. We establish theoretically that reductions in mortgage rates always have a positive effect on prices, whereas the relaxation of loan-to-value constraints has ambiguous effects. A quantitative version of the model under perfect foresight accounts for about one-half of the observed price increase in the United States in the 2000s. When we include shocks to expectations about housing finance conditions, the model’s ability to match house values improves significantly. The framework reconciles the observed disconnect between house prices and rents since, in general equilibrium, financial shocks can decrease rents and increase prices. (JEL E44, G21, R31)

This paper shows that a macro model with segmented …nancial markets can generate sizeable movements in housing prices in response to changes in credit conditions. We establish theoretically that reductions in mortgage rates always have a positive e¤ect on prices, whereas the relaxation of loan-to-value constraints has ambiguous effects. A quantitative version of the model under perfect foresight accounts for about half of the observed price increase in the U.S. in the 2000s. When we include shocks to expectations about housing …nance conditions the model's ability to match house values improves signi…cantly. The framework reconciles the observed disconnect between house prices and rents since, in general equilibrium, …nancial shocks can decrease rents and increase prices.

No abstract

In this article, we propose a recursive equilibrium algorithm for the numerical simulation of nonoptimal dynamic economies. This algorithm builds upon a convergent operator over an expanded set of state variables. The fixed point of this operator defines the set of all Markovian equilibria. We study approximation properties of the operator. We also apply our recursive equilibrium algorithm to various models with heterogeneous agents, incomplete financial markets, endogenous and exogenous borrowing constraints, taxes, and money.