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)