We postulate a continuous‐time heterogeneous agent model with a financial sector and households to study the nonlinear linkages between aggregate and financial variables. In our model, the interaction between the supply of bonds by the financial sector and the precautionary demand for bonds by households produces significant endogenous aggregate risk . This risk makes the economy transition between a high‐leverage region and a low‐leverage region, which, in turn, creates state dependence in impulse responses: the same shock starting from the high‐leverage region gets propagated and amplified more than when the shock arrives when leverage is low. State dependence in impulse responses generates a time‐varying aggregate precautionary savings motive that, by moving the risk‐free rate, justifies the leverage level of the financial sector in each region. Finally, we illustrate the usefulness of neutral networks to solve for the nonlinear perceived law of motion of the model, and the importance of household heterogeneity in driving its quantitative properties.

This paper studies the econometrics of computed dynamic models. Since these models generally lack a closed-form solution, their policy functions are approximated by numerical methods. Hence, the researcher can only evaluate an approximated likelihood associated with the approximated policy function rather than the exact likelihood implied by the exact policy function. What are the consequences for inference of the use of approximated likelihoods? First, we find conditions under which, as the approximated policy function converges to the exact policy, the approximated likelihood also converges to the exact likelihood. Second, we show that second order approximation errors in the policy function, which almost always are ignored by researchers, have first order effects on the likelihood function. Third, we discuss convergence of Bayesian and classical estimates. Finally, we propose to use a likelihood ratio test as a diagnostic device for problems derived from the use of approximated likelihoods.