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.