The Discounted Euler Equation: A Note

We present a simple model with income risk and borrowing constraints which yields a “discounted Euler equation.” This feature of the model mutes the extent to which news about far future real interest rates (i.e., forward guidance) affects current outcomes. We show that this simple model approximates the outcomes of a rich model with uninsurable income risk and borrowing constraints in response to a forward guidance shock. The model is simple enough to be easily incorporated into standard DSGE models. We illustrate this with an application to the zero lower bound.