We use the framework developed by Christensen (2017) and Hansen and Scheinkman (2009) to study the long-term interest rates in the US and Brazil. We apply a nonparametric estimator to US and Brazilian data to identify how the yield of a long-term zero-coupon bond responds to the initial state of the economy. Using a flexible specification for the state process leads to an interesting non-linear response of the yield to changes in the initial state. As a by-product of our work, we assess the performance of Christensen's estimator using Monte Carlo simulations based on two widely adopted asset pricing models (rare disasters and habit formation).