We show how the Joslin, Singleton, and Zhu (2011) factor extraction approach to estimating the Gaussian term structure model can be modified to handle the interest rate lower bound. Our novel approach is exact in a sense that it does not require any approximation in the estimation process. This is important from the perspective of using the model for economic inference, such as measuring term premium or policy expectation. Compared with the standard shadow rate estimation approach based on the Kalman filter, this improves convergence and greatly reduces the computation time. It has the added advantage of producing more robust estimates of the lower bound parameter and the path of the shadow rate. We show that expected inflation and real activity are important unspanned macro factors that drive term premiums as in Joslin, Priebsch, and Singleton (2014).