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Likelihood Inference in Non-Linear Term Structure Models: The Importance of the Zero Lower Bound

This paper shows how to use adaptive particle filtering and Markov chain Monte Carlo methods to estimate quadratic term structure models (QTSMs) by likelihood inference. The procedure is applied to quadratic models for the US and UK during the recent financial crisis. We find that these models provide a better statistical description of the data than Gaussian affine term structure models. In addition, QTSMs account perfectly for the zero lower bound whereas Gaussian affine models frequently imply forecast distributions with negative interest rates. Such predictions appear during the recent financial crisis in the US and UK but also prior to the crisis.