Term structure models are routinely used by central banks to assess the impact of their communication on market participants' views of future interest rate developments. However, recent studies have pointed out that traditional term structure models can provide misleading indications when policy rates are at the zero lower bound (ZLB).
One of the main drawbacks is that they are unable to reproduce the stylized fact that policy rates tend to remain at the ZLB for prolonged periods of time once they reach it. A consensus has recently emerged that shadow rate models, first introduced by Black (1995), are apt to solve this problem.
The main idea is that the shadow rate (i.e., the short-term interest rate that would prevail in the absence of the ZLB) can move in negative territory for long time spans even when the actual rate remains close to the ZLB. Due to their high nonlinearity, shadow rate models are particularly difficult to estimate and have been so far only estimated with approximate methods.
We propose an exact Bayesian method for their estimation. We use it to study developments in euro and US dollar yield curves since the end of the '90s. Our estimates confirm - and provide a quantitative assessment of - the fact that there has been a significant divergence of monetary policies in the euro area and in the US over the past years: between 2009 and 2013, the shadow rate was much lower in the US than in the euro area, while the opposite has been true since 2014; furthermore, at the end of our sample (January 2015), the most likely date of the the first increase in policy rates was estimated to be around mid-2015 in the US and around 2020 in the euro area.