A time series model of interest rates with the effective lower bound

BIS Working Papers  |  No 715  | 
17 April 2018



Over the last decade, nominal interest rates have fallen to very low levels in many countries. Thus, central banks have seen their choices for the appropriate path of policy rates constrained by an effective lower bound, a level below which nominal interest rates cannot fall. Nevertheless, traditional forecasting models neglect this lower boundary, which is equivalent to assuming central banks could steer interest rates as low as they like. But acknowledging the lower bound should evidently matter when forecasting the path of interest rates and for understanding economic responses to policy changes.


We incorporate the lower bound into an otherwise standard econometric model of interest rates and macroeconomic variables. Our model tracks a "shadow rate", which is a hypothetical rate identical to the actual nominal rate except when rates hit the lower bound. In this case, the shadow rate moves below the lower bound. We apply this model to US data. Since US policymakers chose not to move the target range for the policy rate below zero, we take the level of the lower bound to be known. (In other economies, policy rates have been cut below zero, so that the exact depth of the lower bound remains a question for further research.)


Our model generates near-term forecasts for nominal interest rates that compare well with others. Moreover, we also produce forecasts for the longer-run level of the real rate, sometimes known as the "neutral rate". Our estimates of the longer-run level of the real rate have edged down somewhat in recent decades, but not by quite as much as other estimates. Compared with other models, our approach largely sees through the extraordinary depth of the last recession. Our results suggest that real rates can be expected to move back up, approaching the levels seen before.



Modeling nominal interest rates requires their effective lower bound (ELB) to be taken into account. We propose a flexible time series approach that includes a "shadow rate" - a notional rate identical to the actual nominal rate except when the ELB binds. We apply this approach to a trend-cycle decomposition of interest rates and macroeconomic variables that generates competitive interest-rate forecasts. Our estimates of the real-rate trend have edged down somewhat in recent decades, but not significantly so. We identify monetary policy shocks from shadow-rate surprises and find that they were particularly effective at stimulating economic activity during the ELB period.

JEL classification: C32, C34, C53, E43, E47

Keywords: shadow rate, effective lower bound, trend real rate, monetary policy shocks, bayesian time series