Mike Goldby, Lien Laureys and Kate Reinold.

The natural rate of interest is usually defined as the one prevailing when economic activity is at potential and inflation is low and stable. As this has a very similar flavour to the monetary policy objective of many central banks, it is interesting to policymakers. The natural rate is unobservable and needs to be estimated. In this post, we show an estimate derived from a standard macroeconomic model which suggests that the (real) natural rate fell very sharply during the financial crisis, perhaps to as low as -6%, and that, despite a marked recovery since 2012, it remains around zero.

**Introduction**

The economic concept of the natural rate of interest dates back over a century to the writings of the economist Knut Wicksell. There is no one definition used in the subsequent economic literature and terminology varies considerably. But the natural rate (the term we will use) is linked in most definitions to a situation where economic activity is at potential and inflation is low and stable. Such a concept is of potential interest to policymakers, and has been discussed in recent speeches (see e.g. Yellen (2015) and Carney (2013)). The natural rate is unobservable and needs to be estimated. There are many ways of doing this. In this post we use the Bank of England’s COMPASS model. This is a New Keynesian dynamic stochastic general equilibrium (DSGE) model – a standard type widely used in modern macroeconomics. This estimate represents the model’s view of the natural rate, not the MPC’s. When COMPASS is used to support the production of the MPC’s forecast it is supplemented by insights from other models and judgement is applied. Del Negro et al. (2015) have recently used the same DSGE-based approach to estimate the natural interest rate in the United States.

**The concept of the natural interest rate in New Keynesian models**

In New Keynesian DSGE models the natural rate has a specific definition: it is the real interest rate (the nominal interest rate adjusted for expected inflation) that would prevail in a hypothetical environment, where nominal prices and wages can adjust immediately, and where mark-ups in the goods and labour market are constant. Because output is at its potential or natural level when nominal price and wage rigidities are absent, the natural rate is a counterfactual rate that would occur only if all the economy’s resources were fully employed as set out in Del Negro et al. (2015).

DSGE models are typically designed to explain short to medium term fluctuations in variables like the natural rate. This means that the New Keynesian DSGE concept of the natural rate can be distinguished from a longer-run concept that also appears in the literature. For example, Williams (2003) defined the natural rate as the ‘level expected to prevail in, say, the next five to ten years, after any existing business cycle booms and busts have played out’.

One way to think about the relationship between this longer-run concept of the natural rate and the short-run flexible price concept is to think of the former changing gradually through time in response to deep structural factors such as changes in population growth and households’ long-term saving preferences, with a short-run natural rate fluctuating around that in response to a range of additional temporary shocks.

Estimating the natural rate using a DSGE model has some drawbacks, but there are reasons why we think this approach is useful. First, fluctuations in the estimated natural rate are driven by shocks in the model which have economic interpretations, and so provide a narrative for its evolution. This is one benefit compared with other approaches to estimating the natural rate – such as using yields on long-dated inflation-linked government bonds, or models with a more flexible structure (see e.g. Laubach and Williams (2003)).

Another advantage is the concept’s potential use as a guide to optimal policy. A well-known property of this class of models is that if the economy’s actual real interest rate was expected to track the path of the natural interest rate then, under certain conditions, inflation would be at target and the (welfare-relevant) output gap closed (see e.g. Galí (2008)).

**Estimating the natural interest rate using COMPASS**

We produce our estimate with the latest version of COMPASS (originally described in Burgess et al. (2013)). It is a fairly standard medium-size DSGE model with two types of nominal rigidities: sticky prices and sticky nominal wages.

The unobservable natural rate and the shocks that drive it are estimated using a Kalman smoother (see Hamilton (1994)), which returns the most likely path for these variables conditional on the observable data provided, the model structure (e.g. how output is produced, what determines labour supply) and its parameter values. The estimate of the natural rate is therefore highly model specific – one drawback relative to a more data-driven approach. An additional uncertainty is that COMPASS does not include mechanisms for capturing the effects of quantitative easing, or any lower bound on nominal interest rates. So these factors may be affecting the true natural rate in ways that we do not capture.

The centre of the red fan in Chart 1 shows the annualised estimate of the natural rate for the UK, produced using COMPASS. The red fan chart around the estimate captures uncertainty around its path induced by uncertainty about the parameters, conditional on the rest of the model being correct. Since the model is obviously an imperfect approximation of the true structure of the economy, uncertainty around the estimate is in practice much larger than implied by the fan in Chart 1*.*

**Chart 1: Estimate of the real natural rate from COMPASS ^{1}**

** Chart 2: Decomposition of shocks driving the estimated real natural rate in COMPASS**

The volatile estimate of the natural rate in Chart 1 is clearly not a precise guide to the true natural rate, but it does provide a broad indication of how it might have evolved both before and after the financial crisis. It suggests that the natural rate in the UK fell sharply following the financial crisis and moved well into negative territory, perhaps as low as -6%. It has been on an upward trend since 2012, but remains around zero. A markedly negative natural rate in the aftermath of the crisis, combined with the presence of the zero lower bound on nominal interest rates, implies that policymakers needed to use measures other than interest rates to achieve growth and inflation objectives, and helps to rationalise the use of unconventional policy measures such as quantitative easing that the Bank of England and other Central Banks implemented following the financial crisis.

Chart 2 shows that our model ascribes a key role to a ‘domestic risk premium shock’ in explaining the large fall in the natural rate and its subsequent weakness, in line with evidence for the US (Barsky et al. (2014)). This shock enters the model as a spread between the policy rate and the rate at which households and firms can borrow, and so is likely to be picking up factors related to the credit supply shock that the UK has faced in recent years (Barnett and Thomas (2013)). The world shocks have also pulled down on the natural rate, capturing the effects of the global slowdown on the UK, and particularly lower demand for UK exports. The drag from the domestic risk premium shocks and the world shocks have dissipated a little in the past year or two, but the largest contribution to the pickup in the natural rate has been a reversal in the ‘other’ shocks. These are largely accounted for by a selection of UK demand shocks, reflecting the UK’s recent recovery.

It is worth noting that our approach to estimating the natural rate involves an assumption that it will eventually return to a constant long run level of a little under 2.5% (the grey bars in Chart 2). But there is uncertainty about that assumption, particularly given that real interest rates in many countries have exhibited a long-term downward trend. Analysis in the IMF’s 2014 April World Economic Outlook attributes the decline in global real rates since the 1990s to higher saving in emerging market economies, an increase in demand for safe assets, and a sharp and persistent decline in investment rates in advanced economies since the global financial crisis. Smith and Rachel have also recently discussed the factors underlying the fall in global real rates on this blog. As a small open economy, the UK natural rate will be influenced by these global developments, and it may well be that the long-run natural rate is lower than assumed here.

**Conclusion**

Our estimate of the natural rate for the UK derived from a standard DSGE model provides a broad indication of how the natural rate may have evolved in recent years. As with any model-based estimate, it is surrounded by uncertainty. But it suggests that the natural rate fell very sharply following the financial crisis well into negative territory, perhaps even as low as -6%. It has subsequently picked up quite markedly, but still remains low, at around zero.

**Mike Goldby and Lien Laureys work in the Bank’s Monetary Assessment and Strategy Division and Kate Reinold works in the Bank’s Conjunctural Assessments and Projections Division.**

***Update 19/10/2015: The data for chart 1 and chart 2 are available for download in .XLSX format***

**Bank Underground is a blog for Bank of England staff to share views that challenge – or support – prevailing policy orthodoxies. The views expressed here are those of the authors, and are not necessarily those of the Bank of England, or its policy committees.**

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