Phil Milburn

The equilibrium interest rate (r*) in the UK

Phil Milburn

In the Bank of England’s August 2018 Inflation Report, the concept of the “equilibrium interest rate” was introduced to the lexicon for UK investors. On the other side of the Atlantic, the Federal Reserve has been actively discussing this for years; it is affectionately known, at least by economists, as r*. Despite this being a predominately theoretical exercise, as r* is not directly observable, it does have large ramifications for long-term investment in bond markets.

What is r*?

The idea of r* is conceptually simple and attractive.  It is the short-term interest rate which should occur when the economy is at equilibrium. In this case, equilibrium means that unemployment is at the natural rate and inflation is at the 2% target, i.e. when there is no output gap. If r* is the prevailing bank rate, then output should grow at its potential rate and inflation should be around the Bank’s 2% target. If short term rates are below r* then monetary policy is expansionary, with the converse applying if rates are above r*.

Effectively, r* can be considered to be a reasonable proxy for the trend rate of growth in GDP. Clearly, both r* and GDP can be measured in nominal or real (inflation-adjusted) terms. The Bank of England has added an extra wrinkle by having both an r* (equilibrium real rate) and R* (trend real rate) with the difference between the two being s* (a “shorter-term component”). Thus:

r* = R* + s*

Or, in plain English, the equilibrium real rate is the long term trend real rate adjusted for some shorter term stuff! The Bank of England did not publish an estimate of r* or s*, but did state that “…the equilibrium real rate remains well below the trend real rate R*, which is itself well below its longer-term average.”

R* in real terms is estimated by the Bank to be 0-1%, its modal estimate being 0.25%; in nominal terms this translates to 2-3%.  This has fallen significantly since 1990 with the financial crisis taking an exacting toll. Prior to the crisis, the bank rate averaged 5%; indeed this holds over a much longer-term time horizon, “…over the entire period since the Bank of England was founded in 1694, Bank rate has averaged close to 5%.”

Estimated distribution of the trend real rate

Phil Milburn: The equilibrium interest rate (r*) in the UK

  The green line shows a smoothed distribution of the low-frequency component of actual UK real interest rates. The gold line shows a smoothed distribution of the UK trend real rate generated by Bank staff’s model under the range of possible values of R* in 1990, alternative assumptions for the model parameters, and the paths of the main determinants.

What drives R* and why has it fallen so much?

There are myriad factors that drive R* but by far the biggest two are demographics and productivity. As developed markets’ populations age, this lowers the potential trend growth rate. The transmission mechanism for this includes a higher dependency ratio and larger savings pools (R* can be thought of as balancing the return on wealth and the cost of economic capital) or at least the behavioural desire for greater wealth to fund longer retirement periods as life expectancy increases. Both of these demographic factors can be somewhat mitigated by greater older age employment i.e. increasing retirement ages. We are already witnessing this in the UK with the state pension being pushed further out for younger generations. This glacial but powerful demographic force is set to continue with the UN estimating that median average ages in advanced economies will increase from 41 years (in 2015) to 45 years by 2040.

Productivity growth in the G7 economiesPhil Milburn: The equilibrium interest rate (r*) in the UK

Sources: OECD, ONS and Bank calculations.

  Rolling three-year averages for annual growth in output per worker in Canada, France, Germany, Italy, Japan, the UK and US.

Productivity growth has been very disappointing since the financial crisis. The Bank of England argues that “…structural factors, including a decline in trend productivity growth, have reduced businesses’ demand for capital.” I take huge issue with the implied direction of causality here; it is just as conceivable that the lack of private sector capital investment has caused a fall in productivity rates. One should at least acknowledge the circularity between the two. In my opinion one of the factors that has been deterring capital investment is quantitative easing (QE). I am a big believer in the huge influence that incentives have over human behaviour; most Chief Executives are rewarded by increases in the absolute share price, but when equities are rising in conjunction with all other assets due to the loose money injection from QE there is little incentive to take risk on a new capital project and a large incentive to undertake share buybacks and take the large safe pay cheque at the end of each month.

There are many other factors that have affected productivity such as the aforementioned demographics, increased compliance costs in many sectors and for the financial sector in particular, the shift of advanced economies to be more service orientated and the overall hit to aggregate demand from consumer balance sheet deleveraging. There is hope that the rapid pace of technological improvements will lead to increased productivity over the next couple of decades. I am optimistic in this regard but it is unlikely to be enough to take real R* back to its 2.25%-3.25% (modal estimate 2.5%) historic range in the UK.

Why does a lower R* matter?

When factors such as the UK’s fiscal austerity drag on growth and the economic act of self-harm that is Brexit drop out, then s* will tend to zero and r* will become R*. However, real R* even at the top end of the range at 1% is not suggestive of a dynamic economy. If nominal rates in the UK in this cycle are going to peak at 3% (assuming they never become tight), a level that assumes a lot of headwinds fall away, then real returns from investing in government debt will remain poor. On the flip side, those that predict the end of the bond market have not read up on how long this effective financial repression can last for. Even in the USA, which is much further through the monetary cycle, we are unlikely to see base rates above 3%.

The Liontrust Global Fixed Income team continues to believe that running with a lower beta exposure to assets such as government debt is the right way to strategically invest in this environment.  One can then use funds’ risk budgets to target alpha generation and hopefully produce decent positive real returns for investors.

Finally, an important driver for financial markets is the social policy implications that a lower R* has. There has been an intertemporal transfer of wealth from the younger generation to the older one; this is not a complaint, merely an econometric observation. Wealth inequality has increased and economic growth is anaemic. When you combine all these factors, it is of little surprise that social unrest is increasing and one should expect more “shock” election results. Our job as fund managers is to understand the risks, recognise when there is a structural story that should be avoided or just a volatility event that can be exploited to generate alpha. We are indeed living in interesting times!

For a comprehensive list of common financial words and terms, see our glossary here.

Key Risks 

Past performance is not a guide to future performance. Do remember that the value of an investment and the income generated from them can fall as well as rise and is not guaranteed, therefore, you may not get back the amount originally invested and potentially risk total loss of capital. Investment in Funds managed by the Global Fixed Income team involves foreign currencies and may be subject to fluctuations in value due to movements in exchange rates. The value of fixed income securities will fall if the issuer is unable to repay its debt or has its credit rating reduced. Generally, the higher the perceived credit risk of the issuer, the higher the rate of interest. Bond markets may be subject to reduced liquidity. The Funds may invest in emerging markets/soft currencies and in financial derivative instruments, both of which may have the effect of increasing volatility.


The information and opinions provided should not be construed as advice for investment in any product or security mentioned, an offer to buy or sell units/shares of Funds mentioned, or a solicitation to purchase securities in any company or investment product. Always research your own investments and (if you are not a professional or a financial adviser) consult suitability with a regulated financial adviser before investing. 

Monday, August 13, 2018, 9:49 AM