# The difference between nominal, real and natural interest rates

In these strange times of zero and negative interest rates, it might sometimes be hard to understand what Central Banks try to achieve with their unconventional policies. In order to understand the current unconventional policies of Central Banks, you will need to be able to distinguish the 3 most important rates of interest: the nominal, real and natural rate of interest.

The ECB caused something of a stir by setting her most important interest rate below zero. Before we can understand why she did this, we first need to know which interest rate a Central Bank like the ECB governs. A Central Bank has the ability to set the nominal interest rate. This means that, if the Central Bank would set the nominal interest rate at 4%, you would get around 4% on your savings account. Based on this information you can choose whether you want to save or consume. Companies can decide whether they want to invest or not in this interest rate environment.

Considering whether you want to save at this 4% rate, you must also know what the current annual rate of inflation is. This knowledge is important, as you will probably be less inclined to save with an inflation rate of 3%, than with an inflation rate of 0%. In the former, your real interest rate will be 1% (4% – 3%) as in the latter you will get 4% of real interest. The Fisher equation shows the relationship between the real interest rate (r), the nominal interest rate (i) and inflation (π):

r = i – π

So the real rate of interest, is just the interest you get when you subtract the rate of inflation from the nominal interest rate. Because we expect that households and companies are mainly interested in the real rate of interest, we may expect that also the ECB is mainly interested in this rate of interest.

The ECB can’t directly set the real rate of interest, but she can do this indirectly. When the central bank knows that the inflation rate is equal to 2% and if she wants a real rate of 5%, then it will only need to set the nominal rate of interest at 7%.

So what is the natural rate?

The natural rate of interest is the real return on capital. Just as workers get a real wage, capital gets a real rate of return for adding value in production. This rate is also the rate at which the market savings and investments will clear. The theory is that if the central bank is able to set the real interest rate in such a way that it equals the natural rate of interest, the economy will grow at its natural growth. If the real rate is below the natural rate, the economy grows faster than its natural growth rate (positive output gap) and if the real rate is above the natural rate, the economy grows slower than its natural growth rate.

Taylor rule

This brings us to perhaps the most important thing of monetary theory: the taylor rule. The taylor rule gives a choice to the Central Bank. It can either choose to curtail inflation at the cost of lower growth or it can foster growth at the cost of higher inflation. If the central bank wants to curtail inflation, it will aim at a real interest rate that is higher than the natural interest rate. This makes intuitive sense, because a higher real rate will make saving more attractive (less consumption) and investment less attractive.

Liquidity trap

So why are some Central Banks involved in negative/zero interest rate policies at this moment? As mentioned before, the Central Bank can set the nominal rate and by doing this she is also able to set the real rate of interest:

r = i – π

If the Central Bank wants to stimulate economic growth and inflation, it needs a real interest rate that is lower than the natural rate of interest. Economists who believe that we are in a liquidity trap, think that the natural interest rate is below zero at the moment. This means that the Central Bank will need a real interest rate that is lower than zero to support growth and inflation. But how is she able to reach this negative real interest rate when inflation is close to zero? If you look at the equation above, you’ll see that the Central Bank will need to set a negative nominal interest rate in order to get the real rate below zero. It is however well known that the Central Bank cannot set a nominal interest rate that is to negative, as this would incline people to withdraw money from their bank accounts and keep it in a vault at home.