Five years after the beginning of the financial crisis, there are still a lot of people trying to come to grips with monetary policy and inflation. Here is an analogy that TH thinks might (usefully) help make monetary policy setting seem less like rocket science and more like child’s play.

Imagine that you have a stick balancing on the end of your index finger. It’s a nice straight stick, about a metre or so long – perhaps a pool cue made for a child. The stick is unstable, it could fall any which way, but for the sake of this thought experiment, imagine that it can only fall forwards, away from you, or backwards towards you.

If you are standing still and are lucky, you have it perfectly balanced, but at any moment, some random event could cause the still to fall forwards or backwards. If you do nothing, the force of gravity will quickly cause the pace at which the stick falls forwards or backwards to increase. If the stick starts falling forwards, your natural instinct will be to push your finger away from you so that the base of the stick gets out in front of the top of the stick and halts the stick from falling over. With some skill, you’ll soon have it well-balanced on the end of your finger again.

By now, you have a pretty well-developed model in your mind of that stick. It is also a pretty good model of (the Wicksellian cumulative process of) inflation and monetary policy. Where the bottom of the stick is and what it is doing (remember it can’t go sideways, only backward or forward) tells you about the nominal rate of interest; closer to you is a lower rate of interest, further away from you is a higher rate of interest. The top of the stick tells you about inflation – if it is falling forwards, inflation is increasing, backwards and prices are falling. Clearly there is going to be a relationship between interest rates and inflation – you can play with the model in your head – or get a stick and try it out for yourself. The model has some pretty good predictive power. Try pulling the (virtual) stick towards you (cut interest rates) and what see happens to inflation. Anyway, before going further you need two simple equations that might help to better convert our balancing stick into a model of inflation:

r=i-p*,

which simply says that the real rate of interest on a financial investment (a loan) is the nominal rate of interest (i.e. the interest rate on loans, which we will assume to be the same as the policy rate set by the central bank) minus the inflation rate, p*.

The other equation is

p=f(R-r),

In this equation, R is the natural rate of interest – it is the rate of return on physical investments – from building a house or a factory. The equation says that inflation is a function of (which is what the f stands for) the gap between the natural rate of interest and the real interest rate expected to be earned on a financial asset. If r is less than R, so that it is profitable to borrow money and buy a real investment (a house or a factory), then the increased demand for goods such as these will cause the inflation rate to rise.

Let’s return to our stick analogy. Suppose you have the stick perfectly balanced on your finger. It’s not falling forward or backward. The base of the stick is right under the top. You are standing still. Remember that top of the stick tells you about inflation. Since the top of the stick is not moving, inflation is currently zero. The real rate of interest is therefore equal to the natural rate of interest (this comes from the information summarised by Equation 2). If you expect things to stay this way, or at least that the chances of the stick falling forward in the future to be the same as it falling backwards, then the expected rate of inflation would be zero too. And since the expected rate of inflation is zero, it is also the case that the nominal rate of interest must just equal the real rate of interest, which, as we said, is equal to the natural rate of interest. Got it? p* =0 and p=0, so from Equation 2, R=r and from Equation 1, r=i, so i=R too.

Now all the hard work is done, try doing the same thought experiment again. Imagine that you pull your finger towards you just a bit so that you pull the base of stick from under the top. This shock causes the nominal rate of interest and consequently the real rate of interest to fall below the natural rate and stimulates people to borrow and invest. It drives up demand in the economy and prices start to rise – i.e. inflation goes up. The top of the stick starts falling forward. Quickly, people start to realise that, unless something is done soon, there is going to inflation in the future. The higher expected inflation means that, given the nominal rate of interest, the real rate of interest (real cost of borrowing) is now even less than before, which further fuels an increase in investment and inflation. The process feeds on itself in a vicious circle, creating a process of accelerating inflation and the stick is soon accelerating rapidly towards the floor.

The inflationary process can be stopped by pushing forward on the bottom of the stick – this is analogous to increasing the interest rate. Just as you would have to push the bottom of the stick forward to get in front of the top to stop its fall, to make the real rate of interest equal to the natural rate of interest and set inflation back to zero, the increase in the interest rate will have to overshoot the rate of increase in prices. For example, if the shock has caused inflation to increase from 0 to 5%, then the increase in the nominal rate of interest – the policy rate – will have to be more than 5%. This is because of the effect of inflation expectations. Just like the stick has some momentum, so do expectations about future inflation, and the policy rate must increase by enough to offset not only the current rate of inflation but any expectations that are forming based on the current behaviour of the economy about future inflation.

So what does our simple model tell us about current monetary policy? TH reckons it tells us quite a lot. First, monetary policy, like balancing a stick on your finger, is more of an art than rocket science. You don’t need to know the laws of physics to balance the stick, you just need practice. There are also different styles too. Some stick balancers (read inflation-targeting central bankers) could prefer slow graceful adjustments to the policy rate – that allows for longer periods of inflation away from the central bank’s target (Australia says inflation will be around 2 to 3 percent, on average, over the course of the cycle, which could be up to 10 years!). Others might prefer swifter, sharper policy adjustments and more stable prices. Both could work. We could call the two types of policy reactions as Type I and Type II. Australia would be a Type I inflation targeter.

## Expectations about inflation

As you might have guessed, expectations about future inflation are also important in this model. Suppose that the central bank has a zero inflation target, and people are firmly convinced that the central bank will keep inflation close to zero, then an inflationary shock won’t need such a swift or large interest rate response from the central bank because it won’t need to offset the stimulatory, self enforcing effect of inflation expectations causing a reduction in the real interest rate and stimulating demand. To make their life easier, central bankers will continuously remind you of their inflation objective to do what they can to keep you convinced that inflation expectations are “well-anchored.”

## The zero lower bound on interest rates and forward guidance

You can do the inflation thought experiment for deflation too. Imagine that the stick starts falling towards you. What do you do? The obvious thing is to pull the base of the stick towards you and cut interest rates. With some manoeuvring, the deflation will be halted. But what do you do if you can’t pull the still towards you. If there was nothing else you could do, then there would be a deflationary spiral and you would have lost the stick. But of course there are other things you can do. Suppose you were once a quick reacting (Type I) central bank that kept inflation close to target with swift and large if necessary interest rate responses. Now you only have a little bit of lee-way, maybe to cut the interest rate to zero from say, 2%. One trick is to switch type from a Type II central banker into a central banker that prefers slow and small adjustments (Type I). If you don’t tell people that you have switched to Type II from Type I monetary policy, they may mis-read a small interest rate cut for policy ineffectiveness. Those deflationary expectations could start getting away from you, reinforcing the downward spiral. So what do you do? You provide guidance to the markets that you are going to stay “low for long”, possibly until some condition outside of the control of the central bank like unemployment is met, and remind them of your inflation target to keep inflation expectations well anchored. This has become known as forward guidance. TH prefers Open Mouth Operations.

## The zero lower bound on interest rates and quantitative easing

But interest rates are not the only game in town. Everyone knows that printing money (aka quatitative easing) is inflationary right? So another way to prevent deflation when you can’t pull back on the stick is to print money. This will create the expectation that there will be some inflation, which will lower the real rate of interest for borrowers and stimulate demand. Effectively, it’s finding a way to push on the top of the stick. Again, by helping to anchor inflationary expectations (in this case offsetting expectations about deflation), quantitative easing can give help make the interest rate tool more effective at the lower bound.

**Monetary policy to increase inflation with rational expectations**

As noted above, inflation expectations are important in this model . The momentum in the stick, which keeps it falling forward or backwards, even after some policy response, is a proxy for what economists call adaptive expectations. It simply means that people form expectations, at least partly, on the basis of what happened in the past. What would happen if they were fully rational or forward looking? In that case, then things might be a bit topsy turvy. For example, suppose that the central bank announced a new inflation target of 10% (up from 0). If the natural rate of interest was 3%, then, if everyone fully believed that the central bank would hit is target, starting a year from today (or tomorrow at annualised rates), all the central bank would have to do is INCREASE interest rates immediately to 3+10 = 13% to create inflation. Using our stick analogy, the central bank would announce a new inflation strategy, which would stimulate demand and get the top of the stick moving forward, and then simultaneously start walking forward, pushing on the bottom of the stick. The central bank would then just keep on walking forward at a constant pace that was analogous to constant increase in prices of 10% (perhaps ten steps a minute), with the top of the stick perfectly aligned with the bottom.

If you are quick, you might wonder whether the model with adaptive expectations could ever be consistent with the model with rational expectations. After all, in the adaptive expectations case you cut interest rates to create inflation, in the rational case you raise them. The answer is relatively simple, once you think of monetary policy as just balancing a stick on your finger. After all, you know that you could, with practice initiate a process where you went from standing still while balancing the stick, to walking forward at a constant pace of 10 steps per minute. First you would cut interest rates, get inflation moving and soon adaptive expectations would learn that you were serious about targeting 10% inflation. Once you were advancing forwards at close to 10 steps per minute, you would tighten policy by pushing forward on the stick to alleviate the acceleration created by gravity and momentum. It might require a bit of back and forth, but eventually you’ll achieve your goal. You understand this, and so do market participants who seek to learn to come to rational conclusions through adaptive means. All you need to know is that, in addition to cutting rates to increase inflation, you can raise them in the future to prevent accelerating inflation. So long as you know that, you will quite rationally understand that you can raise inflation by cutting interest rates.