## Monday, January 21, 2013

### The Taylor Rule and the Reserve Bank of Australia

[Note: This is an old post I originally wrote in January 2012.]

The Taylor rule is an equation that relates the nominal interest rate to inflation and output (Gross Domestic Product, or GDP). A forward-looking version of the rule could be expressed as follows:

Nominal interest rate = (Underlying) Inflation + Real neutral interest rate + a * (Expected (underlying) inflation - Target inflation) + b * Expected Output Gap

Now that the Reserve Bank of Australia has been publishing its output and inflation forecasts in its quarterly “Statement on Monetary Policy” since early-2008 I thought it would be an interesting nerdly exercise to see if you could relate the RBA’s setting of the cash rate to its output and inflation forecasts using the Taylor rule formula.

First, some assumptions

OK, there’s a lot of assumptions we have to make before we can put the rule into effect. First, we need to assume a value for the real neutral interest rate. The real neutral interest rate is, in theory, the value of the cash rate adjusted for inflation that means that monetary policy is neither expansionary nor contractionary. For those monetary policy newbies, a real interest rate below the neutral rate should tend to heat up the economy and raise output and inflation, while a real interest rate above the neutral rate should tend to slow things down. Understandably, the RBA has been reluctant to say what it thinks the value of the neutral rate is, but we can take an educated guess. A value of 3 per cent or more seems too high, given that the real cash rate has been lower than that for the majority of the “inflation targeting” era. In May 2011, when the cash rate was 4.75 per cent and underlying inflation was 2½ per cent, giving a real rate of 2¼ per cent, the RBA said that “this represents a mildly restrictive stance of monetary policy”. Then in November 2011, when the cash rate was reduced to 4.5 per cent and underlying inflation was 2½ per cent, giving a real rate of 2 per cent, the RBA said that “a more neutral stance of monetary policy was now appropriate”. Based on this, a real neutral interest rate of 2 per cent is good enough for me.

Next, how far in the future should we measure expected inflation and expected output? Gruen, Romalis and Chandra (1997) found that there was an average lag of about five or six quarters in monetary policy’s impact on output growth. So I’m going to assume that the RBA are looking at inflation and output five or six quarters out. Since they publish forecasts at six-monthly intervals, I’ll use the forecasts for five quarters out when those are available, and the forecasts for six quarters out when those are available.

Third, we need to calculate the expected output gap. The output gap is equal to real GDP less the level of real potential output (all divided by real potential output). Real potential output is the highest level of real GDP that can be sustained based on the supply of workers and capital and how productive they are; if real GDP is higher than real potential output than inflation tends to increase. Basically, if you can accurately work out what potential output is you’re an uber-nerd. I’m going to assume that potential output is growing at 3 per cent per year, and that it was less than real GDP back in early-2008 and about the same as real GDP in late-2011. This means that real GDP was expected to be well below potential output (i.e. the output gap was negative) during late-2008 and 2009 due to the effects of the global financial crisis and the resulting downturn in the world economy.

Fourth, I’m going to set target inflation at 2.5 per cent, the mid-point of the RBA's target band for inflation over the medium-term.

As mentioned above, I’m using underlying inflation figures rather than changes in the Consumer Price Index. Underlying inflation strips out the most volatile prices, and is therefore less affected by short-term movements (such as temporary rises or falls in petrol or food prices).

Finally, I’m setting a = 0.5 and b = 0.5, as John Taylor originally did.

So, the results ...

The graph below compares the actual cash rate from the March quarter 2008 to the November quarter 2011 with the cash rate as implied by my Taylor rule and my mangling of the RBA’s forecasts.

I don’t know - it doesn’t look too bad a fit to me ... I could probably make it fit a bit better by fiddling around with the potential output series, but I think you could characterise the RBA’s policy-setting as “Tayloresque”. There’s a bit of a difference around the global financial crisis era, but you could understand if the RBA wanted to be aggressive in cutting rates around that time.

It’s all a bit rough - I don’t imagine any major banks would be staking their millions on using this to accurately predict the RBA’s next move, but in a world of baffling economic models it’s always nice when you can use something simple to explain behaviour.

﻿