When the topic of central banks and the outlook for interest rates comes up, economists often turn to the so-called “star” variables to help with their predictions.

What do we mean by star variables? Why they are important to central bankers, and how do they influence interest-rate decisions?

The star variables relate to key concepts in economic models used by central bankers to help them understand how the economy works.

Star variables are named so simply because they are usually labelled with an asterisk to distinguish them from other variables in economic modelling.

Central bankers don’t normally think about the star variables in isolation. Instead, these variables are better thought of as a “constellation” linking economic growth, the labour market and interest rates together with inflation outcomes.

The three north stars

1. Potential output or y*: This is the economy’s maximum sustainable output that can be produced when all resources are fully employed. It is sometimes referred to as the economy’s speed limit. If economic growth is faster than potential, it can put upward pressure on inflation because demand for goods and services is outstripping supply.

The reverse is also true: if the economy is growing below potential, demand is subdued and inflation will likely fall.

Potential output is closely linked to productivity. Boosting productivity lifts the economy’s speed limit – allowing faster economic growth without fuelling inflation. But falling productivity lowers the economy’s speed limit, meaning it can’t grow as fast as previously without causing inflation to rise. This is the problem currently facing Australia.

2. Non-Accelerating Inflation Rate of Unemployment or NAIRU or u*, a concept that became popular in the 1970s. The idea is there is a “natural” rate of unemployment that doesn’t put pressure on wages or inflation.

3. The neutral interest rate or r* is considered to be the level of the central bank’s key interest rate that is not too low (and stimulating demand) and not too high (and restraining demand). It is a useful guide to the stance of the central bank’s monetary policy, or stance on the policy interest rate.

Good in theory, hard to measure in practice

These three interlinked variables are fundamental to how central bankers think about the economy.

But they are also concepts that are not observable, unlike published statistics on inflation or economic growth. They need to be estimated, and that’s where the uncertainty comes in.

In fact, central bankers must use statistical methods originally developed to track spacecraft to estimate them. This is done by detecting the effects these variables have on other variables that are observable, such as inflation, wages growth and the unemployment rate.

In a recent speech, a US Federal Reserve official wondered whether the three variables are “too abstract and elusive to be of practical value”. He concluded:

The short answer is that they play a central role in macroeconomic theory and have important implications for the conduct of monetary policy.[…] When the stars perfectly align, it means the economy has reached an equilibrium where its resources are fully utilized.

How the variables help with setting interest rates

Most central banks focus on maintaining price stability (low and stable inflation). A few, such as the Reserve Bank of Australia and the US Federal Reserve, have dual mandates to maintain price stability and full employment.

The way central bankers put their objectives into practice is influenced by the star variables. Specifying a target for inflation is seen as the best way to achieve price stability. The Reserve Bank’s target is 2–3% over the economic cycle.

Over time, inflation tends to be steady when the unemployment rate is close to the NAIRU. Because of this, central bankers often use the NAIRU as a rough guide to full employment, which is also broadly consistent with the economy operating near potential.

Understanding the central bank’s objectives is important because they tell us where the economy should go. But they don’t tell us what the central bank will do to get there – that is, what policy interest rate setting is needed to achieve its objectives (what economists call the central bank’s “reaction function”).

This is a way of describing how the central bank adjusts its policy interest rate based on differences between current economic conditions and the star variables.

But this is easier said than done. The uncertainties with estimating the star variables, together with the uncertainties in how interest rate changes flow through the economy, makes it difficult for central bankers to know exactly what decision they should make to achieve their objectives.

All this uncertainty is one reason why central bankers are very cautious. Sometimes it is better to do nothing than make a wrong decision and risk losing credibility.