R-star as an international price

I have written about r-star twice this year. The first post tried to pin down Australia's natural rate the standard way, a Holston-Laubach-Williams state-space model, trend growth and the IS curve doing the identifying work. It couldn't be done. The IS curve coefficient on the real rate gap came out at around minus 0.05, against quarter-to-quarter noise of about 0.7. A signal one-fourteenth the size of the noise floor cannot identify anything. Every variant I tried failed the same way, the latent r-star collapsing onto whichever prior I fed it.

The second post started with the premise that liquidity is global, and in every country investment seeks out the best returns in the world. The standard approach to r-star instead asks Australian output and inflation to reveal the real interest rate that balances desired saving and investment, as though that equilibrium were fundamentally domestic. But saving and investment now meet in a global capital market. A single global market still leaves room for a country-specific wedge, the way a single global oil market leaves room for regional basis differentials between Brent, WTI and everything else. The wedge is the local story. The level it sits on top of is not.

This post takes that global understanding and uses it to model Australia's neutral real rate of interest, r-star. World r-star plus the Australian wedge gives Australian r-star, rather than Australian output, inflation and trend growth being asked to produce one on their own. Australia's own market tells you the wedge on top, not the underlying price.

The model

One latent state: an Australia-specific wedge over world r-star, the mean of the New York Fed's Holston-Laubach-Williams estimates for the US, the Euro Area and Canada. The wedge follows a random walk with fat-tailed, Student-t innovations. Australian r-star is world r-star plus the wedge. The gap between that and the observed indexed 10-year yield is a term premium, given a stationary prior. That's the whole model. No trend growth, no IS curve, no output gap feeding back into the estimate.

Every model I wrote that tried to route r-star through domestic transmission failed: this one's HLW predecessor, a NAIRU-based Phillips system, and a full dynamic-stochastic general equilibrium (DSGE) model. Three different specifications, the same failure, for the reason above: all three were asking domestic macroeconomic data to identify a price set in an international capital market.

What comes out

Real r-star sits at 1.24 per cent, against 2.18 before the GFC, about 57 per cent of that level. The 90 per cent interval around that estimate runs from −0.57 to 3.14, wide enough to straddle zero, so treat 1.24 as the model's best single guess, not a tightly pinned number.

Add the inflation target and you get nominal r-star, the cash rate consistent with neutral policy. That's 3.74, against the current cash rate of 4.35, so policy currently sits about six-tenths of a point above neutral.

A Taylor rule layers a response to current inflation and the output gap on top of that neutral level, and prescribes 5.51, a gap over a point wide. That's not a claim that neutral has moved, or that 5.51 is where the cash rate belongs indefinitely. It's the temporary setting a rule would recommend to bring inflation back to target, after which the cash rate would be expected to ease back toward the 3.74 neutral level itself. Read it as a guide to direction and intensity rather than a setting the Bank ought to hit, more on why below.

The term premium and QE

The model splits the observed bond yield into two pieces: r-star and a term premium. It can only do that because the two are given different rules to obey. R-star is anchored to world r-star and allowed to drift, a random walk, so it can wander a long way over time but only gradually. The term premium is required to mean-revert around a constant average, so however far it swings, it has to come back. Anything in the yield that looks temporary gets read as term premium; anything that looks like a lasting shift gets read as r-star. That's the whole mechanism. The test is whether the resulting split makes sense against events the model was never told about.

I call that second component the term premium, though in a model this stripped down it's really the stationary part of the gap between the ten-year indexed yield and r-star. The textbook term premium is the extra return investors demand for holding a ten-year bond instead of rolling over cash at the short rate again and again, compensation for the risk that rates or inflation surprise them over that horizon. What this model actually estimates can absorb other temporary influences on long real yields as well. Anything that reverts rather than persists gets swept into the same component. So treat "term premium" here as a label for that stationary residual, not a clean isolation of the textbook concept. A component like that should pick up liquidity conditions, risk appetite and central bank bond-buying rather than lasting changes in the economy's underlying capacity to generate returns. That's what makes it useful here: if the model is actually separating the two things it claims to, events like QE should show up in this component, not in r-star.

That's what happens, and the timing holds up in detail. The AU-world spread actually rose in 2020Q1, during the March dash for cash, before the suppression from bond purchases pulled the term premium negative from Q2, to about minus 0.4 through 2020 to 2022, exactly the period the RBA was buying bonds and running yield curve control. Nothing in the model marks those quarters or tells it when QE started or stopped. The suppression appears anyway, in the one place a bond-market model ought to put it: the price investors demand for holding duration, rather than the natural rate itself. That's a useful external check, not independent proof. The model has already been told, through the stationarity prior on the term premium and the random-walk wedge, roughly which kinds of movement should be temporary and which should persist. What it wasn't told is when.

The wedge's single largest move in the whole sample lands at 2022Q2, on liftoff and the exit from QE, not inside the purchase period itself, and the pandemic itself, as distinct from the bond buying that followed it, didn't shift Australia's wedge beyond where the RBA's 2019 easing cycle had already taken it. That's worth flagging rather than asserting: nothing in the model requires the unwind of a liquidity event to be a shift in the natural rate rather than the term premium simply reversing. It could be either. What the model shows cleanly is where the movement sits in time, not why the 2022Q2 jump belongs in the rate rather than the premium.

What the model doesn't claim

The level is only weakly pinned down. The starting wedge and the average term premium trade off against each other almost one for one, so the data fix their sum, the total level of the yield, without fixing the split between "Australia sits above the world rate" and "the average term premium is large." Both intervals run close to two points wide. What holds the level in practice is the assumption that the term premium is stationary, a real assumption doing real work, not a free result.

The model also still carries a Taylor rule, and the rule leans specifically on the cash rate moving output through the standard channel, higher rates, less investment, a wider negative output gap. That's the one channel the first post went looking for and couldn't find in Australian data. It isn't a claim that the cash rate doesn't affect the Australian economy. The Australian dollar is one of the world's most heavily traded currencies despite the economy being nowhere near that rank by GDP, so one plausible explanation is that an important part of the transmission runs through the exchange rate and trade-exposed sectors rather than the domestic interest-rate-to-investment link this rule is trying to identify. The first post showed that the latter is weak in the data. It didn't establish where the missing transmission went. Read 5.51 as what a standard reaction function would recommend, not a forecast of what would follow if the RBA ran it. The gap itself, 5.51 against 4.35, isn't unusual by the standard of the series, something close to it opened and closed repeatedly through the 1990s and 2000s. What's unusual is how far nominal r-star has fallen since the mid-1990s, from above 5 per cent to under 4, which is most of why a 4.35 per cent cash rate now reads as restrictive when it would have read as easy thirty years back.

Where this leaves it

R-star for Australia is not fundamentally a domestic quantity waiting to be revealed by a better model of the Australian economy. The first post showed the domestic channel that ought to identify it is too weak to do the job. The second argued that's because the thing being measured was never primarily domestic. This model takes that seriously: start with the international price of capital, then ask what Australian markets add on top. Australia's real r-star is currently about 1.24 per cent, nominal neutral about 3.74 per cent, and the cash rate at 4.35 per cent is modestly restrictive. A standard Taylor rule, responding to the gaps as well as neutral, would put it higher still, at 5.51 per cent.

It's a soft model. The level is weakly pinned, the 90 per cent interval around 1.24 straddles zero, and the 2022Q2 jump could be r-star or could be the term premium reversing, and nothing here settles which. What it is not is a claim to have finally measured Australia's natural rate. It is a model that starts where the earlier failures ended: stop asking weak domestic signals to identify a price set in a global market. That's it.