From Phillips to Policy: What Should Anchor the NAIRU?

The Expectations Revolution

The original Phillips Curve is a beautiful empirical regularity: lower unemployment meant higher inflation. Policymakers in the 1960s thought they faced a stable menu of choices - trade off a bit more inflation for a bit less unemployment, or vice versa. The current Phillips curve in respect of Australia looks like this.

Then the 1970s happened.

Friedman and Phelps had warned that the trade-off was illusory. Workers and firms aren't stupid. If they come to expect 5% inflation, they'll build that into wage negotiations and price-setting. The only way to keep unemployment below its "natural rate" is to keep surprising people with more inflation than they expected - an accelerating spiral that eventually ends badly.

This gave us the expectations-augmented Phillips Curve:

$$\pi_t = \pi^e_t + \beta(u^* - u_t) + \varepsilon_t$$

Inflation equals expected inflation, plus a demand component (how far unemployment is from the NAIRU), plus supply shocks. The stagflation of the 1970s was exactly what Friedman predicted: once expectations ratcheted up, you couldn't buy lower unemployment with higher inflation anymore. You just got the higher inflation.

The Level Problem

The expectations-augmented framework was a theoretical triumph. But it came with an under-appreciated weakness: it tells us nothing about the level of inflation.

Think about it. The model says inflation will stabilise when unemployment equals the NAIRU and expectations are fulfilled. But fulfilled at what level? 2%? 5%? 10%? The model is agnostic. Any level of inflation is an equilibrium, as long as expectations have settled there.

This matters enormously for policy. If all you have is an expectations-augmented Phillips Curve, you can estimate the NAIRU as "the unemployment rate consistent with stable inflation" - but stable at whatever level expectations happen to be. That's interesting for understanding inflation dynamics, but it's not what central bankers actually need to know.

The Inflation Targeting Solution

Enter inflation targeting. Once a central bank commits to a specific target - 2.5% in Australia's case - the policy question becomes concrete: what interest rate path will return inflation to target?

This reframes the NAIRU question entirely. The policy-relevant NAIRU isn't the unemployment rate that stabilises inflation at current expectations. It's the unemployment rate consistent with inflation at the target. If expectations are sitting at 3.5% but the target is 2.5%, the NAIRU we care about is the one anchored to 2.5% - because that's what determines whether we need restrictive or accommodative policy.

This distinction sounds academic, but it has real consequences. If you anchor your NAIRU to whatever expectations happen to be, you'll conclude policy is neutral when unemployment equals that estimate. But if expectations are above target, you actually need unemployment above the target-anchored NAIRU to push inflation down. The level agnosticism of the pure expectations-augmented framework can mislead you about the stance of policy.

Down the Rabbit Hole: Where Do Inflation Expectations Come From?

All of this requires actually measuring inflation expectations - which is where I fell into an empirical rabbit hole.

For some time, I'd been using an unprovenanced data file from MacroDave containing an inflation expectations series (PIE_RBAQ) that could be from the Reserve Bank of Australia (RBA). The series runs from 1983Q1 to 2019Q1 and appeared to be what the RBA uses as an input to their NAIRU model.

To understand the provenance, I went to Cusbert (2017) - the RBA's published methodology for NAIRU estimation. But here's the thing: Cusbert describes a Kalman filter model for estimating the NAIRU, not for extracting inflation expectations. The expectations series is an input to that model, not an output. Cusbert notes only that the RBA "extracts a common signal of long-term expectations from the various measures after controlling for each measure's co-movement with recent inflation," citing Kozicki and Tinsley (2012).

So the architecture is:

1. Expectations extraction (separate model, briefly described) → produces an inflation expectations series
2. NAIRU estimation (Cusbert 2017, Kalman filter) → uses expectations as an input, along with Phillips curve relationships

I have assumed the MacroDave series is the output of step 1 - but the methodology for step 1 was never fully published. Rather than rely on data I couldn't verify, I decided to build my own expectations extraction model from scratch.

Building the Signal Extraction Model

The approach follows the logic of Kozicki and Tinsley, but implemented as a Bayesian state-space model rather than a classical Kalman filter. The core idea: "true" latent inflation expectations evolve as a random walk, and we observe them imperfectly through multiple noisy measures - surveys of market economists, business expectations, bond market breakevens, and realised inflation itself.

Different measures have different biases. Market economists' 1-year-ahead forecasts read slightly below true short-run expectations. Business surveys reflect own-price inflation rather than CPI. Breakeven inflation includes liquidity and term premia. The model estimates these biases (α) alongside a backward-looking component (λ) that captures how much each measure responds to recent inflation rather than forward-looking expectations.

The Bayesian approach has advantages over classical Kalman filtering: it naturally quantifies uncertainty through posterior distributions, handles regime switches (expectations were more volatile before inflation targeting), and allows for fat-tailed innovations via Student-t distributions - important for capturing the occasional large moves during the 1980s disinflation.

The Pre-1993 Challenge

Survey data only begins in the early 1990s. Before that, you need proxies: nominal bond yields decomposed via Fisher equations, headline CPI (on the theory that expectations were largely adaptive back then), and hourly compensation growth adjusted for productivity. My model produces a smooth decline through the 1980s disinflation - which makes economic sense but doesn't match the MacroDave series, which shows a peculiar sawtooth pattern I can find no justification for in the underlying data.

This matters less for current policy conclusions - the real action is in the post-survey period - but it does underscore that pre-1993 estimates should be treated with appropriate humility.

The Post-1993 Fit - With a Design Choice

Once survey data is available, signal extraction becomes more reliable. My "Target Anchored" model correlates at 0.94 with the RBA series through 2019 (when their series ends), with an RMSE of just 6 basis points in the anchored period after 1998.

The model includes, post-1998, an observation that "true" expectations equal 2.5% with modest noise. This is not an empirical claim that expectations are anchored - it's an identification choice about which equilibrium matters for policy. In an inflation-targeting regime, the central bank is not indifferent across equilibria. It is explicitly trying to select one. The model formalises that by giving weight to the target as an attractor.

What happens if we remove that design choice?

Removing the Anchor

I estimated a parallel "Unanchored" model using identical survey and market data, but without imposing that expectations converge to target. The comparison is revealing:

Target Anchored (current estimate): 2.58%
Unanchored (current estimate): 2.75%

The 17 basis point gap tells you how hard the anchor is working. Right now, it's doing modest work - surveys are reading a bit above target, and the anchor is pulling the estimate down. This isn't "error" - it's the model expressing the policy regime's influence on what we treat as the relevant equilibrium.

But the more interesting story emerges from comparing different horizons.

Short Run vs Long Run: Two Different Worlds

When I estimate expectations using only short-run indicators (1-year-ahead market economist forecasts plus realised inflation), the picture looks quite different from the target-anchored estimate. Short-run expectations are currently sitting at 3.02% - meaningfully above the target band. And they've been elevated since the post-COVID inflation surge, suggesting punters don't yet believe inflation will fully return to target over the next year.

The bond market tells a completely different story. Long-run expectations (extracted from 10-year breakeven inflation) are at 2.24% - actually below the target midpoint.

What's going on? The bond data suggests a fascinating narrative:

1. Markets took years to be convinced the RBA could anchor expectations (breakevens only gradually converged to 2.5% through the 1990s)
2. Then they absorbed the Larry Summers secular stagnation thesis - growth and inflation would be structurally lower
3. Even after the post-COVID inflation spike, they're betting on a return to that secular stagnation low-inflation equilibrium

Short-run forecasters see sticky inflation. Long-run markets see secular stagnation redux. Both can be right - they're just answering different questions.

These distinctions aren't cosmetic. Depending on which expectations measure you use, the implied NAIRU - and therefore the perceived stance of policy - can shift materially.

On Reserve Bank credibility

This divergence between short-run and long-run expectations isn't a sign of failing credibility - it's what credibility looks like during a shock. Short-run forecasters should expect inflation to stay elevated if supply disruptions or demand pressures haven't fully resolved - these shocks can take some time. The credibility test is whether long-run expectations stay anchored despite the short-run miss. At 2.24%, they have. Markets are betting the RBA will eventually do the work to get inflation back to target, even if it takes time. The more interesting question - which the target-anchored NAIRU helps answer - is whether the RBA is currently doing enough to justify that confidence.

Closing the Circle: What Should Anchor the NAIRU?

This brings us back to the policy question. In an inflation-targeting world, what should anchor our estimate of the NAIRU?

Option A: The target itself. This is my preferred approach. If you're a central bank trying to get inflation to 2.5%, the NAIRU you care about is the unemployment rate consistent with 2.5% inflation. Using the target as your anchor makes the NAIRU directly policy-relevant: when unemployment is above this NAIRU, you expect the RBA to take action sufficient for inflation to fall toward target; when below, you expect RBA action to make it rise.

Option B: Estimated expectations. Use whatever the signal extraction model produces - short-run, long-run, or some combination. This tells you about inflation dynamics given where expectations actually are. But it conflates two questions: "where will inflation go from here?" and "where should policy push it?"

Option C: A hybrid. Use all available indicators to extract the signal, but include the target as one of those indicators with a meaningful weight. This is essentially what the Target Anchored model does - it says "expectations are probably close to target, but let the data speak if they've moved away." It is also what the original (perhaps RBA sourced) PIE_RBAQ file did.

The choice matters most when expectations have drifted from target - exactly the situation we're in now. If you use pure estimated expectations (currently elevated), your NAIRU estimate will be lower, and policy will appear adequately restrictive - but this understates how much slack is actually needed to get inflation all the way to target. If you anchor to the target, you see the problem more clearly: policy is still too loose relative to where it needs to be.

What I will be doing

I'll be using estimated expectations in my NAIRU model for the period prior to 1993, phasing to the 2.5% target from 1998 onwards. Not because I'm certain expectations are anchored - the Unanchored estimates above suggest they've drifted somewhat - but because the policy question demands it. The RBA isn't trying to stabilise inflation at 2.75% or 3.02%. It is trying to get it to 2.5%. The policy-relevant NAIRU should tell us what that requires. This is more stringent than the hybrid approach the RBA was perhaps using and may still be using.

Key takeaway: NAIRU estimation without an explicit inflation-level anchor is incomplete in an inflation-targeting regime.