NAIRU

The cleanest definition

NAIRU stands for the Non-Accelerating Inflation Rate of Unemployment. It is the unemployment rate at which inflation does not change. Push the economy below NAIRU and inflation rises; sit above NAIRU and inflation falls. NAIRU itself is the knife-edge in between. The clean operational statement is

Δπ > 0   ⇔   u < u_n
Δπ = 0   ⇔   u = u_n   (= NAIRU)
Δπ < 0   ⇔   u > u_n

where π is the inflation rate, u is the unemployment rate, and u_n is NAIRU. This is the modern macro replacement for the original Phillips curve. The 1958 curve, fit by A.W. Phillips to nearly a century of UK wage data, plotted the level of inflation against the level of unemployment and found an inverse relation. NAIRU re-states the relationship in changes: the relevant question is not where on a Phillips curve you sit, but whether the inflation rate is drifting up, drifting down, or holding steady — and which side of NAIRU you are on tells you that.

Two equivalent names attach to the same object. The natural rate of unemployment is the term Friedman and Phelps used in the late 1960s; it emphasises the labor-market microfoundations (frictional unemployment, voluntary turnover, mismatch, search). NAIRU is the term that came in with the rational-expectations and time-series literature of the 1970s and 1980s; it emphasises the inflation-stability property. The two are essentially the same number and are used interchangeably in most modern work.

Friedman, Phelps, and the vertical long-run curve

The intellectual breakthrough came in two papers in two years. Edmund Phelps's 1967 Economica article and Milton Friedman's 1968 AEA presidential address argued — independently and from different angles — that the Phillips curve as estimated by Samuelson and Solow could not be a stable policy menu. Friedman's argument was a logical one: if firms and workers care about real wages, then any nominal Phillips trade-off must depend on inflation expectations. Once those expectations adapt, the trade-off vanishes.

The story unfolds as follows. Suppose unemployment is at u_n with inflation steady at 2 percent. The central bank decides to push unemployment to u_n − 1 by accepting a one-time jump in inflation to, say, 4 percent. In the short run it works: firms see prices rising and hire, workers — who still expect 2 percent inflation — accept the nominal wage offered, which is now lower in real terms than they realise. Once they update their expectations to 4 percent inflation, their next wage demand jumps to compensate. Real wages rise, firms cut hiring, unemployment returns to u_n. To keep unemployment below u_n the central bank now has to accept 6 percent inflation; then 8 percent; and so on. The long-run Phillips curve is therefore vertical at u_n.

This was a remarkably bold prediction in 1968: the orthodoxy was that high inflation and high unemployment could not coexist. The 1970s — oil shocks, double-digit inflation, double-digit unemployment, in both the US and the UK — settled the question. Phelps received the 2006 Nobel for the work; Friedman had received his in 1976 partly for the same set of ideas. The expectations-augmented Phillips curve became the workhorse of macroeconomic teaching.

The math: the expectations-augmented Phillips curve

The standard textbook form is

π_t  =  π^e_t  +  β · (u_n − u_t)  +  ε_t

where

• π_t — realised inflation in period t
• π^e_t — public's expectation of period-t inflation (formed in t−1)
• u_t — observed unemployment rate
• u_n — NAIRU (may be time-varying)
• β > 0 — slope of the short-run Phillips trade-off
• ε_t — supply shock (oil price, productivity, etc.)

The equation says: inflation equals what people expected, plus a term that depends on how much unemployment differs from NAIRU, plus shocks. In steady state with anchored expectations (π_t = π^e_t) the slack term vanishes and u_t = u_n. The long-run Phillips curve is therefore vertical at NAIRU, just as Friedman and Phelps argued.

Two common refinements:

• Adaptive expectations (Gordon's "triangle" model). Replace π^e_t with a lag of past inflation, π_{t−1}. The system becomes π_t = π_{t−1} + β(u_n − u_t) + ε_t, which makes the relation between Δπ and the unemployment gap explicit. This is the version usually estimated empirically.
• New Keynesian Phillips curve. Replace π^e_t with a forward-looking expectation E_t π_{t+1} and motivate β from Calvo price-setting microfoundations. The form becomes π_t = κ · (mc_t) + β E_t π_{t+1}, with marginal cost mc_t standing in for the labor-market gap. The NAIRU-equivalent here is the level of real marginal cost consistent with steady-state inflation.

Estimating NAIRU — and why it is hard

NAIRU is unobservable. You see the unemployment rate; you see inflation; you don't see u_n. Estimating it requires a model. The standard approach is to fit the augmented Phillips curve and back out the unemployment rate at which inflation is steady. The US Congressional Budget Office, the Federal Reserve, and the OECD all publish their own NAIRU series using variants of this approach, sometimes combined with state-space filters that let u_n drift over time.

The trouble is that NAIRU estimates carry large standard errors. A 1997 paper by Douglas Staiger, James Stock, and Mark Watson — directly titled How Precise Are Estimates of the Natural Rate of Unemployment? — concluded that a typical 95 percent confidence interval for US NAIRU was roughly 5 to 7 percent at a time when point estimates clustered around 6. In other words, the data could not distinguish between very different operational answers. Subsequent work has refined the methods but has not closed the uncertainty meaningfully.

That imprecision matters for policy. If a central bank tries to keep unemployment exactly at NAIRU but is uncertain by a full percentage point, it can spend years above or below the true equilibrium without realising. Olivier Blanchard's 2018 work, drawing on the post-2008 episode, argued the slope β has flattened to near zero in advanced economies, meaning that even a precise NAIRU estimate would no longer translate cleanly into an inflation forecast.

US NAIRU through the decades

CBO estimates of the US long-term NAIRU have drifted as the composition of the labor force, productivity, and labor-market institutions have changed.

Era	CBO NAIRU (approx)	Realised u	Realised π	Drivers of NAIRU level
Early 1980s	~6.0 %	7 – 10 %	4 – 13 %	Young workforce (baby-boomer entry); 1970s inflation overhang in expectations.
Late 1990s	~5.2 %	4 – 5 %	2 – 3 %	Workforce aging into prime years; globalisation; anchored expectations; productivity boom.
Late 2000s	~5.0 %	5 – 10 %	−0.4 – 4 %	Crisis-era hysteresis concerns push estimates briefly higher.
Late 2010s	~4.6 %	3.5 – 4.5 %	1.5 – 2.5 %	Continued aging; tight market without inflation undermines higher estimates.
Post-COVID (2022–24)	~4.4 %	3.5 – 4.0 %	2 – 9 % (supply shock)	Strong wage growth without wage-price spiral; well-anchored expectations.

The trend is downward. Three forces account for most of it: the aging of the workforce out of the high-turnover prime-young-worker bracket; the steady anchoring of inflation expectations after the early-1980s Volcker disinflation; and the globalisation and digitisation of labor markets, which made it easier to substitute toward cheaper labor wherever it was geographically. The post-COVID period revived debate — unemployment sat below most NAIRU estimates for years while inflation eventually returned to target without a recession.

What happens above and below NAIRU

Below NAIRU. Labor markets are tight. Firms compete to retain and attract workers, bidding nominal wages up. If productivity growth does not keep pace, unit labor costs rise, and firms pass them through into prices. Workers, seeing prices rise, demand bigger raises in the next round. Inflation accelerates — not just sits at a higher level, but climbs each year — until expectations or policy intervene. This is the wage-price spiral. Empirically, the most reliable single signal is nominal wage growth running above productivity growth + the inflation target. In the US, that means wage growth significantly above roughly 3.5 percent annually for a sustained period.

Above NAIRU. Slack in the labor market. Workers compete for jobs and accept smaller raises; firms cannot pass cost increases through because customers are price-sensitive. Inflation decelerates. If unemployment stays well above NAIRU for long, there is a real risk of expectations un-anchoring downward — Japan's deflationary trap in the late 1990s and 2000s is the textbook example.

At NAIRU. Inflation is stable. Wage growth equals productivity growth plus inflation target. Unemployment is at the rate consistent with normal frictional turnover, voluntary quits, and structural mismatch. This is the macro equilibrium.

Hysteresis — when downturns scar the equilibrium

One of the deepest critiques of the textbook NAIRU framework is that NAIRU itself may not be fixed. Hysteresis — a term Olivier Blanchard and Lawrence Summers borrowed from physics in their 1986 paper — is the idea that prolonged unemployment can permanently raise the equilibrium unemployment rate. The mechanisms:

• Skill atrophy. Long-term unemployed workers lose technical, social, and habit-of-work skills. After a year or more out of work, employability falls sharply; many never re-enter at their prior wage or occupation.
• Discouragement. Workers stop looking and exit the labor force entirely. Once out, returning becomes progressively harder; some never come back.
• Insider-outsider bargaining. Incumbent employed workers (insiders) negotiate wages in their own interest, with little weight given to unemployed outsiders. Even with high unemployment, wages can keep rising in line with insiders' preferences, blocking re-hiring.
• Stigma. Employers use long unemployment spells as a screening signal even when they shouldn't, perpetuating exclusion.

If hysteresis is strong, a deep recession leaves a permanently higher NAIRU. The original Blanchard-Summers motivation was European unemployment after the early-1980s recession, which failed to retrace despite years of slack. Hysteresis is also a major argument for aggressive monetary stimulus during downturns: if persistent slack permanently damages the supply side, the cost of running policy too tight is much larger than the standard framework suggests.

The post-COVID puzzle

From 2021 through 2024 the US labor market presented a clean test of the NAIRU framework and largely failed it. Unemployment sat below most published NAIRU estimates for three years running. Job openings exceeded unemployed workers by record margins; quits hit all-time highs. By the textbook logic, inflation should have accelerated continuously and required a Volcker-style recession to break.

What happened instead is that inflation did spike, but the spike was concentrated in goods supply chains and energy, not in services or wages, and it receded in 2023–2024 without an unemployment surge. Several explanations have been proposed:

• The true post-COVID NAIRU is well below 4 percent — perhaps in the 3.5 percent range — because of structural changes (older workforce, remote work, higher labor-force participation among women and immigrants).
• The slope β of the augmented Phillips curve has flattened to near zero, so even a meaningful u_n − u gap produces little inflation pressure.
• Inflation expectations were so well anchored after a decade of below-target inflation that the surge was correctly seen as transitory and never propagated into wage demands.
• The inflation spike was a one-off supply-side phenomenon (semiconductors, oil, supply chains) that resolved itself, leaving the demand-side story largely unchanged.

It is probably some mix of all four. The episode dented confidence in tight NAIRU-based policy rules and revived interest in watching wage growth and explicit expectations directly.

The Sahm rule — a NAIRU-free recession signal

Claudia Sahm, then at the Federal Reserve, proposed a simple real-time recession indicator in 2019: when the three-month moving average of the US unemployment rate rises 0.5 percentage points or more above its lowest value in the previous twelve months, a recession is likely already underway. Formally,

Sahm indicator_t  =  u_3MA(t)  −  min(u_3MA(t−12), …, u_3MA(t−1))
Sahm rule fires when  Sahm indicator ≥ 0.5 pp

The virtue of the rule is that it does not require knowing NAIRU. It tracks the rate of change of unemployment from its recent floor, which empirically corresponds well with the start of recessions in the postwar US. Once unemployment is climbing meaningfully off the bottom, household spending and confidence reinforce the rise, making the early signal a useful one. The Sahm rule has fired at the onset of every postwar US recession on record. It famously triggered in August 2024 — and then, somewhat awkwardly for its inventor, the US did not enter recession, an episode that reminded forecasters that even reliable indicators have non-zero false-positive rates.

Related macroeconomic objects

Object	What it measures	Relationship to NAIRU
Natural rate of unemployment u_n	Frictional + structural unemployment in equilibrium	Synonym for NAIRU in most modern usage
Output gap (Y − Y*)/Y*	Deviation of GDP from potential output	Related via Okun's law: Δu ≈ −0.5 × output gap; both gaps drive inflation
Potential output Y*	Output at full employment with stable inflation	The supply-side counterpart: NAIRU and Y* are joint estimates
Labor-force participation rate	Workforce / working-age population	Changes in participation can shift NAIRU's interpretation; "true" slack may show up in participation, not unemployment
U-6 underemployment	Broader slack including marginal and part-time-for-economic-reasons	Some economists prefer U-6 as the labor-market gap measure in low-NAIRU regimes
Beveridge curve (vacancies vs unemployment)	Matching efficiency in the labor market	Shifts in the Beveridge curve are evidence of changes in u_n

Common pitfalls

• Treating NAIRU as a constant. It is not. Demographics, productivity, institutions, and globalisation all move it over time. CBO updates its estimate quarterly for good reason.
• Confusing NAIRU with full employment. NAIRU still includes frictional and structural unemployment — voluntary quits between jobs, location and skill mismatch, new entrants searching. Even at NAIRU, several million people in a large economy are unemployed.
• Over-trusting point estimates. Confidence intervals are typically wider than ±1 percentage point. A 4.5 percent point estimate could correspond to a true NAIRU anywhere from 3.5 to 5.5.
• Ignoring expectations anchoring. The textbook framework assumes inflation expectations adapt. If they are strongly anchored — as the Fed appears to have achieved — the Phillips curve flattens and small NAIRU gaps no longer produce big inflation moves.
• Forgetting hysteresis. Long recessions may permanently raise NAIRU through skill atrophy and labor-force exit, meaning the cost of failing to stimulate aggressively is more than just the cyclical loss.
• Mistaking a Sahm-rule fire for certainty. The Sahm rule is a reliable warning, not a guarantee; like all empirical indicators it has false positives (2024 being the most recent).