Phillips Curve NAIRU: Advanced Framework for Investors

Key Takeaways

• Friedman (1968) and Phelps showed the long-run Phillips curve is vertical: any stable unemployment-inflation tradeoff holds only for unexpected inflation, not after expectations adjust.
• NAIRU is unobserved and estimated via time-varying Kalman-filter models; CBO's U.S. natural rate estimate has ranged between 4.4 and 5.0 percent with revisions of 50–100 basis points across vintages.
• The New Keynesian Phillips curve π_t = β·E[π_{t+1}] + κ·(u_n − u_t) + ε shows that expectations and supply shocks, not just the labor gap, drive inflation outcomes.
• Del Negro et al. (2020) found pandemic-era shocks re-steepened the effective curve in some sectors after decades of flattening from 1990 through 2019.

What It Is

A.W. Phillips's 1958 paper documented an inverse relation between wage growth and unemployment in U.K. data from 1861 to 1957. Samuelson and Solow extended it to prices in 1960. Milton Friedman in 1968 and Edmund Phelps in parallel argued that any stable tradeoff holds only for unexpected inflation: once workers adjust their inflation expectations, the long-run curve becomes vertical at a natural rate of unemployment. That natural rate, operationalized, is NAIRU.

The modern New Keynesian Phillips curve adds forward-looking expectations and a marginal cost term. A common specification is:

π_t = β * E_t[π_{t+1}] + κ * (u_n - u_t) + ε_t

Where π is inflation, E_t[π_{t+1}] is next-period expected inflation, u_n is NAIRU, u is observed unemployment, β is a discount factor (near 0.99 at quarterly frequency), κ is the slope, and ε is a supply shock.

The Intuition

Tight labor markets raise wages. Higher wages raise marginal costs. Firms that reset prices pass some of that through. Inflation rises. Run the process in reverse for slack labor markets. That chain is the Phillips curve in one paragraph.

Two complications dominate post-1970 thinking. First, expectations matter. If workers and firms believe the central bank will not accommodate higher inflation, wage demands and price resets are anchored, and the short-run tradeoff flattens. Second, the slope κ is not a constant. Estimates have fallen substantially since the 1990s, which is why modest unemployment gaps in the 2010s produced modest inflation changes, while the 2021 to 2023 episode surprised forecasters on the upside.

How It Works

Three inputs drive the curve's output:

Cyclical gap:      u_n - u_t        (positive gap = slack, pulls inflation down)
Expected inflation: E_t[π_{t+1}]    (anchor variable)
Supply shocks:     ε_t              (oil, food, shipping, productivity)

NAIRU itself is not observed. It is estimated, typically with time-varying Kalman-filter methods (as in the Fed's and CBO's models), and point estimates vary across vintages. CBO's estimate of the U.S. natural rate has hovered between 4.4 and 5.0 percent over the last decade, while private-sector estimates have ranged lower.

Crucially, if expectations become unanchored, the forward-looking term in the New Keynesian Phillips curve starts to drift, and inflation rises even without a closed labor gap. Central banks watch survey-based and market-based measures (Michigan five-year expectations, five-year/five-year breakeven) precisely to catch that shift.

Worked Example

Take the U.S. late-cycle moment of mid-2022. Unemployment was 3.5 percent, below most NAIRU estimates near 4.5 percent, so the gap u_n - u_t was roughly plus 1.0 percentage point. Survey and market-based inflation expectations had risen: Michigan five-to-ten-year expectations sat near 3.0 percent, up from 2.5 percent a year earlier. Supply shocks from energy and shipping were still adding to ε.

Using a simple calibration with κ near 0.15 and a unit-weight on expectations:

π_t ≈ 1.00 * 3.0 + 0.15 * 1.0 + ε
    ≈ 3.15 + (supply shock of roughly 2 to 3 pp)
    ≈ 5 to 6 percent

That rough walkthrough is inside the band of realized core inflation at the time. The point is not the precision, but that two of the three inputs (expectations and supply shocks) were doing most of the work. A labor-market-only story would have underpredicted the episode sharply, which it did in most Phillips-curve vintages used at the time.

Common Mistakes

1. Treating NAIRU as a fixed number. It drifts with demographics, industry mix, matching efficiency, and measurement. CBO revisions of 50 to 100 basis points across vintages are common. Point estimates carry wide confidence bands.
2. Ignoring expectations. The long-run Phillips curve is vertical only if expectations are rational and the central bank is credible. Historical episodes where expectations became unanchored, the 1970s being the canonical case, produced very different dynamics from stable-anchor regimes.
3. Using a flat slope forever. Slope estimates fell from the 1970s through the 2010s. Recent work (Del Negro et al. 2020) suggests sectoral heterogeneity and reset frequency are crucial, and that pandemic-era shocks re-steepened the effective curve in some sectors.
4. Confusing NAIRU with u.* The Fed's Summary of Economic Projections publishes a long-run unemployment rate (u*) that is conceptually close to NAIRU but defined somewhat differently. Different models and different series do not produce identical numbers.
5. Forgetting supply shocks. The Phillips curve is a cyclical story. Large supply disturbances, whether oil crises, pandemics, or geopolitical shocks, can dominate the cyclical term for several quarters at a time.

Frequently Asked Questions

What is NAIRU and why can't it be observed directly? NAIRU, the non-accelerating inflation rate of unemployment, is the unemployment level at which inflation neither rises nor falls when expectations are anchored. It is not observable because it depends on structural factors like demographic composition, matching efficiency, and industry mix that shift over time. The Fed, CBO, and private-sector economists estimate it using time-varying Kalman-filter models, and point estimates carry wide confidence intervals.

Why did the Phillips curve flatten after the 1990s? After the Fed established credibility for low inflation in the early 1980s, inflation expectations became well anchored. Firms and workers stopped building large inflation adjustments into wage and price decisions, so the labor-gap term (κ × gap) produced smaller changes in inflation. The result was a flat slope: large swings in unemployment during the 2000s and 2010s produced modest changes in realized inflation.

Why did the 2021–2023 inflation surge surprise most Phillips-curve forecasters? Most pre-pandemic Phillips-curve models projected only modest inflation even with a tight labor market, because they used the historically flat slope and well-anchored expectations. The 2021–2023 episode combined a genuine unemployment gap with a large supply-shock term (ε) from energy, food, and shipping, and then saw expectations begin to drift higher. The forward-looking term in the NKPC amplified the supply shock into a more persistent outcome than the gap alone predicted.

How does the New Keynesian Phillips curve (NKPC) differ from the original? The original 1958 Phillips curve was empirical and backward-looking: lower unemployment meant higher wage growth. The NKPC is theoretically grounded and forward-looking: inflation today depends on expected future inflation, not just the current labor gap. That distinction means central bank credibility, which shapes E[π_{t+1}], becomes a first-order policy tool, not just a communication preference.

What do CBO's NAIRU estimates mean for Fed decisions? CBO's estimate of the U.S. natural rate acts as a reference point for whether the labor market is running hot or cold. When unemployment falls well below NAIRU, as it did in 2022 at 3.5 percent versus a NAIRU near 4.5 percent, the Phillips curve predicts upward pressure on wages and prices. But the wide confidence bands around NAIRU mean the Fed cannot rely on any single estimate; it supplements the gap measure with actual wage and price data.

Sources

1. Phillips, A.W. (1958). "The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861 to 1957." Economica 25. https://onlinelibrary.wiley.com/doi/10.1111/j.1468-0335.1958.tb00003.x
2. Friedman, M. (1968). "The Role of Monetary Policy." American Economic Review 58(1), 1 to 17. https://www.aeaweb.org/aer/top20/58.1.1-17.pdf
3. Del Negro, M., Lenza, M., Primiceri, G., Tambalotti, A. (2020). "What's Up with the Phillips Curve?" NBER Working Paper 27589. https://www.nber.org/papers/w27589
4. Federal Reserve Board. "FEDS Notes on the Phillips Curve." https://www.federalreserve.gov/econres/notes/feds-notes/
5. Congressional Budget Office. "NAIRU Estimates in the Budget and Economic Data." https://www.cbo.gov/data/budget-economic-data

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.