Phillips Curve: Inflation, Unemployment, and the NAIRU

Key Takeaways

• The original 1958 Phillips curve was a statistical pattern; Friedman (1968) and Phelps (1967) showed the long-run curve is vertical at NAIRU, no permanent inflation-unemployment tradeoff exists.
• The expectations-augmented formula: pi = pi_e − beta*(u − u*) + epsilon; inflation expectations and supply shocks drive inflation as much as the unemployment gap.
• The "flat Phillips curve" of the late 1990s through 2019 occurred when unemployment fell well below NAIRU estimates without triggering sharp inflation, epsilon and pi_e were dormant.
• The 2021–2023 inflation surge showed supply shocks (epsilon) and expectations (pi_e) can dominate even a flat curve; the curve is not dead, just non-linear.

What It Is

In 1958, New Zealand economist A.W. Phillips published "The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957" in the journal Economica. He plotted nearly a century of British data and found a striking downward-sloping curve: years with low unemployment had fast wage growth, years with high unemployment had slow or negative wage growth.

Economists Paul Samuelson and Robert Solow reframed the relationship in 1960 in terms of price inflation rather than wages, and the resulting trade-off appeared to give policymakers a menu: accept more inflation to get lower unemployment, or vice versa. That interpretation did not survive the 1970s.

The Intuition

Tight labor markets give workers bargaining power. Firms must raise wages to retain and recruit, and those wage increases feed into prices. When unemployment is high, workers accept slower wage growth, and inflation pressures ease.

The original curve was a purely statistical pattern. Its theoretical foundation came later. What destroyed the simple trade-off was that policymakers tried to exploit it, and in doing so, changed workers' and firms' expectations about inflation.

How It Works

The modern expectations-augmented Phillips curve, developed by Milton Friedman (1968) and Edmund Phelps (1967), is:

pi = pi_e - beta * (u - u*) + epsilon

Where:

pi      = actual inflation
pi_e    = expected inflation
u       = actual unemployment rate
u*      = non-accelerating inflation rate of unemployment (NAIRU)
beta    = sensitivity parameter, positive
epsilon = supply shock (oil prices, tariffs)

The crucial addition is pi_e, expected inflation. Friedman and Phelps argued that if policymakers tried to push unemployment below NAIRU, workers would eventually expect higher inflation, demand higher wages, and shift the short-run curve up. In the long run, the curve is vertical at NAIRU, and no trade-off exists.

The stagflation of the 1970s confirmed the vertical long-run view: unemployment and inflation both rose together, which the naive Phillips curve said was impossible. Both Friedman and Phelps received Nobel Prizes, partly for this work.

Modern New Keynesian Phillips curves further refine the formula by using forward-looking inflation expectations and an output gap measure rather than unemployment:

pi = beta_f * E[pi_{t+1}] + kappa * (y - y*) + epsilon

Worked Example

Suppose the Fed's NAIRU estimate is 4.0 percent, inflation expectations are anchored at 2.0 percent, and the sensitivity parameter beta is 0.3. If actual unemployment falls to 3.5 percent, the simple expectations-augmented curve predicts:

pi = 2.0 - 0.3 * (3.5 - 4.0)
pi = 2.0 - 0.3 * (-0.5)
pi = 2.0 + 0.15
pi = 2.15%

Running the economy 50 basis points below NAIRU adds only 15 basis points to inflation. That mild response reflects the so-called flat Phillips curve period observed from the late 1990s through 2019, when US unemployment fell well below most NAIRU estimates without triggering sharp inflation.

The 2021 to 2023 inflation spike, driven largely by supply shocks and shifts in inflation expectations rather than unemployment alone, reminded economists that epsilon and pi_e are not permanently sleeping. When either moves, inflation can surge even with a flat curve.

Common Mistakes

1. Treating the original curve as a stable menu. The 1960s interpretation, that policymakers could just pick a point on the trade-off, is exactly what the 1970s disproved. The short-run curve shifts when expectations change.

2. Assuming a constant NAIRU. The non-accelerating rate of unemployment is unobservable and drifts over time with demographics, technology, and labor market frictions. Using a stale NAIRU estimate gives misleading inflation forecasts.

3. Attributing all inflation moves to the labor market. The epsilon term captures supply shocks, such as oil prices, semiconductor shortages, or tariffs. Ignoring them is why many 2021-2022 Phillips-curve-based forecasts missed inflation badly.

4. Confusing short-run and long-run curves. In the short run, there is a trade-off along a given expectations path. In the long run, the curve is vertical at NAIRU and monetary policy cannot permanently lower unemployment.

5. Declaring the curve dead. After years of "it's dead" claims through the 2010s, the 2021-2023 inflation surge made the curve look very much alive, just with a heavier weight on expectations and supply shocks than on the unemployment gap. The honest answer is that it is alive and non-linear.

Frequently Asked Questions

What is the Phillips curve? The Phillips curve is the inverse relationship between unemployment and inflation. The original 1958 version by A.W. Phillips was a purely statistical pattern from 97 years of UK data. Economists Paul Samuelson and Robert Solow reframed it in terms of price inflation in 1960, suggesting policymakers had a menu: accept more inflation for lower unemployment, or vice versa.

Why did the original Phillips curve break down in the 1970s? Because policymakers tried to exploit the trade-off and in doing so changed inflation expectations. Milton Friedman (1968) and Edmund Phelps (1967) predicted this: if workers and firms expect higher inflation, they will demand higher wages and prices, shifting the short-run curve up. The long-run curve is vertical at NAIRU, no permanent trade-off exists. The 1970s stagflation, where both unemployment and inflation rose together, confirmed this view.

What is NAIRU? NAIRU is the Non-Accelerating Inflation Rate of Unemployment, the unemployment rate at which inflation is neither rising nor falling. It is unobservable and must be estimated; it drifts over time with demographics, technology, and labor market frictions. Using a stale NAIRU estimate produces systematically wrong inflation forecasts, which was a major source of error in 2021 forecasting.

Why did inflation surge in 2021–2022 even though the Phillips curve seemed flat? The flat curve observed from the late 1990s through 2019 was partly because inflation expectations were well-anchored (pi_e was stable) and supply shocks (epsilon) were quiet. In 2021–2022, both changed: supply chains seized, commodity prices spiked, and inflation expectations rose, activating the supply shock and expectations terms in the formula. The curve was never dead, those components were dormant.

How does the New Keynesian Phillips curve differ from the original? The New Keynesian version (NKPC) replaces backward-looking inflation expectations with forward-looking ones and uses an output gap rather than an unemployment gap. The formula becomes: pi = beta_f * E[pi_next] + kappa*(output gap) + supply shocks. This forward-looking structure means inflation is determined partly by where the economy is expected to go, not just where it has been, which gives central bank credibility a direct role in controlling inflation.

Sources

1. Econlib. "Phillips Curve." Concise Encyclopedia of Economics. https://www.econlib.org/library/Enc/PhillipsCurve.html
2. Mankiw, N.G. and Reis, R. "Friedman and Phelps on the Phillips Curve Viewed from a Modern Perspective." NBER Working Paper 24891. https://www.nber.org/system/files/working_papers/w24891/w24891.pdf
3. Phelps, E.S. "Phillips Curves, Expectations of Inflation and Optimal Unemployment Over Time." https://www.columbia.edu/~esp2/PhilipsCurvesExpectationsofInflationandOptimalUnemploymentOverTime.pdf
4. Federal Reserve Bank of San Francisco. "Has the Phillips Curve Become Flatter?" https://www.frbsf.org/research-and-insights/publications/economic-letter/2019/09/has-the-phillips-curve-become-flatter/

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.