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Phillips Curve Calculator

Calculate actual inflation using the Phillips Curve formula π = πe − β(u − un) + s. Enter expected inflation, unemployment, NAIRU, slope, and supply shocks for instant results.

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What Is the Phillips Curve?

The Phillips Curve describes the short-run trade-off between inflation and unemployment in a macroeconomy. Originally documented by economist A.W. Phillips in 1958 using UK wage and unemployment data spanning 1861–1957, the relationship reveals that periods of low unemployment tend to coincide with higher wage inflation. The modern expectations-augmented Phillips Curve, developed independently by Milton Friedman and Edmund Phelps in 1968, extended this framework by incorporating inflation expectations and the concept of a long-run natural rate of unemployment, fundamentally reshaping how policymakers model price dynamics.

The Phillips Curve Formula

The calculator applies the standard expectations-augmented Phillips Curve equation used in contemporary macroeconomic analysis:

π = πe − β(u − un) + s

  • π — Actual (realized) inflation rate, the output of the equation
  • πe — Expected inflation rate, reflecting what households and firms anticipate; often anchored to the central bank's stated target or lagged inflation readings
  • β — Phillips Curve slope, measuring inflation sensitivity to the unemployment gap; empirical U.S. estimates post-1990 range from 0.3 to 0.5, indicating a relatively flat curve
  • u — Current unemployment rate (BLS U-3 headline measure)
  • un — Natural Rate of Unemployment (NAIRU); the Congressional Budget Office estimates the U.S. NAIRU at approximately 4.4% as of 2024
  • s — Supply shock term capturing exogenous inflationary or disinflationary forces such as oil price spikes, commodity disruptions, or pandemic-driven goods shortages

Understanding the Unemployment Gap

The expression (u − un) is the unemployment gap — the primary driver of demand-pull inflation in this model. When actual unemployment falls below NAIRU (u < un), the gap turns negative, labor markets tighten, wage growth accelerates, and firms pass higher costs on to consumers, pushing realized inflation above expected levels. Conversely, when unemployment exceeds NAIRU (u > un), spare capacity in labor markets cools wage growth and inflation falls short of expectations. With β = 0.4, each 1 percentage-point negative unemployment gap adds 0.4 percentage points to realized inflation.

The Role of Supply Shocks

The supply shock term s captures inflationary pressures that operate entirely outside the unemployment-inflation dynamic. A positive supply shock (s > 0) — such as the 1973 OPEC oil embargo, which raised U.S. crude prices by roughly 300%, or the 2021–2022 pandemic supply chain collapse — adds directly to inflation regardless of labor market slack. A negative supply shock (s < 0), such as a technology-driven productivity surge or a sharp commodity price decline, is disinflationary. Including s in the model resolves the 1970s stagflation paradox, where high inflation coexisted with high unemployment — a scenario impossible to explain under the original two-variable curve.

Worked Example

Consider a stylized U.S. scenario with the following inputs:

  • Expected inflation (πe) = 2.5%
  • Current unemployment (u) = 3.8%
  • NAIRU (un) = 4.4%
  • Phillips Curve slope (β) = 0.4
  • Supply shock (s) = 0.5% (moderate energy-driven pressure)

Applying the formula: π = 2.5% − 0.4 × (3.8% − 4.4%) + 0.5% = 2.5% − 0.4 × (−0.6%) + 0.5% = 2.5% + 0.24% + 0.5% = 3.24%. Tight labor markets and a modest supply shock together push realized inflation to 3.24%, above the Fed's 2% target — a result consistent with 2021–2023 U.S. inflation dynamics when unemployment averaged near 3.7% and supply disruptions were widespread.

Methodology and Sources

The formula implemented here follows the specification in the CBO Working Paper: Inflation, Inflation Expectations, and the Phillips Curve (2019), which provides empirical β estimates and anchored-expectations analysis for the U.S. economy. The NAIRU estimate of 4.4% reflects current CBO projections. Slope and flattening dynamics are drawn from the Federal Reserve memo on Phillips Curves and inflation forecasting (2017). Foundational context is available at Investopedia's Phillips Curve overview and the Khan Academy Phillips Curve explainer. Advanced structural decomposition is available in NYU Stern's Anatomy of the Phillips Curve.

Key Limitations

The Phillips Curve is a short-run relationship. In the long run, fully adjusted expectations render the curve vertical at NAIRU — no permanent unemployment-inflation trade-off exists. The slope β has flattened markedly since the 1990s: large unemployment gaps now produce smaller inflation responses than in earlier decades. Globalization, enhanced Fed credibility, and well-anchored expectations have all contributed to this structural change. Treat calculator outputs as directional estimates rather than precise point forecasts, and update β and NAIRU inputs to reflect current empirical conditions for the economy under analysis.

Reference

Frequently asked questions

What is a Phillips Curve Calculator and who uses it?
A Phillips Curve Calculator estimates the actual inflation rate using expected inflation, the current unemployment rate, NAIRU, the curve slope (β), and a supply shock term. Economists, monetary policy analysts, graduate students, and financial professionals use it to model short-run inflation dynamics, evaluate central bank policy stances, and stress-test macroeconomic forecasts under varying unemployment and supply-shock scenarios.
What is NAIRU and what is the current U.S. estimate?
NAIRU stands for Non-Accelerating Inflation Rate of Unemployment — the unemployment rate at which inflation neither accelerates nor decelerates. The Congressional Budget Office estimates the U.S. NAIRU at approximately 4.4% as of 2024. When actual unemployment falls below this threshold, excess labor demand pushes wages and prices higher, driving realized inflation above expectations. When unemployment exceeds NAIRU, slack cools wage growth and inflation decelerates toward or below expected levels.
Why is the Phillips Curve slope (β) so flat after 1990?
The Phillips Curve has flattened considerably since the 1990s, with empirical U.S. estimates placing β between 0.3 and 0.5, down from values exceeding 1.0 during the 1970s. Key drivers include improved Federal Reserve credibility anchoring long-run inflation expectations near 2%, globalization dampening domestic wage pressure, and structural labor market shifts. A flat β means that even a 2-percentage-point negative unemployment gap adds only 0.6 to 1.0 percentage points to realized inflation.
How do supply shocks affect the Phillips Curve inflation estimate?
Supply shocks add to or subtract from inflation entirely independently of the unemployment gap. A positive supply shock — such as the 2021–2022 global shipping crisis or a 50% crude oil price spike — raises the s term and pushes realized inflation higher even when unemployment equals NAIRU. The 2021–2023 U.S. inflation surge combined a tight labor market with large positive supply shocks, helping explain why headline CPI peaked above 9% year-over-year in June 2022, far above what the unemployment gap alone would imply.
What is the difference between the short-run and long-run Phillips Curve?
The short-run Phillips Curve slopes downward because inflation expectations adjust slowly, creating a temporary trade-off between unemployment and inflation. In the long run, expectations fully adjust and the curve becomes vertical at NAIRU — no permanent reduction in unemployment is achievable simply by tolerating higher inflation. Milton Friedman formalized this distinction in his landmark 1968 American Economic Association presidential address, arguing that attempts to permanently exploit the short-run trade-off would generate accelerating inflation without lasting employment gains.
How do central banks use the Phillips Curve in monetary policy decisions?
Central banks, including the Federal Reserve, embed Phillips Curve relationships in large-scale forecasting models such as FRB/US to calibrate interest rate decisions. When unemployment falls significantly below NAIRU, policymakers typically raise the policy rate to cool demand and prevent inflation from overshooting targets. The Fed's 2022–2023 tightening cycle — lifting the federal funds rate from near 0% to 5.25–5.50% across 11 consecutive hikes — directly reflected a deeply negative unemployment gap combined with substantial positive supply shocks driving inflation to a 40-year high above 7%.