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Phillips Curve Calculator

The Phillips curve describes the inverse relationship between unemployment and inflation rates in an economy. Economists, policymakers, and central banks use this framework to understand price dynamics and labour market conditions. This calculator lets you explore three theoretical versions—traditional, New Classical, and New Keynesian—each reflecting different assumptions about how expectations and price-setting behaviour drive inflation.

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Creators Arturo Barrantes, MSc Finance
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Historical Origins and Core Concept

A. William Phillips's 1958 empirical study of British wage and unemployment data established a striking pattern: periods of low unemployment coincided with rising wages, whilst high unemployment brought wage declines. This observation challenged earlier economic thinking and prompted researchers to examine whether similar trade-offs existed in other industrialised economies.

The relationship reflects a fundamental economic mechanism: tight labour markets push up wages as employers compete for scarce workers, whilst slack labour markets suppress wage growth. Over decades, economists broadened this insight to encompass inflation itself, creating a framework linking cyclical unemployment to price-level changes. The Phillips curve became central to post-war macroeconomic policy because it suggested policymakers could choose between lower unemployment (accepting higher inflation) or price stability (accepting higher unemployment).

Three Versions of the Phillips Curve

Traditional Phillips Curve: This earliest formulation directly links money wage growth to the unemployment rate. It captures the empirical observation that wage pressure emerges when joblessness falls, without explicitly modelling inflation expectations or supply shocks. Policymakers initially treated the trade-off as stable and exploitable.

New Classical Phillips Curve: Building on the Lucas critique and rational expectations theory, this version incorporates the natural rate of unemployment (NAIRU) and expected inflation. The equation recognises that workers and firms anticipate future price changes when negotiating wages. Only unexpected inflation—or deviations from the natural rate—move unemployment in the short run. This model explains why sustained inflation fails to lower unemployment permanently.

New Keynesian Phillips Curve (NKPC): Introduced in 1995, this framework grounds inflation dynamics in firms' pricing decisions under sticky prices. The NKPC shows inflation depending on expected future inflation, the output gap (deviation from potential output), and supply shocks. This version underpins modern central bank models because it better captures how monetary policy transmission works through firms' real marginal costs and forward-looking behaviour.

Mathematical Formulations

Each Phillips curve version has a distinct mathematical structure reflecting its theoretical assumptions:

Traditional:

π = πᵉ − b(U − Uₙ) + v

New Classical:

π = πᵉ − b(U − Uₙ) + v

New Keynesian:

π = βEₜ(πₜ₊₁) + κỹ + v

where κ = [λ((1−α)σ + φ + α)] / [(1−α) + αε]

and λ = [(1−θ)(1+θβ)] / θ

  • π — Current inflation rate
  • πᵉ or Eₜ(πₜ₊₁) — Expected inflation (current or forward-looking)
  • U — Unemployment rate
  • Uₙ — Natural rate of unemployment (NAIRU)
  • b — Sensitivity of inflation to unemployment gap
  • ỹ — Output gap (actual minus potential output)
  • κ — Slope parameter linking inflation to output gap
  • β — Households' discount factor
  • θ — Price stickiness (duration of fixed prices)
  • σ — Intertemporal elasticity of substitution
  • φ — Inverse labour supply elasticity
  • α — Labour's share of output
  • ε — Firms' price elasticity of demand
  • v — Unexpected supply shocks

Key Considerations When Using the Calculator

The Phillips curve remains a powerful tool, but several assumptions and real-world complications can affect its predictive accuracy.

  1. Expectations matter enormously — In modern economies, inflation expectations anchor behaviour more than actual unemployment rates. If central banks lose credibility, expected inflation can rise even when joblessness is high, flattening the Phillips curve. Always check whether your expected inflation assumptions align with survey data or market expectations.
  2. The natural rate is unobservable — Economists debate the true NAIRU or natural rate constantly, and it shifts over time due to demographics, technology, and labour market institutions. Small changes in your assumed natural rate can dramatically alter the unemployment gap and predicted inflation, so sensitivity analysis is essential.
  3. Supply shocks create large deviations — Oil price spikes, pandemic disruptions, and wage-cost pressures can push inflation far above or below what the unemployment rate alone would predict. The shocks term (v) captures these, but in real time identifying their magnitude is difficult, making short-term forecasts volatile.
  4. The long-run Phillips curve is vertical — All three versions predict that permanently lower unemployment requires ever-accelerating inflation—a trade-off that cannot be sustained. In the long run, inflation returns to expectations and unemployment to its natural rate, so the Phillips curve offers no escape from the inflation-unemployment dilemma.

NAIRU versus Natural Rate of Unemployment

These terms are often used interchangeably, but they have distinct meanings. The natural rate of unemployment reflects structural labour market features—skills mismatches, job search frictions, sectoral shifts, and geographic immobility. It is a feature of the economy's long-run equilibrium independent of inflation.

NAIRU (non-accelerating inflation rate of unemployment) is the specific unemployment level consistent with stable, non-accelerating inflation. In low-inflation equilibrium, the two concepts align, but during periods of changing inflation trends or credibility shifts, they can diverge. Central bankers focus on NAIRU because breaching it risks triggering upward spirals in wage and price growth.

Frequently Asked Questions

How does the Phillips curve explain stagflation?

The 1970s stagflation—simultaneous high inflation and unemployment—challenged the traditional Phillips curve, which predicted an inverse relationship. The culprit was a shock: oil embargoes and commodity booms raised inflation independently of labour market slack. The New Classical and New Keynesian versions account for this via the supply shock term (v). When large adverse shocks hit, inflation rises and unemployment rises together, temporarily breaking the negative correlation and exposing the Phillips curve's limitations.

Why do central banks rely on the Phillips curve today?

Modern central banks embed Phillips curve logic into their monetary policy frameworks because it captures how demand pressures translate into inflation. The New Keynesian version—with its focus on the output gap and forward-looking inflation expectations—fits the dynamics policymakers observe. By targeting inflation expectations and managing demand to keep output near potential, central banks use the Phillips curve implicitly to maintain price stability and full employment.

Can the Phillips curve slope change over time?

Yes. The slope (b or κ) can flatten or steepen depending on inflation credibility, labour market institutions, and how easily firms adjust prices. When central banks are credible and inflation expectations are anchored, workers and firms are less sensitive to unemployment changes, flattening the curve. Conversely, high-inflation regimes with volatile expectations often show steeper curves as price-setters respond more urgently to joblessness. Recent decades have seen flatter curves in many developed economies, puzzling policymakers.

What does the output gap measure in the New Keynesian Phillips curve?

The output gap (ỹ) is the percentage deviation of actual real GDP from its potential (trend) level. It captures aggregate demand pressure: when actual output exceeds potential, firms operate above normal capacity, raising marginal costs and inflation. Conversely, output below potential signals slack and disinflation. The NKPC uses the output gap instead of unemployment because it directly reflects firms' pricing incentives, making it more theoretically coherent for monetary policy transmission analysis.

How do inflation expectations shift the Phillips curve?

Higher expected inflation shifts the Phillips curve upward—meaning at any given unemployment rate, actual inflation will be higher if workers and firms anticipate greater price growth. This is why central bank credibility is crucial: credible promises to keep inflation low anchor expectations downward, improving the trade-off policymakers face. When credibility erodes, expectations rise, the curve shifts up, and policymakers must tolerate higher inflation at any employment level to avoid uncontrolled acceleration.

Is the Phillips curve still relevant for forecasting?

The Phillips curve remains a key reference point, but modern forecasters combine it with other models and real-time data on expectations, supply shocks, and labour market slack. The relationship is less tight than it was in earlier decades, and forecasters must account for measurement uncertainty around the natural rate and changing structural features. Many central banks use the Phillips curve as one input alongside wage growth, commodity prices, and survey expectations to form inflation outlooks.

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