MACROECONOMICS • LONG-RUN GROWTH & POLICY TRADEOFFS

Phillips Curve & Expectations

Understanding the inflation–unemployment tradeoff and why expectations reshape it over time.

Historical Context & Motivation

For much of the twentieth century, policymakers believed they could permanently reduce unemployment by tolerating a bit more inflation. This belief rested on an empirical regularity first documented by New Zealand economist A. W. Phillips in 1958, who found a stable inverse relationship between wage inflation and unemployment in nearly a century of British data. The discovery electrified the economics profession because it seemed to offer governments a concrete policy menu: choose a preferred combination of inflation and unemployment, then use fiscal and monetary levers to reach that point on the curve.

The intellectual landscape shifted dramatically in the late 1960s when Milton Friedman and Edmund Phelps independently argued that the tradeoff was only temporary. Once workers and firms adjusted their inflation expectations, unemployment would return to its natural rate regardless of the inflation level. The stagflation of the 1970s—simultaneous high inflation and high unemployment—provided a stark empirical confirmation, and the debate over expectations became the central battleground in macroeconomic theory.

1958
Phillips's Original Study
A. W. Phillips published his landmark paper showing an inverse relationship between wage inflation and unemployment in UK data spanning 1861–1957, giving birth to the original Phillips Curve.
1960
Samuelson & Solow Adaptation
Paul Samuelson and Robert Solow reframed the relationship using price inflation instead of wage inflation, popularizing the curve as a policy menu for U.S. policymakers.
1968
Friedman–Phelps Critique
Milton Friedman and Edmund Phelps independently introduced the concept of adaptive expectations, arguing the long-run Phillips Curve is vertical at the natural rate of unemployment.
1973–75
Stagflation Arrives
OPEC oil shocks combined with expansionary policy produced stagflation—rising inflation alongside rising unemployment—discrediting the stable tradeoff view.
1976
Lucas & Rational Expectations
Robert Lucas extended the critique with rational expectations, arguing that even the short-run tradeoff disappears when policy is anticipated, reshaping macroeconomic modeling.

The central question the Phillips Curve framework addresses is deceptively simple: Can a society permanently buy lower unemployment with higher inflation? As we will see, the answer depends critically on how economic agents form and revise their expectations about future inflation—a distinction with profound implications for central bank credibility and the design of monetary policy.

Core Principles & Definitions

Before exploring the mathematical framework, it is essential to anchor several foundational concepts. The Phillips Curve story revolves around the interaction between inflation, unemployment, and the expectations that link them across time horizons. Each of the principles below builds upon the last, moving from the original empirical observation toward the expectations-augmented framework that dominates modern macroeconomic thought.

1

Short-Run Phillips Curve (SRPC)

A downward-sloping curve showing the inverse relationship between the inflation rate and the unemployment rate, holding inflation expectations constant. Each level of expected inflation generates a distinct SRPC.
2

Long-Run Phillips Curve (LRPC)

A vertical line at the natural rate of unemployment (Uₙ). In the long run, once expectations fully adjust, there is no tradeoff between inflation and unemployment—output returns to potential.
3

Natural Rate of Unemployment (Uₙ)

Also called the non-accelerating inflation rate of unemployment (NAIRU). It includes frictional and structural unemployment but excludes cyclical unemployment. The economy gravitates toward Uₙ in the long run.
4

Adaptive Expectations

The hypothesis that agents form expectations about future inflation by looking at recent past inflation. Adjustment is gradual, allowing short-run policy tradeoffs that vanish as expectations catch up.
5

Rational Expectations

The hypothesis that agents use all available information—including knowledge of government policy rules—to forecast inflation. Under rational expectations, even the short-run tradeoff may disappear for anticipated policies.
KEY TAKEAWAY
Think of the Phillips Curve like a GPS route: in the short run, a detour (expansionary policy) can temporarily get you to a destination of lower unemployment. But the GPS (expectations) recalculates, and eventually the route takes you right back to the natural rate—except now you are stuck with a higher inflation toll. The more sophisticated the GPS (rational versus adaptive expectations), the faster the recalculation occurs.

Visual Explanation: Short-Run vs. Long-Run Phillips Curve

The diagram below illustrates the core visual insight of the expectations-augmented Phillips Curve framework. Two short-run Phillips Curves are plotted—one for low expected inflation (πᵉ = 2%) and one for higher expected inflation (πᵉ = 6%)—alongside the vertical long-run Phillips Curve at the natural rate of unemployment. Observe how the short-run curves shift upward as inflation expectations rise, while the long-run curve remains fixed.

Point A represents long-run equilibrium at Uₙ = 5% with π = πᵉ = 2%. An expansionary policy moves the economy to point B (lower unemployment, higher inflation) along SRPC₁. As expectations adjust upward to πᵉ = 6%, the curve shifts to SRPC₂ and the economy settles at point C—back at the natural rate but now with 6% inflation.

The diagram captures the essential dynamic of the expectations-augmented Phillips Curve. The movement from A to B represents a short-run tradeoff: policymakers stimulate the economy, unemployment falls below the natural rate, and inflation rises. However, this position is inherently unstable. Workers observe the higher inflation and begin demanding higher wages, firms raise prices further, and inflation expectations ratchet upward. The SRPC shifts vertically, and the economy transitions from B to C. In the long run, the economy operates at the natural rate regardless of the inflation rate, which is why the LRPC is vertical.

Mathematical Framework

The expectations-augmented Phillips Curve provides a compact algebraic representation of the inflation–unemployment relationship. Several key equations formalize the visual intuition developed in Section 3, moving from the original Phillips relationship to the modern expectations-augmented version and finally to the supply-shock extension.

ORIGINAL PHILLIPS CURVE
π = −β(U − Uₙ)
where π = actual inflation rate, β = sensitivity coefficient (β > 0), U = actual unemployment rate, Uₙ = natural rate of unemployment. This version implies a stable tradeoff—lower U always raises π—but it ignores expectations.
EXPECTATIONS-AUGMENTED PHILLIPS CURVE
π = πᵉ − β(U − Uₙ)
where πᵉ = expected inflation. This is the Friedman–Phelps modification. When U = Uₙ, actual inflation equals expected inflation (π = πᵉ), confirming the long-run vertical curve. The short-run tradeoff exists only when π ≠ πᵉ.
SUPPLY-SHOCK AUGMENTED PHILLIPS CURVE
π = πᵉ − β(U − Uₙ) + ε
where ε = supply shock variable. A positive ε (e.g., an oil price spike) raises inflation at every unemployment level, shifting the SRPC upward. This term explains stagflation: both π and U can rise simultaneously if ε > 0.
ADAPTIVE EXPECTATIONS RULE
πᵉₜ = πₜ₋₁
Under simple adaptive expectations, agents set expected inflation for period t equal to the inflation actually observed in period t−1. More general forms use a weighted average of past rates: πᵉₜ = λπₜ₋₁ + (1−λ)πᵉₜ₋₁, where 0 < λ ≤ 1.
📐 Long-Run Implication
Setting π = πᵉ in the expectations-augmented equation gives 0 = −β(U − Uₙ), which implies U = Uₙ. This confirms the vertical LRPC: in the long run, unemployment cannot be held below the natural rate regardless of the inflation rate. Attempts to do so simply accelerate inflation without any lasting employment gain.

Adaptive vs. Rational Expectations in Detail

The behavior of the Phillips Curve hinges on how agents form their inflation expectations. Two dominant paradigms—adaptive expectations and rational expectations—yield fundamentally different predictions about the effectiveness of monetary and fiscal policy. Understanding the distinction is critical for business professionals who must anticipate how central bank actions will affect interest rates, demand, and hiring conditions.

Left panel (Adaptive): The economy zigzags through multiple short-run curves (A→B→C→D→E) as expectations slowly catch up to actual inflation. Right panel (Rational): If the policy is anticipated, agents adjust expectations immediately and the economy jumps directly from A to A' along the LRPC—no temporary drop in unemployment occurs.
Comparison of expectation formation mechanisms
FeatureAdaptive ExpectationsRational Expectations
Information usedPast inflation onlyAll available info, including policy rules
Speed of adjustmentGradual (multi-period lag)Instantaneous (for anticipated policy)
Short-run tradeoff?Yes—exists until expectations adjustOnly for unanticipated policy shocks
Systematic errors?Yes—agents persistently under- or over-predictNo—errors are random and unbiased on average
Policy implicationCentral bank can temporarily exploit the tradeoffOnly surprise policy moves real variables

The practical implication for business strategy is significant. Under adaptive expectations, a central bank that announces a rate cut can predictably stimulate spending and hiring in the near term because wage and price setters will be slow to adjust. Under rational expectations, the mere announcement may trigger immediate price and wage adjustments, neutralizing the real effects of the policy before any output gains materialize. Most contemporary macroeconomists accept a middle ground: expectations are forward-looking and informed, but rigidities in contracts, information costs, and behavioral biases allow some short-run policy traction even when agents are broadly rational.

Worked Example: Expectations-Augmented Phillips Curve

Suppose the economy is characterized by the following expectations-augmented Phillips Curve: π = πᵉ − 0.5(U − Uₙ). The natural rate of unemployment Uₙ is 5%, and initial expected inflation πᵉ is 3%. The central bank pursues an expansionary policy that drives unemployment down to 3%. We want to determine the resulting inflation in the short run, and then trace what happens in the next period under adaptive expectations.

Multi-Period Phillips Curve Analysis
1
Step 1 — Identify Given ValuesWe are given the expectations-augmented Phillips Curve: π = πᵉ − 0.5(U − Uₙ). The parameter values are: Uₙ = 5%, πᵉ = 3% (initial), and the policy-driven unemployment rate U = 3%.
Uₙ = 5%, πᵉ = 3%, U = 3%, β = 0.5
2
Step 2 — Compute Short-Run Inflation (Period 1)Substitute into the equation: π = 3% − 0.5(3% − 5%) = 3% − 0.5(−2%) = 3% + 1% = 4%. Expansionary policy has pushed inflation above expected inflation by 1 percentage point while reducing unemployment by 2 percentage points.
π₁ = 4%
3
Step 3 — Update Expectations (Adaptive Rule)Under simple adaptive expectations, agents set πᵉ for the next period equal to the inflation they just observed. Since actual inflation in Period 1 was 4%, expected inflation for Period 2 becomes πᵉ₂ = 4%.
πᵉ₂ = 4%
4
Step 4 — Compute Period 2 Inflation (if U stays at 3%)If the central bank continues to hold unemployment at 3%, the new inflation rate is: π₂ = 4% − 0.5(3% − 5%) = 4% + 1% = 5%. Inflation has accelerated by another percentage point. This illustrates the accelerationist hypothesis: maintaining unemployment below Uₙ does not just sustain higher inflation—it causes inflation to keep rising each period.
π₂ = 5%
5
Step 5 — Long-Run ImplicationIf policymakers insist on U = 3% indefinitely, inflation will rise by 1 percentage point each period (3% → 4% → 5% → 6% → ...) without bound. Eventually, the costs of accelerating inflation force the central bank to abandon the policy and allow unemployment to return to Uₙ = 5%. The conclusion: there is no permanent tradeoff between inflation and unemployment.
Long-run U = Uₙ = 5% regardless of π

Strengths, Limitations & Policy Implications

The Phillips Curve framework, particularly in its expectations-augmented form, remains one of the most widely used tools in macroeconomic analysis and central banking. However, it is not without its critics and limitations. Understanding both its strengths and weaknesses is essential for any business professional who must interpret Federal Reserve communications, forecast interest rate movements, or plan corporate strategy around the business cycle.

Strengths and limitations of the Phillips Curve framework
StrengthsLimitations
Provides a clear, intuitive framework for understanding the inflation–unemployment tradeoff that remains central to central bank communicationThe natural rate (Uₙ) is unobservable and must be estimated; estimates vary widely and change over time
Correctly predicted the stagflation of the 1970s once augmented with expectations (Friedman–Phelps)The curve appears to have flattened significantly since the 1990s—large changes in unemployment produce small inflation responses
Integrates naturally with the AD–AS model and the Taylor Rule, forming a coherent monetary policy frameworkSupply-shock augmentation (ε) is ad hoc; the model does not explain the source or persistence of shocks
The expectations mechanism highlights the crucial role of central bank credibility in anchoring inflationAssumes a single, stable natural rate; in practice, hysteresis (prolonged downturns permanently raising Uₙ) may apply
Flexible enough to accommodate both adaptive and rational expectations, depending on the modeling contextGlobal supply chains, digitalization, and labor market changes may weaken the domestic inflation–unemployment link
KEY TAKEAWAY
The Phillips Curve is like a weather model for the economy: invaluable for directional guidance and scenario planning, but imperfect in its precision. Just as meteorologists update models when atmospheric conditions change, economists must recalibrate the Phillips Curve as structural features of the economy—globalization, technological disruption, labor market composition—evolve. The model's greatest contribution may be conceptual rather than predictive: it forces policymakers to confront the role of credibility and expectations management in the conduct of monetary policy.

Connection to the New Keynesian Phillips Curve & Modern Policy

The expectations-augmented Phillips Curve laid the groundwork for the New Keynesian Phillips Curve (NKPC), which is the workhorse inflation equation in most modern central bank models. The NKPC differs from the traditional version in two crucial respects: it is derived from explicit microeconomic foundations (firms setting prices under monopolistic competition with staggered price adjustment), and it is entirely forward-looking, replacing backward-looking πᵉₜ = πₜ₋₁ with the rational expectation of future inflation, Eₜ[πₜ₊₁].

Traditional vs. New Keynesian Phillips Curve
FeatureTraditional Phillips CurveNew Keynesian Phillips Curve
ExpectationsBackward-looking (adaptive) or general rationalForward-looking rational: πₜ = βEₜ[πₜ₊₁] + κx̃ₜ
Activity variableUnemployment gap (U − Uₙ)Output gap (x̃ₜ) or real marginal cost
Micro foundationsEmpirical/reduced-form relationshipDerived from Calvo (1983) staggered pricing model
Inflation persistenceBuilt in through lagged inflation termsArises only from persistent driving forces; pure NKPC has no intrinsic persistence
Policy credibilityImportant but not explicitly modeledCentral—credible commitment to low inflation directly lowers current inflation through expectations channel

For business professionals, the practical lesson from the NKPC is that central bank communication matters as much as central bank action. Forward guidance—explicit statements about the intended path of future interest rates—works precisely because the NKPC says that today's inflation depends on expectations of future policy. This is why Federal Reserve press conferences, dot plots, and minutes are scrutinized so intensely by bond markets and corporate treasurers. In advanced coursework, you will encounter the NKPC embedded within a three-equation New Keynesian model (alongside a dynamic IS curve and a Taylor Rule), which forms the canonical framework for modern monetary policy analysis.

Practice Problems

PROBLEM 1CONCEPTUAL
Explain why the long-run Phillips Curve is vertical. In your answer, discuss what happens to the short-run Phillips Curve when expected inflation changes and why this prevents a permanent inflation–unemployment tradeoff.
PROBLEM 2BASIC CALCULATION
An economy has the Phillips Curve π = πᵉ − 0.4(U − Uₙ) with Uₙ = 6% and πᵉ = 2%. If the actual unemployment rate is 4%, what is the current inflation rate?
PROBLEM 3INTERMEDIATE
Using the same parameters as Problem 2 (π = πᵉ − 0.4(U − Uₙ), Uₙ = 6%), suppose the central bank holds U at 4% for three consecutive periods. Under simple adaptive expectations (πᵉₜ = πₜ₋₁), calculate the inflation rate for each of the three periods, beginning with πᵉ₁ = 2%.
PROBLEM 4APPLIED
A country experiences a negative supply shock (ε = +2%) while its Phillips Curve is π = πᵉ − 0.5(U − Uₙ) + ε, with Uₙ = 5% and πᵉ = 3%. The central bank wants to keep inflation at exactly 3%. What unemployment rate must it accept? What does this imply about the real-world cost of maintaining price stability during a supply shock?
PROBLEM 5CRITICAL THINKING
Under rational expectations, anticipated monetary policy cannot affect real output or unemployment. Yet central banks around the world routinely announce policy changes and observe real economic effects. Evaluate this apparent contradiction. Under what conditions might anticipated policy still have real effects, and what does this imply for the shape of the short-run Phillips Curve?

Phillips Curve & Expectations — Summary

The Phillips Curve describes an inverse relationship between inflation and unemployment. In the short run, with inflation expectations held constant, policymakers can exploit this tradeoff—pushing unemployment below the natural rate (Uₙ) at the cost of higher inflation. However, the Friedman–Phelps expectations-augmented framework shows that this tradeoff is temporary. As agents revise their inflation expectations upward, the short-run Phillips Curve (SRPC) shifts vertically, and the economy returns to Uₙ at a higher inflation rate. The long-run Phillips Curve (LRPC) is therefore vertical at the natural rate.

The mechanism of expectation formation is decisive. Under adaptive expectations, agents adjust slowly, allowing a multi-period short-run tradeoff. Under rational expectations, anticipated policies are immediately priced in, eliminating even the short-run tradeoff for predictable policy moves. The modern New Keynesian Phillips Curve builds on these insights with explicit microfoundations, making central bank credibility and forward guidance central to inflation management. The key equation—π = πᵉ − β(U − Uₙ) + ε—remains one of the most important relationships in macroeconomics, encapsulating the interplay of demand pressure, expectations, and supply shocks in determining the price level.

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