ECON6002 · Macroeconomic Analysis
The New Keynesian Phillips Curve
The New Keynesian Phillips Curve (NKPC) is Topic 8 of ECON6002 Macroeconomic Analysis at the University of Sydney, and the most heavily examined result in the unit. It replaces the old reduced-form inflation trade-off with a derived aggregate-supply relation: current inflation depends on expected future inflation and on real marginal cost (equivalently the output gap). Everything flows from one friction — under Calvo pricing firms cannot reset prices every period, so they price with an eye on the future, which makes inflation a purely forward-looking asset price of expected output gaps. Topic 8 is examinable on the 55% closed-book final (Topics 7–10), where it anchors an extended-response question.
What this chapter covers
- 011. Why we need nominal rigidity — RBC money neutrality fails three data facts (money non-neutrality, inflation–output co-movement, sticky prices lasting ~4–11 months)
- 022. The three NK building blocks — optimising households (dynamic IS), monopolistically competitive firms under Calvo stickiness (the NKPC), and a Taylor-rule central bank
- 033. Calvo pricing — each period a firm resets its price with constant probability (1−θ); average price duration is 1/(1−θ), so θ = 0.75 means prices last 4 quarters
- 044. The optimal reset price — a mark-up over a βθ-weighted average of current and expected future nominal marginal cost, because a reset price may stick for many periods
- 055. The NKPC, marginal-cost form — π̂ₜ = β·Eₜπ̂ₜ₊₁ + λ·m̂cₜ with slope λ = (1−θ)(1−βθ)/θ; β multiplies EXPECTED, not lagged, inflation
- 066. The NKPC, output-gap form — π̂ₜ = β·Eₜπ̂ₜ₊₁ + κ·ỹₜ with κ = λ(σ+φ), using the mapping m̂cₜ = (σ+φ)ỹₜ from the labour-supply condition
- 077. Inflation as an asset price — solving forward gives π̂ₜ = κ·Σ βᵏ·Eₜỹₜ₊ₖ, so inflation is the discounted stream of expected future output gaps
- 088. Properties and the hybrid NKPC — purely forward-looking, no intrinsic persistence, costless credible disinflation, Lucas-critique immunity; the hybrid adds πₜ₋₁ for persistence
Solve the forward-looking NKPC for inflation as a function of the output gap
- +1Guess that inflation is proportional to the gap: π̂ₜ = ψ·ỹₜ for some constant ψ to be found. This is the standard method of undetermined coefficients for a linear forward-looking equation.
- +1Take expectations of the guess one period ahead: Eₜπ̂ₜ₊₁ = ψ·Eₜỹₜ₊₁ = ψ·ρ·ỹₜ, using the AR(1) property that Eₜỹₜ₊₁ = ρ·ỹₜ.
- +1Substitute the guess and this expectation into the NKPC: ψ·ỹₜ = β·(ψ·ρ·ỹₜ) + κ·ỹₜ.
- +1Cancel ỹₜ and solve for the coefficient: ψ = κ/(1 − β·ρ) = 0.1/(1 − 0.99×0.5) = 0.1/0.505 ≈ 0.198. So π̂ₜ ≈ 0.198·ỹₜ.
- +1(b) Evaluate at ỹₜ = −0.04: π̂ₜ ≈ 0.198 × (−0.04) ≈ −0.0079, i.e. inflation runs about 0.8 percentage points below its steady-state value.
- +1Persistence: because inflation is just ψ times the gap, it inherits the gap's AR(1) decay rate ρ = 0.5 — it is exactly as persistent as the driving gap and has no persistence of its own.
Key terms
- New Keynesian Phillips Curve (NKPC)
- The micro-founded aggregate-supply relation of the NK model: current inflation equals discounted expected future inflation plus a loading on real marginal cost (or the output gap). Derived from Calvo pricing, not assumed.
- Calvo pricing
- A tractable model of price stickiness in which each firm may reset its price with a constant probability (1−θ) each period, independent of how long the price has stood; the average price duration is 1/(1−θ).
- Real marginal cost
- The fundamental driver of the NKPC; in logs m̂cₜ = (σ+φ)ỹₜ, so it is proportional to the output gap. Empirical work prefers the labour share as its proxy because the gap is badly measured.
- NKPC slope (λ and κ)
- The sensitivity of inflation to its driver. In marginal-cost form λ = (1−θ)(1−βθ)/θ; in output-gap form κ = λ(σ+φ). Both fall as prices get stickier (higher θ), flattening the curve.
- Intrinsic vs inherited persistence
- Intrinsic persistence comes from a lagged-inflation term in the equation itself; inherited persistence is borrowed from the driving process. The pure NKPC has only inherited persistence.
- Hybrid NKPC
- π̂ₜ = γ_b·π̂ₜ₋₁ + γ_f·Eₜπ̂ₜ₊₁ + κ·ỹₜ. Adding the backward-looking term (rule-of-thumb pricing or indexation) generates intrinsic persistence to fit the data, at the cost of weaker micro-foundations.
- Costless disinflation
- Under a fully credible policy and the purely forward-looking NKPC, target inflation can be lowered with no output cost because expectations reset immediately; any backward-looking term (γ_b > 0) makes disinflation costly.
- Lucas critique
- The warning that reduced-form policy relations shift when policy changes. The NKPC is immune because it is structural — built from deep parameters (tastes, θ) rather than an estimated trade-off.
The New Keynesian Phillips Curve FAQ
Is the New Keynesian Phillips Curve on the ECON6002 exam?
Yes, and it is one of the most heavily examined topics. Topic 8 is examinable on the 55% closed-book final (which covers Topics 7–10 only, not the in-semester test), where it typically anchors an extended-response question — derive the NKPC from Calvo pricing, state it in both forms, solve it forward, and discuss its properties. The final provides a formula sheet with the standard log-linearised NK model, and practice comes from Tutorials 7–10.
How is the NKPC derived from Calvo pricing?
Under Calvo pricing a firm resets its price only with probability (1−θ) each period, so a firm that does reset chooses a mark-up over a βθ-weighted average of current and expected future nominal marginal cost. Combining that optimal reset price with the aggregate price index p̂ₜ = θ·p̂ₜ₋₁ + (1−θ)·p̂*ₜ and using inflation π̂ₜ = p̂ₜ − p̂ₜ₋₁ collapses the algebra to π̂ₜ = β·Eₜπ̂ₜ₊₁ + λ·m̂cₜ. Because pricing is forward-looking, so is inflation.
What is the difference between the λ form and the κ form of the NKPC?
They are equivalent. The marginal-cost form π̂ₜ = β·Eₜπ̂ₜ₊₁ + λ·m̂cₜ uses real marginal cost, the fundamental driver, with λ = (1−θ)(1−βθ)/θ. The output-gap form π̂ₜ = β·Eₜπ̂ₜ₊₁ + κ·ỹₜ substitutes the labour-supply mapping m̂cₜ = (σ+φ)ỹₜ, so κ = λ(σ+φ). The gap form is the one that plugs into the three-equation NK model in the next topic.
Why is inflation described as an asset price?
Solving the NKPC forward and ruling out bubbles gives π̂ₜ = κ·Σ βᵏ·Eₜỹₜ₊ₖ: today's inflation is the discounted stream of all expected future output gaps. That is exactly the structure of an asset price, whose value is the discounted stream of expected dividends — here the 'dividends' are future marginal-cost pressure. This one result delivers the properties markers reward: forward-looking, no intrinsic persistence, and costless credible disinflation.
Can AI help me with the New Keynesian Phillips Curve?
Yes — ask Sia to walk through any New Keynesian Phillips Curve problem or concept step by step, the way University of Sydney tests it. Sia is an AI tutor that explains the Calvo reset-price algebra, the collapse to the two slopes, and the forward asset-price solution, so you learn how to reproduce the derivation closed-book rather than just seeing a final number.
What are the most common NKPC exam mistakes?
Four recur: writing β in front of LAGGED inflation instead of EXPECTED inflation (that turns the pure NKPC into the hybrid by accident); getting the slope direction backwards (stickier prices, higher θ, make the curve FLATTER, so κ falls); treating the output gap as the fundamental driver instead of real marginal cost; and claiming disinflation is free without stating that this needs BOTH full credibility AND the purely forward-looking form. Link any disinflation cost directly to the backward-looking weight γ_b > 0.
Studying with AI? Sia — free AI economics tutor works through ECON6002 step by step.
Exam move
Because the final is closed-book and the NKPC anchors an extended-response question, rehearse the full derivation until you can reproduce it without notes — the marks are in the derivation and the property discussion, not a final number. Practise a five-step arc: (1) motivate the friction — RBC money neutrality fails the data, so add monopolistic competition plus Calvo price stickiness; (2) derive the optimal reset price as a mark-up over a βθ-weighted average of current and expected future marginal cost, then combine it with the aggregate price index; (3) state both equivalent forms, π̂ₜ = β·Eₜπ̂ₜ₊₁ + λ·m̂cₜ and π̂ₜ = β·Eₜπ̂ₜ₊₁ + κ·ỹₜ with κ = λ(σ+φ), and be able to recover λ = (1−θ)(1−βθ)/θ from Calvo primitives; (4) solve the equation forward to the asset-price form and read off the four properties (forward-looking, no intrinsic persistence, costless credible disinflation, Lucas-critique immunity); and (5) note the hybrid NKPC fix and that estimation (Galí–Gertler for the US, Kuttner–Robinson for Australia) finds the forward-looking term dominant but the backward term significant, with the labour share as the marginal-cost proxy. Work Tutorials 7–10 under timed conditions, and always check that you have written β in front of EXPECTED inflation.
