Phillips Curve

Definition

The Phillips Curve describes the empirical relationship between unemployment (or the output gap) and inflation. In its modern reduced-form incarnation — Gordon's "triangle model" — inflation depends on three sides: (1) inertia from lagged inflation; (2) excess demand measured by unemployment relative to the NAIRU (Non-Accelerating Inflation Rate of Unemployment) or by the output gap; and (3) explicit supply shocks. The natural-rate hypothesis imposes that lag coefficients on inflation sum to unity, so that there is no long-run inflation–unemployment tradeoff.

Key Ideas

Inertia: Lagged inflation $a(L)p_{t-1}$ captures inflation persistence. Under the natural-rate hypothesis the coefficients sum to one, implying any inflation rate is self-sustaining absent a demand or supply shock.
Excess demand: The output gap $G_t$ or unemployment gap $U_t - U^N_t$ transmits demand pressure to inflation. In Gordon (2005) the output gap equation residuals — "IS shifts" — explain over two-thirds of output gap variance in both sub-periods.
Supply shocks: Explicit supply shock variables $z_t$ are essential for correct inference. Gordon (2005) identifies five: (i) change in relative price of non-food, non-oil imports; (ii) food-energy Personal Consumption Expenditures (PCE) deflator effect; (iii) medical-care PCE effect; (iv) Hodrick-Prescott (HP)-filtered productivity trend acceleration; (v) Nixon-era price control dummies. Omitting them forces the NAIRU to absorb unmodelled inflation variance (above 8% in the 1970s without supply shocks).
Time-varying NAIRU (TV-NAIRU): $U^N_t$ follows a random walk with variance $\tau^2$ estimated by the Kalman filter. U.S. estimates: stable 5.6–6.3% (1962–88), falling to 4.5% minimum (1998), rising to 4.85% (2004Q4).
Supply shock dominance: In Gordon (2005), supply shocks account for ~80% of pre-1984 U.S. inflation variance; the output gap error accounts for only ~20%.

How It Works

Gordon's Triangle Model (Gordon 1982, 2005)

The core inflation equation:

$p_t = a(L)p_{t-1} + b(L)(U_t - U^N_t) + c(L)z_t + e_{pt}$

where $p_t$ is the inflation rate, $U^N_t$ is the TV-NAIRU, $z_t$ is the supply shock vector, and $\sum a_i = 1$ (natural-rate restriction). In the four-equation macro model of Gordon (2005), this is augmented by:

Taylor rule (with feasible generalized least squares (FGLS) autoregressive (AR(1)) correction): $R_t = T^* + p^* + d(L)(p_t - p^*) + f(L)G_t + e_{Rt}$
IS (investment-saving) / output gap equation: $\Delta G_t = h(L)\Delta p_{t-1} + j(L)\Delta R_t + e_{Gt}$
Okun's Law: $U_t - U^N_t = k(L)G_t + e_{Ut}$

where $T^* = 3\%$ (real rate target) and $p^* = 2\%$ (inflation target).

New Keynesian Phillips Curve (NKPC)

The NKPC derives inflation from forward-looking optimal price-setting under Calvo pricing: $\pi_t = \beta E_t \pi_{t+1} + \kappa \hat{x}_t$ where $\hat{x}_t$ is the welfare-relevant output gap and $\kappa$ depends on the Calvo parameter. Unlike the triangle model, it de-emphasises lagged inflation and supply shock variables, though hybrid variants add a backward-looking term.

Why It Matters

The triangle model's supply shock variables explain why inflation spiked in the 1970s and fell in the 1980s without requiring a policy change narrative: Gordon (2005) shows that the Burns-era and Greenspan-era Taylor Rule coefficients are statistically identical after AR(1) correction (~0.57 inflation coefficient), and only Volcker (1979–90, coefficient ~1.46) differs meaningfully.
Omitting supply shocks from a Phillips Curve biases the NAIRU estimate upward during adverse supply episodes (1970s oil shocks), creating the illusion of a high natural rate and understating the role of exogenous inflation pressure.
The natural-rate hypothesis embedded in the triangle model rules out a permanent inflation–unemployment tradeoff, anchoring long-run monetary policy design.

Open Questions

Flattening: Post-1990 evidence suggests the slope of the Phillips Curve (sensitivity of inflation to the gap) has declined, raising questions about the structural stability of $b(L)$ .
Expectations anchoring: If central bank credibility anchors expected inflation, the persistence term $a(L)p_{t-1}$ may overstate true inertia by confounding backward-looking expectations with well-anchored rational ones.
Endogenous supply shocks: Import prices partly reflect the exchange rate, which is itself affected by monetary policy. Treating $z_t$ as fully exogenous may attribute too little of the disinflation to tight money (Gordon acknowledges ~⅓ of the 1981–85 supply-shock reversal was endogenous to Volcker policy).
Output gap mismeasurement: Real-time output gap estimates differ substantially from revised estimates, complicating inference on the demand term.