Phillips Curve

Phillips Curve is a central macroeconomic relationship in Business & Economics Theory that describes the short-run empirical and theoretical inverse link between the rate of Inflation (or nominal wage growth) and the unemployment rate relative to its structural equilibrium. Originating in a 1958 empirical study of nearly a century of British wage data by New Zealand economist A. W. (Bill) Phillips, the relationship evolved through three major theoretical paradigms: the static wage-inflation trade-off of the 1960s, the expectations-augmented natural-rate formulation developed independently by Milton Friedman and Edmund Phelps in 1967–1968, and the microfounded New Keynesian Phillips Curve (NKPC) used by modern central banks to conduct Monetary Policy.

In his seminal 1958 paper in Economica, A. W. Phillips plotted annual percentage changes in nominal money wage rates (ġ_w) against the percentage unemployment rate (u) in the United Kingdom from 1861 to 1957. Phillips identified a convex, downward-sloping empirical locus showing that when labor markets were tight (low u), employers bid up nominal wages rapidly, whereas high unemployment depressed wage demands—albeit with a floor induced by workers' resistance to nominal wage cuts.

In 1960, Paul Samuelson and Robert Solow translated Phillips's wage schedule into a price-inflation schedule for the United States by noting that aggregate price inflation (π_t) equals nominal wage growth minus labor productivity growth (g_A). In linear form, the early static Phillips Curve was expressed as:

where α > 0 measures the sensitivity of inflation to labor market tightness and u^* denotes the unemployment rate consistent with stable prices. Samuelson and Solow presented this schedule as a stable menu of policy choices, suggesting that policymakers could use Fiscal Policy and monetary expansion along the IS–LM Model to permanently purchase a lower unemployment rate at the cost of a moderately higher, stable rate of inflation.

During the late 1960s and 1970s, the stable downward-sloping Phillips Curve broke down empirically across advanced economies as unemployment and inflation rose simultaneously—a phenomenon termed stagflation. Remarkably, Milton Friedman (1968) and Edmund Phelps (1967) had predicted this breakdown theoretically prior to the 1970s oil shocks.

Friedman and Phelps argued that the early Phillips Curve confused nominal wages (W) with real wages (W ÷ P). Both workers supplying labor and firms demanding labor care about the real purchasing power of wages. When a central bank attempts to hold actual unemployment (u_t) below the natural rate of unemployment (u_tⁿ)—also called the Non-Accelerating Inflation Rate of Unemployment (NAIRU)—the resulting surprise inflation temporarily erodes real wages if workers' inflation expectations (π_t^e) are anchored at past levels, inducing firms to hire more labor. However, once workers and firms revise their inflation expectations upward to match actual inflation, real wages return to equilibrium, unemployment reverts to u_tⁿ, and inflation remains permanently higher. Incorporating expected inflation (π_t^e) and supply shocks (ν_t, such as energy or commodity price spikes) yields the Expectations-Augmented Phillips Curve:

Under adaptive expectations, where agents expect current inflation to equal last period's inflation (π_t^e = π_t−1), the equation becomes the accelerationist Phillips Curve:

This formulation implies that keeping u_t < u_tⁿ requires continuously accelerating inflation (Δπ_t > 0). In the long run, when expectations adjust fully (π_t = π_t^e) and supply shocks average zero, the Long-Run Phillips Curve (LRPC) is vertical at u_t = u_tⁿ.

By linking the unemployment gap (u_t − u_tⁿ) to the percentage output gap (y_t − y_tⁿ) via Okun's Law—which states that a 1 percentage point increase in cyclical unemployment corresponds to roughly a 2 percentage point shortfall in real Gross Domestic Product below potential: (y_t − y_tⁿ) ≈ −2(u_t − u_tⁿ)—macroeconomists express the Phillips Curve directly in terms of the output gap or real marginal cost.

In the New Keynesian Phillips Curve, derived from explicit microfoundations of monopolistically competitive firms facing staggered price adjustment (Guillermo Calvo, 1983) or quadratic price-adjustment costs (Julio Rotemberg, 1982), only a fraction (1 − θ) of firms can reset their nominal price in any given quarter, while the remaining fraction θ must keep their existing price unchanged. Because a firm resetting its price today knows there is a probability θ^k that its chosen price will still be in effect k quarters in the future, optimal price-setting is intrinsically forward-looking. Aggregating across all firms yields the benchmark NKPC:

where β ∈ (0, 1) is the subjective intertemporal discount factor, E_t[π_t+1] is the rational expectation of next period's inflation, u_t is a cost-push markup shock, and the slope coefficient κ = [(1 − θ)(1 − βθ) ÷ θ] × (σ + φ) decreases as price stickiness θ rises.

Over the past four decades, empirical estimates of the slope α (or κ) of the Phillips Curve in advanced economies declined from roughly 0.5 in the 1970s to 0.1–0.15 between 1995 and 2019—an empirical phenomenon known as the flattening of the Phillips Curve. Economists attribute this flattening to firmly anchored central bank inflation expectations, global supply-chain integration, and demographic aging.

However, recent theoretical and empirical work by Pierpaolo Benigno and Gauti Eggertsson (2023) demonstrates that the Phillips Curve is piecewise non-linear (convex) rather than globally flat. When labor markets are slack, the ratio of job vacancies to unemployed workers (v ÷ u, the Beveridge ratio) lies below 1.0, downward nominal wage rigidity binds, and the Phillips Curve is relatively flat. Once aggregate demand pushes the vacancy-to-unemployment ratio above the threshold v ÷ u > 1.0 (a labor shortage regime), firms compete intensely for already-employed workers, and the Phillips Curve steepens sharply, generating rapid price pressures from small additional declines in unemployment.

What is the sacrifice ratio during a disinflation?

The sacrifice ratio measures the cumulative percentage-point loss of annual real GDP (or excess point-years of unemployment above the NAIRU) required to permanently reduce the trend inflation rate by 1.0 percentage point. Under purely backward-looking adaptive expectations (π_t^e = π_t−1), reducing inflation by 1 percentage point when α = 0.25 requires 4 point-years of excess unemployment. For example, during the 1979–1982 Volcker disinflation in the United States, reducing inflation by roughly 6 percentage points entailed a sacrifice ratio estimated by Laurence Ball (1994) at approximately 1.8 to 2.4 percent of annual GDP per percentage point of inflation reduction.

What is unemployment hysteresis and how does it affect the NAIRU?

Proposed by Olivier Blanchard and Lawrence Summers (1986) to explain European unemployment persistence, hysteresis occurs when a prolonged cyclical recession permanently raises the structural natural rate of unemployment (u_tⁿ). Long spells of unemployment erode workers' human capital skills, weaken labor-force attachment, and lead insider unions to bargain wages on behalf of a smaller employed workforce, causing u_tⁿ to track past actual unemployment u_t−1.

Why does the Lucas Islands Model predict that anticipated monetary expansions have zero effect on real output?

In Robert Lucas's (1972) imperfect-information model, competitive producers located on separate "islands" observe changes in their own local nominal product price before observing the economy-wide price level. If a monetary expansion is unannounced, producers partially mistake the general inflation for an increase in the relative demand for their specific good and expand output. If the monetary expansion is anticipated, producers immediately recognize that all prices are rising proportionally, leave real output unchanged, and raise nominal prices one-for-one.

1. Phillips, A. W. (1958). The relation between unemployment and the rate of change of money wage rates in the United Kingdom, 1861–1957. Economica, 25(100), 283–299. https://doi.org/10.2307/2550759
2. Phelps, E. S. (1967). Phillips curves, expectations of inflation and optimal unemployment over time. Economica, 34(135), 254–281. https://doi.org/10.2307/2552025
3. Friedman, M. (1968). The role of monetary policy. The American Economic Review, 58(1), 1–17. https://www.jstor.org/stable/1831652
4. Galí, J., & Gertler, M. (1999). Inflation dynamics: A structural econometric analysis. Journal of Monetary Economics, 44(2), 195–222. https://doi.org/10.1016/S0304-3932(99)00023-900023-9)
5. Benigno, P., & Eggertsson, G. B. (2023). It's Baaack: The surge in inflation in the 2020s and the return of the non-linear Phillips curve. NBER Working Paper No. 31197. https://doi.org/10.3386/w31197