Inflation Dynamics and the Phillips Curve Study Guide

Intermediate Macroeconomics: Inflation Dynamics and the Phillips Curve

• This lecture, delivered by Dr Angeliki Theophilopoulou, focuses on the transition from labor market models to inflation dynamics via the Phillips Curve.

• Learning Objectives:     - Derivation and interpretation of the Expectations-Augmented Phillips Curve (EAPC).     - Understanding the role of the natural rate of unemployment ($u_n$) and the Non-Accelerating Inflation Rate of Unemployment (NAIRU).     - Analysis of how expectation formation ($\theta$) impacts inflation dynamics.     - Explanation of the absence of a long-run trade-off between inflation and unemployment.     - Calculation and interpretation of inflation paths within policy experiments.

Linking the Labour Market to Inflation

• Review of Medium-Run Equilibrium:     - The previous lecture established the Wage-Setting (WS) and Price-Setting (PS) relations.     - These determine the natural rate of unemployment ($u_n$) where the real wage is stable.

• The Key Research Question:     - What are the consequences when the actual unemployment rate ($u$) deviates from its natural rate ($u_n$)?

• Causal Mechanism of Inflation:     - Low Unemployment: When $u$ is low, workers possess high bargaining power. This leads to increased wage growth. Firms, in turn, raise prices to maintain markups, resulting in increased inflation ($\pi$).     - High Unemployment: When $u$ is high, wage pressure diminishes. Price increases slow down, leading to a decrease in inflation.     - Conclusion: Inflation is intrinsically dependent on the level of tightness in the labor market.

Historical Context of the Phillips Curve

• The Original Phillips Curve (1958):     - A.W. Phillips identified a negative empirical relationship between unemployment and wage inflation.     - Later, economists Paul Samuelson and Robert Solow interpreted this as a stable trade-off between price inflation and unemployment.

• The 1960s Belief:     - Policymakers believed they could choose a target level of unemployment on a menu of inflation costs (e.g., lower unemployment could be "bought" with higher inflation).

• The 1970s Challenge:     - Data from the 1970s contradicted this stable trade-off.     - Inflation rose significantly even while unemployment remained high, leading to the question of whether any permanent trade-off actually exists.

• UK Long-Term Data Trends:     - The transcript references data for UK unemployment (1881–2017) and inflation (1948–2016).     - Sources: Denman and McDonald (1996) "Unemployment statistics from 1881 to the present day," and Office for National Statistics (ONS) data for MGSX (1995–2017) and RPI percentage changes.     - Historical periods mentioned include the eras of Baldwin, Lloyd-George, Churchill, Attlee, the OPEC crisis, Thatcher, Blair, and Cameron.

Formal Wage and Price Setting Foundations

• Wage Setting with Expectations:     - The nominal wage ($W$) is set based on the expected price level ($P^e$) and labor market conditions:     - $W = P^e F(u, z)$     - $P^e$: Expected price level.     - $u$: Unemployment rate.     - $z$: Catch-all variable for labor market structure (e.g., unemployment benefits, union power).     - Key Property: Lower unemployment results in higher nominal wages, as workers prioritize the expected real wage ($W/P^e$).

• Price Setting:     - Firms set prices ($P$) based on a markup ($m$) over the nominal wage ($W$):     - $P = (1 + m)W$     - Dividing by $W$ yields the real wage determined by price-setting: $\frac{W}{P} = \frac{1}{1 + m}$.

• Combined WS-PS Relation:     - Substituting the wage-setting equation into the price-setting equation:     - $P = P^e (1 + m) F(u, z)$     - This implies that the actual price level depends on expectations and current labor market tightness.

Deriving the Expectations-Augmented Phillips Curve (EAPC)

• Linear Assumption:     - Assume a specific functional form for labor market conditions: $F(u, z) = 1 - \alpha u + z$.     - The price level equation becomes: $P = P^e (1 + m)(1 - \alpha u + z)$.

• Inflation Notation:     - This relationship can be expressed in terms of inflation ($\pi$) and expected inflation ($\pi^e$):     - $\pi = \pi^e + (m + z) - \alpha u$ (Equation 1)

• Deriving the Natural Rate of Unemployment ($u_n$):     - At the natural rate, actual inflation equals expected inflation ($\pi = \pi^e$).     - Substituting into Equation 1: $0 = (m + z) - \alpha u_n$.     - Solving for $u_n$: $u_n = \frac{m + z}{\alpha}$.

• The Expectations-Augmented Phillips Curve Equation:     - We can rewrite Equation 1 using the definition of the natural rate:     - $\pi - \pi^e = -\alpha(u - (\frac{m + z}{\alpha}))$     - $\pi - \pi^e = -\alpha(u - u_n)$

The NAIRU and Inflation Dynamics

• NAIRU (Non-Accelerating Inflation Rate of Unemployment):     - Defined as the unemployment rate at which inflation is stable.     - In this macroeconomic model, the NAIRU is equivalent to the natural rate ($u_n$).     - Characteristics of NAIRU:         - It is not necessarily the socially optimal rate of unemployment.         - It is determined by structural labor market characteristics ($z$) and firm markups ($m$).         - It is dynamic and can change over time.

• The Short-Run Phillips Curve (SRPC):     - If u < u_n, then \pi > \pi^e. This leads to increasing inflation over time.     - If u > u_n, then \pi < \pi^e. This leads to decreasing inflation.     - If $u = u_n$, then $\pi = \pi^e$. Inflation remains stable.     - The SRPC implies a downward-sloping relationship between the inflation gap ($\pi - \pi^e$) and the unemployment gap ($u - u_n$).

• The Long-Run Phillips Curve (LRPC):     - In the long run, expectations adjust fully such that $\pi = \pi^e$.     - This forces $u$ to equal $u_n$, making the LRPC a vertical line at the natural rate.     - Conclusion: There is no permanent trade-off between inflation and unemployment in the long run.

Expectation Formation ($\theta$)

• The behavior of inflation is critically dependent on how agents form expectations ($\pi^e$).

• General Case Equation:     - Assume expectations are formed based on a factor $\theta$ of past inflation: \pi^e = \theta ext{ } pi_{t-1}.     - Substitute into the PC: \pi_t = \theta ext{ } pi_{t-1} - \alpha(u_t - u_n).

• Scenario 1: Fixed Expectations ($\theta = 0$):     - $\pi = -\alpha(u - u_n)$.     - Expectations remain constant regardless of past inflation (no inflation persistence).     - This allows for a permanent trade-off (the 1960s interpretation).

• Scenario 2: Partially Adaptive Expectations (0 < \theta < 1):     - \pi = \theta ext{ } pi_{t-1} - \alpha(u - u_n).     - Inflation is persistent; past inflation partially feeds into current inflation. The speed of adjustment is gradual.

• Scenario 3: Fully Adaptive/Accelerationist PC ($\theta = 1$):     - $\pi_t = \pi_{t-1} - \alpha(u_t - u_n)$.     - This can be written as: \Deltapi = -\alpha(u - u_n).     - It is not the level of inflation that is determined by unemployment, but the change in inflation.

• Impact of Rising Expectations:     - If $\pi^e$ increases, wage demands rise, firms raise prices, and the entire Phillips Curve shifts upward. At any given level of unemployment, inflation will be higher.

Wage Indexation (\lambda)

• Definition: A fraction (\lambda) of wages is automatically adjusted/indexed to actual inflation ($\pi$).

• The Augmented Equation:     - If wages are indexed: W = W_{t-1}(1 + pi)_t.     - The Phillips curve becomes: \pi = \pi^e - \alpha(u - u_n) + \lambdapi.

• Rearranging for Inflation:     - $(1 - \lambda)\pi = \pi^e - \alpha(u - u_n)$.     - $\pi = \frac{1}{1 - \lambda} [\pi^e - \alpha(u - u_n)]$

• Intuition:     - If $\lambda = 0$, we return to the standard EAPC.     - If \lambda > 0, inflation becomes more sensitive to unemployment gaps. Higher indexation amplifies inflation dynamics and increases persistence.

Step-by-Step Policy Experiment

• Scenario: A government attempts to permanently reduce unemployment below the natural rate.

• Model Assumptions:     - Phillips Curve: $\pi = \pi^e + 0.1 - 2u$     - Current Target: $u = 3\% = 0.03$     - Expectation Formation: \pi^e = \theta ext{ } pi_{t-1}

• Step 1: Calculate the Natural Rate ($u_n$):     - Set $\pi = \pi^e$     - $0 = 0.1 - 2u_n$     - $u_n = \frac{0.1}{2} = 0.05 = 5\%$

• Step 2: Case of Fixed Expectations ($\theta = 0$):     - Assume $\pi^e = 0$     - $\pi = 0.1 - 2(0.03) = 0.1 - 0.06 = 0.04 = 4\%$     - Inflation is constant at $4\%$. However, this is considered unrealistic because agents will eventually revise their expectations upward if inflation is consistently $4\%$.

• Step 3: Case of Fully Adaptive Expectations ($\theta = 1$):     - Assume previous inflation $\pi_{t-1} = 4\%$     - $\pi_t = \pi_{t-1} + 0.1 - 2(0.03)$     - $\pi_t = \pi_{t-1} + 0.04$     - Inflation increases by 4 percentage points every year.

• The Inflation Path ($\theta = 1$):     - Year $t$: $\pi = 8\%$     - Year $t+1$: $\pi = 12\%$     - Year $t+2$: $\pi = 16\%$     - Year $t+3$: $\pi = 20\%$     - Key Result: Maintaining unemployment below $u_n$ (3\% < 5\%) leads to continuously accelerating inflation.

Summary of Main Takeaways

• Tightness and Pressure: Inflation depends on labor market tightness. Falling below $u_n$ creates inflationary pressure.

• Temporary vs. Permanent: The original concept of a permanent trade-off (1950s/60s) was debunked by 1970s reality. Trade-offs only exist in the short run while expectations are adjusting.

• Role of Expectations: $\theta$ determines the speed of adjustment and the persistent nature of inflation.

• Accelerating Inflation: Keeping unemployment artificially low results in a repeating cycle: tight labor market $\to$ wage pressure $\to$ inflation exceeding expectations $\to$ expectations adjusting upward $\to$ PC shifting upward. This repeats until $u$ returns to $u_n$.

• Further Reading:     - Blanchard, Olivier (2025), Macroeconomics, Global Edition, 8th or 9th Edition, Chapter 8.     - Mankiw, N. Gregory (2023), Macroeconomics, 11th edition, Chapters 14-15.