Wage dynamics parameters (wage_p, wage_q)

Table of contents

Overview

These parameters govern the dynamics of wage adjustment in the G-Cubed model. They determine how wages respond to expected inflation and labor market conditions, implementing a Phillips curve relationship that captures the trade-off between inflation and unemployment.

Parameters

wage_p

SYM Declaration:

parameter wage_p(regions)    'exp infl weight in wage equation'

Definition: The weight on expected inflation in the wage equation. This parameter determines how much wages respond to expected future inflation versus past realized inflation.

Calibration: Default value: 0.4

# Employment parameter in the wage equation
WAGE_P: float = 0.4

Usage in Model: Used in the wage dynamics equation:

lead(WAGE) = WAGE
           + wage_p*(lead(PRCT) - PRCT + PRXX)
           + (1-wage_p)*(PRCT-PRCL)
           + wage_q*(ln(LABO) - ln(LABX))

Where:

  • wage_p*(lead(PRCT) - PRCT + PRXX): Expected inflation component
  • (1-wage_p)*(PRCT-PRCL): Past inflation component

wage_q

SYM Declaration:

parameter wage_q(regions)    'employment parameter in wage equation'

Definition: The sensitivity of wage growth to labor market tightness. This parameter determines how much wages respond to deviations of actual employment from trend employment.

Calibration: Default value: 0.35

# Expected inflation weight in the wage equation
WAGE_Q: float = 0.35

Usage in Model: Used in the wage dynamics equation:

lead(WAGE) = WAGE
           + wage_p*(lead(PRCT) - PRCT + PRXX)
           + (1-wage_p)*(PRCT-PRCL)
           + wage_q*(ln(LABO) - ln(LABX))

Where:

  • LABO: Actual labor supply/employment
  • LABX: Trend or natural level of employment
  • ln(LABO) - ln(LABX): Employment gap (log deviation)

Wage Equation Structure

The wage equation can be written as:

\[W_{t+1} = W_t + \pi^e + \gamma (L_t - L^*)\]

Expanding the inflation expectations:

\[W_{t+1} = W_t + \alpha \cdot E_t[\pi_{t+1}] + (1-\alpha) \cdot \pi_t + \gamma (L_t - L^*)\]

Where:

  • $W_t$: Wage level (logged)
  • $\alpha$: wage_p (weight on expected inflation)
  • $\pi^e$: Expected inflation
  • $\pi_t$: Current/past inflation
  • $\gamma$: wage_q (employment sensitivity)
  • $L_t - L^*$: Employment gap

Economic Interpretation

Inflation Expectations (wage_p)

  • Higher wage_p (more forward-looking):
    • Wages respond more to expected future inflation
    • Inflation expectations become self-fulfilling faster
    • More rapid adjustment to monetary policy changes
    • Can lead to faster disinflation if expectations are anchored
  • Lower wage_p (more backward-looking):
    • Wages respond more to past realized inflation
    • Inflation is more persistent
    • Slower adjustment to policy changes
    • Greater inflation inertia

Labor Market Tightness (wage_q)

  • Higher wage_q:
    • Steeper Phillips curve
    • Wages more sensitive to employment conditions
    • Stronger link between output gaps and inflation
    • Faster wage adjustment to demand shocks
  • Lower wage_q:
    • Flatter Phillips curve
    • Wages less responsive to employment
    • Weaker output-inflation trade-off
    • More stable wages despite employment fluctuations

Phillips Curve Interpretation

The wage equation implements an expectations-augmented Phillips curve:

\[\Delta W = \pi^e + \gamma (U^* - U)\]

Where unemployment is inversely related to employment:

  • When LABO > LABX (tight labor market): wages rise faster
  • When LABO < LABX (slack labor market): wage growth slows

Policy Implications

Monetary Policy

  • wage_p affects the speed of disinflation
  • Higher wage_p allows faster inflation control if credibility is established
  • Lower wage_p requires more persistent policy to anchor expectations

Labor Market Policy

  • wage_q determines the output cost of disinflation
  • Higher wage_q means larger unemployment impact from contractionary policy
  • Lower wage_q allows more “painless” disinflation
Variable Description
WAGE Wage rate (logged)
PRCT Consumer price index (logged)
PRCL Lagged consumer price index
PRXX Expected inflation shock
LABO Actual labor/employment
LABX Trend/natural employment

References