Grasping Reality on TypePad, by Brad DeLong

The Phillips curve, expectations, and monetary policy

• Aggregate supply and the Phillip curve
  • Unemployment
    • Unemployment and Okun's Law
    • (Y - Y)/Y = 2.5(u* - u)
    • Where Y* is potential output and u* is the "natural" rate of unemployment
    • Costs of high unemployment
  • Aggregate supply
    • The modern Phillips curve: π = π^e - B(u - u*) + S
    • Where: π is the inflation rate, π^e is expected inflation, u* is the natural rate of unemployment, and S is a supply-shock term.
    • What is expected inflation? We will deal with that later...
    • When unemployment is at its natural rate u*, inflation is at its expected value π^e, and vice versa
• Monetary policy, aggregate demand, and inflation
  • Think of the Federal Reserve choosing three numbers--a "normal" level of unemployment, a target level of inflation, and a degree of aggressiveness in response to deviations of inflation from the target--as follows:
  • The Federal Reserve chooses a value of the interest rate r
    • (A gross shortcut, but let's make it)
  • When the Federal Reserve's choice of the interest rate r is at its normal value, then we go to the IS curve:
    • Y = A₀/[1-MPE] - (I_r + X_ee_r)/[1-MPE]
      • Where A₀ = C₀ + I₀ + G + X_fY^f + X_ee₀ + X_ee_rr^f
    • And find that Y is at some value Y₀, and thus that the unemployment rate is at value u₀--what the Federal Reserve thinks is the "normal" value of the unemployment rate
      • This should be, but may not be, the natural rate of unemployment u*
  • When inflation is higher than the Federal Reserve's desired target value π^T, the Federal Reserve gets nervous and pushes interest rates up--pushing investment and exports down, pushing output down, and pushing unemployment up above u₀
  • When inflation is higher than the Federal Reserve's desired target value π^T, the Federal Reserve gets nervous and pushes interest rates down--pushing investment and exports up, pushing output up, and pushing unemployment down below u₀
  • We model this with John Taylor's Monetary Policy Reaction Function (MPFRDF):
    • u = u₀ + o(π - π^T)
• Equilibrium
  • We have:
    • u = u₀ + o(π - π^T)
    • π = π^e - B(u - u*) + S
  • And thus:
    • π = π^e/(1+Bo) + π^T/(1+Bo) - B(u₀ - u*)/(1+Bo) + S/(1+Bo)
  • Give us a rule for understanding how inflation expectations are formed, and we will be done.

Inflation expectations

• Three kinds:
  • Static
  • Adaptive
  • Rational
• Static inflation expectations
  • Will exist only if fluctuations in inflation are small
  • Produces an economy that moves back and forth along a stable downward-sloping Phillips curve
    • π = π^e/(1+Bo) + (Bo)π^T/(1+Bo) - B(u₀ - u*)/(1+Bo) + S/(1+Bo)
    • u = u₀ + o(π - π^T)
  • With static expectations, only the sticky-price model is relevant
  • The U.S. in the 1950s and 1960s
• Rational inflation expectations
  • Will exist in a sophisticated economy if the variation in government policy and in inflation is large
  • Produces an economy with a vertical Phillips curve (except for supply shocks): unemployment = u* plus supply-shock terms; changes in government policy and in the economic environment affect the rate of inflation only
  • π = π^T - (u₀ - u*)/o + S/(Bo)
  • Mitterand 1981
  • Only the flexible price model is relevant
• Adaptive inflation expectations
  • Exponential convergence
    • [π_t - (π^T - (u₀ - u*)/o)] = (1/(1+Bo))[π_t-1 - (π^T - (u₀ - u*)/o)]

The natural rate of unemployment

• Natural rate vs. NAIRU
• Demography
• Institutions
• Productivity growth
• Past unemployment rates