Lecture: October 10: The Phillips Curve, Expectations, and Monetary Policy

• 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