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Lecture 7

Lecture 7. Intermediate Targets, Money Supply or Interest rates?. Examine the problems related to the pegging of the rate of interest Examine Friedman’s argument in the context of adaptive expectations.

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Lecture 7

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  1. Lecture 7 Intermediate Targets, Money Supply or Interest rates?

  2. Examine the problems related to the pegging of the rate of interest • Examine Friedman’s argument in the context of adaptive expectations. • Confirm the Sargent- Wallace finding for the instability of an interest rate peg with rational expectations • Show that an interest rate target is feasible under RE

  3. The Friedman critique of interest rate pegging • Friedman showed that pegging the rate of interest leads to instability of inflation and output • The argument owes a lot to Thornton (1806) and Wicksell • A positive real shock can lead to accelerating inflation and above capacity growth.

  4. The model • Let m = money, y = output, r = real rate of interest, R = nominal rate of interest and  = rate of inflation (e = expected inflation) • R = r + e • Let the demand for money be given by md - p = y - R • Let the IS curve be y = -r • Let the ‘Phillips’ curve be  = (y-y*)+ e

  5. Instability of of the interest rate peg with Adaptive Expectations

  6. A dynamic analysis- let R = R*

  7. A positive IS curve shock R LM R* IS(e)’ IS+u IS Y Y*

  8. Sargent & Wallace confirm the same result with RE • Should the monetary authorities use the interest rate or the money supply as its instrument of control? • It depends on the flexibility of prices and relative magnitudes of demand (real) versus nominal shocks • S&W show that if money is the instrument of control, there is a determinate price level • If R is the control variable, there is not.

  9. The S-W Rational Expectations Model

  10. Price level is determined

  11. If R is pegged - P is indeterminate

  12. McCallum (1981) (1986) • If the monetary authorities follow an interest rate rule, it is possible to obtain a determinate price level. • mt = m* + a(Rt-R*) • In a simple model with a forward expectations IS curve and a LM curve and a price surprise supply curve. • There is a deterministic solution and a stochastic solution

  13. Monetary Policy - intermediate targets • The role of monetary policy in a stochastic environment • The intermediate target - money supply or interest rate to stabilise output? • When is the money supply the most appropriate intermediate target? • When the interest rate? • When a combination?

  14. Assumptions • Authorities know the structure of the economy • Uncertainty is additive • Shocks to the IS curve are given by u and E(u) = 0 and E(u)2 = 2u • Shocks to the LM curve are given by v and E(v)=0 and E(v)2 = 2v • The price level is fixed and we are in the short-run

  15. IS-LM Model • IS Schedule y = y0 - R + u • LM Schedule m = y - R + v • A positive u shifts the IS curve up • A positive v shifts the LM up to the left.

  16. u, v > 0 LM+v R LM IS+u IS y

  17. Solving for the equilibrium R and y (eqns 1 & 2)

  18. Loss function LR = (R-R*)2

  19. Minimising the loss function

  20. The variance of output

  21. With an interest rate intermediate target

  22. R* with only IS shocks R R* IS+u IS IS-u Y

  23. R* with only LM shocks LM+v • R LM LM-v R* Y Y*

  24. Variance of output with a money supply intermediate target

  25. M* with only IS shocks • R LM IS+u IS IS-u Y

  26. M* with only LM shocks • R LM+v LM LM-v IS Y

  27. If only IS shocks - which is best intermediate target? • R LM IS-u R* IS+u IS Y

  28. If LM shocks only - which is best intermediate target? • R LM+v LM LM-v R* IS Y* Y

  29. Combination policy • R LM if IS shocks only LM if IS & LM shocks LM if LM shocks only IS Y

  30. Summary • Interest rate is best intermediate target if LM shocks dominate • Money supply is best intermediate target if IS shocks dominate • Combination policy is superior to both if shocks come from both IS and LM

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