The Dornbusch overshooting model

Transcription

1 4330 Lecture 8 Ragnar Nymoen 12 March 2012

2 References I Lecture 7: Portfolio model of the FEX market extended by money. Important concepts: monetary policy regimes degree of sterilization Monetary model of E with endogenous expectations formation not trivial to anchor expectations about a nominal variable M targeting is the nominal anchor in that model. R-VI with regressive expectations has the same properties as the monetary model in the case where a monetary expansion is expected to be temporary

3 References II In this lecture, the link is again to Regime-VI of the portfolio model, as we extend the monetary model to the real side of the economy In Lecture 9 and 10 we will return to the discussion of the other regimes extended to the real economy. Model is dubbed Mundel-Fleming-Tobin model Short-run analysis first OEM Then dynamics, OEM 6.7 and 6.8 for this lecture, the relevant model section in OR is Ch 9.2.

4 Motivation I Bretton-Woods system of fixed rates collapsed in 1971 Major countries began floating (USA, Japan, Germany, UK) Volatility of exchange rates became higher than anticipated by economists These events and observations invited modelling: Led to an extension of the monetary model to the real side Home and foreign goods are imperfect substitutes in final use. Price of home goods does not jump (short run nominal price rigidity)

5 Model description I IS LM (Demand side) Phillips curve (supply side) UIP (FEX market) Model consistent and perfect exchange rate expectations Equations: Y = C (Y ) + X (EP /P, Y, Y ) (1) M/P = m(i, Y ) (2) Ṗ/P = γ(y Ȳ ) (3) Ė /E = i i (4) Endogenous variables: Y, i, P and E (as functions of time)

6 Model description II Exogenous variables: Y, P, i, M Initial condition: P(0) = P 0 Because this is a more complex dynamic model, it is useful to look at the long-run solution first, assuming that the long-run solution corresponds to a stable steady-state of the dynamic model. This simplifies the analysis of the long-run effects of exogenous changes (which we are interested in). But the relevance of the answers hinges on the assumed stability, so have to come back to the stability issue.

7 Steady-state solution I If a steady state-solution exists, it is defined by Ṗ P = 0 Ė E = 0 and the steady state-solution is given by the long-run model: Y = Ȳ (5) i = i (6) Ȳ = C (Ȳ ) + X (EP /P, Ȳ, Y ) (7) M/P = m(i, Ȳ ) (8)

8 Steady-state solution II (8): The long-run price level is determined by M. Consequence: Long-run inflation is Ṗ P = µ where µ the exogenous growth rate of M. In a stationary steady-state we set µ = 0. (7) represents internal-balance. It determines the equilibrium real exchange rate R from

9 Steady-state solution III Since R is by definition Ȳ = C (Ȳ ) + X ( R, Ȳ, Y ) R = EP P we have that the long-run nominal exchange rate must satisfy E = R P P The model obeys the classical dichotomy between the monetary and real side

10 The long run effect of a monetary expansion I This is conceptually different from the continuous growth measured by µ. Consider a completely stationary steady-state. What is the effect of a monetary expansion (a market operation)? Find El M P from (8): and therefore, using and (7), internal-balance: El M P = 1 E = R P P El M E = El M R + El }{{} M P = El M P = 1 =0

11 The long run effect of a monetary expansion II Hence El M E = 1 (9) as in the monetary model of the exchange rate. However the short-run effect and the dynamics are different, as we shall see next.

12 Solving the dynamic model I The temporary equilibrium, defined for the values that E and P take at a given moment in time. Solve (1) and (2) for Y and i : Y = Y (EP /P, Y ) (10) Insertion in (3) and (4) gives the dynamics: i = i(m/p, EP /P, Y ) (11) Ṗ = Pγ[(Y (EP /P, Y ) Ȳ ] = φ 1 (P, E; Y, P ) (12) Ė = E [i(m/p, EP /P, Y ) i ] = φ 2 (P, E; M, Y, P, i ) (13)

13 Solving the dynamic model II The stationary equilibrium Ṗ = 0 Y = Y (EP /P, Y ) = Ȳ (14) Ė = 0 i = i(m/p, EP /P, Y ) = i (15) Determines stationary values of P and E that we have already discussed. Questions: Does the economy move towards the stationary equilibrium in the long run? Is the stationary steady-state stable? How to determine the initial value of E? How is the path from the initial temporary equilibrium to the stationary equilibrium?

14 The phase diagram

15 Deriving the phase-diagram for P and E I Internal-balance: The Ṗ = 0-locus Ṗ = 0 Y = Y (EP /P, Y ) = Ȳ Y depends on ratio P/E. To keep Y constant at Ȳ, E must increase proportionally with P. P above Ṗ = 0 means Y low, P declining The Ė = 0-locus Ė = 0 i(m/p, EP /P, Y ) = i E = i M /P M P + i R R P P Ė =0 i R R E, i M /P < 0, i R > 0

16 Deriving the phase-diagram for P and E II Ambiguous slope since we have i M /P < 0 and i R > 0. The Ė = 0-locus is drawn with a negative slope E < 0 P Ė =0 based on the assumption that the money supply effect of increased P on the interest rate, dominates the money demand effect (through R and Y ). E above the Ė = 0-locus means i high, and E depreciating

17 Deriving the phase-diagram for P and E III In the phase-diagram, the arrows point away from Ė = 0 and towards Ṗ = 0. H is stationary equilibrium Starting point anywhere on P 0 -line A, B accelerating inflation forever D, E accelerating deflation until i = 0 C saddle path leading to stationary equilibrium

18 Along the saddle path I Inflation and appreciation together (left arm) Deflation and depreciation together (right arm) External and internal value of currency moves in opposite directions For the record: All exogenous variables, including M, constant over time Slope of saddle path (and Ė = 0-locus) the opposite if increased P lowers i

19 Monetary expansion: Overshooting I

20 Starting from A Locus for internal balance unaffected Locus for Ė = 0 shifts upwards Same price level, lower interest rate, higher E needed to keep money market in equilibrium C new stationary equilibrium Look for saddle path leading to C Immediate depreciation from A to B Gradual appreciation from B to C Along with gradual inflation and i < i

21 The short-run effect overshooting the long-run effect I Occurs because P is a predetermined variable that change gradually over time (not a jump variable) Also happens in response to shocks to money demand or foreign interest rates Increases the short-run effect on output of monetary disturbances May explain the high volatility of floating rates Empirical evidence mixed May occur in other flexible prices too?

22 A negative shock to the trade balance I

23 Real-depreciation needed to keep Y at Ȳ constant Ṗ = 0-locus shifts up Same depreciation keeps i = i (by keeping money demand constant) Ė = 0-locus shifts up equally Nominal exchange rate jumps from A to B No dynamic adjustment process in this case

24 Summary of results and caveat I A floating exchange rate insulates against demand shocks from abroad A floating exchange rate also stops domestic demand shocks from having output effects Caution! Studied only permanent shocks Less damping of temporary shocks (see Ch 6.4) Less damping if money supply deflated by index containing foreign goods Structural change may meet real obstacles

25 Extending the analysis I Can be solved for any time paths for the exogenous variables. (Log)linearization necessary for closed-form solutions. (OR Ch 9)) As in monetary model, the present exchange rate depends on the whole future of the exogenous variables. Phillips-curve witthout expectations is problematic in an inflationary environment.

26 Modifying the Phillips curve I ) e Ṗ (Ṗc P = + γ (Y Ȳ ) P c With model-consistent expectations (Ṗc P c Insert in the Phillips-curve above: ) e (Ė ) = αṗ + (1 α) P E + Ṗ P or Ṗ P = Ė E + Ṗ P + γ 1 α (Y Ȳ ) Ṙ/R = γ(y Ȳ ) = γ(y (R, Y ) Ȳ )

27 Modifying the Phillips curve II Together with Ė /E = i(mr/ep, R, Y ) i can then re-draw phase diagram in terms of R and E.

28 A steady state with constant inflation I Assume: Ṁ/M = µ and P P = π, constant Definition of steady state: Ṙ/R = 0, π = Ṗ/P = Ṁ/M = µ Then: Internal balance: Ė E = µ π From UIP, i = i + Ė /E: Ȳ = C (Ȳ ) + X (R, Ȳ, Y ) i = i + µ π i π = i π = ρ

29 A steady state with constant inflation II Hence real interest rate parity ρ = i π = ρ is implied. Finally, write money demand as: and long-run E as P = M/m(ρ + µ, Ȳ ) E = RP/P = RM/P m(ρ + µ, Ȳ ) Superneutrality: Neither shifts in M (market operations) nor changes in µ affect real economy

30 Wider implications Fixed versus floating exchange rates I Assuming (close to) perfect capital mobility in both cases Floating dampens the output effects of demand shocks Floating speeds up the demand response to shocks to potential output Fixed rate insulates the real economy from monetary shocks Fixed rates dampen the output response to pure cost-push shocks Shocks from exchange rate expectations / risk premium - difference can go either way fixed - main impact through interest rate floating - main impact through exchange rate effects have opposite sign

31 Wider implications Fixed versus floating exchange rates II Fixed versus floating exchange rates: Does one regime lead to more noise than the other? Different credibility of fixed M and fixed E? Floating exchange rates require good forecasting abilities Floating with inflation target is different from floating with money supply target.