Introduction Thelong-run Thedynamics Some extensions

The Dornbusch overshooting model 4330 Lecture 8

Ragnar Nymoen

Department of Economics, University of Oslo

12 March 2012

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

ReferencesI

I Lecture 7:

I Portfolio model of the FEX market extended by money. Important concepts:

I monetary policy regimes I degree of sterilization

I Monetary model of E with endogenous expectations formation

I not trivial to anchor expectations about a nominal variable I M targeting is the nominal anchor in that model.

I 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

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

ReferencesII

I 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

I In Lecture 9 and 10 we will return to the discussion of the other regimes extended to the real economy.

I Model is dubbed Mundel-Fleming-Tobin model I Short-run analysis first OEM 6.1-6.5 I Then dynamics, OEM 6.7 and 6.8

I for this lecture, the relevant “model section” in OR is Ch 9.2.

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

MotivationI

I Bretton-Woods system of fixed rates collapsed in 1971

I Major countries began floating (USA, Japan, Germany, UK)

I Volatility of exchange rates became higher than anticipated by economists These events and observations invited modelling:

I Led to an extension of the monetary model to the “real side”

I Home and foreign goods are imperfect substitutes in final use.

I Price of home goods does not jump (short run nominal price rigidity)

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Model descriptionI

I IS LM (Demand side) I Phillips curve (supply side) I UIP (FEX market) I Model consistent and perfect exchange rate expectations I Equations:

Y = C (Y ) + X (EP /P, Y , Y ) (1) ∗ ∗ M/P = m(i, Y ) (2) P˙ /P = γ(Y Y¯ ) (3) − E˙ /E = i i (4) − ∗ I Endogenous variables: Y , i, P and E (as functions of time)

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Model descriptionII

I Exogenous variables: Y , P , i , M ∗ ∗ ∗ I Initial condition: P(0) = P0 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.

I This simplifies the analysis of the long-run effects of exogenous changes (which we are interested in).

I But the relevance of the answers hinges on the assumed stability, so have to come back to the stability issue.

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Steady-state solutionI If a steady state-solution exists, it is defined by

P˙ = 0 P E˙ = 0 E and the steady state-solution is given by the long-run model:

Y = Y¯ (5)

i = i ∗ (6) Y¯ = C (Y¯ ) + X (EP /P, Y¯ , Y ) (7) ∗ ∗ M/P = m(i ∗, Y¯ ) (8)

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Steady-state solutionII

I (8): The long-run price level is determined by M. Consequence: Long-run inflation is

P˙ = µ P where µ the exogenous growth rate of M. In a stationary steady-state we set µ = 0.

I (7) represents internal-balance. It determines the equilibrium real exchange rate R¯ from

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Steady-state solutionIII

Y¯ = C (Y¯ ) + X (R¯ , Y¯ , Y ) ∗ Since R is by definition EP R = ∗ P we have that the long-run nominal exchange rate must satisfy

P E = R¯ P∗ The model obeys the classical dichotomy between the monetary and real side

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

The long run effect of a monetary expansionI 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)?

I Find ElM P from (8): ElM P = 1 and therefore, using P E = R¯ P∗ and (7), internal-balance:

ElM E = ElM R¯ + ElM P = ElM P = 1 =0

The Dornbusch overshooting model | {z } DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

The long run effect of a monetary expansionII

Hence ElM E = 1 (9) as in the monetary model of the exchange rate.

I However the short-run effect and the dynamics are different, as we shall see next.

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Solving the dynamic modelI

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) ∗ ∗ i = i(M/P, EP /P, Y ) (11) ∗ ∗ Insertion in (3) and (4) gives the dynamics:

P˙ = Pγ[(Y (EP /P, Y ) Y¯ ] = φ1(P, E; Y , P ) (12) ∗ ∗ − ∗ ∗ E˙ = E [i(M/P, EP /P, Y ) i ] = φ2(P, E; M, Y , P , i ) (13) ∗ ∗ − ∗ ∗ ∗ ∗

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Solving the dynamic modelII The stationary equilibrium

P˙ = 0 Y = Y (EP /P, Y ) = Y¯ (14) ⇐⇒ ∗ ∗ E˙ = 0 i = i(M/P, EP /P, Y ) = i (15) ⇐⇒ ∗ ∗ ∗ Determines stationary values of P and E that we have already discussed . Questions:

I Does the economy move towards the stationary equilibrium in the long run? Is the stationary steady-state stable?

I How to determine the initial value of E? I How is the path from the initial temporary equilibrium to the stationary equilibrium?

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

The phase diagram

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Deriving the phase-diagram for P and EI

I Internal-balance: The P˙ = 0-locus

P˙ = 0 Y = Y (EP /P, Y ) = Y¯ ⇐⇒ ∗ ∗

I Y depends on ratio P/E. To keep Y constant at Y¯ , E must increase proportionally with P. I P above P˙ = 0 means Y low, P declining

I The E˙ = 0-locus

E˙ = 0 i(M/P, EP /P, Y ) = i ⇐⇒ ∗ ∗ ∗ M ∂E iM /P P + iR R P = , iM /P < 0, iR > 0 ∂P E˙ =0 iR R E |

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Deriving the phase-diagram for P and EII I Ambiguous slope since we have iM /P < 0 and iR > 0. I The E˙ = 0-locus is drawn with a negative slope

∂E < 0 ∂P E˙ =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 ).

I E above the E˙ = 0-locus means i high, and E depreciating

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Deriving the phase-diagram for P and EIII

I In the phase-diagram, the arrows point away from E˙ = 0 and towards P˙ = 0.

I H is stationary equilibrium

I Starting point anywhere on P0-line I A, B accelerating inflation forever

I D, E accelerating deflation until i = 0

I C saddle path leading to stationary equilibrium

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Along the saddle pathI

I Inflation and appreciation together (left arm)

I Deflation and depreciation together (right arm)

I 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 E˙ = 0-locus) the opposite if increased P lowers i

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Monetary expansion: OvershootingI

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

I Starting from A

I Locus for internal balance unaffected

I Locus for E˙ = 0 shifts upwards

I Same price level, lower interest rate, higher E needed to keep money market in equilibrium

I C new stationary equilibrium

I Look for saddle path leading to C

I Immediate depreciation from A to B

I Gradual appreciation from B to C

I Along with gradual inflation and i < i ∗

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

The short-run effect overshooting the long-run effectI

I Occurs because P is a predetermined variable that change gradually over time (not a jump variable)

I Also happens in response to shocks to money demand or foreign interest rates

I Increases the short-run effect on output of monetary disturbances

I May explain the high volatility of floating rates

I Empirical evidence mixed

I May occur in other flexible prices too?

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

A negative shock to the trade balanceI

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

I Real-depreciation needed to keep Y at Y¯ constant

I P˙ = 0-locus shifts up

I Same depreciation keeps i = i (by keeping money demand constant) ∗

I E˙ = 0-locus shifts up equally

I Nominal exchange rate jumps from A to B

I No dynamic adjustment process in this case

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Summary of results and caveatI

I A floating exchange rate insulates against demand shocks from abroad

I A floating exchange rate also stops domestic demand shocks from having output effects Caution!

I Studied only permanent shocks

I Less damping of temporary shocks (see Ch 6.4)

I Less damping if money supply deflated by index containing foreign goods

I Structural change may meet real obstacles

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Extending the analysisI

I Can be solved for any time paths for the exogenous variables.

I (Log)linearization necessary for closed-form solutions. (OR Ch 9))

I As in monetary model, the present exchange rate depends on the whole future of the exogenous variables.

I Phillips-curve witthout expectations is problematic in an inflationary environment.

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Modifying the Phillips curveI

e P˙ P˙ c = + γ0(Y Y¯ ) P Pc −   With model-consistent expectations

e P˙ c P˙ E˙ P˙ = α + (1 α) + ∗ Pc P − E P    ∗  Insert in the Phillips-curve above:

P˙ E˙ P˙ γ0 = + ∗ + (Y Y¯ ) P E P 1 α − ∗ − or R˙ /R = γ(Y Y¯ ) = γ(Y (R, Y ) Y¯ ) − − − ∗ − The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Modifying the Phillips curveII

Together with

E˙ /E = i(MR/EP , R, Y ) i ∗ ∗ − ∗ can then re-draw phase diagram in terms of R and E.

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

A steady state with constant inflationI Assume: M˙ /M = µ and P˙ P = π , constant Definition of steady state: ∗ ∗ ∗

R˙ /R = 0, π = P˙ /P = M˙ /M = µ

Then: E˙ = µ π E − ∗ Internal balance:

Y¯ = C (Y¯ ) + X (R, Y¯ , Y ) ∗ From UIP, i = i + E˙ /E: ∗ i = i + µ π i π = i π = ρ ∗ − ∗ ⇐⇒ − ∗ − ∗ ∗ The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

A steady state with constant inflationII

Hence real interest rate parity ρ = i π = ρ is implied. Finally, write money demand as: − ∗

P = M/m(ρ + µ, Y¯ ) ∗ and long-run E as

E = RP/P = RM/P m(ρ + µ, Y¯ ) ∗ ∗ ∗ Superneutrality: Neither shifts in M (market operations) nor changes in µ affect real economy

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Wider implications

Fixed versus floating exchange ratesI Assuming (close to) perfect capital mobility in both cases

I Floating dampens the output effects of demand shocks

I Floating speeds up the demand response to shocks to potential output

I Fixed rate insulates the real economy from monetary shocks

I Fixed rates dampen the output response to pure cost-push shocks

I Shocks from exchange rate expectations / risk premium - difference can go either way

I fixed - main impact through interest rate I floating - main impact through exchange rate I effects have opposite sign

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo Introduction Thelong-run Thedynamics Some extensions

Wider implications

Fixed versus floating exchange ratesII

Fixed versus floating exchange rates: Does one regime lead to more noise than the other?

I Different credibility of fixed M and fixed E?

I Floating exchange rates require good forecasting abilities Floating with inflation target is different from floating with money supply target.

The Dornbusch overshooting model DepartmentofEconomics,UniversityofOslo