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The Dornbusch Overshooting Model 4330 Lecture 8 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 = g(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˙ = m P where m the exogenous growth rate of M. In a stationary steady-state we set m = 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 solution III 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 m. 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 expansion II 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˙ = Pg[(Y (EP /P, Y ) Y¯ ] = f1(P, E; Y , P ) (12) E˙ = E [i(M/P, EP /P, Y ) i ] = f2(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 j 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 j 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 E III 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˙ =
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