The Mundell-Fleming Dornbush Model

Transcription

1 The Mundell-Fleming Dornbush Model (1) i t1 i e t1 e t (2) m t p t i t1 y t (3) y d t y e t p t p t q (4) q e p p logp /P (6) p t1 p t y d t y e t1 e t

2 Transition equations (7) Δq t1 q t1 q t q t q (9) Δe t1 e t1 e t e t 1 q t q m t where p y i 0.

3 The steady state Note that equation (9) is derived from (8) m t e t q t e t1 e t q t q Therefore, in a steady state where Δq t1 Δe t1 0, we have (10) e m q which implies that p m using equation (4) and the normailization that p 0.

4 The Phase Diagram Suppose that m t t0 m for all t. Draw and interpret the Phase Diagram.

5 An unanticipated rise in money from m to m In the the long run, using equations (7) and (9), the exchange rate and price level increase in proportion to the money supply p p e e m m where the long run interest remains i. Thus e e In the short run, the price level is predetermined. On the initial date (11) p 0 m which implies (12) q 0 e 0 m

6 Thus q 0 and e 0 must change proportionately.

7 Overshooting and the Transition Diagram

8 Intuition (2) m t p t i t1 y t. Money Suppy Side: The increase causes an increase in real money balances since p is initially fixed. Money Demand Side: Suppose the exchange rate jumped to its new steady state value - implying by equation (3) that output would rise on impact by m m: money demand wouldrisebym m. Ifweassume that 1, the rise in money demand is less than the increase in money supply. Thus the home interest rate must fall below i to restore money-market equilibrium. This is in contradiction to our assumption that e jumps immediately to its steady state. for i i implies an expected fall in e by UIP equation (1).

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10 Is overshooting necessary? Overshooting is not necessary. If output responds sharply to exchange rate depreciation ( is large) and the income elasticity of money is large ( is large). In this case the schedule for Δe is downward sloping. What does the transition diagram look like? Are there any similarities between undershooting and overshooting cases? In both cases, the dynamics of real exchange rate and output are quantitatively the same. The nominal depreciation of domestic currency implies a real apreciation (since prices are

11 sticky). This real depreciation raises aggregate demand, so output rises temporarly above it steady state.

12 Analytical Solution for SS Given any date t deviation of the real exchange rate from its long run value, the soultion to equation (7) is (13) q s q 1 s t q t q s t whereweassume1 1. Solve eq (9) for e t and then subtracting q yields (9) e t q e 1 t1 q 1 1 q t q m t 1 By iterative forward substition for e s q, we obtain (14) e t q 1 1 st 1 s t ms 1 1 st 1

13 after eliminating bubbles by the condition lim T 1 T ett 0

14 If the money supply is constant at m as we assumed in the diagrams, eq (14) becomes (15) e t q m 1 1 st 1 s t qs q To evauate (15), we use (13) to get e t q m 1 1 q t q st 1 s t 1 which simplifies to the sadle path SS e t m q 1 1 q t q Note that the slope depends on 1

15 More general Money supply process What is the exchange rate correlation with real and nominal interest rates. In our Dornbusch model we have shown that a permanent unanticipated increase in the money supply leads to lower nominal rates associated with depreciations In chapter 8, we showed that a positive shock to money supply growth leads to higher nominal rates associated with depreciations What are the effects of monetary growth shocks in our current model? Read pg for the theory, then look at the empirical evidence on the following pages. We will look at this in the

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17 Models of Credible Government Policy Credibility is central to monetary design. Can central bank commit to an exchange regime? Can central bank commit to an inflation path? Kydland-Prescott (1977), Barro-Gorden (1983) were the first to investigate this sort of question. Provide reasons why commitment is important

18 Think of ways that create commitment.

19 The Model Output is a function of the real wage (26) y t y w t p t z t where y t is log of output. The nominal wage is set to give output at the natural level (27) w t E t 1 p t The monetary authority sets period t policy after observing shocks and wages are set. They set inflation (27) t p t p t 1

20 The monetary authority seeks to minimize the loss function (29) L t y t y 2 t 2 where (30) y y k 0 Substitute the relevant equations into (29), we get (29) L t t t e z t k 2 t 2 where t e E t 1 t E t 1 p t p t 1. Timing of the game

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22 Questions Will inflation be high enough to force unemployment below the natural rate? No. What is the solution to this commitment problem? We will look at trigger strategies in a repeated game We will also consider why might pegging the exchange rate help central bank gain anti-inflaton credibility

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