OvershootingModel

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ECGA 7020 Macroeconomic Theory Fall 2005

Notes on Dornbuschs Overshooting Model

Rudiger Dornbusch was one of the first to explore the implications

of rational expectations for standard macroeconomic models. In 1976,

shortly after the Bretton Woods system of fixed exchange rates broke

down he published a JPE article exploring a standard open-economy IS-

LM-BP or Mundell Fleming model with rational expectations (perfect

foresight) but where output prices adjust slowly and asset markets clear

instantly. The q theory of investment offers a similar model where K

adjusts slowly but stock prices (q) can jump up or down instantly.

Dornbuschs key result was that even though agents have perfect

foresight the nominal exchange rate can overshoot its long term value.

At times, for example the exchange rate depreciates sharply, only to

appreciate again at a steady rate. This excessive volatility seemed to

match the behavior of newly floating exchange rates, and it matches what

happens when an economy jumps onto its saddle path. The results

derived from Dornbusch overshooting model made him famous and

bolstered the rational expectations revolution in macro-economics,despite complaints that the Mundell-Fleming model lacks micro-

foundations. Since the focus is short term price dynamics we take the

level of output is fixed (sy y= ) because our focus is on short-run

dynamics. Lowercase letters are the natural logarithms of the

corresponding variables denoted by uppercase letters, asterisks refers to

foreign variables. For instance. ( )p Ln P= is the natural log of the

domestic price (P), and for example

P

p P=

.

The version of the model developed in this handout is in continous time,

for a slightly different discrete time version of the model see see Obstfeld

and Rogoff (1996) Chapter 9 section 9.2 page 609.


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I. The Dornbusch-Mundell-Fleming Model

1.Goods Market: GDP or supply of ysis fixed at someconstant, exogenous level

sy y= (1.1)

2.Demand for domestic output depends on the real exchangerate and the real interest rate:

( * ) ( )dy s p p i p g = + +, (1.2)

where s is the natural log of the nominal exchange rate (S), and i

is the nominal interest rate, p is the actual and expected rate of

inflation, g is the natural log of government spending expenditures,

while and are positive constants.

3.Price adjustment: if demand exceeds supply, inventories aredrawn down, and the prices increase in proportion to excess

demand. This is a standard Phillips curve ( Obstfeld and Rogoff(1996) section 9.2 use an expectations augmented Phillips curve)

( )dp y y= . (1.3)

4.The asset market is a standard LM money demand schedule,

m p y i = , (1.4)where m is the natural log of nominal money supply M, and are positive constants.


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5.Last, assume uncovered interest parity:*i i s= + (1.5)

Other Assumptions:

i* is exogenous and constant. m, g and p* remain constant over time, therefore we have three time-

dependent variables: s, p and i.

I. Deriving the law of motion for exchange rates and prices

Using money demand equation (1.4) we solve for i,

y m pi

+= (1.6)

and then substitute this expression into (1.5) to get the law of

motion for the nominal exchange rate,

* *y m ps i i i

+= = . (1.7)

When 0s = then *p i m y = + , and note that

10

s

p

= >

Substituting (1.2) into (1.3) and solving forp , we have:

[ ( * ) ]1

p s p p i g y

= + +

. (1.8)


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Next substitute (1.6) into (1.8) and to get the law of motion for p,

{ ( *) ( ) }

1

y mp s p p g y

= + + +

. (1.9)

When 0p = then,

1{ ( *) }

( )

= + +

+

y mp s p g y

,

Implying that

0

( )

= >

+

p

s , 01

= >

p

s

and

( )0

1

+=

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