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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
+=