lecture 2: monetary models of the exchange ratemchinn/lecture2.pdf · monetary models of the...

Lecture 2:Monetary Models of the Exchange

Rate

Prof. Menzie ChinnKiel Institute for World Economics

March 7-11, 2005

Lecture Outline• Flexible price monetary model

• PV model of flexible price monetary approach

• Sticky price formulation

• Dornbusch model

• An application: the USD/EUR rate

I

The Flexible Price Monetary Model

Derivation of the Flex Price Model

Assume UIP and rational expectations

Invoke PPP:

Money demand functions in the two countries:

Combine with money market equilibrium:

II

A PV model of the FPMA

A Rat-Ex/PV Formulation

Assuming perfectly flexible prices, the Fisherian

model of interest rates should hold:

So it is assumed that real int. rate is constant

Derivation (I)

Recall UIP and ex ante rel. PPP:

Hence the FPMA can be re-expressed as:

Rearranging:

Imposing Rat-Ex:

substituting into the previous eqn:

But note:

substituting iteratively:

Conclusion: The current spot rate is the PDV of

the future stream of fundamentals, where

discount rate is the semi-elasticity of money

demand.

Special Cases (I): AR(1)

Substituting into previous expression:

Note: The relationship between the current spot

rate and current fundamentals will change if

either 8 or D (the driving process for the

fundamentals) change.

Consider no autocorrelation, D=0:

If the fundamentals are a white noise processaround a mean, ::

Special Cases (II): Random Walk The fundamentals:

Substitute D=1 into the PV equation

Current spot rate equals the current

fundamentals as all future fundamentals

are expected to equal the current value.

Or set all the EtMt+i's equal to Mt in the PV

equation:

What if the fundamentals follow a random walkwith drift?

Let:

re-arranging:

Let

and

subtracting this from the previous equation:

“Magnification Effect”:

Hold M constant,

change growth

rate:

News

What moves asset prices? “News”

What is the actual exchange rate at time t?

What is the exchange rate expected at time t

based on time t information?

What is the revision in the exchange rate?

What is News?

Revisions in expectations in ( ).

For J=0, this is a “surprise”:

Example: EUR/USD & CB Res.

Application: USD/EUR bond yields

III

The Sticky Price Monetary Model

The Flex Price Model as the Long RunRecall:

Assume long run PPP:

Assume flex price model applies in long run:

"Overshooting":

• 2 is the rate of reversion.

• If 2 = 0.5, 0.10 (10%) undervaluation induces a

0.05 (5%) exchange rate appreciation in the next

period.

• "Rational Expectations"

By UIP:

Solving for s:

Substitute in the long run s:

This expression can be rewritten as:

IV

The Dornbusch Model

(1)

(2)

(3)

Consider UIP (where r is nominal, e is s):

Ad hoc model of exp’d depreciation:

Solving for (p-m) and substituting in (1):

substituting in for x from equation (2):

rearranging yields (4);

(4)

(5)

Solve for p - p- , noting the LR version of (4) is:

solve for 8r*

substitute this in for r* in (4):

(6)

(7)

solving for e yields:

The domestic macroeconomy is described as:

(8)

• ln(D/Y) is log excess demand

• (e-p) is the real exchange rate (since p* = 1)

• u is a fiscal shift parameter

One can solve for long run values of e and p by

setting p. =0, r = r*, in equation (8):

(10)

Notice that (1) and (2) imply:

but (6) implies a rel’n betw (e-e- ) and (p-p- ):

substituting into (8):

but equation (9) is an expression for e- ,

where the last line is obtained by recalling from

(1), (2) and (6) that:

(11)

Then one obtains (10) :

for the following expression (11) holding true:

(12)

Solving (10) yields:

Substituting (12) into (6) yields:

but since

(13)

and

(14)

This result implies (14):

Hence the ad hoc expression for exchange rate

depreciation in (2) is equivalent to the perfect

foresight expression if:

Using the quadratic formula, dropping the neg.

root:

(15)

This yields (15):

(4)

Convergence is faster (2 larger):

• the larger *, F, B are

• the smaller 8 is

Recall in (4):

implies for de- = dm = dp- , that:

(16)

but dp/dm = 0 in the short run, due to sticky

prices:

substituting (15) into (16) yields (17):

(17)

Degree of overshooting depends on 8 and the

rate of convergence to PPP. The more rapid the

convergence rate, the less overshooting.

The p. dot=0 line (combined goods and money

market equilibrium), is given by:

Notice in (17) as:

• If output responds to AD/mon. shocks,

overshooting may be dampened.

• If 1-N:* < 0 then the exchange rate will

undershoot (where : = 1/(1-(), and ( is the

income elasticity of demand for domestic

goods).

Time series of macro variables in Dornbusch Model

Implications• Both the flex price and sticky price models try

to explain the volatility in exchange rates.

• In both models, exchange rates will be more

volatile than the fundamentals.

• The Dornbusch model illustrates one way to

get volatility: hold one variable constant, so

the other variable has to undertake all the

adjustment (p fixed, e very flexible).

• A general principle in models. E.g. current

account and net foreign assets.

V

An Application

Johansen Cointegration Results: 1991M08-1999M12

Panel 2.1: Long Run Coefficients

[1] [2] [3] [4]

LR 158.0 136.8 162.4 133.4

c.v. 111.0[144.3] 103.2[134.2] 111.0[144.3] 103.2[134.1]

CR’s 2[1] 2[1] 3[1] 2[0]

mUS-meuro 0.396*** 0.396*** 0.687*** 0.658***

(0.086) (0.086) (0.088) (0.082)

yUS-yeuro -2.219*** -2.217*** -0.754** -0.703***

(0.478) (0.480) (0.291) (0.278)

iUS-ieuro 0.968 0.947 0.129 -0.084

(1.195) (0.556) (0.808) (0.791)

BUS-Beuro 10.797*** 10.881*** 13.626*** 13.542***

(2.302) (2.319) (3.181) (3.044)

T~ 2.057** 2.070** 1.323 1.268

(0.898) (0.902) (1.132) (1.082)

-.2

-.1

.0

.1

.2

1997 1998 1999 2000

S S S E Q E C M 9 1 9 8 S S E Q E C M 9 1 9 9

Ac tu a lE C M n o tre n d9 1 M 8 -9 8 M 1 2

E C M n o tre n d9 1 M 8 -9 9 M 1 2

Tracking the Euro