Transcript Lectures 18 & 19: MONETARY DETERMINATION OF EXCHANGE RATES • Building blocs - Interest rate parity - Money demand equation - Goods markets • Flexible-price version:

Lectures 18 & 19: MONETARY
DETERMINATION OF EXCHANGE RATES
• Building blocs
- Interest rate parity
- Money demand equation
- Goods markets
• Flexible-price version: monetarist/Lucas model
- derivation
- applications: hyperinflation; speculative bubbles
• Sticky-price version:
Dornbusch overshooting model
• Forecasting
Motivations of the monetary approach
Because S is the price of foreign money (vs. domestic money), it is
determined by the supply & demand for money (foreign vs. domestic).
Key assumptions:
• Perfect capital mobility => speculators are able
to adjust their portfolios quickly to reflect their desires.
• There is no exchange risk premium => UIP holds:
Key results:
• S is highly variable, like other asset prices.
• Expectations are central.
i  i*  s e
Building blocks
Uncovered interest parity
+ Money demand equation
+
Flexible goods prices => PPP
=> Lucas model.
or
+
Slow goods adjustment => sticky prices
=> Dornbusch overshooting model .
INTEREST RATE PARITY CONDITIONS
Covered interest parity
i  i*  fd
+
No risk premium
fd  s
e
}
=>
e
i

i
*


s
Uncovered interest parity
,
+
Ex ante Relative
Purchasing Power Parity
=>
Real interest parity
}
s     *
e
e
e
i  i*     *.
e
e
Monetary Approaches
Assumption
P and W are perfectly
flexible =>
New Classical
approach
If exchange rate is
fixed, the variable
of interest is BP:
MABP
If exchange rate is
floating, the variable of
interest is E:
MA to Exchange Rate
Small open
economy model
of devaluation
Monetarist/Lucas model
focuses on
monetary
shocks.
RBC model focuses on
supply shocks ( Y ).
P is sticky
Mundell-Fleming
(fixed rates)
Dornbusch-MundellFleming
(floating)
MONETARY MODEL OF
EXCHANGE RATE DETERMINATION
WITH FLEXIBLE GOODS PRICES
PPP:
s  p  p*
Money market equilibrium: m  p  L( y, i)
Solve for price level:
p  m  L(, )
Same for Rest of World:
p*  m *  L * (, )
Substitute in exchange rate equation:
s  [ m  L(, )]  [ m *  L * (, )]
 [m  m*] [ L(, )  L * (, )]
Consider, 1st, constant-velocity case: L( )≡ KY
as in Quantity Theory of Money (M.Friedman): M v=PY,
or cash-in-advance model (Lucas, 1982; Stockman, 1980; Helpman, 1981):
P=M/Y,
perhaps with a constant of proportionality from MU(C).
=>
s  (m  m*)  ( y  y*)
Note the apparent contrast in models’ predictions, regarding Y-S
relationship. You have to ask why Y moves.
Recall:
i) in the Keynesian or Mundell-Fleming models, Y=> depreciation
-- because demand expansion is assumed the origin, so TB worsens.
But
ii) in the monetarist or Lucas models, an increase in Y originates
in supply, Y , and so raises the demand for money => appreciation.
Velocity is not in fact constant.
Also we would like to be able to consider the role of expectations.
So assume Cagan functional form:
L(Y , i)  y  i ,
(where we have left income elasticity at 1 for simplicity).
Then,
s  (m  m*)  ( y  y*)  (i  i*) .
Of the models that derive money demand from expected utility
maximization, the approach that puts money directly into the
utility function is the one that gives results similar to those here.
(See Obstfeld-Rogoff, 1996,
579-585.)
A 3rd alternative, the OverLapping Generations model, is not
really a model of demand for money per se (as opposed to bonds).
s  (m  m*)  ( y  y*)  (i  i*)
Note the apparent contrast in models’ predictions,
regarding i-S relationship. You have to ask why i moves.
In the Mundell-Fleming model,
because KA .
i  => appreciation,
But in the monetarist or flex-price model, i  signals
Δse & π e . They lower demand for M => depreciation.
Lessons:
(i) For predictions regarding relationships among endogenous
macro variables, you need to know exogenous source of disturbance.
(ii) Different models are useful in different circumstances.
The opportunity-cost variable in the monetarist/
Lucas model can be expressed in several ways:
s  (m  m*)  ( y  y*)  ( fd )
s  (m  m*)  ( y  y*)   (s e )
s  (m  m*)  ( y  y*)  (   *)
e
Example -- hyperinflation, driven by
steady-state rate of money creation:
e
    gm
e
Spot rate depends on expectations
of future monetary conditions
~   (s e )
st  m
t
t
Rational expectations:
=>
where
~  (m  m *)  ( y  y *)
m
t
t
t
t
t
se  ste1  st  Et st 1  st
~  (E s  s )
st  m
t
t t 1
t
=>
st 
1 ~

(mt ) 
( Et st 1 )
1 
1 
E.g., a money shock known to be temporary has a less-than-proportionate effect on s.
Use rational expectations:
1 ~

st 1 
(mt 1 ) 
( Et 1st  2 )
1 
1 
1

~
Et st 1 
( Et mt 1 ) 
( Et st  2 )
1 
1 
Substituting, =>
1 ~

1

~
st 
(mt ) 
[
( Et mt 1 ) 
( Et 1st 2 )]
1 
1  1 
1 
Repeating, to push another period forward,
1

 2 ~
~
~
st 
[( mt )  (
)( Et mt 1 )  (
) ( Et mt 2 )]
1 
1 
1 

(
) ( Et st 3 )]
1 
3
And so on…
Spot rate is present discounted sum of future monetary conditions
1 T    ~ 
st 
) Et mt  
 (
1    0  1  

Speculative bubble:
lim (last term)
t 
Otherwise,
Two examples:
Future shock
Trend money growth g M   :

(
)T 1 Et st T 1
1 
+
≠0
.
1 
  ~
st 
(
) Et mt  )

1    0 1  
1
 T
~
st 
(
) Et m
t T
1  1 
~  g
st  m
t
m
Illustrations of the importance of expectations (se):
• Effect of “News”: In theory, S jumps when, and only when,
there is new information, e.g., regarding monetary fundamentals.
• Hyperinflation:
Expectation of rapid money growth and loss in the value of currency
=> L => S, even ahead of the actual inflation and depreciation.
• Speculative bubbles:
Occasionally a shift in expectations, even if not based
in fundamentals, causes a self-justifying movement in L and S.
• Target zone: If a band is credible, speculation can stabilize S
-- pushing it away from the edges even before intervention.
• “Random walk”: Today’s price already incorporates information
about the future (but RE does not imply the zero forecastability of a RW)
In 2002, when Lula pulled ahead of the incumbent
party in the polls, fearful investors sold Brazilian reals.
The exchange rate in Zimbabwe’s hyperinflation
“Parallel rate”
(black market)
Official rate
A generalization of monetary equation
for countries that are not pure floaters:
s  [m  m*]  [ L(, )  L * (, )]
can be turned into more general model of other regimes,
including fixed rates & intermediate regimes
expressed as “exchange market pressure”:
s  [m  m*]  L * (, )  L(, ) .
When there is an increase in demand for the domestic currency, it
shows up partly in appreciation, partly as increase in reserves
& money supply, with the split determined by the central bank.
Limitations of the monetarist/Lucas model
of exchange rate determination
No allowance for SR variation in:
the real exchange rate Q
the real interest rate
r.
One approach: International versions of Real Business Cycle
models assume all observed variation in Q is due to variation in
LR equilibrium Q (and r is due to r ),
in turn due to shifts in tastes, productivity (Balassa-Samuelson,…)
But we want to be able to talk about transitory deviations
of Q from Q (and r from r ), arising for monetary reasons.
=> Dornbusch overshooting model.
DORNBUSCH
OVERSHOOTING MODEL
DORNBUSCH OVERSHOOTING MODEL
PPP holds only in the Long Run, for S .
In the SR, S can be pulled away from S .
Consider an increase in real interest rate r  i - pe
(e.g., due to sudden M contraction; as in UK or US 1980, or Japan 1990)

Domestic assets more attractive

Appreciation: S 
until currency “overvalued” relative to S
=> investors expect future depreciation.
When  se is large enough to offset i- i*,
that is the overshooting equilibrium .
DORNBUSCH OVERSHOOTING MODEL
Financial markets
UIP + Regressive expectations
See table for evidence of
regressive expectations.
 interest differential
pulls currency above
LR equilibrium.
What determines
i & i* ?
SR
LR
=>
Inverse relationship
between s & p to
satisfy financial
market equilibrium.
Some evidence that expectations
are indeed formed regressively:
∆se = a – θ(s- s).
Forecasts from survey data
show a tendency for
appreciation today to induce
expectations of depreciation
in the future, back toward
long-run equilibrium.
The
Dornbusch
Diagram
Because P is tied down in the SR,
its
S overshoots its new LR equilibrium
PPP holds in LR.
p  p   (s  s)
new p
Experiment: a one-time
monetary expansion
old p
In the SR, we need not be on the
goods market equilibrium line (PPP),
but we are always on the financial
market equilibrium line (inverse
proportionality between p and s):
B
A
?
C
If θ is high, the line is
steep, and there is not
much overshooting.
The experiment:
a permanent ∆m
How do we get
from SR to LR?
I.e., from inherited P,
to PPP?
P responds gradually
to excess demand:
Neutrality
at point B
at point C
= overshooting from
a monetary expansion
Solve differential
equation for p:
Use inverse proportionality between p & s:
Use it again:
Solve differential
equation for s:
We now know how far s and p have moved along
the path from C to B , after t years have elapsed.
In the instantaneous
overshooting
equilibrium (at C),
S rises more-thanproportionately to
M to equalize
expected returns.
Excess Demand
at C causes P to
rise over time
until reaching LR
equilibrium at B.
Now consider a special case: rational expectations
The actual speed with which s moves to LR equilibrium:
s   (s  s)
matches the speed it was expected to move to LR equilibrium:
se   (s  s)
in the special case:
θ = ν.
In the very special case θ = ν = ∞, we jump to B at the start -- the flexible-price case.
=>Overshooting results from instant adjustment in financial markets
combined with slow adjustment in goods markets.
POSSIBLE TECHNIQUES
FOR PREDICTING THE EXCHANGE RATE
Models based on fundamentals
• Monetary Models
• Monetarist/Lucas model
• Overshooting model
• Other models based on economic fundamentals
• Portfolio-balance model…
Models based on pure time series properties
• “Technical analysis” (used by many traders)
• ARIMA, VAR, or other time series techniques (used by econometricians)
Other strategies
• Use the forward rate; or interest differential;
• random walk (“the best guess as to future spot rate
is today’s spot rate”)
Empirical performance of monetary models of exchange rates
In early studies, the Dornbusch (1976) overshooting model had some
good explanatory power. But these were in-sample tests.
In a famous series of papers, Meese & Rogoff (1983) showed all
monetary models did very poorly out-of-sample. In particular, the
models were “out-performed by the random walk,” at least at short
horizons. I.e., today’s spot rate is a better forecast of next month’s
spot rate than are observable macro fundamentals.
By the 1990s came evidence monetary models were of some help
in forecasting exchange rate changes, especially at long horizons.
E.g., N. Mark (1995): a basic monetary model beats RW at horizons
of 4-16 quarters, not just in-sample, but also out-of-sample.
At short horizons
of 1-3 months
the random walk
has lower prediction
error than the
monetary models.
At long horizons,
the monetary models
have lower prediction
error than the random walk.
Nelson Mark (AER, 1995):
a basic monetary model
can beat a Random Walk
at horizons of 4
to 16 quarters,
not just with parameters
estimated in-sample
but also out-of-sample.
SUMMARY OF FACTORS DETERMINING
THE EXCHANGE RATE
(1) LR monetary equilibrium:
M /M *
Q
S  ( P / P*)Q 
L(, ) / L * (, )
(2) Dornbusch overshooting:
SR monetary fundamentals pull S away from S ,
in proportion to the real interest differential.
(3) LR real exchange rate Q can change,
e.g., Balassa-Samuelson or oil shock.
(4) Speculative bubbles.
Appendix