Lectures 19 & 20:
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
• Appendix: 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: i  i *   s
Key results:
• S is highly variable, like other asset prices.
• Expectations are central.
e
Building blocks
Uncovered interest parity
+ Money demand equation
or
+
Flexible goods prices => PPP
=> Lucas model.
+
Slow goods adjustment => sticky prices
=> Dornbusch overshooting model.
INTEREST RATE PARITY CONDITIONS
Covered interest parity
i  i *  fd
+
No risk premium
}
fd   s
e
=>
Uncovered interest parity
i  i*   s ,
e
+
}
Ex ante Relative
Purchasing Power Parity
s     *
=>
i
Real interest parity
e
e
e
e
 i *  * .
e
Monetary Model of Exchange Rate Determination
With Flexible Goods Prices
PPP:
s = p – p*
Money market equilibrium: m–p = l( , ) ≡ log L( y, i)
Solve for price level:
Same for Rest of World:
p = m - l(,)
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; 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 flex-price or Lucas model, an increase in Y originates
in supply, 𝑌 , and so raises the demand for money => appreciation.
But 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 – λi ,
(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,
pp. 579-585.)
A 3rd alternative, the Overlapping Generations model (OLG), 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 flex-price /
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
e
   gm
Spot rate depends on expectations
of future monetary conditions
e
~
st  m t   (  st )
Rational expectations:
=>
~  ( m  m *)  ( y  y *)
m
t
t
t
t
t
where
 s  s t 1  s t  E t s t 1  s t
e
e
~   (E s  s )
st  m
t
t t 1
t
=>
st 
1
1 
~ )
(m
t

1 
( E t s t 1 )
E.g., a money shock known to be temporary has less-than-proportionate effect on s.
Use rational expectations:
s t 1 
1
1 
~ )
(m
t 1

1 
( E t 1 s t  2 )
E t s t 1 
1
1 
~ )
(Et m
t 1

1 
( E t st  2 )
Substituting, =>
st 
1
1 
~ )
(m
t

[
1
1  1 
~ )
(Et m
t 1

1 
Repeating, to push another period forward,
( E t 1 s t  2 )]

 2
~
~
~ )]
st 
[( m t )  (
)( E t m t 1 )  (
) (Etm
t2
1 
1 
1 
1
(

1 
3
) ( E t s t  3 )]
And so on…
Spot rate is present discounted sum of future monetary conditions
  

~
st 
(
)
E
m
 
t t  
1    0  1  

1
T
+
(

1 
)
T 1
E t st  T 1
Speculative bubble: lim last term ≠ 0 .
t 
Otherwise,
st 
1
1 


 0
 

~ 
(
) Etm
t  
 1 


Two examples:
Future shock:
 st 
Trend money growth g M   :
1
(

1  1 
~
) Etm
t T
T
~  g
st  m
t
m
Example: In 2002, when Lula pulled ahead of the incumbent
party in the polls, fearful investors sold Brazilian reals.
Brazil’s real depreciated again when Dilma Rouseff was reelected.
Real/$ exchange rate
2014
Oct.28
BBC News, Nov.3, 2014
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)
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 or productivity.
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.
Monetary Approaches
Assumption
If exchange rate is
fixed, the variable
of interest is BP:
MABP
P and W are perfectly Small open
flexible =>
economy model
New Classical
of devaluation
approach
If exchange rate is
floating, the variable of
interest is E:
MA to Exchange Rate
Monetarist/Lucas model
focuses on
monetary
shocks.
RBC model focuses on
supply shocks ( Y ).
P is sticky
Mundell-Fleming
(fixed rates)
Dornbusch-MundellFleming
(floating)