1. 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

2. 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.

3. Building blocks Uncovered interest parity + Money demand equation
+ Flexible goods prices => PPP   => Lucas model. or + Slow goods adjustment => sticky prices => Dornbusch overshooting model .

4. INTEREST RATE PARITY CONDITIONS
Covered interest parity +
No risk premium
=>
Uncovered interest parity ,
 Ex ante Relative Purchasing Power Parity } }
=> Real interest parity

5. Monetary Approaches Assumption
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
P and W are perfectly flexible => New Classical approach
Small open economy model of devaluation
Monetarist/Lucas model focuses on monetary shocks.
RBC model focuses on supply shocks ( ).
P is sticky
Mundell-Fleming (fixed rates)
Dornbusch-Mundell-Fleming (floating)

6. MONETARY MODEL OF EXCHANGE RATE DETERMINATION WITH FLEXIBLE GOODS PRICES
PPP:
Money market equilibrium:
Solve for price level:
Same for Rest of World:
Substitute in exchange rate equation:

7. 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).
 =>
  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, , and so raises the demand for money => appreciation.

8. So assume Cagan functional form: ,
Velocity is not in fact constant. Also we would like to be able to consider the role of expectations.
 So assume Cagan functional form: ,
 (where we have left income elasticity at 1 for simplicity).
Then,
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, )
 A 3rd alternative, the OverLapping Generations model, is not really a model of demand for money per se (as opposed to bonds).

9. In the Mundell-Fleming model, i  => appreciation, because KA .
Note the apparent contrast in models’ predictions, regarding i-S relationship. You have to ask why i moves. 
In the Mundell-Fleming model, i  => appreciation, because KA .
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.

10. The opportunity-cost variable in the monetarist/ Lucas model can be expressed in several ways:
Example -- hyperinflation, driven by steady-state rate of money creation:

11. Spot rate depends on expectations of future monetary conditions
where
Rational expectations:
=>
E.g., a money shock known to be temporary has a less-than-proportionate effect on s.
Use rational expectations:

12. Substituting, => Repeating, to push another period forward,
Repeating, to push another period forward,
And so on…

13. Spot rate is present discounted sum of future monetary conditions 
Speculative bubble: (last term) ≠
Otherwise,
Two examples:
Future shock
Trend money growth :

14. 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)

15. In 2002, when Lula pulled ahead of the incumbent party in the polls, fearful investors sold Brazilian reals.

16. The exchange rate in Zimbabwe’s hyperinflation
“Parallel rate”
(black market)
Official rate

17. A generalization of monetary equation for countries that are not pure floaters:
can be turned into more general model of other regimes, including fixed rates & intermediate regimes expressed as “exchange market pressure”: .
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.

18. 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 (and r is due to ), in turn due to shifts in tastes, productivity (Balassa-Samuelson,…)
But we want to be able to talk about transitory deviations of Q from (and r from ), arising for monetary reasons.
=> Dornbusch overshooting model.

19. DORNBUSCH OVERSHOOTING MODEL

20. DORNBUSCH OVERSHOOTING MODEL
PPP holds only in the Long Run, for In the SR, S can be pulled away from .
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 => investors expect future depreciation.
When  se is large enough to offset i- i*, that is the overshooting equilibrium .

21. 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.

22. Some evidence that expectations are indeed formed regressively:
∆se = a – θ(s- ).
Forecasts from survey data show a tendency for appreciation today to induce expectations of depreciation in the future, back toward long-run equilibrium.

23. The Dornbusch Diagram Because P is tied down in the SR,
S overshoots its new LR equilibrium
its
PPP holds in LR.
new B
Experiment: a one-time
monetary expansion
old A ? C
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):
If θ is high, the line is steep, and there is not much overshooting.

24. The experiment: a permanent ∆m
How do we get
from SR to LR?
I.e., from inherited P, to PPP?
Neutrality
at point B
at point C
= overshooting from
a monetary expansion
P responds gradually to excess demand:
Solve differential equation for p:
Use inverse proportion-ality 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.

25. Excess Demand at C causes P to rise over time
In the instantaneous
overshooting equilibrium (at C), S rises more-than-proportionately to M to equalize expected returns.
Excess Demand at C causes P to rise over time
until reaching LR equilibrium at B.

26. Now consider a special case: rational expectations
The actual speed with which s moves to LR equilibrium:
matches the speed it was expected to move to LR equilibrium:
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.

27. 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”)

28. 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.

29. 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.

30. 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.

31. SUMMARY OF FACTORS DETERMINING THE EXCHANGE RATE
(1) LR monetary equilibrium:
(2) Dornbusch overshooting: SR monetary fundamentals pull S away from , in proportion to the real interest differential.
(3) LR real exchange rate can change, e.g., Balassa-Samuelson or oil shock.
(4) Speculative bubbles.

32. Appendix