lectures 18 & 19: monetary determination of exchange rates building blocs - interest rate parity...

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: esii *

Key results:• S is highly variable, like other asset prices.

• Expectations are central.

Uncovered interest parity + Money demand equation

+Flexible goods prices => PPP  => Lucas model.

or

+Slow goods adjustment => sticky prices

=> Dornbusch overshooting model .

Building blocks

INTEREST RATE PARITY CONDITIONS

Covered interest parity

+

No risk premium

=>

Uncovered interest parity ,

+

 Ex ante Relative Purchasing Power Parity

fdii *

esfd

esii *

*eees

** eeii

}

=> Real interest parity .

}

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)

Y

MONETARY MODEL OFEXCHANGE RATE DETERMINATION

WITH FLEXIBLE GOODS PRICES

PPP:

Money market equilibrium:

Solve for price level:

Same for Rest of World:

Substitute in exchange rate equation:

*pps

),( iyLpm

)(,Lmp

)(,*** Lmp

)](,**[)](,[ LmLms

)](,*)(,[*][ LLmm

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.

*)(*)( yymms

Y

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, 579-585.)

 A 3rd alternative, the OverLapping Generations model, is not really a model of demand for money per se (as opposed to bonds).

iyiYL ),(

*)(*)(*)( iiyymms

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.

*)(*)(*)( iiyymms

*)(*)(*)( eeyymms

)(*)(*)( esyymms

)(*)(*)( fdyymms

The opportunity-cost variable in the monetarist/ Lucas model can be expressed in several ways:

me g

Example -- hyperinflation, driven by steady-state rate of money creation:

Spot rate depends on expectationsof future monetary conditions

)(~ ettt sms *)(*)(~

ttttt yymmm where

Rational expectations:

=>

=>

E.g., a money shock known to be temporary has a less-than-proportionate effect on s.

Use rational expectations:

ttttet

e ssEsss 11

)(~1 ttttt ssEms

)(1

)~(1

11

tttt sEms

)(1

)~(1

12111

tttt sEms

Substituting, =>  

Repeating, to push another period forward,

And so on…

)(1

)~(1

1211

tttttt sEmEsE

)](1

)~(1

1[

1)~(

1

1211

tttttt sEmEms

)]()1

(

)]~()1

()~)(1

()~[(1

1

33

22

1

tt

tttttt

sE

mEmEms

Spot rate is present discounted sum of future monetary conditions

  +

Speculative bubble: (last term) ≠ 0 .

Otherwise,

Two examples:

Future shock

Trend money growth :

limt

0

)~)1

(1

1

ttt mEs

TttT

t mEs

~)1

(1

1

Mg mtt gms ~

T

ttt mEs0

~)1

(1

1

1

1)1

(

TttT sE

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:

can be turned into more general model of other regimes, including fixed rates & intermediate regimesexpressed 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.

)(,)(,**][ LLmms

)](,*)(,[*][ LLmm s

Limitations of the monetarist/Lucas modelof 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.

Q r

Q r

DORNBUSCHOVERSHOOTING MODEL

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 .

SS

S

DORNBUSCH OVERSHOOTING MODEL

Financial marketsUIP + Regressive expectations

See table for evidence ofregressive expectations.

interest differentialpulls currency above

LR equilibrium.

=>Inverse relationshipbetween s & p to satisfy financial market equilibrium.

What determinesi & i* ?

LR

SR

Some evidence that expectationsare 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 towardlong-run equilibrium.

s

itsThe

DornbuschDiagram

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

C

If θ is high, the line is steep, and there is not much overshooting.

)( sspp

A

PPP holds in LR.

Because P is tied down in the SR,S overshoots its new LR equilibrium

Experiment: a one-time monetary expansion

old p

new p

?

How do we get from SR to LR?I.e., from inherited P, to PPP?

The experiment:a permanent ∆m

at point B

at point C

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:

Neutrality

= overshooting from a monetary expansion

We now know how far s and p have moved along the path from C to B , after t years have elapsed.

Excess Demand at C causes P to rise over timeuntil reaching LR equilibrium at B.

In the instantaneous overshooting equilibrium (at C), S rises more-than-proportionately to M to equalize expected returns.

Now consider a special case: rational expectations

The actual speed with which s moves to LR equilibrium:)( sss

matches the speed it was expected to move to LR equilibrium:

)( ssse

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 TECHNIQUESFOR 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 horizonsof 1-3 months the random walk has lower prediction error than the monetary models.

At long horizons, the monetary models have lower predictionerror 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:

(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.

QLL

MM

)(,*/)(,

*/QPPS *)/(

Q

S

Appendix