- Denmark decided to peg its currency, the krone, to the euro at a fixed exchange rate. This means the Danish central bank must set its interest rate equal to the rate set by the ECB, sacrificing monetary policy autonomy in the short and long run. - Under a fixed exchange rate, a country faces constraints on monetary policy from both the domestic interest rate being determined by UIP and the long-run price level/interest rate being outside of the country's control. - The monetary policy trilemma states that a country can only achieve two out of three goals: a fixed exchange rate, free capital mobility, and monetary policy autonomy. Denmark's peg means it lost autonomy but gained exchange rate stability and

1. Eco 328
Pegging and the trilemma

2. • Here we focus on the case of a fixed rate regime without
capital controls so that capital is mobile and arbitrage is free to
operate in the foreign exchange market.
• Central banks buying and selling foreign currency at a fixed
price, thus holding the market exchange rate at a fixed level
denoted E.
• We examine the implications of Denmark’s decision to peg its
currency, the krone, to the euro at a fixed rate: EDKr/€
• The Foreign country remains the Eurozone, and the Home
country is now Denmark.
2
What Would Happen in a Fixed Exchange Rate Regime?
—
—

3. • In the long run, fixing the exchange rate is one kind of nominal
anchor.
• Even if it allowed the krone to float but had some nominal
anchor, Denmark’s monetary policy would still be constrained
in the long run by its chosen nominal target.
• What we now show is that a country with a fixed exchange
rate faces monetary policy constraints not just in the long run
but also in the short run.
3
What Is a Fixed Exchange Rate Regime?

4. The Danish central bank must set its interest rate equal to i€, the rate
set by the European Central Bank (ECB):
Denmark has lost control of its monetary policy: it cannot
independently change its interest rate under a peg.
4
Pegging Sacrifices Monetary Policy Autonomy in the Short Run
DENDENDENDENDKrDENDENDEN YiLPYiLPM )()( €

5. Our short-run theory still applies, but with a different chain of causality.
Under a float:
o The home monetary authorities pick the money supply M.
o In the short run, the choice of M determines the interest rate i in
the money market; in turn, via UIP, the level of i determines the
exchange rate E.
o The money supply is an input in the model (an exogenous
variable), and the exchange rate is an output of the model (an
endogenous variable).
5
Pegging Sacrifices Monetary Policy Autonomy in the Short Run

6. Our short-run theory still applies, but with a different chain of causality.
Under a fix, this logic is reversed:
o Home monetary authorities pick the fixed level of the exchange rate E.
o In the short run, a fixed E pins down the home interest rate i via UIP
(forcing i =i*); in turn, the level of i determines the level of the money
supply M necessary to meet money demand.
o The exchange rate is an input in the model (an exogenous variable), and
the money supply is an output of the model (an endogenous variable).
6
Pegging Sacrifices Monetary Policy Autonomy in the Short Run

7. 7

8. • The price level in Denmark is determined in the long run by PPP. But if
the exchange rate is pegged, we can write long-run PPP for Denmark
as:
• With the long-run nominal interest and price level outside of Danish
control, monetary policy autonomy is impossible. We just substitute
and into Denmark’s long-run money market
equilibrium to obtain:
8
Pegging Sacrifices Monetary Policy Autonomy in the Long Run
EURDKrDEN PEP €/
€iiDKr  EURDKrDEN PEP €/
MDEN = PDEN LDEN (iDKr )YDEN = EDKr/€ PEURLDEN (i€ )YDEN

9. Our long-run theory still applies, but with a different chain of causality.
Under a float:
o The home monetary authorities pick the money supply M.
o In the long run, the growth rate of M determines the interest rate i
via the Fisher effect and also the price level P; in turn, via PPP, the
level of P determines the exchange rate E.
o The money supply is an input in the model (an exogenous variable),
and the exchange rate is an output of the model (an endogenous
variable).
9
Pegging Sacrifices Monetary Policy Autonomy in the Long Run

10. Our long-run theory still applies, but with a different chain of causality.
Under a fix, this logic is reversed:
o Home monetary authorities pick the exchange rate E.
o In the long run, the choice of E determines the price level P via
PPP, and also the interest rate i via UIP; these, in turn, determine
the necessary level of the money supply M.
o The exchange rate is an input in the model (an exogenous
variable), and the money supply is an output of the model (an
endogenous variable).
10
Pegging Sacrifices Monetary Policy Autonomy in the Long Run

11. Consider three equations and parallel statements about desirable
policy goals.
11
The Trilemma
A fixed exchange rate
• May be desired as a means to promote
stability in trade and investment
• Represented here by zero expected
depreciation
0
€/
€/€/


DKr
DKr
e
DKr
E
EE
International capital mobility
• May be desired as a means to promote
integration, efficiency, and risk sharing
• Represented here by uncovered interest
parity, which results from arbitrage
iDKr = i€ +
EDKr/€
e
- EDKr/€
EDKr/€
1.
2.

12. Consider three equations and parallel statements about desirable
policy goals.
12
The Trilemma
Monetary policy autonomy
• May be desired as a means to manage the
Home economy’s business cycle
• Represented here by the ability to set the
Home interest rate independently of the
foreign interest rate
3.
€€/ iiDKr 

13. 13
The Trilemma
o 1 and 2 imply not 3 (1 and 2 imply interest equality,
contradicting 3).
o 2 and 3 imply not 1 (2 and 3 imply an expected change
in E, contradicting 1).
o 3 and 1 imply not 2 (3 and 1 imply a difference between
domestic and foreign returns, contradicting 2).
• Formulae 1, 2, and 3 show that it is a mathematical
impossibility as shown by the following statements:
• This result, known as the trilemma, is one of the most
important ideas in international macroeconomics.

14. The Trilemma
Each corner of the triangle represents a viable policy choice. The labels on
the two adjacent edges of the triangle are the goals that can be attained;
the label on the opposite edge is the goal that has to be sacrificed.
14

15. 15
Intermediate Regimes
• The lessons of the trilemma most clearly apply when the
policies are at the ends of a spectrum:
• a hard peg or a float,
• perfect capital mobility or immobility,
• complete autonomy or none at all.
• But sometimes a country may not be fully in one of the three
corners: the rigidity of the peg, the degree of capital mobility,
and the independence of monetary policy could be partial
rather than full.

16. The figure shows selected central banks’ base interest rates for the period 1994 to
2010 with reference to the German mark and euro base rates.
In this period, the British made a policy choice to float against the German mark and
(after 1999) against the euro. This permitted monetary independence because
interest rates set by the Bank of England could diverge from those set in Frankfurt.
16
The Trilemma in Europe

17. No such independence in policy making was afforded by the Danish decision to peg
the krone first to the mark and then to the euro. Since 1999 the Danish interest rate
has moved in line with the ECB rate. Similar forces operated pre-1999 for other
countries pegging to the mark, such as the Netherlands and Austria. Until they joined
the Eurozone in 1999, their interest rates, like that of Denmark, closely tracked the
German rate. 17
The Trilemma in Europe