Eco 328Pegging and the trilemma

• 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?

—

—

• 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?

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 )()( €

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

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

• 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 = PDENLDEN (iDKr )YDEN = EDKr/€ PEURLDEN (i€ )YDEN

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 ivia 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

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

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.

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

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.

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

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.

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

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