international economics #7 the exchange rate · 1. the foreign-exchange market 2. the monetary...
TRANSCRIPT
1. The foreign-exchange market2. The monetary approach and purchasing-
International Economics #7The exchange rate
1
2. The monetary approach and purchasing-power parity
3. Interest-rate parities4. Exchange-rate determination
1. The foreign-exchange market
2Bénassy-Quéré & Coeuré
International Economics 2009-2010
What is the foreign-exchange market?
• The market where currencies can be traded– Only convertible currencies
• A global, almost continuousmarket– Very large turnover: USD 3,200 Bn per day
interbank– Mostly interbank: only 17% of turnover involves non-financial agents– Manual transactions only marginal
• Three kinds of transactions:– Spot: delivery within 24 hours– Forward: delivery at a future date at a price set in advance– Swaps: two transactions of opposite directions at different dates; rates set in advance
• A concentrated market– Few currencies (mainly US dollar, euro, yen)– Few marketplaces (mainly London. New York)– Few banks (Ex.: in New York, 10 banks account for 75% of transactions)
3Bénassy-Quéré & Coeuré
International Economics 2009-2010
A few figures (April 2007)
Transactions quotidiennes sur le marché des changes
Daily transactions: USD 3,210Bn/day = 15 × World GDP ; 48 × World trade
Daily transactions on the foreign-exchange market
In April 2007
× World GDP ; 48 × World trade• Top pairs: EUR/USD 27% ; JPY/USD
13% ; GBP/USD 12%• Top pivotal currencies: USD: 86% of
transactions, EUR: 37%• Top marketplaces: London 34%; New
York 17%
4
Source: Bank of International Settlements, Triennial Survey of Foreign Exchange and Derivatives Markets, December 2007.
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
Why so many transactions?
• A decentralized market (no auctioneer, no consolidation of transactions except on electronic brokerage platforms)
• Arbitrage to take profit from spreads across marketplaces or products• Speculation(gambling): mostly intra-day
– Covered position, ex.assets in USD = liabilities in US;≠– Uncovered position, ex.assets in USD ≠ liabilities in USD;
• Long position, ex.assets in USD > liabilities in USD;• Short position, ex.assets in USD < liabilities in USD.
• Hedging: transactions aimed at offsetting foreign exchange risk– Ex.Airbus is to receive $60M in 6 months. It can cover its long position by
transacting with a bank:• Selling $60M on the forward market, or• Swapping its position (buying $60M today and selling $60M in six months), or• Buying a put option for $60M
– Unless the bank has an underlying FX position, it will hedge itself or sell its exposure on Airbus on the market
– Etc. (‘hot potato’ chain of transactions)5
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
International currencies: theory
Function Private sector Public sector
Means of payment Vehicle Intervention
6
Adapted from Paul Krugman, “The International Role of the Dollar: Theory and Prospects,” 1991.
Unit of account Denomination Anchor
Store of value Investment Reserve
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
International currencies: factsFunction Dollar Yen Euro Other
Trade with non-€ partners, 01 (1)
- Exports- Imports
--
--
45.444.4
--
Forex turnover, April 01 (2) 90.3 22.7 37.6 49.4
Outstanding amount of international bonds (extensive definition). end 99 (3)
Outstanding amount of international bonds (restrictive definition). end 99 (4)
45.9
48.9
18.7
16.0
21.2
20.7
14.1
14.4
Outstanding amount of cross-border bank loans (extensive definition). end 08 (5)
59.5 11.6 14.0 14.9
Function Dollar Yen Euro Other
Trade with non-€ partners, 07 (1)
- Exports- Imports
--
--
56.946.7
--
Forex turnover, April 07 (2) 86.3 16.5 37.0 60.2
Outstanding amount of international bonds (extensive definition). end 08 (3)
Outstanding amount of international bonds (restrictive definition). end 08 (4)
39.8
44.7
14.2
6.8
29.5
32.2
16.6
16.3
Outstanding amount of cross-border bank loans (extensive definition). end 08 (5)
51.6
54.3
3.2
5.9
22.2
17.6
23.0
22.21999
2008
7
Source: A. Bénassy-Quéré and B. Cœuré , Economie de l’euro, 2nd edition, 2010.
Notes: (1) Unweighted average for eight countries; (2) Out of 200%; (3) Including domestic issues (e.g. bonds in Euro area); (4) Excluding domestic emissions; (5) Including loans/deposits to/from banks located in the USA. the UK. Switzerland and the Eurozone and denominated in their own currencies; excluding interbank loans/deposits; (6) ) Excluding loans/deposits to/from banks located in the USA. the UK. Switzerland and the Eurozoneand denominated in their own currencies; excluding interbank loans/deposits; (7) Excluding unallocated reserves; (9) Share of currencies that are hardly or softly pegged. excluding the Euro area. Sources: BIS, ECB, IMF.
Outstanding amount of cross-border bank loans (restrictive definition). end 99 (6)
61.1 7.8 7.4 23.7
Cross-border bank deposits (extensive definition), end 99 (5)
Cross-border bank deposits (restrictive definition). end 99 (6)
60.0
66.5
4.7
6.2
20.8
13.9
14.6
13.4
Forex reserves. end 99(7) 71.0 6.4 17.9 4.7
Forex pegs, June 03(9) 31.3 0.0 13.6 -
Outstanding amount of cross-border bank loans (restrictive definition). end 08 (6)
54.3 5.9 17.6 22.2
Cross-border bank deposits (extensive definition), end 08 (5)
Cross-border bank deposits (restrictive definition). end 08 (6)
59.3
52.3
2.1
3.2
22.4
21.7
16.2
22.8
Forex reserves. end 08(7) 64.0 3.3 26.5 6.2
Forex pegs, April 08 (9) 45.4 0.0 18.6 -
1999
2008
Exchange rate: definitions
Different exchange rates:
• 1€ = x$ versus 1$ = x€
• Spot/ forward
Euro/dollar, 1970-2009
iPSQ =• Nominal / real
• Bilateral / effective
8
j
iijij P
PSQ =
∏=j
ijijQQ
α
Sources: Banque de France and IMF.
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
A reactive and volatile price
The euro/dollar on November 3rd 2006
1,275
1,28
Revision of non-farm payrolls
9
1,265
1,27
11:
00:0
0
11:0
8:00
11:1
6:0
0
11:2
4:0
0
11:
32:0
0
11:
40:0
0
11:4
8:00
11:5
6:0
0
12:0
4:0
0
12:
12:0
0
12:
20:
00
12:2
8:0
0
12:3
6:0
0
12:
44:0
0
12:
52:0
0
13:0
0:0
0
13:0
8:0
0
13:
16:0
0
13:
24:0
0
13:3
2:00
13:4
0:0
0
13:4
8:00
13:
56:0
0
14:0
4:00
14:1
2:0
0
14:2
0:00
14:
28:0
0
14:3
6:00
14:4
4:00
14:5
2:0
0
15:0
0:00
15:
08:
00
15:1
6:00
15:2
4:0
0
15:3
2:00
15:
40:0
0
15:4
8:00
15:5
6:0
0
Source: Reuters
Note: At 1:30 PM GMT, the U.S. Bureau of Labor Statistics disclosed an upward revision of Augustand September non-farm payroll increases from 188,000 to 230,000 and from 51,000 to 148,000.
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
2. The monetary approach and purchasing power paritypurchasing power parity
10Bénassy-Quéré & Coeuré
International Economics 2009-2010
Money and external adjustment in a fixed exchange-rate regime
The deflation of the 1930sDavid Hume, 1711-1776
David Hume,Political Discourses, 1752
11
Trade deficit
Fall in reserves
Money contraction
Deflation
Domestic price > World price
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
Purchasing power parity
Gustav Cassel, “Abnormal Deviations in
The Brazilian currency, 1991-1994Gustav Cassel, 1866-1945
Gustav Cassel, “Abnormal Deviations in International Exchanges,” The Economic
Journal, 1918
12
Fall in money demand
Deflation
Domestic price> World price
PPP
Source: IMF.
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
The monetary approach of the balance of payments
(Frenkel, 1976; Mussa, 1976; Bilson, 1978)
The model
p = m ; m = r ; b = β(p*-p-s), β > 0
Fixed exchange rate: s = 0, dr = b
dp= dm = dr = b = β(p*-p) > 0 as long as p < p*
p: domestic price
p*: world price
s: nominal exchange rate dp= dm = dr = b = β(p*-p) > 0 as long as p < p*
Long-run equilibrium: p* = p
Flexible exchange rate: dr = 0
dp = dm= dr = 0
b = dr = 0 ⇒ s= p* - p
Quicker adjustment than with a fixed exchange rate
s: nominal exchange rate
m: money
r: official reserves
b: current account
13Bénassy-Quéré & Coeuré
International Economics 2009-2010
PPP in practice
Big Mac index (July 2009)Nominal and real effective exchange rate of the euro
Country Big Mac price in
USD
ImpliedPPP
againstUSD
Under (-)/over (+) valuationagainst USD
USA 3.57 - -
Eurozone 4.62 1.08 +29%
14
Source : The Economist, July 18th 2009.
Against 52 countries, CPI-deflated. Source: ECB.
4.62 1.08 +29%
Japan 3.46 89.6 -3%
UK 3.69 1.56 +3%
Switz. 5.98 1.82 +68%
China 1.83 3.50 -49%
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
PPP as a long-run relationship
Unit-root test:
H0: ρ = 0 against H1: ρ < 0
• H0 rejected → the real exchange rate does not follow a random walk but reverts to its mean value after a shock.
t
p
kkttt QQQ ερ +∆+=∆ ∑
=−−
11 lnlnln
• Half-life of adjustment = date T when half of the adjustment is completed
Ex. ln Qt = (1+ρ)ln Qt-1 = (1+ρ)2ln Qt-2 =… = (1+ρ)Τln Qt-T
ln QT =(1+ρ)Τ ln Q0
(1+ρ)T = ½ ⇒ T = - ln 2 / ln (1+ρ)Empirically, ρ ≈ -0.15 i.e. T≈ 4 to 5 years for advanced economies
15Bénassy-Quéré & Coeuré
International Economics 2009-2010
Ln Q0
Ln QT
Ln Qt
T t
Developing economies: the Balassa-Samuelson effect (1964)
Intuition
Wages < world levelProductivity <
world level
Tradables
Law of one price
General price level < world level
16Bénassy-Quéré & Coeuré
International Economics 2009-2010
Price < world level
world level
Productivity = world level
Non-tradablesUndervalued currency
relative to PPP
Productivity catch-up
(tradables)Wage increase
Rise in non-tradable prices
Real exchange-rate appreciation
Dynamics
Developing economies: the Balassa-Samuelson effect (1964)
The model
• Two sectors:– Tradables: YT = πT LT; PT = PT*/S (law of
one price) ;
– Non-tradables: YN = πN LN; PN. PN*
– Y . L . π . P = production. employment.
• Tradables
• Non-tradables
***; TTTT PWPW ππ ==
*
**;
NN
NN
WP
WP
ππ==
– Y i. Li. πi. Pi = production. employment. productivity. price (i=T.N)
• Nominal exchange rate S
• Inter-industry labor mobility– Same wage in the two sectors. W
• Perfect competition– Price = marginal cost → Pi = W/πi
• Same abroad (*)
17
NN ππHence:
*
***;
N
TTN
N
TTN
PP
PP
ππ
ππ ==
• Law of one price
*
*
* /
/
/ NN
TT
N
N
SP
P
ππππ=1
/*=
SP
P
T
T and
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
The Balassa-Samuelson effect (cont’d)
Real exchange rate:
−−
−−=
*
*
*
*
)1(N
N
N
N
T
T
T
T dddd
Q
dQ
ππ
ππ
ππ
ππα
( ) ( )( ) ( )
αα
αα
αα
ππππ
−−
−
−
=
===
1
*
*1
*1**
1
* /
/
//// NN
TT
N
N
NT
NT
SP
P
SPSP
PP
SP
PQ
18
Developing country:
πT < πT*
πN ≈ πN*Q < 1
*
*
T
T
T
T dd
ππ
ππ >
0*
*
≈≈N
N
N
N dd
ππ
ππ
0>Q
dQ Real appreciation due to rise in non-traded
prices
Undervaluedcurrency
compared to PPP
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
The Balassa-Samuelson effect in practice
PPP GDP per capita and real exchange rates in 2006
China: insufficient appreciation against the US dollar
19
Source: IMF, World Economic Outlook, Sept. 2008. Source: Cheung, Chinn and Fuji (2007).
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
3. Interest-rate parities
20Bénassy-Quéré & Coeuré
International Economics 2009-2010
Covered interest parity
How to invest X euro over n years without any foreign-exchange risk?
Two strategies:
If one strategy dominates the other, there is a window for making riskless profit
At market equilibrium, both strategies should be equivalent:
Fn/S = (1+i*)n/(1+i)n or in log,Two strategies:1) Invest in euro at domestic interest rate i
– Value in n years: X (1+i)n euro2) Convert X in dollars at spot rate S,
invest on US market at US interest rate i* and sell the proceeds on the forward market at rate Fn
– Value in one year: X (1+i*)n Sdollar– Once converted back to euro:
X (1+i*) n S / Fn euro
Covered interest rate parity
If n = 1, then:
21
Fn/S = (1+i*) /(1+i) or in log,
i* - i = (1/n)(f – s)
F1/S = (1+i*)/(1+i) or in log,
i* - i = f – s
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
Covered interest parity (cont’d)
• Valid if:– Free capital movements– Negligible transaction costs– No country risk
• January 8th 2008– Euro/yen
• 161.1 spot• 155.7 1-year forward
22
– No country risk • 155.7 1-year forward
– 1-year money market interest rate• i = 4.60% in euro• i* = 0.91% in yen
– (1+i)/(1+i*) = 1.03657– S/F = 1.03468
0.18% spread, explained by transaction cost
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
Assuming risk neutrality,a higher return under the second strategy induces investors to borrow in euro and invest in dollar, which raises the spot price of the dollar against the euro until both strategies yield the same expected return:
Uncovered interest parity
Again, consider investing X euros during nyears, but assume that the investor is willing to bear foreign exchange risk
Two strategies:1) Invest in euro at domestic interest rate i
(1+i)n = (1+i*)n S/Sne or in log,
i - i* = (1/n)(s - sne)
Uncovered interest rate parity
If n = 1, then:
23
1) Invest in euro at domestic interest rate i– Value in n years: X (1+i)n euro
2) Convert X in dollars at the spot rate S,invest on US market at US interest rate i* and convert the proceeds in n years at the expectedspot rate Sn
e
– Value in n years: X (1+i*)n Sdollar– Expectedvalue in euro:
X (1+i*)n S/Sneeuro
i - i* = (1/n)(s - sne)
(1+i) = (1+i*) S/S1e or in log,
i - i* = s – se
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
Assume n = 1:• Covered interest parity: Arbitrage condition (no risk)
• Uncovered interest parity: Speculation condition (forex risk)
Because Se cannot be observed, UIP cannot be tested directly
Indirect test• If both CIP and UIP apply, then: F = Se: the forward rate is an unbiased proxy of the
Empirical evidence
i
i
S
F
++=
1
*1
i
i
S
Se
++=
1
*1
• If both CIP and UIP apply, then: F = S : the forward rate is an unbiased proxy of the expected rate
• Assuming rational expectations, Se = E(S) (mathematical expectation).• Under CIP, UIP and rational expectations, we thus have: F = E(S): the forward rate is an
unbiased predictor of the future spot rate, which at each time t writes:St = Ft-1.t + ut with Et-1(ut) = 0
Empirical test st - st-1 = a + b (ft-1.t - st-1) + ut Empirical result: b < 0 !
Possible explanations: variable risk premium; non-rational expectations; ‘peso problem’; market inefficiency
24Bénassy-Quéré & Coeuré
International Economics 2009-2010
Implications for exchange-rate dynamics
• Flexible exchange rate:
The spot exchange rate reflects market expectations of monetary policies and the long-run value of the exchange rate;
If i is expected to fall relative to i* by 1 percentage point during 3 years, then the exchange rate immediately depreciates by 3% relative to its long-run value, i.e. the exchange rate is more volatile than the interest-rate differential
∑∞
=++∞++ −+==−+=
0
*,
*1, )(...)(
k
ekt
ekt
etttt
ettt iisiiss
25
exchange rate is more volatile than the interest-rate differential
• Fixed exchange rate:
Suppose the exchange rate is expected to depreciate by 10% within 1 month. To maintain the peg. monetary authorities must raise the interest rate by 120% (=10%/nwith n=1/12). Defending a peg can be very costly … and market operators know it
Ex.Sweden, 1992.
( )te
nttntnt ssn
ii −−= +,*,,
1
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
4. Exchange-rate determination
26Bénassy-Quéré & Coeuré
International Economics 2009-2010
Simplified BoP equilibriumSmall economy under free float
Net financial inflows ∆Fin - ∆out > 0
Financial outflows
Financial inflows∆Fin
ExportsX
ImportsM
Current account balanceB = X-M < 0
27
Note: the capital account is neglected.
Financial outflows∆Fout
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
The portfolio-choice model(Branson, Halttunen and Masson, 1979)
Two countries, two currencies(euro, dollar)• Domestic country: net foreign asset position ΩΩΩΩ = A + F/S (in euro)
A: net assets in the domestic currency (in euro)
F: net assets in the foreign currency (in dollar)
S: number of dollars in one euro (rises when the euro appreciates).
• Foreign country: ΩΩΩΩ* = A*/S + F* (in euro)A*: net assets in the domestic currency (in dollar)
F*:net assets in the foreign currency (in euro)
• Two-country model: ΩΩΩΩ + ΩΩΩΩ* = 0Euro market equilibrium: A = -F*
Dollar market equilibrium: A* = -F
Hence: Ω = -F* + F/S = -Ω*
• Small-economy assumption: the domestic currency (the euro) is not used internationally: A = -F* = 0
28Bénassy-Quéré & Coeuré
International Economics 2009-2010
Assumptions• Domestic real wealth:
D Gross wealth in the domestic currency
F/S Net assets in foreign currency
P Consumer price index
f = F/PSW
• Household’s utility function: u(w)with w = ln W u’>0, u’’<0
P
SFDW
/+=
• Household’s utility function: u(w)with w = ln W u’>0, u’’<0
Risk aversion:
• Only two sources of risk: exchange rate, domestic price
29
0/
²/² >∂∂∂∂−=wu
wua
idtD
dD =
dtiF
dF*=
SSS dzdtmS
dS σ+= E(dzS) = E(dzP) = 0
with: V(dzS) = V(dzP) = dt
‘Wiener process’PPP dzdtmP
dP σ+=
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
Solving the model
• f is chosen so as to maximize the variation of expected utility:
• Order-two expansion:
• Hence:
22
2
2
1)()( dw
w
udw
w
uwudwwu
∂∂+
∂∂+=+
( ) ( )221
)( dwEu
dwEu
duE∂+∂=
dt
EduMax
f
• Hence:
• Normalize by ∂u/∂w around initial wealth. The program simplifies as:
30
( ) ( )222
1)( dwE
w
udwE
w
uduE
∂∂+
∂∂=
dt
Vdwa
dt
Edw
dt
EduMax
f 2−=
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
• Differentiate domestic wealth:
22
)/(
P
dPSFD
PS
FdS
SP
dF
P
dDdW
+−−+=P
dP
S
dSf
F
dFf
D
dDf
W
dWdw −−+−== )1(
Solving the model (cont’d)
• Introduce return and exchange-rate processes:
• Which yields the expectation and the variance of wealth variation:
31
[ ] PPSSPS dzdzfdtmfmfiifdw σσ −−−−+−= *)1(
)*( imifmidt
EdwSP −−+−= SPPS ff
dt
Vdw σσσ 2222 ++=
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
• FOC:
• mS is the expected exchange-rate variation:
• Denotef0 = - σSP/σS² (‘share of minimum risk’) yields:
( ) ⇒=+−−−=∂∂
0)*( 2SPSS faimi
f
u σσ 22
*
S
S
S
SP
a
imif
σσσ −−+−=
sssdt
EdS
Sm ee
S −=∆== 1
Model solution
0 SP S
• Balance of payment equilibrium:fPW= Ω. Replacingf by its value:
32
20
*
S
a
a
isiff
σ−∆−+=
Ω−+∆−=PW
fasii Se
02* σ
Risk premium
−Ω+−+= 02*)( f
PWaiiss S
e σor
Bénassy-Quéré & CoeuréInternational Economics 2009-2010
If a = 0, UIP holds.
Application to the euro/dollar
33Sources: ECB and US Bureau of Economic Analysis.
1999 2000 2001 2002 2003 2004 2005 2006 2007
EUR/USD (USD for 1 EUR) 1.07 0.92 0.89 0.95 1.13 1.24 1.24 1.26 1.37
US current account. USD bn -299.8 -415.2 -389.0 -472.4 -527.5 -665.3 -791.5 -869.1 -731.3
Euro area current account. EUR bn -23.9 -88.8 -22.1 57.0 32.4 55.6 18.1 -1.3 26.6
Net FDI flows from the Euro area to the United
States. USD bn62.3 126.2 2.2 -41.0 -10.0 -67.0 -44.4 40.2 -21.1
3-month interest-rate differential (EUR-USD) -2.5 % -2.1 % +0.5 % +1.2 % +1.1% +0.5% -1.4% -2.1% -1.0%
Bénassy-Quéré & CoeuréInternational Economics 2009-2010