Embed Size (px)
Citation preview
INTERNATIONAL
MONETARY
ECONOMICS
Lecture Notes
Stanley W. Black
University of North Carolina
International Monetary Economics Requirements: term paper due last day of class, final exam. Balance of Payments is record of all transactions (not just payments) between residents
of home country and other countries in given time period [flow]. Appears as foreign
sector in various national accounts: GDP, Flow of funds, commodity flows[input-output].
Pure trade theory assumes commodity trade is balanced (except in growth and capital
movements literature). Monetary theory does not assume balanced trade.
Residency rules: IMF - center of individual’s interest. US – live in country for 6 ½
months. Applies to individuals and corporations and subsidiaries or branches (agencies
abroad treated as part of domestic corporation).
Timing of transactions for goods and services can be on basis of orders, payments, or
deliveries (when goods move across borders). Some countries have all three (Japan) or
two (Sweden, Denmark). Transit time lag between export of goods and import leads to
“world trade imbalance” [~2 ½ % of world imports in 2000-2002 = $157 billion], also
due to valuation problems and recording problems, especially in investment income.
Fluctuates with dock strikes, wars, etc.
Financial claims recorded at date of claim.
Currency Contract Period Production lag Transport lag Entry lag Payment lag Currency Contract Period (McKinnon, p. 150) – importer bears risk of exchange rate
change unless hedged forward.
Pass-through Period - importer has time to adjust prices, but quantities don’t adjust yet.
Quantity-adjustment period – quantities demanded and supplied adjust, but domestic
prices and costs not yet fully adjusted to exchange rate change. Real exchange rate R =
SP*/P changes.
Purchasing Power Parity domestic prices and costs change to offset exchange rate, so
real exchange rate unchanged.
1
Trade Finance as source of capital flows: TFt = (Et – Rt)-( It – Pt)= (Et – It)-(Rt – Pt)
So Et – It = TFt + (Rt – Pt). Changes in payment times lead to changes in capital flows –
leads and lags. Importer usually has flexibility in time of payment.
Measurement Problems: Exports fas or fob, Imports fas, fob, or cif. Transfer prices. Over-
or under-valued exchange rates. Smuggling. Currency denomination of trade (Grassman:
2/3 exporter, 1/3, importer).
Concepts of Deficit or Surplus:
Current Balance CB=Xg&s- Mg&s –Tr = ∆NFA (=Y-A = S-I) = ∆LTK + ∆STK + ∆Res
Basic Balance BB=CB – ∆LTK = ∆STK + ∆Res = ∆STNFA = ∆NMF + ∆MF
Non-Monetary Balance NMB = CB – ∆LTK – ∆NMF = ∆MF= ∆NFAb
Official Settlements Balance OSB = CB – ∆LTK – ∆STK = ∆Res = ∆NFAcb
Relation of BoP to National Accounts:
GNP = GDP + r*NFA + w*NLA
GDP = Q = Cd + Id+ Gd + X = C - Cm + I - Im + G – Gm +X = (C+I+G) + X – M = A + B
Y = Q + F = C + I + G + X – M + F = C + Sp + T – R
I + X – M + F + R = Sp + T – G
I + NFI = Sp + SG
Relation to Monetary Sectors:
∆NFAb + ∆DCb = ∆M2, ∆NFAcb + ∆DCcb = ∆M0 (= Curr + Bank Reserves)
2
Intertemporal Trade and the Current Account Balance, Obstfeld & Rogoff Ch. 1 Small, open economy, single tradable good, two periods, given world interest rate r. Individuals with perishable endowments to maximize),( 21
ii yy
Assume identical individuals. Let population = 1, then aggregate C = ci, Y = yi.
If β=1/(1+r), then equilibrium C1 = C2.
C1Y1
C2
Y2
2111 BCYCA =−=
Autarky real interest rate:
3
Investment Y= F(K), F’>0, F”<0. Wealth Wt+1 = B t+1 + K t+1.
Saving ∆B t+1 + ∆K t+1 = Y t + rB t - C t -G t
Current Account CA t = ∆B t+1 = Y t + rB t - C t -G t – It = St – It
Intertemporal Budget Constraint:
C1
C2
Y1- I1
Y2- I2
if C2 = 0, C1 = K1 + F(K1) if C1 = 0, C2 = F(K1 + F(K1)) + K1 + F(K1)
4
Forward Market Arbitrage:
S = Spot €/$, F = 3 mos. Forward €/$,
R, R* = 3 mos. Interest rate in $, €
$1 = € S → (1+R*)S → (1+R*)S/F = $ (1+R)
S/F - 1 = (1+R)/(1+R*) – 1
(S-F)/F ≈ R – R* or s – f = R – R*
j− i+ s+( ) α⋅ γ ε⋅+ α γ+( ) 0.8=
α− j⋅ α i⋅+ α s⋅+ γ ε⋅+( )α γ+( )
f =
γis inversely proportional tof ε−risk premium =
ε 0.5=
tends to infinityαCIP holds if s i+ j− 0.92=CIP:
0 0.5 10
1
2
Speculators' SalesArbitrageurs' Purchases
Forward Market
f 1− .9−, 1.5..:=
α i j− s+ f−( )⋅ γ f ε−( )⋅Spot arbitrage sales=Forward arbitrage purchases=Speculative Forward sales
Forward Market Equilibrium:π 1:=p 2:=ε .5:=j .06:=i .05:=f 1:=s .93:=γ 2:=β 2:=α 5:=
Spot and Forward Foreign Exchange Markets (see Hallwood & MacDonald)let i = home interest rate, j = foreign interest rate, s = log spot price of foreign currency,f= log forward price of foreign currency, p = log domestic price, pi = log foreign price
5
γ( )Spot Market Equilibrium:
γ
α γ+
i j− s+ ε−( )⋅ β p π− s−( )⋅ Arbitrageurs' spot sales = Hedgers' purchases for (net) imports
PPP exchange rate s = p π− 1=s 1− .9−, 2..:=
0 1 22
0
2
4
Hedgers' purchasesArbitrageurs' sales
Spot MarketUIP: j i− ε+ 0.51=
PPP: p π− 1=
γ
α γ+0.286=
β 2=
s = p π−( ) α γ+( )⋅ β⋅ γ j i− ε+( )⋅+
α γ+( ) β⋅ γ+0.939=
6
Keynesian Elasticities Model of Balance of Payments
Pegged exchange rate π, 2 goods (exportable, importable),
prices fixed in producer market (Kenen in Handbook V.2)
Exportable x1, p1 fixed, p*1 = p1/π, c1, c*1, g1
Import good x2, p*2 fixed, p2 = πp*2, c2, c*2, g2
Domestic consumption
C = p1 c1 + π p*2c2 = Y – T – S = Y – T – s(r, Y – T)
Foreign consumption
C* = (p1/π)c*1 + p*2c*2 = Y* – T* – S* = Y* – T* – s*(r*, Y* –
T*)
Market Equilibrium exportable c1 + c*1 +g1 = x1
importable c2 + c*2 +g*2 = x2
with fixed prices, let p1 = 1, p*2 = 1
consumption share functions ci = fi(p1, πp*2, C),
c*i = f*i(p1/π, p*2, C*)
so equilibrium conditions are
f1(1, π, C) + f*1(1/π, 1, C*) + g1 = Y
f2(1, π, C) + f*2(1/π, 1, C*) + g*2 = Y* Marshall-Lerner –Robinson Condition for Elasticity Adjustment Given Y, Y*, prices p1, p*2, assume dπ (Note B = Sp + Sg = S + T
– g1)
),,1(),1,1( 2**
12*2
*11 CfCfcpcpB ππ
ππ −=−=
7
let *1
*11
*11
/1c
fe π−= and
22222 c
fe π−= Take derivative with respect
to π:
( )ππ
ππππ
πππ
πππ
πππππππ
ππ
deecdcecec
dcdcc
fdcc
fdcdfdfdB
)1(
/1
22*11
*12222
*11
*1
222
22*1*
1
*112222
*11
−+=−+=
−
−+
−=−−−=
if initial B = 0 (c*1 = πc2)
Finite Supply Elasticities (Bruce & Purvis, Handbook V2, Ch.
16-1.2)
Imports Exports
( )
f
fm
mf
m
msmm
dm
eP
ePP
ePIPI
εηε
εη
+=
−=−
=
ˆ
ˆˆˆˆ
)/()(
( ) ( )( )
εηη
εη
+=
=−−
=
f
fx
xxf
xs
xd
eP
PeP
PXePX
ˆ
ˆ
ˆˆˆ/
Effect on BoP in domestic currency NX = PxX - PmIm
( ) ( )( ) ( )[ ] ( ) ( )
( ) ( )( )( ) eZ
ZPPZ
PIIPPXXPdNX
ff
ffff
f
f
f
f
mx
mmmmxx
ˆ11
11ˆ1ˆ1
ˆˆˆˆ
++
−++++=
+
−−+
+=−−+=
+−+=
εεηηηηεεεεηη
εηεη
εηηεηε
8
9
Effect on terms of trade t = Px/Pm
( )( )ff
ff
f
f
f
f
mx PPetεηεη
εεηηεη
εεη
η++
−=
+−
+== ˆ/ˆ/ˆ
Armington Model (IMF Staff Papers 1969) derivation of trade
share matrix. Importers j=1,…,n, Exporters i= 1,…,n 1/
11 11 1 1
0 11 1 0
0
1 CES 1
( , ) ( ( , , ), ) separable utility
( , , ) demand for tradable good
from aggregation theory
( ) wher
jj jj n n j
j
j j j n
j j j j
j ijij
ij ij
ij ij j j
X b X b X
U U X X U f X X XX X Y P PdP dP
SP P
Min P X X X
ρρ ρ σρ
λ
−− − = + + = +
= =
=
=
− −
∑
…
0e ( , , )
and j
j
j j j ji
j ij ijij j ij
ij j j
X X Y P P
X X PP P b
X X P
σ
σλ λ−
=
∂= = ⇒ = ∂
∑
Absorption Approach
Assume less than full employment, fixed prices and interest
rates, monetary effect of deficit or surplus sterilized, pegged
exchange rate.
f1(1, π, C) + f*1(1/π, 1, C*) + g1 = Y
f2(1, π, C) + f*2(1/π, 1, C*) + g*2 = Y*
1-m1(1-sy) = 1-(1-m2)(1-sy) = m2(1-sy) + sy = m + sy
( )( ) ( ) ππππππ
ππ
πππ
π
π //1*
1**/
**1**1
/**
****
****
1111
11111
111112
111112
111121
111121
2122
1112
de
ed
eeee
cdecec
ecec
decec
ececd
ffff
dYdY
msmmms
y
y
−
=
−+−−+
=
−−−+−
=
−−+
=
−−
=
+−
−+
∆ = sysy* + msy* + m*sy
ππππ π
π
π des
sd
ee
msmmms
dYdY
y
y
y
y
−∆
=
−
+
+
∆=
*1/***1
*
ππ
ππ
ππ
πππde
ssdemsmsdemdYdYmdB yyyy
∆=
+
∆
−−=+−=
*1
****
10
Laursen-Metzler Effect of change in Terms of Trade on
Absorption
(Dornbusch, p. 79)
real income Z = PY/Q, price index Q = Pβ(eP*)1-β so
Q/P = (eP*/P) 1-β = p1-β
assume real absorption V = V(Z) where V = PE/Q
then expenditure in terms of domestic goods
E = (Q/P)V(Z) = p1-βV(Yp1-β) = E(p, Y)
( ) ( ) ( )( )log 1 1 1 1log
logwhere 1log
d Ed p
d Ed Z
β ε β ε β
ε
= − − − = − − >
= <
0
If E = E(Y), spend at A', since Y in terms of domestic goods is
constant at E. In this case V falls by –Mdp.
If real expenditure V is to remain constant, income must be
raised by Mdp to offset the terms of trade loss.
In general, with E = (Q/P)V(Z), choose an intermediate point.
Spending in terms of domestic goods rises (or saving falls).
A'
A
Domestic goods E
11
Imports M
Non-Traded Goods and Purchasing Power Parity
Law of One Price Pt = e Pt*
Equilibrium in goods markets γ = Pn/Pt
P = α Pt + (1 – α) Pn = [α + (1 – α)γ]Pt = θPt
P* = θ* Pt*
Absolute PPP e = Pt/ Pt* = (P/P*)(θ/θ*)
given M = PL(r,y) e = (M/M*)(L*/L)(θ/θ*)
Relative PPP ( ) ( ) ( )θθ ˆ*ˆˆ*ˆ*ˆˆˆ −+−+−= LLMMe
Capital and Labor in Non-Traded Goods Model (O&R, sec. 4.2)
Assume capital internationally mobile at rate r
( )TT Arfk /1−=
MPL:
0N
dpdk
<
MPK:
0dpdk
>N
12
Effect of productivity shifts on p:
Traded Goods – Non-Traded Goods Model
Small country case, if εf , ηf go to ∞, then dNX/de = Z(η + ε)
and if Px = Pm = Pt then exportables and importables are a composite
good T and dNX/de = ZT(ηT + εT) N
13
P B
C
A
T
Labor Market Equilibrium: T NT N
w wL Lp p
L+ =
or MPLN = w/pN
T TT
N N T
p p wMPLp p p
= =N
wp
w/pN (pT/pN)MPLT MPLN LN LT Goods Market: Expenditure E = DN + pDT Internal Balance:
,
0
T TN N
N N
T
N NE
Np Np
p pD E Yp p
pdp D
dE Y D
=
= <−
External Balance: pT/pN
E=Y
TT
NN
,
0
T TT T
N N
T
N TE
Tp Tp
p pD E Yp p
pdp D
dE Y D
=
= >−
E,Y
14
Corden – Neary Model of Dutch Disease Three sectors, Manufacturing (m), Services (s), and Energy (e)
m s em s e
s sm s
m m s m
e ee
m e m
w w wL L L Lp p p
p pw wMPL MPLp p p p
p pw MPLp p p
= + +
= = =
=
=
Goods Market:
15
Resource Movement Effect due to upward shift in LE and LT, because of rise in MPLE.
Assume 0sDE
∂=
∂ so demand goes from a to f, but supply to b at same p. p must rise, Ls
shifts up to Ls', raising real wage and reducing Lm. Spending Effect Assume Le = 0. No direct effect on labor market, but
production point vertically above a. Income-consumption line On takes
demand to c, requiring rise in p, again raising Ls. So increase in real
wage again reduces Lm.
16
Monetary Model of BoP Adjustment
Expenditure Approach Y = E + T, Y = Yf
( , , ), 0, 0, 0Y r M BP
M BE e Y r E E EP ++
= > < >
P = SP* all goods are traded, pegged exchange rate, so P fixed
M = SR + Bg + J exchange reserves + gov’t. securities + fiat money
* , ,
, ,
Hoarding Function:
, ,
0
e
e
M BP
M BM SR SP T P Y E Y rP
M B ML Y rP P
M B MM P L Y rP P
M PEM
π
π
+
+ = = = −
+ + =
+ = + −
∂= − <
∂
M
M
Walras’ Law: (PL – M) +P(E – Y) = 0
Allow for variable Y with sticky wages or prices.
( ) ( ) ( )/ , ) with /s sfY P W W W W Y P W Yδ= − =
Endogenous monetary policy via sterilization with
( ) so 1J SR M SR J SRφ φ= − = + = −
Capital Mobility implies 3 markets: goods, assets, money
D
excess supp ly o f goods A -A excess supp ly o f assets
excess supp ly o f m oney0
D
Y E TSF A B SF
M M MT SF M
T A M
− =
= − = +
− = −
− − =
= +
17
Non-traded Goods and Money (Dornbusch, Ch. 7, Mundell, Ch. 8)
Pegged Exchange Rate, money supply as adjustment mechanism
( )
( )( )
1Traded Goods
Nontraded Goods
Money 1
Adjustment (Mundell):
TT T
T N
TN N
N N
N T
N N N
VH PD Y
P P
PVHD YP P
PY VH P P P
P f D Y
H
γ
γ
γ γ
− = =
= =
= = + −
= −
= ( )Adjustment (Dornbusch):
T T
T T
g Y D
H Y D
−
= −
TT
NN PN
H
Flexible Exchange Rate (Mundell, Appendix)
( )*
1Traded Goods
Nontraded Goods
Money
TT T
T N
TN N
N N
VH PD YeP P
PVHD YP P
PY VH
γ
γ
− = =
= =
=
18
Polak Monetary Model
o Y = nominal income, M = M2 money stock M = imports
o
o
Y vMM mY
M B D F DF X M K
==
∆ = + ∆ = ∆ + ∆
∆ = − +
Example, Ghana (Franco, J. Dev. Studies 15(2), 1979, “Domestic Credit
and the Balance of Payments in Ghana”)
( )
( )
( )
1
3.93231 .15 .81
4.15.60.60 .37.37 , 2.47
1.60 .151 .37 .63
o
o
o
Y MM Y FM D F
F X M KFY D F
F D F
F D D Y D
M D D
−
== + + ∆= +
∆ = − +∆
∆ = − = ∆ + ∆
−∆ = ∆ + ∆
− −∆ = ∆ = − ∆ ∆ = ∆ = ∆
−∆ = − ∆ = ∆
D
Santaella “Stylized Facts Before IMF Adjustment” IMF Staff Papers
(1996) 91 countries 1973-91 Program Countries Controls
Median Government Borrowing 3.6%(of GDP) 1.2%
Median Fiscal Balance (% of GDP) -6.9% -3.4%
Domestic Credit (% change) 25.1% 20.4%
Dom. Credit to Govt. (% change) 42.4% 15.9%
M2 (% change) 18.9% 19.7%
19
Flow of Funds
Markets\Sectors Private SOE's Gov't. Banking Foreign
Saving Sp Ssoe T-G M-X
Investment -Ip -Isoe
Money -∆M ∆M
Credit DCp DCsoe DCg -DC
Foreign Assets -∆NFA ∆NFA
Capital Flows ∆Kp ∆Ksoe -∆K
Monetary Approach to the Balance of Payments (Mundell, Ch. 8)
Assume full employment, single tradable good, perfect capital mobility
( *)
ˆ ˆ ˆ ˆ ˆ*
ˆˆ ˆ ˆFixed Rate *ˆˆ ˆ ˆFloating Rate *
ˆˆ ˆ ˆ ˆExchange Market Pressure *ˆˆ ˆ ˆ ˆEffect of Devaluation *
Sterilization
D R k i PYD Rd r p e y
M Mr p y d
e d p y
r e p y d
r p y e d
+ =∆ ∆
+ = + = + +
= + −
= − −
− = + −
= + + −ˆ ˆ d rα φ= −
Conolly-Taylor (Economica 1979) 17 LDC’s and 10 DC’s
2
2
ˆˆ ˆLDC's .28 .74 , .69 (.09) (.14)
ˆˆ ˆDC's .27 1.27 , .90 (.52) (.39)
r e d R
r e d R
= − =
= − =
20
Cagan Monetary Model of Exchange Rate (O&R, 8.2.7, H&M, 9.3)
1
1 1 1
1
1 1
1
1 1
**
* *( * *) ( )
( )1 1 1( ) ...
1 1 1 1 1 1
11 1
t t t t
t t t
t t t t t
t t t t t t t
t t t t t t t t
t t t t t
t t t t t t t t t
t
m p i yp e pi i E e ee p p m y i pe m y i p E e ee f E e e
e f E e f E f E e
e
1 2
η φ
φ ηφ η ηη
η η ηη η η η η η
ηη η
+
+ + +
+
+ +
+
+ +
− = − +
= +
= + −
= − = − + −
= − + − + −
= + −
= + = + ++ + + + + +
= + +0
s
t t ss
E f∞
+=
∑
+ + =
21
Fleming-Mundell Model
( ) ( )
( )
( ) ( )
( )
, ,0,1 ,
,
, , *
: ,
: 0,
: 0,
r Y Y Y
rY r
Y
Yr Y
r
rr
Y A r Y B Y GA A s B mM L r YpR B Y F r r
dr AIS s m dY A drdY s m
dr LLM L dr L dYdY Ldr mFB mdY F drdY F
π
π
= + +
< − = = −
=
∆ = +
+ = =+
+ = = − >
− + = = >
0
0
0
<
Internal Balance: Y = Yf r FB
External Balance: ∆R = 0
Policy Dilemma for expenditure policy
in regions I and III.
Mundell solution: use fiscal & monetary Yf Y
policy in opposite directions
Regio n I: monetary expansion, fiscal contraction
Region III: monetary contraction, fiscal expansion
22
Differential effects of r and G on Y:
( )
[ ]
( )
1, 0
0
1 10 but 1
r Yr
r rY
Y r r
Y rr r
drA dr dG s m dYdG A
mmdY F dr A dr dG F drs m
dr mdG s m F mA
s AF Am
+ = + = − >
− + = − + + =+
=+ −
= > < − + −
r
r External
Internal
G
Slope of FB vs. LM: or as Yr
r r
Lm FF L
> < − ≤ ∞
r FBL LM
FBH
IS
Y
Case of perfect capital mobility: r = r*. Fiscal policy impotent with
flexible rate . Monetary policy impotent with pegged rate.
23
Effect of Devaluation (Kenen) (assume mdY is small enough not to matter
for Y*)
( )
( )
( ) ( )( )
( , ) ( *, , )
,
( *, , ) , *
*0 0 /
0 0 * * *
* * 0
*1 * 10 0 0
* *0 * *
r
Y r
r Y r
r
rr
Yr
s r Y T B Y Y g TM L r Yp
R B Y Y F r r
s m s m dY eL L dr d
s m dY e
Det s m L s m L s
e s mdY sL esd Det s m s m Le s m L
dr
π
π
π
π
π
π
π
π π
π
− = + −
=
= +
+ − = + −
= + + − <
− = = + + − − +
>
*/1 *0 0
* *0 * *
* 1 0* *
**
* 0* *
or as slope LM > or < slope FB
Y rY
rY
r
r
r YY r
r r
rY
r
Yr
r
s m e mL LsL esd Det s m s m Le s m L
dY ed s mdR dY dY drm m e Fd d d d
s Ls L FL Ls ess m s m L
LLF mL
π
π
π
π
π
π
π
π
π π π π
+ − = = − + + − − +
= − <+
= − + +
− −= >
+ + −
− > <
0>
24
r LM
FBH
IS
Y
Effects of Variable Prices
1. Supply Curve p(Y) shifts LM left as p rises, FB shifts up as πp*/p
falls.
2. If ( )1/ with *p p pM p ββ π −= then LM shifts left even more.
This assumes fixed money wage, so Ys(p/w) increases with p.
3. Assume instead fixed real wage
( )11
*
w *then product real wage p
w wp p p
p pp p
ββ
β
ωπ
ω πω
−
−
= =
= =
increases with devaluation and Y falls, contractionary devaluation.
4. Flexible real wage
*D S S S Sw w w pN N N Y Y pp p p p
π = = → =
p
5. Note if real wage is flexible and interest rate is fixed by policy or
perfect capital mobility, then *D S *p pYYp p
π π =
and p ~ π
25
6. So far, we assume exchange rate expectations don’t matter. But if
, *e
F F r r π ππ
−= +
and Fr→∞, then if with <1ed dπ σ π σ=
Then ( )1dr dσ π= − < 0 at least in the short run. Assignment Problem Internal
π
External
“Swan” Diagram
Internal Balance: Y = Yf
( ) 1, 0ds m dY e d dGdG eπ
π
ππ+ = + = − <
External Balance: ∆R=0
0
, 0
e dGdB mdY e d m d e ds m s m
d mse d mdGdG se
ππ π
ππ
π π
ππ
= − + = − + + = + +
= = >
π
G
If External Balance line steeper, m>s, assign exchange rate to
internal balance, fiscal to external.
If Internal Balance line steeper, m<s, assign exchange rate to external
balance, fiscal policy to internal.
26
Gylfason & Risager “Does Devaluation Improve the Current account?” (EER 1984)
( ) ( )( )
1
: : * *
trade balance current account *expenditure , ,
ˆ ˆˆ ˆˆ ˆ 1 =private share of debt, =debt/wealth
if initial t
E EGDP y e x z n GNP y y r DP P
b y e b y eyP M A EDe e P E
e y P E
ψ ψτ
α α τφ τ φ
−
′ ′= + − − = −
′ ′= − = −
+ − = Π = Π Π
= + −Π − − +Π
( )( ) ( )( )( )( )
( )( )
rade deficit is , then , 1 1
ˆ ˆˆexports
ˆ ˆ ˆ ˆ ˆˆˆ ˆˆfinal goods imports
ˆ ˆ ˆ ˆˆ ˆintermediate imports 1
Production , labor, imported input ˆˆ 1 n n
xx e yy
x E P
z e P E P e E P
n E P y E W
q q l n n
q l
ωω ρ ρ
η
δ ψ δ
σ
θ θ
= = + >
= −
= +Π − − − = + − −
+ − = + − −
=
= − + [ ]
( ) ( )
( )
( )
l l
l
ˆ if 1 in general 1ˆˆˆ ˆˆ ˆintermediate imports 1 since ˆ ˆ
1 ˆ ˆˆ ˆ ˆconsider case =0 and 1 1
1ˆ ˆ ˆ ˆ ˆ ˆcosts 1 [or if <1]
let
n n
n
n
n n
nn n
n
n ln q E WE W
Ey q n y q E P nP
P W E W E q
θ θ θ θ θ
θ σ σ
θµθ θ
θθ θθ θ θθ θ θ
+ = + = <
−= − − − = −
−
= − = − − +− −
−= − + + +
( )( )* * ˆ ˆˆ ˆ if =0 and =1, then 1nEr D y q E W
Pyµ µ θ θ σ= = − − −
27
Effect of devaluation on income:
(case * *1, 0, 0Er DPy
θ φ µ= = = = )
substitute for ˆ ˆ ˆˆ, , , from above ine x z n
( ) ( )
( )
( )( )
( )( )
1 2 3
2 1
2
ˆ ˆ ˆˆ ˆ ˆˆ11 1
,1ˆ ˆ ˆˆ
ˆ ˆ ˆso if =1, 0,ˆˆ
1where 1 1 0,1
1 [Marshall-Ler1
n
n
n
n
n
n
n
n
xy e z E P n
z Eny Py
y a P a E a W
W P E
y a a E
a
θρ λ β βθ ω
θλθ
θ θ
θ
θλ ρψ βθ
η β δ ψ βω
= + + − − − − + − +
= = −
= − + +
= =
= −
= + Ω− −Γ − > ∆ −
Ω = + − − −+
ner ]
=1- + [=s+m]
η δ
α αλ
+
∆
P
AS
θnĚ AD
y
28
Effect of devaluation on trade balance (y'-e) or current account (y-e)
( )
( ) ( ) ( )
( ) ( ) ( ) ( )
ˆ ˆ
ˆ ˆˆ ˆ ˆ1 1 1
ˆ ˆ/ ˆ1 1 1 1ˆ ˆ ˆ ˆ
db dy de y y edb y e y P Ey
db y y P PE E E E
ρ
ρ αρ ρ α ψ ρ α φ ψ
αρ ρ α ρψ ρ α φ
= − = −
= − = − + − − + − +
= − + − + − + − >
0
income wealth terms of trade debt
effect effect effect effect
Overall effect positive if ˆ
ˆ 0 and 0 1 terms of trade worsenˆPyE
> < <
Empirical estimates show ˆ 0y < often but other effects make db>0
Increase in wages shifts up AS curve, more likely that y falls and tot
improves.
Example Brazil:
( ) ( )
.3, .4, 1.7, .7, .05, .39, .44,.03, .42, .04, .33, .10, .50
ˆ ˆ10% 1.6%,ˆˆ
income effect: 1 0.4, wealth effect: 1 0,ˆ ˆˆ
terms of trade effect: 1 0.3, debt effeˆ
n l
E y
y PE E
PE
σ η δ α θ θ θλ β µ ε φ ω
αρ ρ α
ρψ
= = = = = = == = = = = =
= → = −
− = − − =
− =
( )ct: 1 0.3,
total / 0.2%db y
ρ α φ− =
=
29
Intertemporal Model – Obstfeld & Rogoff
Two regions, two periods, one good, one bond
r r S1* S1 S1 S1* Slope of Savings Schedule: Maximize
subject to
yields first order condition
Take logs and differentiate to get
since
we get
so that curvature of indifference
curve depends on elasticity of intertemporal substitution. Slope of
savings function from response of C1 to r. Differentiate
30
to get
If then
so from
( ) ( ) ( ) ( )( )( )
( )( )
( ) ( )
( ) ( ) ( )
( )( )
( )( ) ( ) ( )
21 2 1 2 2 1
2 2
22 1
1 2 1 12
2 1 1 12 2
2 1 1 1
1 1
divide both sides by / and use to get
C 1 1-
u C
C 1Since 1
u C
we
u C r u C dC u C r u C Y C dr
u C C
u C r rdC C Y C dr
u C C u C rC CrC u C C
β β β
σ
β ββ
σ σ
ββ
σ
′′ ′′ ′ ′′ 1 + + = + + − ′−
′′ + ++ = − + − ′
′′ ′′ += + = −
′ ′
( )( )( ) ( )
( )( )
1 1 2 1 1 21
2 2 2 1
1
1 / 1 find or 0
1 /1 1
r Y C C Y C C rdCCdr r C Cr rC
σ σ+ − − − − += = >
+ ++ + +<
The substitution effect reduces consumption and raises saving, while the
income or terms of trade effect Y1 - C1 is positive if saving is positive,
negative if it is negative.
Given isoelastic utility,
( )( )
( )
1/
1/ 1/1 2
21 11
( ), , so Euler condition is
1 , from budget constraint
111 1
u C u C c
C r C
YC Yrr
σ
σ σ
σ σ
β
β
−
− −
−
′ =
= +
= + + + +
31
Substitution effect > or < income effect as σ> or <1.
Metzler Diagram for Investment and Savings
( ) ( )( )( )
* * * *
2 1 1
* * * * *2 1 1
,
from
from
Y AF K Y A F K
I A F K I r
I A F K I
= =
′ + =
′ + = r r r I*
S*
S I
S,I S*,I*
req
Increase in β shifts S left, raises r; I and I* fall.
Increase current productivity of capital A1, shifts S right, I and I* rise.
Increase future productivity of capital A2, shifts I right, shifts S left.
Suppose initial CA=0, then new CA<0 so CA*>0. Effect on world
investment I+I* depends on relative shift of I and S. From A2F'=r,
vertical shift in I+I* is
2 2 21ˆ ˆ/ so O&R show S+S* shifts up by
1 /rdr r A dr rC dr A rArα
+= = = >
+ˆ
since α<1. Net effect on I+I* is negative. r I+I*
S+S*
World S,I
32
Multiperiod Model (O&R, Ch. 2)
T periods subject to
or
iterating,
so
First order conditions:
Terminal
condition
Infinite Horizon as T→∞
33
From
( ) 1 so 11
s t
s s s s s ts t
TB Y C G I r B TBr
−∞
=
= − − − + = − + ∑ s
Suppose steady growth in output ( )1 1s sg+ = +Y If B/Y is
constant
Y
( )1 1s sB g B+ = +
So 1s s s s sB B gB rB T+ − = = + B and therefore
is consistent with a stable debt/GDP ratio. Higher
surplus if r > g.
Permanent level of Xt such that or
If ( )1 1, sr+ = Cβ is constant. O&R show
that and so ( )t t t t tC rB Y G I= + − −
Bt acts as a buffer stock.
If ( )1 rβ + ≠1but utility is isoelastic, O&R show that
where ( )1 1 r σ σϑ β= − +
So if 11 r
β >+
Ct is increasing over time (decreasing if 11 r
β <+
).
34
Stochastic Model (2.3)
with same budget constraint, first order
condition is
Quadratic utility if
, ( )1 1, then r uβ ′+ = ( ) 01C a C= −
So
and then or
1t trC W
r=
+
Factors affecting the Current Account (O&R, 2.3.5)
Net Output gives t t tCA Z E Z= − t
Where
( )
( ) ( )2
111
1 21 11 1
111 111
1 1 111
11111 1 1
1 11 11 1
1 11 1 1 1
11
11 1
1
1since 11 1
s t
t t t s t ss t r
t sr r
rrt t t t t tr r
r
r rr r r
r r
r rE Z E Z E Zr r r L
r L L E Zr
LtZ E Z E L Z E Z
L
LL L
−∞
−= +
− −+ +
−− +−
+ + −+
−+ + +
− −+ +
= = + + + −
= + + + +− ∴ − = − − = −
− −− = =
− −
∑
( )1
111
111
1
1 so
11
1 1
r
r
tt t t t
r
L
LZZ E Z E
r L
−+
−+
+−
+
−
−
∆− = −
+ −
35
Current account depends on future
changes in output minus absorption Z.
Forecast output changes from
So
Premultiply by vector [ to get ]0 1
Then the predicted current account is
For example, for Belgium,
and the hypothesis [ ]ˆ ˆ 0 1Z CA∆ Φ Φ = is rejected.
36
To include additional factors such as changes in the real interest rate,
the terms of trade, or the real exchange rate, one must include
additional goods (importable and non-traded). See Bergin & Sheffrin
(2000) and Goodger.
For example, Goodger derives
( )1
(1 ) (1 )(1 )st t t s t s t s t s
s
CA E Z r a q a b pρ γ γ γ∞
+ + + +=
= − ∆ − − − ∆ − − − − ∆ ∑
Where q is the price of non-traded goods and p is the price of
importables. Unfortunately, these generalizations do not appear to add
a lot of explanatory power. More successfully, Ventura (2002) adds the
concepts of risk premia and adjustment costs for investment.
Open Economy RBC Models
Razin Investment behavior
1 2
2
1 2
2
1 2
1 1 1
t 1 1 1
1 1
, , (1
( ) if 1
or I ( 1) ( )
if 0, ( 1)
t
t
Igt t t t t t t K
t t t
t t
t t
Y A K A A Z I
I I b A
I b A
I I
α
λ λλ
λ λλ
ρ
λ ρ
λ
ρ λ
−
− −
− −
−
= = = +
= + ∆ =
∆ = − ∆ + ∆
= ∆ = − ∆
)
so positive correlation of ∆I with country-specific ∆A if and only if ρ>0
(productivity shocks are persistent, not transitory). Global productivity
shock will raise world interest rate, have less effect on investment.
37
Consumption behavior
212
1
1
110
Max ( ), ( )
subject to , F=foreign assets
if 1/ , ( ) ,
it t i
i
t t t t
iRt t t t t iR
i
E u C u C hC C
C F Y RF
R C W W E R Y RF
δ
δ
∞
+=
−
∞−
t+ −−=
= −
+ = +
= = = +
∑
∑
Conclusions: if ρ = 1, effect of ∆A on ∆C is larger than effect on ∆Y
because increase in permanent income W is larger than increase in
current income Y. But not in case ρ = 0. Current account affected
negatively by permanent productivity shock, positively by transitory
productivity shock (since output rises, but not C or I).
Empirical evidence: high levels of persistence in Y, C, I. Common factors
explain significant fraction (20%-40%) of cross-country variation in Y,
C, I. Volatility of current account and output low for industrial
countries, NIC’s. cor(TOT,TB) > 0 for most countries.
Two-Country RBC Model (Backus, Kehoe, Kydland, AER 1994)
2 countries, 2 goods, consumers maximize
each country produces its own good, Home a Foreign b, using k and n.
with
consumption is a composite commodity
38
Investment has a one-period (J=1) lag in
Shocks are AR(1). Homogeneity of G(a,b) implies that ,it itz g
where are prices, so output
is
1 2,t tq q
1 1t t ty a 2a= +
= absorption + net exports. 2 /t t 1tp q q= is the terms of trade.
Define as the net export ratio to GDP.
Calibration: 11.99, .34, 1, .36, .025, 1.5ρβ µ γ θ δ σ += = = − = = = =
Import shares = .15, autocorrelation of shocks = .91. Results:
Absorption varies more than output, because of investment, cov(nx,y)<0.
Since cov(y,p) > 0, this implies cov(nx,p) < 0.
39
Observe J-curve, regardless of σ. In this model Marshall-Lerner
condition always satisfied, but cov(nx,p) > or < 0 as σ > or < σ*.
40
Feldstein-Horioka Puzzle (EJ, 1980)
Feldstein and Horioka estimate (3.1) across 15 industrial countries
1960-74, find β = .88 (.07), not significantly different from unity. In first
difference form, β = 1.04. Instrumenting for simultaneity bias with
dependency ratios makes no difference. Feldstein & Bachetta estimate
60’s 70’s 80’s
.91 .86 .79
Implication: capital mobility low in 60’s, increasing over time. But
Dooley et al (IMFSP, 1987) estimate β lower for developing countries
than for industrial countries.
O&R (3.4) show that for OLG economy with population growth n and
technical progress g, (1 )( ), (1
I Sn g ng n g ngY r Y
α β αβ−
= + + ≅ + ++
)
Sachsida and Caetano argue that β = 1 implies only that γ = 0 in the
substitutability equation.
41
Kraay and Ventura (QJE, 2000) argue that F&H results come from
costs of adjustment and risk premia. Simple case is foreign loans x<1
with return ρ and domestic capital with return equal to flow of
production less “operating costs” related to investment. Flow of
production is
2
where is a Wiener process[ ] 0, [ ]dt dE d E d dtπ σ ω ω
ω ω
+
= =
Operating costs are 1 dkk dt
α λ= , effectively a negative externality.
Consumers maximize
( )
0
2
2
22
ln( ) subject to
[(( )(1 ) ) ] (1 )
* , * 1 max ,0
(1 ) demand = supply of capitalkInterior Solution 1 impliesa
and
tE c e dt
da x x a c dt x a d
c a x
x a k dk
x
k ka a
δ
π α ρ σ ωπ α ρδ
σ
π α ρσ
π α ρσ σσ
∞−
= − − + − + −
− − = = −
− = +− −
= − =
− − =
∫
( )
( ) ( )
2
2
2
2 2 21
π α ρσ
π α ρπ α ρ π α ρπ α ρ ρσ σ σ
− −=
− −− − − − − + − = +
42
( )2
2
2
1 2
22
1 or solution
ka
da dt da
dk kk dt adk k dtk a
da kdt da a
π α ρ π α ρρ δ ωσσ
λ α π ρ σ
λ π ρ σ
σ ρ δ σ ω
−
− − − − = + − ⋅ +
= = − −
= − −
= + − +
let 1 1 ( ) dx, then CA=x S+
dtda d x aS CA
a dt a dt⋅
= ⋅ = ⋅ is a rule that allocates
part of saving to foreign assets in proportion to the existing share x and
requires another component due to portfolio rebalancing.
42a
The standard intertemporal model says that K/L ratio depends only on
technology and world interest rate r, independently of wealth. Excess
wealth is invested in foreign assets. Windfall effects only affect saving in
foreign assets: CA = ∆F = ∆W = S. Test via regression
it it itCA S uα β= + + Should find β = 1, but Ventura & Kraay find β =
0.214 for 21 industrial countries 1966-97. This is equivalent to F&H.
43
44
But Kraay and Ventura’s rule applies if there is a risk premium on
investment and if diminishing returns on investment are low.
Now changes in wealth lead to changes in K to keep K/W constant
(points A & C). Test via it it it itCA X S uα β= + + Result β = .939.
45
46
Exchange Rate Dynamics
Monetary Approach – Frenkel, Bilson, Mussa, Barro
Assume flexible prices, full employment
* * * *ˆ* * UIP & PPP in short run
* * ( *) ( *)
m p y rm p y rr r Eee p p m m y y
φ λφ λ
π πφ λ π π
− = −− = −
− = = −= − = − − − + −
Forward solution (see Frenkel & Mussa, Handbook, Vol. 2, Ch. 14, sec.
4.2)
1 1
1 1 1
1 1
1
1
1
, * * * ** PPP
* UIP* * ( *) ( *)
( *) ( *) ( )( )
1 11 1 1
t t t t t t t t
t t t
t t t t t
t t t t t t t t t
t t t t t t t t
t t t t t
t t t t t
m p r y m p r yp e pr r E e ee p p m m y y r re m m y y E e ee f E e e
e f E e f
λ φ λ φ
φ λφ λ
λλ λ
λ λ λ
+ +
+ + +
+ +
+
+
+
− = − + − = − +
= +
= + −
= − = − − − + −= − − − + −
= + −
= + = ++ + + 1 1 2
0
1( )1 1 1
11 1
t t t t
s
t t t ss
E f E e
e E f
λλ λ λ
λλ λ
+ + +
∞
+=
+ =+ + +
= + + ∑
...
47
Sticky Price Model (Dornbusch – Frankel)
1
ˆ* Rational Expectations and UIPln( / ) [ ( ) ]
in long run, *, * , , *ˆin short run, ( ) because p-p= (r-r*)
[ ( ) ( ) ( *)][ ( ) (
m p y rr r Eep D Y e p y r y
r r p m r y m p e r rEe p p
p e e p p r rp e e
λ
φ λ
π π δ γ σλ φ
λπ δ δ σπ δ δ
− = −− == = − + − −
= = + − = = == −
= − − − − −
= − − )( )]p pσλ+ −
p
e Rational Expectations solution: 1
2
ˆ ( ) so ( ) ( )( ) [ ( ) ( )( )]
( )
or
Ee e e e e p pp p p e e p p
p p
λ
σλ
θ θθ π δ δ
δ σπ δλθ λδ σθ πσ πδθ π δ θ πδ θλθ λ
= − − = −
= − = − − + −
= + + − + = + = + λ
+
Overshooting
1 11 1de de dpdm dm dmλθ λθ
= + = + > from 1 ( )e e p pλθ− = −
Notice output is still assumed to be at full employment, but demand can
differ from supply (D<Y ).
48
Buiter-Miller model (EER, 1982) LM
( ) ( ) IS Phillips curve
Expected inflation [alternatives ( ) or ]* UIP
real balances real exchange rate
Solution
m p ky ry r Dp e pDp y
Dm p pDe r r
m pc e p
r
λγ δφ π
π π ξ π
− = −= − − + −= +
= = −= −
≡ −≡ −
π =
[ ]
[ ]
1
1
substitute in IS
1
( ) ( ) ( )1
( )1* (
( )
k
k
k
y
y y y Dm c
y Dm c
y Dm ck k k
D Dm Dp y Dm ck
Dc De Dp r r y Dm k c Dm rk
D
λ λ
λ λ
γ γλ λ
γ φ δ
γφ γ δ
γ γλ δλλ γ λφ λ γ λφ λ γ λφ
φ γφ γλφ δλφλ γ λφ
φ δ λφλ γ λφ
= −
= − − − − + + − = + +
= + ++ − + − + −
−= − = − = + +
+ −−
= − = − − − = − − + −+ −
) *λ
2 2
01 11 ( ) ( ) *
( ) 0( ) 0 if 0
DmDc k c k r
kkA
φγ δλφ γλφδ φλ λ λ γ λφ
γ λφ λφγδ φλ φδλ φδ φδ
= + − − + −∆ ∆
∆ = − − <− − − ∆
= = = < ∆ <∆ ∆ ∆
49
[ ]0 0 / / 0
0 ( ) ( ) * 0 / 1/ ( )
ˆ 0ˆ *
D c Dm dc d
Dc k c Dm k r dc d k
c Dmr
δλγ
γδ
0
λ γ δλ
δ λφ λ λ γ λφ δ λφ
λ λ
= ⇒ + + = ⇒ = − <
= ⇒ − − + + + − = ⇒ = − >
= − −
1 0.5 0 0.5 115
10
5
0
5
10
15
Dl=0Dc=0SSUU
0
c
R
Suppose a fall in money growth (dµ < 0). Then ˆd dλ µ= − > 0.
0.1 0.05 00.2
0.1
0
0.1
cdt
ldt
0 50 1000.2
0.1
0
0.1
cdt
ldt
t
50
Calculating the initial jump in the real exchange rate c:
11 121
21 22
11
2
, ,
Define canonical variables0
, so 0
choose (0) so that (0) 0 on saddle path
B BDA B B B AB B
B BDc c c
s Ds sB
u c Du uc u
c
−
−
′ ′ ′ = = Λ = = ′ ′ ′
′ Λ = = ′ Λ
′ =
′′
11 12
21 22
11 12 11
21 22 211
21 11
(0) (0) (0) (0)(0) (0) (0) (0)
so (0) (0)
B Bs sB
B Bu uB s B u B s
c B s B u B s
c B B −
= = ⇒
′ = + =′ = + =
′ ′=
Λ
Suppose Rational Expectations for prices as well as exchange rate:
1
1 1
or then 0 so from IS curve( )
* ( ) *
*with a positive root
so ( )
Dp yr Dp e p
De r r e p Dp r
Dc De Dp c r
r D Dm Dp Dm r Dp rD Dm e p Dm c
δγ
δγ
δγ
λ
δ δγ λ γ λ
π φ= →∞ =− = −
= − = − + −
≡ − = −
= − ≡ − = + − −
= + − + = + +
both roots positive. System totally unstable, but jumps to new
equilibrium. c DR = 0
De = 0
R
51
Portfolio Model (Black & Salemi, JIE 1988)
1
2 11
11 12 21
1 12 2
11
( * ) portfolio allocation( * ) current account
ˆ ( * )ˆ *
ˆ00 ˆ
0
1= ,
1
0
f r De rDf e p p
f r re p p
Df f fDe e e
A I
B
BAB
αη αη
αη
α
ηα
λ ηλ λ α η
α λ
αηλ α η
αη
α η
−
−−
−
−
−−
= + −= + −
= −= −
−= −
−− = = − =
−
−± = = −
−=
( )( ) ( )1
11 10 022
0
0
0
ˆˆSaddle path: ( )
ˆ 1ˆ
e e f f
e ef f
αη
α η
αη
−
−
− = − −
−= −
−Assume df0 < 0
1 06
4
2
0
2
4
6
Df=0SSUU
Phase Diagram
0 50 1001
0
1
2
3
et
f t
t
e
f
52
Black & Salemi derive ( )2 2
1 1* so f r r De αρσ ρ
= − + =σ where ρ is the
coefficient of risk aversion and σ2 is the conditional variance of the
exchange rate. An increase in the volatility of interest rates will raise σ2
and thus lower α, thereby causing the slope of the saddle path to be
steeper and further raising the volatility of the exchange rate.
Alternatively, increased central bank intervention to reduce σ2 will raise
α and flatten the slope of the saddle path, further dampening exchange
rate fluctuations. This is the “Harrod” effect.
Empirical Tests:
Frankel (AER, 1979) test of extended Dornbusch “sticky price” model
Meese and Rogoff (AER, 1983) show that the monetary models cannot
beat a random walk. Cointegration tests by MacDonald and Taylor
(JIMF, 1994) find a long run dollar-mark cointegrating relationship of
with an error-correction
adjustment mechanism that beats a random walk.
( *) ( *) 0.049 0.05 *t t t t t t ts m m y y i i= − − − + −
53
Black and Salemi (JIE, 1988) estimate the portfolio model in the form * *
1( ) and ( )t t t t t t t t t tf e p p f r E e e rη α +∆ = + − = + − − and find that the model
explains the dollar-mark exchange rate over the period 1965-83,
allowing for differences in monetary policy behavior. The estimated η =
.038 and α = ρσ2 varies over different monetary policy regimes, with ρ =
4.08.
MacDonald and Marsh (RESTAT, 1997) test a portfolio-type equation of
the form and find cointegrating
relationships of the exchange rate with both relative prices and interest
differentials for the dollar-mark, dollar-pound, and dollar-yen, again
beating a random walk over all but the shortest horizons.
1( *) ( * et t t t t ts p p i s iα µ +− + = +∆ − )
54
Chaotic Exchange Rate Dynamics (DeGrauwe, 2002)
Given 0
11 1
i
ti
s αα α
∞
t t iE f +=
= + + ∑
, 11
( )T
c t ti
E s β α+=
∆ = ∑
with ft = εt a random walk without drift,
the fundamental solution for the exchange rate is st * = εt. Assume that
market beliefs about the exchange rate depend on chartists with
expectations that extrapolate recent changes i t is∆ −
and fundamentalists with expectations that return to equilibrium
where C is the level of transactions costs beyond which fundamentalists
will act on their beliefs [so
2, 1 1 1 1 1 1 1( ) ( *) with 0 if * and 0 if *f t t t t t t t tE s s s s s C s s Cθ θ θ+ − − − − − −∆ = − < − > > − < −
, 1 1 1( ) 0 if *f t t t tE s s s C+ − −∆ = − < ]. Combining
these with weights of 0.5 on each type and setting T = 1 and C = 0 with st
* = 0, De Grauwe finds 21 2 11
2 2 2t t t ts s s sβ β θ− − −
= + − +
which gives a logistic function for the exchange rate.
Near the long-run equilibrium (zero), the extrapolative elements
dominate and the exchange rate moves upward. Eventually, the
55
fundamentalist factor becomes more important and the curve slopes
downward. Higher speeds of adjustment θ cause the fundamentalists to
take over sooner. If shocks are added to the fundamental equilibrium
and transactions costs are considered, both rates will vary over time,
but the market rate can deviate for long periods from fundamental
equilibrium.
56
Simple Chaotic Exchange Rate Model (De Grauwe, et al, 1993)
1 1 1 2 3 2
1 1 1
21
Chartists: ( ) / ( / ) ( / )
Fundamentalists ( ) / ( * / )
Weighting on Chartists 1/(1 ( *) )
ct t t t t t t
ft t t t
t t
E S S S S S S
E S S S S
m S S
γ γ
α
β
+ − − − − −
+ − −
−
=
=
= + −
st
mt
st 1−( )b 1 γ mt⋅+ α 1 mt−( )⋅− ⋅st 2−( ) 2− b⋅ γ⋅ mt⋅
st 3−( )b γ⋅ mt⋅
1
1 β st 1− 1−( )2⋅+
:=
0 200 4000.8
1
1.2
1.4
s t
t 0.8 1 1.2 1.4
0.8
1
1.2
1.4
s t
s t 1−
0 0.5 10.8
1
1.2
1.4
s t
mt
57
Model with Money and Prices
1
1
(1 )( ) / (1 ) /(1
/
ct t t t
t t t t ft
kt ft
t tt
M Y P r)E S S r r
S PP P
P
α −
+
−
= += + +
=
Expectations as above
st
mt
pt
st 1−( )b 1 γ mt⋅+ α 1 mt−( )⋅− ⋅st 2−( ) 2− b⋅ γ⋅ mt⋅
⋅ st 3−( )b γ⋅ mt⋅⋅
pt 1−( )
1
c1 k+( )
k⋅
1
1 β st 1− 1−( )2⋅+
st( )k
1 k+ pt 1−( )1
1 k+⋅
:=
0 100 2000.8
1
1.2
1.4
s t
p t
t
0.96 0.98 1 1.02 1.040.8
1
1.2
1.4
s t
p t
0.8 1 1.2 1.40.8
1
1.2
1.4
s t
s t 1−
58
Equilibrium Models of Exchange Rate Behavior
Money in the Utility Function (O&R, 8.3)
if ( , ) and ( / )s s s s sL L L M P C= su C due to time required to change assets if
M/P is low. Subject to
substitute into U
first order conditions
Substitute from (35) into (36)
1
1 1
1 1 1(1 )
where 1 (1 )(1 )
C Mt t t p
t t
u uP r P P
i r π+
+ +
− = +
+ = + + 1t+
1 11
1 1
/ 1or 1 11 1 1
Mp t t t
tC t
uP P i
iu r i i
+ +
t+
+ +
= − = − = ≈+ + +
59
111
11
( / ) 1 1If we assume ( , ) then 11
tt
t t
C M P MMu C CP P
σγ γ
σ
γγ
−−
+
− = = − i+
Cash in Advance Model (O&R, 8.3.6)
S. t.
Assuming equality if r > 0,
since 11
t tt
t t
M PC
P P+
+= Substitute from (59) into (57) and maximize over Bs
First order conditions
or
where 1
1 11 ) 1 ss s
Pi r
P+
+ +
+ = + + 1 (
s
Money demand is
60
Stochastic General Equilibrium Model with N countries (O&R, 8.7)
Maximize
1 1
N Nn Wt t
n nC Y Y
= =
= =∑ nt∑ endowments
The first order condition for the single good:
or
Suppose there is a riskless bond that pays 1 + rt+1 . Then
But ( ) ( ) ( ) ( )1 1 11
1 1 tt t t t t t
t
Pr E u C E i u C
P+ + ++
1+
′ ′+ = +
does not imply
since the
components of ( )11
tt
t
Pu C
P ++
′ are random and correlated with each other.
61
The first order condition for money is
So
Given Purchasing Power Parity, we have
Given identical utility functions, consumption is
shared proportionally, so
In the Cash in Advance case
/ or velocity = unity and with PPPn n m
n n n nm t t tt t t t m m n
t t t
P M YP M Y
P M Yε= = = ⋅
62
Two Countries, Two Goods Case (Lucas, 1982; O&R, App 8A)
Maximize
( )( )
* *
*
* *
* *
* * * *
*
* * * **
( , )subject to ,
Stochastic Per capita Endowments (2 ,0), (0, 2 ), ,Pooled Equilibrium , .If 0, ,
, / and /,
s tt t s s t t t t t t
s t
C C C
C CC
U E u C C M PC M P C
Y Y M MC Y C Y r M PY M P Y
u Y Y u uP P M Yu uP M Yu Y YP
β
εε
∞−
=
= ≥
= = > = =
= ⋅ = ⋅=
∑ * *
*
≥
*1 *1ln lnln 1 1 if
ln ln ln 1 1ln ln ln1 from so 0ln ln ln
C Cd u d ud CU
d Y d Y d Yd P M d d PPd Y Y d Y d Y
γ δ
γγ δ
ε
ε
− −
= − + − = − + = +− −
= − = > >
C
based on supply shocks only. Stockman & Dellas (JIE, 1989) add
demand shocks and show that ( ) ( )ln lnd Var d PVar ε > is possible. Lucas
Model timing: asset trades occur after current state of economy is
known. So M = PY. Svensson (JPE, 1985) assumes asset trades occur
before state is known, giving rise to a precautionary demand for money.
Grilli & Roubini (JIE, 1992) develop a model that assumes cash must
also be held in advance for asset transactions. Two countries, two goods,
two bonds, two moneys, three-member household. One receives
endowment, sells for cash to be used next period, second takes cash and
buys goods, third takes remaining cash and buys assets ( )1 2,t tB B Cash in
advance constraints for each country i = 1,2
63
( ) ( )
( )
1 1 1 2 2 2
1 1 2 2 1 1 2 2
1 1 1 1 2 12 2
2 2 2 2 1 21 1
,
let be cash held for asset transactions
then / and
it t it it t it
it it t it it t it t t it
j j jit it it
i i i it t t t
N P C N P C
M N s M N q B s q B
Z M N
P M Z y
U UP q M Z y qsU UP q M Z y q
≥ ≥
− + − ≥ +
≡ −
= −
−= ⋅ ⋅ = ⋅ ⋅ ⋅
−
Therefore fluctuations in asset prices q affect exchange rate even if M is
constant (and therefore prices don’t change).
64
Portfolio Approach to Exchange Rates
Asset market Model – due to Black (1973), Girton & Henderson (1974,
published 1977); see Branson & Henderson in Handbook Vol 2.
Partial equilibrium model of asset markets: 4 assets domestic money
and bonds M, B; foreign money and bonds N, F, held by domestic
(non-*) or foreign (*) residents.
( )( ) ( ) ( ) ( )
* * * *
i
* * * * *
* * *
Private wealth ( ), ( ) /allocated as functions of r , , where X is income
( ) ( ), ( ) ( )
Asset stocks , , ,adding up condition
W M B E N F W M B E N FX W
W m n b f EW m n b f
M M M N N N B B B F F F
= + + + = + + +
= ⋅ + ⋅ + ⋅ + ⋅ = ⋅ + ⋅ + ⋅ + ⋅
= + = + = + = +
( ) ( )( )
*
*
* * * *
* *
* *
s 0, 1
Simplify by assuming no currency substitution 0Money demands independent of wealth and foreign return i
, /
, , ,
, , , ,
k k k k W W W Wm n b f m n b f
M N
W M B EF W B E N F
m i PX M n i EP Y EN
b i i PX W b iε ε
+ + + ≡ + + + ≡
= =
= + + = + +
= =
+ + −( )( ) ( )
* *
* * * * *
,
, , , , ,
i EW B
f i i W f i i EP Y EW EFε ε
=
+ + − =
*
*
Short-run equilibrium, given asset stocks, incomes PX, P*Y, expected
change in exchange rate ε. Because of adding –up conditions, only three
of four equilibrium conditions is independent (Tobin’s Law)
F0 B0
N0
M0
i
i*
65
Above BB, excess demand for B, i falls; to right of FF, excess demand
for F, i* falls. FF steeper than BB: if not , excess supply in all markets.
Depreciation of exchange rate (rise in E) shifts BB and FF down. Open
market operation shifts MM and BB down, MM by more,
since . Depreciation then shifts BB and FF to new
equilibrium with lower i.
0dM dB+ =
ib*i im b− < +
Effects of intervention on the exchange rate. Slope of FF curve:
( )( )
* * * * * **
*
* * ** *
*
/0
1
i W i Y W
i i
W Y W
FdE f di f FdE f di f P YdE f N F dE
f f FdEdi F P Y N Ff f f
F F F
= + + + + +
+= <
+− − −
E M
B
F
i
BB steeper than FF because * *i i i ib b f f+ > +
Open Market Operation dM dB= − MM shifts left along the FF curve.
Unsterilized Intervention: dM dF= − MM shifts left along the BB
curve, largest effect on E.
Sterilized Intervention: dB EdF= − BB and FF shift up, no effect on i.
66
Stock-Flow Equilibrium * * * * *Let , / , ln( ), / , initial 1
At equilibrium 0, . Then
1 1 if
e i w
ie w
i
e w i
i
w M B EF w B E N F e E de dE E E P P
d b de b di b d b dw dB
bb dM dB b de b dw
m
b b bde dw dM dB dM
mb b b
ε
ε
ε ε ε
ε ε ε ε
ε
ε
ε ε
= + + = + + = = = = =
= = + + + =
= − + − −
= − − − + = −
= Asset Stock Equilibrium 0we w OMO
e
dede dw dMdw
εε ε
ε+ − = − <
Goods market Equilibrium with sticky (fixed) prices w deη=
e
S ε=0
0w =
w
Transfer of wealth shifts w up or down. OM
Equilibrium up or down, shifting the saddle
Flexible price case: assume local goods prefe
raises spending on local goods, deteriorates t
so 0dew de dwdw
βα βα
= − = > so the 0w = cu
O shifts Asset Stock
path SS.
rred, so wealth transfer dw
rade balance
rve slopes upward.
67
Net Foreign Assets Version of Model (Black & Salemi)
( ) ( )( ) ( )
* * * *
* *
* * * * *
* *1 2 1 2
* * * * * * * * * * * *1 2 1 2
, /,
Net Private Wealth , /
, , 0, 0, , , 0, 0
/ , , 0, 0, , , 0,
e e
e e
W M B SF W N F B SB B B F F F
V W M B SF B V W N F B S F
B b i i s W b b SF f i i s W f f
B S b i s i W b b F f i s i W f f
V SF B
= + + = + +
= + = +
= − − = − = − − = −
= + ∆ > < = + ∆ < >
= − ∆ > < = − ∆ < >
= − ( ) ( )0
( )( )
* * * * *
* 2 **
*
, ,
VAssume 1/ . Then W+SW
e e
es
f i i s W b i s i SW
f b v i s i
v s p p
α ρσ α
η
= + ∆ − − ∆
= − ≡ = ≡ = + ∆ −
∆ = + −
Empirical Tests of Portfolio Model (Frankel, JIMF, 1982) 5
1
1 1 1 1 1 1 1 1 1 1 1
1 1 1
1 1
Portfolio shares , , , , , 1
Real rates of return , , , , , ,
1
DM Fr C it t t t t t t t
i
DM Fr C j j jt t t t t t t t t t t t t
t t t
t t t t t
x x x x x x x x
r r r r r r r i s r i
z r r
W W x r W
π π
ι
=
+ + + + + + + + + + +
+ + +
+ +
= + =
= ≡ − − ∆ ≡ − ⋅
′− = +
∑£ ¥ $ $
£ ¥ $ $ $ $ $
$
( )
= −
( )
1
1 11 1 1 1
11 1
1
Maximize 2 2
First order condition , or
ex ante real risk premium , UIP if
it t t
t tt t t t t t t t t t t t t t t t
t t
t t t t t t
t t t
x r W
W W2
E V x E z x E z E z x x E z x xW W
x E z x E z
E z x
ρ ρ
ρ ρ
ρ
+
+ ++ + + +
−+ +
+
−
ρ′ ′ ′′− = − = −
Ω = = Ω
= Ω
∑ $
[ ]1 0 1 1 0 1
0or 0Test as t t t t t t tz x z E z x u
ρα ρ α ρ+ + + +
= Ω =
= + Ω + − = + Ω =
′Ω
Assumes rational expectations ( ) ( )1 1 1 1 1; 0,t t t t t t t t tz E z u E u E u u+ + + + + 0− = = = ,
no error term in portfolio optimization, and constant variance-
covariance matrix Ω. Results support UIP and reject portfolio model (ρ
= 0). If there is an error term vt in the portfolio choice condition, then xt
68
is correlated with vt, and OLS is not acceptable. Simultaneous equations
approach required. See Black & Salemi for joint estimation of xt and
zt+1, which also includes current account equation explaining ∆ xt.
Other generalizations include assuming that the CPI depends on
consumption shares, so there is a risk-minimizing portfolio:
( ) ( ) ( )
( )1
1 , , , , ,US DM Fr Ct t t t
t t t
s
E z x
π α π α ι π π π π π π π
ρ α+
′ ′ ′= − ∆ + − =
= Ω −
$ £ ¥ $
where α is a vector of international consumption shares allocated to
goods of country i. Or if the αj vary across countries and wt is a vector of
shares of world wealth, then ( ) ( )1 1, , ,t t t tE z x w 2 5ρ α α α α α+ = Ω − =
Other recent studies using the portfolio model:
Dominguez & Frankel (AER, 1993) “Does Foreign Exchange
Intervention Matter? The Portfolio Effect” uses weekly data,
time-varying variance-covariance matrix, central bank
intervention data, and survey-based (non-rational) expectations
Black (1995) “The Relationship of the Exchange Risk Premium
to Net Foreign Assets and Central Bank Intervention” follows
Dominguez & Frankel
MacDonald and Marsh (RESTAT, 1997) test a portfolio-type equation of
the form , find cointegration of the
exchange rate with both relative prices and interest differentials
for the dollar-mark, dollar-pound, dollar-yen, beating a random
walk over all but the shortest horizons.
1( *) ( * et t t t t ts p p i s iα µ +− + = +∆ − )
Evans & Lyons (2001), “Portfolio Balance, Price Impact, and Secret
Intervention,” NBER Paper #8356
Hau & Rey (2002), “Order Flows, Exchange Rates, and Asset Prices.”
69
Exchange Market Efficiency
Prices fully reflect available information. Excess returns above normal
should be mean zero, uncorrelated over time.
( ), 1 , 1 , 1 |j t j t j t tz r E r+ + +≡ − Φ is mean zero, uncorrelated over time.
Depends on (i) equilibrium hypothesis, (ii) information set. Weak form
test use only past price information. Strong form tests use all other
information.
Risk neutrality implies unbiased forward market: 1( )t t tf E s +=
Perfect capital mobility implies Covered Interest Parity:
(CIP) *t t ti i f s− = − t
t
Tt
CIP & risk neutrality imply Uncovered Interest Parity:
(UIP) ( )*1t t t ti i E s s+− = −
Law of One Price implies *Tt tsπ π= ∆ + for traded goods.
( ) ( )
( )
* * * * *
* * * * *
* * * * * * *
* * * * *
*
1 , 1
( ), ( )
( ) ( ) ( ) (
( ) ( )
( )
N T N Tt t t t t t
T N T T N Tt t t t t t t t
T T N T N T N T N Tt t t t t t t t t t t t t
N T N Tt t t t t t t t t
N Tt t t t
s
i i E
π απ α π π α π α π
π π α π π π π α π π
π π π π α π π α π π α π π α π π
π π α π π α π π
ρ ρ α π π
= + − = + −
− = − − = −
− = − + − − − = ∆ + − − −
− = − − − + −
= − − * * *( )N Tt tα π π+ −
* )
Tests of market efficiency (Levich):
1. CIP holds for offshore markets except in turbulent times, also for
some onshore markets (US vs. euro, etc.)
2. Random walk approximately true for spot exchange rates, some
evidence of mean reversion, auto-regressive conditional
heteroscedasticity (ARCH), fat tailed distributions.
3. Filter rules show profits for Buy if or sell if T Pt t t ts s k s s k− > − >
70
4. Forward bias tests:
a. Level tests 1t t 1ts f uα β+ += + + find β = 1, but s and f are
integrated of order 1 [I(1)], so non-stationary.
b. Difference tests ( )1 1t t t ts f s uα β+ ++ − +∆ = find 0 > β > -2
c. ( ) (Var s Var f s∆ > − )
Covered Interest Parity defines the forward rate (O&R, 8.7.5.3)
The first order condition for the return on any asset m is
so for any two assets n and m,
(116)
Equivalence of real interest rate differentials and forward premia:
( ) ( ) ( )* *11 1 1
*1 11
11 1t tt t t t t t
t tt
i Pi P i PP PP t
ε++ + +
+ ++
++ + ℑ −− = ⋅ ℑ
substitute in (116)
and factor out the first term (which is date t information), results in
( )( )
1 1
1
0t t tt
t t
u CE
u C Pε+ +
+
′ ℑ −⋅ = ′
This does not imply 1t t tE ε +ℑ = unless there is (a) no uncertainty or
(b) risk neutrality.
71
Jensen’s Inequality: both and 1
1 1t
t t
Eε +
= ℑ
are not
possible at the same time, since
Gap depends on Var 1( )tε +
Hansen & Hodrick (1980) tested for forward bias in
for seven
currencies using weekly data for 3-month forward premia. Rejected
null hypothesis for deutschemark-dollar. When cross-currency forecast
errors included, null rejected for three of five currencies.
Results, replicated many times, show that UIP does not hold.
72
Suppose CRRA preferences and lognormal disturbances. Then
1
1 1
11 1 1 1 12
0
( ) var( ) cov( , ) cov( ,
t t tt
t t
t t t t t t t t
CE
C P
1 )f E e e e p e c
ρ
ρ
ε +
+ +
+ + + + +
ℑ − = ⇒ − = − − +
which is not equal to zero even if ρ = 0 due to Jensen’s inequality for the
real risk premium.
73
Domowitz & Hakkio (JIE, 1985) consider Lucas model with Cobb-
Douglas utility to try to explain the risk premium
( ) ( ) ( )
( )
1-t t
0, with , =Ax y with random endowments = ,
divided between Home and Foreign Home: ( ,0) Foreign: 0, subject to , , random ( , )
Equilibrium under complete mt t
tt
t
t t
x t t y t t t t
E U x y U x y
p M p N M N
α αβ ψ
ξ η
ξ η
∞
=
≤ ≤
∑ ξ η
( ) ( )( )
( )2 2
1 1
arkets ( , ) ( , )
1 1 1Marginal rate of substitution
/1 1Spot exchange rate /
Intertemporal marginal rate of subs
t
t
y ty t
x t
x t t t tt y t
y t t t t
x y
U Ax y xpU yaAx y
p M MS p
p N N
ξ η
α α
α α
ψ α ξα αψψ α
ξ ξα αα η η α
−
− −
=
− − −= = = ⋅ = ⋅
− −= ⋅ = ⋅ ⋅ = ⋅
( )( )
α η
1
1
1 1
1 1 11 1
1 1 1 2 1 2
1 1 3 2 1 4
//
titution /
/
let ln , ln , ln , ln , , .,
assume di
t
t
t t
x t x t tmt
x t x t t
t t
t t t t t t t t t t t t t t
t t t t t t
it
MU p
QU p M
x y m M n N x x u y y um m u n n u
u
α
α
ηβ
β ψ ξ ξψ η
ξ ξξ η ρ ρ
γ γ
+
−
+ +
+ + ++ −
− −
− −
≡ =
= = = = = + = +
= + = +
( )
( )
2
1 2 3 4
21 2 1 1 11 2 1
2 1 3 12
1 1 2
stributed as lognormal with variances , , ,
ln (1 ) (1 )(1 ) (1 )ln exp
(1 ) / 2
1From , ( ) ln 1 /
From
t t t t
t t t tmt
t t
tt t t t t
t
h h h h
x y m hEt Q
h h
MS E s m n
N
αβ α ρ α ρ γ
α
α α α γ γα
+
++ +
+
− − − − − + − + + = − + −
= ⋅ = − + −
( ) ( )
( )
1 121 2 3 1 4 1
1
121 3 1 4 1
, ln 1 /
so ( )
Nt t
t t t t t t tMt t
t t t t t
E QS f m n h h
E QE s f h h
α α γ γ++ +
+
+ + +
ℑ = ⋅ = − + − − −
− = −
Note 1
3
( )0t ts f
h+∂ −
>∂
, which has the wrong sign!
74
Since Cobb-Douglas has elasticity of substitution σ = 1, there is no risk
aversion. The “risk premium” arises from Jensen’s inequality because
the lognormal is skewed. 21
2ln , if 0, ln 0E z e Ez E zµ σ µ+= = = >
Domowitz and Hakkio empirically test ARCH-in-mean:
( )1 1
20 1 1 1
42 2 2 2
1 0 11
/ ( ) /
, (0, )t t t t t t t t
t t t t
t j t jj
S S S P S S
P h N h
h
1β ε
β θ ε
α α ε
+ +
+ + +
+ + −=
− = + ℑ − +
= +
= +∑
∼
If D&H assume β1 = 1, cannot reject θ = 0. Reject joint hypothesis β1 = 1,
θ = 0.
Dutton (JMCB, 1993) shows that in this type of model 11
2
1
t tt
t t
M XS
N X
σ−
= ⋅
So if σ = 1, the exchange rate is independent of the
real risk in the model. Zengin (2000) simulates such a model and
generates realistic risk premia if there are random deviations from
purchasing power parity and 1σ ≠ .
Explanations for failure of UIP (bias in forward market) (Lewis,
Handbook, Vol. 3, ch. 37) *
*1 1 1
1 1 1
1 1 1 1 1
CIP
excess return predicted excess return ( ) ( )ex post excess return , where is the forecast
t t t t
t t t t t t t
t t t t t t t t t t
t t t t t t t
i i f s
er i s s i s fper E er E s f s E s f
er per s E sε ε
+ + +
+ + +
+ + + + +
− = −
= + − − = −= = ∆ − − = −
= + = −
1 1
1 1 1
1 1 1
1 1
error
risk premium , where the "market" expectation is
"market" forecast error
rational expectations
m mt t t t t t
mt t t t
t t t t tmt t t t
rp E s f E s
s E ser s f rp
E s E s
ηη
+ +
+ + +
+ + +
+ +
= −
= −= − = +
=
75
Fama decomposition
1 0 1 1
1 0 1 1 1
1 1 1 1 0 0 1 1
1 1 11
( )ˆ( ) , 2!
so 1, 0, 0( , ) ( , ) ( ,ˆ
( ) ( ) ( )
t t t t t
t t t t
t t t t t t t
t t t t t t t t t t t t
t t t t t t
f s f s v
s f s uf s s f s u v
Cov s f s Cov E s f s Cov E s f sVar f s Var f s Var f s
V
1 )
α α
β β βα β α β
εβ
+ +
+ +
+ + + +
+ + + +
− = + − +
∆ = + − + ≈ −− + ∆ ≡ − + ≡ + ≡ + ≡
∆ − ∆ + − ∆ −= = =
− − −
1 1
1 1
121
( ) ( ) ( ) 2 ( , )( ) ( ) 2 ( ) ( )
if
t t t t t t t t t
t t t t t t t t
ar per Var E s Var f s Cov E s f sVar E s Var f s Var f s Var E sβ
β
+ +
+ +
= ∆ + − − ⋅ ∆ −= ∆ + − − ⋅ − > ∆
<1
1t
so variance of the risk premium, or the predicted excess return, is high.
Explanations:
1. Time-varying risk premium. Assume rational expectations. Then
1t ter rp ε+ = + +
1
and variance of the risk premium is the explanation.
Portfolio model or general equilibrium model, for example.
2. Expectational errors. If the risk premium is constant, but
expectations are not rational, 1 0t ter rp η+ += +
Frankel & Froot (QJE, 1989) 1 0 1 ( )t t ts f s 1tuβ β+ +∆ = + − +
76
F&F use survey data to identify expectational errors.
1 0 1 1
1 1 1 1 1
1 1 1 11
1
( )
, ( )
( , ) ( , ) ( , )ˆ( ) ( )
( , ) ( ,( )
t t t tm m m
t t t t t t t t t t t tm mt t t t t t t t t t t t
t t t t
t t t t t t
t t
s f s u
s E s rp E s f E s f s
Cov E s f s Cov E s f s Cov f sVar f s Var f s
Cov rp f s f s Cov fVar f s
β β
η
η ηβ
η
+ +
+ + + + +
+ + + +
+
∆ = + − +
∆ = ∆ + = − = ∆ − −
∆ + − ∆ − + −= =
− −+ − −
= +−
1
1 1
) ( , ) ( ,1
( ) ( ) ( )1
( , ) ( , ) ( ) ( , )where
( ) ( ) ( )(
and
t t t t t t t t
t t t t t t
rp re
m mt t t t t t t t t t t
rpt t t t t t
re
s Cov rp f s Cov fVar f s Var f s Var f s
b b
Cov rp f s Cov rp E s rp Var rp Cov rp E sb
Var f s Var f s Var f sCov
b
η
η
+
+ +
− −= + +
− −= − −
− − − ∆ − − ∆= = =
− − −
= −
)s−−
1 , )( )t t t
t t
f sVar f s
+ −−
Expectational errors appear to be dominant. Frankel & Froot (AER,
1987) examine the properties of expectational errors, as defined by
survey expectations, and find them to include adaptive and regressive
components.
Alternative explanations:
1. “chartists” and “fundamentalists” (DeGrauwe)
2. “optimists” vs. “pessimists” (Ito, AER, 1989)
3. Learning effects and “peso” problem (Lewis, AER, 1989)
77
4. “end-of-month” effect (Breuer, EJ, 1996)
5. Endogenous interest rates (McCallum, JME, 1994)
Learning about Regime Change at time τ (Lewis, AER, 1989)
1 1 1
1 1 2 1
1 1
( ) (1 ) ( | ) ( | ), probability of old regime as of time t > ( , , , | )
Bayes' Rule (1 ) ( | ) ( | )
if change actually ocurred at time , then
t t t t t t t t t
t t t tt
t t
E s E s N E s OL s s s s O
L N L Op
τ
λ λ λλ
λλ λ
τ
+ + +
− − − +
− −
= − + ≡∆ ∆ ∆ ∆
=− ⋅ + ⋅
[ ]
τ
1 1 1 1 1 1 1
1 1 1
1 1 11
lim 0. During the learning period, the forecast error is
( | ) ( | ) ( | )
let ( | ) ( | ),1 1Mean ( ) 0
Supp
t
N Nt t t t t t t t t t t t
t t t t tT
t t t t t tt
s E s s E s N E s O E s N
s E s O E s N
er s E s sT T
λ
η λ
λ
+ + + + + + +
+ + +
+ + +=
→
− ≡ = − − − ∇ ≡ −
= − = − ∇ ≠∑ ∑1
1 1 1
1
ose 0, then and( , ) ( , )
( ) ( )If forecasts in each regime are uncorrelated and variances are the same in each regime
(1 2 ) 0 if
t t t t t
t t t t t tre
t t t t
re t t t
rp f s E sCov f s Cov E s
bVar f s Var E s
b
η η
λ λ λ
+
+ + +
+
= − = ∆
− ∆= − = −
− ∆
= − − > > 11 and therefore 1 12 rebβ = − <
“Peso” Problem: anticipation of future change in policy
[ ]1 1 1
1 1 1 1 1 1 1
1 1 1 t+1 1 1
( ) (1 ) ( | ) ( | ), probability of shift to alternative A
( | ) ( | ) ( | )
let ( | ) ( | ) then as
t t t t t t t t t
C Ct t t t t t t t t t t t
Ct t t t t t t t
E s E s C E s A
s E s s E s C E s C E s A
s E s C E s A s
η
η η
+ + +
+ + + + + + +
+ + + + +
= − + ≡
− ≡ = − − − ∇ ≡ − = + ∇ before
Engel & Hamilton (AER, 1990) estimate a segmented trend model, show
the significance of allowing for multiple regimes, using only weak form
information to identify regime changes. Regimes are different, but
probability of regime change is small, so small effect on bias. Kaminsky
(AER, 1993) adds information about central bank intervention and
credibility of Fed chairmen, finds significant effects.
78
Endogenous interest rates (McCallum, JME, 1994)
[ ]*1 1
* *1 1
*1 1
1 1 2 3
1 1
UIP: ,
Exchange rate (or interest rate) rule ( )
(*) , where
let
then (**)
et t t t t t t t t t
t t t t t t
t t t t t t t t t
t t t t
t t
s R R u f s u u u v
R R s R R e
E s s R e u R R R
s R e u
E s R
λ γ
λ γ
φ φ φ
φ
+ −
− −
+ −
−
+
∆ = − + = − + = +
− = ∆ + − +
∆ = ∆ + + + ≡ −
∆ = + +
∆ = ( )( )
( )
3 1 1 3
1 1 1 2 3 1 3
1 1 2 3 1
21 1 1 1
1 2 1 2
1 3 3 3
Equating (*) and (**),
Equating coefficients, :: 1: 1
From
t t t t t t
t t t t t t
t t t t t t
t
t
t
u s R e u
R e u R e u
R e u R e u
Reu
φ φ λ γ φ
φ λ φ φ φ γ φ
λ φ φ φ γ
φ λ φ γ λφ γφ λφ φ λφφ λφ φ λφ
−
− −
− −
−
+ = ∆ + + +
+ + + + + =
+ + + + +
+ = +
+ = ++ = +
22
1 1 1 1
2 1 1
3 1
1
1( ) ( ) 4 : ( ) 0,
2
1: (1 ) / ( 1)
1: 1/(1 ) (1 )1( / ) (1/ ) and 0
1
t
t
t
t t t t
R
e
u
s R e u
λ γ γ λ γλλφ γ λ φ γ φ γλ
λφ φ λ φ λφ λ φ λ γ λ
γγ λ λ βγ λ λ
−
−
− ± − + + − − = = = −
= − − = −
= − − = − −
∴∆ = − − + = − <− −
Meredith & Chinn (NBER WP# 6797, 1998) Long Horizon Bias [=0]
Combine UIP with Taylor Rule, Phillips curve, and IS curve. *
1
1 1, ,
t 1
UIP shocks to risk premiumTaylor Rule .5( )
Phillips curve .6 .94 .25 .1 ( )
IS curve y .1( ) .5( ) .5
where long
et t t t t t t
t t t te
t t t t t t te e
t t t t t t
s R R R Ri y
y s p v
s p i y
η ηπ π
π π π
π ε
+
− +
−
∆ = − ≡ − ≡− = +
= + + + ∆ − +
= − − − + +5 5
, ,, 1 , 1
1 1
1 1 rates are ,5 5e e e e
t t s t t t s ts s
i i π π+ − + −= =
= =∑ ∑
Shocks v and ε push i up and s down, given se. η shocks push i , s same.
79
Assume and simulate. 2 2 29.7%, 1.3%, 1.1%vησ σ σ= = =ε
Estimated UIP coefficients Horizon
1 year 5 years 10 years
Simulated data -.5 .82 .78
Actual data -.82 1.01 .71
80
Sticky Price Intertemporal Model (O&R, Ch. 10)
Goods z are distributed continuously on the interval [0,1], home goods
[0,n], foreign goods [n,1]. Produced by individuals in monopolistic
competition. Aggregate consumption is an Armington CES function
with elasticity of substitution θ > 1. Consumers maximize
where
subject to the constraint including money M and real bond holdings B
World consumption is
The first order conditions are [similarly for the foreign consumer]
with transversality condition
81
Long-run Equilibrium:
If initial 0 0B = , then and
As 0, 1yθ →∞ → / k . Since preferences are assumed identical,
Deviations from long-run equilibrium (allowing goods prices to vary):
From
we find
(27)
(28) where * * *
0 0 0/ , / , ( ) ( ) / ( ), ( ) ( ) / ( )t t t t t t t t 0p dP P e d p h dp h p h p h dp h p hε ε≡ ≡ = =
(29) Demands for output are
(30), (31)
82
(32)
Supplies of output are
(33), (34)
Linearized Euler equations are
(35), (36)
Demands for money are
(37), (38)
Subtracting m* from m and
using PPP,
(39)
Steady-state consumption-income identities are (40), (41)
where 0/ , / Wc dC C b dB C= ≡ 0 , etc. are changes in steady-state values
7 equations (30-34, 40-41) in 7 unknowns c, c*, y, y*, p-p(h), p*-p(f), cW.
Subtracting (31) from (30) and using PPP,
(42)
Subtracting (34) from (33),
(43)
83
Subtracting (41) from (40), as deviations in the equilibrium, using PPP,
(44)
Using barred versions of (42) and (43) in (44), and eliminating y-y*,
(45)
Wealth transfer b leads to interest income gain δb which raises
consumption but also lowers work effort. 1 1*2 1
y y bn
δ − = − − so
terms of trade improve
Adding up the supply equations (33) and (34) weighted by n & 1-n,
Using this with Wtc W
ty= from (32)
gives (47) so bδ has no effect on global cW or yW.
Given sums xW and differences x-x*, compute levels via * *(1 )( ) and ( )W *Wx x n x x x x n x= + − − = − − x . From (47) and (45),
(48), (49)
and so on. Real variables are independent of nominal variables, because
of price flexibility. Prices depend on money supply relative to demand.
(50), (51) Using PPP gives (52)
84
Short-Run Equilibrium
Producer prices p(h) and p(f) are sticky in the short run, as monopolistic
competitors price above marginal cost and adjust output instead of
price. Consider an unanticipated permanent money shock
where 1 0( ) /M M≡ − 0m M Note full
adjustment to equilibrium takes place in period two, when prices are
free to adjust to long-run equilibrium. Producer prices are fixed for one
period, flexible in next (long-run) period, output is variable. So agents
not on supply curves (33), (34). Income not equal to expenditure.
Current account surplus is
(54) Linearized, this is for
home and foreign:
(55) (56)
The new foreign asset holdings are permanent, since (long-run) outputs
and consumptions are permanent.
Solving for short run changes (un-barred)
From the consumption Euler conditions, (57)
From (39), since et+1 is the same as e
(58)
The solution (52) for e and (57) imply that
85
Substituting this in (58) and using the permanence of the money shock
(53)
We get (60), which is similar to the
Lucas model result. Also e e= , so there is no over-shooting in this
model. This gives a downward-sloping MM schedule between e and c-c*
with intercept m-m*. The second relationship comes from the balance of
payments equations (55)-(56):
From (42) , we substitute out (63). And from (45) we can
substitute out *1 2 ( )1
nb cθδ θ− = +
c− using (57). The result gives an
upward-sloping GG schedule (64)
e
M G
c-c*
M
G
m-m*
Depreciation of the exchange rate raises home output relative to foreign,
allowing a rise in c-c*.
86
Combining equations (60) and (64) gives the solution
so the exchange rate
is not neutral even in long-run equilibrium, since e e= . The
depreciation generates a surplus, which raises wealth and leads to a fall
in home goods supply and an improvement in the terms of trade.
Other solutions are and
. O&R show that
and and
so that global monetary expansion lowers world interest rates and
expands world consumption and output, temporarily. Using this with
(63) gives
By (65), a foreign monetary expansion
appreciates the exchange rate and shifts world output towards foreign
goods. So home output falls (since θ >1), as in the Fleming-Mundell
model:
87
Welfare Effects of Monetary Shocks
General monetary expansion raises world output and consumption and
therefore welfare, since in monopolistic competition, price is above
marginal cost and output is below the optimum.
Country-specific monetary expansions also raise world consumption,
but have different effects on consumption and output due to exchange
rate. For example, a foreign monetary expansion matched with a
domestic contraction causes the exchange rate to fall (appreciate),
domestic consumption, output, and foreign assets to fall. The fall in
interest earnings will cause future output to rise even as future
consumption falls. These effects can be aggregated in the (real part of
the) welfare function
and, surprisingly, they offset, leaving
so that monetary changes that do not affect world
money supply do not affect individual country welfare.
88
89
Exchange Rate Dynamics and the Welfare Effects of Monetary Policy in
a Two-Country Model with Home-Product Bias,Frank Warnock
Journal of International Money and Finance (2003).
“Under OR’s assumption of identical tastes, consumption baskets are identical across countriesand thus, not surprisingly, both relative and absolute consumption-based purchasing power parity(PPP) hold at all times. The assumption of identical preferences also precludes exchange rateovershooting: interest rates, both real and nominal, are identical across countries, and byuncovered interest parity (UIP) conditions, the nominal exchange rate jumps immediately to itslong-run level.
“Allowing for a home-product bias makes the model consistent with two aspects of observedexchange rate behavior that macroeconomic models are notoriously poor at replicating: theextreme volatility of nominal exchange rates and the remarkable persistence of deviations fromPPP. As home bias increases, Dornbusch (1976) type nominal exchange rate overshootingbecomes more pronounced, as long as the elasticity of substitution between consumption and realbalances is not unitary. Moreover, when there is home bias, nominal exchange rates are morevolatile than fundamentals such as price levels and money supplies. Wealth transfers thataccompany net foreign asset positions are spent disproportionately on domestically producedgoods and, therefore, induce movements in the real exchange rate.
“When preferences are identical (and initial net foreign assets are zero), the standard ‘beggar-thy-neighbor’ effect of a monetary expansion is no longer present. By decomposing into twocomponents, the shifting effect of increased world demand and the switching effect of anunexpected exchange rate depreciation, it is clear that this result is due to the assumption ofidentical preferences. The shifting effect is identical across countries and is not affected by thedegree of home bias, but the switching effect, only apparent when there is home bias, increasesHome utility at the expense of Foreign utility. With strong enough preferences for domesticgoods, the switching effect is greater than the shifting effect and Foreign utility falls. That is,with enough home bias monetary policy is beggar-thy-neighbor.”
Table 1: A Typical Home Producer/Consumer’s Problem
(T1.1)
(T1.2)
(T1.3)
(T1.4)
90
home bias " 0 (0,2)
where cH(z), z0 [0,n], and cF(z), z0 (n,1], are a Home individual’s consumption of a product z
Table 2: First-Order Conditions
(T2.1)
(T2.2)
(T2.3)
Table 3: Steady State Solutions equal sizes (n = 1 - n = ½) and identical bias parameters (" = "*)
(T3.1)
(T3.2)
(T3.2*)
Initial Steady State Assumptions
91
Initial Steady State Levels
(T3.3)
(T3.4)
Table 4: Long-Run Equations real exchange rate, Q, and terms of trade, t
(T4.1)
(T4.2)
(T4.3)
(T4.4)
(T4.5)
(T4.6)
Table 5: Short-Run Equations
(T5.1)
(T5.2)
(T5.3)
(T5.4)
Table 6: Long-Run Semi-Reduced Forms
(T6.1)
(T6.2)
92
(T6.3)
Table 7: M M and GG Curves
Money Shocks
(T7.1)
(T7.2)
Government Spending Shocks
(T7.3)
(T7.4)
Productivity Shocks
(T7.5)
Exchange Rate Overshooting (if , 1 and " 1) 1
93
Figures
Small Open Economy Model (Gali & Monacelli, NBER 8905) (see also Clarida, Gali, & Gertler, AER, May 2001)
Consumers maximize utility of consumption, including home and foreign goods, less effort (α is an index of openness):
( ) ( )
( )1 1 111
00
, ,
(1)
1 (
tt t
t
t H t F t
E U C V N
C C Cη
η η ηη η ηη
β
α α− − −
∞
=
−⎡ ⎤⎣ ⎦
⎡ ⎤= − +⎢ ⎥⎣ ⎦
∑
2)
where home and foreign goods are aggregated from
( ) ( )1 1
1 11 1
, , , ,0 0
;H t H t F t F tC C i di C C i diε εε ε
ε εε ε
− −− −⎛ ⎞ ⎛
= =⎜ ⎟ ⎜⎝ ⎠ ⎝∫ ∫
⎞⎟⎠
+
η is elasticity of substitution between home and foreign goods, ε is elasticity of substitution within types of goods. Budget constraints are
(3) 1
, , , , , 1 10
( ) ( ) ( ) ( )H t H t F t F t t t t t t t t tP i C i P i C i di E Q D D W N T+ +⎡ ⎤+ + ≤ +⎣ ⎦∫where Qt,t+1 is the stochastic discount factor for nominal dividends Dt+1. Complete contingent claims exist, but no durable goods. Optimal allocation of goods within types imply:
,, , ,
, ,
( ) ( )( ) ; ( )H t F t,
,H t H t F tH t F t
P i P iC i C C i C
P P
ε ε− −⎛ ⎞ ⎛ ⎞
= =⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
F t (4)
for all i, where ( ) ( )1 1
1 11 11 1, , , ,0 0
( ) ; ( )H t H t F t F tP P i di P P i diε εε ε− −− −≡ ≡∫ ∫ .
Optimal allocation between domestic and foreign yields
, ,, ,(1 ) ;H t F t
H t t F tt t
P PC C C
P P
η η
α α− −
⎛ ⎞ ⎛ ⎞= − =⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠tC (5)
where ( )1
11 1, ,1t H t FP P P t
ηη ηα α −− −⎡≡ − +⎣ ⎤⎦ is the CPI. Then the budget constraint becomes
, 1 1t t t t t t t t t tPC E Q D D W N T+ ++ ≤ + + (6) Assuming 1
1( ) ; ( )tCt tU C V N
1
1tNσ φ
σ φ
−
−≡+
+≡ the consumer optimality conditions are:
i
1, 1
1
tt t
t
t tt t
t t
WC NP
C P QC P
σ φ
σ
β−
++
+
=
⎛ ⎞ ⎛ ⎞=⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
(7,8)
Expectation of (8) gives Euler equation
1
1
1t tt t
t t
C PR EC P
σ
β−
+
+
⎧ ⎫⎛ ⎞ ⎛ ⎞⎪ ⎪ =⎨⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎪ ⎪⎩ ⎭
⎬ (9)
where 1, 1t t t tR E Q−+= is the price of a riskless one-period bond, Rt is its
gross return in domestic currency. Money does not appear in the model. In log-linearized form (7) and (9) can be written as
11 1( )
t t t t
t t t t t
w p c nc E c r Eσ
σ φπ ρ+ +
− = +
= − − −
where logρ β≡ − is the time discount rate and logt t tp Pπ ≡ Δ ≡ Δ is CPI inflation. Log linearization of the CPI formula around a steady state with , ,H t FP P= t
ts gives
, , ,(1 )t H t F t H tp p p pα α α≡ − + = + (10) where is the terms of trade. (10) holds exactly if η = 1. The rate of inflation of domestic goods is
,t F t Hs p p≡ − ,t
, , 1 ,H t H t H t tp p tsπ π α+≡ − = − Δ Assume that the small open economy doesn’t affect world inflation, so
* *,t F tπ π= . Also assume law of one price, so , * *
, , ,( ) ( ), ; or F t t F t F t t F tP i P i i P Pε ε= ∀ = ,
,where εt is the nominal exchange rate. Hence *,F t t F tp e p= + so the terms of
trade will be *
,t t t H ts e p p≡ + −
Define the real exchange rate as *
t tt
t
PQP
ε≡ so that its log is
, (1 )t t H t tq s p p stα= + − = − With complete markets, the return on a riskless foreign bond in domestic currency is * 1
, 1 1t t t t t tR E Qε ε−+ += , which combines with
1, 1t t t tR E Q−+= to yield uncovered interest parity (!)
*, 1 1( / )t t t t t t tE Q R R ε ε+ +⎡ ⎤ 0− =⎣ ⎦
ii
Linearizing(!), *
1t t t tr r E e +− = Δ (17)
Using the terms of trade in (17) yields * *
1 1( ) ( )t t t t t t t t t 1s r E r E E sπ π+ += − − − + + (18) which can be solved forward in the usual way. Firms produce differentiated products with linear technology
( ) ( )t t tY i A N i= Log marginal cost is common across firms
1; where nt t t t a tmc w a a a tν ρ ε−= − + − = +
Linearizing aggregated output,
t ty n a= + t (20) Prices are set by a staggered Calvo (1983) process, as 1 θ− randomly selected firms reset prices each period, resulting in
,0
(1 ) ( )k nH t t
k
p Eμ βθ βθ∞
+=
= + − ∑ t kmc
*t
(21)
World output is determined by market clearing *ty c= and the
consumer Euler equation:
* * * *1
1 ( )t t t t t ty E y r E 1π ρσ+= − − −+ (22)
Because of risk-sharing under complete markets, domestic consumption will be cointegrated with world consumption via
1*t tC C Qt
σϑ= (15) or
* 1t tc c sα
σ−⎛ ⎞= + ⎜ ⎟
⎝ ⎠t (16)
Market clearing in the small economy gives
1
*, ,
, , , * **
,
, , ,* **
,
( ) ( ) ( )
( )(1 )
( )(1 )
t H t H t
H t H t H tt t
H t t t t
H t H t H tt t
H t t t t
Y i C i C i
P i P PC Y
P P P
P i P PY Q
P P Pσ
ε η η
ε η η
α αε
ϑ α αε
− − −
− − −
= +
⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎢ ⎥= − +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎣ ⎦
⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎢ ⎥= − +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎣ ⎦
(23)
iii
Aggregating via 1 11 1
0( )t tY Y i di
εε
ε−−⎡≡ ⎢⎣∫
⎤⎥⎦
leads to 1* *(1 )t t t tY Y S Qσ ηηϑ α α−⎡ ⎤= − +⎣ ⎦ (24)
approximated as *t t
wty y α s
σ= + (25)
where 1 (2 )( 1)wα 0α α ση≡ + − − > depends on openness α. Using (16) to eliminate st leads to
* 1(1 ) with t t t wc y yα
αα α α
−= Φ + −Φ Φ ≡ (27) Substituting (27), (25), (11) into the consumer’s Euler equation gives
*1 , 1( ) ( 1)t t t t t H t t t
wy E y r E w E yααπ ρ 1σ+ += − − − + − Δ + (29)
The level of domestic output is negatively related to current and expected future real interest rates and to anticipated world output growth with a coefficient 1wα − whose sign is positive if 1ση > .
Trade Balance: Let ,
1 tt t
H t
Pnx Y C
Y P⎛⎛ ⎞≡ −⎜⎜ ⎟⎜⎝ ⎠⎝ ⎠
t
⎞⎟⎟ be net exports as a percent
of steady state output. If 1σ η= = , from (15) and (24), ,H t t t tP Y PC= so trade is always balanced in this special case. More generally,
t t tnx y c stα− − which with (25) and (27) implies * *(1 )( ) ( )t t t t tnx y y s y y
wαα
tαα Λ
= −Φ − − = − ,
where (2 )( 1) (1 )α ση σΛ ≡ − − + − , which is zero if 1σ η= = . 0Λ > is the equivalent to the Marshall-Lerner condition in this model.
Supply Side: Marginal Cost and Inflation Dynamics For the world economy, optimal staggered price setting yields
** *1 tt t tE mcπ β π λ+= + (31)
where * *t tmc mc μ≡ + is the (log) marginal cost expressed as a deviation
from its steady state value μ− and the slope coefficient is (1 )(1 )θ βθλθ
− −≡ .
Real marginal cost is * * * * *
* * * *
* *
( )
( ) (1 )
t t t t
t t t
t t
mc w p a
c n a
y a
ν
ν σ φ*ν σ φ φ
= − + − −
= − + + −
= − + + − +
(32)
iv
where * log(1 )*ν τ≡ − − with the optimal subsidy * 1ετ = defined below.
Marginal Cost and Inflation Dynamics for the Small Open Economy Domestic inflation follows
, , 1 tH t t H tE mcπ β π λ+= + (33)
where ,
,
*
( ) ( )
(1 )
t t t H t
t t t H t
t t t t
t t t t
mc w a pw p p p ac n s a
y y s a
t
ν
ν
ν σ φ α
ν σ φ φ
= − + − −
= − + − + − −
= − + + + −
= − + + + − +
(34)
and log(1 )tν τ≡ − − . Substituting from (25) to eliminate the terms of trade , ts
*11 (1t t tmc y y aw wα α
σ ) tν φ σ φ⎛ ⎞ ⎛ ⎞
= − + + + − − +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
(35)
Canonical Representation of the World Economy: Let the output gap relative to flexible price equilibrium be t ty y y≡ − t , and similarly for the world output gap. Under flexible prices, real marginal costs will be constant at *
tmc μ≡ − . Evaluating (32), we have *
0 0ty = Ω + Γ *ta (36)
where *
0 01 and ν μ φ
σ φ σ−
Ω ≡ Γ ≡+ +φ
+ . Also, the deviation of real marginal cost
from steady state is * *( )t tmc yσ φ= +
which yields the New Keynesian Phillips Curve: * *
1 0t t t*tE yπ β π κ+= + (37)
where . Then (22) can be written in terms of the world output gap as
0 (κ λ σ φ≡ + )
** * * *1 1
1 ( tt t t t t ty E y r E rrπσ+ += − − − ) (38)
where * * *0(1 )t a trr aσ ρ ρ≡ − − Γ + is the natural real rate of interest.
Equations (37 and (38) with an interest rate rule describe the evolution of the world economy.
v
Dynamics of the Small Open Economy: The natural level of output comes from setting tmc μ= − in (35) and solving for
*t ty aα α α= Ω + Γ + Θ ty (39)
where ( ) (1 ) (1 ), 0,w ww w
α α
α α
ν μ φ σα α α
ww
α
ασ φ σ φ σ φ− +
+ +Ω ≡ Γ ≡ > Θ ≡ −+ . Also real marginal
cost will be related to the output gap by
ˆt tmc ywα
σ φ⎛ ⎞
= +⎜ ⎟⎝ ⎠
combined with (33) yields the New Keynesian Phillips Curve , , 1H t t H t tE yαπ β π κ+= + (40)
where ( wασ
ακ λ φ≡ + ) , which depends on openness. Using (29), the “IS” curve of the small open economy becomes
( )1 ,t t t t t H t tw
y E y r E rrα πσ+ += − − −1 (41)
where
*1
(1 )(1 )t t trr a E y
wα
αα
tσ φ ρ
ρ φσ φ +
+ −≡ − − Θ Δ
+
the open economy’s natural rate of interest. Thus the IS curve for the open economy is analogous to that of the closed economy, but with a coefficient that depends on openness. Optimal Monetary Policy in the World Economy Choose an optimal employment subsidy * 1
ετ = to offset the monopolistic distortion in the goods market, and similarly in the small open economy. Hence the optimum is the flexible price equilibrium. In the special case
1σ η= = where trade is always balanced, Gali & Monacelli show that the utility of the representative consumer , as a percent of steady state consumption, is
22,
0
(1 ) (1 )2
tH t t
t
W yα εβ π φλ
∞
=
− ⎡ ⎤≈ − + +⎢ ⎥⎣ ⎦∑ (52)
Clarida, Gali, and Gertler maximize this subject to (40) and (41) under discretion and derive a “leaning against the wind” rule on inflation of the form
,( / )
(1 ) H tty ακ ε λ πφ
= −+
vi
Black Markets and Parallel Exchange Markets
Edwards (Ch. 3)
Tradable and non-tradable goods, domestic and foreign money, fixed
commercial exchange rate E, floating financial rate δ.
( )0
*
, ,
Portfolio Balance , 0
Capital controls 0, 0
Goods demand = supply ( , ) ( ), , 0, 0, 0
( , ) ( ), 0, 0, 0, 1
Government Budget
T T T e T a T eN
N N N e T a N e T
A M FA M F a m FE E E E
m F
F FEC e a Q e e C C QP
C e a Q e C C Q P
δ δδ ρ ρ
δσ ρ σδ
= + = = + = + =
′= <
= >
= = < > >
= > > < ≡
0
, ,
,
External Balance ( ) ( , )
International Reserves , , 0
Long-run Equilibrium , 0, 0, 0Internal Balance ( , )
TN N T
N
N N NN T N
T T T
N N
EGG P G EG G t D
GP G GGg g g g
E E eCA Q e C e a G
R CA M D ER R
G t D CA RC e a eg
λ= + ≡ = +
≡ = + ≡ =
= − −
= = + >
= = = =+ =
0 0 0 0 0 0 0 0
( ) ERER ( , ), 0, 0
Portfolio Equilibrium given , , 0
External Balance ( ) ( , )
Given , , ERER ( , ) ( , )
NN N a
NT T
LR N N
Q e e v a g v v
mE L LF
G tm Q e C e ae E
m e v a g v m F g
ρ δρ δ ρ
ρ ρ
⇒ = <
′= = <
= − + −
= = +
g <
ρ 0ρ =
S
S 0m =
B
m0 m1 m
94
At B, m1 > m0, the spread Eδρ = jumps, followed by appreciation
0δδ < . At B, e is over-valued, since 0( )vde dm F d
aρ 0∂
= ⋅ + <∂
appreciates
( ). So P0av < N rises relative to E. During the transition back to
equilibrium, m falls as due to BOP deficit. Devaluation (rise in E)
accelerates the return to equilibrium as m, ρ fall with rise in E.
0R <
Suppose reserves are insufficient. Then devaluation will be anticipated
at time t1, when reserves run out. Therefore δ will jump to the unstable
path that leads to the saddle path after the devaluation takes place.
ρ D
E
m0 m1 m
B C
At time t0, m0 jumps to m1, ρ jumps to C > B, then depreciates further to
D at time t1, when reserves run out. Devaluation drops down to E on SS
and so back to equilibrium.
95
Black Markets (Kharas & Pinto, Restat, 1989)
Commercial rate e, black market rate b. X2 is illegal foreign trade, X3 is
legal foreign trade, importable inputs I purchased at black market rate
b. Final goods H produced with imported inputs and labor.
( )
11
2
2 3 2 1 2 3
2
12
Production functions , ,Cost of smuggling ( ), (0) 0, 0, 0Maximize ( ) ( )
(1 ( ))
1let , , 1
BOP
i i
H x x x
x x
H L I X LC X C C C
p H bp X ep X bp C X w L L L bIbp C X ep w
bc C X ce
α α
φ φ
−
−
= =′ ′′= > >
+ + − − + + −′− = =
′= = = −
( )( )
2 3 ( ) , government imports
Portfolio Balance , , 01
Assume = 0,so ,all production is exportedPrivate Spending ( )
let , Then
x
H
x
p X X I g F g
bb MM bF
M bFbb
H IP H a M bF
mMm F p L g a Fe
λλ λ
λ
α
φ
+ = + + =
′= = <+−
== +
= = − − +
( )
( )( )
ˆ( )
Portfolio Balance implies 1
Steady-state Equilibrium 01
0ˆ
1 and
ˆHence or ˆ
x
x x
xx
M D e g t m g t m em FF
p L g m FF Fa
g tm me
p L g p L gmFa a
a g tm a a g t ee p L gp L g
φ λ
φ λ
λ λφ
φ φλλ λ
= = − ⇒ = − − ⋅
+ =−
−= ⇒ = + =
−−
= ⇒ =
− −∴ = − ⋅ = ⋅
⋅ −⋅ −= = ⋅ ⋅ =
⋅ −⋅ − ⋅ ( )xp L g−
96
Observe government deficit is financed by inflation tax. Let eθ λ≡ ⋅ be
the unit inflation tax.
F θ φ 0m =
0F =
m e eKeep inflation tax on the positive side of the Laffer curve. Note tradeoff
between black market tax on exports φ and inflation tax , for given
deficit g – t. Therefore, rise in inflation tax reduces need for export tax
revenue.
e
97
Balance of Payments Crisis Models
Type I Crisis – Fundamentals are inconsistent with pegged exchange
rate. Krugman (1979), O&R (Ch. 8.4.2)
Demand for money * * * *ln , , 0, , 1tt t t t t t t t t
t
Ma i i i e i P E P P
Pη
= − = + ≡ = +
≡
and with fixed exchange rate
Money supply expanding because of growth in
government debt, bought by central bank and held as domestic asset BH.
As long as the exchange rate is pegged and output is
fixed, the demand for money remains constant. Thus rise in BH requires
fall in BF. The inconsistent fundamentals will become
evident as reserves fall towards zero. Prior to the time of collapse, it will
become evident that *0 and therefore t tEe >
,t H tm b
i i> so the demand for M will
fall, as speculators attack the currency. To find the effect on behavior
prior to collapse, find the “shadow” exchange rate that would prevail if
the attack has already occurred and and te µ= = :
The collapse occurs when Te e= . Otherwise there
would be a perfectly foreseen jump in the exchange rate, which would
either bring the collapse forward or back.
e
e
BF
T 98
Time of attack T from substituting into the shadow
rate equation at time T to get , whence
or
Larger initial reserves BF,0 postpone the attack. There is a regime shift
at time T.
Type II Crisis – Fundamentals ok, speculators anticipate a regime
change induced by the attack itself. (Obstfeld, 1996, O&R Ch. 9.5.4)
Government objective function
Public behavior and
( )
( )
2 2
2 2
e
e
k z
k z 0
π π χ
π π χπ
= − − − +
− − − + =
L π
z z
FIXL+ C(π)
Devalue if + C(π) < for z > FLEXL FIXL z
Revalue if + C(π) < for z < FLEXL FIXL z
FLEXL + C(π)
99
Assume z is uniformly distributed over the interval [-Z,Z]. Then
Also, Eπ = πe, so that πe has possible multiple equilibria, as shown by
O&R:
Eπ
100
π1 π2 π3 πe
Additional types of crisis behaviors:
1. Contagion, either through goods markets or asset markets.
(Buiter, Corsetti, & Pesenti, Princeton Studies in Intl. Finance,
1998)
2. Herding behavior in asset markets. Bikhchandani & Sharma
(IMFSP, 2000)
3. Convertibility crises. (Black, et al, IMF WP 01/210, 2001)
“Convertibility Risk: The Precautionary Demand for Foreign Currency in a Crisis” IMF WP 01/210
Stanley W. Black, Charis Christofides, and Alex Mourmouras
Outline of Paper • Background – the Korean Crisis of December 1997 • Exchange Market Pressure • A Model of Currency Inconvertibility
– Model Structure – Effects of Convertibility Risk on Private Behavior – Interest Rate Defense of Domestic Currency – Devaluation as an Alternative
• A Cross-section Estimate of Convertibility Risk • An Empirical Estimate of Demand for Money in Korea allowing for Convertibility
Risk • Implications for Exchange Rate Policy Management
Background - the Korean Crisis of December 1997
• Pressure on reserves from banks’ unwillingness to roll over dollar loans after Thai baht collapse.
• 5% daily limit on exchange rate movements, up from 3%. • Dec. 6 IMF Agreement limited loss of reserves for month. • Combined price and quantity limits led to shortened market days, effective market
closure, rationing of dollars. • Panic dollar buying as response of public to rationing. • Shift in demand for money offset gain from rationing. • New IMF Agreement Dec. 24 dropped 5% limit as of Dec. 16. Exchange rate dropped
sharply, then recovered.
101
10
20
30
40
50
60
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
97:01 97:04 97:07 97:10 98:01 98:04 98:07 98:10
Forex Holdings (Left Scale) Won/$ (Right Scale)
Billio
ns o
f US
Dol
lars Percent change
Figure 3. Foreign Exchange Holdings and Exchange Rate
Exchange Market Pressure Girton-Roper (1977)
• Money Demand: m - p = y - v • m = dlog(M/M*), p = dlog(P/P*), y = dlog(Y/Y*) • Money Supply: m = d + r • d = (D/M)-(D*/M*), r = ( R/M)-(R*/M*) • Purchasing Power Parity: e = p (- p*) • Md = Ms : d + r = e + y - v • Exchange Market Pressure = r - e = y - v - d
Figure 2. Exchange Market Pressure
10
5
0
5
10
10 5 0 5 10
0
%DR
-%DE
-0.3
-0.2
-0.1
0.0
0.1
0.2
-0.3 -0.2 -0.1 0.0 0.1 0.2
Fore
x R
eser
ves
(per
cent
cha
nge)
Won/$ (- percent change)
Figure 4. Exchange Market PressureJanuary 1997 - December 1998
102
A Model of Currency Inconvertibility • Two periods • Two nonstorable goods • Tradable domestic good x with price p • Imported good y • Two assets: • domestic currency h • foreign currency f , exchangeable for h at 1 today • Many agents, each with endowment W units of x • utility of consumption: u(x, y) in next period • gross rate of return on domestic currency R>1 • " = probability agents are rationed out of forex market • b= forex purchase if not rationed next period
• State 1: Convertibility State 2: Inconvertibility • Probability 1- " : Probability " : • h/p + f = W h/p + f = W • x1 = Rh/p – b x2 = Rh/p • y1 = f + b y2 = f If " = 0, set f=0. When " > 0, set f > 0. EU = (1- ") u[(W-f)R-b,f+b] + " u[(W-f)R, f] b: u1(x1, y1) = u2(x1, y1) f: (1- ")(R-1) u1(x1, y1) = "[-R u1(x2, y2) + u2(x2, y2)]
0)1)(1(])([
1
222
222112112
2 >−−+++−
×−
= 12222
1
uRuuuRuRuR
ddf
αααα
Figure 1. Share of Assets Held in Foreign Currency
0
0.2
0.4
0.2 0.4
Probability "
103
Interest Rate Defense • Raise domestic interest rates to increase attractiveness of domestic vs.
foreign assets. • Possible offset to increased precautionary demand or foreign currency.
The Interest Rate defense is ineffective if " is high
0 5 100
0.2
0.4
0.6
alpha = .05alpha = .25alpha = .50
f/W
R
Devalue Exchange Rate vs. Rationing • Alternative option of devaluation to e < 1 to avoid market closing. • Precautionary demand for foreign currency depends on expected return vs.
domestic: "(1/e - R) + (1- ")(1 - R) • So interest rate is a defense against devaluation risk (higher R offsets risk
of e < 1). • But interest rate less effective against rationing risk.
Tradeoff of Interest Rate vs. Devaluation (for given f/W)
104
0123456789
10
0.5 1
alpha = 0.1alpha = 0.3alpha = 0.5
R
e
Cross-section Demand for Money • Vi = α + β πi + γ Yi + δ Di + ui • Vi = velocity of M2, 1991-1995 • πi = consumer price inflation, 1991-1995 • Yj = per capita GDP in US$, 1991-1995 • Di = current account inconvertibility, IMF • Sample of 135 countries • Vi = 0.762 + 0.367 i – 0.058 Yj + 0.103 Di , R2= 0.77 (0.121) (0.111) (0.014) (0.044) • Upper bound for estimated effect: 10.3 % of M2 Time Series Demand for Money in Korea • Long run demand for M2, monthly 1970-2000
log( ) 7.17 0.85log( ) 0.01 0.01 0.08log( ) 0.11t tt t t t
t t
h Ry i e
p Mπ= + − + + + + tu
Short run demand for money
11
1
log( ) 0.02 0.015 0.1 log( )
0.09 log( ) 0.0004 0.004 0.09 log( ) 0.01 ( )
t tt
t t
tt t t t
t
h hseasonals u
p pR
y i eM
π
−−
−
∆ = + − + ∆ +
∆ − ∆ − ∆ − ∆ + ∆ tv+
105
Simulation of Korean Forex Crisis of December 1997
• Actual decline in money stock: - 3 % • Predicted decline in money stock: - 1.7 % • In absence of crisis, M2 would have risen 1.9 % • Decline due to crisis variables: -3.5% • Alternative estimate - 4.5% (based on actual decline vs. predicted in
absence of crisis) • Magnitude of predicted reserve loss: $5.6-7.1 bil., vs. total reserves end-
Nov. 1997 $24.4 bil.
Foreign Currency Deposits - Korea
0
5000
10000
15000
20000
1990
01
1991
01
1992
01
1993
01
1994
01
1995
01
1996
01
1997
01
1998
01
1999
01
2000
01
2001
01
Conclusions: • Importance of avoiding simultaneous price and quantity rationing of
foreign exchange. • Interest rate not effective to offset decline in demand for money due to
convertibility risk. • Devaluation or float option may be preferable. • Interest rate can be effective against devaluation risk.
106
Central Bank Intervention
Henderson Model (1984). Portfolio approach, no UIP, risk averse agents
* * *0 1 2 3 4 5 6
* *
0 1 2
0 1
0
IS Curve ( ) ( )real interest rate ( )CPI (1 )( )ProductionLabor Demand Wage indexing ( ), where
Y y y Y Y y r y r y e p p y e y pr i q q
q hp h e p q eY x x L xw p Lw w q q w p
α
ββ
µ
= + + − − + + − + − +
= − −
= + − + = += + +
− = − +
− = − = + 1
*0 1 2 3 4
* * *0 1 2 3 4 5 6 7 8 9
* * *
Money ( )
Bonds ( ) ( )
Assume 0, foreign country uses monetary and fiscal policy to keep , , constantIf shoc
fL
M m m p m Y m i m i e e
B b b p b Y b i b i e e b i e e b i b e b p b Y
Y p i
γ δ* γ ε
µ
−
= + + − − + − + +
= − − + − + − + − + − + − − − +
=
0 1
ks are temporary, , , etc.Wages are set at , , eliminate with production function to get
ˆ ˆ ˆ:ˆ ˆ ˆ ˆ:
ˆ ˆ ˆ ˆ:
L i e
L i e
L i e
Ep p Ee ew p w L Y
XX y L y i y e y
MM M m L m i m e m
BB B b L b i b e b
β
β
β
β
α β
β γ δ
β γ ε
= == − + −
= − + +
= − + − + +
= − + + + − +
Pegged regime: i, e fixed, B, M variable. Floating regime: i, e
variable, B, M fixed.
i X M
x B
Demand shock α shifts XX. Given M & B, i rises, creates excess demand
for B at given e, so e falls, shifting XX back, MM down, BB up to point x.
Output [employment] moves to L1 > Lf. If rates are fixed, L moves to L2.
Flexible rates give better stabilization of demand shocks.
Lf L1 L2
107
Financial shock ε shifts BB up. Keeping rates constant implies central
bank offsets demand shifts with ∆B + ∆F = 0. Flexible rates implies rise
in i, e, fall in L, in response to fall in demand for B. Fixed rates give
better stabilization of financial shocks.
Feedback rule based on response to current variable e:
Instruments: M+B and i, Target: Lf. Add together MM and BB:
( )
ˆ ˆ ˆ ˆ ˆ:ˆ ˆ: ,
ˆ ˆˆ ˆPolicy Rule: ˆˆ , substitute in
ˆˆ ˆ, solve for
ˆ
L e
L e
L e
e L
LL e
e
e LL
e
B B B B M b L b e
X X y L y e y
B e b L b e
b e b L X X
b Ly L y L
b
y b yy L
b
β
δ ε
θ θ α β
ψ δ ε
ψ δ ε
δ εθ
ψ
θψ
′ ′ ′ ′ ′= + = + + +
′ ′ = + = +
′ ′ ′= = + + +
′ ′− ⋅ = + +
′ + += + ′−
′ − ⋅ = + ′−
′ ′
( )
( )2 2
22
2 2
2
ˆMinimize
e
e
e
e
e LL
e
ee
L L
b
yb
Ly b
yb
yb
y b
θ δ
δ ε
θ
δ εψ
σ σψ
ψ
σ σψ
σ
+′−
+ + ′− =
′ − ′−
+′= − ′
2εσ
e B' X(α+β')
L δ+ε
Shocks to XX, set ebψ ′= to make B'B' vertical. Shocks to B'B', set
108
ψ → −∞ or B'B' horizontal. In general, use managed intervention in
response to mix of shocks. More intervention if shocks are mainly
financial.
Episodes of Central Bank Intervention:
1. Carter-Blumenthal Dollar support package, November 1978.
2. Jurgenson Report, March 1983 – denigrated intervention.
3. Plaza Accord, September 1985 – pushing the dollar down.
4. Louvre Agreement, February 1987 – target ranges for $, DM, ¥.
5. 1989-1990 Abandonment of target ranges.
6. Resumption of intervention by Clinton Administration, 1993-95.
Dominguez & Frankel, “Does Foreign Exchange Market Intervention
Matter? The Portfolio Effect” (AER, 1993) weekly data, 1982-1988.
* 21 0 1 2
1 1
1 0 1 1 2 1 3 4
moving variance of past , cumulative intervention
survey expectation of
( ) ( ) announc
et t t t t t t t
t t i tet t
e e et t t t t t
rp i s i v v x u rp x
v s x
s s
s s s s s s AN INTAN
β β β ρσ
α α α α α
+
−
+ +
− − −
≡ + ∆ − = + + + = = ∆ =
∆ = ∆
− = + − + − + +
= ements of intervention actual interventionINT =
INT=$100 m s
AB=.08%
BC=2.7% rp, given se se(x)
C
B A
x
109
Vitale (JIE, 1999) uses Kyle (EC, 1985) dealer market framework
Dealer transacts with liquidity traders and central bank, prior to the
announcement of the fundamental value f of the exchange rate, which is
known to the central bank, but not to others. Its mean value s0 is known.
[ ]
20 0
1
21 1
( , ),central bank order , liquidity orders (0, )Competitive dealer makes zero profits, so |
Central bank minimizes ( ) ( ) , where is degree of commitment to target Supp
fl
m
f N s x Ns E f I
c s f x q s s q
ε σΣ
=
= − + −
∼ ∼
s
1 0 0
012 2
0
0 0
ose the central bank's target is known, as is . Let [ ( )]
where . Substitute into and optimize to derive rule for .( )
Then ( ) ( ), depends on misalignment
f
fl
s q s s x h s s
s c x
x f s s s
λ ε
βλ
β σβ γ
= + + − −
Σ=
Σ += − + −
( )
2 2 21 0 0 0
21 1 0
and deviation from target
Then [ ( ) ], where is the positive root of 4 (1 ) (1 2 )1+2 q, 2 The conditional variance is E | =
(1 ) 2(1+ q)
fl
f fm
s s f s q q
q f s Iq
λ β ε λ λ λ σ λλβ γ
λ λ λ
= + − + + = + Σ
1 = = Σ ≡ − 2 +Σ
The liquidity coefficient λ determines the responsiveness of the exchange
rate to the order flow. The market maker filters out the target
component 0( )s sγ − , but cannot do so if the target is secret. If it is secret,
but the central bank announces falsely that 0s s= , the dealer’s pricing
rule will then be 1 0 ( )s s xλ ε= + + and the central bank order 0( ) /x s s λ= −
can achieve the target exactly. Also λ will be smaller if the target is
secret, so the variance of the exchange rate will be smaller. This is a
signaling equilibrium, where the central bank provides a signal about
its target through its intervention. More recent paper includes Barro-
Gordon type objective for central bank. Signaling intervention then can
reduce the variance of the real variables.
110
Target Zone Model (due to Krugman, see Svensson, JEP, 1992) EMS
0 1* * * * *
0 1*
*
* * *1
* *1
1 ( ) /
( ) ( )
, where ( ) ( )
[ ( )]
t t t t t
t t t t t
t t t t
tt t t t
tt t t t t t t t t t
tt t t t t t t t t t t t
t st t
m p y i v
m p y i v
s p p qds
E i idt
dss q m m y y E v v
dtds
s f E f q m m y y v vdt
s e E f sα
*
α α α
α α α
ρ
α α αρ
α α
α − −
− = + − +
− = + − +
= − +
= − −
αρ
∴ = + − − − + + − −
= + = + − − − + − −
=2
1 ( ) /
solution for floating exchange rate
Suppose ( ), random walk without drift. ( ) 0, ( ) 10,
Suppose ( ), random walk with drift.
( ( ))
t
t
t t t t
t
t st t tt
ds
df dz t Edz t Edz tE df s f
df dt dz t
s e f s t ds fα
σ
η σ
α η
∞
∞− −
= == =
= +
= + − =
∫
∫
=
[ ]
1 2
212
212
2
2
1 2
1,2
Float bounded by interventions. Suppose ( )
Ito's lemma
( )
2
( ) with solution2
( )
roots of
t t
t f t ff t
t f ff
tt f ff
f ff
f f
s S f
ds S df S df
ds S dt dz t S dt
dsE S Sdt
S f f S S
S f f A e A eλ λ
αη
η σ σ
ση
σα η
αη
λ
+
=
= +
= + +
= +
= + +
= + + +
1 2 1 2
2 22
1,2
1 1 2 2 1 1 2 2
1,2
1 0, if 0, 2 /2
Target zone boundaries ( , ) ( ), ( )
"smooth pasting" ( ) 0, ( ) 0
1 0,1 01 1 sinh(If 0and ( ) , , ( )
2 cosh( )
f f
f f f f
f f s S f s S f
S f S f
A e A e A e A eff A S f f
f f f
λ λ λ λ
λ ασ λαη η λ ασ
λ λ λ λλη φ
λ λ
+ − = = = ±
⇒ = =
= =
+ + = + + =
= = = = −−
)cosh( )fλ λ
111
At , 0, Prob( ) 0, Prob( ) 1s Eds ds ds+ −≤ = = ”Honeymoon”effect, flatter than free float. Implications: i. U-shaped distribution of s rejected.
ii. Rotated S distribution for i-i* rejected.
iii. Nonlinearity rejected.
Modifications:
1. Imperfect credibility of zone- realignment of parities (Svensson)
t t t
*
, within band, central parityE E Et t t t t
t t t
t tt t t t t t t
t tt t t t
s x c x cds dx dc
dc dx dxx f c E E h E
dt dt dtdc dx
i i E Edt dt
α α α
= + = == +
= − + + = +
− = +
t
composite fundamental ht does appear to have “honeymoon” effect.
Use regression to predict *( )tt t tdx
tE a i i bxdt
= − +
Estimate *ˆ ˆ tt t t tdc dx
E i i Edt dt
= − − t Relate to size of reserves.
2. Intra-marginal intervention at s s< or mean-reverting
fundamental ttdh
tE hdt
ρ= − will center distribution.
3. Sticky price target zone model (Miller & Weller, EJ, 1992) Note
that monetary model assumes UIP, real exchange rate and output
constant, removes reasons for central bank intervention. Modify
latter two assumptions to get Dornbusch-type target zone model.
112
Costs and Benefits of Currency Union • Costs of Currency Union • Benefits of Currency Union • EC Snake – 1973-78 • EMS –1979-99
Costs of Currency Union • Loss of Independent Monetary Policy • Costs of transition to common inflation rate • Differences in labor market institutions • Different uses of inflation tax • Openness of Economy
– Pass-through of exchange rate into costs – Fiscal policy impact on BOP or GDP
Loss of Independent Monetary Policy
P0
P0
– Demand Shocks: F-, G+ → F deficit, unemployment; G surplus, boom – Adjust via wage flexibility or labor movement – Immobile labor or inflexible wage requires exchange rate change – Effect temporary, since shifts S as well as D
113
Costs of transition to common inflation rate
Germany
Italy
• Phillips curve: π - π e = f(u - un), f’<0
– π e = expected inflation – un= “natural” rate of unemployment
• Italy vs. Germany
Differences in labor market institutions • highly centralized bargaining internalizes the inflation
externality • decentralized bargaining internalizes the firm-specific increase in
cost and loss of market share
Degree of centralization
π
114
Different uses of inflation tax • high reliance on seigniorage in Southern Europe
– ÄM/PY = 2.5-3.5% vs. < 1% in North – effect of fall in ð on Italian budget deficit
• Seigniorage 1979-87
% tax rev % of GDP Portugal 10.0 3.4 Greece 9.6 3.5 Spain 9.3 3.2 Italy 6.4 2.1 Ireland 2.3 0.9 France 1.3 0.5 Germany 0.7 0.3
Openness of Economy • Speed of pass-through into costs faster if economy is highly open (import
share m) • Impact of fiscal policy on BOP higher if open
– Y-A = B, C=(1-s)Y, M=mY – Y - (C+I+G) = X-M – Y* = (X+I+G)/(s+m) – dY/dG = 1/(s+m), dB/dG = -m/(s+m)
0 0.5 10
1
2
3
4
BOP multiplierGDP multiplier
3.333
0.333
m
s m+
1
s m+
0.80.1 m
• Lower cost of union if highly open
115
Benefits of Currency Union • Reduced Transactions Costs
– EU estimates ½% of GDP • Less Price Discrimination
– market less segmented • Reduced uncertainty of prices – gain vs. loss • Reduced Misalignment of exchange rates • Gain in Credibility of Monetary Policy • Effects on Growth
Credibility of Monetary Policy • Gain for “wet” govt. such as Italy • Steep preference trade-off ( π, u) gives high π, same un; reduce π by tying
to low inflation currency with flat trade-off
Benefits vs. Costs • Benefits (transactions cost, risk, credibility) increase with openness. • Costs (loss of monetary policy, slow pass-through) decrease with
openness.
116
Benefits vs. Costs • Relatively closed prefer flexible, open prefer fixed exchange
rate. • EC mi = .25-.75, mEC = .123, mUS = .10, mJP = .114 • Monetarists believe costs are low, Keynesians believe they are
high. EC “Snake”
• Werner Report (1970) - Monetary Union by 1980 – Narrow margins (± 2¼%) after Smithsonian (Dec 1971) ±4½% allowed
crossrates ±9%. Float March 1973. – Membership reduced to DE, BeNeLx, DK, SW. – Weak financial support mechanism
EMS – 1979-99 • Schmidt/Giscard d’Estaing proposal
– reduce dependence on then-weak $, spread adjustment burden – Intervention Rules
• ECU = Σwiei, with ECU parity rates ei and bilateral parities eij =ei/ej. • Parity Grid ±2¼%. Both CB’s intervene at margins. • If ei is EXR/$ & gi is DM/CU, gi = edm/ei then using Greek letter for parity: • |(gi - γi)/γi| = |(edm - εdm)/εdm - (ei - εi)/εi|#.0225 • Unlimited Short-Term Credit for 75 days. EMCF credit up to 6 mos. $42 bil of gold & $ reserves.
EMS Grid
ECU Sept.’89 amt EXR/$ amt in $ EXR/ECU wt. DM/CU (1) (2) (1)/(2) (2)x1.05 (1)/(4) (4)/i Deutschemark .6242 1.9619 0.318 2.059 30.3 1.00 £ sterling .0878 0.6859 0.128 0.72 12.2 2.860 French franc 1.332 6.5714 0.203 6.904 19.3 29.82 Italian lira 151.8 1412.93 0.107 1483.58 10.2 0.1388 . . . . . . . ECU wi ei $1.05 1.00 100.0
• DM/FF=2.059/6.904=29.82 pfennig ±2¼%. • Mutual Agreement for parity changes - to be frequent if needed 79-83(5); 84-87(3);
88-91(1) • Basel-Nyborg Agreement 1987: change interest rates more frequently.
117
Effects of EMS • reduced short-run variation in bilateral nominal & real exchange rates • no change in SR variation of multilateral RER • increased LR variation of multilateral RER, except DE. • reduced inflation in FR, DK, others? increased inflation in DE.
LR VAR RER 1960-79 1979-85 Deutschemark 12.3% 10.9% Belgian franc 3.4% 14.1% Dutch guilder 8.1% 9.2% French franc 5.2% 11.1% Italian lira 3.8% 6.1%
• Capital controls used by FR, IT to stay in EMS, until 1990 Single Market rules.
• Credibility – up to 1987, frequent devaluations, low credibility. – Speculative crisis implied run on currency. – Assymmetry - German as hegemon set money growth, others peg to
DM. Germany sterilizes intervention. Magnifies business cycle in periphery. Spreads shocks from center.
Convergence of Inflation • Convergence of Inflation Rates - 1980’s
– French & Italian π fell sharply 1983-87. But also in non-EMS countries.
– Unemployment rose to ’87, fell to ’90, then rose. – Unemploy. rose less, fell sooner, in non-EMS. – Mon-Fiscal Pol. tighter in EMS. – Slow reversal of π,U spiral in EMS suggests low credibility.
Collapse of EMS • end of capital controls in 1990 • rise in German interest rates after Unification • failure of Danish referendum on Maastricht • recession outside Germany
– Sept. 16, 1992, UK, IT withdrew, SP, PT devalue. – Aug. 2, 1993, FR, DK, BG, SP, PT ±15% margins.
• Fundamentals or Speculative attack?
118
119
from Demertzis, Hughes Hallet, and Rummel (1998) “Is a Two-Speed System in
Europe the Answer?”, Ch.11 in S. Black and M. Moersch (eds.) Competition and
Convergence in Financial Markets (Elsevier, 1998).
Appendix A
Bayoumi’s Model of Currency Union
In Bayoumi (1994), each region has the same production structure but produces its
own goods with a fixed amount of labor:
(A.1)
where Yi is the output of region i, Li the labor input in region i, gi is a disturbance
with mean zero and independent of the exchange rate regime. The capital stock is
normalized at 1. In logs
(A.2)
In a competitive market, labor is employed up to the point where real wages equal
the marginal product of labor in the common currency:
(A.3)
where ei = the (log of the) bilateral exchange rate with region 1. The level of wages
and prices are Wi and Pi with their log counterparts in (A.3). To incorporate wage
stickiness, assume that full employment wages, w6=log("), hold when there is full
employment (Li=1) and no shocks (gi=0), and that the exchange rate is at its parity
value (Ei=1). If there is excess demand for labor when Wi=", then wages will be
raised until the demand falls to Li=1. But if there is excess supply at Wi=", then
wages remain at this level and unemployment results.
Each region has to choose its own exchange rate regime. If regions i and j
120
form a currency union then their exchange rate ratio, Ei/Ej, is fixed at unity and they
have a common currency. If they choose separate currencies then Ei/Ej may vary, but
there is a transactions cost between the two currencies. This cost implies that, in
value terms, goods exported from region i "shrink" by a factor (1-Ti) when they arrive
in region j. For simplicity, let Ti=T for all regions.
Finally on the demand side, if production is owned locally, region i's income will be
PiYi. Utility levels are given by the Cobb-Douglas function
(A.4)
where Cji is the consumption of good i in region j, and is a constant. The
$ji parameters are subject to the normalizations .
Since $ji is the proportion of region j's income spent on goods produced in
region i, these restrictions ensure total income is spent and that aggregate demand
exhausts income spent on each good (before payment of transactions costs Tj). Under
these conditions the demand for good i from region j is
(A.5)
where vji is another normally distributed disturbance with zero mean arising on the
demand side. Note that production in region i will be expected to equal unity in
the absence of shocks (yi=0 in (A.2) at full employment). Now let prices be
normalized such that P1=1, so that E(P1,Y1)=1 where E denotes expectations. That
121
means all other national incomes are also unity in expectation since, if PjYj=1,
then
(A.6)
which implies PiEYi=1. But P1Y1=1, so PiEYi=1 for
i=2 ...N. Hence, in the long run, output in each region will be independent of the real
exchange rate, but in the short term actual output will depend on relative prices. Thus
if region j and region i do not form a currency union, the equilibrium consumption of
good i in region j will be
(A.7)
where the production of good i is given by (A.6) and, for simplicity, Tj=T. This
implies
(A.8)
where dji=vji+gi is a composite disturbance term, since full employment with
equilibrium wages and exchange rates implies yi= -pi =gi. Each region's utility level
is therefore
(A.9)
where J=log(1-T).
Now suppose region j and region k decide to form a currency union. Equations
(A.6) to (A.9) hold with k replacing j and Tk=0. The external exchange rate will be
the mean of the free float exchange rates which, under the normalization of Ej=Ek=1
vs. region 1, implies ejk=ej-ek=(gj+gk)/2 and e6jk=0. Suppose wages adjust to provide
full employment in the high demand region (region j say) but are sticky downwards
122
in the other region. Then
(A.10)
using (A.3) and the results above for ej and pj, where w6 is the log equilibrium real
wage with no shocks and Ej=1. Substituting back into (A.3), using (A.2) for yk, yields
(A.11)
for region k. Now evaluating the difference between (A.9) and the utilities generated
by (A.10) and (A.11), we find the utilities gained by being in the currency union are
(A.12)
while the loss to region 1 (say) staying outside the Union is
(A.13)
where )vji is the increase in region j's demand
for goods produced in region i as a result of joining the currency union; that is the
trade creation and trade diversion effects of the monetary union itself.
Since the shocks are symmetrically distributed around zero, with gj<gk with
probability one-half and gj>gk with probability one-half, the ex ante expected benefit
of being in a currency union is
(A.14)
123
For the non-members, the expected welfare costs are
(A.15)
where N(0) is the density function of a standard jointly normal distribution of random
variables and
(="/(2(1-")).
Extending this analysis to a Union of several countries, 1 ...k, region j will have
full employment if its supply (productivity) shock is above the average for the
remainder of the Union; wages adjust up to give full employment if demand is above
the level of the other members since, if wages did not adjust, labor would move to
region j (not possible under our current assumptions) or wages would be bid down
elsewhere (also not possible given inflexible labor costs). Hence the expected output
loss in region j, without full employment, is
(A.16)
where 6g j , F6j are the mean and standard deviation of the disturbances of the Union
excluding region j. Since each region will have this output loss, and the disturbances
are symmetrically distributed so that each region has an equal chance of receiving a
shock below or above the average of its partners, the expected welfare changes are:
(A.17)
for members j and k, and
1 It is possible to decompose the second term of (A.17) to show the costs to region j when it decides to jo in
an existing union, and the costs to region i in an existing union when region j jo ins (Bayoumi, 1994). We do not use
those terms in this paper, but they imply a periphery country sufficiently similar to the core average will certainly
want to join when it can, but the core countries will probably want to keep it out unless it is a major trading partner
with the existing core. Alesina and Grilli (1993) make a similar point in a political economy context.
124
(A.18)
for nonmembers, k is a member . The conclusion is the same; the costs inside and
outside the Union diminish only if the shocks are of similar size and well correlated
within the core.1
Introducing Market Flexibility
(a) Labor mobility:
All this analysis has been conducted assuming no labor mobility. However,
suppose instead that a proportion * of the number remaining unemployed (X) in a
depressed region migrates to a full employment region. If the latter had had full
employment of 1, then a migration equilibrium implies employment of 1-*X and
1+*X respectively. If X is small, log(1±*X) ±*X and (A.10) and (A.11) become
(A.19)
respectively, where region j is the excess demand region (gj>gk). Aggregate output
has simply been reallocated between members of the Union. Hence repeating the
steps to (A.15) we get the ex ante expected welfare benefit from being in the
currency union
(A.20)
125
and the cost of being left outside is
(A.21)
under the usual symmetric distributions assumption. Hence the costs of forming a
currency union have fallen for both insiders and outsiders (0<*<1), but the
interpretation is exactly the same. Comparison with (A.14) and (A.15) shows that the
costs still vary with D, Fj and Fk, but will vanish if *61. Hence full mobility will
offset the costs of a monetary union for both insiders and outsiders.
(b) Wage Flexibility:
A similar kind of outcome can be achieved if wages and non-wage costs are
flexible downwards in region k. Suppose wages fall sufficiently to re-employ the *X
employees, who might otherwise have migrated to region j. That leaves employment
of 1 and (1-(1-*)X) in regions j and k respectively. Evidently region j is unaffected:
(A.22)
But region k will now achieve
(A.23)
These expressions are identical to (A.10) and (A.11), except for the fact that
((1-*) has been substituted for ( in (A.11) and wk has fallen by *(gj-gk)/2.
Consequently the costs of forming a monetary union, and the costs for outsiders, are
reduced. But the interpretation remains the same; the costs depend on D, Fj and Fk,
and will vanish if *61. Hence fully flexible wages restore full employment in region
k and remove the costs of a currency union.
Exchange Rate Policy Outline of Lecture
• Analytical Framework – Real Targets Approach (Internal-External Balance) – Anchor Approach – Optimal Currency Area Approach
• Key Issues – Volatility and Trade – Independence and Credibility of Monetary Policy – Assymmetric Shocks and Openness – Capital Mobility
• Exchange Rate Management Real Targets Approach
• Targets: Internal and External Balance – Mundell-Fleming or Traded-Nontraded Model – Maintain Equilibrium Real Exchange Rate – Allow ER to offset shocks to BOP – Use ER to Promote Exports
• Offset RER effect of domestic inflation – Passive Crawling Peg – RER target
• Internal Balance also a target Internal and External Balance
e
External Balance
e*
G
Internal Balance
126
Anchor Approach – Hard Peg option • Inflation Control as Primary Objective • Target Exchange Rate, Inflation or Money Growth • Hard Peg excludes consideration of internal target • Active Crawling Peg as anchor - tablita • Currency Board as option when credibility is lacking • Inflation Targeting allows more flexibility • Dollarization as extreme case
Optimal Currency Area – Exchange Stability • Benefits
– Reduced Transactions Costs – Price Stability if within-bloc trade share large – Increased Credibility for Weak Monetary Authority
• Costs – Loss of Independent Monetary Policy – Loss of Seigniorage Revenue – Need for Political Control of Area Central Bank – Fiscal Flexibility and Fiscal Transfers
ER Regimes: Range of options • Currency union or dollarization
• Currency board • Peg
Fixed Horizontal bands
• Crawling peg Without bands With bands
• Floating Managed Independent
FIXED
FLEXIBLE
127
Key Issues: Exchange Rate Volatility & Trade • Does Volatility Reduce Trade?
– Are firms risk averse? – Can hedging offset risk?
• Evidence on Industrial Countries Mixed & Weak • Emerging Market Economies
– Stronger evidence of negative effects (Arize, Osang & Slottje, J.Bus.Econ.Stat., 2000) (8 of 9 studies negative)
– Due to foreign currency denomination of exports? – Less opportunity to hedge risks.
128
Independence of Monetary Policy • Pegged exchange rate loses monetary independence with high capital
mobility • Flexible rate restores monetary independence • Desirability of monetary independence depends on responsibility and
credibility of monetary authority • Fiscal dominance - need for seigniorage revenues • Monetary dominance – control of inflation
Nature of shocks Suppose the objective is to stabilize real output in an environment of
high capital mobility. If the prevalent Then the desirable shocks are… ER regime is... • Real Flexible • Nominal
– Domestic Fixed – External Flexible
Response to Asymmetric Shocks
• ER flexibility useful if economy not too open. • High pass-through coefficient undermines exchange rate adjustment
process • Pass-through coefficient higher for EMC’s than IC’s, but still low in most
countries (Calvo & Reinhart)
Openness vs. Size • Openness raises benefits of OCA • Fiscal effects on BOP stronger, pass-through higher, so exchange rate
adjustment less effective • Effect of reduced transactions costs and price stability stronger • Small economies more open than large ones • Large economies more diversified than small, so have fewer asymmetric
shocks
129
Impact of Openness • Let Y-A - G = sY - G = X- mY • Then Y* = (X+G)/(s+m) • dY/dG = 1/(s+m), lower if m large • Given B = X – mY, dB/dG = -m/(s+m), higher if m large • Pass-through effect of exchange rate on prices proportional to openness m,
so effectiveness of exchange rate adjustment inverse to m. • Conclusion: peg or CU for more open economy
Costs vs. Benefits of Currency Union Benefits
Benefits
Costs
Openness
130
Capital flows
(Percent of GDP; sample of developing & transition countries) Source: Michael Mussa & others, “Exchange Rate Regimes in an Increasingly Integrated World Economy” IMF Occasional Paper 193, April 2000
.The Impossible Trinity
Full financial integration
iinnccrreeaassiinnggccaappiittaall mmoobbiilliittyy
Exchange ratestability
Monetary independence
FULL CAPITAL CONTROLS
PURE FLOAT
131
MONETARYUNION
Corner Solutions vs. Institution Building • Increased capital mobility leads to base of triangle • Middle options: crawling peg, fixed but adjustable rate, managed float • Middle ruled out if central bank lacks credibility • Either choose corners or build credibility or limit capital mobility • How to build credibility? Central bank independence, fiscal restraint,
political stability
Active vs. Passive Crawling Peg • Active Crawl
– Pre-announced devaluation path to promote disinflation – Liable to over-valuation of RER – Invites “carry-trade” capital inflows if i>i*+∆e – Unsterilized capital inflows raise money growth
• Passive Crawl – Keeps RER stable – Feeds inflation process – Uncertain ∆e keeps capital inflows down
Government Credibility
• High Credibility allows Inflation Targeting option – Flexible response to shocks
• Low Credibility may be overcome via OCA or Currency Board – Requires sound banking system as no bailouts allowed – High risk for large country of RER misalignments – Especially if asymmetric shocks likely – Argentina – Exit option from CB hard to arrange unless to OCA
132
Bayoumi & Eichengreen study • Compare shocks in EU & US 1960-90:
– EC members growth & inflation correlation 0.58 w/DE. – US regions growth & inflation correlation 0.68 w/mid-East region. – Decompose demand shocks & supply shocks, permanent & temporary – Because EC permanent shocks are larger & more asymmetric than US,
lack of exch. rate adjust. is worse.
Measure Type of shock EC/Ger. US/East Correlation Permanent 0.33 0.46 Temporary 0.18 0.37 Size of Shocks Permanent 2.1 1.5 (std. Dev.) Temporary 1.7 2.1*
* due to specialization in US
Correlation of Shocks vs. Trade Shares
US States Optimal Currency Area
Correlationof income shocks
Belgium, Netherlands
Monetary independence
Japan US, EU
EU membercountries
Extent of trade among
EastAsia
e
members
OCA lin
133
European Monetary Union • Political goals explicit in EU Treaties • Within-bloc trade shares high • Asymmetric shocks remain important • Correlation of shocks may rise endogenously after EMU created
(Frankel) • Flexibility of labor markets low, but may rise after EMU • Labor mobility included in EU goals
Exchange Rate Management • Regime-specific Aspects of Management
– Choice of Peg or Basket – Intervention Currency – “Fear of Floating” vs. Dangers of Pegging
• Policy Problems – Capital Flows and other shocks – Moral hazard
• Policy Options – Central Bank Intervention – Interest rate policies
Choice of Peg or Basket
• Real vs. Nominal Stability – Anchor or Real Targets
• Nominal stability choose $ peg – Allows one-way bet, moral hazard, capital flows
• Real stability choose basket peg – Promotes trade, but less transparent than nominal peg
• Trade Shares (Asia: $ 40%, ¥ 30%, € 30%) • Debt Shares (Asia: $ > ¥ > €)
134
Exchange Rate Responses: Asia β in regression ∆log(X/$)t=α+ β ∆log(DM/$)t over 125 day window, (McCauley, BIS)
Exchange Rate Responses: Europe
135
Source: Bank for International Settlements Annual Report 2000.
Intervention Currency • US Dollar the largest forex market (91% in April 1998) • Other currencies mainly traded vs. US dollar
– Because of low costs & high volumes in bilateral $ markets (economies of scale and competition)
• Euro growing as an alternative, but slowly, and more in European markets
136
Forex Market Transactions
Currency Pair Volumes, April 1998
91%
6% 1% 2%
US Dollar Deutsche mark Japanese Yen Other
Source: Bank for International Settlements, 1999
“Fear of Floating” • Evidence shows volatility of floaters not very different from peggers (ex.
US, Japan) [Average probability that monthly percent change <"2.5%]
– Floating Rate Currencies: 79.27 – Managed Float Currencies: 87.54 – Limited Flexibility Currencies: 92.02 – Fixed Rate Currencies: 95.88 Source: Calvo and Reinhart (2000)
Explanations for “Fear of Floating”
• Lack of Credibility of Monetary Authority • Contractionary devaluations • Liability dollarization • Banking instability • Negative effects of volatility on trade
137
Dangers of Pegging
• One-way bet against peg • Danger of misalignment due to third country effects ($/€ or $/¥
or real/$) • Reliance on wage flexibility or fiscal policy in response to
shocks • Encouragement of foreign borrowing
Policy Problems • Capital Inflows if short-term and denominated in foreign currency can
create serious problems: – Maturity mismatch – short vs. long – Currency mismatch – foreign vs. domestic – Reversibility – possible rapid outflow – Monetary expansion or currency appreciation – Unsustainable domestic expansion – especially if sectoral
• Capital Outflows can lead to sudden collapse in investment and imports, loss of reserves, currency depreciation.
Policy Responses to Capital Flows • Sterilize capital inflows
– Can lead to quasi-fiscal deficit if i > i* – Pegged rate invites further inflows
• Allow exchange rate appreciation – Over-values real exchange rate – Flexible rate increases uncertainty of returns
• Tax-subsidy to promote long-term flows – FDI vs. short-term flows
• Financing Consumption or Investment?
Moral Hazard and Agency Costs • Pegged exchange rate offers:
– Guaranteed return to foreign investor, i > i* – Cheap borrowing rate to domestic borrower, i* < i
• Currency mismatch shifts risk to government • Deposit insurance (implicit or explicit) can also create moral hazard • Government or private managers may fail to represent public or
shareholders’ interests
138
139
Policy Options to Manage Exchange Rate • Central Bank Intervention
– By rule (peg) or discretionary (disorderly mkts) – Spot or Forward – Sterilized or Unsterilized
• Interest Rate Policy (unsterilized intervention) • Capital Controls
– Prohibition on offshore markets – Limits on capital flows
Central Bank Intervention
• FA = Foreign Assets • DA = Domestic Assets • MB = Monetary base • Sterilized: ∆FA + ∆DA = 0, Sale of dollars vs. purchase of domestic bonds or other
domestic currency assets. Buying dollars may generate quasi-fiscal costs if i > i*. • Unsterilized: ∆FA = ∆MB, Sale of dollars reduces domestic monetary base.
Policy Coordination • Coordinated Interest Rate Policies • Swap Agreements: G10 ($30 bn), US-Mexico ($6 bn), EMS
– Reciprocal borrowing arrangements – G10 (expired) & US-Mexico to support intervention – EMS (expired) to support pegged rate system
• ASEAN+3 Swap Agreement – May 2001 – $9.5 bn swaps: Japan, China, Korea+ASEAN – 10% available without strings – To be used for Central Bank Intervention
Further Reading
• Corden, Max, “Exchange Rate Policies for Developing Countries,” Economic Journal 103, January 1993.
• Frankel, Jeffrey, “No Single Currency Regime Is Right for All Countries or at All Times,” Princeton Essays in International Finance No. 215, August 1999.
• Fischer, Stanley, “Exchange Rate Regimes: Is the Bipolar View Correct?” International Monetary Fund, January 2001.
INTERDEPENDENCE
Mundell (Monetary Theory, Ch. 16)
n-1 problem: with fixed exchange rates among n countries, 1
n
iB R= ∆∑
only n-1 of the targets Bi are independent. Mundells’ solution: assignment
of targets and instruments. Example: US vs. Europe targets: inflation and
BOP US sets m to control world inflation, Europe
uses m* to peg to US dollar, control BOP, converge at point A. Equivalent
n-1 story available for exchange rates, Europe controls e, US controls π.
* *,m m B m mπ = + = −
Monetary Conflict
0 1 2 30
23 m−
m
m
m*
m
B* N
A
B
Alternative analysis of conflict over inconsistent targets (Hamada, 1985).
Given preferences for each country, suppose US targets B<0 and Europe
targets B*<0 . Then US wants m*<m and Europe wants m*>m. Nash-
Cournot reaction functions lead to excess money growth at point N.
Cooperation could lead to improved outcome for both at point A on
contract curve BB.
140
Canzoneri and Henderson Analysis of Exchange Rate Policy
2 2
* *
2 2
*
(1 ) , is a negative productivity shock
(1 )( )
( ) &Let , ,
( )
(1 ) ( )
e e
y n x xw p n xm p yp m y m n xm p n n x n w p x x m w nMin En E m w w m n m mz e p p y y z q p z
Max n k q
q p z m n x y y
m
αα
αα
δ β
σββ αδ
= − −− = − −− == − = − − +− = − − = + − + − ⇒ − =
= − ⇒ = = −
= + − − = = +
Ω = − − −
= + = − − + + −
= * *
2 2
* *
12
(1 )( ) (1 )( ) (1 )( ) ( ) ( )
( )2 ( ) 2 ( ) 0
( ) and ,
Let or Then
( ) ( )
e e
e
em
e e e e em
e e
m
m m x n n m m m x m m m m
Max m m k qm m k q
E k q q m m k m k
m m m m m m
m k k m
βα α α ε εδ
σ
σ α εσ σσ α ε
α ε α εδ δ
σσ δ α ε δα ε
− − − + + − − = − − − + + − − −
Ω = − − − −
Ω = − − − − + =
Ω = − + = ⇒ = =+ +
− = = +
− Ω = − + + ++
*e e
*
2 *
* ** *
2 2
*
(1 ) 0
( ) ( ) ( ) Find Nash-Cournot reaction function as
( ): , slope 1, : slope 1( ) ( )
Joint solution ,(
m x m m
m x m
m mR m m x Rm m
m m x
α δ εδ εδ
σ α ε δ α ε ε α ε δ
ε α ε α ε δ δδ δδ δσ α ε σ α ε
α εδ δσ α ε
− − + + − = + + = − + + +
+ += − > <
+ + + +
+= = −Φ Φ =
+ +
*
1
2 2
*
* *2 2
2*
( )1) ( )
Finding focal point : 0 as above and 0
(1 ) 0( )( ) and ( ) ( )
( ): ,( )
optm m
e
opt
U q
q m m m x m m
m m x k m m x
xU m k m k
ε α εσ α ε
ε
δ α δ εδ εδσ ε α ε α εα ε δ εδ δ δ
α ε σ α ε σ α ε
σ α εδ δε α ε σ
− +− + +
Ω = Ω = = ⇒
= + − − + + − =+ +
+ = − − = − ⇒+ + + + +
+ += = + +
0, if 0x kσ
= =
141
Symmetric Inflationary Shockm*
4 2 0 2 45
0
5
10
Home Reaction RForeign Reaction R*45 degree lineaxis
0
m
R
U C
U* R*
N
Fixed exchange rate requires *m mδ δ= on 45 degree line, imposes
cooperative solution, avoids excessively contractionary monetary policy at
point N.
Asymmetric shock u causes shift away from domestic goods onto foreign
goods. * *
*2 2
*
*2 2
*2
Let 0 so 0( ):( ) ( )
since shock is asymmetric, set so
( )1+ ( ) ( )
0( ) ( )
e ey y z u k m m
R m m
m m
m u
m m
δε α ε α εδ δ
σ σ ε δ σ σ ε
δ δ
ε α ε α εδσ σ ε δ σ σ ε
α εδ δδ σ σ ε ε α ε
− = − = = =+ +
= ++ + + +
= −
+ += ⇒ + + + +
+= =
+ + + +
u
− >
Note change in exchange rate required in response to asymmetric shock.
142
Asymmetric Shock
4 2 0 2 410
5
0
5
Home Reaction RForeign Reaction R*45 degree lineaxis
0
m*
m 1−:= m
R
R*
Credibility Effect of Currency Union
Closed economy 0 assuming no shocks
Flexible rate open economy
q m k
q k
σεασ
ε α
= ⇒ = =
=+
Inflationary effect of depreciation acts to discipline monetary policy.
Suppose that German k* < Italian k. For Italy, joining EMS with * *q kσα
=
will be a gain if and only if *
**
k kk kk
σ σ εα ε α α
−< ⇔ <
+,
incentive to depreciate (loss of discipline) is less than credibility gap.
0 2 40
2
4
6
8
GermanyItaly
Inflation Bias k>0
q
k
k*
k
143
Sachs & McKibben Static Model – includes UIP and IS curve, sticky prices
Home Foreign * * * * *
* * * *
* * * *
* *0
* * *
** 0
(1) (1 )(2) ( ) (2 ) ( )(3) (1 )( ) (3 ) (1 )( )Assume ,
(2) (2 ) ( ) / 2 , substitute in (1) + (1 )2
/ /(1
c c
m p q i m p q iq e p p i q e p p ip p p e p p p e
p p p i i
i q qpm mq q
φ β φ β
δ σ δ σ
α α α α
σ
φ β σ φ β σ
− = − − = −
= + − − = − + − −
= + − + = + − −
= = =
+ ⇒ = − +
++ = −
+ +
*
* * * *
* * **
* * *12 1 2 1 2 0
1 2
2 2 *0
) (1 ) ( ),substitute in (2) - (2 )
,2 2
(4) ( ) ( ) ( )
2 ,(2 2 ) (2 2 )
1( ) , ( ),2
Noncooperative Equ
c c
m m q qq q m m m me q q
q q q q q m m p
MinU q p p p m m
φ
δ δφ φ
σφ β βφ σφ β φ σφ β
αµ γ γδφ
− ⇒ − = −
− − −= = − =
= + + − = Ω −Ω − Ω −Ω +
Ω = Ω =+ +
−= + = + − =
* *1 2 1 2 0 1 0
2* 1 2
1 2 0 1 2 21
* * 1 1 20 0
1 1 2
0
ilibrium
0
(5) ( ) ( ) 0
Reaction function , 1
( )similarly for R ,solve jointly for
( )
,
cc
c
q pq pm m
m m p p m m
m m p
m m p p
p p
µ
µ γ γ
µγµγ
µγ
∂ ∂ + = ∂ ∂ Ω −Ω − Ω −Ω Ω + + − =
Ω Ω += Γ + Γ Γ = <
Ω +Ω Ω −Ω −
= = <Ω Ω −Ω
⇒ =
01
*
1 2 1 2 1 2 0
*0
0
Cooperative Equilibrium, take account of
, 0 ( ) ( )
, 0
c
q p
m mq p m pm mm m p q
µγ= − <
Ω
=
∂ ∂= Ω −Ω = ⇒ Ω −Ω = Ω −Ω
∂ ∂= = =
144
Symmetric Inflationary Shockm*
4 2 0 2 45
0
5
10
Home Reaction R
Foreign Reaction R*45 degree lineaxis
0
m
R
R*
U
U* C
N
145
Dynamic Model (McKibbin & Sachs, Ch. 7)
* * *
* *
1*
1* * *
1 1
(1) (1 ) ( ) 2
(2) ( ) (2 ) 2(3)
(4)
(5) (3 ) ( )
(6) (1 ) substitute (2 ) (3 ) into (1 )
(7)
t t t t
t t t t t
t t t t t
t t t t t
t t tc c
t t t
m p q i m m p p q q r
q e p p r q q rr i p p
i i e e
p w q p p w w q q
w p p
p
φ β φ β
δ σ σ
θ θ
ζ ζ
+
+
+ +
′− = − + = + + + −
′= + − − + = −= − +
= + −
′= + + = + + +
′ ′ ′= + − + ⇒* *
* *
* ** * *
1
* * * *
* *1 2 1 2
( ) ( )(1 )( ) (4 )/
( ) ((8) (1) (1 )&(5) (5 )
1 ( ) ( ) ( ) ( )2
(9) ( ) ( ), where 1/ 1/( / )
solv
ct t t t
c c ct t t
m m w wp p e q q
m m w wp p q q
q m m w w m m w w
q m w m w
α αθ φ β σ
πθ φ
θ φ
β β β β θ φ β
−
+ − +′= + − + + =+ +
− − −= − − − ⇒ − =
+
Θ= + − + + − − − Θ + ∴ = − + − + = Θ = + +
*
* *1 2 1 1 2
2 20
0
0
e (2)-(2 ) for and substitute into (7) and then (8) to get(10) ( ) ( ) where /
Welfare (1 ) ( )
Noncooperative Equilibrium ( ) 0
in equili
c ct
st s t s
s
T T
ew m w m w p
Max q q
qq qm m
π γ γ γ γ θ
η µπ
πµπ
−
∞−
+ +=
= + − + − − + = Θ
+ − +
∂ ∂− + =
∂ ∂
∑
[ ] [[ ]
* *
1 2 1 2 0 1 1 1 2 1 2
0 1 1 1
1 1 1 1 1 1 0 1 1
1 1
1 1
brium, , , using (9) and (10)( ) ( ) ( ) ( )
0
( ) ( )
1
T T T T
cT T T T T T
cT T T T
T T
m m w wm w q w m w
m w q w m w p
m w w q p
m w
β β β β β µγ γ γ γ γ
β µγ θ θ
β θµγ β µγ θ µγ β µγ
µγ ββ µγ θ
−
−
= =
+ − + − + + + − +
− −Θ + Θ + − −Θ = + = + − Θ + Θ + Θ
Θ Θ= − + +
[ ]
10 1
1 1 1 1
11 1 1 0 0
1
If with rational expectations 1in (6) then solution is
( ) , 0
cT
c
c c cT T T T
q p
m w p
p p q q q
µγβ µγ θ β µγ θ
ζ
βµγ β π
µγ
−
−
Θ+
+ +
= = =
Θ − = Θ ⇒ = =
] 0T =
)
σ
146
1 2 1 2
10
1
1 2 1 11 1
1 1rd
Cooperative equilibrium 1/ , /
1 1Solution is , 0
( )(1 ) 1But or 2
if (Rogoff - due to 3 party wage
c Noncoop CoopT T
Noncoop Coop
qm m
q q
πβ β γ γ θ
βπ π π
θφ µβ β α γ β
γ θβ θδ β γ θ
π π φ µ
∂ ∂= + = Θ = + = Θ
∂ ∂
= = ∴ >< ⇔ ><
− −= + ⇒ > <
γ θφ
∴ < <
0 01 1 1 1
0 02 2
1
1
setters)But if wage setters look backward ( 0),
1Noncooperative ,1 / 1 /
1Cooperative ,1 1
if which it is.
c
c
Noncoop Coop
q q q
q q q
ζθπ
θµγ β θµγ βθπθ µ θ µ
γπ π θ
β
=
= =+ +
= =+ +
> >
Policy Simulations with McKibbin-Sachs Model
Social Welfare Function Weights
Employment Inflation Govt. Deficit Current A/CUS .4 .8 .3 .1 Japan .4 .8 .8 .4 Germany .3 1.2 .2 .1 Global Disinflation – early 1980’s
Noncooperative Cooperative % Difference US -3.08 -2.33 24.35 Japan -0.67 -0.60 10.45 Germany -1.26 -0.88 30.16 Rest of OECD -3.69 -3.53 4.34 Rest of EMS -0.63 -0.49 22.22 LDC’s -36.10 -5.52 84.71
Note large welfare gains, especially for LDC’s because of lower interest
rates from less restrictive monetary policies.
147
Trade Balance Adjustment – Fiscal Changes with Monetary Policy to
Minimize Loss
Year US Fiscal ∆ (%GDP) Ger. & Jap. Fiscal ∆ 1 -0.5 +0.5 2 -1.0 +1.0 3 -1.5 +1.5 4 -2.0 +1.5 5 -2.5 +1.5
Welfare losses are small for all groups, no difference between Cooperative
and Noncooperative solutions.
148
Monetary Politics of the ECB (Alesina & Grilli, in Canzoneri, et al,
Establishing a Central Bank, 1992) A central bank without a political union
will choose a different policy from national policies chosen separately.
First, consider behavior of “Europe” as a unit: 2 2
22
2
2 212
ECB ( ) , 0
subject to 0
( ) 0
1Biased ,1 1
1vs."Optimal" ,1 1
(1 )Voting on preference parameter
( )
Median voter pr
e
e
x
j j
E b x x x
x Ex
b x
bbx xb b
b xb b
bb
E b x x
ε
π
π π ε
π π π επ
π ε ε
π ε ε
σσ
π
12 Ω = + − >
= − + =∂Ω
= + − + − =∂
= − =+ +
= − =+ +
=+
Ω = + − 2 21
2
2 2
222 2 2 2 2
2 3 3 3
2
efers action according to : ( )
1 12 1 1
( )(1 ) (1 ) (1 ) (1 )
Optimal 0 , 0, 0
m m
b
m
b
m mm
mm
E b x x
bE bx b xb b
b b bbx bx b bb b b b b
db dbb b bd db
Min
Min
εε ε ε
ε
π
ε ε
σσ σ σ
σ
Ω + −
− + − + + ∂Ω
= + − − = − − =∂ + + + +
∋ < < > >
0
Median voter prefers a “conservative” central banker.
149
ECB without Political Union:
2 2
22
, Outputs differ, but
National welfare functions ( )
1ECB policy (*) ( )2 1 1
1National policy would be ,1 1
ei i i
ii i i
iECB i i i
ii i i i i i
i i
y
E y y
b bE bx yb b
y y
π π µ π π
π β
ε β µ ε
βπ β µ µ
β β
12
= − + ≡
Ω = + − ⇒ Ω = − + − − + +
= − =+ +
2 2
222 2 2 2 2
1 12 1 1
Difference between ECB and National policies (if )
1 ( ) (1 ) 22 1 1 1 1
i iN i i i i i i
i i
i
i i i iECB N i i i
i i
E y y
x y
b bx bb bε µ εµ
ββ µ β µ
β β
β ββ β σ σ β σ
β β
⇒
Ω = − + − + +
=
Ω −Ω = − + + − − − + + + +
22
2 2 2
22 2 2 2
22 2
Political Differences only: , ( 0, )
1 ( ) (1 ) 0 if2 1 1
Economic Differences only: ( )
12 1
i
i i iECB N i i i
i
i
i iECB N
b
bx b bb
b
bb
µ
µ ε εµ
ε µ
σ
β µ σ σ σ σ
ββ σ β β
β
β
σ σ
≠ = = = =
Ω −Ω = − + − + < < + +
=
Ω −Ω = ++
( )
( )
( )
2 22 2
22 2 2
2
2
1(i) high correlation: 1, 02 1
1(ii) low correlation 1, 1 02 1
Voting on Governors of ECB, choose to minimize (*)
1
i
i ii ECB N
i ii ECB N i
bb
bb
b
bx
ε µ
ε µ ε µ
ε µ ε
ρ σ σ
ρ σ σ σ σ
ρ σ σ σ ρ
−
= ≠ Ω −Ω = − > +
< = Ω −Ω = − > +
+ +( ) 23 2 0 0, 0
(1 ) (1 )i
ii
b db dbd db bε εµ
µ
ββ σ σ
σ ρ− = ⇒ > >
+ +
if i iLoss in national welfare due to ECB depends on political and economic differences. Since ECB N ib βΩ < Ω < , credibility gain from political differences. But if ε µσ σ>< , ECB stabilizes either too much or too little.
, so there is a loss due to asymmetric shocks. if 1i iECB N iρΩ > Ω <
150
Transactions Costs and Vehicle Currencies (Black, JIMF, 1991)
Model of Bid-Ask Spreads – based on economies of scale, zero profit for
bank dealers
( ) ( )( ) ( )
( ) ( )
Liquidity Traders Buy ,Sell Dealers Sell at ,Buy at
Speculators buy ,sell
Market equilibrium , market rate, expected rate
Dealer's profit -
d s a b
s d
d a s b
Q Q P P
a P P b P P
Q b P P Q a P P P P
Q P P Q P Pπ
− −
+ − = + − = =
= + − ( )( ) ( )
( ) ( )( )
2
2
+
Expected profit ,
Bid-ask spread
s d b d a b
s d p
p
Q Q P P Q P P
Cov Q Q P P Qt a b Qt
a bt
Q
π σ
σ
= − − −
= − − + = − + +
+=
Estimated on panel data for 7 major currencies vs. $, 1980,83,86,89
20.023 0.000605 0.038 0.52
(2.66) (4.56) (2.58)
ppt R
Qσ
σ= + + =
P
aP ( )a b P P( )+ −
bP
d sQ Q−
151
Model of Vehicle Currency Use – direct trade transactions between
currencies i,j can be mediated through vehicle currency n. Fraction
mediated is s.
( ) ( ) ( )
( ) ( )
( ),
1 1
Transaction costs between ( , ) ,
Direct exchange
,1 1
1
1
1 1
( )
ij ij in nj
ij
ij inij in
ij ijij
ij ij
inin
in
in ni ini
ij iji j n
inin ni
i j T t t t t
U u
u u sq q
s sa b a b s
tq u
a b st
u su u t
u t
s su u
s
σ σ
σ
τ
σ
τ φ
≠
− −
= > +
=
+= =
+ ++ + +
= =
+ +=
+
+=
+ ++
= =
∑∑
( )( )
max,
, 0, 0, (
( ), 0
, 0 1
10
i
iji j n
s
s s s
s iffs
0)φ φ τ φσ
θ τ θ
λ θ φ λ
λθφ λ θ φ
≠
′ ′′< > =
′= <
= − < < ∂ ′ ′ ′= − < < ′∂
∑
∑
τ
s* 1-un s
τmax
τ*
152
Currency area reduces σij, raises σnj, so tij falls relative to tin, τ = φ(s)
shifts up, s* falls.
Communication costs or imperfect competition imply cij > 1 in
( ) ij ijij
ij
a b ct
qσ+
= , so falling costs in non-vehicle currencies or increased
competition shifts φ(s) shifts up, s* falls.
Recent study by Hartmann confirms these findings.
153
International Monetary System
Arrangements for a payments system among countries with different
currencies to promote international trade and investmentvia
convertibility. Requires: (1) vehicle currencies and convertible reserve
assets, (2) exchange rate arrangements – pegged or floating, (3)
adjustment mechanisms – to promote external balance, (4) financing –
access to reserve assets to avoid excessive adjustment.
Demand for Reserve Assets – opportunity cost of holding asset
r = MPK – i* vs. reduced need for adjustment (Heller, Hamada-Ueda,
Kelley-Clark)
Heller – assumes constant marginal cost of adjustment, postpone
adjustment to the last
minute.
( )
12
/12
/
*
surplus binomial with step size with probability .
Given initial , probability of exhaustion in / steps
1 11Cost of adjustment so expected cost = marginal cost of holding2
R h
R h
R h
R R h
rm m
R
∆ ±
=
= = =
=
∼
log ( ) log( )log (0.5) 0.69
rm rm hh = −
Ignores all other than straight-line paths. Hamada-Ueda find
probability of exhaustion ( )1 1
22 1
Rh
Rh
> −
Minimize expected cost
over entire path ( )*1 11
2 2 1
rR R hR rmm h
+ ⇒ = +
−
154
Kelley-Clark assume increasing marginal cost of adjustment due to a
welfare function that depends on mean and variance of income, so
partial adjustment makes more sense. Analysis shows the choice
between adjustment and financing.
( ) ( )
( )
( ) ( )
( )
( )
* 2
22
*2 *2
12
*0
1 2
Partial adjustment , 0,
2
Tcebychev inequality 02 2 2
Income variability2
Mean income
Welfare function , , 0, 0
u
uR
uR
uRy
y
R R R u u N
P RR R
m m
Ey Y rR
MaxU Ey U U
γ σ
σσ
γ γ
σσγ γ
γσγσσ
γ γ
σ
∆ = − +
⇒ =−
≥ = =−
= = −
= −
> <
∼
Ey
U lower r
σy R*
lower P(R>0)
γ
Lower opportunity cost r = MPK – i* implies higher R*, lower γ.
Lower P(R>0) implies higher R* and γ.
Expectation that floating rates would reduced demand for reserves was
disappointed, since “fear of floating” and “dangers of pegging” plus
increased capital mobility have raised demand for reserve assets.
155
Seigniorage – if marginal cost of issuance of reserve asset is ε, then
seigniorage is MPK – i*- ε.
MPK
MPK – i*
S MPLiq+i*
ε MPLiq
Miller & Williamson, “Analysis of Alternative Regimes” (EER, 1988)
Alternative Regimes:
Floating Rates Pegged Rates Managed Rates Symmetrical Monetary Growth
Targets (73-85) Gold Standard Louvre Target
Zones (85-89) McKinnon* Nominal Income
Targets Bretton Woods Williamson Target Zones**
Hegemonic Dollar Standard (68-73)
EMS (79-93)
*McKinnon: Global monetary growth targeted to π = 0, national
monetary policies targeted to peg exchange rates.
**Williamson Target Zones: Global monetary growth targeted to
Nominal Income target, national monetary policies and central bank
intervention aimed at real exchange rate target zones.
156
Model Home Foreign * * * * *
* * * *
* * * *
*
* * * * *
LM
IS
PC
UIP Arbitrage + FadFad w/ mean regression
, , ,
m m
y y
p p
m p ky i m p ky iy Er c s y y Er c s y
Dp y Dp y
EDe i i EDfDf f
r i Dp r i Dp Er i y Er i
λ ε λ ε*γ δ η ε γ δ η
φ π ε φ π ε
ψ ω
φ π
− = − + − = − +
= − + + + + = − − + + +
= + + = + +
= − += − +
= − = − = − − = −
( ) ( )
ε
( )( )
* *
* 2
*** *
1
, fiscal policy, 0, , 0,
ˆDefine , , ,2 2
Global economyLM
IS
PC
Differences
m ma m d m m m
a a a a m a a a m a
a a a a a a y
a a a p
d
y
c e p p s N N
y yy y y y
m p ky i i p ky m
y i y s yDp y
m p
ε ω
φ π
ε σ ω σ
ε εε ε
λ ε λ ε
γ φ π η ε
φ π ε
−
−
= + − =
++= = = − = −
− = − + ⇒ = − + −
= − − − + + +
= + +
−
∼ ∼
ˆˆ2
ˆ
d d d m
d d d d y
d d d p
d
ky iy Er c s yDp yEDe i f
λ εγ δ η ε
φ π ε
ψ
= − += − + + − +
= + +
= −
2
ε ε
Global solution with given monetary targets ma growing at rate µa with
πa = µa , substitute LM into IS:
( )1 1 1 1
1 1 1
22 2 2 2
1 , 1
Let 0, fixed money supply, neutral fiscal pol.
12 m y p
a a a a a m y aa
a a a p a a a
a a m y p sa a a a
pa ss a
y p m s k
Dp y m s
Dp p
ε ε ε
γλ γλ γµ γλ ε ε γλ φγ η
φ µ ε µ
φγλ φγλ φ φγλε ε ε ρ
φσ ρ σ σ σρ
− − − −
− − −
= − + + + − + ∆ = + − −∆= + + = = =
= − − + + ⇒ = −∆ ∆ ∆ ∆
= + + ∆
2
157
( )
( )
0
2 2 ( ) 2
02 2
2 2 2 ( ) 2 2
0
1 11 1
Solution for Variance:
( )
1lim lim2 2
National Differences: 2 / , 1
McKinnon Rule: with
t a t s
t a t s
att a t sx t t
s
a M a
Dx axdt dz x t e dz
x e ds
eEx e dsa a
k
i p
σ σ
σ
σσ σ σ
ρ φ γλ δθ γλ φγ η
β
−
−
−
→∞ →∞
− −
= + ⇒ =
=
−= = = =
−
= − + ∆ ∆ = + − +
=
∫∫
∫
( )
1 2
1 2
s 2 21
3 3
, 0 in LM and omit
Williamson Rule: , 1, ,omit
McKinnon: 2 / , 1and change to
Williamson: / , 1Floating Rates with National Monetary Tar
m
m
M
a W a a W
ss
k
i p y kε
ε
β λ σ
β β λ σ
ρ φδ φγ ηρ
ρ φσ σ η
−
−
= =
= + = =
= − ∆ ∆ = − + ∆ = − ∆ ∆ = + +
( ) ( )
* * * *
*
gets:ˆLet , ,
,ˆˆ2 0 0
1 11 2 0 0 1 0 0ˆ0 0 0 0 0 0
d d d p
d d d
m
d d y
d
p
m p m p D y
Dc De Dp Dp EDc Ei f Ey
DEDc k cDf f
φ ε
ψ φ µε
φγ φλδ φγ φλ φγλ εη δ φλ ψ λ η µ
ψ εω
= − = − = − ⇒ = − −
= + − = − − −
−∆ = + − −∆ + + ∆ ∆ −∆ ∆
( ) s1 0, 0 two stable roots: ,dk sγ λ φγ η ρ ψ
∆ = − − − + < = ⇒ −If ψ = 0, saddle path is SS. If -ψ = ρs, trajectory with fads is TT.
A fad which raises the value of the currency (lower c), reduces
competitiveness and slows adjustment to origin (c is below SS). A fad
which lowers the value of the currency (higher c), raises competitiveness
and speeds adjustment to origin (c is above SS).
158
c T
S
d
S
T
McKinnon and Williamson proposals change the speed of adjustment
and 2pσ . Empirical estimates based on standard parameter values:
Supply Demand shocks shocks Averages: ∆ sρ 2
pσ 2yσ 2
pσ 2yσ
Money or Nominal Income Target 0.90 -0.14 3.60 0.28 1.11 1.32
Price Level Target 0.65 -0.19 2.60 0.38 1.54 2.59
Differences:
Floating w/ Money Targets 1.10 -0.54 0.93 1.10 0.20 1.10
McKinnon: Fixed Rates, M Targets 0.85 -0.59 0.85 1.20 0.30 1.80
Williamson: Fixed Real Rates, PY 1.60 -0.16 3.20 0.30 0.30 0.40
159
Obstfeld & Rogoff Stochastic Model “Global Implications of National
Monetary Rules” (QJE May, 2002) – Individuals maximize
where labor is used in production of Nontraded goods and Home traded
goods. Goods produced use imperfectly substitutable labor
Firm i’s demand for use of labor of
type j is K in the utility function is a
country-wide productivity shock. Consumption is 1 / (1 )T NC C C 1γ γ γ γγ γ−= −−
F
with constant shares for traded and nontraded
goods and The optimal preset money wage is 1/ 2 1/ 22T HC C C=
, a markup over the expected marginal
disutility of work. Price markups are the same in both countries
Real expenditure denominated in traded
goods is and since we
have
Assume the (log) shocks are jointly normal, with identical
means and variances for the productivity shocks and let
160
Then the (log) terms of trade are
Note that
weκσ is affected by the monetary policy rule and so affects labor effort.
The expected level of expenditure in terms of tradables is
ω and λ are constants
depending on the moments of κ and κ*. Since w and w* are
predetermined, O&R find the effects of shocks on z and e, through m
and m*. The innovations to spending and the exchange rate are then
In the case of log utility
with And foreign
expected utility is
Cooperative monetary policy would be chosen to maximize
by choosing policy rules
161
where carets over the variables denote innovations
and
Under flexible wages with log utility, monetary policy is irrelevant and
if ρ = 1.
Under sticky wages with log utility
( ) ( )
2 22 2
2 2* * 2 2
11 1 1 22 2 8 2 2
11 1 1 22 2 8 2 2
w d
w d w d
w d
w d w
z e z e ze e z
z e z e ze e
EU EU
EU EU
κ κκ κ κ κ
κ κκ κ κ κ
σ σ γλ σ σ σ σ σ σ σ
σ σ ν γλ σ σ σ σ σ σ σ
+ −= − + − − − − − + +
+ −= − + − − − − + + +
d z
Note that 0weκσ > raises demand for Home output when disutility of
work is high, thus lowering Home utility (and raising Foreign utility).
O&R show that optimal cooperative monetary policies under sticky
prices and mimic the flexible price
equilibrium. With log utility, there are no gains from cooperation and
the optimal policy is the same either with or without cooperation. If ρ is
not equal to one, there are (small) gains to cooperation.
162
Canzoneri, Cumby, & Diba, “The Need for International Policy
Coordination” (2004) point out some restrictive conditions in the O&R
model that limit the applicability of its conclusions:
1. balanced current account
2. constant expenditure shares in consumption
3. log utility of money
4. No differential productivity shocks in traded and nontraded
goods.
The exchange rate completely insulates the economy from any foreign
shocks, so that cooperative and non-cooperative equilibria coincide.
Changes in any of the four assumptions remove the insulation property
and leads to tradeoffs between inflation and output that provide ample
room for differences between cooperative and non-cooperative
equilibria. In particular, assume asymmetry in productivity shocks to
sectors producing tradable goods for domestic consumption (D) and
export (E).
163
164
International Monetary Cooperation Clarida, Gali, & Gertler, (JME, 2002)
Nash Non-Cooperative Equilibrium: Fiscal authority chooses subsidy rate τ to satisfy
(1 )(1 )(1 )(1 ) 1w pτ μ μ γ− + + − = where μw is the wage markup over the marginal disutility of labor and μp is the price markup over marginal cost and 1-γ is the share of home goods in consumption. The central bank’s objective function is
220
0
(1 )2
H tt t
t
W Eγ β π α∞
=
− Λ y⎡ ⎤≡ − +⎢ ⎥⎣ ⎦∑
subject to 1t t t tE ty uπ β π λ+= + + ;
it chooses t and ty π each period as t ty tλ π ξπα
= − = − which leads to
and ρ is the autocorrelation in the shocks. And similarly for the foreign economy. Combining this with the IS curve
1 and where [(1 ) ] 0t t t tu y uπ ψ ξψ ψ βρ λξ −= = − = − + >
( )11 1t t t t t t ty E y r E rrσ π−+ += − − −
yields an interest rate rule 1
1 with 1 (1 ) 1t t t tr rr Eϑ π ϑ ξσ ρ ρ −+= + = + − >
Same for the other country. They show that if γ = ½ , the terms of trade * *( ) (t t t t )ts u u a aωξψ= − − + −
depends on the price shocks and the productivity shocks. The exchange rate will also respond as
* * *1 1 ( ) (t t t t t t t t t t t te e s e u u a a u uπ π ωξψ ψ− −= + Δ + − = − Δ − Δ + Δ − Δ + − *)
which implies appreciation in response to a price shock, since 1ωξ > . Cooperative Equilibrium: Fiscal authorities in each country set (1 )(1 )(1 ) 1w pτ μ μ− + + = and joint maximization of world welfare leads to policy rules
*0t ty κ
tξ π πκ
⎛ ⎞= − +⎜ ⎟⎝ ⎠
and similarly for the other country, where 0(1 ) , ( 1)κ σ γ γ φ κ γ σ≡ − + + ≡ − Note the consideration of both countries’ inflation rates iff 1σ ≠ .
165
