'^^,
[ubrasoeb]
^
Digitized by the Internet Archive
in
2011 with funding from
Boston Library Consortium IVIember Libraries
http://www.archive.org/details/equilibriummodelOOcaba
DEVVE>
HB31
.M415
01-
Massachusetts Institute of Technology
Department of Economics
Working Paper Series
An
Equilibrium Model of "Global Imbalances"
and Low Interest Rates
Ricardo
J.
Caballero
Emmanuel
Farhi
Pierre-Olivier Gourinchas
Working Paper 06-02
January 14,2006
RoomE52-251
50 Memorial Drive
Cambridge,
This
MA 02142
paper can be downloaded without charge from the
Network Paper Collection at
Social Science Research
httsp://ssrn.com/abstract= 2 a9 5 87—
-
<^noo2
^'^'^fVM^^S^oE^'''''^
1_I
_BR ARIES
1
An
Equilibrium Model of "Global Imbalances"
and Low
Ricardo
J.
Interest Rates
Emmanuel
Caballero
Pierre-Olivier Gourinchas*
Farhi
This Draft: January 27, 2006
Abstract
Three of the most important recent
facts in global
macroeconomics
— the sustained
rise in
current account deficit, the stubborn decline in long run real rates, and the rise in the share of
in global
portfolio —
Instead, in this paper
appear as anomalies from the perspective of
we provide a model
the
US
US
assets
conventional wisdom and models.
that rationalizes these facts as an equilibrium outcome of two
observed forces: a) potential growth differentials
among
different regions of the world and, b) hetero-
geneity in these regions' capacity to generate financial assets from real investments. In extensions of the
ba.sic
model, we also generate exchange rate and FDI excess returns which are broadly consistent with
the recent trends in these variables. Unlike the conventional wisdom, in the absence of a large change in
(a) or (b),
our model does not augur any catastrophic event. More generally, the framework
enough to shed
light
JEL Codes: EO,
on a range of scenarios
F3, F4,
in
a global equilibrium environment.
deficits, capital flows, interest rates, global portfolios
growth and financial development asymmetries, exchange
•Respectively:
flexible
Gl
Keywords: Current account
We
is
MIT and NBER; MIT;
Berkeley and
NBER.
rates,
FDI, intermediation
and equilibrium,
rents.
E-mails: caball@mit.edu, efarhi@mit.edu, pog@berkeley.edu.
thank Daron Acemoglu, Olivier Blanchard, Mike Dooley, Francesco Giavazzi, Maury Obstfeld, Ivan Werning, and seminar
participants at Berkeley,
thank the
NSF
IMF, MIT, MIT-Central Banks Network and SCCIE
for financial support. First draft:
September 2005.
for their
comments. Caballero and Gourinchas
Introduction
1
Three
Fact
facts have
dominated the discussion
The US has run a
1:
in global
in recent times:
persistent current account deficit since the early 1990s, which has accelerated
dramatically since the late 1990s. Today,
illustrates this path, as a ratio of
it
World's
The
exceeds US$600 billions a year.
GDP
be apparent below, but
for reasons that will
macroeconomics
solid
dark
(this line also includes the deficits of the
it
is
line in
Figure 1(a)
U.K. and Australia,
overwhelmingly dominated by the U.S. pattern).
The
counterpart of these deficits has been driven by the surpluses in Japan and Continental Europe throughout the
period and, starting at the end of the 1990s, by the large surpluses in Asia ex-Japan, commodity producers,
and the turnaround
Fact 2:
The
of the current account deficits in
long run real interest rate has been steadily declining over the last decade, despite recent efforts
from central banks to
Fact
Conundrum"). See Figure
raise interest rates (the "Greenspan's
The importance
3:
most non-European emerging market economies.
of
amounts to over 17 percent
US
assets in global portfolios has increased
1(b).
throughout the period and now
of the rest of the world's financial wealth, which
is
equivalent to 43 percent of
their annual output. See Figure 1(c).
Despite extensive debates on the factors behind and sustainability of this environment, there are very few
formal structures to analyze these joint phenomena. The conventional view and their recent formalizations,
attempt mostly to explain (the
The
first
half of) fact
1,
largely ignore fact
2,
and take 3
as
an exogenous anomaly.
analysis about the future then consists of telling the story that follows once this "anomaly" goes away.
However, capital flows are primarily an asset market phenomenon and hence the paths of interest rates and
portfolios
must be made an
the current situation and
The main purpose
integral part of the analysis
how
it is
likely to get
of this paper
important side product, shed some
is
light
out of
to provide a
on the above
if
we
are to conjecture on
framework to analyze global equilibrium and, as an
The model
facts.
of different shocks on global capital flows, interest rates
1
into
it.^
is
fairly
and provides a simple asset-demand and (most importantly) -supply framework
the patterns in Figure
what got the world
and
We
portfolios.
standard
in its ingredients
to characterize the impact
use this model to show that
(together with observed exchange rate and gross flows patterns) can arise naturally
from observed growth and financial market shocks, which interact with heterogeneous degrees of financial
market development
We
U.K.)
US
the world.
divide the world into three groups:
([/);
'Recently,
for
in different regions of
The US (and
the EuroZone/Japan {E); and the rest {R).
some
of the debate in policy circles also has
The
latter include
began to highlight the
current account deficits. See especially Bernanke (2005) and
we have developed our framework.
"similar" economies such as Australia
IMF
(2005).
emerging markets,
oil
and the
producing
role of equilibrium in global capital
We
will revisit the "saving glut"
markets
view after
% of World GDP
1.5%
1990 1991
1992
1993 1934 1995 1996 1997 1998 1999 2000 2001
^— USA.
AuslralB,
UK -O-EU. Japan
2002 2003 2004
-^ROW
Current Account by Region (percent of world output)
(a)
1992
1990
1994
1996
(b)
2D00
199S
-o- US-long
-*-worid-short real
World and US Real
2002
real
Interest Rates
pwzarn
45
40
3S
30
25
20
15
^-"^^™""°^
^_a
'm
:
Hi
^
It
III
^
10
5
1994
1996
1
^^Flnancial Wealth
(c)
Share of
US
Assets
in
-Output
Rest of the World's Output and Financial
Wealth
Figure
1:
Three Stylized
Professional Forecasters,
Facts.
(c)
Sources: (a)
WDI
World Development
Japan and Authors' calculations
(see appendix)
and Deutsche Bank,
Indicators,
Bureau
3
of
(b) International Financial Statistics
and Survey of
Economic Analysis, European Central Bank, Bank
of
countries,
U
and
E
and high saving newly industrialized economies, such as Hong-Kong, Singapore and Korea. Both
produce good quality financial instruments. R, on the other hand, has high growth potential but
has episodes when
cannot generate "enough" reliable savings instruments.^
it
we
In this world,
investigate the implication of a growth
We
asset markets in R.
capital flows toward
U
,
show that both shocks point
slowdown
same
in the
U
,
these are tenuous, as
t/'s
E
and, primarily, a collapse in
terms of generating a
direction, in
a decline in real interest rates, and an increase
global portfolios. Importantly, while there are natural forces that
in
in the
undo some
importance of
rise in
f/'s assets in
of the initial trade deficits in
current account never needs to turn into surplus and capital fiows indefinitely
toward U.
The key
Regions
U
feature of the
and
R coupled with
E
compete on
is
that
it
focuses on the regions' ability to supply financial assets to savers.
Region
asset production.
U and
E. More growth potential in
model productive assets are
U
(implicitly)
relax these assumptions in extensions. In the
main reason
is
FDI from U
to
first
financial assets. Thus, fast
E
than in
means that a
demand
R
The exchange
run by local agents and there
one we allow
U
we
for saving
for foreign direct
is
a single good.
rate patterns generated by the
There are several recent
to finance
expanded model
—
and anticipate a very limited and slow depreciation
articles related to the
Giavazzi and Sa (2005) analyzes
investment (FDI), whose
permanent trade
in R,
and
in the process
deficits.
US
in
response to the shocks highlighted above are
in particular,
U
appreciates vis a vis both,
R and E—
of f/'s exchange rate in the absence of further shocks.
U—E
analysis in our paper.
For instance, Blanchard,
external imbalances from the point of view of portfolio balance theory
Kouri (1982). Their approach takes world interest rates as given and focuses on the dual
exchange rate
We
allow for heterogeneous goods and discuss (real) exchange rate determination.
broadly consistent with those observed in the data
result
in
larger share of global saving
improves the financial quality of assets created from investments
In the second extension
relative
growth
transfering "corporate governance" standards from one country to the other. In this context
generate rents for U. Moreover, these rents allow
la
demands
t/.
In the basic
a
R
their inability to generate local store of value instruments increases their
instruments from
flows to
model
in allocating portfolios
demand through the terms
from exogenous increases
between imperfectly substitutable domestic and foreign assets and
of trade. In their model, the large recent
in U.S.
demand
for foreign
Their model predicts a substantial future depreciation of the
^See Caballero and Krishnamurthy (2006) for a model
generate reliable financial assets.
When
role of the
conglomerates, degree of "cronysm," and so on.
in
US
current account imbalances
in foreign
demand
for U.S. assets.
dollar since the exchange rate
is
the only
of bubbles in emerging markets as a result of their inability to
local bubbles crash, countries
could arise from a fundamental shock due to a change
goods and
US
need to seek store of value abroad. This pattern also
public perception of the soundness of the financial system and local
equilibrating variable
and current account
deficits
must be reversed. Obstfeld and Rogoff (2004) and (2005)
consider an adjustment process through the global reallocation of
demand
for
traded versus non traded and
domestic versus foreign goods. Their analysis takes as given that a current account reversal needs to occur
in
the US, as well as the levels of relative supply of traded and non-traded goods in each country. Because the
current account deficits represents a large share of traded output, they too, predict a large real depreciation
of the dollar. These papers differ from ours in terms of the shocks leading to the current "imbalances", our
emphasis on equilibrium
in global financial
markets and, most importantly, on the connection between this
equilibrium and the countries' ability to produce sound financial assets.
For the
Far hi and
U— E
part, the closest paper in terms of
Hammour
and low global
(forthcoming 2006),
interest rates.
opportunities in E.
ignores the role of
R
One
of the
who
asset supply,
in that
paper
is
is
triggered by a
in this
(forthcoming 2006) analyze an environment similar to that in Caballero et
US bubble
but
it
in
booms
in
U
investment
on the investment side of the problem and
which are central to our analysis
allocation of excess global savings to a
slowdown
Caballero,
is
present several models of speculative investments
mechanisms theydiscuss
However the emphasis
and
themes and some of the implications
al..
paper. Kraay and Ventura
Their emphasis
is
on the
does not connect capital flows to growth and
domestic financial markets fundamentals as we do here.
For the
U—R
part, Dooley, Folkerts- Landau
2006) have argued that the current pattern of
and Garber (2003) and Dooley and Garber (forthcoming
US
external imbalances does not represent a threat to the
global macroeconomic environment. Their "Bretton
flows
is
Woods
11" analysis states
that the structure of capital
optimal from the point of view of developing countries trying to maintain a competitive exchange
rate, to
develop a productive traded good sector, or to absorb large amounts of rural workers
sector.
Unlike theirs, our analysis emphasizes the role of private sector capital flows and argues that the
exchange rate
Section 2
is
is
in the industrial
mostly a sideshow.^
the core of the paper and presents the main model and mechanisms. Section 3 introduces a
foreign direct investment margin, while Section 4 analyzes exchange rate determination. Section 5 concludes
and
is
followed by several appendices.
''We do not deny the existence of large reserves accumulation by China and others. Nonetheless,
most of these reserves
First,
bonds
in
are indirectly held
by
their local private sectors
three observations.
a context with only limited capital account openness. Second, US gross flows are an order of magnitude larger than
official fiows
- rather than imputing Chinese reserves accumulation to financing the
equally well (or poorly) argue that they are financing
interventions was
more
we make
through (quasi-collateralized) low-return sterilization
most important
persistent trends.
at a time
when
FDI
the
US
current account
deficit,
one could
flows to emerging markets, including China. Third, the role of oflicial
US was
experiencing a temporary slowdown, while our analysis refers to
A
2
Model with
In this section
we develop a
model that endogenizes and captures the broad patterns of capital
stylized
and global
flows, interest rates
market
Explicit Asset Supply Constraints
portfolios
We
for global saving instruments.
shown
Figure
in
1.
The model
highlights the supply side of the
the world into three groups: [/-countries have deep financial
slice
markets and good growth conditions; S-countries have deep financial markets but (perhaps temporarily)
bad growth conditions;
finally, i?-countries
(perhaps temporarily) do not have deep financial markets but
have exceptional growth conditions.
we show
In this context
markets
in
R compound
growth conditions
in
R
that both the depressed growth conditions in
to generate large
and
exacerbate rather than
persistent capital fiows to
In the
we study
one,
first
U
global equilibrium in a world with
and has the dual
closest to the conventional analysis
and the depressed
financial
Moreover, the exceptional
.
offset this pattern."^
After a series of preliminaries explaining the essence of our framework,
parts.
E
U
role of
we
and
split
E
the argument into three
This
countries only.
is
the
showing the workings of our model and studying
the equilibrium impact of a persistent decline in £"s growth conditions, as experienced by Japan from the
early 1990s
and Continental Europe more
recently.
That
global interest rates almost indefinitely.
is,
This decline raises capital flows from
E
U
to
and lowers
the automatic rebalancing forces, regardless of the extent of
home-bias, are tenuous in the absence of a reversal
in
the factors that led to the original imbalances, namely
depressed growth conditions in E.
In the second part
of our model.
rates drop
We
we study
global equilibrium in a world with
show that
first
if
and capital flows from
U
R
to
U
permanently.
in financial
than
U—E
in the
R
countries only. This
is
the core
development
is
if
growth potential
in
R
is
In particular, long run rates decline by
deficits indefinitely.
That
is,
if
above that
more than
the initial
not undone, the automatic rebalancing forces are even more tenuous
world. This part primarily captures the events following the Asian and Russian crises, as
well as the fast growth
afterwards.
Moreover,
can finance very significant current account
asymmetry
and
R's capacity to generate reliable financial assets crashes, global interest
of the rest of the world, both effects are exacerbated.
short rates, and
U
It also
and (favorably) high commodity
prices experienced
by much of the
R
region shortly
captures some of the elements following the crash of the Japanese bubble in the early
1990s.
We
parts,
close this section
we show
by integrating the three regions. Aside from adding the
that the shock in
''Thus, the view that growth of
be a factor
has a larger (favorable) impact on
trading partners
is
in explaining the large capital flows to the
growing faster and who
those that
US
R
demand
is
assets
growing slower than the US.
grow
faster,
U
effects of the previous
than on E. The reason
on average similar to that of the US, so that
US,
If
is
misguided from our perspective.
those that compete with the
then both factors play in the same direction.
US
It
in asset
differential
is
two
that the
growth cannot
matters a great deal
who
is
production grow slower and
lower interest rates resulting from the asset markets collapse in
in the region
R has
a larger positive effect on asset values
with better growth prospects.
Preliminaries
2.1
A
2.1.1
closed
economy
Time
evolves continuously. Infinitesimal agents (traders) are born at a rate 9 per unit time and die at the
same
rate;
of (1
— S)Xt which they
population mass
is
save in
resources at the time of death.
that
is
its
entirety until they die (exit).
The term
(1
— 5)Xt
their
accumulated
should be interpreted as the share of national output
arbitrage, the instantaneous return from hoarding a unit of a tree,
Vj
is
SXt per unit time.
in local trees.
rtVt
ratio
all
vehicles are identical "trees" producing in aggregate a dividend of
Agents can save only
where
Agents consume
endowment
not capitalizable.
The only saving
By
constant and equal to one. At birth, agents receive a perishable
the value of the trees at time
t.
As
=
6Xt
rt, satisfies:
+ Vt
(1)
standard, the return on the tree equals the dividend price
is
5Xt/Vt plus the capital gain Vt/Vt.
Let
Wt denote the
(deaths),
savings accumulated by active agents at date
t.
Savings decrease with withdrawals
and increase with the endowment allocated to new generations and the return on accumulated
savings:
Wt
In equilibrium, savings
= -eWt +
(1
(3) into (1),
S)Xt +rtWt.
must be equal to the value of the
Wt =
Replacing
-
and the
Replacing this expression back into
trees:
Vt.
(3)
result into (2), yields a relation
Wt =
(1),
using
(3),
(2)
f.
we obtain an
between savings and production:^
(4)
expression for the instantaneous equilibrium
interest rate:
rt
^By Walras' Law,
noticing that
dWt corresponds
to
Xt
= ^+5e,
(5)
consumption, we can re-write this relation as a goods-market equiUbrium
condition:
eWt =
Xt.
Conditional on exogenous output Xt, the interest rate
of growth of financial wealth
rises
demand {W), and hence
We
and
it
rises
capitalizable
is
with 6 because this lowers financial wealth
assume that the
total
endowment
in the
the rate
lifts
the expected capital gains from holding a tree;
with 6 because this increases the share of income that
assets;®
with growth because the latter
rises
and hence
demand and hence
economy, Xt, grows at rate
g.
it
raises the
it
supply of
asset prices/
Hence
rt is
given by raut
where
=9 + 59.
Taut
A
2.1.2
now open
Let us
Open Economy
Small
Assumption
the (small) economy, which faces a given world interest rate,
1 g
<
r
<
g
r,
such that:
+9
Definition 1 (Trade Balance and Current Account): Let us denote the trade balance and current account
at time t as
The
TBt and CAt,
definition of the trade balance
the financial account and
To
respectively, with:
is
is
TBt
=
Xt-9Wt
CAt
=
Wt-Vt
standard.
The
current account
is
also standard. It
is
the dual of
defined as the increase in the economy's net asset demand.
find the steady state of this economy,
we
integrate (1) forward
and
(2)
backward:
Jo
^Given our particular parametrization, a
but
it is
rise in 5 also lowers asset
demand. This
effect reinforces
our asset supply mechanism
not robust to alternative parametrizations.
'^Note that (5) differs from the usual equation that
horizon consumption model.
would prevail
if
we were
to adopt the standard frictionless infinite
There, the interest would be determined entirely by the (asset)
demand
side:
only on consumption growth, the rate of time preference and the elasticity of intertemporal substitution.
parameterizes the supply of financial assets, would play no
model, a reduction in
consumption. That
i5
is,
role.
The reason
changes the relative importance of financial to
as
we reduce
6,
the drop in financial savings
is
human
it
would depend
Hence,
5,
which
that in the standard frictionless infinite horizon
wealth, without changing total wealth and hence
— the demand
for financial assets
— exactly
offsets the
drop in financial asset supply, leaving the interest rate unaffected. Thus, in order to introduce an equivalent role for supply
of financial assets in that model,
Our
we would have to introduce
preferences and demographic assumptions achieve the
collateral constraints
same more
efficiently.
and
link collateral to capitalizable income.
W _
X
l-i5
g+e-r
(Demand)
faut
W/X
Figure
Assumption
1
The Metzler diagram.
2:
implies that asymptotically
Xf
t->oo r
—
Wt
Xt t-oo g
Equation
(6)
is
just Gordon's formula.
the size of the economy,
It
a decreasing function of
is
equilibrium in a supply and
If r
<
cross at r
=
(6)
g
l-S
+ e-r
(7)'
^
shows that the asymptotic supply of
assets which, normalized by the size of the economy,
demand curve
V/X
,
demand diagram, a
Equation
r.
is
(7) describes the
an increasing function of
r.
variation on the Metzler diagram.
assets,
normalized by
asymptotic demand
for
Figure 2 represents the
The supply curve and
raut-
Taut
S
r
and domestic
asset supply exceeds
-
>
g
1-5
g+e-r
demand. Since along the balanced growth path Wt
= gWt
and
Vt
=
gVt,
the above inequality implies that the small country runs an asymptotic current account deficit (financed by
an asymptotic capital account surplus):
CAt
Xt
Note
[rant
t^<=o''\g
r-gj
+ e-r
also that, asymptotically, the trade balance
is
{g
The
in surplus:
+
e
-
-
r)
r)(r
-
g)'
(8)
lower rate of return on savings depresses
wealth accumulation and, eventually, consumption
TBt
Xt
raut
*-oo g
+
-
r
(9)
(
Importantly, however, this asymptotic trade surplus
liabilities
of the country, which
is
why
when
r
>
Conversely, note that
is
not enough to service the accumulated net external
the current account remains in deficit forever.
Taut, (8)
and
(9) still hold,
but now the economy runs an asymptotic
current account surplus.
We
can prove a stronger result that will be useful later on.
Lemma
Consider a path for the interest rate {rt}t>o such that limt_,oo
1
Xt t—'CO r —
g'
CAt
Xt
t^oo
"
[g
Xt
+6—
t->oo g
[Taut - r)
+ -r){r-
r with g
<
r
<
g
+ 6.
Then
r
TBt
-r
g+Q - r
Taut
Xt
g)'
=
ft
t-^oo
Proof. See the appendix.
2.2
A
World with Symmetric (and Developed) Financial Markets {A U — E
*
World)
Let us
now study
same setup
which
is
global equilibrium with two large regions,
common
in
V^
is
country
i
{U,E}.
Each
of
them
is
described by the
the value of country
at date
(10)
rt,
across both regions and satisfies:
i's
tree at time
=
and
5Xi
Let
t.
+
W^
V^
(10)
denote the savings accumulated by active agents
t:
Wi = ~ewi +
Adding
=
as in the closed economy, with an instantaneous return from hoarding a unit of either tree,
rtV^
where
i
(11) across
both regions,
(1
- 5)Xi + rtWl
(11)
yields:
nVt
=
Wt = -9Wt +
dXt
(1
-
+
Vt
(12)
S)Xt
+ rtWt
+ Vt^,
Xt
(13)
with
Wt =
From now
W^ + Wt^,
Vt
=
Vt^
= Xf+Xf.
on, the solution for global equilibrium proceeds exactly as in the closed
eWt
= Xt.
economy above, with
(14)
and
rt
Let us
now
specify the initial conditions
=
(15)
Y^+59.
and follow with our
10
first
shock.
Assumption
2 (Initial Conditions)
common
rate of growth,
Suppose now
Lemma
The world
i
=
0,
is initially
symmetric, with equal levels of XI and a constant
There are no (net) capital flows across the economies and
to both countries, g.
that, unexpectedly, at
the rate of growth of
2 (Continuity): At impact, r absorbs the shock while
Proof. At any point
It
:
follows that
in time,
Wt does not jump
conclude that Vj does not
jump
it
at
V
E
and
drops permanently to
W
remain unchanged.
must be true that
i
=
either:
:
Vq-
Wq- = Wo+ =
=
=
Vo+
Xq/Q. Since Wt
Xq/O. But
=
^
^
+69 <ro-=g +
Vt
must hold
absence of a decline
for this
to be consistent with the asset pricing equation, the growth slowdown in
ro+
=
E must
be
offset
at all times,
in
V
we
at impact
by a drop
in r:
5e
that reflects a decline in world output growth.*
While global wealth and capitalization values do not change
economies does.
On
one hand,
it
stands to reason that the lower growth in
rise since
both dividend streams are discounted at the
Wq /Wq'
rises or
home
not depends on the agents'
bias in these portfolios,
established fact of
home
Wq /Wq
common
Xf
implies that Vq' /Vq'
global interest rate.
initial portfolio allocations.
On
we assume an extreme form
our mechanisms more starkly.
home
bias,
is
some
Because the conventional view has taken the well
rises as well.
of
must
the other, whether
However, as long as there
bias as a key force bringing about rebalancing of portfolios,
well, as this isolates the contribution of
propositions
at impact, the allocation of these across
we
Moreover, for
shall
assume
clarity, in
it
as
the main
but then extend the simulations and figures to other
cases.
Assumption 3 (Home
Bias). Agents first satisfy their saving needs with local assets
and only hold foreign
assets once they run out of local assets.
This assumption implies that, at impact, local wealths' changes match the changes
in the value of local
trees one-for-one:
^0+
2
~
°+
2
^0+
2
~
'^°+
2
^According to the World Development Indicators, average output growth
the 1990s and 2.75% since 2000.
11
for
U,
E
and
R
was 3.41%
in
the 1980s, 2.77% in
These changes
in
wealth have a direct impact on consumption, which are reflected immediately in the trade
balance and current account.
Before describing these
effects, let
us digress momentarily. At times,
to note that the current account can also be written as the
sum
will
it
be convenient
of trade balance
for exposition
and net income from global
holdings:
Lemma
3 (Alternative Formulation of the Current Account)
= Xi-ewt+rt{a'^W^-oP/V,')
CAi
= TBi+rM''Vt^-c4''v;)
where
i
/
j, aj'-' is the
trees held by agents in
share of country j
country
's
trees held by agents in country
i,
aj'^ is the
share of country
i 's
j.
Proof. See the appendix.
Note that our current account definition excludes, as does national accounts, unexpected valuation
(unexpected capital gains and losses from international positions)
the only surprise takes place at date
this issue
when
0,
when agents
.
This
is
not a relevant issue for
are not holding international assets.
We
effects
now
since
shall return to
relevant.
Also note that since
both. Henceforth,
we
CAf + CA^' — 0,
we only need
shall describe the behavior of
one of the current accounts to characterize
to describe
CA^, with
the understanding that this concept describes
features of the global equilibrium rather than [/-specific features.
Finally,
without any substantive implication (see the Appendix
for the general case),
we make an
as-
sumption to narrow the asymptotic cases we need to analyze:
Assumiption 4 (Bounded Growth
Proposition
1
Decline): {g
—
g^)
<
(Persistent Current Account Deficits in
persistent decline in
E
's
rate of growth
from g
to
g^ <
(1
—
U ):
g,
5)9.
Under assumptions
turns
CAf
in deficit in the long run (although vanishing asymptotically relative to
Proof. At impact, we have
CA'^
For
t
>
0,
using
OWt
=
Xt and 9Vt
=
= TB^ = X^ -
eVo"+
<
Xt we have
CA'^
=
Wt"
-
Vi'
12
= Vf -
W^
1 to 4,
an unexpected and
into a deficit at impact
X^ ).
and remains
.
Prom equation
(15)
and g > g^ \\m.t^^rt
,
=
Lemma
r'^ut-
Vf
shows that
1
5
X^ *--
- 9"
r^ut
Wl
{1-5)
and
CAf
CAY
Finally,
it
follows immediately from g
The impact
effect of a decline in
down E's wealth one
for
E's consumption which
> g^
5^(rL-^f.,)
,
that
CA^ /X^
B's rate of growth
a decline in the value of E's assets which drags
in
not matched by a drop in E's current income. Thus E's trade balance, which
is
is
initial
to absorb this surplus by running a trade deficit.
results
vanishes asymptotically.
one given the extreme home bias assumption. This leads to an immediate drop
equal to the current account in the symmetric
which
is
<0.
from an increase
not stem from any increase
in [7's
in f/'s
equilibrium, goes into surplus. In equilibrium,
The
latter
achieved by an increase in
is
C/'s
U
has
consumption,
wealth following the appreciation of U's assets. This appreciation does
growth prospects, but from the
fall in
interest rates
brought about by E's
slowdown.
Suddenly
assets look relatively
L'''s
more
attractive,
and hence a share of E's saving begins to flow to
these assets. Over time, the return on these assets raises E's wealth and consumption (relative to output),
eventually overturning the initial trade surplus, and hence U'
s
trade
deficit.
However, U's eventual trade surpluses are never enough to service the accumulated net-foreign
in full,
is
and hence U's current account remains
in deficit forever.
a sustained accumulation of U's assets by E.
importance of
U
assets in E's portfolio rises until
The counterpart
This accumulation
is
g-9^
^
in the limit,
Of course,
this
E
continuously accumulates U's assets at a rate
g^
does not mean that our model violates the intertemporal approach to the current account.
Integrating forward the equation:
w^
we
to:
>0.
^
{{l-5)e-{g-g'^)){{g-gE)+5e)
Thus,
of this persistent deficit
very fast early on, as the relative
converges (asymptotically)
it
liabilities
-
v^"
= x^ -
ew}'
+ n{wi' -
V,")
find the usual expression:
/oo
{x^ -ew^)e-i't^-''^ds
/oo
13
In particular
/•OO
= W^+ -V^+ = -
TB^e-
I
J'o
''''^'dt.
Jo
Since the
surpluses
is
initial
net asset position
The trade balance
zero.
is
balanced in our basic scenario, the net present value of trade balance
TB^
is
initially in deficit
TBl^_TBl
t::^gE
xf
xf
and eventually turns
g-g^
+ e-r^^,
E due to
Importantly, however, increased net interest payments to
t/'s
accumulation of net foreign
exceed the trade balance surpluses and generate a chronic current account
We
can understand the asymptotic result
economy
in
and
Section 2.1,
its
Figure
2.
into surplus since:
deficit in
liabilities
U.
the proposition with reference to the simple small open
in
First, since in the long
U
run
dominates the global economy, the
equilibrium interest rate converges to the Autarky interest rate for U:
Thus
W^ /X^
the gap between
interest rate exceeds the
and
V^
new Autarky
r^o
=
jX^
is
g
+ Se.
.
However, note that the limit
asymptotically vanishing.
rate in E:
roo
=
+ Se >
9
means that the asymptotic gap between
+ Se =
g"
V^ jXf
Thus the asymptotic gap between Wf' /Xf and
this
=
Taut
W^ jXf
is
r^^t.
Moreover, by global equilibrium
strictly positive.
and V^^ jXf
is
strictly negative.
Let us now turn to a characterization of the entire path. Figure 3 portrays an example of the impact of
a growth slowdown
for
parameters calibrated to match some key aspects of the data.^ Our only goal here
to consolidate the insights from the proposition and to argue that the effects
significant.
We
do not attempt to match the exact paths
Still,
gradual and capital flows remain large
which are more robust to the absence
Panel
A
of Figure 3
shows that
V^
relative to
initial global portfolio to
loss.^°
More
V^
5%
.
costs.
would require additional
Absent
these, adjustments
note that even in this frictionless environment, adjustments are
many
years after the shock. Also note that the cumulative results,
of frictions, are large
C/'s
current
account/GDP
of output, which converge to zero only gradually.
shock lowers
describe are quantitatively
in the data, as that
smoothing mechanisms, such as gradual globalization, and other adjustment
are too large at impact and too fast.
we
is
Panel
Since in order to
(rather than the
centrally, the large initial current
0%
B
exhibits large initial deficits of 17 percent
reports C/'s net external position.
match Figure
1(c),
in the proposition),
we
U
calibrated U's
The growth
assets share in
suffers a small initial valuation
account deficits worsen rapidly U's net foreign asset position
^See the appendix for a discussion of the calibration. The drop in E's growth rate is about one percent.
^"That is, the initial jump at t = 0+ reflects the unexpected valuation effect from C/'s holdings of E's asset. Recall that our
convention, similar to
NIPA
or
BoP
accounting, excludes these valuation effects from the current account.
14
Panel
Panel
-2
2
4
6
A:
Panel
Interest Rote
C:
8
CA/Output
10
12
16
14
18
20
Panel
24
22
Net Foreign Assets/Output
B:
D:
Global Portfolio Share
26
years
Figure
from zero to -75 percent
in
A
g^
Collapse in
15 years. Eventually, the net foreign asset position converges to zero (relative to
domestic output), but panel
B
illustrates that this
denominator (output growth) since
initial real interest rate
3:
U
is
slow,
and
in fact
comes
entirely
from the
never runs a current account surplus. Given our parameter values, the
C
equals 6 percent. Panel
then climbs back very slowly to pre-shock
wealth, under the assumption that
convergence
U
shows that
levels. Finally,
maintains
it
drops by about 60 basis points at impact,
the last panel shows the share of
its initial
holdings.
f/'s assets in
B's
This portfolio share increases rapidly
from 5 percent to 25 percent, and asymptotes to 34 percent.
The model
(Fact
1);
Up
U.
is
thus able to generate simultaneously large and long lasting current account deficits
a decline in real interest rates (Fact 2) and an increase in
to now, differential
But there are other
differences, ranging
We
growth limited the aggregate
A
Let us
now
share in the global portfolio (Fact
ability to create valuable assets in
E
U
3).
relative to
factors that create comparative advantage in asset creation, such as institutional
from corporate governance to transparency of the financial system and policymaking.
turn to this analysis next, which
2.3
f/'s
in
is
at the core of our explanation for recent global imbalances.
World with Asymmetric Financial Markets
turn to the interaction between
U
now. The key element of this part of the model
and R. For
is
that
15
R
is
clarity,
we
(a
U— R World)
shall
remove
E
from the analysis
for
able to grow and generate income for savers but
is
limited in
its ability
In this section
in
we develop our argument
an environment where
now
in
R
and
an environment where
How
sound financial assets
to generate
R
U
is
realization that corporate governance
?
property rights protection, and so on.
The formulae
rate g. Second,
>
5 drop from 6 to
U
5,
g.
alia,
in a bubble; the
benign than once thought; a significant loss of informed and
—
^justified
— of
or not
"crony capitalism"; a sharp decline
All of these factors -and more- were
(e.g.
a crash
mentioned
in the events
Fischer (1998)).
U—E
are very similar to that in the
model, but there are some differences that need to
U
be highlighted. Let quantities without superscript denote world aggregates (now made of
than
5^ <
we repeat the experiment but
This could result from, inter
be.
is less
surrounding the Asian/Russian crises
let /?'s
In general, as the realization that local financial instruments are
intermediation capital; the sudden perception
in
same
growing faster than U, g^
should we interpret a drop in 5
we
steps: First, at date
are growing at the
sound than they were once perceived to
less
two
in
for these savers.
and R, rather
and E), then:
and
=
nVt
with x^
= X^ /Xt-
Similarly,
we have
5Xt -
(1
- xf )
[5
- 5^)Xt +
Vt
that:
Ty« =
(1
- 5«)x« + [n - e)w^
(5
-
and
Pi/,
Finally, using the
=
[l
_
5
equihbrium conditions
+
5«)(1
-
x,^)]
Xt
+
(r,
- B)Wt
W — V — X/9, and the arbitrage equation
for
V
,
we can
solve for
the equilibrium interest rate as before:
n =
xf{g
+ 5e) + {l-xY){g + 5''e)
(16)
= r,^„,-(l-xn(<5-5V
Proposition 2 (Crash
same
rate g.
deficit at
The
impact and remains in
interest rate falls
Proof. Note
interest rate
first
Symmetric Growth): Assume
in R's Financial Markets with
Under Assumption
3,
if
5 drops in
R
to 5
deficit thereafter, with
permanently below
(17)
<
5
,
R
and
then the current account of
CA^/X^
U
U
grow
at the
turns into a
converging to a strictly negative constant.
r^^^.
that since both regions are growing at the same rate,
remains constant after dropping at date
0:
16
x^ = Xq
for all
t
>
Q,
and the
.
rt
=
Next, because the interest rate
= r^^, -
r+
(1
- x^)i5 - 5^)0 < r^-
(18)
constant, the values of the trees change immediately to their
is
new
balanced growth path:
Vt'-
=^T^.
r
9
^t
^
ff
Let us now describe the balanced growth path and then return to describe transitory dynamics. In the
balanced growth path, we know from
Lemma
*
1
that
+ g-r+
e
*
e
+ g-r+
and
CAY— =
—O
For transitory dynamics, define w^^
= W^/X[^
with a balanced growth equilibrium value of
Prom home-bias Assumption
since
<
r"*"
Since
r^„f.
r"*"
<
That
r^„j
<
is, u;/^ is
g
+
6,
3
we have
below
its
—
(1
5
)/ {9
That
deficit.
is,
The
its
now even
latter
is
if
ih^
when w^
>
CAf =
is
i
below
collapse in 5
0+.
its
steady state, or equivalently:
> gW,^
V/^
—
Wf''
is
in deficit
-
in fact,
a larger deficit- before
path.
both regions have similar rates of growth,
If
and hence must
U
runs a permanent current account
who have
resort to [/-assets. In balanced growth, il-savings
few reliable
grow
at the rate
i?-savings are below (output-detrended) steady state, then the rate of accumulation
exceeds the rate of growth of the economy and capital flows toward
The
=
the counterpart of the increasing flow of resources from JJ-savers,
local assets to store value
of growth of income.
r"*")
balanced growth path at
we must have
new balanced growth
+g—
that
also have that [/'s current account
converging to
<
so that
W,""
Thus we
- r+
r^ut
2i£i
decreases the global supply of
be capitalized. As before, the shock
is
decline in the global dividend rate from
Eissets
U
grow
at a fast rate (faster than g).
by reducing the share of R's income that can
entirely absorbed via a decline in world interest rates, reflecting a
(5
to
<5
—
(1
—
xq) {6
—
S'^).
While global wealth and capitalization do
not change at impact, the allocation of wealth and assets across countries does.
17
The
collapse in 5
implies
(Demand)
NA" >
(Supply)
w"/xVv"/x"
Figure
that Vq' /Vq^ must
w'^/x^
The Metzler diagram
4:
an unchanged stream of
rise as
Correspondingly, under our
home
Vs
for
a permanent drop
dividends
bias assumption, the ratio
is
this,
(5
Wq /W^ must
note that the equihbrium interest rate
v«/x«
.
now discounted
Again, we can resort to the analysis of a small open economy in Section
the asymptotic result. For
in
.
at a lower interest rate.
also rise.^^
2.1,
and
falls
its
Figure
2,
to understand
between the two
to a level in
ex-post Autarky rates:
Thus
the gap between
W^ /X^
and
V^ /Xf
other region's perspective, the gap between
is
negative and non-vanishing (see
W^- jX^ and
V^ jX^
is
rate r„„j, the decline in
shifts the
(5
V^/X^
curve to the right (increase in asset demand).
foreign assets in
U [NA^ =
W^ -V"
curve to the
The world
<Q) and
left
A
interest rate declines just
R
Or, from the
and A* with a world
(decline in asset supply)
the net foreign assets in
1).
and non-vanishing. Figure 4
positive
presents the asymptotic result. Starting from a symmetric equilibrium at
Lemma
[NA'^
interest
and the W^/X'^
enough so that the net
= W'^ -
V'^
>
0)
sum
to
zero.
Figure 5 characterizes the entire path following a collapse of 5
by 50% on impact
trajectory of the
(see the
US
appendix
U—E
'^It
is
The
a discussion).
current account following the Asian
quantitatively significant. Panel
of 20 percent.
for
A
calibrated so that R's asset prices drop
Again, our objective
crisis,
is
not to match the precise
but to argue that the
effects
we describe
of Figure 5 shows that U's current accounts exhibit large initial deficits
current account remains negative and asymptotes at -2.8 percent of output.
case, the large initial current account deficits
easy to show that
if
&
capture this flavor through the
C/'s
rise in
As
in
the
worsen rapidly the net foreign asset position from -6
crashes to zero, then a bubble must arise in (/-trees.
captures the flavor of the behavior of
are
While that drop
asset markets in recent years. In the less extreme version
we have
in
5^
is
extreme,
highlighted,
the value of U's fundamentals following the decline in equilibrium interest rates.
18
we
it
still
Panel
-2
A:
2
4
Current Account/Output
G
e
10
M
12
16
20
IB
24
22
Panel B: Net Foreign Assets/Output
1-2
26
10
8
6
4
2
yeors
Panel C: Interest Rate
Panel
Figure
percent at impact to -95 percent (panel B).
and remains permanently
12
14
16
IB
20
22
A
5:
The
D:
26
Global Portfolio Share
Collapse in 5^
real interest rate
drops by slightly more than 50 basis points
Finally, U's share in R's portfolio increases gradually
lower.
24
years
from 11 percent
(immediately after the shock) to 55 percent. -"^
Once
in
U
again, the
(Fact
I);
model
a dechne
is
able to generate, simultaneously, large and long lasting current account deficits
in real interest rates (Fact 2)
and an increase
in
the share of U's assets in global
portfolios (Fact 3).
Importantly,
now
CA^ /X^^
does not vanish asymptotically as
it
converges
CAl = _g Jini^Kl^^D^ <
{e
The reason
Note
in
is
that excess savings needs in
large
and persistent
importance of
because
'^The
deficits in
U
with
Ws
.
—
Xq)).
In practice,
0.
output, which grows in tandem with
deficit in
U
(relative to output)
C/'s
is
output.
increasing
This observation hints at an important additional source of
i?'s
funding of [/-deficits
rate of growth exceeds that of U,
rises over
time
— both, because of
and hence the
differential
relative
growth and
countries are gradually globalizing.
now turn
initial
(equal to (1
this source of
many R
Let us
R
R grow
permanent current account
also that the size of the
the relative size of
+ g-r+){r+-g)
to:
and explore the
effect of
a crash
5 to 11 percent reflects the drop in H's wealth
and jump
in
to our second experiment
jump from
19
V^
at
in
t
5^ that takes place
= O"*".
in
an
.
environment where;
9'^>9-
The instantaneous
interest rate in this case
r,
is:
= xf(9 +
R
Let us assume that the additonal growth in
+
50)
(l-a;f)(ff«
+ 5«^).
(19)
not enough to offset the effect of a lower 5
is
on
interest
rates:
Assumption 5 (Lower
Proposition 3 (Crash
5 hold, but that g^
>
in
=
r^^^
+ 95 <
g^
r^^j
—
^(1
— Xq){6 —
5
)
<
r^^f
R's Financial Markets with High Growth in R) Suppose that Assumptions 3 and
5 drops to 6
date
g. If at
^aut
and the asymptotic current account
g'^
R)
ex-post autarky rate in
=
in R, then:
>
ro-
U
deficit in
ro+
>r^ =
rf^^
relative to its output is larger
when g^ > g than when
= g:
CA"
,.
hm
9
CA'^
,.
< hm
--77-
>9
—-rf-
<
„
=9
9
Proof. See the appendix.
The
its
result in this proposition
demand
for financial assets.
financial assets, these assets
is
intuitive given the previous proposition:
Since this rise
must be found
in
and
interest rates
fall
demand
As
more than the short term
for assets,
R,
before, let us
in the long
Autarky
run
rises
now
interest rates because the relative
X^,
the global economy
that gap
is
larger
when 5^ >
g,
U.
Long run
The
interest
2,
from Section
2.1.
First, since
the equilibrium interest rate converges to the
=
r^ut
=
g''
the gap between W^^ and V/^
is
vanishing,
roo
,
deficit in
rise.
it!:
However, note that this limit interest rate
Thus, relative to X^
does
importance of the country with excess
describe the asymptotic result in terms of Figure
r-oc
Thus, relative to
rises, so
over time.
R dominates
interest rate for
growth
drop as the price of [/-assets
corresponding increase in capital flows finances the larger current account
rates
i?'s
not matched by an increase in R^s ability to generate
is
U
As
the gap between
when g^ >
g than
=
g""
is
+ SH <
=
s^e.
and
so
below the Autarky rate
W^ and V^
when g^
+
is
g.
20
g
+
56
=
is
in
that between
W^
and
V^
U:
r'i^,.
negative and not vanishing. Moreover, since
The Three Regions World {U - E - R)
2.4
we
In this section,
consider a
U—E- R
sub-worlds described above, but there
then the asset appreciation
are directed to
U
in
U
is
environment.
one additional
Much
is
insight: If the crash in 6
(much) larger than that
is
of this world
in
simply the
takes place
sum
of the two
when g^ > g^,
E, and the bulk of the capital flows from
R
"
rather than to E.
Since the dynamic equations follow directly from those discussed above,
pendix and state the main proposition
directly, after
we
relegate
them to the
ap-
making an assumption on the parameter region under
consideration:
Assumption 6
r^^^
= g^ + 6^9 <
=g + S9,
r^^t
Proposition 4 (Disproportionate Flows toward U)
increase in
V^ /V^ and
<g^ + e,g'^<g.
r^^
If
Assumption 6
leads to an
holds, then a crash in 5
a "disproportionate" (to relative output) allocation of R's capital outflows to
E. Asymptotically
^^
^^
F
g'^
Too-
vJ^TP^
g-g F
^
U
over
,
Proof. See the appendix.
In words, the reduction in world interest rates stemming from the crash in 5
?7-assets since these are
a decline
growth
more leveraged than ^-assets when g > g^. This
calibrated so that
in S
differential g
—
V^
collapses
=
g and
5^
=
5),
with x^
Then, at
disproportionately affects
for
V^. This
results in
in net liabilities in
3
U
= g^
and a
1.1 percent
g^, the ratio of asset price elasticities equals 1.43.
= x^ =
reduces world interest rates to 5.5
inflows (panel D).
difference can be quite large. For
by 50 percent on impact, with g
=
Figure 6 traces the entire path in the case where g
{g'
has a larger impact on
i
=
%
5,
x^ =
and increases
we decrease
V'-' relative
much
0.425 and
to
V^:
5
V^
g^-
We
start the
0.15.
We
Panel
D
R
and
U
symmetric equilibrium
i
=
illustrates that the collapse in 5
U
relative to
0.
This
as both regions receive capital
increases by 12 percent at
larger current account deficits in
in a
then reduce S's growth at
asset values in
.
economy
i
E
=
5,
and
V^
compared to 8 percent
and an additional build-up
(panel A).
Foreign Direct Investment, Excess Returns, and Persistent Trade
Deficits
Let us now add an investment margin to the
We
U—R
model and a reason
capture the former with the emergence of options to plant
21
new
for foreign direct
trees over time,
investment (FDI).
and the
latter
with U's
Panel
Panel
A:
C:
CA/Output
Ponel B: Net Foreign Assets/Output
Interest Rate
Panel D; Asset/Output
J~
-2
4
2
6
8
10
12
14
16
18
20
22
24
26
years
Figure
ability to convert
6:
A
R
trees into 5 (rather
new
the trade surpluses that
As long
stronger result:
and there
is
any rent
for
U
Collapse in
g^
followed by a collapse in S
than 5
)
as there are no
FDI
its
3.1
An
Investment Margin
Let us
split
aggregate output in each region into the
U
will
all
of trees, TV,
reduce
we show a
In fact,
investment can be done by U)
run permanent trade
number
FDI
rents from
persistent early deficits.
obstacles (in the sense that
Ifs intermediation service,
U-E-R model
The intermediation
trees. ^^
needs to generate to repay for
in the
deficits}'^
and the output per
tree,
Z:
xi = Nizi
'^Note that
in
a three regions version of the model
E
also could convert
R
trees.
Although
in this case, a
good question
is
which rate of growth would the output of those trees have.
^''The view here
the Bretton
Woods
is
not unrelated to that in Despres, Kindleberger and Salant (1966) and Kindleberger (1965),
era argued that the
US had
a unique role as a provider of international currency liquidity.
Gourinchas and Rey (forthcoming 2006) have documented that the total return on
US
who
More
during
recently,
gross assets (mostly equity and FDI)
consistently exceeded the total return on gross liabilities (mostly safe instruments) by an average of 3.32 percent per year since
1973.
Of course part
investments.
Our
of this excess return
is
due to the risk-premium
analysis omits this risk dimension
Table
1).
US
have risen from $222
billion in
nature of
US
and focus on the "intermediation" rent obtained by the US.
Everything suggests that this "intermediation" role of the
to/from the
differential associated to the leveraged
1990 to $2.3
US
has only grown in importance as total gross capital flows
trillion in
2004 (see
BEA, US
International Transactions Accounts,
See also Lane and Milesi-Ferretti (forthcoming 2006) for a systematic analysis of cross border flows and positions for
a large sample of countries.
22
At each point
new
trees arise.
new
trees
in time, g'^N^ options to plant
tree grows at the rate g^. Planting the g"'N^
shall £issume that
n
is
low enough so that
aggregate output grows at rate
g,
all
first
that
II:
investment options are exercised (see below), and hence
=
+ g'-
g^
the region where the tree
S^ is specific to
nVi =
where
consumes resources
with (equal for both regions):
g
Suppose
time, the output of each planted
= kxi
li
We
At the same
5'xi
+
Vi
is
planted
it.
Then
- 5"V/
(20)
(new and old) trees planted at time
V^ represents the value of all
who
planted, not to
t
in region
i,
and V"/— g"V/ represents
the expected capital gains from those trees.
The
exercise
options to invest are allocated to
them by
t
who immediately
within each region,
investing I}}^ Thus,
Wi =
As
those alive at time
all
[n
- e)Wi +
(1
-
5')Xi
+ g^Vi -
II
usual, aggregating across both regions to find the equilibrium interest rate, yields:
TtVt
=
5Xt -
Wt = [n - e)Wt +
(1
(<5
- <5^)Xf + Vt-
- 5)Xi +
(<5
g'^Vt
(21)
- 5^)X^ +
g^'Vt
-h
< r'i,^
am =
+ ^^,
fZ^
(22)
so that:
and
T
=
g'
+ r^(<5
^' 1 - K
which amounts to the same model as
of output per-tree enters,
interest rate (since
it
(5
V-
-
5^)
x^),
, -
in the previous section,
and that the investment
~
e5_
g'
.
(23)
with the exceptions that only the rate of growth
cost reduces wealth accumulation
and hence
lowers the price of trees).
'^Note that the share of options that are allocated to existing owners of trees are subsumed within the
we can
trees.
in
reinterpret the
model
in Section 2 as
The only reason we modified the
a more realistic
raises the
an investment model where
all
allocation of options in this section
manner (otherwise the
Z
component. In
is
to spread the excess returns from
entire capitalized excess returns accrues to the first generation in U).
23
fact,
the options are allocated to the owners of existing
FDI
over time
3.2
An
Intermediation Margin: Foreign Direct Investment
Let us now assume that
R
residents can sell the options to the
Pt
where X/*" denotes the output from the
process but
its
particular value
is
news
trees to
U
residents at price, P:
= KpXf ".
We think of this price as the result of some bargaining
trees sold to U.
not central for our substantive message as long as
it
leaves
some surplus
tot/.
There are gains from trade:
If
U
that can be capitalized rises from 5
residents. In fact, the following
to
R trees,
new
residents plant the
Suppose that Pt
S.
U
assumption ensures that
is
the share of output from the
such that
all
and
R
investors
new
R
sellers
new
trees are planted
trees
by
U
gain from foreign direct
investment along the entire path.
Assumption 7 (Asymptotic Bilateral Private Gains from FDI)
9
raut
Proposition 5
If
Assumption 7 holds, then
>
r
-
9^
U
+ Kp
K
>ff"
Taut
-
Let
up and
{5
—
5
)
he
such that:
9
runs an asymptotic trade
deficit
financed by
its
intermediation
rents.
Proof. Let us assume that enough time has passed so that the output of the old
relative to the total
output produced by trees planted
R
in
by U.
We
R
trees
is
negligible
have:
irt+gnvi = 5Xi + V^
{rt+9nVt = 5Xt +
W^ =
(n - e)Wi'
W,^
Wt =
=
{rt
+
{rt
(1
-
-
+ g^Vt -
<5)Xf
9)Wt''
- e)Wt +
+
(1
Vt
(1
-
-
<5)Xf
5)Xt
[I^
+
+ I^) -
Pt.
Pt.
+ 9"Vt -
(24)
It
so that:
Wt =
Vt
= {l- k)^.
and
r
=
raut
=
9"
+
1
i
It
—
(25)
Ki
follows from derivations analogous to those in previous sections that:
^u
Xy
{1-5- k)+ 5"-^ + S"^^ 9 + g- raut
24
(«
+
Kp) x^lx^
and
TSf = -OW}^ -
since
—
-rrrrr
+ X^ we
Rgn
the trade balance
is,
ensured by Assumption
Does
not.
mean
this
;rrrm
U,aut
e+g-r
^
_
U + Kp)
+
-
Taut
X^
That
have that:
,
-o'
*
X^
Jf
is
g
in deficit in the long
run as long as there
and, assuming Taut
>
U
TBI'
5 so the integral converges,
and R,
Figure 7 reports the path of
when Kp
when
is
+ g^y!" it
no FDI takes
to f
=
which
is
when the
\J (i.e.
g^ -VbQj (1
—
for
Certainly
the
initial
+ ^p)^/"
follows that:
y
.^
place. Second,
when
all
is
consider three cases:
when
all
inequality of assumption 7 holds exactly).-'^
first
k) where 5
We
the rents asymptotically go to
the second inequality of assumption 7 holds exactly) and lastly
very similar to the model of section
Ta^ut
(«
trade balance following a collapse in b
t/'s
sufficiently high that
asymptotically go to
from
rent,
which case, we have:
respectively. In
/+00
is
an intermediation
Alternatively, one could account for these intermediation services as
deficits.
tb" =
FDI
Kj
simply means that the intermediation rents rather than future trade surpluses pay
It
(i.e.
-
that the intertemporal approach of the current account has been violated?
"non-traditional" net exports and imports for
R
is
(1
7.
(and now permanent) trade
first,
1-
2.3:
following a collapse in
b^ the
,
the rents from
The model without
permanently
interest rate falls
the fraction of world income that can be capitalized.
consequences are well known: the wealth transfer to
U
generates a trade
deficit,
FDI
By now,
the
an accumulation of foreign
debt, eventually followed by trade surpluses (panel D).
In the presence of FDI, the results are starkly different. Let's start with the long run.
effect of
FDI
is
to increase the supply of [/-like assets sufficiently to offset the initial shock. This has a strong
implication for the path of net foreign assets (panel B): since
(Panel C), the Metzler diagram
Kp
^^We
R
calibrate the decline in 5
as before, to a drop in
we assume k =
also choose 5 so that Taut
=
6%.
We
0,
converges to Vaui a^ long as
trees (n;p) as long as
controls the distribution of wealth between
'^For this simulation,
rt
FDI
takes place
us that long run external imbalances disappear asymptotically. This
tells
independent of the cost of ownership of the
that
The asymptotic
= p = 0.03,
& = 0.24.
3"
obtain
U
and
/?,
Assumption 7
is
satisfied.
The reason
is
is
leaving total wealth unchanged.
V^ of 50%. See the appendix for details of the simulation.
= and we vary «p between 5% and 12%. For comparability, we
g^
25
Panel
A:
Current Account/Output
Panel
Net Foreign Assets/Output
B:
O
o
o
:\ V
u
\
2
ti
Q.
-
1
--
''*•'•'.
m.m..?rM?r,.rr.'
1
1
in
^^—
- -
o
o
no nji
^MB
CO
Koppo^M
no FDI
1
ltoppop-12X
ift
4
2
6
10
8
14
12
18
16
o
o
_
.
-2
20
22
24
-2
26
2
4
10
8
6
12
14
16
18
20
22
24
yeors
years
Panel C: World Reol Interest Rate
Panel D: Trade Balance/Output
26
IS
s
"'y:i^:^^^^'-'
-
^ -
-"
*
^^
- -
-
^
to
^
^^
— -
'
no FDI
n»
no FOl
Ke>ppo,-52
itoppop-121
,
8
10
12
IB
16
14
20
22
24
26
10
Figure
12
14
16
IB
20
22
24
26
years
yeors
A
7:
with and without
Collapse in 5
Consider the short run now. The interest rate
FDI
satisfies:-^®
,-Rol
(26)
Xt
where xf'" (resp
a;^^")
denote the new
represent the value of one
<
rt
f since Vq^
demand
new
> Vq° and
(resp. old)
=
Xq'^
0.
relative to total asset supply
In the short run,
FDI
(resp.
R
The
tree.
The
last
term of
reason for this last term
when
increases asset
old) R's trees share of
there
is
FDI
(g" (l^^
demand -which
world output and u/^"
this
is
(resp.
equation makes clear that
the
initial
+ N^v^^) >
,,fio\
initially
rapid increase in U's
aisset
5"Vt).
lowers further interest rates; in the long run,
it
increases asset supply, which brings interest rates back to raut-
From
Kp
(20)
and
(as long as
(26)
FDI
we note
dynamics of
also that the
takes place).
Hence, the
initial
interest rates
increase in C/'s wealth
of FDI. It follows that t/'s initial trade imbalance (equal to
Indeed,
we observe on Panels
A
and
D
that
and
f/'s initial
asset values are independent of
is
also independent of the cost
Xq — 9Wq — Iq)
is
also independent of Kp.
current accounts and trade deficits are the
same
for
different realizations of Kp.
A
to
4%
lower value of
Kp
(higher rents for U) implies a permanently larger trade deficit in U, ranging from
of output (Panel D).
^®See the appendix for a derivation.
26
To understand why
U
runs asymptotic trade deficits as soon as
pluses, consider first the case
trade deficit either. Yet, Panel
on
rents
its
U
where
D
has no
FDI
U
indicates that
FDI investment along
has strictly positive asymptotic sur-
U
rents asymptotically. In that case,
never runs a trade surplus.
the path, which allow
can define these rents (over total wealth W'^)
it
it
has no asymptotic
The reason
is
that
U
earns
to run trade deficits in every period. In fact,
we
as:
g-^N^v^'^
-
{Kp
Xt
+
kX^
X^"" -
k)
wi'
Asymptotically, these rents converge (from above) to
<5
,
Xoo
which
is
We
equal to zero
when
can now understand
the
first
(/^p
Too- g
+
x^
k)
(27)
w,u
inequality of assumption 7 holds exactly.
why U can run permanent
trade deficits:
When Assumption
7 holds
intermediation rents remain strictly positive and provide the resources to finance permanent trade
some
show that adding such dimension
to
is
cases quantitative) features of the results.
to the
model does not
a vis both,
R
and
interest rates
and amplification
(to
a
lesser extent)
alter the qualitative (and in
While adding multiple goods allows us to generate exchange
rate patterns from our shocks that resemble those observed in recent data
4.1
However, the main
to now, our conclusions have abstracted from (real) exchange rate considerations.
point of this section
and
deficits.
Multiple Goods and Exchange Rates
4
Up
strictly,
E, when asset markets collapse
in
— particular, U appreciates
R— the behavior of capital flows
vis
in
remain largely unchanged with the exception of some attenuation
in
some
U—R
U—E
in the
context
cases.
Preliminaries
Let us return to the framework in Section
differentiated goods.
Each country
i
2,
without an investment margin, but extend
produces one type of good
X\
while
its
it
to consider
consumers have the following
constant elasticity preferences (CES):
where a represents the -constantcoefficients
'y^j
elasticity of substitution
between the goods from any two countries. The
meeisure the strength of preferences for the various goods and satisfy ^^
8 below imposes that agents have a preference for their
empirically. It also generates relative
demand
7^ =
home good. This assumption
effects that will
27
•
be important
for
is
1.
Assumption
well-established
exchange rate dynamics.
Assumption 8 (Consumption Home
Let
q^
=
X^
and the
be the numeraire good and define
Given
1).
Bias) Each agent has a preference for the
real
q^ as
home
the price of good j in terms of good
U
good: 7^^
=
7>
0.5.
(with the convention
(28), the Fisher-ideal price indices are:
exchange rate between countries
and k
i
is
1/(1-^)
(^-)
^ E,7.,V
^,,_p'
This expression highlights the importance of consumption home bias
for all j,
7fc,-
Given
for
exchange rate movements:
then purchasing power parity obtains and the real exchange rate
CES
preferences, the
and equilibrium
in the
demand
for
good j by residents of country
i
is
equal to
if
7^
=
1.
satisfy:
goods market imposes
Y^Xij
=
Xj, Vi.
i
Substituting P*C"
= OW^
condition for good
i
(where domestic wealth
can be rewritten
now measured
is
in
terms of
C/'s
good), the equilibrium
as:
•E7.5($)^^-^^v,.
4.2
AU- E World
We now
specialize the
terms of the numeraire.
model to a symmetric
By
U—E
world, and denote by
rt
the instantaneous return in
arbitrage, rt satisfies
rtVi
=
SqiXi
+
Vi
while wealth dynamics follow
Wl = {\-^)ct,X\^{rt-e)Wl
ks, before,
adding across countries and using the equality between global wealth and global asset values, one
obtains:
m=
14
28
=
f
.
where Xt
= X^ +
qfXf^.
Following the same steps as before, the instantaneous interest rate
The
only notable difference
satisfies:
that the (inverse of the) terms of trade
is
qf -and hence the
real
exchange
rate- enters into the determination of global wealth and of the equilibrium interest rate via Xt
In turn, the terms of trade are determined by the equilibrium on the market for X'^ (by Walras' Law,
X^
the market for
is
also in equilibrium):
e-yw^ pI'^'-"^
+ » (1 - 7) wf pf (^-") = xy.
Let Assumptions 2 and 3 hold, so that the world
and there
is
extreme portfolio home
that the interest rate
bias.
is
initially
symmetric with a common rate of growth
Given the symmetry assumption,
it is
immediate that g^
=
1,
g,
so
satisfies:
while asset values and wealth satisfy
As
before, suppose that at
The main
i
=
E
9" <
9-
with Section 2
initial difference
absorb the shock at impact. To see
Assumption 3 (extreme home
the growth rate of
this,
is
drops unexpectedly and permanently
now both the
that
observe that the decline
interest rate
in
g^ decreases E's
portfolio bias), this impoverishes £"s residents.
bias assumption (Assumption 8), the associated decline in £"s consumption
E
goods. Equihbrium in the goods markets then requires that q^
that
f/'s real
exchange rate appreciates
portfolio biases.
at impact. It is a direct
Over time, however, the increase
and the
falls.
real
to:
exchange rate
asset values.
With
Given the consumption-homefalls
mostly on the demand
This relative demand
for
effect implies
consequence of both home consumption and
in the relative supply of C/'s
good requires that
its real
exchange rate depreciates.
How
large
is
the initial
fall
and eventual increase
see this, observe that the relative
demands
.
From
this,
we
q^ depends on the
elasticity of substitution a.
To
satisfy
Asymptotically, the ratio of relative demands for at
X^/X"
in
letist
one country must equal the ratio of relative supply,
infer that:
-£
= -5-5
29
)•
.
Let us rule out the region a
the
(T
=
between
1 CcLse
E
<
I
since
implies immiserizing growth. In the feasible region, consider
it
which yields the starkest departure from the previous section. Given the
and U, one can show that now terms of trade
initial
first
symmetry
satisfy
which implies,
when growth
In this extreme case,
and a gradual increase
return in terms of
X^
in q at rate [g
is
down
slows
— g^)
E
there
is
no change
in the
is
exchange rate at impact,
constant, the instantaneous
f E
^
Q^
+:^^
also check that
Hence neither country needs
to run current account imbalances in response to the collapse in
g^ The reason
.
that the terms of trade offset perfectly the relative dechne in output growth, leaving relative wealth
and
relative
dynamics!
output unchanged (when measured
realistic case
a smaller rate than the growth
a growth
in the
same
units).
Log preferences eliminate the model's
-"^^
Consider now the more
at
in
and equal to
also constant
1
is
1
2
thereafter. Since the output share
2^+21^
One can
y
*
where a >
\.
From
the previous discussion,
For instance, with
differential.
differential of 1 percent per year, the
cr
model impUes that
=
4
f/'s
we
infer that
q^
increases
—not an unreasonable value^" — and
terms of trade would worsen at 0.25
percent per year. This implies an even slower real exchange rate depreciation, which eventually converges
to a steady state value of ((1
We can
rates.
—
7) /7)
From
x^
'
prove a result similar to Proposition
rt
= Xt/Xt + 56, we
tends to
1,
we
1
and the associated Metzler diagram
have
n=
Since
"'''
'
gx'i
+
(ff^
+
qtlqt) (1
-
x'^)
+
86.
obtain:
lim
t—>oo
rt=g +
56
=
r^^j.
From
Wf
TtVf
=
{n-6)Wf + {l-d)qfxi
= 5qtXf + Vf
shown by Cole and Obstfeld
'^This well-known result was
first
^"See later in this section
a discussion of the calibration of
for
30
(1991).
cr.
in
presence of exchange
.
.
it is
apparent that
W^
(1
-
5)
gfXft-.<^r^^,-{g^ + ^{g-gE))
Thus, the asymptotic wealth and asset values are similar to those of Proposition
that
g^ has
By a
-{g — g^)
+
g^
to be replaced hy
reasoning analogous to that in
CA^
CAf
( E
,
As we discussed above, when
tends to infinity
we
^
ct
=
1
Lemma
there
1,
we
obtain:
apparent:
The
is
no current account
recover the deficits from Proposition
possibility of long-run
{1-5)
5
movement. While there can be non-monotonicities
rate
the only difference being
< g^
E\
I
1,
1
At the other extreme, when a
deficit.
since there
<0
is
no
offsetting long-run
in the intermediate region, the general
exchange
message
exchange rate movements attenuates rather than exacerbates the
wealth effects associated with differential growth and hence attenuates asymptotic current account
The main reason behind
initial
trade deficits in
the latter
U
is
that the reduced wealth effects at impact
and hence smaller accumulated net external
when a < oo
confirms our conclusions from the one-good model -see Figure
in
both
figures,
we observe that
deficits.
leads to smaller
liabilities.
Figure 8 presents a simulation of a decline in g^ in the two-goods model when a
Comparing panels A-D
is
=
4 and
7
=
0.9.^'
It
3.
relative price
movements
limit the size of the
current account deficit (Panel A, 8.2 percent versus 17 percent in the single good model) and limit accordingly
the build-up in net foreign debt (Panel B, -57 percent after 24 years versus -75 percent of output after 15
years in the single good model). Accordingly, the increase in the share of
(Panel D). Panel
C
in panel
C
in figure 3:
The
trajectory of the world real interest rates
more muted
is
very similar to the
from 6 percent, the world interest rate drops to 5.41 percent on impact,
then climbs very slowly back toward 6 percent. Finally, Panel
On
in global portfolios is
reports the world's real instantaneous rates of return, defined as the output-weighted
average of both countries real returns.
one obtained
U
E
reports the real exchange rate A
= P^/P^
impact A appreciates by about 7.8 percent, then gradually but persistently depreciates. Importantly,
our model
it is
the latter effect that dominates (dampens) wealth effects and hence limits the
initial
in
current
account deficits in U.
^'Feenstra (1994) finds a value of 4 for a while Broda and Weinstein (2004) report estimates ranging from 17 at 7-digit
between 1972-1988 to 4
for 3-digit
Rogoff (2000) used a value of
6.
goods
in
1990-2001.
Obstfeld and Rogoff (2004) use an elasticity of 2 while Obstfeld and
Obstfeld and RogofI (2004) use a weight on domestic tradeable of
0.7.
But they
also
assume a
share of expenditure on non-tradeable equal to 0.75. This corresponds to a share of domestic consumption on domestic goods
7 of 0.925, not
far
from our
0.9.
31
1
Panel
A:
Current Account/Output
Panel
Net Foreign Assets/Output
B:
^^^^^^^^^^^^^™
**
m
c
V
u o
«
—
^
^
•7
o
-2
6
4
2
B
10
12
14
16
18
20
22
24
1-2
26
4
2
6
B
10
12
14
16
18
20
22
24
26
yeors
years
Pone!
Ponel C: World Real Interest Rote
Global Portfolio Share
D:
to
«1
-
s
•
-
tfl
R
•
-2
<
2
E
B
10
12
14
16
18
20
22
24
-2
2e
4
2
6
B
10
12
14
16
IB
20
22
24
26
yeors
Panel
E:
Real Exchange Rate
Figure
8:
A
Finally, Figure 9 presents the case of
in
g^
is
now
currency at
t
Collapse in
g^
in the
two-good model
an unexpected reversal
in
g^ back
to g after ten years.
associated with a sharp reversal of the current account deficit in
=
10,
but followed by a gradual appreciation so that by year 25,
The purpose
U
The
increase
and a depreciation
C/'s
exchange rate
is
of its
at 1.02
rather than the 1.06 in Figure
8.
a sharp reversal
account and exchange rate, but this would stem from a fundamental shock,
in the current
of this figure
and not from the exogenous and spontaneous correction
have
it.
32
is
to highlight that in our setup there can be
of an "anomaly," as the conventional view
would
Panel
Current Account/Output
A:
o
Net Foreign Assets/Output
B:
^^^^^^^^^___
— —
c
tJ
Panel
^H
e
a
o
-2
4
2
S
6
10
12
14
16
18
20
22
24
'-2
26
2
4
6
B
10
Panel
14
16
IB
20
22
24
26
Pone! D: Global Portfolio Share
World Reo! Interest Rote
C:
12
yaors
yeors
•6
rf>
"a
•^
s
<^
-2
4
2
6
B
10
14
12
16
IB
20
22
24
-2
26
Panel
E:
2
4
6
8
10
12
14
16
IB
20
22
24
26
years
years
Real Exchange Rote
1
V,,^
s
^^«»»,^^
^***-*—««„
s
^H —
— — — — —^^«^— — — — —
— — —
^^^
9
O
—
^r
y^
a>
O
r
g
o
1
-2
2
4
E
ID
12
14
16
18
20
22
24
26
yeors
Figure
9:
A
Collapse in
g^
in the
two-good model, followed by a reversal at
33
t
=
10
AU - R World
4.3
now
Consider
U
the interaction between
and R. As before,
=
5^ < 5 while g^
capitalize financial assets drops from 5 to
let's
consider a scenario where R's abihty to
g.
Following the same steps as before, we obtain:
where Xt
= X^ +
gf Xf
,
=
Vt
+
Vf^
Wt =
V/^ and
W^ +
W^'^.
The instantaneous
rate of return
now
satisfies:
n = rL +
which
is
(1
- xY)
-
e{5
- 5«))
similar to equation (16), except for the rate of change of the terms of trade.
Since output growth
is
the
same
both countries, a reasoning similar to the previous section implies
in
that q^/q^
=
asymptotically.
are stable.
On
impact, however, the relative
The absence
of relative supply effect implies that the long run terms of trade
demand
value of R's financial assets which, under portfoho
consumption home
for i?'s
(I
bias, the decline in financial
good and induces a decline
effect is still present:
home
wealth in
the decline in 5
reduces the
bias, reduces i?'s financial wealth. Finally,
R
reduces disproportionately the relative
due to
demand
in g^.
Asymptotically, substituting q^/q^
—
into the expression for rj,
we
see that the interest rate reaches
the value:
=
\rmr,
rj,
= r^ -
(l
- x^)
where x'^ represents the asymptotic share of U's output.
6"
V^t«
V}"
X^
1-6^
q^X^t-^'^e + g-rto'
Wy
and the asymptotic current account
The
differ
r+
<
,
C7
f
initial
applies, so that
5
t-
9
\-5
X^ t^^ 9 + g - r^^
1-6
runs a permanent current account
results of Proposition 2 carry
from the
1
r^^,
satisfies
CA^
> r+
- 5^)6 <
Now Lemma
q^Xf'i^^rt.-g'
W^^
Since r^^(
[5
output share Xq
r+, or, from the formula for r+
,
5
\
deficit.
through with one exception: the asymptotic output share
.
It is
immediate that the current account
if
X,^
<
34
Xfi
.
deficit will
i^ may
be larger
if
Since
x^
= X^
ciates asymptotically,
to the single
+ Xq)
/ (flt'XQ
good
which
,
this
is
q^ >
equivalent to
Qq
>
or Aoo
Aq. If the real
does in our simulations, the asymptotic current account worsens, compared
it
case.
The conventional rebalancing channel has
implications for exchange rate
our calibrated parameters, adding the exchange rate dimension allows
account
Vs
deficits
and hold
larger net foreign liabilities.
share of output (a;^). This
is
movements but does not
else in global asset markets. ^^ In fact,
the core story for capital flows, which Hes somewhere
for
exchange rate depre-
The reason
U
although small
to run larger asymptotic current
that the long run depreciation reduces
is
equivalent to a further reduction in the global supply of assets
world interest rates lower (Panel C), reducing
borrowing
C/'s
affect
and pushes
costs.
Figure 10 presents the results of a simulation similar to Figure
5.
E
Panel
demonstrates that the
exchange rate appreciates on impact by 17 percent, then depreciates slowly, returning to Aq-
real
in 12 years,
then depreciating by another 3.5 percent. Given the previous discussion, the long run depreciation of the real
exchange rate implies that the asymptotic current account
model
(99%
liabilities
than
good
in the single
good model) with a correspondingly higher permanent
(-2.96 percent versus -2.85 percent in the single
accumulation of net foreign
deficits are (slightly) larger
of output versus 95%). Panel
C
shows that our conclusion with
respect to the decline in interest rates from the single good model remains largely unchanged.
Finally, Figure 11
we observe that when
10 and 11,
rate depreciates,
by
documents the paths when 5
R residents
5
jumps,
and then appreciates
f/'s
slowly.
returns unexpectedly to 5 ^Xt
4.4
is
10.
Comparing Figures
current account deficit turns around and
The
latter
(panel D). Again, the point of this figure
must be a reversal of the causes that triggered the
forces
=
its real
exchange
comes with a rapid de-cumulation of claims on
U
that for these sharp reversals to take place, there
is
initial shift, since
the strength of automatic rebalancing
tenuous at best.
The Three Regions World
For completeness, we conclude this section by integrating the three regions. The results are as expected,
when g^ <
g,
and, given financial
home
bias,
on
V^
has a disproportionate effect on
with the additional insight that since a crash in 6
W^
,
at
impact
[/'s
relative to
currency appreciates not only vis-a-vis
R's currency but also vis-a-vis £"s currency (due to consumption-home-bias). However, this effect
relative to the depreciation of
R exchange
vis-a-vis
both
U
(g'
^^The rebalancing channel
with the consumption
^^We
also
home
=
g and
refers to the
<5'
=
5),
with
x'q
=
x^
=
U E
,
and R.
0.425 and Xq
mechanism whereby the rapid accumulation
—
We
start the
We
0.15.^^
of claims
on
(/
by
bias assumption requires a future a depreciation of the real exchange rate.
assume that the home good preferences are such that
35
^^^
is
small
and E.
Figure 12 reports the bilateral real exchange rates between
symmetric equilibrium
V^
= 0.9,
7^,'
=
0.05 for
i
^ j.
economy
in
a
then reduce £"s
/{ residents,
together
A:
Current Account/Output
C:
World Real Interest Rate
Panel
Panel
Panel B: Net Foreign Assets/Output
Pone!
D:
Global Portfolio Shore
•^
o
»>
r-
10
3
_
10
V
in
.
c
fc-"
"g
--
y^
rft
s
-2
6
4
2
e
10
12
14
16
IB
20
24
22
-20246
26
yeors
Panel
E:
at
i
=
5,
increases
t
we
0.
decrease b
E
16
18
20
^
22
24
26
Real Exchonge Rote
A
Collapse in
(5
in
the two-good model
so that
V^
decreases by 50%.
which increases the relative demand
The
for
in section 4.2.
Then,
figure confirms our intuition: the crash in
good
U
and appreciates
V
s real
(5
exchange rate
by 2%.
Final
In this paper
14
This leads to an immediate appreciation of U' s real exchange rate, as
V^ jV^
relative to
5
=
12
yeors
Figure 10:
growth at
10
Remarks
we have proposed a framework
capital flows, portfolio shares
and
to analyze the
interest rates.
efi^ects
The framework
36
of different structural shocks on global
highlights the connection between a region's
Panel
A:
Current Account/Output
-2
4
G
2
S
10
12
U
16
20
IS
22
24
Ponel B: Net Foreign Assets/Output
26
yeors
Ponel
Panel
World Reol Interest Rote
C:
^^^^^^^^^^^^^T^^^^^^^^^"^^^^^^^^^^^^^^^^
^^_^^_^^_^^_^^_^^_^^_^^
-2
4
2
6
8
10
12
14
^^mm^^m^^
16
20
18
22
24
-20246
26
10
Figure
relative
assets
We
A
fundamentals -
- and
its ability
Collapse in S
in the
The second one
is
18
20
22
in particular, its
two-good model, followed by a reversal at
growth potential and the quality
24
26
i
=
10
(or acceptance) of its financial
to produce financial assets for global savers.
used the framework to discuss two shocks that we view
"global imbalances"
16
Real Exchange Rate
E:
11:
14
12
years
yeors
Ponel
Portfolio Shore
D: Global
~»^^^^^^^^^^^^^
and the
a collapse
"interest rate
conundrum." The
2ls
first
particularly relevant in explaining recent
one
in the capacity to generate assets in R.
is
a sustained growth slowdown in E;
The former captures
well the effect of
a relative slowdown in the Euro area and Japan. The second captures aspects of the Japanese bubble crash
in the early 1990s
Asia
in
and the developments
in
much
of emerging markets
and newly industrialized economies of
the aftermath of the Asian and Russian crises at the end of the 1990s.
effects of the interaction
between R's limited financial markets and
37
its fa^t
We
also explored the global
potential growth. All these effects
.
\
)
J
Exchange Rates
Real
Bilateral
>»
.
V
^
-------
1
'
^ , - '
'
-
^
1
1
^
1
.
i
y
1
/'
/
/
^
^^
-^
.
-
-
U-E
U-R
E-R
1
1
1
.
1
,
,
22
24
1
o -2
10
U
12
15
-
.
1
20
18
1
26
years
Figure
Real Exchange Rates
12: Bilateral
in (5^ at
i
U-E-R model. Collapse
in ^-^ at
=
i
followed by a collapse
=5
point in the
same
in the "global
To a sustained
direction:
The framework
trivial to
in the
is
flexible
enough
imbalances" debate.
analyze
reallocation of savings toward
U
and
to explore a variety of experiments
and
to lower interest rates.
issues that
For example, a dimension we did not develop
in
have been postulated
the main text but
that of an increase in a regions' saving propensity (for example, a decline in
is
).
is
The
implications would be similar in terms of the path of capital flows, measured saving rates, interest rates and
the interaction with fast growth in
entirely different for
as those following a crash in 5
i?,
V^: While a drop
comes with an
in 8
the propensity to save does the opposite. This distinction
capital flows
This
is
more
toward the
US
in the late 1990s
not to say that a drop
Q
is
recent increase in saving rates by
asset prices) or even to capture
pressure on long rates
b^ that most
in the
fast
capital flows to
One could
also
came with a crash rather a
growth
R
to
in R.
it is
values in R.
rise in asset
a convenient short-cut to represent the
slump story
is
local
(7
However,
in
terms of timing
it is
the crash in
V
naturally leads to a domestic investment slump
of Section 3, a crash in 8
R, as the return on projects not implemented by
and
in
asset prices,
Moreover, such drop further strengthens the downward
factors.
the massive flows from
well with the facts, as the investment
important since the dramatic acceleration
crash in
commodity producing economies (which have come with high
demographic
model
K&
in
not part of the story, as
when combined with
likely started
Note also that
in
in
R
from
However the implications would be
an increase
initial
is
.
or
£
falls.
one that
is
This
is
yet another impUcation that goes
used often to explain low real interest rates
t/.
model some of the aspects of
indeed lead to current account deficits
in
U
fiscal deficits in
but
it
the
US
as an increase in Q
would increase rather than reduce
38
.
This would
interest rates,
and
hence
it is
probably not the main factor behind current "global imbalances."
Similarly,
one could model the process of globalization as one
in
which regions are gradually allowed to
participate in global capital markets. In that case, one could generate a
economies are integrated.
rates as low S
This probably accounts
for
downward trend
some
of the
in
global interest
downward
pressure
observed on rates since the 1990s.
Finally, a
metries
with
of
U
word of caution. Our framework also highlights that the current configuration of global asym-
likely to
is
risks.
We
vis-a-vis
continue building the already large net external
E,
model and add a
little
U. Leverage always comes
have already illustrated within our framework how a reversal in the relative growth advantage
or in i?'s financial underdevelopment (perhaps the
lead to a sharp reversal in capital flows, interest rates
has
liabilities of
and exchange
credit-risk concern with U's liabilities
to say about the latter possibility, although
it
most
rates.
likely reversal channel),
One
would
could also go outside the
and generate a more harmful
reversal.
Our model
seems remote. Moreover, one of our main points
has been that such risk does not follow as an unavoidable outcome of the current scenario, as the latter
consistent with current global asymmetries in growth potential
39
and
financial development.
is
References
Bernanke, Ben, "The Global Saving Glut and
the U.S. Current Account Deficit," Sandridge Lecture,
Virginia Association of Economics, Richmond, Virginia, Federal Reserve Board
Blanchard, Olivier, Francesco Giavazzi, and Filipa Sa,
Account, and the Dollar,"
in
March
2005.
"International Investors, the U.S. Current
"Brookings Papers on Economic Activity" Spring 2005.
Broda, Christian and David E. Weinstein,
"Globalization and the Gains from Variety,"
NBER Working
Paper 10314, National Bureau of Economic Research, February 2004.
Caballero, Ricardo J. and Arvind Krishnamurthy, "Bubbles and Capital Flow
Volatility:
Causes and
Risk Management," Journal of Monetary Economics, January 2006, 53:1.
,
Emmanuel
Farhi,
Mohammad
and
L.
Hammour,
"Speculative Growth: Hints from the U.S.
Economy," American Economic Review, forthcoming 2006.
Cole, Harold and Maurice Obstfeld, "Commodity Trade and International Risk Sharing:
Do
How Much
Financial Markets Matter?," Journal of Monetary Economics, 1991, 28, 3-24.
Despres, Emile, Charles Kindleberger, and Walter Salant, "The Dollar and World
Minority View," The Economist, February 5 1966, 218
Dooley, Michael and Peter Garber,
Bretton
Woods
"Is It
Liquidity:
A
(5).
1958 or 1968? Three Notes on the Longevity of the Revived
System," in Richard Clarida,
ed.,
G-7 Current Account Imbalances:
Sustainability
and
Adjustment, forthcoming 2006.
Dooley, Michael
P.,
Woods System,"
David Folkerts-Landau, and Peter Garber, "An Essay on
NBER Working Paper
the Revived Bretton
9971, National Bureau of Economic Research September 2003.
Feenstra, Robert C, "New Product Varieties and the Measurement of International Prices," American
Economic Review, 1994, 84
Fischer, Stanley, "The Asian
(1),
157-77.
Crisis:
A
View from the IMF," Address
at the Midwinter Conference of the
Bankers' Association for Foreign Trade, Washington, D.C. January 1998.
Gourinchas, Pierre-Olivier and Helene Rey, "From World Banker
to
World Venture Capitahst: US
External Adjustment and the Exorbitant Privilege," in Richard Clarida,
Imbalances: Sustainability and Adjustment, forthcoming 2006.
IMF, World Economic
Outlook,
Washington DC: IMF, 2005.
40
ed.,
G-7 Current Account
Kindleberger, Charles, "Balance
in International Finance^
Kouri, Pentti, "Balance
of
May
of
Payments
Deficits
and the International Market
MIT
Kraay, Aart and
Account,"
in
Essays
1965, ^6.
Payment and the Foreign Exchange Market:
Model," in Jagdeep Bhandari and Bluford Putnam,
change Rates,
for Liquidity,"
eds.,
A Dynamic
Partial Equilibrium
Economic Interdependance and
Flexible Ex-
Press, 1982, pp. 116-156.
Jaume
Ventura, "The Dot-Com Bubble, the Bush
Richard Clarida,
ed.,
G-7 Current Account Imbalances:
Deficits,
and the U.S. Current
Sustainability
and Adjustment,
forthcoming 2006.
Lane, Philip R. and Gian Maria Milesi-Ferretti, "A Global Perspective on External
Richard Clarida,
G-7 Current Account Imbalances:
ed.,
Sustainability
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and Adjustment, forthcoming
2006.
Obstfeld, Maurice and
Is
Common
There a
Annual,
and
MIT
Kenneth RogofT, "The
Six Major Puzzles in International Macroeconomics:
Cause?," in Ben Bernanke and Kenneth Rogoff,
Press Cambridge
MA
eds.,
2000, pp. 73-103.
"The Unsustainable US Current Account Position Revisited,"
,
N.B.E.R. Macroeconomics
NBER Working Paper
10869,
National Bureau of Economic Research, November 2004.
and
,
"Global Current Account Imbalances and Exchange Rate Adjustments," in "Brookings
Papers on Economic Activity" Spring 2005.
41
A
Appendix
Proof of
A.l
We
Lemma
1
have
/oo
roo
SXst-
Vt
-^t
'•"'^''ds
=
5Xt
/.'('•--s)'^"
e-
/
=
Wt
Jo
=
The Lemma
{l-5)Xt
-9)du^g
p/o'K-e)^^
^
[{1-S)X,
Jo
follows from the fact that
lim
r°°
/
e-^'(ru-9)du^^
^
1
_i
r-9
1
t
en(r.-e~9)du^^
lim
*^°° Jo
g
+ e~r
and
Wo
hm — TT-r^e
t-oo
when
g
A. 2
By
<
r
<
g
Lemma
we can
3
write:
W/ =
and the net
- S)Xt
+ 9.
Proof of
definition,
(1
asset
demand
<T^ + (1 - aj'^)^
as:
so that:
A. 3
The
role of
=
(l-(5)X,'-eW/+rtW/t^-y/
=
(1
-
(5)x,^
by
this change,
assumption that g^
>
1//)
+ 5X1
assumption 4
Suppose that assumption 4 does not hold.
affected
- ewi + n {wi -
0,
This appendix shows that the essence of our analysis
although the expressions are
so that g
>
(1
-
6)9
if
less friendly,
if
we
Assumption 4 does not
42
are willing to
hold.
make
is
not
the minimal
Let
a;"
= X^ /Xthe
the relative size of country U's endowment. Since
^
*
It will
X^e^*
X^e3t + Xie9^t
prove useful to compute J^ x" ds
in closed
^
Xq = Xq, we have
1
1
+
e-(9-9^)t
form
du
I
u
1
ff-5
Note that we can express
rt
=
In
£
1
1
+u
In
)*
^ + 59 as
A-,
rt
=
5e
+ g^+x'^{g-g'')
Solving forward the differential equation for V^^
Vf
,
9-9"
-(s-9E)t
+ u)
n + e^s-s
e-{9~9 E)i u(l
-i:
5Xfe-
J''
,
we
get
'"'^"ds
-i:
= 6Xf
/
e-^o^'-'^-^s-G^^^'^'^'^ds
'•I
l
it
Similarly,
we can
l
+ e-(9-9^)*
+ e-(9-s^)^
solve forward the differential equation for
V^
/oo
5X^e-^'^-d-^ds
/OO
^-5e{s-t)-g^(s-t)-{g-g^) // ^d/i^;^^ gS(s-t)^g
/OO
We
can also solve the differential equation
for
W^
43
and Wl' with
,
initial
conditions
W^^ and
W^
^
w^
Jo
Wf^ exp [-(1 -
+ g^t +
S)9f.
(5
- g^) f x^tds
Jo
+(1 - 5)Xf
J
exp -(1
-
5)0{t
-s)
+ {g-
l
Jo
+
g^)
J'
e-(9-s
xl dh ds
)*
{ru-e)du
Jo
W^^ exp
-il-6)et
+ g^t + {g-g'
Jo
- 5)X^
+(1
uej2+:
=
J
,gt
Wr0+'
exp -(1
-
5)d{t
-s)-ig-
e-H-m + (1 _ s)X^u
f'l
l
g^){t
-
+
s)
{g
- g")
J
x^dh ds
+ e-i9-9^)\_n{l-5)9it-s)^^
+ e-(9-9'')s
Hence
vf = 6Xf
^^^—
/
t^oo g
- g^ +69
»''*
Wt =
g-(g-S^+ifl)(s-t)^^
+ e9' g-(l-<S)et
_(i
M/o'h-
2
l
^ (^ _ 5)^£
l
+ e-(9-9^)*
+ e-(s-s^)
„(g-(l-i5)«)t
/•*
70
„ e{9-{^-i)B)t
Therefore,
it is
(1
- 5)Xo^e(s-(i-W*
/
o-(9-S^)«
l+e-(s-s^)=
/>00
+
_u
-1
L^e-(«-«"-(^-''W^ds
easy to see that
^^L
V-
H^f ^^^
1
(s-g^-(l-<S)e)(t-s)^g
(g
-
(1
-
<5)^)eC-(^-^)«)*
«, +
(1
-
5)Xo^)
44
Q + J^^ __-L__e-(P-.^-(i-W.d,j
Hence
(->oo
^^'"^
e
Now
~oo
-(^ -
(^
-
'5)^)^^^'^'-*''''
the decomposition
«- +
(1
-
^)^o^)
(^ +
^'''''^"''''^"^^^
/°°
i+e-U-)-
is:
t
—^OO
t—*oo
Therefore, the trade balance
is
positive while
income flows are negative (and larger
in absolute value
than
the trade balance), as in the main text.
Proof of proposition
A. 4
The
first
inequality of the
3
statement follows directly from
first
inequality follows from the fact that
Prom Lemma
1,
we know
x^
{5
—
5
)
>
as in Proposition
0,
declines over time. Asymptotically,
rt
2.
The second
converges to r^u^.
that
'^"t
i
'
„
,
x^
aut
{g + e-
-^ oo
'
aut
r^,t) (r«
t
-
<0
g)
g^>g
we
Dosition 2
I
CAY
^f
hai
'
i
^ oo
5^ =
where
r~^
=
r^„j
in the proposition
—
6 (l
— Xq)
now
follows since
—
{5
5
{g
is
increasing with respect to
A.5
The U -
)
+
n
"^
5
(see (18)).
9
^
aut
^9 + e-r+){r+-g) ^
-r){r -
From assumption
g
g)
+ 9 -r
5,
r
r"*"
-
> r^^ and
g
r.
E-R model
In this case the equations describing the dynamics of each country's wealth are
45
the second statement
-ew^ + {1 - 5)x^ + nwy
=
w^"
wf = -ewf + {i-s)xf + nwf
which aggregate to the following
differential equation for global wealth
Wt =
(l
-
5
+
(^6
- S^^ x^) Xt +
- e)Wt
{rt
(29)
Similarly, the a^set pricing equations for each country's tree are
=
nV,"
sxi'
+ v,"
nvf = 5xf + vf
which imply the following equation
for the total
nVt
As
=
(5
-
value of world assets
(5
- 5^) xf ) Xt +
Vt
(30)
usual, investment equals savings in the world market:
Wt =
Vt
(31)
^
(32)
which implies a goods market clearing condition
^t
The equilibrium
Hence the world
relative size of the
interest rate can
be solved
=
x'^g"
=
a;[^(p^
interest rate
endowment
is
=
for
+ xfg^ + x^g^ + Q
+
?>Q)
+ xf
a average of g^
[g^
(5(1
- xf + S'^xf)
+ bS) + xf (ff^ + 5«^)
+ bB, g^ + 59
of each country.
46
)
and g^
+ 6^9
with weights given by the
Proof of proposition 4
A. 6
<
Define Too the asymptotic interest rate, r^j
Too
<
r^^t with equality
when g^ >
g.
Note
that:
gE +e^roo
*
t-oo
'
t_oo 5
+ 61
ff«
Too
+e-
roc
and
t^oo Too
- 5^
i-^oo Too
-
t^oo roo
- g^
!/,«
g
Hence
S^ dVf
Vf 55«
<5^
_
dr
Too
- 5^
Too
-5
5(5^
"t
Vl"
55«
5J^
which implies
5« 9 V,"
r-oo-S^
<5«
That
in
E.
is,
We
^oo
l,'-"'
roo- 9
-ff
the long run proportional increase in the value of assets following a collapse in 5
The
results
wealths are
A. 7
SV-E
on the current account follow immediately from
less sensitive
than
initial
its
definition
and the
is
larger in
fact that
U than
asymptotic
wealth to interest rate changes.
Investment and gross flows
need to distinguish between the old trees (with 5
tree, v/^"
the value of a
The aggregate
value of
new
U
R
trees
tree
is
)
and the new
and v^ the value of a
U
rtv^°
=
j'^Zf
rtv^-
=
<5Zf
V^ = N^vl'
nv^,^
=
and
tree.
+
We
if"
+ if"
satisfies
5x,"
nt/U
+ v;^-5"^t
47
trees.
have
Define v(^° the value of an old
R
"
The aggregate
value of
new
R
trees in
rtl/,^"
is
=
V^^"
« O
-
=
(5
=
<5Zf "
+
-
(7V/^
Nq^) v^^ and satisfies
Zf +
(AT,^
-
TVo^)
if
- 5"Arf wf
14^"
Finally, define the aggregate value of the old trees in iJ as V/^°
rtVt^
"
"
= 5^X^° +
= N^v^°.
It satisfies:
Vt^°
Aggregate wealth then evolves according to
=
rtVt
Let's
now
<5
(Xf +
Xf") + 5'^X^° + Vt- g^V^
-
(/"A^f vf
consider wealth accumulation equations:
=
Wt^
in -
e)
w^ + (1
-
5)
xf " +
(1
-
<5^)
xf ° + Pt
Aggregating, we obtain:
W, =
Now
equate W^
(Tt
=K
-d)Wt + {\-
and
<5)
{X'i
+ Xf ") +
=Xt{\-
k)
interest rate satisfies
r,
=
|i +
Xt
As
- 5^) Xf" + g"V;^ + ^"iVf t;f " - h
infer
eWt
and the
(1
for
g [^ {x^
"^
L
+ .f") + J^xf °]
^
'
'
^
/ (1
'
-
.)
i'
-
^g" ^" ^^f""^^
'
'
-ff
i-k"
Xt
aggregate output growth, we have
+9'
Y =9"
so that:
(33)
The
last
term makes clear that the
The reason
is
that 5"
interest rate will initially be lower with
(V^ + N^v^^) > g^Vt
FDI. This depresses even more interest
so the asset
rates.
48
demand
in
FDI,
U
increases
more when there
is
Asymptotically, the last term disappears (since
and x^° tends
to
i;/*"
=
65
+
9
—K
1
v[^'^
The
X
grows at rate g)
so that
0,
roo
Since
and v^° grow at rate g^ while
> v^° and
<
5^xf-°
=
rant
dx^°, we have:
solution for the interest rate requires that
we
feed in a solution for the asset values v/*"
and v^°.
Integrating forward, they satisfy:
/oo
so that v^°/v^"-
= 5^/5
and we obtain:
where
/OO
yRo
e-//(r.-s=)<iu^3
=
l/«°
What
complicates the problem
V/^/X^° which
To
in
-5^JCf °
interest rate
= V/^°/Xt^ =
can be expressed
=
rt
we note
upon the current value
further that
5^
x^°
+
y4^
[<5
in
(1
It satisfies
terms of v^° and x^°
- x^) +
<5«xf °]
as:
- J-g^v^o^^o ^g/^R _
i)
follows simple dynamics:
obtain a single equation for
-^
1-
= -g^xf"
with a forcing term x^°
Ro
dv^
dt
v^°/Z^.
= (n-5^)0f°-5«
if°
we
(36)
turn depends upon the entire sequence of future interest rates.
^
If
+ rtVt^°
that the equilibrium interest rate depends
is
solve this problem, define v^°
and the
(35)
-[5(1- xf °) + 5
V
49
:
- 9"^f °^f° [5/5^ -
l)] if"
- 5^
of
We
can solve this differential equation by 'reversing time'. Since
rt
—> raut, v^° settles
to:
5 6
So we can
start at oo with
Finally, after
using luf
we
= Wl'/X^
find the solution,
{rt
and v^°
close to
we can
= v^
then move 'back'
in
We
-
e)
Wt^
+
(1
-
<5)
-
Xf + g'^Vi" + ff"7V/^u«"
X^
Ptt
—
it
-
.
- gwtu
=
{rt-e-g)w^+(^l-5-~^+g-(^vl' +
=
in-e-g)y.r+(i-S-^)+g-C-^ij-v^''^^(l-^)-./-^
vRn
~ZU
'^P
~ir
/
\
t
t
s
^
\
^Rn
\
/
t
last line uses:
Solving the
Model with Exchange Rates
use a shooting algorithm to solve for the initial terms of trade
Define wt
xq°
u
t
A. 8
=
integrate backward the budget constraint to obtain wealth
Ro /
where the
time until x^°
and
^t
u
x^° very
= W^ /Xl'
and
Xt
=
m
1
X^
=
=
/
^.
q\Xl.
The system
gQ_^
and asset values
VQ_^_
after the shock.
{wt, Xt, ql) satisfies:
{rt-e-g)wt + il-S)
e^«;,P^^(-^)
+
(1
_
^)
(37)
("1 _
Xt
= Xt{l-xt)(g-9'-^)
rt
=
xt{g
p;(--i)
flt,,)
(38)
(39)
+ 69) + {l-xt)(g' +
^ + 5'e)
(40)
It
Equation (37)
for
is
the wealth dynamics for country
good U. Equation (39)characterizes the law
i.
of
Equation (38)
motion of
is
the equilibrium condition on the market
relative output.
Unlike the one-good model,
the path for future interest rates depends upon the future sequence of terms of trade, which depends upon
the current and future asset values.
We
start with a guess for the asset values
allocation,
we
infer the initial
trade go+- Finally,
we
Vq^ immediately
wealth distribution W^^.
We
after the shock.
Given the
then use (38) to solve
for
the
initial portfolio
initial
terms of
integrate (37)- (40) forward to construct the path of future interest rates and terms of
50
trade rt^Qt consistent with equilibrium on the goods markets.
We
then use
/OO
Jo
/•OO
_
i
Xq
Jo
to update our guess for Vq^, where 6t
A.9
=
J2i^t^^
^^^ average (time-varying) capitalization ratio.
'^
"Calibration"
This section discusses the choice of parameters underlying Figures 3-12.
requires parameter values for
approximately based on
xq, Qq'^, Qq^*, {g
aggregate data. Table
5
x^
x§
p^^
0.25
3%
0.12
0.5
0.3
0.05
According to
we should think
(4),
1:
{5
—
NA^JX^
g
Table
— g^) and
5
).
'cahbration' of the model
We
chose to assign parameters
summarizes our parameter assumptions.
1
6
Parameter
Value
US
5, 6, g,
The
^\t=o
[g
trillion in 2004.^4
In the simulations,
we round
We
2004 equals 3.33%.
this
round
GDP
parameter to
Average output growth
set the
good
oil
turn to the output shares.
asset suppliers,
We define U
US Flow
— g)/9 =
0.12.
as the U.S., the U.K.
and experienced robust growth
in
in the U.S.
growth rate g to 3 percent.
value of Taut equal to 6%. This imphes a value of 5 of (r
We now
X/W. We
of $11.73 trillion in 2004, this implies 6
0.25.
number and
this
0.07
Main Parameters
of 9 as the output to financial wealth ratio,
With a US
{5-5'')
1.11%
-0.5
estimate of ly as the net financial worth of the household sector. According to the
equal to $48.52
- 9^)
the past decade.
obtain an
of Funds,
= i|^ ~
it is
0.24.
between 1950 and
Finally,
we assume a
^^
and Australia. These countries are
We
identify
E with
developed non-
producing countries with sound financial markets, but a lackluster growth performance. Accordingly, we
define
E as countries from the European Union
Finally,
we
identify
R with
developing and
oil
(less
the UK), Iceland, Japan,
New
Zealand, and Switzerland.
producing countries with a good income growth potential, but
limited asset production capacity.^®
^•See the Balance Sheet Table BlOO, line 42 of the September 2005 release.
^^ Another possible
S&P
way
to calibrate 6
is
to observe that in steady state, the
500 averages 18.2 for the period 1950- 2005. (see Robert
This yields 5
economy
•^®The
=
0.22,.
This value of
are capitalizable,
list
we
i5
would imply a
prefer our estimate of
Shiller's
webpage
risk free rate of
8%
P/E
ratio
is
V/SX =
1/69.
The P/E
ratio for the
at http://www.econ.yale.edu/'shiller/data.htm).)
which we view as too high. Since not
all
assets in the
5.
includes Argentina, Brazil, Chile, China, Colombia, Costa Rica, Ecuador, Egypt, Hong-Kong, India, Indonesia,
Korea, Mexico, Malaysia, Nigeria, Panama, Peru, Philippines, Poland, Russia, Singapore, Thailand and Venezuela.
data
for
Poland and Russia starts
in 1990.
51
Output
We
measure the
initial
output share as the average output share between 1980 and 2003.^^
X,
We
find
^0.50
x§ + x^
X, R
we assume
Lastly,
that the
financial wealth, as estimated in figure 1(c).
the ratio of
US
We
adopt an
US, the
EU
To estimate the
latter,
we
US
value of 0.05. Figure 1(c)
initial
BEA's US
gross external liabilities (from the
of the World's financial wealth.
for the
share for [/-trees equals the share of
initial portfolio
assets in
is
ROW
constructed as
International Investment Position) to the Rest
calculate the ratio of financial wealth to output
We
and Japan between 1982 and 2004.^8
find
a
GDP
weighted average of 2.48.
apply this ratio to the Rest of the World GDP. For 2004, we estimate a financial wealth of $72
We
trillion for
ROW and $36 trillion for the US.
the
We
set:
^°-
where
i
=
^
G {E,R}. Furthermore, we assume that the
=
0-05
initial
(41)
net foreign asset position
is
0.^^
This implies
that
— wL vL
"0- =
^-°-
•''^0-
Substituting into (41),
we obtain
^^i"-
which
yields:
.^^
=
0.05
i^"
=
0.02.
Finally, since
<_ - V^o- = c^o'vL - ai^Vo'L
we
=
find
=
We now describe
According to the
the parameters for our shocks.
WDI,
lJ-o_
=
We set
0.05
the decline in E's growth rate, {g
— g'^) =
1.11%.
E's average growth rate between 1980 and 1992 was 2.73% and only 1.63% between
1992 and 2003 (ppp-adjusted).
^^We
use
^^Sources:
cial
GDP
data
in
current dollars from the World Development Indicators.
US; Flow of Funds, Table BlOO
and capital account of the non
line 8,
household financial assets; EU: Table 3.1 of the
financial sector; Japan:
Flow of Funds, households
Bureau of Economic Analysis, the US had a zero net foreign asset position
52
Bulletin, finan-
total financial assets, available at
http://www.boj.or.jp/en/stat/stat_f.htm.
^^ According to the
ECB
in 1988.
We
crisis.
6
=
calibrate the decline in S
Prom
(xq5
+
so that
matches the decline
it
Section 2.3, R's assets price drops from VqI.
(l
— Xq)
(5
j
is
= X^/d
around the time of the Asian
,
=
5^15 -
1<
= 5^/65Xq where
values at t =
is
before the shock to Vq^
the world capitalization index. Hence the drop in asset
t=o
Solving this expression for 5
in asset values
0.
we obtain
ro^[l
(5-5^) =
+
r1.
^U=o
1-
(5
I
V ^|,=o(l-0-xo^
The
decline in dollar asset values
Indonesia.^"
We
was 37 percent
Hong-Kong, 75 percent
in
Korea and 83 percent
- 5^) =
0.07;
5^
=
calculated the decline between July 1997 and January 1998 of the
0.05
Hang Sen Composite Index (Hong Kong), the KOSPI
(Korea) and the Jakarta Stock Index (Indonesia). All price indices were converted into dollars using daily exchange rates.
53
r
'
in
conservatively consider a decline of 50 percent. This implies:
{5
^°We
in
-
Date Due
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MIT LIBRARIES
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