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Massachusetts Institute of Technology
Department of Economics
Working Paper Series
BUBBLES AND CAPITAL FLOWS
Jaume Ventura
Working Paper 02-36
October 2002
Room
E52-251
50 Memorial Drive
Cambridge, MA 02142
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://papers.ssrn.com/abstract_id=341140
MASSACHUSETTS INSTITUTE
_OFTECHNOLOGY_
I
JAN 2
1 2003
LIBRARIES
Bubbles and Capital Flows
Jaume Ventura
Pompeu Fabra and MIT
CREI, Universitat
October 2002
and asset price
bubbles. Its central insight is that bubbles tend to appear and expand in countries
where productivity is low relative to the rest of the world. These bubbles absorb local
savings, eliminating inefficient investments and liberating resources that are in part
used to invest in high productivity countries. Through this channel, bubbles act as a
Abstract: This paper presents a stylized
model
of international trade
substitute for international capital flows, improving the international allocation of
investment and reducing rate-of-return differentials across countries. This view of
asset price bubbles has important implications for the way we think about economic
growth and fluctuations. It also provides a simple account of some real world
phenomenae that have been difficult to model before, such as the recurrence and
depth of financial crises or their puzzling tendency to propagate across countries.
Comments
are
welcome
at iaume(5)mit.edu or
providing excellent research assistance.
MIT
for their useful
paper.
I
am
jaume. ventura@crei.upf.es
also grateful to the
comments. Of course, none
of
them
is
.
members
I
thank Pol Antras for
of the Faculty
Macro Lunch
responsible for any error or omission
in
the
at
This paper presents a stylized model of international trade and asset price
bubbles.
where
1
Its
central insight
productivity
is
that bubbles tend to
is
appear and expand
in
countries
low relative to the rest of the world. These bubbles absorb local
savings, eliminating inefficient investments and liberating resources that are
used
to invest in high productivity countries.
Through
this channel,
in
part
bubbles act as a
substitute for international capital flows, improving the international allocation of
investment and reducing rate-of-return differentials across countries. This view of
asset price bubbles has important implications for the
growth and fluctuations.
phenomenae
that
It
way we
also provides a simple account of
have been
difficult to
think about
some
economic
real world
model before, such as the recurrence and
depth of financial crises or their puzzling tendency to propagate across countries.
Tirole [1985]
has argued that markets create asset price bubbles
investments.
inefficient
2
His argument goes as follows: Consider an
to eliminate
economy where
the growth rate exceeds the rate of return to capital. In this economy, a bubble can
create
its
own demand
without outgrowing savings by offering a rate of price
appreciation above the rate of return but below the growth rate.
part of the
The bubble absorbs
economy's savings, crowding out investment and reducing the
capital
stock and output. Since the resources devoted to investment (roughly growth times
the capital stock) exceed the resources obtained from such activity (roughly the rate
of return times the capital stock), the bubble raises
welfare.
from
The key
insight of Tirole's theory is that the bubble takes
inefficient investors
An
implicit
rate of return.
consumption and improves
assumption
Assume
economy contains
and puts them
in
in
Tirole's
the hands of consumers.
argument
is
that
instead that, as a result of frictions
efficient investors that
away resources
all
in
investors face the
same
financial markets, the
enjoy rates of return
in
excess of the growth
By a bubble or asset price bubble, refer to the difference between an asset price and the net present
value of its dividend flow or fundamental value.
I
Tirole's paper builds on the path-breaking work of Samuelson [1958], who was the first to note that
useless assets might be valued in a competitive economy and that this would be Pareto improving.
and also
rate,
its
inefficient investors that
own demand
within the
group of
do
not. In this
economy, a bubble can create
outgrowing their
inefficient investors without
savings by offering a rate of price appreciation above their rate of return but below the
growth
rate.
The bubble crowds out
can be used not only
that
to raise
investments and liberates resources
inefficient
consumption, but also to increase
investments. Through this channel, the bubble can
capital stock
and output. Since
inefficient investors
investment than they obtain from
now
in
is
The goal
the bubble
consumers and efficient
of this
still
away resources from
that the bubble takes
the hands of both
it,
paper
is
price bubbles for the theories of
to
now
lead to an increase
raises welfare.
hypothesis
is
examine the consequences
economic growth and
policies are richer but
that international financial
cross-country differences
such as policy-induced
sovereign
rate of
4
risk.
If
trade
in
first
do not grow
markets have
economic growth while
frictions in
that
all
one
3
is
below the
common
To do
this,
I
keep
that international
is
economic growth are
faster.
save more and have
3
The second
due
to a variety of frictions
asymmetries and
same
countries share the
long-run
asset trade allow countries to have different
rates of return, asset price bubbles naturally arise
return
and puts them
limited ability to arbitrage
rates of return. This might be
goods ensures
insight
of this view of asset
fluctuations.
barriers, transaction costs, information
in
the
investors.
sufficiently integrated that long-run rates of
and
The key
inefficient investors
positively linked across countries. This implies that countries that
better technologies
in
devote more resources to
two maintained hypotheses throughout the paper. The
goods markets are
efficient
or world growth rate.
in
those countries where the rate of
5
ample evidence in support of this view. Despite
and technology, the world income
distribution has been relatively stable in the second half of the twentieth century. Howitt [2000] has
argued that this stability might be due to technology spillovers, while Acemoglu and [2002] have argued
that
might be due to terms-of-trade effects. Through any of these channels, countries with bad
characteristics are able to grow fast and keep up with the rest of the world.
4
These frictions do not preclude all international capital flows, although the latter are much smaller than
what theories based on frictionless markets predict. See Kraay et al. [2000] for a review of the evidence.
5
In an influential paper, Abel et al. [1989] noticed that the capital share exceeds investment in industrial
countries. Since this implies that the average rate of return is above the growth rate, many have used
Leaving a few miracles and disasters aside, there
large cross-country differences
in
economic
is
policies, saving rates
I
it
To study
equilibrium
the implications of this observation,
model
trading assets
in
which the cost of trading goods
prohibitive. This is
is
I
construct a stylized world
is
negligible while the cost of
a crude but effective
way
to capture the
two
maintained hypotheses discussed above. The model has equilibria with bubbles,
addition to the bubbleless equilibrium that
we always
in
take for granted. These are
country bubbles, since they can be sold only within the country.
6
Bubbles appear
in
countries with low productivity, eliminating domestic investment and raising domestic
consumption. This
shift in
consumption goods
productivity.
done
all
demand
lowers the price of investment goods relative to
over the world, raising investment
in
countries with high
Since the transfer of resources from low- to high-productivity countries
via prices
and without any actual or recorded
capital flow, this could
is
be aptly
described as a theory of capital flows with zero current accounts.
Since bubbles act as a substitute for international capital flows,
effects are akin to those that
one would expect from
many of their
financial integration.
By
improving the average efficiency of investment, asset price bubbles tend to raise the
world growth rate. By shifting investments towards countries with high productivity,
asset price bubbles tend to
make
the world
economy more
these countries and less sensitive to shocks
in
sensitive to shocks
in
other countries. By providing low-
productivity countries with a better savings vehicle, asset price bubbles also tend to
improve the world income
distribution.
By expanding
at the
end
of
booms and
contracting at the end of recessions, bubbles tend to amplify the effects of
productivity
shocks on investment while dampening
their effects
on consumption.
All
of these effects, which are typically associated with financial integration, arise here as
observation to question the empirical validity of Tirole's model. But this conclusion rests on the
assumption that financial markets are frictionless. Even if the average rate of return exceeds the growth
rate, the economy might contain pockets of investors with low rates of returns that are willing to buy a
bubble. Hence it is not possible in general to rule out the presence of bubbles by comparing the
aggregate capital share and investment.
6
In Ventura [2002],
consider the case in which financial markets are well integrated in the sense that
domestic and international transactions are subject to the same sort of frictions. In this case, bubbles are
traded across countries and refer to them as global bubbles.
this
I
I
the sole result of asset price bubbles since capital flows are not possible and trade
is
always balanced by assumption.
Bubbles also have
some
effects that are different from those that
one would
expect from financial integration. For instance, domestic and foreign shocks lead to
movements
Through
in
this
the size of the bubble that generate potentially large wealth effects.
channel, the presence of bubbles magnifies the effects of productivity
and other shocks on aggregate
to
Another effect of bubbles
activity.
is
open the door
to
shocks to expectations as a new source of macroeconomic fluctuations. Bubbles
are inherently unstable, since they arise
coordinate to one
among
effects of productivity
in
environments where agents need to
a variety of possible equilibria. Since bubbles magnify the
shocks and open the door
to expectational shocks, low
be more
productivity countries that
have large bubbles tend
productivity countries that
have small bubbles. But the relationship between
and
productivity
is
to
volatile
than high
volatility
nonlinear. Countries with intermediate levels of productivity tend to
have smaller but more
volatile bubbles. In particular,
external shocks generate
movements
in
I
find that in
these countries
the size of their bubbles that have potentially
large wealth effects. This observation can be used to provide a theoretical justification
to the notion that middle-income countries are very vulnerable to small
fluctuations
in
high-income countries.
It
economic
can also be used as key building block
in
an
attempt to sketch a theory of the international contagion of financial crises.
The paper
is
organized as follows: Section one presents a stylized model of
trade and growth and describes the world equilibrium without bubbles. Section two
shows
that there are additional world equilibria with bubbles
them. Sections three to seven present
macroeconomic
effects of bubbles.
five
The
substitute for international capital flows.
examples designed
first
to illustrate the
two emphasize the
role of
The remaining three deal
of financial fragility, vulnerability to external
concludes.
and formally describes
bubbles as a
with the concepts
shocks and contagion. Section eight
1
.
A
Productivity-Based View of the Growth Process
In this
section
tool or vehicle to
their
I
present a simple model of trade and growth that
will
serve as a
study the conditions under which asset price bubbles can exist and
macroeconomic
effects.
The model has some
unrealistic features
such as the
prediction that factor prices are equalized across countries or the assumption that the
law of one price applies to
however
all
goods. These aspects of the model are not important
and have been chosen only
for the results of this paper,
discussion.
The two
features of the model have already been discussed
critical
introduction: while trade in
goods ensures
return differentials across countries.
There are various models
critical
the
asset trade preclude the elimination of rate-of-
in
share these two
in
economic growth are
that long-run rates of
equalized across countries, frictions
that
to streamline the
of trade
and growth
features without predicting that goods and factor prices
are equalized across countries. For instance,
Acemoglu and
I
[2002] wrote a model
with these characteristics recently.
Consider a world economy with J countries, indexed by j=1,2
two factors of production: labor and
capital,
and they are used
two intermediates: K- and L-products. These intermediates are
produce two
final
the production of
in
in
turn
goods are
used
to
negligible.
countries there are competitive firms with access to a
technology to produce intermediates.
To produce one
To produce one
one
unit of labor.
Since
employment
of factors implies that both intermediates are
unit of capital.
final
unit of the L-product,
goods production only requires intermediates,
Perfect competition ensures that the rental and the
in all
common
unit of the K-product,
firms require
and L-products
There are
goods: consumption and investment. The costs of transporting
factors are prohibitive, while the costs of transporting
In all
J.
wage
produced
these
they need one
full
in all
countries.
are equal to the prices of K-
countries, while international trade ensures that the prices of
these intermediates are equalized across countries.
It
follows that factor prices are
equalized across countries as well.
K-products) and
wage
technology to produce
rt
(or price of L-products) at date
final
goods. To produce one
0<a<1 To produce one
.
one
unit of the
unit of the K-product.
Since
Perfect competition then ensures that
1
-a
rt
(1)
1
(2)
q =r
t
where q
t
firms
all
unit of the
common
consumption good,
(or labor)
share equal to a,
in all
countries face the
goods are also the same
same
in all
goods prices equal these production
price
countries.
costs:
t
is
the price of investment and consumption
structure of countries
generations model with constant population.
new
generation of consumers
The consumers' goal
When
consumption.
in their life is
their
t.
-w?
The demographic
date, a
rental (or price of
investment good, firms have a technology that
of intermediates, the costs of producing final
=
and w, as the common
Cobb-Douglas technology with a L-product
firms have a
requires
Define
countries there are also competitive firms with access to a
In all
with
7
what
in life is
to
is
is
All
is
the numeraire.
that of a two-period overlapping
generations have size one.
born that
lives
In
two periods: young and
maximize the expected value
of old
each
old.
age
young, consumers work and save their wage. The only decision
do with these savings.
to
When
old,
consumers use the
savings to purchase consumption goods. This formulation
is
return to
nothing but a stark
version of the popular life-cycle model of savings.
7
This result
Helpman
is
due
[1985]).
to
Samuelson [1948] and applies
What
is
perhaps surprising here
is
to a
wide range of models (See Krugman and
any cross-
that factor prices are equalized for
country distribution of capital-labor ratios. This is a special but very convenient property of this specific
production structure that borrow from Ventura [1997].
I
each generation, some of the young create and operate firms that purchase
In
investment goods
in their
old age. For simplicity,
and
that there
is
youth and convert them into capital that can be used
assume
I
enough
that this entrepreneurial activity requires
talent in the country so as to drive the
entrepreneurs to zero. The entrepreneurs of country
producing
7ij
units of capital with
+1
productivity of country
support that
and
is strictly
positive
we have
Ki +1 =7i! +1
(3)
that
Assuming
I
t
of
are capable of
refer to n) +1
as the
can vary stochastically over time within a
ij
and Kj be the investment
that capital fully depreciates in
one
-l{
———
unit of
income invested
in
country
j
yields a
71^
r
rate of return equal to
q
firms issue shares and sell
produced and distributed
its
date
effort
that:
Given these assumptions, each
of
it
and bounded above. Let
capital stock of the country.
generation,
at
each investment good.
and assume
j
j
wage
no
in their
.
To finance
their
purchases of investment goods,
t
them
in
in
the domestic stock market. After output has been
the form of dividend, the firm has no assets and the value
shares drops to zero.
A
key assumption
is
that the costs of trading
negligible, while the costs of trading in foreign stock
asymmetry
in
the domestic stock market are
markets are
prohibitive. This
costs could be due to a policy-induced barrier such as prohibitive
in
capital controls, or
it
could be due to the inability of countries to commit not to
expropriate foreign investments. Whatever the reason, the young are forced to invest
all
of their savings in the
(4)
qt -l{=w
(5)
C|=r
t
t
-K|
domestic stock market, and
this implies the following:
Equation
save the
investment
(4) states that
wage. Equation
entire
(5)
shows
is
equal to labor income, since the young
that
consumption
equal to capital
is
income, since the old have no bequest motive.
Define world averages by omitting the country subscript. For instance, the
-i
world average capital stock
is
K,
=
- VK{
.
lemma
Applying Shepard's
to
Equations
J
i
(1)
and
(2),
we
1
— (X
1
—
•
q,
•
find the world
+
I,
products are
K and
t
K =q
(6)
r
(7)
w =a-C,
t
K and
C.
,
respectively. Since the
L-products as
average supplies of these
w,
rr
r,
for
ex
and
C.
average demands
t
l
t
1,
international
(1-a)C
t+
commodity markets clear
such
quantities
if:
t
that
equilibrium of this world
equilibrium.
dropped.
By Walras'
show
I
economy
consumers optimize and markets
distribution of capital stocks,
next
law,
some
Equations
clear.
(1)-(7) provide a
one among Equations
a set of prices and
is
Together with an
initial
complete description of
(4)-(7) is
this
redundant and can be
properties of this world equilibrium.
Let R{ be the rate of return to the portfolio of country
contains only domestic investment,
we can use
Equations
j.
Since
(1), (2)
this portfolio
and
(7), to find that:
R!=g, -«-7r|
1
where g
which
and only
t
The competitive
(8)
if
t
is
this
the growth rate of world consumption,
growth rate
is
positive.
i.e.
g =
t
Q
—
—
.
Despite the continuous decline
Consider the case
in
the rental rate,
in
the rate of return remains constant because the price of investment goods also
declines at the
same
This follows from Equation (2) and
rate.
of the assumption that only capital
is
used
idea that there exists a core of capital
same
core of capital goods
is
in
goods
is
good
only one capital
It
is
can be produced using only
that
AK version
in this
of this
model
which
in
core.
(3), (5)
and
the world growth rate of
(7) that
given by:
t
The world growth
is
the labor share
the higher
common
is
rate
in
depends
positively
on a and R The higher
t
income and the higher
income
the average return obtained from these savings.
growth rate
in
the long run. The reason
distribution stable.
is
All
in
consumption
simple: growth
ones and
C
R
—
- = —-
this
we
is
R
t,
in
high-return
keeps the world
all
countries
j
j
(9),
the
reflect differences in rates of return.
note that Equations (3)-(5) imply that
Solving Equations (8) and
is a,
countries share a
Since wages are equalized internationally,
save the same, and differences
this,
.
world savings. The higher
is
countries improves the terms of trade of low-return
To see
this
g =oc-R,
(9)
higher
The
the basic tenet underlying the linear growth model of
follows from Equations
consumption
a direct consequence
the production of investment goods.
Rebelo [1991]. Here we have adopted the extreme
there
is
C
t
R
8
.
t
obtain this stylized description of the growth
process as a function of the exogenously specified productivity processes:
(10)
1-a
t
)
would be straightforward to introduce labor-augmenting productivities differences across countries as
Ventura [1997]. This would generate cross-country differences in wages and savings.
It
in
g,=(a-7i
World growth depends on average
in
productivity, while
each country's position
depends on
the world distribution of consumption or wealth
its
relative productivity.
This world therefore encapsulates a traditional or productivity-based view of economic
growth and fluctuations. This view
some
most
of the
reasonable and has the potential to explain
interesting growth experiences,
miracles or worldwide
based view
is
changes
in
rates of
such as the existence of growth
economic growth. But the
not well suited to explain other real world
is
productivity-
phenomenae such as
the
recurrence and depth of financial crises or their puzzling tendency to propagate
across countries.
reality
push
key question
is
therefore:
How can we model
that the implicit (and unjustified)
fundamental value
it
is
these aspects of
without losing the basic insights of the productivity-based view?
of this paper
their
A
aside,
it
is
is
A central
assumption that asset prices
the obstacle that stands on the
way
of doing this.
claim
reflect
Once we
possible to catch an eye-opening glimpse of what the productivity-
based view has been leaving behind.
2.
Country Bubbles
If
is
R{ > g, for
unique. But
if
all j
and
R{ < g, for
t,
the world equilibrium described
some and
j
t,
I
refer to
the previous section
there might be other equilibria
useless assets or firms are valued and traded
convention,
in
in
in
which
the stock market. Following standard
9
these useless assets or firms as pure bubbles. To be
clear,
these bubbles are rational since their existence does not rely on the presence of
individuals that are incapable of processing publicly available information or that
behave
in
a
manner
that
is
inconsistent with the usual axioms of choice theory. In the
bubbly equilibria studied here, the old
The
in
distinction
sell
bubbles to the young. The
later
understand
between productive assets and pure bubbles is useful as a theoretical device. However
sometime seem to appear in productive assets. Olivier [2000]
the real world asset price bubbles
shows how to modify the theory
to allow for bubbles that are "attached" to productive assets.
10
that these bubbles
will
never deliver a dividend, but they
expect a return
rationally
in
in
assets are
is,
the bubble
the value of
j
at date
stock market of country
B{ +1
(11)
where
initial
+1 is
the growth rate of the bubble or
value,
B >
that
is
-lj+B!=w
B|
the
J[0,w
t
]
t,
if
if
t
in
rate of price appreciation.
Note that
general the value of the bubble at date
not available at date
by
(4)
t.
I
define a country bubble as
i.e.
u.j +1
for
all
t>0.
young since they
We
this pair:
Et
RJ<E K^l
E
{uU=E
t
t
j^l^
t
I
w
since
its
t
if
j
in
to hold the capital stock, the country bubble, or both.
must therefore replace Equation
t
the useless firms traded
of a bubble enlarges the portfolio choice of the
now can choose whether
q
all
and a price appreciation process,
J
i.e.
The presence
(12)
bubbles are
= mIi-B{
depend on information
t+1
prohibitive,
This bubble grows according to this process:
j.
might not be known as of date
u.{ +1
an
u.j
i.e.
t,
still
they are country bubbles. Let BJ be the size of
only traded within the country. That
country
buy them because they
the form of price appreciation.
Since the costs of international trade
in
still
E
t
9t
RJ>E j^!±i
t
Equation (12) shows that the young
now
distribute their savings
between the
stock of capital and the bubble. Equation (13) describes the choice of country
11
portfolio
as a function of asset returns. The return to holding a bubble
is its
r
rate, i.e.
u.{
+1
;
while the return to holding capital
is
the dividend,
—
.
-^
i.e.
growth
jr^
^-. Since
q.
the young are risk-neutral, they choose the asset that offers the highest expected
return.
If
between holding
capital, the
The presence
now
same expected
both assets offer the
return, the
young are
indifferent
bubble or both.
of the bubble also implies that the
consumption of the old
given by their capital income plus the proceeds of selling the bubble. Therefore,
we must
(14)
replace Equation (5) by:
C{=r -K{+B{
t
The
rest of the
model remains the same. For a given
capital stocks, a competitive equilibrium of the world
initial
economy
distribution of
consists of a set of
country bubbles such that Equations (1)-(3), (6)-(7) and (11)-(14) hold for
realizations of the world
among Equations
all
possible
economy. Once again, by Walras' law we can drop one
(6), (7), (12)
equilibrium obtains by setting
t.
is
and
(14).
Bj,=0
This equilibrium always exists, as
for
The
productivity-based view or bubbleless
all j;
and Et ^i{+1 }<E,j—
shown
in
——
the previous section. But
and
[
for
it
might not be
all
j
unique.
Since the country
need no longer be equal
bubble
in
portfolio
now might
contain the bubble,
to the rate of return to capital. Define bj
the country portfolio or savings,
i.e.
b{
B
=
j
—
r.
q -lj+Bi
t
country j's portfolio
is
its
now given
by:
12
The
rate of return
as the share of the
rate of return to
:
(15)
R^g^tt'-a-bj^ + ^b^
A
of algebra
bit
However,
that Equation (9)
still
a function of exogenous impulses using Equations
need
describes the world growth rate.
not possible to provide a complete description of the growth process as
is
it
shows
exogenously not only the path of
to specify
(9)
and (15) alone. To do so we
productivity, but also
how
countries
coordinate to a particular equilibrium. For instance, the derivation of Equation (10)
implicitly
assumes
that:
(i)
the bubbleless equilibrium
is
unique
or, alternatively,
(ii) all
countries coordinate to the bubbleless equilibrium with probability one. Either of these
two assumptions or views
is
sufficient to justify the productivity-based
growth process. But they are not the only
As a prelude
equilibrium,
it
to
making assumptions on how countries coordinate
bubbles that are feasible
Proposition #1
in
world equilibrium.
Consider J sequences
{bj
set of country bubbles defined by these
E t -jg t+1 --^-l>EJg£f
andt, (C1)
possibilities.
useful to obtain a simple characterization of
is
view of the
The
the sets of country
following proposition
|~™ such that bj
e
sequences
is
b|=1
if
-jijL with
all
[0,1]
feasible
to a given
if
for
does
all t
and only
the inequality
this:
and
if,
is strict;
j.
for
The
all
j
and
b{
v-
f
a
(C2)g t+i
i
,.
Li
*V- a
2>i + i-(1-bj)
v
The
proof simply consists on substituting Equation (11) into (13) and using
equilibrium prices to obtain (C1),
obtain (C2).
The
proposed set
proposition
of country
is
and
useful
bubbles
is
to substitute
because
it
Equation (15)
into
Equation
(9) to
allows us to check whether a
feasible by solving a small system of equations.
13
To develop
intuitions
about the macroeconomic effects of bubbles,
next five examples. Together, they reveal a
process
in
and somewhat
surprising ways.
bubbles substitute for capital flows and, as a
similar to those of financial integration.
of
recurring
result, their
Another theme
is
theme
is
and
that
main effects are akin or
that
movements
presence of bubbles also opens the door
become
expectations to
part of the
in
the size
have low
=
H
Jt
the world contains
productivity,
L
>
7t
.
n\
i.e.
The goal
is
Equations
infinitely
;
example
affects both the world growth rate
It
for
= n l while the
of this
for
and
to
is
Long-Term Capital Flows
many
rest
countries of two types. Half of
have high
to determine
and the
productivity,
distribution of wealth
(9) that in this equilibrium
them
i.e.
how the presence
of bubbles
across countries.
useful to start by describing the bubbleless equilibrium.
(8)
shocks
macroeconomic landscape.
Bubbles as a Substitute
Assume
n|
A
roles,
bubbles create large wealth shocks. These movements might be driven by shocks
to productivity. But the
3.
develop
new and broader view of the growth
which both productivity and asset price bubbles play central
interact in interesting
I
It
follows from
the following applies:
1-a
71+71
a
(16)
2
V
-a
(17)
R =g
J
1
-«Tt'
The world growth
rate
depends only on average
productivity, while the cross-
country distribution of rates of return (and consumption or wealth) depends on
14
how
dispersed this productivity
As discussed
is.
already, this
is
the essence of the
productivity-based view of economic growth.
But this might not be the only equilibrium of this world economy. Consider the
possibility that country
j
deviates from the others and coordinates to an equilibrium
with a stationary bubble,
rate
is
constant and there
=b
b{
i.e.
for
all
t.
Is this
possible? Since the world growth
no uncertainty, condition (C1)
is
bubble can be
for this
written as follows:
1
(18)
g
1
To create
"a
>n
its
j
own demand,
the bubble must grow at a rate that
is
no lower than the
-a
rate of return to capital,
i.e.
g
1_a
j
Tt
.
To ensure
bubble must grow at a rate that
is
Equation (19) says that there
room
rate
exceeds the
does not outgrow savings, the
for
we have
a bubble
in
rate,
country
j
if
i.e.
Therefore,
g.
and only
Except for the knife-edge case
if
in
the growth
which
that:
b=1
(19)
is,
the bubble crowds out
all
productivity country this bubble
check
this,
is
the investment of the country.
not feasible
some parameter values.
has low
defined by an
If
because condition
substitute Equation (16) into condition (18) with
productivity country the bubble might
If it
it
no higher than the growth
rate of return to capital.
inequality (18) holds strictly,
That
is
that
i=
7i
country j
a high-
(18) never holds (To
H
7t
is
). If
country j
is
be feasible because condition (18) holds
a low-
for
10
productivity, country
j
might also have any of a continuum of non-stationary bubbles
value bo'e(0,1] and sequence of b\ such that (C1) holds with
bubbles vanish gradually over time and will be ignored in the rest of this paper.
initial
15
strict equality.
These
—
—
Consider the case
in
which a fraction $ of the low productivity countries
coordinate to the bubbly equilibrium, while the rest coordinate to the bubbleless one.
refer to
as the size of the world bubble.
<j)
(
g =
(20)
(1- -<t>)
a-
fg
R'~|
.
g
1
+
.
71
follows from Equations (9) and (15) that:
_H > 1-a
Tt
2- a<|>
V
(21)
_L
It
I
,
if
b{
=
if
bj
=
1
-a
^a
•7T
j
Equations (20) and (21) describe the world growth rate and the return to the
country portfolios
(18),
we
in
the bubbly equilibrium. Substituting Equation (20) into condition
find that this equilibrium exists
if
and only
Ot
71
productivity
is
sufficiently high,
i.e.
if
—n-<
n
Using Equation (20),
it
is
investments
high-productivity ones.
consumption
(or
all
The key
intuition is that
low-productivity countries
An
is
increase of one percent
nl This lowers the
over the world.
all
.
A
in
efficient
over the world.
A one
price of investment
—
is -
percent increase
a
percent
(See Equations
in
(7)
investments
in
countries
goods and
means
wage means
in
that
where
raises the
each
unit of
that savings
the world bubble leads to an
the rest of the world where average
and
(12)).
Since Equations (18) and
2-a-<(>
—
(A
(20)
ensure that the bubble
is
feasible
if
and only
if
i\\\
TT^~
_l_
L
n < a--
2-a<|)
16
in
the world bubble increases
lower price of investment goods
increase of investment spending of
productivity
the bubble eliminates
and raises
savings buys more investment goods, while a higher
increases
from now on.
this
reduces investment spending) by one percent
average productivity
wage
in
-a
in
straightforward to check that the world growth rate
increases with the size of the bubble.
inefficient
cross-country dispersion
Assume
•
2
if
TT^
,
we have
that
an increase
in
level of production
rate applies
in
the
the size of the bubble increases the world capital stock for a given
and
limit
Using Equation
this raises
the world growth rate.
where the bubble
(21),
we
is
as large as
it
The maximum world growth
can be,
i.e. <j>-»1.
also find that the presence of bubbles raises the rate
of return of the portfolio of the countries that hold the bubble relative to the rest of the
world. This
means
that these countries
move up
in
the world distribution of
consumption and wealth. Since countries that have a bubble also have low
productivity, the
presence of bubbles tends to reduce rate-of-return
differentials
and
C- = —R
—
-).
j
improve the world
In fact,
distribution of
consumption and wealth. (Remember that
the most equalitarian distribution applies
large as
it
can be,
in
the
limit
when
C
the bubble
R,
t
is
as
i.e. <J>->1.
This example illustrates the role of bubbles as a substitute for long-term
capital flows.
Since the
later are not possible,
alternative or second-best
Bubbles arise
liberating
in
to
improve the world allocation of investment.
low-productivity countries, eliminating inefficient investments
resources that are used
countries. This transfer
is
since
we have assumed
zero.
By increasing the
rate.
mechanism
stock markets generate bubbles as an
By reducing
made
in
via
part to increase investment
changes
in
throughout that trade
prices
is
in
and
high-productivity
and without actual
capital flows,
balanced and current accounts are
efficiency of world investment, bubbles raise the world growth
rate-of-return differentials across countries, bubbles
world income distribution.
17
improve the
4.
Bubbles as a Substitute
Consider next a world with
Productivity fluctuates
assume
that productivity
and
j
is
The world
t.
infinitely
Short-Term Capital Flows
many
between a high and a low
probability of transitioning
across
for
countries of a single type.
state,
from one state to the other
The goal
of this
is
example
is
to
in
{n:
,7t
i.e.
E
equal to
each
starts with half of the countries in
H
L
e
known before making investments,
the invariant distribution, the proportion of countries
time.
n\
i.e.
A.
j
t
{nj +1
and
state.
each state
H
with
is
7i
}=
> nL
n{ +1
.
I
The
.
independent
Since
this is
constant over
is
determine how the presence of bubbles
determines the way countries react to productivity shocks.
The bubbleless
previous example,
now
all
i.e.
equilibrium of this world
as described
in
economy
is
the
same as
in
the
Equations (16)-(17). The only difference
is
that
countries are ex-ante identical and each of them spends half of the time being
low-productivity
productivity
and
half of the time being high-productivity.
become permanent and we approach
the world
As X—>0
we
differences
analyzed
in
in
the
previous subsection.
Consider the
to
possibility that
country j deviates from the others and coordinates
an equilibrium with a stationary bubble,
In this
i.e.
bj
= bH
if
n\
= n H and
bj
= bL
if
n\
= nl
.
case, condition (C1) implies the following:
1
(22)
b
L
g
1-
1
a
>7t
L
1-X+X-—TT
H
and
g
1
~a
>ti
h
b
1
Since
create
h
ti
its
> g
1
a
the bubble must expand at the end of high productivity periods to
own demand,
i.e.
b L >b H This
.
in
turn implies that the bubble
18
must contract
at
1
the end of low productivity periods. Except for the knife-edge case
inequalities hold strictly,
L
(23)
b =
b
1
it
H
in
which both
follows from (22) that:
=X+
——
-
,1-a
Now either all
Note also
that
the countries can have the bubble, or none of
shocks
to productivity generate
movements
in
them can have
it.
the bubble. Transitions
to the high state lead to contractions of the bubble, while transitions to the low state
lead to expansions. Equation (23)
positively related to the world
is
shows
growth
that the size of these
rate.
The
larger
movements
the latter the
is
more
is
attractive
the bubble inside high productivity periods, and the smaller are the expansions at
the end of these periods that are required to support the
Equation (23) also shows that there
these movements
in
is
for the bubble.
a positive relationship between the size of
the bubble and the persistence of shocks.
transition probability the lower is the likelihood that the
result,
demand
The smaller
is
the
bubble expands and, as a
the larger are the expansions that are required at the end of high productivity
periods.
Consider the case
which a fraction
in
ty
of the countries coordinate to the
stationary bubble, while the rest coordinate to the bubbleless equilibrium.
from Equations
(9)
and (15)
(1-(}))-7t
(24)
L
+(1-(|)-b
2-a-<j>-(1 + b
is
the fraction of
all
H
—>0,
all
follows
H
)-7l
H
)
countries with a bubble, while
the formulas
in
in
the previous example $
Since the previous example obtains as the
the previous section are valid under both definitions.
fraction of low-productivity countries with a bubble.
H
which \^>0 and b
It
that, in this case:
g
Note that now §
11
19
was
the
limit in
1
g -«-7t
-a
r°
R =
i
(25)
H
-(1-b
TtH
j9'
(
H
)
+ g-b
H
- bH ) + 9
1
g
g b
where
I
exists.
if it
it
is
easy
the previous example.
The
and
=
if
7i|
=
it
if
Tt{
=
7t{
if
n{
= nl and
n{ +1
H
and
+1
+1
= nL
nj +1
= nH
ti|
= nL
L
have used the finding that b =1. Equations (23)-(25) provide a
of productivities. In fact,
in
n|
H
of the bubbly equilibrium,
than
= nH
if
to
1
latter requires
show that
H
a sufficiently high dispersion
now
and g are obtained by crossing Equations
(24)
that
it
this restriction is
is
satisfied
shows how these values depend on
more
from now on.
<|)
and
A..
An increase
world bubble raises the world growth rate and, for the reasons discussed,
the size of the bubble
increase
in
in
high productivity countries (compare points
the transition probability raises the size of the bubble
countries and, as a result,
rate
(compare points
In this
it
A and
reduces
efficient
is
in
with domestic productivity.
investment expands.
contracts. This
is
In
An
is
of the
do not have a
determined solely
countries that do have a bubble, investment fluctuates
When
When
B).
high productivity
A first effect
not sensitive to domestic productivity and
by the savings of the young.
increases
of a bubble not only raises the long-run rate of
hat increases the volatility of investment. In countries that
is
A and
the
C).
example the presence
bubble, investment
it
in
investment and lowers the world growth
growth, but also affects the nature of economic fluctuations.
bubble
description
stringent
Assume
equilibrium values for b
(25). Figure
The
full
productivity
productivity
how bubbles break
is
the
is
high, the
bubble contracts and
low, the bubble
link
expands and investment
between changes
in
domestic
investment and the savings of the young, just as international capital flows would do
they were possible.
20
if
A second
effect of the
impact on consumption.
one
their
In
bubble
is
to create potentially large wealth effects that
countries without a bubble, consumption fluctuates one-to-
with domestic productivity. This
is
not the case
consumption depends on both the return to
bubble. Conditional on being
transition
in
normal times
in
countries with a bubble, since
capital
(i.e.
and the
periods
which a country does not
in
from one state to the other), countries with a bubble have a smoother
consumption process than those without a bubble. The reason
return to their portfolio
all,
is
higher
we would conclude that
in
the low state but lower
the bubble reduces the
international capital flows
would do
also generate a source of
volatility in
in this
context
movements
in
in
if
is
that the rate of
the high state.
If
consumption
volatility of
this
just
were
as
they were possible. But bubbles
consumption that
financially integrated world. During the transitions
we would
not observe
a
in
from one state to the other, the
the size of the bubble generate wealth effects that might potentially
have a large impact on consumption and welfare.
end
rate of growth of the
of high-productivity periods there
productivity periods there
This world
is
is
In particular,
we have
that at the
a consumption boom, while at the end of low-
a consumption bust.
economy provides another example
of
how
stock markets create
bubbles as a substitute for international capital flows. Bubbles expand when the
economy
inefficient
transitions to the low productivity state, absorbing savings
investments. Bubbles contract
productivity state, releasing savings
movements
in
the bubble
shift
when
the
economy
and making room
and eliminating
transitions to the high
for efficient investments.
These
investments from low to high productivity countries,
improving the world allocation of investment and reducing rate-of-return differentials
across countries. As a result of the movements
more
volatile
smoother
in
in
the bubble, investment
becomes
than what standard models would predict, while consumption becomes
normal times but subject to potentially large wealth shocks associated
with expansions
and contractions
in
the bubble.
21
Some
factors that
of the implications of the theory are
would generate a
productivity period
capital outflow
(i.e.
ending) generate growth
is
of investment. Conversely, the
same factors
the realization that a low productivity period
in
that
is
becoming clear now. The same
the realization that a high
the bubble as a prelude to a collapse
would generate a
capital inflow
ending) generate a collapse
in
(i.e.
the
bubble as a prelude to an investment boom. Provided that the country always
coordinates to the stationary bubble, the
tied to
movements
in productivity.
the stationary bubble?
But
The answer,
movements
why would
of course,
is
the
that
of the later are therefore closely
economy always coordinate
it
does not have
to
to.
Financial Fragility
5.
same
Consider the
world as
the previous example, but
in
now assume
that
all
countries coordinate to an equilibrium using a country-specific sunspot variable that
says
BUBBLE with
probability
<|>
NO BUBBLE with
and
probability
sunspots are independent across countries and over time.
When
1-<J>.
These
a country switches
from the bubbly to the bubbleless equilibrium, the old find that the value of the bubble
they are holding collapses to zero and they suffer a loss.
When
a country switches
from the bubbleless to the bubbly equilibrium, the old find themselves able to
sell
a
useless object to the young and experience a windfall. The world starts with a fraction
$ of
all
the countries having a bubble. Since this
proportion of countries in each state
to
show how
expectations.
is
the presence of bubbles
In fact,
it
is
is
the invariant distribution, the
constant over time. The goal of
makes
example
this
is
countries fragile to shocks to
tempting to think about this example as a model of financial
fragility.
This change
in
assumptions implies a few minor adjustments
of the previous subsection.
If
the
th
j
sunspot variable says
22
in
the argument
NO BUBBLE, we
have
that
1
b{
=0.
If
the
th
j
sunspot variable says BUBBLE,
very similar to the one
1-X + X-
b^
b
L
g
1-ct
now
is
a probability that the
implies that:
L
1-A. + X-
and
-())>7i
b
Except for the knife-edge case
from Equation (26)
then a stationary bubble
the previous section. Since there
in
bubble bursts, condition (C1)
(26)
we have
in
H
g
1
-"
r
-<t)>7i
which both inequalities hold
strictly,
that:
L
b =
(27)
X+
n
-
4>-g
Conditional on remaining
basically the
same as
in
in
1-cc
the bubbly equilibrium, the behavior of the bubble
the previous example. Of course,
and reappears with some
probability. Also,
probability of bursting
The presence
affect real variables
makes
now
we can show that
productivity required to sustain the bubbly equilibrium
is
the dispersion of
higher here, since the
the bubble less attractive.
of the bubble
opens the door for shocks
to expectations to
such as investment and consumption. Conditional on not
and without a bubble
countries
do
not.
is
the
go through periods
When
in
same as
the previous example. But
in
countries
now
in
all
which they
the bubble bursts, consumption declines as the wealth of the old
consumption increases
When
in
which they have a bubble and periods
collapses and investment increases.
ones.
is
the bubble also bursts
changing the equilibrium, the behavior of consumption and investment
with
follows
it
in
In
the aftermath of the bursting of the bubble,
high productivity countries but declines
in
low productivity
the bubble appears, consumption increases and investment declines. In
23
the aftermath of the appearance of the bubble, consumption declines
productivity countries but increases
An
to expectations.
wealth
when
high
low productivity ones.
between shocks
interesting finding relates to the interaction
and shocks
in their
in
in
to productivity
Since countries tend to have a large bubble component
productivity
is
shocks
low,
have more
to expectations tend to
extreme effects on macroeconomic aggregates and welfare during recessions.
Conversely, during
booms
countries are less fragile or
more
expectations because the bubble component of wealth
shocks
that
to productivity
is
resilient to
shocks
smaller. Therefore,
to
we find
and expectations multiply the effects of each other and
tend to increase the amplitude of economic fluctuations
if
they are positively
correlated.
Although the model cannot predict the onset of expectations-driven crises,
still
12
it
offers fresh insights into old problems. Consider for instance the popular view that
some
countries should impose a Tobin tax or
probability of costly financial crises
and help
example presented here depicts a case
a result of impediments to asset trade.
in
In
stabilize small
which financial
in
would be no room
to expectations
shocks
financial fragility that
open economies. The
fragility
the high productivity countries.
therefore suggests the opposite view that
reduce the
arises precisely as
the absence of these impediments,
investment would be located
for
sort of capital controls to
in
and
In
all
world
such a world, there
their wealth effects.
The theory
order to eliminate bubbles and the
accompanies them one should not add
frictions in financial
markets, but remove them instead.
12
This would certainly be too
much
of productivity-driven crises either.
specify a path for both productivity
why
I
label
to ask from the model. After all, the model cannot predict the onset
To determine the equilibrium path of the world economy, we must
and expectations. Both variables are taken as given here and this is
them shocks.
24
External Shocks
6. Vulnerability to
Consider a world economy with two countries. North's productivity fluctuates
between a high and a low
constant but low: n
s
<n l As
.
investments are made,
fluctuations
have
state,
i.e.
E
t
in
i.e.
tc^
h
l
g
{ti
,7i;
}
n H > n L while South's
with
;
previous examples, this productivity
{Tt^+1 }=7i^+1
their origin in North.
In this
.
The goal
world economy,
of this
example
presence of bubbles makes low and middle-income countries
is
is
is
known before
productivity
all
to
show
that the
particularly vulnerable
to productivity fluctuations in rich countries.
If
world
the North-South productivity
economy
investment
in
the bubbleless one.
is
North and the rest
in
gap
is
small, the unique equilibrium of this
In this equilibrium,
As
South.
a result,
the world allocates half of
we have
its
that:
1-a
71,
(28)
9t
= a-—
71
2
V
(29)
+
J
R?"
Equations (28) and (29) describe the evolution of world growth and the world
distribution of
Figure 2
shows
of productivity
suffer
consumption or wealth
the bubbleless equilibrium.
The world growth
this evolution graphically.
shocks
more from
If
in
its
in
North. Since
own shocks than
the North-South productivity
each country invests
The
top panel of
rate fluctuates as a result
at
home, North tends
to
South.
gap
is
large, there
which South has a stationary bubble defined by bf =
25
1
is
for
a bubbly equilibrium
all t.
Assume South
in
coordinates to this equilibrium with probability one. Then,
North and, as a result,
(30)
g,
(31)
*L =
we have
the investment
is
done
in
that:
1^
a
Rf
The middle panel
relative
all
consumptions
the world growth rate
in
of Figure 2
shows the
the bubbly equilibrium.
more
fluctuations
in
The presence
sensitive to productivity shocks
shocks not only raise the rate of return
of South's bubble.
evolution of the world growth rate
The presence
North and South.
in
of the bubble
makes
now these
North, since
to North's investment but also the growth rate
of the bubble also tends to synchronize
In
and
economic
the bubbleless equilibrium, the return to each
country portfolio depends more on the country's
own
productivity than
in
the
productivity of the other country. In the bubbly equilibrium, the returns to both
countries' portfolios
depend only on North's
generates a perfect correlation
more
their
volatile productivity
As
country portfolios and wealth. Despite North having
than South, both countries experience the
is
the North-South productivity
large,
South
is
gap
is
better off not investing
small,
South
is
same
volatility in
intermediate however, South might be better off investing
is
low, but might
be better
off
holding a bubble
such behavior possible? The answer
intermediate, there
increase
in
is
is
when
'almost'.
a bubbly equilibrium
in
better off investing.
and instead holding a bubble.
is
that
a result, the bubble
consumption and wealth.
If
gap
in
productivity.
If
when
i.e.
gap
the
is
high. Is
the North-South productivity
gap
which South's bubble expands with an
H
bf = b
26
the
North's productivity
North's productivity
North's productivity and contracts with a decrease.
South has a stationary bubble,
If
If
if
7$ = n
H
To see
and bf = b L
this,
if
assume
L
n" = n
.
is
Assume
HL
g = g
also that the growth rate has four states,
if
t
J
jt
J +1
=
h
< = nH
(this
ji
<
and
+1
= nl
,
LL
g =g
n? =
1
if
t
i.e.
<
+1
g,
= g HH
if
= n l and
n" =
g,
ji^+1
= g HL
if
= nH
it*
=
,
L
rc
and
turns out to be the right guess, of course). With these definitions,
condition (C1) implies that:
(32)
LH
LH
(1-X)g LL +X-^-g > (1-A)-(g LL )^+A-(g )^
0-X)-g»» + X .*
-g
and
7i
> (1-A)-(g HH )^ + X-(g HL )^
HL
Except for the knife-edge case
in
which both inequalities are
strict,
it
follows
that:
LM
(33)
b
g
L
(1-X)-(g
This bubble
is
and
LH
&
n -g
)^+X-(g )^
similar to those
high, the bubble
found
in
LL
b
is
previous examples.
low, the bubble contracts
Using condition (C2),
we
H
=
1
-(1-A)
When
expands and reallocates investments from South
North productivity
to South.
LL
-x
North productivity
to North.
When
and reallocates investments from North
also find the following process for the growth rate
as a function of the bubble:
(
HH
(34)
g
. a-
_h a 1-a
71
and
g
-g
2-a
(
L"
= a
x1-a
„H
HL
= a-
7l"+ (1-b
is
2-ab
L\ Jl.\
L
)-7t'
1-o
2-a
27
L
(
,g
LL
= a
„H
7t"
+(1-b LL\)- „LA
7t'
2-ab
L
1-a
where
H
have used the finding that b =1. Equations (33) and (34)
I
growth process and the behavior of the bubble.
solved analytically, although
it
is
In
implicitly
define the
general, these equations cannot be
quite straightforward to solve the system
numerically.
The bottom panel
of Figure 2
the world distribution of consumption
normal times
other),
(i.e.
periods
in
shows the
in this
evolution of the world growth rate
equilibrium. Conditional
on being
and
in
which a country does not transition from one state to the
South experiences a smoother consumption process than North. During a
boom, South holds the bubble
to take
During a recession, South shifts
in its return.
But,
as
in
its
advantage
portfolio
of the high productivity of North.
towards investment to moderate the
fall
previous examples, bubbles generate potentially large wealth
effects during the transitions. In particular, the onset of a recession leads to a
collapse
bubble.
if
the bubble while the beginning of a
in
On
impact, recessions and
they have their origin
affect relatively
in
booms are
boom
felt
leads to an expansion
much more
changes
North. After the dust clears,
more North than South. This world economy
bubbles create a channel for small productivity shocks
changes
in
asset prices
in
South. These
large effects on consumption, wealth
This example also provides a
economic reforms and
in
South productivity gap. Assume
some encouragement from
South even
North productivity
therefore illustrates
how
North to create sharp
asset prices
new
in
turn generate
perspective on the connection between
The key observation
initially
that this
gap
is
large
at raising
until
28
that
the North-
In their first
stage,
South's productivity, but they have no
that, despite this
decides to pursue reforms even further
in
is
and South, perhaps with
North, decides to implement reforms.
Assume
in
the
and welfare.
consumption or welfare since South
rather than to invest.
in
in
South lead to a progressive reduction
these reforms might be successful
its
in
vulnerability to external crises.
successful economic reforms
impact on
movements
strongly
in
still
prefers to hold the bubble
apparent lack of success, South
the productivity gap
becomes
some convergence towards
intermediate. In this second stage, South notices
average levels of consumption and wealth. But
more vulnerable
Small drops
to North shocks.
at the
in
same
time, South finds
that
made consumption
South reacts to
this
itself
North productivity create sharp
financial crises. Small increases in North productivity lead to asset price
reforms have
North's
higher on average, but
by further implementing reforms
much more
until
booms. The
volatile.
Assume
the productivity gap
small. At this point. South finally enjoys high
and stable consumption. The bubble
gone, and so are the wealth effects that are
at the root of the
is
is
sharp crises and
booms.
The bubble
also determines the distributive effects of reforms.
Whenever we
reach stage two of the reforms, a conflict arises between the young and the old.
Successful economic reforms
for the
bubble and leading to
consumption and the welfare
consumption,
all
is
costly, the
on the need
to
contraction or bursting. This leads to a
of the old. After this
initial
To the extent hath
if
in
demand
fall in
wealth and
off
as a
result of
transferring resources across different
presence of a bubble makes more
of the bubble
decline
South (and North) are better
implement reforms. The key reason
harm the owners
7.
its
investment more attractive, reducing the
future generations in
the economic reforms.
groups
make
is
difficult to
that
reach a consensus
these economic reforms
they are successful.
Contagion
Consider a world economy with three countries, West, East and South; with
productivities equal to
know
that
w
7i
s
E
>ji >7t ==0,
West cannot have
respectively. With this assumption,
a bubble and that South can.
bubble or not depends on parameter values.
I
assume
that
South uses a sunspot
the probability to transition from
29
already
Whether East can have a
variable to coordinate to a given equilibrium. This sunspot variable has
BUBBLE and NO BUBBLE; and
we
one
two
states:
state to the
other
When
given by X.
is
the bubble bursts
zero there. The goal of this example
South, consumption and wealth drop to
to study
how these
expectations-driven
South are propagated to West and East.
financial crises in
The
is
in
structure of this
financial crises in
example
is
South taking up the
East productivity gap
is
very similar to that of the previous one, with
role of productivity
small, East cannot
shocks
in
North.
If
the West-
have a bubble and the equilibrium
is
given
by:
^W^E
(35)
g
a3-a-b t+v
t
R =g
j
(36)
V- a
,
1
t
-«-7i
j
for j=
W,E
and
g.
ifbf=bf+1 =1
— oo
if
bf =
if
bf = bf+1 =
if
bf =
Rf=oo
The world growth
transfer resources to
world growth rate.
and bf+1 =
and bf+1 =
that are invested
more
efficiently, raising
the world growth rate. Through this channel,
movements
world growth rate and the distribution of consumption.
a proportional increase
in
w
i.e.
9L
cf
in
in
s
7i
=0), lowering
the bubble affect the
When
the bubble bursts, there
the return to the portfolios of both North and South, as
the lower growth rate implies a slower decline
Hence, movements
the
the bubble bursts, these resources return to South where
they are invested with very low efficiency (essentially wasted since
is
1
rate fluctuates with South's bubble. Increases in the bubble
West and East
When
1
in
the price of investment goods.
the bubble do not affect their relative consumption or wealth,
n
71
30
the West-East productivity
If
defined by bf =
we have
one. Then,
(37)
g,
all t.
=
Assume
is
large,
East can have a stationary bubble
East coordinates to
this
Vl-cc
w
CC--
3-oc-(1+b?+1 )
1
-a
-Tt
t
w
,
Rf=g
and
t
g.
ifbf
— oo
if
Rf=.
Once
bf =
it
if
did in the bubbleless equilibrium. But
differently to
bf =
cr
and bf+1 =
now the shock
it
now reduces
1
to expectations in
is
still
the return to East's because the
the world growth rate decreases the return to East's bubble.
^w
and bf+1 =
East and West. While the bursting of the bubble
the return to West's portfolio,
shocks
1
again, the world growth rate fluctuates with South's bubble for exactly
same reasons
propagated
=bf+1 =1
ifbf=bf+1 =0
oo
the
bubble with probability
that:
n
Rr=g
(38)
for
1
gap
South have a larger
effect
When
raises
fall in
East has a bubble,
on East than on West,
i.e.
w
1-a
The most
intermediate.
interesting
case
is
the one
Then East has a bubble
in
which the productivity gap
that contracts
expands when South's bubble re-appears. To see
Equations (32) and (33) apply
E
now to
n and use the superscripts "H" and
Moreover,
we can
when South's bubble
bursts and
use condition (C1)
to find that
this,
East's bubble, provided that
"L" to indicate bf
also use condition (C2) to find that:
31
is
=
1
we
and bf =
replace
,
s
rc
by
respectively.
HH
(39)
a-
g
A
1-cc
g
LH
.w
HL
g
3-a-2
and
where
-W
n
TC
a
A
1-a
n
LL
= a-
3-ab L
W +(1-bL )-7tEV"
3-a-2
—
growth process and the bubble. The behavior of East's bubble
in
E
.
7I
L
<
.
described
L
+(1 _ b )
3-ab
H
have used the finding that b =1 Equations (33) and (39)
I
W
a-
g
the previous example. This reinforces the
is
message
implicitly define
analogous
the
to that
that middle-income
countries are especially vulnerable to external shocks, regardless of whether the
origin of
these shocks
coordination failure
in
a drop of productivity
is
phenomenon
we sometimes observe
of financial crises that
in
South's bubble generate positively correlated
insight of this
example
is
the world raise the world growth rate and
at
home.
the West-East productivity
be supported
if
and only
if
there
is
that
resembles the "contagion"
the real world. Note that
movements
in
complements. That
that bubbles are
in
If
high productivity countries or a
low productivity ones.
This example also gives rise to a
in
in
gap
make
is
a bubble
it
more
East's bubble.
is,
The key
bubbles elsewhere
likely that
a bubble appears
intermediate, a large bubble
in
movements
in
East can
South. Under these circumstances,
South's bubble bursts East's bubble sharply contracts. This positive correlation
in
if
the
bubbles of South and East happens even though there are few direct linkages
between them.
have
ruled
Naturally, there are
them out from the
such a way that there
is
start.
no
capital flows
between East and South since
I
Moreover, the example can also be constructed
no commodity trade between these countries
either
in
13
The patterns of trade in this world are straightforward. When South has a bubble, East and South are
exporters of L-products, while West is an exporter of K-products. As a result East and South do not trade
with each other. When South does not have a bubble, South is still an exporter of L-products, while
North is still an exporter of K-products. Whether East remains an exporter of L-products or becomes now
an exporter of K-products depends on parameter values. For instance, if a is large the demand for Lproducts is strong enough that East remains an exporter of L-products. In this case, East and South
never trade.
32
8.
Conclusion
The theory developed here provides
market-generated device to
world.
in
The
markets.
resources that are
asset price bubbles as a
flows
central insight
countries where productivity
These bubbles absorb
liberating
new view of
facilitate international capital
frictions in international financial
appear and expand
a
is
is
in
that
part
used
bubbles tend to
low relative to the rest of the
local savings, eliminating inefficient
in
the presence of
investments and
to invest in high productivity countries. This
improves the world allocation of investment and reduces rate-of-return differentials
across countries.
As
a result, bubbles allow the world
economy
to operate at a higher
level of efficiency.
This theory of asset price bubbles extends and complements the standard
productivity-based view of economic growth, providing
wide range of
for a
real
before. With the help of
somewhat
world
phenomenae
that
some examples, have
I
and how
this interaction
with the potential to account
had proved quite
derived a
surprising results regarding the interaction
productivity
it
difficult to
number
model
of suggestive
and
between bubbles and
shapes the growth process. While some
of these
results are likely to withstand realistic extensions of the theory, others will certainly
not.
I
regard the model proposed here as a
of the connection
between asset
first
step towards a better understanding
price bubbles, international capital flows
economic growth.
33
and
References
Summers and R.J. Zeckhauser [1989], "Assessing
Theory and Evidence," The Review of Economic Studies, 56,
Abel, A.B., N.G. Mankiw, L.H.
Dynamic
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1,
1-19.
Acemoglu, D. and J. Ventura [2002], "The World Income
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Helpman,
E.
Distribution," Quarterly
and P.R. Krugman, Market Structure and Foreign Trade, MIT Press.
Howitt, P. [2002], "Endogenous Growth and Cross-country Income Differences,"
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Kraay, A., N. Loayza, L. Serven and
working paper W7795.
Olivier,
J.
Ventura [2000], "Country
Jaques [2000], "Growth-Enhancing Bubbles,"
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Economic
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Samuelson, P.A. [1958], "An Exact Consumption-Loan Model of Interest with or
Without the Social Contrivance of Money," Journal of Political Economy, 66, pp. 467482.
Tirole, J. [1985],
"Asset Bubbles and Overlapping Generations," Econometrica, 53,
pp. 1499-1528.
Ventura,
J.
[1997], "Growth
and Interdependence," Quarterly Journal of Economics,
CXII, 1,57-84.
Ventura,
J.
[2002],
"Economic Growth with Bubbles," MIT, work
34
in
progress.
Figure
1
35
Figure 2
Small
Gap
Boom
Recession
Recession
R, N /R, S
*
Large Gap
Boom
Recession
.
Intermediate
Recession
i
Boom
Gap
i
36
Recession
R, N /R, S
late
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