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Massachusetts Institute of Technology
Department of Economics
Working Paper Series
Bubbles and Capital Flow Volatility:
Causes and Risk Management
Ricardo
J.
Caballero
Arvind Krishnamurthy
Working Paper 05-20
August 25, 2005
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MASSACHUSETTS INSTITUTE
OF TECHISIOLOGv
NOV
1
4 2005
LIBRARIES
I
Bubbles and Capital Flow
Volatility:
Causes and Risk Management
Ricardo
J.
Arvind Krishnamurthy*
Caballero
This version: August 25, 2005
Abstract
Emerging market economies are
estate
and other
fertile
ground
for the
development of
financial bubbles. Despite these economies' significant
potential, their corporate
and government
real
growth
sectors do not generate the financial
instruments to provide residents with adequate stores of value.
Capital of-
ten flows out of these economies seeking these stores of value in the developed
world. Bubbles are beneficial because they provide domestic stores of value and
thereby reduce capital outflows while increasing investment. But they come at
a cost, as they expose the country to bubble-crashes and capital flow reversals.
We
show that domestic
underdevelopment not only
financial
facilitates
the emergence of bubbles, but also leads agents to undervalue the aggregate
risk
embodied
in financial bubbles.
be welfare reducing.
We
alleviate the bubble-risk.
study a
We
In this context, even rational bubbles can
set of
show that
capital inflows and structural policies
"collateralized"
JEL Codes:
by future revenues,
aggregate risk management policies to
liquidity requirements, sterihzation of
aimed at developing public debt markets
all
have a high payoff in this environment.
E32, E44, F32, F34, F41,
GlO
Keyw^ords: Emerging markets, bubbles, excess
reversals, public debt market, financial
•Respectively:
MIT and NBER;
krishnamurthy@northwestern.edu. This
Conference Series on Public Policy.
Rigobon, and the referee
for their
underdevelopment, dynamic
Northwestern
is
We
volatility, crashes, capital flow
E-mails:
University.
paper has been prepared
are grateful to Douglas
for the
inefficiency.
caball@mit.edu,
a-
2005 Carnegie- Rochester
Diamond, David Lucca, Roberto
comments. Caballero thanks the
NSF
for financial support.
Introduction
1
Emerging market economies (EM's) are plagued by episodes
These episodes begin with a "bubble" phase where
and capital
Examples
mid
inflows, all grow,
economies
credit, investment, asset prices,
and end with a bust phase when these variables
of these episodes include Argentina in the 1990's,
Mexico
1990's,
of bubble-like dynamics.
in the early 1990's,
Chile,
collapse.
South East Asia
in the
Mexico and other Latin American
in the early 1980's.
Academic
theories of bubbles focus on two elements: the role of information in
coordinating agents' actions to grow and ultimately prick bubbles; and, the role of the
macroeconomic environment
in facilitating bubbles.
We
present a model that draws
on the second element.
We
first
element
namic
for
argue that an aggregate shortage of stores of value
bubble formation highlighted
inefficiency)
—
is
sector
stores of value to the economy.
government to
is
EM's
Fiscal
literature
(i.e.
dy-
Poor investor protection,
and sovereign-default concerns
issue reliable debt.
financial systems.
the key
is
unable to capitalize future earnings and provide
McKinnon
nancial repression" that, for example,
aspect of
macroeconomics
prevalent in emerging markets.
means that the corporate
ability of the
in the
— which
The
also
hmit the
These factors contribute to the
"fi-
(1973) has argued to be a prominent
limited investment outlets, such as poor bank-
ing systems and conglomerates with severe corporate governance problems, receive
investment flows despite their deficiencies. Real estate investment, which
is
one of
the best protected investment vehicles in EM's, serves as prominent store of value as
well. Finally,
where possible, agents actively seek high quality stores of value abroad
by purchasing developed economies' safe
In this context,
EM's
assets.^
present a fertile macroeconomic environment for the emer-
gence of bubbles. Starting from this premise, we develop a simple overlapping generations
(OLG) model
of stochastic bubbles. In the model, the absence of an adequate
quantity of high-quality domestic financial instruments to store value induces domestic
agents to seek this financial service abroad through systematic capital outflows.
These outflows are costly
for
EM's because they
divert resources that
may
otherwise
be spent growing the domestic economy; foreign interest rates are low relative to
'In this light, the surge in
demand
for U.S. assets since the late 1990s, is
shortage of high-quaUty stores of value in
period.
EM's
a symptom of the
following the crash in local bubbles during that
these economies' growth potential and marginal product of capital. For reasons akin
economy
to those found in the closed
on dynamic
literature
inefficiency, the
tween low external returns and high domestic growth rates creates a space
bubbles on unproductive local assets to
gap be-
for rational
For concreteness, we refer to these as
arise.
Real Estate Bubbles. They are a response to agents'
demand
for
more
profitable store
of value instruments.
In the classical
OLG
is
unambigu-
(see,
Samuelson
model, the emergence of these rational bubbles
ously good as they complete a missing "intergenerational" market
1958 and Tirole 1985).
This
is
the case, at least in an ex-ante sense, even
if
these
bubbles can crash as in Blanchard and Watson (1982) and Weil (1987). In contrast,
in the
emerging markets setup we describe, the presence of
fragility in
bubbles can
render them socially undesirable, despite their service as a store of value.
We
OLG
modify the standard
issues that
we
are interested
in,
model
and
in
two ways to address the emerging markets
to arrive at our results.
investment, rather than consumption, related
demand
for
First,
a store of value. Each gen-
eration of agents has an entrepreneurial and a banking sector.
when agents
arise in the entrepreneurial sector,
are old.
Investment projects
Young agents demand some
liquidity in order to fund these future investment projects. Second,
tantly,
we
follow Caballero
need to import international goods
market
is
To
in order to
undertake investment projects. How-
segmented from the international capital market,
for
endowment
amount
places a ceiling on
We
investment projects.
their investment
with international investors, we endow each generation
facilitate trade
of domestic agents with a limited
ternational
in the
At the margin, domestic entrepreneurs
and international investors do not lend to domestic agents against
projects.
and more impor-
and Krishnamurthy (2001) by modelling constraints
domestic and international capital market.
ever, the domestic capital
we introduce an
of international goods/collateral.
how many goods
The
in-
the country can import
assume that only the domestic banking sector has the
capability to lend to the entrepreneurial sector.
The
international goods
turing the idea that an
future.
ment
The high growth
of a bubble.
the old
EM
sell
endowment
As
endowment
grows
fast
rate of this
in the
of the generations grows at a high rate, cap-
and
will
be able to import more goods in the
endowment
standard analysis of
creates
OLG
some space
for the develop-
models, welfare
may improve
if
a bubble asset to the next generation, collecting their international goods
in
exchange, and so on.
We
study an economy with a stochastic bubble
that provides the required liquidity to young agents, but
may
burst at am- date.
Our main
result can be understood
by considering the liquidity demand
These agents purchase a portfolio
bankers.
liquidity
foreign
(i.e.
bank account)
when
trepreneurial sector,
to repay all loans, in general the
if
bubble asset and international
be
in a position to lend to the en-
the entrepreneurial sector cannot
banker receives a return that
marginal product of entrepreneurial investment. In particular,
both bankers and entrepreneurs are unable to
international
endowment
entrepreneurial sector
liquidity chosen
is
young
of the
in order to
However,
old.
of
sell their real
if
commit
lower than the
is
the bubble crashes
estate holdings for the
of the next generation. In this event, the investment in the
constrained by the ex-ante portfolio share of international
by bankers and entrepreneurs. However, since the banker does not
share fully in the return of entrepreneurial investment, the banker has a lower incentive to store the international
goods that are required, at the margin, to finance
entrepreneurial investment projects in the crash, and
We
more
of
all
an incentive to chase
show that welfare
is
often improved
During the growth phase of the bubble, the economy sustains high
levels of invest-
the higher return promised by the bubble.
by reducing investment
in the bubble.
ment. Entrepreneurs and bankers are able to
liquidity with
sell their
which they finance investment projects.
bubble asset
for international
Capital inflows during this
period are high as agents are actively borrowing against the international collateral
of the country.
Domestic credit grows as bankers are flush with resources to lend
to the entrepreneurial sector.
When
the bubble crashes, entrepreneurs and bankers
are unable to trade for the international liquidity of other agents.
domestic credit and investment
verse,
bubble dynamics
An
cerns
in
falls. ^
Capital flows re-
Thus, our model successfully reproduces
emerging economies.
important policy discussion in emerging markets (and developed ones) con-
managing the
risks created
by a bubble. In our model, rational bubbles
arise
endogenously as a result of the economy's dynamic inefficiency but can be welfare
reducing, because the private sector underestimates the costs of fragility.
There are two types of
policies that
can improve upon this outcome. The
first
are
short-term risk-management policies that aim at discouraging excessive reallocation
of liquidity
^This
is
and savings toward
local real estate.
in stark contrast witli the canonical
OLG
Banking regulations such as
model, in which bubbles crowd out private
investment, so that the bubble and private investment are negatively correlated.
Farhi and
Hammour
inter-
See Caballero,
(2004) and Ventura (2004) for models that also exhibit positively correlated
bubbles and investment.
These
national liquidity requirements reduce bubbles.
policies are similar to those
discussed in Caballero and Krishnamurthy (2004) in the context of overborrowing and
the dollarization of habilities problems.
sterilization of capital flows.
A
more novel
We show that
if
model
liquidity policy in our
is
the government has sufficient capacity to
tax current endowments, then by issuing one-period government debt and using the
proceeds to directly invest in international liquidity, the government can insure the
private sector against the fragility of the bubble. In the crash, the government injects
its
international liquidity to offset the insufficient liquidity of the private sector.
The second type
these economies.
of policies are
They
more
directly linked to the source of bubbles in
are aimed at improving the supply of domestic financial assets
whose prices are not governed by bubble dynamics.
has sufficient credibility and
enough public debt
commitment
We
show that
a government
if
to securitize future taxes, then
(a sort of collateralized
Diamond, 1965, debt)
to
it
can issue
crowd out the
bubble while solving the dynamic inefficiency problem.''
The paper
is
related to several strands of literature.
rational bubbles in general equilibrium,
and
builds on the
It
work on
on Tirole (1985) and on
in particular
the segmented markets version in Ventura (2004). However, unlike the conclusion of
these papers and that of
much
of the literature, bubbles
may
be socially
inefficient in
our model. This insight informs most of our discussion.
Saint-Paul (1992) also develops a model where rational bubbles
inefficient.
However
his context is entirely different
More
capital spillovers.
focus on fragility,
that of Caballero, Farhi and
is
socially
from ours, as in his case the
inefficiency arises from bubbles crowding out physical capital in an
model with positive
may be
endogenous gi-owth
closely related to our paper in
Hammour
terms of the
(2004) where bubbles
may
increase the chance of a crash in a multiple equilibria economy. In their context too,
the reason
why
Instead, in our
itself
this
is
potentially inefficient
is
an externality
in capital
model the welfare implications stem from the
and from the private
accumulation.
riskiness of the
bubble
sector's distorted perception of the aggregate risk of their
choices.
In the literature on liquidity provision,
Holmstrom and
Tirole (1998) note that
financial constraints lead to too little stores of value. In this context, they
government debt can improve on the allocation
^Of
course, this solution
pledge future taxes
itself
may be
may be
of the private sector.
fragile in itself, as expectations over the
variable.
But
show that
Hellwig and
government's ability to
this is uncertainty of a very different nature, unless
it
can feedback into the governments ability or commitment to deliver on each of these fronts.
in
Lorenzoni (2004) study an economy where agents have limited commitment in repaying debt contracts.
They show
that in economies which are dynamically inefficient,
long term debt can be sustained even under this hmited
commitment
constraint.
In terms of the source of the pecuniary externality and private undervaluation of
international liquidity, the
murthy
mechanism
is
similar to that in Caballero
However, the focus on these papers
(2001, 2003).
is
and Krishna-
on the externality and
not on the possibility of bubbles, their efficiency properties, and solutions to manage
bubbles. Moreover, in the current paper the main problem
not one of insufficient
is
country-wide international liquidity during crises but one of significant capital outflows due to a coordination failure.
emphasis on preventive policies to manage bubble-risk rather than ex-
Finally, our
post interventions contrasts with the views expressed by,
Bernanke (2002)
for
Dornbusch (1999) and
developed economies, where ex-ante and ex-post interventions
take a more balanced role.
that while developed
e.g.,
The main reason
for
our emphasis on ex-ante policies
economy policymakers can count on
is
access to resources during
a bubble-crash, EM's governments and central banks often find themselves entangled
in the crisis itself.
The paper
is
organized as follows. Section 2 describes the structure of the economy,
while Section 3 introduces bubbles. Section 4 establishes the excessive volatihty of the
market outcome with bubbles. Section 5 and 6 discuss aggregate
and
financial
A
2
market development
risk
management
policies, respectively. Section 7 concludes.
Productive Dynamically Inefficient Emerging
Economy
The emerging economy
is
OLG
populated by an
produce and consume only when
old.
of risk-neutral
There are two types
domestic agents that
of goods, international
and
domestic goods. The domestic goods are perishable, but the international goods can
be saved abroad
at the world interest rate of r*.
Domestic goods and international
goods are perfect substitutes in the domestic consumers' preferences. While
for inter-
national investors, only the international goods are tradeable and offer consumption
value.
These assumptions
effectively limit foreign investors' participation in
domestic
markets.
Each agent
is
endowed with some date
t
goods and some date
t
+l
goods. Agents
are born at date
receive an
t
with an endowment of Wt international goods.
endowment
of
RKt
endowment
as the returns
with. Thus,
endowments
At date
i
+
from a domestic plant of
at
(i, i
+
1) for
produces RIt+i units of domestic goods
an agent born at time
for
t
born
is
are {Wt, RKi).
become entrepreneurs, and
i
an investment of
direct investment opportunities, but
entrepreneurs (see below).
We
may
/(+i units of international
The bankers do not
This production occurs instantaneously.
goods.
receive
any
be in a position to lend to the investing
note that agents are ex-ante identical, while ex-post
heterogeneity.
is
We
can think of the latter
Ki that the agent
size
one-half of the agents of generation
1,
We
1).
old, agents
become bankers. The entrepreneurs receive an investment opportunity, which
one-half
there
>
domestic goods [R
When
are centrally interested in
how
the young agent saves his international goods
to finance investment (directly or indirectly)
that the young agent saves
rate of r*
.
generation
Let
i,
W^
all
when
old.
For this section, we assume
of his international goods abroad at the world interest
denote the international goods available at
i -t-
1
to a
member
of
so that:
Wl={l + r')\\\.
At each date there
is
a domestic financial market, where entrepreneurs with
vestment opportunities borrow from bankers. The financial market
in the
same sense
as production
is
instantaneous.
At date
i
+
1,
is
in-
instantaneous
an entrepreneur with
an investment opportunity borrows U+i international goods from a banker, offering to
repay pt+i/j+i domestic goods when production
is
complete.
We
impose a
collateral
constraint on this loan;
Vt+ih+i
where
ip
^The
parameterizes the tightness of the collateral constraint.''
collateral constraint
we have imposed
output from the new investment of /j+i
different
< ipRKt
is
requires that loans be collateralized
not considered collateral.
by xpRKi
.
Any
This latter assumption
is
than the standard credit constraints model, which would require that
Pt+ih+i < i'RiKt
where again
tp
<
1
+
It
+ i)
parameterizes the tightness of the collateral constraint.
borrower saturates this collateral constraint,
Assuming that the
yields:
pt+i
where the
first
term
is
the familiar "equity" multiplier that arises in models of credit-constraints.
Our model assumes
eign investors nor the
that the domestic capital market
young
of generation
t
+l
is
segmented. Neither
for-
participate in the loan market. Within
the logic of the model, this occurs because loans are repaid in perishable domestic
goods, which have no consumption value to either generation
vestors.
More
we
generally,
i
+
or foreign in-
1
think that foreign investors have limited participation in
debt markets because of lack of local knowledge, and fear of sovereign expro-
local
The
priation/selective default.
debt literature
(e.g.
Likewise,
limit.
latter concern
Bulow and
we think
is
studied extensively in the sovereign
Rogoff, 1989) which motivates a country-level debt
of the bankers of generation
dealing with the entrepreneurs of generation
/
as having
more experience
t.
Equilibrium in the loan market requires that,
1
<
Pt+i
<
R,
since at a price below one, lenders will not lend,
will
and
at a price above
R
borrowers
not borrow.
The supply
of loans
WI/2 and
is
assume throughout that
tJjR
Utilizing these conditions,
we
<
I
the constrained
demand
for loans is
and we normalize quantities and
set
^^^'
We
= Wf
.
Kt
find that in equilibrium:
Vi+\
=
1,
so that bankers, in equilibrium, have international goods that are not lent to the
entrepreneurs.
On
average, emerging market economies grow
assuming that the endowments (Wi, R^i) grows
g>r*
fast.
We
capture this feature by
at a rate g such that:
.
Substituting this expression and solving for the amount borrowed, yields:
As the domestic
capital
market
is
segmented, the aggregate supply of loans comes from the resources
of bankers. In total, the loan supply
is
W('/2 and the aggregate
demand
for loans
is
li^\j2. Thus,
pt+i =max[l,i^'/?(2-l- A'(/VK/)] =max[l,3i/>/?]
which
some
is
very similar to the expression we derive under our assumption. Our assumption simplifies
of the algebra later in the paper without distracting from the substance of the results.
.
Thus, our basic economy behaves as a dynamically inefficient economy, in the sense
that store of value (rather than the marginal product of capital) has a lower return
than the rate of growth of the endowment.
In this context,
many
dynamic
means that the country
is
At each time
a capital outflow of Wt and an inflow of
there
f
the net outflow
is
lending (or leaving) too
positive outflow
omy.^
is
of value instrument
(1
+
>
0.
r*)Wt-i, thus
Wt -
+
(1
r*)Wt-i
=
-
[g
r*)Wt-i
highly inefficient for a resource-scarce emerging market econ-
among domestic
demand
for a higher return store
agents.
Real Estate Bubbles
3
Young agents need a
store of value to finance investment opportunities
In the basic structure
arise.
is
=
also hints at the presence of a large latent
It
international goods abroad.^
is:
NetOutfloiUt
The
inefficiency
dynamically
inefficient
we have
outlined, the (saving side of the)
and the only store
of value
abroad at the safe but low world interest rate of
The
familiar
Wt endowment
their
there
>
r*
on
inefficiency
no mechanism
is
is
for all
genera-
Rather than lending Wt abroad, the young transfer
of international goods to the old,
its
economy
r*
and when
Wt+i endowment of the new young, and so on. Each generation,
a return g
these
lending international goods
is
Samuelson (1958) solution to dynamic
tions to enter a social contract:
when
old, receive the
effectively, receives
OLG
model
and young to write such contracts. Thus,
in the
international goods endowment.^ However, in an
for the old
context of emerging markets that concerns us here, the
OLG
assumption captures the
dimension of financial underdevelopment that limits contracts beyond a small groups
of
contemporaneous market participants.
We
suppose that in this context an unproductive and irreproducible asset
estate," for short)
price
A
only
traded domestically. Since the asset
must be a pure bubble.
We
if
unproductive, any positive
is
necessarily fragile, as the asset retains value
current generations expect that future generations will
^This
is
is
is
"real
denote this price by Bt.
positive price on the bubble asset
by Abel
®It
is
(
demand
the asset.
We
the analog to the corporate-cash-flow empirical concept of dynamic inefficiency proposed
et al (1989) for the context of closed economies.
only matter of relabeling to translate these excessive outflows into depressed inflows.
^And the
first
generation receives an additional return.
capture this fragility by assuming that as of time
across generation ends,
and the young of i +
abroad instead of purchasing the bubble
1
t,
with probabihty A the coordination
choose to save their international goods
asset. In this case, the
bubble crashes to a
value of zero.
If
the bubble does not crash,
the interest rate
(this is
is
grows at the rate
it
t^.
We
at the highest possible level consistent
focus on the case where
with rational expectations
the only case where the bubble does not vanish asymptotically in the absence
of a crash), so that:
r^
Thus the expected return from investing
?>
=
g.
in the
bubble
is
= g-\{l+g)
and
B.t+\
^l +
r^
= {l-\){l+g)<l+g.
B,
If
invest
A
is
not too high and the spread
some
A
.b
—
r*)
is
sufficiently large, agents
of their international goods in the bubble. This will hold true as long as:
rb-r* = {l-\)/\? -\{l +
Recall that the young at date
t
are
endowed with
!•*)>{}.
(VFj,
RKi). They divide
holdings of the bubble asset and saving in the international market.
share of bubble assets in the portfolio by aj, and
held by generation-i at date
i
+
f is either g (no crash) or
At date
i
transactions.
return f
.
+
1,
We
W't into
denote the
write the international goods
1 as:
W[ = Wt{l +
where
now
(1)
—1
r*
+at{f-r*))
(crash).
an entrepreneur with an investment opportunity enters into two
First,
he
sells his
bubble asset to the next generation to receive the
Next, he borrows U+i at price pt+\ from the bankers, to yield total output
of,
•
RKi + RW[ + {R -
Pt+i)lt+i,
where
^(+1
< -.*^K..
Pt + l
10
.
As long
Assuming
output
as pt+i
<
R,
it
much
pays for the entrepreneur to borrow as
now and
this case for
,
maximum
substituting in the
as possible.
loan size gives total
of,
RKt + RW; + {R- p,+,)^Kt.
Pt+i
A
banker at date
t
+
to the next generation
1
goods by selling his real estate assets
collects international
and then lends these goods, along with any savings from date
As a
international lending, to the investing entrepreneurs.
total
goods
bankers receive
of,
RKt +
Rolling back to date
or bankers at date
bubble asset to
t
+
t
1.
W'iPt+i.
agents are equally likely to find themselves as entrepreneurs
Thus the
decision problem
is
to choose a portfolio of the
solve:
+
DL-max X?
W,
+ W'^+P'
Ei<f Rht
'2
,
0<at<l
At an
result, the
t
interior solution
order condition
{
^ - Pt+1
I
,
-{
2
— ht>.
i^R
/„s
\
,.
pt + i
(2)
J
(we make parameter assumptions so this
is
the case), the
first
is:
(1
-
^)l^(^ + pf+i)
MR + p?+i)
-
=
(3)
where pf^^ and p^j represent the equilibrium price of loans when the bubble survives
and crashes,
respectively.
In words, the young agent gets an excess return of
crash,
if
which happens with probabihty
the bubble does crash.
When
1
—
A.
He
Ar^
the bubble does not
trades this off against the loss
old, the agent is either
an entrepreneur,
the returns from the bubble funds investment that yields R;
in
if
or,
in
the agent
(
— 1)
which case
is
a banker,
which case the returns from the bubble are used to lend to the entrepreneur at the
price pt+i
Thus returns on
The supply
entrepreneurs
of funds
is
at
R + pt+i
the bubble are valued by the agent aX
from bankers
is
at
most
VV^
,
while the
most S^Kt- Thus, market clearing
demand
in the loan
for
.
funds from
market yields
for
the no-crash state,
pf,
Note
1
= max
—
< 1
that, as in the previous section,
when
tl)R
<
1
we
find
p^
=
1.
For the crash state, market clearing yields:
pf
= max
mm —
.
1
.
,
<
jjR
rj-
,
l+r*){l-at)'
11
H„
(4)
We now
script
consider the equilibrium determination of pf and
p stands
problems are the same
First note that agents' decision
for private).
(where the super-
a'l
across each period that the bubble does not crash. Thus, without loss of generality,
we drop time
Denote
subscripts.
a^{p'^) as the solution to the agents decision problem, (2), given
note p'^(a) as the solution to the market clearing condition,
We
(4),
p'-'
.
De-
given choices of a.
are looking for a fixed point {a^,p'-^) that solve both (2) and (4).
We
begin the characterization by considering
program, the solution
is
a step function. Note that
the objective with respect to
a
Given the linearity of the
a''{p'-'').
=
if p*"
then the derivative of
1,
is:
il-X)-^^{R + l)-X{R + l)>0
+
1
where the
asset
last inequality follows
dominates saving
r*
by condition
(1).
In words,
bank account,
in the international
an adjoining assumption by considering the case where
possible).
At
this price, the derivative of the objective
= R
(the highest value
is:
assume that
(l-A)Ar^-A(l +
which can hold along with condition
Ari'+'i+r*
-
Under condition
dominates saving
Conditions
is
so that
p'-^
= 1, the bubble
a = 1. We make
+ r*
1
We
if p'-'
(1)
in the
and
illustrated in Figure
(1) as
=
(5), if p*"
9/?
r*)^^<0
long as
/?
>
1
(5)
and
^^t^_L^n|^r)_(_^^6)
< A <
saving in the international bank account
/?,
bubble asset.
(5)
guarantee an interior solution to our problem. The solution
1.
The
solid line depicts a^[p'^), the step function solution
to the agents decision problem. Note that under conditions (1) and (5) there exists
a unique value of
condition
is
p*^
that
satisfied
lies strictly
between zero and one, whereby the
with equality. The s-shaped dashed curve in the figure
solution to the market clearing condition,
In
first
summary, under
agents hold a fraction
(1)
<
and
qP
<
(5), in
1
p'~'{n).
The unique equilibrium
its
return
is
the
at point
each period that the bubble does not crash,
of their portfolio in the bubble asset. If the bubble
crashes, the banker's (gross) return in the loans market
bubble does not crash,
is
order
is
ingredient in the welfare statements
p^
=
1.
we make
12
is
1
<
p"^
The banker's return
next.
<
of
/?,
p
is
while
if
the
the central
Figure
1:
Equilibrium determination of a^ and
P^
Solution to
Decision Problem
ap
a
Notes:
The
figure illustrates the equilibrium determination in the crash state.
the decision problem for agents traces out the solid-tine step function.
If
The
solution to
agents expect higher
returns on lending international liquidity in the crash-state, they cutback on purchase of bubbles,
and increase
their holdings of international liquidity.
market clearing condition as a result of these choices.
then
in
higher,
less
If all
international liquidity
traces out the
agents hold more of the bubble asset,
if
the bubble crashes and
P
will
be
a^ denotes the equilibrium.
Excess Volatility
4
If
equilibrium there will be
The s-shaped dashed curve
A
=
0,
and the bubble
is
not
fragile,
then
its
existence
is
unambiguously beneficial
(Samuelson 1958).
4.1
Crash and Credit Crunch
However,
ment
will
it
seems extreme to assume that a coordination-dependent financial instru-
always be stable.
When
A
>
0,
the
economy trades higher
(or lower net outflows)
while the bubble
reversal in capital flows
and the consequent crash
is in
13
capital inflows
place, for the possibility of a
in the
sudden
domestic real estate market.
.
Consider the expression
for total
output at date
^
If
there
is
no crash, then W^
is
high and
^^W,
(1
+
f/B
=
Starting from this level,
are
two
if
r*
+
t:
2
75(+i
a,Ar'')
we consider the
=
+
pt+i
=
p^
!(/?
Output
1.
-
\)i>RK^
date
effect at
i
+1
in this case
+
is,
RK,.
of a
fall in
W[, there
falls,
curtailing
effects that arise.
First, the direct effect
his date
is
that the investing entrepreneur's wealth
investment and reducing output. In the case of the crash, wealth
i
falls to
(l-Q,)M';(l+r*).
Second, the banker has
i
+
1.
As
less
funds to lend to the investing entrepreneur at date
real estate falls in value,
banks are unable to
collect as
much
goods from the next generation, and so they cut back on loan supply.
the supply of funds
is
sufficiently large, the result
interest rates rise causing investment
is
and output
which entrepreneurial investment
at the point at
international
If
the
fall in
a domestic "credit-crunch''
loan
:
This credit crunch occurs
to
fall.
is
constrained by the quantity of
international goods of the current generation of bankers
point, since the supply of loanable international goods
is
and entrepreneurs. At
this
limited, banks' loan interest
rates rise above one.
At date
agents choose at and this leads to variation in \\\. 'We define a "small
i,
crash" as a circumstance where at
enough
fall in
W^ that only the
f^cs
However,
in pt+i
if
at
is
"large crash."
sufficiently large
crash case
is
From Figure
where at
in the
1,
small, so that the bubble crash leads to a small
first effect arises.
^ ^-LlwtiX -
above one, resulting
is
we
at)[\
+
r')
In this case,
+ h^R - \)^RKt + RKf
then the contraction
in loan
supply leads to a
domestic credit crunch. 'We refer to this event as a
see that the threshold between the small and large
= a^
In the large crash, p^^^ rises above one to
q i^.tH^ y
We
can substitute and find
that,*^
The complete
U = R mm
expression for the output in the case of both large and small crash
<
(1
—
rise
Q( ) Pv J
,
>
14
+ max
<
,
is:
>
+ Rh
t
This
expression
last
intuitive. In the large crash, all of the international
is
the bankers and entrepreneurs are being invested at date
goods produces a gross return of R, which
t
+ 1.
Each
in addition to the
goods of
of these invested
endowment
RKt,
of
yields the expression for U^'^.
Finally, the crash in the
The next
of value.
bubble asset leads to a permanent
generations invest
all
of their
domestic stores
loss of
endowment abroad causing
capital
outflows.^
Overexposure to Large Crashes
4.2
Although bubbles lead to the
possibility of crashes, they
increasing growth while they last.
the
economy make
We
show that the private
do provide the benefit of
The next question we address
this risk/return trade-off optimally
is
whether agents
from society's point
of view.
sector's choices lead to overexposure to large crashes.
Consider the choice of at that maximizes expected aggregate output (which
equal to the generation
in
i's
welfare),
when
at
is
such that the economy generates a
is
large crash:
max
XU^'^
+
- X)U^
(1
(6)
a'^<a(<i
The
derivative of this function with respect to at
(l-A)(/?
+
Ar*
l)
at the
optimum
case from (3)
r*
for private agents, the first order condition for the large crash
is:
{I
When p^i =
2XR.
+
I
But
is:
/? it is
- X){R +
= X{R + pf^,).
1)^^
evident that these two
first
order conditions coincide, and the
However,
if
p^i < R, then the
planner's solution to the program in (6) yields an Qj that
is
strictly smaller
private sector's choice
The
is
constrained
distortion in the agents' decision can be
the banker's portfolio decision.
^
efficient.
An example
of this
phenomena
At date
in practice
+
t
may
most
I,
easily understood
social
than qP.^°
by considering
the value of international goods in
be the behavior of EM's following the
EM
crises
of the late 1990s. These economies turned aroimd from being significant net borrowers before the
crises, to
become
substantial net lenders to the developed world, and the
^"It is clear that
p^i <
that qP
Ris
We
the
first
US
in particular.
order conditions differ between the private and planner programs
can assert that Q(
is
strictly smaller
than a^ because conditions
at an interior, so that at least one of the first order conditions
•
15
is
(1)
valid.
and
(5)
when
guarantee
.
the crash-state to the banker
.
proportional to pf+i-
is
international goods in the crash-state
However, the social value of
proportional to R, since these goods are
is
always used by entrepreneurs to undertake investment projects."
that
p^i < R, the banker has
less of
To the extent
an incentive to ensure that he has sufficient
international goods to lend to entrepreneurs in the crash-state. Moreover, recall that
r
p,,
,
=
mm
^^
—
r
<
-,
R
so that less domestic financial development, captured by smaller values of
p^j and increases
lowers
ip,
this distortion.
Ex-ante, the low return on lending to entrepreneurs translates into a lack of pru-
dence in the date
/.
Bankers chase higher returns by investing
portfolio decisions.
excessively in the risky real estate bubble, rather than retaining
some international
liquidity to be in a position to lend to the entrepreneurial sector.
Lack
of financial
development, in the dimension of tighter domestic collateral constraints, overexpose
economy
the
Welfare Maximizing Choice
4.3
We
to the risky bubble.
conclude this section by deriving the welfare maximizing portfolio share.
For each generation that the bubble does not crash, the planner chooses a to solve:
max XU^ + (1-X)U^.
(7)
0<a<l
There are two cases to consider
note that
Ua >
a^
p'-^
p'-'
,
W^ =
Thus,
We
=
1
>
in deriving the solution. If
a <
and the economy avoids the credit crunch. In
I
and the economy enters the credit crunch
a'^,
from Figure
this case, t/^
if
=
we
if^-^
the bubble crashes.
U^'^.
note that under
(5),
the
first
order condition that maximizes (7)
f/*^'-^,
indicates choosing the lov/est possible value of a.
from
(1)
that in the range where
U'-^
=
t/"^"^,
the
On
first
when
the other hand,
it
the boundary where
a
is
the credit crunch situation.
1,
some
—
order condition indicates
lie
at
equal to a^
In v/ords, a social planner chooses an
=
U'-'
follows
choosing the highest possible value of a. Thus, the welfare maximizing a must
'^When pf^i
1
a that
is
as large as possible so as to avoid
This choice maximizes the intergenerational transfers
international goods stored by the bankers/entrepreneurs go unused by the
entrepreneur. For this reason, the undervaluation argument only applies in the case of large crashes.
16
afforded by the bubble, while avoiding the credit crunch where international goods
are scarce.
due
is
We
also note that the stark result of avoiding the credit
to the linearity of our model,
and conditions
(1)
and
(5).^^
crunch completely
On
the other hand,
the model does highlight the novel aspect of our welfare analysis of bubbles.
Aggregate Risk Management Policies
5
We now
focus on the case where the rational real estate bubbles are welfare reducing
and consider a
variety of corrective
government
policies that
implement qP
=
a^.
In practice, a bubble crash in a developed economy leads the central bank to inject
liquidity into the banking sector to offset the credit crunch.
may
be helpful in our model, in practice
governments
bank are
banking
in EM's.^'^ In a
likely to
us unlikely to be readily available to
bubble crash, the credibility and Hquidity of the central
be low, so that the central bank
sector. Thus,
we
the exposure to bubble
is
in the
same
position as the
aim
focus in this section on ex-ante policies that
to reduce
risk.
Liquidity Requirement
5.1
One
it
While such a pohcy
solution to the risk problem
we have
raised
is
agents of generation
for all
enter into a contract requiring that each agent hold a fraction
(1 — a^)
t
to
of their wealth
in foreign reserves.
The most
natural interpretation of such a social contract
requirements on the banking system. Such requirements are
ing markets.
is
in
terms of liquidity
common
in
many emerg-
For example, during the period of Argentina's currency board banks
were required to hold significant dollar-reserves.
But such a
solution requires
some
policing
tive for one agent to deviate from holding 1
I
— a^
.
From Figure
1,
bursts, the credit crunch
we
is
agent's decision problem at
'^For example,
(5)
is
see that
p'-^
=
and enforcement. Consider the incen-
— a^ when
1 at q'^
avoided). But, from the
p*^
when A goes toward
=
1 is
a =
1.
An
all
(i.e.
same
other agents are holding
at q'^, even
if
the bubble
figure, the solution to the
agent will prefer to invest only in
zero, intuition suggests that the
optimal q will
rise.
However,
violated in this case.
'^See Caballero and Krishnamurthy (2005) for a model of (ex-post) extreme events interventions
in
economies with developed (complete) financial markets.
17
the bubble asset.
We
^'^
can also see
agent to choose
where the
this
a =
1
by considering the program in
versus
a
=
if all
,
from
last inequality follows
Intuitively,
a^ when p^
=
(2).
The
utility gain for
an
1 is,
(1).
agents are holding sufficient international liquidity, a crash avoids
the credit crunch. Thus, a deviating agent values the bubble asset purely for the ex-
pected return
it
offers
and does not assign any additional cost to the bubble crashing.
This leads the agent to invest
If
portfolio decisions are costly to observe, a liquidity requirement will be costly
to impose.
the costs are high enough, the
If
we have described
5.2
An
of his wealth in the bubble asset.
all
earlier
=
where a
economy
will revert to the equilibrium
a''.
Capital Inflow Sterilization
alternative policy to implement the optimal investment in the bubble
inflow sterilization.
As we show
is
capital
next, this sort of policy avoids the policing issues of
the liquidity requirement, but instead recjuires that the government having credible
powers of taxation.
Central banks often respond to capital inflows by sterilizing. They
debt proportionate to the quantity of the capital inflow. The practice
sell
is
government
conventionally
seen as an attempt to reduce the monetary expansion created by the capital inflow, but
note that, as
If
we show
the sterilization
bubble assets,
it
is
next,
large
it
has power even in the abscence of a monetary friction.
enough to provide the private sector with alternative non-
has the potential of reducing investment in real estate bubbles.
Government debt crowds out the bubble,
Suppose that the government
t
at interest rate rp. In addition,
goods endowment of generation
raising interest rates in the process.
issues one-period debt with face value of Gt at date
raises taxes at the rate of Tj
it
t.
The revenue from the debt
invested at the international interest rate of
^*Jacklin (1987)
He argues
makes a
r*.
is
and the tax are
sale
Finally, the debt
related point in the context of the
that the Diamond-Dybvig bank
on the international
is
Diamond and Dybvig
not coaHtion incentive-compatible
side-trades.
18
repaid at date
if
(1983) model.
agents can
make
—
i
+
1,
so that the government balances
+
rsWt
its
budget:
G
Y^)^^ + ^')-Gt=Q-
(8)
Agents purchase act of these bonds with their international endowment ("a capital inflow") at interest rate
W[ =
where
f
is
rf Then, the wealth equation
.
M/, (1
+
either g (no crash) or
r*
—1
+ acAr? -
decision problem for an agent
max
Et
0<QG,,+a,<l
We
<
at{f
-
generation
t
becomes,
r*))
(crash), and,
Wt = Wt{l The
+
r*)
for
is
T,).
now:
'2
RKt + W^
[
Kt
^:
1
2
pt+i
note that government bonds provide the same stable cash-flows as investing
the international
endowment abroad. Thus,
as long as acj,
+
ott
<
1,
government
bonds and international liquidity are perfect substitutes and rp must be equal to
r*.
From
the government's budget constraint, in this case
government debt are accommodated by a reduction
the private sector, and the sterilization has no
For the sterilization to have any
efl:ect, it
Tg
=
0.
Any
sales of
in the international liquidity of
eflPect.
must be
sufficiently large.
Again denoting
by qP the portfolio share that the private sector's optimally chooses to invest in the
bubble, the sterilization has any effect only
Gt>G: =
if,
{l-a^)Wt{l +
r').
Let us consider such "large" sterilizations. For these cases, the private sector reduces
its
international liquidity holdings to zero and only holds government debt and the
bubble
asset:
W;^Wt{l+rf + ai{f-rf).)
The
private agents'
(1
-
first
X){g
- rf){R + pf^,) -
At the welfare majcimizing
solving for rp,
order condition, at an interior solution for
solution
A(/?
+ pf+J(l +
we know that p^
we obtain
19
=
rf )
jf
=
=
1.
Qj, is
now:
0.
Rewriting, and
the government sells debt that raises (1
If
—
a''^)Wt resources at date
i,
agents
purchase both this debt as well as the welfare-maximizing amount of the bubble
any investment
asset. Since
government debt reduces investment
in the
asset one-for-one, the interest rate on the debt has to rise to
f'',
in the
bubble
the expected return
on the bubble.
However,
in
implementing the optimal portfolio share, the government has to
taxes. Using the government's budget constraint, (8),
some
=
r,
(1
-a^^
1
A
+
we can
raise
solve to find that,
r*
higher return on the bubble or a lower international interest rate, raise the required
taxes.
The need
government
to collect taxes to support the sterilization raises a concern.
is
limited in
its ability
sterilizations (or sterilizes with
of the public).
to raise taxes, then
it
bonds that have a low
But, small sterilizations have no
If
the
can only implement small
effective return, in the eyes
effects.
Thus, effective sterilization
requires a government with sufficiently large tax powers.
.J
Public Debt Market Development
6
Sterilization has the potential to solve the inefficiency
stemming from
agent's under-
valuation of the systemic risk generated by bubbles. However, the optimal solution
is
not to eliminate bubbles altogether, but to reduce their amount to a^ in Figure
1.
The bubble
is
the endogenous market solution to the dynamic inefficiency created
by domestic financial underdevelopment. Sterilization, as we describe
instrument to reduce the
fragility created
by
this
market
stitute for the missing "intergenerational" contract.
both reduce
fragility
and
alleviate
dynamic
solution.
Can we
inefficiency?
We
find
it, is
It is
merely an
not a sub-
mechanisms that
turn to answering this
question next.
The reason our
is
sterilization policy does not solve the
that the interest rate spread of
tion.
Thus, on net, there
This
is
in
is
f'-'
—
r* is
dynamic
inefficiency
problem
financed with taxes on the same genera-
no intergenerational transfer associated with
sterilization.
sharp contrast to Diamond's (1965) perpetually rolled-over public debt,
which does represent a solution to the dynamic inefficiency problem. However, Dia-
mond's public debt
is
a bubble in itself and hence raises the
20
same
fragility
concerns
surrounding the real estate bubble.
If
the next generation does not roll-over the debt,
the bubble crashes.
We
next show that public debt that
supported by future rather than current
is
taxes achieves a compromise: Such debt implements intergenerational transfers (like
Diamond), as well
as reduces fragility risk (like our sterihzation policy).
We
pledging future taxes requires credibility and commitment.
Of
course,
thereby establish a
natural connection between a government's credibility and ability to raise taxes and
the extent to which the government can solve the economy's dynamic inefficiency
problems, while limiting the fragility costs of the bubble.
Suppose the tax base of the government
is t\'\'\.
However, because of credibility
concerns the market discounts the future tax revenues at the rate
(1
—
p) such that
the pledgeable tax revenues are:
(1
We
assume that
at
t
-
p)VVK,+,
the government issues the
these future (potential) taxes.
5
>
0.
maximum debt
With such a debt
can, collateralized
it
by
structure, a high p can be interpreted
as very short-term maturity structure of debt, while a low p corresponds to a long-
term maturity structure of debt. Let the value of the stock of outstanding government
debt be denoted by Dt. The value
=
^
Wt
satisfies,
(l-/^)(l
of
-^E.|±i|.
+n
1
[
Assume, momentarily, that the stock
of agents' store of value
+ ^)|r +
Wt+i
government debt, Dt,
demand, that agents use
is
is
constant.'^ Let
r^ denote
D/W
is
sufficient to satisfy all
this as the only saving instrument,
maximum
and that the government maintains the practice of issuing the
debt at each point in time. Then,
(9)
J
equal to one at
all
this equilibrium interest rate,
collateralized
dates and the interest rate
which from
(9) satisfies:
^^=T(l-p)(l + r^)-/,.
It is
apparent from this expression that
that p
is
^^D/W
small relative to
is
r,
if
the government has enough credibility so
then the dynamic inefficiency can be completely removed
always equal to one, while the tax base
between these statements because,
collateral for the debt.
If all
is
equal to tU',
.
There
is
in equilibrium, the taxes are not levied; the)'
of the taxes of
rWt were
would shrink toward zero over time.
21
no contradiction
simply sen'e as
levied, then ratio of debt to
endowments
as the
r^ that solves the above equation exceeds
efficient equilibrium, the
g.^^
To implement
this constrained
government issues enough public debt to bring r^ exactly
to g.
While the pledgability
of future taxes
needs to collect taxes to pay
new
with
debt.
That
not bubbly since
To
it is
is,
for this debt, as it
is
debt
is
by taxes.
fully collateralized
by
collateralized
T—
1
will
— p)tWt
(1
buy up
fully repaid.
2 also
is
Suppose
t.
to (1
— p)tWt
young agent
1,
T—
T >
L
the young agent
of generation T, the
bond
knows
will
be
the young at generation
1,
Since every bond in the stock of government
so on.
collateralized by a specific, dated, tax revenue, the
entire stock of
T—
at date
face value of this bond, since he
Anticipating this behavior by generation
buy the bond, and
bond matures
this
revenues. Then, at date
that regardless of the behavior of the
debt
fully finance the expiring
see the role of collateralization, consider one of the bonds in the stock of
of generation
T—
can
the collateralized debt behaves as Diamond's debt, but
outstanding government debt at time
and
the government actually never
critical,
is
argument applies to the
government debt.
The same argument does
not apply to Diamond's debt solution, or the real estate
T—
bubble. In these cases, the young of generation
they believe that the young of generation
coordination dependent asset
T
1
buys the bubble only because
do likewise.
will
Of
course, such a
is fragile.
Collateralized public debt also dominates the real estate bubble as a savings vehicle
since:
r^ -
The
f*
=
-
r^
+
5
A(l
-f
collateralized debt eliminates the bubble,
Note that
then even an infinitesimal tax base
more
> r^ -
and
is
p
>
0.
its fragility.
where the government
in the limit case
public debt.^' In the
5)
is
fully credible, so that
enough to implement the
realistic case of a
first
=
0,
best with stable
government with limited
government may be unable to generate enough
p
credibility, the
reliable store of value instruments to
^^For smaller values of r relative to p for which the government cannot issue debt such that
D/W
if
ecjuals one, there
is still
parameters allow for a
solution.
room
D/W =
for
1
improvement on the market bubble outcome. For example,
— Q5 <
1,
then the government can opt for the sterilization
But, in contrast to the solution in the previous section, the sterilization leverages future
taxes and not current taxes.
^^This limit result
is
akin to the point
made
in
McCallum
(1987) and extended in Caballero and
Ventura (2002), that well defined property rights even over an infinitesimal share of an economy's
growing output, can eliminate the possibility of bubbles.
22
fully
crowd out the bubble.
When
=
p
the the government can only sterilize but
1,
is
unable to implement intergenerational redistributions without incurring risks similar
to those of the market bubble.
Remarks
Final
7
One view of emerging markets crises describes normal
times as periods with significant
capital inflows, which are suddenly interrupted by liquidity crises.'®
This paper highlights a different view. Normal times are those with net capital
outflows. These normal periods are occasionally interrupted by speculative bubbles,
many
Moreover, we show that in
which can crash.
instances these bubbles, while
rational, are socially inefficient since they introduce excessive aggregate fragility.
Both views stem from some form of
bubble-view
reflects a
financial
more primitive domestic
underdevelopment. However, the
financial market,
where residents
find
limited trust-worthy local assets.
Ingredients of both views probably coexist and vary in relative importance across
economies and times. During the mid 1990s,
large
amounts
of capital inflows,
and a crash
series of crises that started with
to the rest of the region,
in local bubbles.
example. South East Asia received
which financed both productive investments and fed
Real Estate bubbles. In this context, the
and soon spread
for
had elements of both a liquidity
Over time, the
bubble-assets were not recreated.
The
Thailand
latter
crisis
liquidity crunch disappeared, but the
phenomenon has played out
much
in
of the
Emerging Market world
^From
the point of view of our analysis, the disappearance of the bubble assets
as well as in
some newly industrialized economies.
important factor behind the acceleration of the capital inflows to the
US current account
the worsening of the
the same
its
lines, despite the
deficit- since the
savers are forbidden from accessing
may
Asian/Russian
crises.
an
hence
Along
attention that China's dollar-reserves accumulation and
potential reversal has received, the real danger
capital controls
US — and
is
US
may
lie
elsewhere. Today, Chinese
instruments directly.
A
normalization of
lead to a crash in their buoyant real estate market and increased
capital outflows toward the US.
It
goes without saying that ours
is
a highly stylized characterization of emerging
market dynamics. For practical purposes, we do not mean
'®E.g.,
Furman and
Stiglitz (1998),
to highlight the multiple
Calvo (1998), Caballero and Krishnamurthy (2001), Chang
and Velasco (2001).
23
equilibria nature of bubbles, or even the
extreme form of rationality we have required
on agents. They simply capture the high
volatility in
emerging markets and the
of speculation and expectations. Moreover, although the bursting of bubbles
nous in our model, one could extend
for instance,
it
and
link the
exoge-
bubble bursting to fundamentals;
any domestic or external factor that
raises the relative
eign assets, could crash the bubble in our model.
volatile
is
role
Bubbles
for
appeal of
for-
us represent highly
domestic financial assets which are not backed by solid fundamentals, sound
government
policy,
and
domestic markets, rich
institutions.
in
They have the
potential to yield high returns
if
funds but poor on quality assets, choose to speculate on
them, but they are also susceptible to large drops
24
if
fundamentals turn sour.
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^28^ 03!
1,
in
Overlapping Generation
Feb 1987, 1-22
Date Due
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