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NBER
WORKING
PAPERS
NBER WORKING
PAPERS SERIES
SERIES
ASSET BUBBLES
BUBBLES AND
AND ENDOGENOUS
ENDOGENOUS
GROWTH
ASSET
GROWFH
Noriyuki Yanagawa
Noriyuki Yanagawa
Gene
M. Grossman
Grossman
Gene M.
Working Paper No. 4004
Working Paper No. 4004
NATIONAL
BUREAU OF ECONOMIC
RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
1uzu assacnusctts Avenue
Cambridge, MA 02138
Cambridge, MA 02138
February 1992
1ebruary 199Z
We are grateful to Ben Bemanke, Elhanan Helpman, Jean Tirole, and Harald Uhlig for
We are grateful to Ben Bernanke, Elhanan Helpman, Jean Tirole, and Harald Uhlig for
comments on an earlier draft. Grossman thanks the National Science Foundation for financial
comments on an earlier draft. Grossman thanks the National Science Foundation for financial
support. This paper is part of NBER’s research program in Growth. Any opinions expressed
support.
is part
program
in Growth.
Any opinions
are
those This
of thepaper
authors
andofnotNBER's
those ofresearch
the National
Bureau
of Economic
Research.expressed
are those of the authors and not those of the National Bureau of Economic Research.
NBER Working
Paper #4CKI4
NBER
Working Paper
#4004
February
1992
tebruary 1992
ASSET bUII3L1S
BUBBLES ANI)
AND NUUUbNOU
ENDOGENOUS (JROWI1-i
GROWTH
ASShI
ABSTRACT
A flflVIn A iflfl
/D
I icn. I
We study the interaction between productive and nonproductive savings in an
We study the interaction between productive and nonproductive savings in an
economy that grows in the long run due to endogenous improvements in labor productivity.
economy that grows in the long run due to endogenous improvements in labor productivity.
As in the neoclassical growth setting with overlapping generations studied by Tile
(1985),
As in the neoclassical growth setting with overlapping generations studied by Tirole (1985),
asset bubbles can exist in an economy with endogenous growth provided they arc not too
asset bubbles can exist in an economy with endogenous growth provided they are not too
large and that the growth rate in the equilibrium without bubbles exceeds the interest rate.
large and that the growth rate in the equilibrium without bubbles exceeds the interest rate.
Since the growth rate in the bubbleless equilibrium is endogenous, the existence condition
Since the growth rate in the bubbleless equilibrium is endogenous, the existence condition
reflects parameters of tastes and technology. We find that bubbles, when they exist, retard
reflects parameters of tastes and technology. We find that bubbles, when they exist, retard
the growth of the economy, perhaps even in the long run, and reduce the welfare of all
the growth of the economy, perhaps even in the long run, and reduce the welfare of all
generations born after the bubble appears.
generations born after the bubble appears.
Noriyuki
Yanagawa
Department I i1JI4W4
of Economics
IuL1yUr.J
Princeton University
Department
of Economics
ri
iUI.LVI1 U11LViLL
Princeton,
NJ 08544
and University
of Tokyo
Princeton,
NJ 08544
._i
TT.!_
ailu univcrsiy or..ti'n_I__..
oicyo
Gene M. Grossman
IVh J1VILIQ11
Woodrow
Wilson School
'jvizc
Woodrow
Wilson School
Princeton University
rriiicvuii
Princeton, UNJIIivci
08544
Princeton,
NJ
08544
and NBER
x
——
anu 1DCI
I. Introduction
Introduction
I.
Can the
the market
market price
price of
of an
an asset
asset deviate
deviate from
from market
market fundamentals
fundamentals (i.e.,
(i.e.,
Can
the present
present discounted
discounted value
value of
of dividend
dividend payments)
payments) in
in aa world
world populated
populated by
by
the
rational,
farsighted investors
? Tirole
Tirole (1982)
(1982) has
has shown
shown that
that it
it cannot,
cannot, if
if
rational,
far-sighted
investors?
the economy
economy comprises
comprises aa finite
finite number
number of
of infinitely-lived
infinitely-lived
traders, while
while
the
traders,
Wallace (1980)
(1980) and
and Tirole
Tirole (1985)
(1985) have
have shown
shown that
that the
the same
sameis
is true
true inin aa
Vallace
non-growing
economy no matter how long are investors’
trading
horizons.
But
non-growing economy no matter how long are investors' trading horizons. But
Tirole
(1985) and Veil (1987) have established
that “bubbles”
sometimes can
Tirole (19S5) and Veil (19T) have established that bubblesu sometimes can
exist in the general equilibrium
of a growing economy with overlapping
_..:1
!1TX
UT
TV1U mflTTflTTTflb Tfl V 9IITMflT9 Cmniin IIITM IITC!dPT1An
1
generations.
UVi3LdUdO A rational
investor
will
only hold an asset priced differently
than its
A rational investor will only hold an asset priced differently than its
fundamentals
if she expects that the bubble component will
yield
at least a
fundamentals if she expects that the bubble component will yield at least a
normal rate of return;
i.e.,
that it will
grow at least at the real rate of
normal rate of return; i.e., that it will grow at least at the real rate of
interest.
But if bubbles grow at the rate of interest
eventually
their
in every period,
interest. But if bubbles grow at the rate of interest in every period,
value will
exceed the income of the young generations
who
eventually their value will exceed the income of the young generations who
must purchase these assets from the old, unless the income of these
must purchase these assets from the old, unless the income of these
generations
is growing at least as fast.
Tirole
(1985) investigated
the
generations is growing at least as fast. Tirole (1985) investigated the
conditions
under which a DiamondI 1AflflP
(1965) economy with
an expanding population
!I ——
-
-
conditions unaer wnicn a iiiamona nrnoj economy wnn an expanoing pupuiatiun
would grow fast enough to allow for the existence of bubbles in asset prices.!
4,
UW.C..4
LO 1LVU5JL bU
WVULU
Be related
the existence
Hp rp1t.prI th pyistntp
general
equilibrium
, .,k1oc n
,11, .C,.
IL
LVJ. +1,
condition
to the intertemporal
efficiency
of the
tnnditinn to the intertemnoral efficiency of the
without
bubbles.2
Of course, in the Diamond economy with
general equilibrium without bubbles.2 Of course, in the Diamond economy with
a neoclassical
production
function
and no technological
progress,
per capita
a neoclassical production function and no technological progress, per capita
incomes stagnate in the long run.
incomes stagnate in the long run.
‘Veil
(1987) used a similar
framework to study “stochastically-bursting
bubbles.(1987)
I1 used a similar framework to study "stochastically-bursting
IVeil
biihhl es
2See Tirole
(1990) and Blanchard and Fischer
(1989, ch.5) for excellent
introductions
to this
2See
Tirole (1990)
and literature.
Blanchard and Fischer (1989, ch.5) for excellent
.LUL,iUUUtbiUH I() UILLb
iC.IULV.
- 2-2-
we extend
extend Tirole's
Tirole’s (1985)
(1985) results
results to
to include
include economies
economies
In
this paper,
paper, we
In this
that grow
grow in
in the
the long
long run
run at
at an
an endogenous
endogenous rate.
Asisis well
well known
knownby
by now,
now,
that
rate. As
long-run
economy in inwhich
long-run growth
growthcan
canbe
besustained
sustained inin an
an economy
whichrealrealreturns
returns toto
whatever capital
capital goods
goods are
are being
being accumulated
accumulated (physical,
(physical, knowledge,
knowledge, or
or human)
human)
whatever
are bounded
In other
other
are
bounded from
from below
below by
by a
a number
number that
that exceeds
exceeds the
the discount
discount rate.
rate. In
words, there
there must
must be
be non-decreasing
non-decreasing returns
returns to
to accumulable
accumulable factors
factors inin the
the long
long
words,
These non-aecreasing
non-decreasing returns
returns may
may oe
be innerent
inherent to
to tne
the proauction
production
run. 'rnese
run.
---
I__
_._t__
ii,
—
(1 1.JuIIc
1 Banuelli
1
1 (Afl\ or they may
.. ....,
Rebel0 I1991,
Jones and
1990)
ariseuuc
due
technology
(e.g.,
vi
aLIu
QiULii
iic
(e(.II1Iu.Luy
Is.,
n.uJu
ivj
to externalities
thenrntess
process of
capital rnmii1tinn
accumulation (eD'
(e.g., tt-..
pyfprnlit.ip generated
unrted inin he
rf nit1
Bomer
choose aa simple
simple specification
specification that
that includes
includes
1986, 1990;
1988). VeVe choose
1986.
1990; Lucas
Lucas 1988).
externalities
from physical
physical capital
capital (following
(following Romer
Romer 1986)
1986) and
and investigate
investigate the
the
externalities
from
existence conditions
conditions for
for bubbles
bubbles and
and the
the effects
effects that
that bubbles
bubbles have
have on
on the
the
existence
growth rate
rate of
of the
the economy
economy and
and on
on the
the welfare
welfare of
of the
the various
various generations
generations of
of
growth
agents.3 YeYefind
find that
that the
the conditions
conditions under
under which
which bubbles
bubbles can
can exist
exist are
are
agents.3
similar
to those identified
by Tirole (1985), but that bubbles are not so
similar to those identified by Tirole (1985), but that bubbles are not so
benign in this setting
as they are in the Diamond economy with an exogenous
benign in this setting as they are in the Diamond economy with an exogenous
growth rate.
growth rate.
II.
TT
IL.
n-
A
Bubbles
L Diamond-Romer Economy Vithout
n..Lt.1
P. UIdJtIUILU LtUUIeL 1KOI1QU1Y IILL1QUb DUUUIb
As
in Diamond
agentsS Slive
for
two
periods.
4.ac..II.JsI..A
1TI
fliffiAflel (1965),
(1Q\
On+C
rrT '+%IA
TAr1EIIC
S U JIJ
j a4I U 1I
S ¶.J S Un
U j1¼. A SVU U
They
work,
consume,
'Fhsv
flUS f'ATICIIlnA
S S(.# J urrr
0I —--a--— -
and save when they are young, and enjoy the fruits
of their
savings when they
and save when they are vonn. nd enjoy the fruits of their savings when they
-.
are old. Each period a new generation of young is born, endowed with a fixed
are old. Each
period a new generation of young is born, endowed with a fixed
amount of potential
working time, which it supplies
inelastically
in the labor
amount of potential working time, which it supplies inelastically in the labor
3Ve choose this specification
with capital
externalities
to bring out the
3Ve
choose this
with capital
to bring
out the
similarities
withspecification
the Tirole (1985)
analysisexternalities
of the Diamond
economy.
But the
similarities
with
the
Tiro].e
(1985)
analysis
of
the
Diamond
economy.
But the
existence conditions for bubbles are similar in economies with other sources
existence
conditions
bubbies
simIlar (1991).
in economies with othr sources
of endogenous
long-run for
growth;
seeaeYanagawa
of endogenous long-run growth; see Yanagawa (1991).
-3-
- 3-
-
•,I__
1_1___
They use
use uieir
their iauor
labor income
income to
to uuy
buy output
output ior
for consumption
consumption ana
and
market. iney
inarxet.
nr
+r
+1
f'r+l
c+,.1,
1A
investment
purposes
and
to UVrlIIr,'hCA
purchase
the
existing
capital
old.
Lit V CO L#LIILI ?tI'TAOC
U
fr/US VIJ¼.O
USSU
jJUS ..LIikQi..
Ut&.vcfn
.aSu UJ.LI
,UfrJS
UUS
Ustock
U'JA I. Sfrom
VIII the
IsIIC IJAU
Ve ssnme
assumefor
for
V
CV -—
nowthat
that canital
capital goods
goods are
are the
the only
only store
store of
of value.
value. Frir
For
now
simplicity,
that the
the economy's
economy’s population
population is
is constant
constant through
through time
time
we assume
assume that
simplicity, we
and equal
to 2L.
2L.
and
equal to
A representative
representative
member of
of the
the generation
generation born
born at
at time
time tt consumes
consumes
A
member
units of the homogeneous final
cYt
good when young, and cot+l units
of this good
units of this good
units of the homogeneous final good when young, and
She chooses her consumption profile
when old.
to maximize a utility
function,
when old. She chooses her consumption profile to maximize a utility function,
subject to an intertemporal
budget constraint.
Letting
on savings invested
at time t, the
rt+l
be
UCcyt c0+i),
3 %t+l) subject
9
U(c
to an interteniporal budget constraint. Letting ri be
the rate of return
(or real interest
rate)
the rate of return (or real interest rate) on savings invested at time t, the
constraint can be written as
constraint
can e written as
Cot+l
=
It ’
Cyt + cot+1
l1 ++ rt+l
rt+i
(1)
(1)
where It is the individual’s
labor income earned at time t.
is the individual's labor income earned at time t.
where
The consumer’s optimization
yields
equality
between the marginal
rate of
The consumer's optimization yields equality between the marginal rate of
intertemporal
substitution,
Ur/IJ2, and one plus the interest
rate,
1 +
rt+l,
intertemporal substitution, U1/U2, and one plus the interest rate, 1
as usual.
This equation
generates an implicit
as usuai. mis equation generates n iWiiib
savings function,
viIt i.uiiciuu,
st —=
—
Ve assume henceforth that individual
preferences represented by
TJ
.ecitm hn,o-cArfh that 4niI4vjg1ii1
rnrsnted by
•
U(a) are homothetic.
homothetic.
Then s(I.r
-' , are
S T5 +1'
Firms hire the available labor force, L (half the population, namely the
S(ItJt+J
l
0 St , S + 1'
nrfren'c
£t At # S 'd S VAt
V4&U •tt 1 d
'
S ' +'
Then
s(JIt,rt+l)
=
Wt,rt+l)
l
Firms hire the available labor force, L (half the population, namely the
young generation),
and the available
aggregate capital
stock, Kt, and produce
young generation), and the available aggregate capital stock, Kt, and produce
the homogeneous output,
Yt.
the homogeneous output, ''•
old generation
A firm i that rents Ki units of capital
A firm i that rents
from the
units of capital from the
that owns it and that employs Li young workers generates net
old generation that owns it and that employs L young workers generates net
output
(after
accounting
for capital
depreciation)
of
output (after accounting for capital depreciation) of
- -I4-—
Y; = F[K;,
A(Kt)Li],
F[K, A(K)L'],
where A(.)
A(.) represents
represents labor
labor productivity,
productivity,
A’ >>
where
A'
0.
0.
Here
incorporated aa
Here we
we have
have incorporated
positive spillover
spillover from
from the
the size
size of
of the
the aggregate
aggregate capital
capital stock
stock to
to the
the
positive
productivity
of workers
workers in
in individual
individual firms,
firms, in
in the
the manner
manner suggested
suggested by
by Arrow
Arrow
productivity of
(1962) and formalized
by Sheshinski (1967) and Bomer (1986).4
Ve assume that
(1962) and formalized by Sheshinski (1967) and Ranier (1986).4 Ve assume that
fli
I’(.,.)
1
I that firms - Ibehave
I
constant returns-— to scale and
competitively.
1!L
exhibits
exnioits constant returns to scaie ana tnat rirms oenave competitively.
In hriny
hiring capital,
i'n+l
In
ignores 4+
itsU USLLJ
tiny SLLSSL&t._SL¼_..
influence rn
onVII the
+hthein,individual
,itl flrmfirm4c,nrrc
4nc1,,øn'
IJLI
aggregate cauital
capital stock
stock and
and thus
thus on
on the
the productivity
of its own workers.
azreate
Droductivitv of its own workers.
Thus, each firm hires capital
up to the point where its (private)
marginal
Thus, each firm hires capital up to the point where its (private) marginal
product equals the rental
rate,
rt,
and it hires workers until
their
marginal
product equals the rental rate, r, and it hires workers until their marginal
product equals the wage rate.
In view of the homogeneity of degree one of
product equals the wage rate. In view of the homogeneity of degree one of
t h’1s g’Ives the following
F(Y),
relationships
at the aggregate
level:
F(.,.), this gives the following relationships at the aggregate level:
rt
(2)
q
(2)
Fl(Kt,
A$)
Fi(Kt, AtL)
(3)
f’(kJ
f'(kt)
t'
= F&s
A$) - vKtF1(Kt,
ktf’(kt),
n/v
n Iv A$) = f&J \ -- 1_
t,I1 t
Wt—
wt
Ekflt,
where At = A(KJ,
where A4
f(kJ
=
At) - tnlt,
k, 3 Kt/AtL (capital
h
—
t'
per unit of efficiency
labor),
V,
Combining
(2) and (3) gives a relationship
and
A(K4'j, t.k4 K/AL (caDital per unit of efficiency laborL and
b
z F(Kt/AtL,
f(k)
equilibrium
1).
between
F(K/AL, 1). Combining (2) and (3) gives a relationship between
factor
prices,
equilibrium factor prices,
‘As we noted in the introduction,
we are not wedded to this specification
of
the
technology.
Alternative
formulations
thatwedded
preserve
long-run
incentives of
As we
noted in the
introduction,
we are not
to this
specification
for
capital accumulation
would
serve equally
For long-run
a general incentives
discussion
tne tecnnology.
Alternative
tormulations
thatwell.
preserve
of
what
is
needed
to
sustain
long-run
growth
in
a
model
of
capital
for capital accumulation would serve equally well. For a general discussion
.u bUL1fl
._and
1___
- _.J.1
_f
-1
accumulation,
see Grossman
Helpman__.L
(1991, ch.2).
WII4 1 iieueu
iong- run gruwii in a mouei 01 capuai
accumulation, see Grossman and Helpman (1991, ch.2).
- 5-5-
(4)
(4)
=
I'rrociuct
- I - __Imarket
—— equilibrium
_ts_f__
twneit
S_ investment
-Product
obtains
aggregate
equals
inarxet
equnioriuin
ooainswhen
grtge invesunent
equais
aggregate
savings,0
7
'1 fl tO S V
the unhI,ln
young and desired
,l4riI savings by
hi, +hA
fanQ.nsan,...'rn.,n.amn
I n Qnn flirn fl 0 Y 7
the
sum of desired
a nie 0
i.e.,
4
V.
fl
3U
old wish
to dissave their entire holdings of
dissavings
by
the P10
old. Since the p[O
suTssp
4ST?( O AesStp 1T4 J'Ua SUp(OI O
— - IJ Aq
-v capital, Kt, this implies Kt+l - Kt = s(wtAtL, rt+l)
or
r1) -- Kt ,, or
capital,
Kt+1 = s(wtAtL
(5)
(5)
rt+&
s(wtAtL, rt+i).
Kt+i
Equations
s(w+A+L,
K., this implies V'S
K1 -
(3),
(4), and (5) determine the dynamic evolution
of the economy
Equations (3), (4), and (5) determine the dynamic evolution of the economy
(factor
prices
and capital
stock) from any initial
stock of capital,
KO.
(factor prices and capital stock) from any initial stock of capital, K0.
In order to ensure the existence of a steady state for this economy, we
In order to ensure tile existence ox a steaciy state tor tnis economy, we
take a particular
functional
form for the capital
£...... £.
iaxe a pariicuii £UULiVLLL LVLUI iUL tLIC ..diJ.LLdL
linear
14nøy
aa.I
(6)
(6)
Vithout
externality,
making it
ALuaL.Ly w11I5 +
in the aggregate capital
i.e.,
ailtA rnt.1stock;
tnk! Le
n +h
—— — 7-
A&)
= Kt/a.
A(K) = K1/a.
further
loss of generality,
we normalize the size of the population
to
Vithout further loss of generality, we normalize the size of the population to
two, so that L = 1.
Then kt = a for all t, and (3) and (4) imply
two, so that L = 1.
Then kt = a
for all t,
(3’)
rt = P
(3')
rt = p
(4’)
fA\
.t )
Wt = i(P)
—
for all t, and (3) and (4) imply
for
all t,
for all t,
L
cI%r 411 +
is homogeneous of degree one in its first
where p s f’(a).
Now since s(s,*)
where D
Now since sC.1.) is homogeneous of degree one in its first
f'(a.
-6- 6-
1I.
).
—
—A
argument, s(wtAtL,
argument,
SWAb rt+l) = AtLs(wt,rt+l
.,A
(R\ equation (5) h'nmpc
and (4’),
'-I ) , '.'j"." becomes
K
t+l =Ks[(p),
Kts[d09
K÷1
LI 'A.
—
Then, after
f\ f\
substituting
,T'L
(6),
(g’),
d/a.
p]/a.
The capital
capital stock
stock grows
grows at
at the
the rate
rate
The
1,
gt = s/a - 1,
g=Ia-
(7)
(7)
r,, ..
where s E s[d(p),
sLp),
w1ere S
.
p]-I .
pj.
By (6),
productivity
I#I labor
I
.1
A(.) grows at this same rate
iJy (p), iaoor proauctivity At.) grows at tnis same rate
r1
has constant ,-1-eu,-nc
returns to +j
scale,
so does per capita income.
, -.) 1.-,,
ctl cr
U
- J 1100 ,U1tOU0ltU S..V(ISI&IJ
ys¼#I.ys.Ias1I.Im.
Before leaving this section, we note that the dynamic equilibrium
without
and since I’(.
OLLU QJ.iI SP1.-
Before 1eavinc_Ithis
eauilibrium
without
- section. I we note that the dynamic
.
bubbles is not Pareto efficient.
For suppose that at time t the old were to
bubbles is not Pareto efficient. For suppose that at time t the old were to
consume as in the above equilibrium
while the young saved an additional
amount
consume as in the above equilibrium while the young saved an additional amount
ds.
This would increase the capital
stock at t+l by ds and would generate
ds. This would increase the capital stock at t-i-1 by ds and would generate
additional
output of (dYt+l/dKt+l)ds
= (Pl + F,Ja)ds > rt+lds.
additional output of (dYt+i/dK+i)ds =
entirety
(F1
+
F2/a)ds
>
rt+ids.
If the
If the
of this extra output in period t+l were given to the (then)
old, then
entirety of this extra output in period t+1 were given to the (then) old, then
the utility
of this.generation
would rise (since it has set its marginal
rate
the utility of this. generation would rise (since it has set its marginal rate
of intertemporal
substitution
equal to l+rt+l, the extra output in the second
01 intertemporai substitution equal to 1+r+i, tne extra output in tne secona
period of life yields more utility
than the loss from the consumption foregone
pci LVU Vi iiic .Lciu hut C Ut,L.LJ.
tjijt (,IIC iV ijuw iic I..JLIuIU}flJ.uLt ivi 5Vuc
in the first period) while no generation would lose. Of course, the
in th first nrin vhi1 nn enrtinn vnnld 1ns. flf niirs. th
inefficiency
of the market equilibrium reflects the fact that (small)
4.
inefficiency of the market equilibrium reflects the fact that (small)
individual
agents have no incentive
to incorporate
the spillover
effect
from
individual agents have no incentive to incorporate the spillover effect from
capital
in their
private
investment decisions.
capital in their private investment decisions.
- 7-7-
III. Existence
Existence of
of Asset
Asset Bubbles
Bubbles
III.
Ve now
now assume
assume that
that the
the generation
generation that
that is
is old
old at
at time
time 00 possesses
possesses IMpaper
paper
Ve
assets that
that are
intrinsically
worthless.
That is,
is, tne
the assets
assets proauce
produce no
no real
real
assets
are intrinsically
wortnless. inat
output
and therefore
no UV
dividends.
db iIV
uciiu •
UU
pu dIIU
ILL LUiV generate
assets
cetc
'ri,
The
old
LILc,i,i
vu
,
attempt to Oçi
sell LLC
these
to
young t
at .a nnsitive
positive nrie
(in terms
terms nf
of goods)
for esi'h
each piece
fn the
the vniin
nnds fnr
niece
rprice npO(in
r0
of paper.
paper. Vould
Vould aa rational,
rational, foresighted,
foresighted, young
young investor
investor be
be willing
willing to
to
of
purchase one
? Only
Only if
if she
she believed
believed that
that she
she could
could resell
resell the
the
purchase
one of
of these
these assets
assets?
asset when old (i.e.,
in period
1) to a member of the next young generation
asset when old (i.e., in period 1) to a member of the next young generation
for a price that includes
a real rate of return
comparable to that available
for a price that includes a real rate of return comparable to that available
on other assets.
The real
(gross)
rate of return
on alternative
assets is
on other assets. The real (gross) rate of return on alternative assets is
l+rl
units of output in period 1.
Therefore,
the young investor
in period 0
1+r1 units of output in period 1. Therefore, the young investor in period 0
is willing
to buy the intrinsically
useless asset if she expects its price in
is willing to buy the intrinsically useless asset it sne expects its price in
period I1 to be at least pl = (l+rl)po.
Similarly,
i.
the young generation
in any
— 11..
.,,,,
P[10U I U Ut d.L itd b
U, 4I 7VuLt 51ILa.LwI ii;,.aLLJ
period ft mtif
must pynpr'f
expect the
price nf
of the
paper to be pt(l+rt+l)
in period t+l, if
if
t.h nri(P
th nnr tn h n(1+r.
t+i' in neriod t41.
it is to acquire
it
rr
the asset from the old generation
at that time at a price pt.
is to acauire the asset from the old generation at that time at a price p÷.
If all of these expectations
for capital
gains on the asset can be fulfilled,
If all of these expectations for capital gains on the asset can be fulfilled,
then the intrinsically
useless paper can be traded indefinitely;
that
is,
then the intrinsically useless paper can be traded indefinitely; that is,
there can exist a bubble.
there can exist a bubble.
Let Bt = ptY be the aggregate value of the bubble at time t, and assume
Let Bt =
be the aggregate value of the bubble at time t, and assume
for the moment that the self-fulfilling
prophecy can be realized.
By the
for the moment that the self-fulfilling prophecy can be realized. By the
condition
of no-arbitrage
between bubbles and other assets, we have
condition of no-arbitrage between bubbles and other assets, we have
(8)
Io\
lo)
Ve define
Bt+l =
(1 + rt+l)Bt— Ii
D
t+i
—
b, I B,/A,L as the aggregate value of the bubble per efficiency
t
unit
Ve define b. B/LL as the aggregate value of the bubble per efficiency unit
of labor.
of labor.
-8-
- 8-
The
young generation
generation must
must purchase
purchase the
the entirety
entirety of
of existing
existing bubbles
bubbles from
from
The young
the old
period.
the
old generation
generation inin each
cacti
period.The
me condition
Conditionforbr goods
gooas market
marxet equilibrium
equiiirium
becomes
oecomes
xt+i -K.1
(9)
(9
'- ,
=
=
K
KtI.
AtLs(wt,rt+l)
- (Bt ++ K4)
Kt) ;
ALs(w4,r41)
-U
- U UTj (B4
U
the
left-hand side
side is
is net
net investment,
investment, while
while the
the right-hand
right-hand side
side is
is the
the
the left-hand
difference
between savings by the young and dissavings
by the old (the term in
difference between savings by the young and dissavings by the old (the term in
Note that (3’) and (4’) continue to
parentheses
on the far right of [9]).
parentheses on the far right of [9]). Note that (3') and (4') continue to
describe
prices when At = Kt/a and
L = 1. Substituting
these
Kt/a and L = 1. Substituting these
- —
—
i.* = (S
,_ -- bt)/a.
SI
into
(9), we derive
Kt+l
= At(gI— -- bt), or
or Kt+l/Kt
into (9), we derive Kt+i =
At(S
factor
describe factor prices when At =
expressions
expressions
-
Thus,
S
Inus,
S - b,
gt =‘a - b - 1.
(10)
(10)
- 1.
a
Ye now discuss ..k.L
whether, given an initial
bubble of size B.
such that
D
ouI.4L +1.+
vi
e iiuw uiu WUL.IIeL Lveu .it U1iI,i6i UUUUi ..C
Bo/A(Ko), the dynamics described by (8) and (10) are sustainable.
If
bO = fl
/1(W' flip vntiii' ,1perhp,4 hv (S ni (1fl
sustain.h1 - ——
If
01
they are, then an initial
bubble of size B. can exist in an economy that has
can exist in an economy- that has
they are, then an initial bubble of size B,.
V
an initial
capital stock of Ko. Note that labor productivity
grows at rate
an initial capital stock of K. Note that labor productivity grows at rate
gt, so (8) and (3’)
imply
so (8) and (3') imply
l+P
1 +p
bt+l =-bt.
bt÷l = 1 + g,
(11)
(11)
i
Substituting
(10) into (11) gives a single,
—---—--.o
Siihstitntin (ifl
i
ntn (ii' ,iveq
recursive
equation
for the
sin1p rtiirsive enuation for the
- -
- 9-9-
evolution of
of the
the value
value of
of the
the bubble
bubble per
per efficiency
efficiency unit
unit of
of labor,
labor,
evolution
1.
Ut
bbt+l
a(1 ++ p) - bt
.
t+1 == a(1
p) 6 - b,
h
(12)
(12)
The curve labelled
BB in the top part of figure
1 depicts this relationship
The curve labelled BB in the top part of figure 1 depicts this relationship
between the (normalized)
size of the bubble in successive periods.
Clearly,
between the (normalized) size of the bubble in successive periods. Clearly,
when this curve lies
above the 45 degree line,
the
bubble is growing relative
when this curve lies above the 45 degree line, the bubble is growing relative
to the stock of efficiency
labor (and, therefore,
aggregate output),
whereas
to the stock of efficiency labor (and, therefore, aggregate output), whereas
when the curve lies below the 45 degree line,
the bubble is shrinking
relative
when the curve lies below the 45 degree line, the bubble is shrinking relative
to efficiency
labor.
to efficiency labor.
Ve
t.
see from the figure
IC bCC irum bliC ilULe
: £L.. :i
that,
if the initial
£l
LIIC OUVUIC lb bULU
size of the bubble is such
1Lb ii LLC iLIIbI&L biC UI
* the normalized bubble shrinks monotonically over time. In this
b0 < b*,
h
fhø nirml,ptI hiihhlp
mrlnMnnt'11v nvPr fimp In thig
case, the assumed existence of the initial
bubble does not lead to any
that
tht
hrnr
h
case, the assumed existence of the initial bubble does not lead to any
contradiction.
Asymptotically,
the bubble becomes arbitrarily
small in
contradiction. Asymptotically, the bubble becomes arbitrarily small in
relation
to the stock of efficiency
labor,
and the economy converges to the
relation to the stock of efficiency labor, and the economy converges to the
steady state described
If,
in section 2.
alternatively,
the initial
size of
steady state described in section 2. If, alternatively, the initial size of
the bubble is such that b0 > b*, then the normalized bubble grows
the bubble is such that b0 > b
monotonically
over time.
,
then the normalized bubble grows
Eventually,
at some T, bT > 6.
monotonically over time. Eventually, at some T, bT >
aggregate savings of the young do not suffice
But then the
. But then the
to allow them to acquire the
aggregate savings of the young do not suffice to allow them to acquire the
bubble from the old generation
at the required
price.
The old at T would have
bubble from t?ie old generation at the required price. Inc Old at 1 would nave
foreseen this eventuality
at T-l,
1UIL L,Ili V1LLUdil. db 1
from the (then) old generation
I
and so would not have purchased the bubble
....
..,.4
11U DV WOUIU LIVl.
at that time.
.......,..A
pULILaDCU l.u UUIJUI
The bubble unravels
back to
frn th (thn\ nltl PnPrtiAn t thf. tinm. Th hiihb1 iinrv1s hk tn
time 0; i.e.,
an initial
bubble of the assumed size cannot be sustained.
time 0: i.e.. an initial bubble of the assumed size cannot be sustained.
Finally,
Finally,
in fixed
in
it is possible
that b. = b*.
*
it is possible that bA =
proportion
b
.
Then the bubble and the economy remain
Then the bubble and the economy remain
V
to one another
and the economy immediately enters a steady
fixed proportion to one another and the economy immediately enters a steady
- 10
10 state.
state.
Evidently,
bubbles can
can exist
exist in
in this
this economy
economy provided
provided their
their initial
initial size
size
Evidently, bubbles
Notice the
the similarity
similarity between
between the
the existence
existence condition
condition
is
is no
no larger
larger than
than b*.
b*. Notice
for
here and
and that
that described
described by
by Tirole
Tirole (1985)
(1985) for
for the
the Diamond
Diamond economy.
economy.
for bubbles
bubbles here
NO
bubble of
of any
any size
size will
will be
be possible
possible if
if the
the UB
BB curve
curve is
is steeper
steeper at
at the
the
No bubble
— ,_____
?lI
t_ DDBBcurve
The
slope 01of£tne
the
curve at
at tne
the origin
origin
than tile
the 45
degree 1.__
line. me
jine.
siope
origin
origin tnan
' aegree
equals
a(l+p)/S.
ciua Arp/j.
'r....
Thus
L1IU
h,4J.1c
bubbles ,.n
can
exist if an only if s/a --- 1 ,> //.
p. UU
But
1
s/a -1
is the
the ennnmv's
economy’s rnwth
growth rate
rate in
in the
the absence
absence of
is
-1 is
nf any
any bubbles,
bubbles. while
hi1e rp
n is
the
interest rate,
rate, so
so here,
here, as
as in
in Tirole,
Tirole, the
the existence
existence of
of bubbles
bubbles
the real
real interest
requires
that the
the growth
growth rate
rate exceeds
exceeds the
the interest
interest rate
rate in
in the
the equilibrium
equilibrium of
of
requires that
the
bubbleless economy.
economy.
the bubbleless
Of
course, in
in the
the model
model with
with exogenous
exogenous growth,
growth, the
the bubble
bubble cannot
cannot affect
affect
Of course,
the
Here, that
The bottom
bottom portion
portion of
of the
the
the long-run
long-run growth
growth rate.
rate. flere,
that is
is not
not true.
true. The
figure
The line
line
figure illustrates
illustrates the
the effect
effect that
that bubbles
bubbles have
have on
on the
the growth
growth rate.
rate. The
GG,
depicting equation (lo), shows the relationship
between the (normalized)
CC, depicting equation (10), shows the relationship between the (normalized)
If the initial
bubble
size of
size
of the
the bubble
bubble at
at time
time tt and
and the
the growth
growth rate.
rate. If the initial bubble
-—
___ B*
y* such that
I___ Y1*1I#
'Y = b*,
1_k
L__ the
L_ tt1_1
happens
to t__
be of__rsize
B*/A(KO)L
then
bubble permanently
nappens o oc oi size D' SUCfl tnat
O, nen tne DUDDIC permanentiy
lowers +A
the rate
of
,growth from g, ——= s/a0 —-- I1A to
g, ——= p.• (Smaller
initial
1AIJA1C
#;,1
t
VS S V fl tail
U
S
.11 A U S OS
is.. s..
.1.
A S
Of
bubbles
in every
every nerind.
period, hut
but the
the denressinn
depression nf
of the
the
bubbles reduce
reduce the
the rate
rate of
nf growth
rovth in
growth rate asymptotically
approaches zero as t grows large.)
The reason is
growth rate asymptotically approaches zero as t grows large.) The reason is
straightforward.
The existence of the asset bubble diverts
savings away from
straightforward. The existence of the asset bubble diverts savings away from
productive
investment in capital, and it is capital investment that drives
productive investment in capital, and it is capital investment that drives
long-run
growth in the Diamond-Bomer model.
long-run growth in the Diamond-Roiner model.
—
It —- 11
IV. Bubbles
Bubbles and
and IntertemDoral
Intertemporal
Efficiency
IV.
Efficiency
Tirole
(1985, 1990)
1990) has
has shown
shown for
for the
the Diamond
Diamond economy
economythat
that the
the
Tirole (1985,
asymptotically
bubbly equilibrium
equilibrium (in
(in which
which the
the bubble
bubble remains
remains in
in fixed
fixed
asymptotically
bubbly
proportion to
to the
the size
size of
of the
the economy
economy in
in the
the long
long run)
run) is
is intertemporally
intertemporally
proportion
The bubble eliminates
overaccumulation
of capital,
which can arise
efficient.
efficient.
The bubble eliminates overaccumulation of capital, which can arise
in the Diamond model because living
generations
cannot trade with the as yet
in the Diamond model because living generations cannot trade vith the as yet
unborn.
In fact,
the bubbles can exist
in that setting
if and only if the
unborn. In fact, the bubbles can exist in that setting if and only if the
bubbleless
equilibrium
is inefficient.
bubbleless equilibrium is inellicient.
One might expect —
a different
_,_t_r_._result
___i. in our model
_i_'i of_f externality-based
__
t___1
,l__
one mignt expect a oiiieren resui in our mouei. ox externaiity-oasea
As
we haa
have man
seeneGat+l.n
the anti
end ofn man44nn
section 02,+ha
the nnnnp*itr
economy
Le on
lLJU
tLL JLI'JU1J
without
bubbles hs
has 1ss
less ianita1
capital fnrmatinn
formation than
is required for intertemporal
withniit hiihh1s
than is rerniird fnr intrt.mrr1
efficiency.
Bubbles divert savings from productive use in financing capital
endogenous
growth.
anAI.nflnfll.1, n.-nn+'h
1Iuu5c&tuu 5L VW LI •
efficiency. Bubbles divert savings from productive use in financing capital
accumulation
into an unproductive
store of value and thereby exacerbate the
accumulation into an unproductive store of value and thereby exacerbate the
existing
distortion
in the market equilibrium.
existing distortion in the market equilibrium.
Suppose that a bubble of size B. first
appears in the economy at time 0.
Suppose that a bubble of size B0 first appears in the economy at time 0.
implications
Vhat are the welfare
? The generation
that is old at time 0
Vhat are the welfare implications? The generation that is old at time 0
benefits
of course, as their
sale of the new asset to the young enables them
benefits of course, as their sale of the new asset to the young enables them
to consume more than otherwise.
The labor income of the generation
that is
to consume more than otherwise. The labor income of the generation that is
young at time 0 depends upon K. and Ao, both of which are predetermined
at
young at time 0 depends upon I and A0, both of which are predetermined at
time 0.
Their savings accrue interest
at rate rt+l
= p with or without
the
time 0. Their savings accrue interest at rate r+i = p with or without the
bubble.
So this generation,
which has (indirect)
utility
given by
bubble. So this generation, which nas (inairect) utility given y
V[d(p)AO,
p],
bubble. All subsequent
_.j byt. the tt1
Iii ....L
is not affected
generations
are
ic
bubble and
V1c(p)A0, pj, is nO aiieci.eu oy ne uuuuie. iii. uuequeu ueLdtiuIIb
harmed, however,
as growth of labor productivity
,t
5LVW(I VL £IJ.JL n
ItaJ.UIcu, ILuWcv.L
therefore
thrfnr
each generation
npr2fitn
would have otherwise.
wonid have otherwise.
It is interesting
is reduced by the
h +h
n,l
born after time 0 earns less labor income than it
hrrn ftr tim O rns 1 1ahr inrtm than it
to note that the generation
that is born at time 1, by
It is interesting to note that the generation that is born at time 1, by
-- 12
12 --
itself,
income losses
losses from
from the
the bubble
bubble that
that are
are sufficiently
sufficiently
large that
that
itself, suffers
suffers income
large
-.
-11 more than
—- -.&._, _.
I Pfor tneir
.1 •
P
this
generation
their
gain iron
from
tttls
generation could
couia more
tnan compensate
compensate the
tne initial
initiai old
oia ior
gain
,1,, there were .aa way to effect
Ct.4 this
the
bubble, ifC
only
intergenerational
I1tiD ..4
L.lIe UULJU.LC
iL VUiJ
AUIi5ci&iabiVLtO.i
The
bubble allows
initial nltI
old totn increase
'Fh hiihh1
11ov ththeinit.121
inerpqp their
t.hirconsumption
trniimnHnn inn
transfer.
trnpr
Theslowdown
slowdowninin Droductivity
productivity
growth causes
causes the
the generation
generation
period
Deriod 0
0 by
by Bo.
L. The
growth
U
that
is young
at time
time 11 to
to lose
lose wage
wageincome
income inin period
period
young at
that is
(i, -1 1ofof(A.1
S
AI)
==
A1)(p)
S
where aa circumflex
circumflex indicates
indicates aa variable
variable in
in the
the equilibrium
equilibrium
A()(&)g0)(p), 9where
A0(- &)M(P)
without
Noting the
the growth
growth rates
rates recorded
recorded inin (7)
(7) and
and (10),
(lo), wewefind
find
vithout bubbles.
bubbles. Noting
Thus, the income loss at time 1 equals Bod(P)/a.
Since this
= ho/a.
i()go =
- g0
b0/a. Thus, the income loss at time 1 equals B0(p)/a. Since this
comes one
one period
period later
later than
than the
the gain
gain to
to the
the initial
initial
old, the
the value
value of
of this
this
comes
old,
income
where we
wehave
have used
used the
the
income loss
loss discounted
discounted back
back to
to time
time 00 is
is Bog(p)/a(l+p),
B0(p)/a(1+p), where
market
interest rate
rate (which
(which equals
equals also
also the
the intertemporal
intertemporal rate
rate of
of substitution
substitution
market interest
.
e_
i -aiscounting.
__.'_ I
LI for
perform
the
discounting.
Nowwe
we- caicuiate
calculate
the
ior every
every generation)
generaion oto periorm
me
now
tne
difference
between
the yVU1I
young at time
and the gain
i.,
,..... to
UcLWcIL the
(.tICdiscounted
Ui..UUUbU loss to
iIuc .LI1.....1
aiiu
IV .I...
(LL
k..,..
the {niti1
initial nid
old
th
(1
(13)
6Lfl
as
B(+(P) _ * =
BO
B0
- MO — _______
rA\
Cl(P) -- a(1 + 141.
P)J.
a(1
+
14
O
a(1 + PI
a(1 + p)
a(1 + p)
B0#(p)
The
condition IU
for a bUb(,4LLIDJ.
sustainable UUUUi
bubble requires
or
'rk
Inc existence
LC4UIL ?J/a
/ d.-- I1I > p, VI
IOI,LL tUIIUAJ...[UI1
S > a(1 + p).
Since the
wealth&'rn+m4ri+.
constraint rDnhlirpQ
requires uw = l(p) > S, t}p
the fe'rm
term in
nL Sinr
+h u1+h
in
Fl.
rrj -
—
square
brackets on the far right-hand side of (13) is positive.
This
sauare brackets on the far rifht-hand side of (13 is Dositive. This
establishes
our claim.5
establishes our claim.5
Sin fact, it can be shown that any eneration born after the period in which
born
after
51n fact, it can be shown that
gain
to the
the period
initial inoldwhich
the
bubble forms suffers a greater generation
Poss than the
the bubble forms suffers a greater loss than the 2am to the initial old
eneration (even after allowing for discounting).
The loss to the generation
the generation
%orn at time(even
generation
n, discounted to time zero, is
born at time n, discounted to time zero, is
-- 13
13 -But
that the
the young
young born
born at
time 11 could
could bribe
old at
at time
time 0o
But the
the fact
fact that
at time
bribe the
the old
to "retire"
“retire”
the bubble
bubble asset
asset does
does not
not wean
mean that
that the
the bubble
bubble can
can be
be made
made to
to
to
the
Theproblem
problem isis that
that these
these two
two generations
generations do
do not
not trade
trade with
with one
one
disappear. The
disappear.
another.
Thetransfer
transfer
another. The
from the
the young
young at
at time
time 11 to
to the
the old
old at
at time
time 00 must
must be
be
front
..
——
. through
-.
.
a
tfl - this generation
effected
ettectect
througflthetnegeneration
generationthat
tnatisisyoung
youngatattime
time0.u. Vhen
nen tnis generation
1A
pays the
to ILI
theLIL.LbiaA.
initial
old, +
it .11
will want +r
to collect
(.1I bribe
ULAU (.U
Jiu,
(1
+b
(1 ..+ n\
p) +mOc
times the
amount that
laid nut
out from
from the
young
atat-—--time
In the
the interim.
interim, I it
it - has
has
niniinf.
f.1if.it it has
hs laid
the
voun—time1.1. In
an
“IOU” that is exactly like the bubble asset.6 The young at time 0 divert
an "IOU" that is exactly like the bubble asset.6 The young at time 0 divert
savings
from capital
capital formation
formation in
in order
order to
to pay
pay the
the bribe,
bribe, with
with the
the result
result that
that
savings from
the potential
gain from the intergenerational
transfer
scheme disappears.
The
the potential gain from the intergenerational transfer scheme disappears. The
harm
caused by the bubble to generations born after time 0 cannot be avoided
harm caused by the bubble to generations born after tine 0 cannot be avoided
by a simple tax/subsidy
scheme that redistributes
income across generations.7
by a simple tax/subsidy scheme that redistributes income across generations.7
A()#(P)
a”(l+p)”
4—n
[8”-
a(1+p) I
Since g(p) >
Since
born at(p)
time>
~
(S-
1=0
bi)]*
( b.)j.J
8 > a(l+p), the difference
between the loss to the generation
a(1+p),
the to
difference
loss to the generation
n >and
the gain
the old atbetween
time 0the
exceeds
U
hnrn 1- time n
-- and the rain to the old at time 0 exceeds
~ (‘-
r
bo)[S”-
~
(‘-
bi)]
> 0.
> 0.
11
aThis IOU is like a national debt. O’Connell and Zeldes (1986 and Tirole
publitand debt
in
like a national
debt.between
O'Connell
andbubbles
Zeldes and
(1986)
Tirole
(1990) IOU
haveisdiscussed
the analogy
asset
This
analogy
remains
aptand
in public
the present
generations themodels.
(1990) have discussed
analogy The
between
asset
bubbles
debt in
overlappin
context.
s eegenerations
Alogoskoufis models.
and van
Ploe ernais,apt
(1990) for in
an analysis
of the
overlapping
Thederanalogy
the present
anaiysis ulgrowth.
iue
ior ofan endogenous
%ased1U)
model
effects ofSee
public
debt in anand
externalitiescontext.
Alogoskoulis
van cler rioeg
debt in an externalities-based model of endogenous growth.
effects
Velfare ofof public
all generations
can be improved, however, by a policy that
stimulates of investment
and causes
to internalize
the externality
TVelfare
all generations
can beindividuals
improved, however,
by a policy
that
associated investment
with capital andformation.
stimulates
causes individuals to internalize the externality
associated with capital formation.
-- 14
14 -TU
IV.
Conclusions
11. U1IUvtIo
In sttins
rIrivnbyhvinvestments
nvp5f.tnpntQ
in wc1
In
settings whr
where1nn-rnn
long-run
growth is
is driven
in physical,
—-—--o
•--———--o
——-- rnvth
human, or
or knowledge
knowledge capital,
capital, the
the existence
existence of
of an
an unproductive
unproductive asset
asset ---human,
one
one
that yields
yields aa financial
financial return
return but
but does
does not
not contribute
contribute to
to the
the production
production of
of
that
harmful to
growth. The
Theunproductive
unproductive asset,
asset, oror bubble,
bubble,
real output
output --can
real
--can be
be harmful
to growth.
attracts savings
Each new
new generation
generation
attracts
savings away
away from
from more
more productive
productive uses.
uses. Each
purchases the
the asset
asset at
at least
least partly
partly at
at the
the expense
expense of
of investment
investment in
in growthgrowthpurchases
promoting capital.
promoting capital.
In this
this
In
paper, we have
have examined
examined the
the conditions
conditions under
under which
which asset
asset bubbles
bubbles
can exist
exist in
simple __i_1
model _P
of __1
endogenous growth.
As in the neoclassical
ca
n aa ___1_
simpie mouei or enuogenous growtn. AS in tne neoclassical
paper, we
—
growth
setting, a hiihhl
bubble pn
can surviveY' 'ISIS1
only AS
if +1,o
the equilibrium
growth rate
rtwfh pftinE,
4
1,.SUMI
.,,-.,+%,
USI .I.jUSSSIJA
1.11 LabC
exceeds the
the interest
interest rate
in the bubbleless economy. Here, however, the
exceeds
rate in the bubbleless economy. Here. however. the
equilibrium
growth rate,
like
the interest
rate,
is determined
by parameters
equilibrium growth rate, like the interest rate, is determined by parameters
of tastes and technology.
Bubbles are more likely
to be possible
when
of tastes and technology. Bubbles are 'ore likely to be possible when
households are patient
(i.e.,
savings propensities
are high for a given
households are patient (i.e., savings propensities are high for a given
interest
rate)
and when investments
in capital
generate
spillover
benefits
to
interest rate) and when investments in capital generate spillover benefits to
labor productivity.
Vhen bubbles do exist,
they retard
economic growth along
labor productivity. Vhen bubbles do exist, they retard economic growth along
the transition
path to the steady state and possibly
even in the long run.
the transition path to the steady state and possibly even in the long run.
The LtL,__
bubbles also harm all generations
mt...
born after
the
.. period
in which the
asset
-.
me ouooies aiso narm au generations Dorn alter tne period in winch the asset
first
firQ+
appears, and to an extent that exceeds the gain to the generation
41,.4.
:.
t.
that
lJ I AIIb bIL ACCU (.11W L1I bU 1,11W W1&Wj d,b.LV2I 1,11db
benefits
from the bubble.
benefits from the bubble.
In our model, a bubble can exist only on intrinsically
useless assets.
In our model, a bubble can exist only on intrinsically useless assets.
That is, there cannot be any bubble in the price of capital.
This is because
That is, there cannot be any bubble in the price of capital. This is because
new units of an asset must have the same price
as old, and it is always
new units of an asset must have the same price as old, and it is always
-- 15
15 --
possible to
to create
create aa new
new unit
unit of
of capital
capital at
at aa cost
cost of
of one
one unit
unit of
of output.8
output.8
possible
Thus, competition
competition from
from potential
potential new
new supply
supply prevents
prevents exponential
exponential growth
in the
the
Thus,
growth in
price of
of real
real capital.
capital.
price
This
raises the
the fundamental
fundamental question
question about
about asset
asset bubbles:
bubbles: what
what determines
determines
This raises
their
supply ? tvery
Every indiv1ual
individual
their suppiyi
willing toto exchange
exchange aa worthless
worthless piece
piece of
of
isiswilling
paper
for a positive
amount ofvigoods.
If asei
asset ouvuies
bubbles uodoappear
appear inin tne
the
pubiive d.muuitt
vuub. ii
P.PL_ J.UL
economy,
there
any
nay fri
to predict
time
how
many
and h41.h
which ones?
P&AnAmv is
uv
rirprH'f ahead
h1l rifof+m
hAt,
y.,fl -' nu
ian.,mn1,
fitt%n' ' n +hr
t...n t.i,s nfl
urn,,. flit., ,Trtrg. OflTTfl
Is
any way
their
where their
SI— --there
Ia4.
AU
A1I to
O prevent
¶UAIU
1T(1.
UOtW1OJ in
UT situations
SUOTBIS IJ4M
—
- - formation
C
I.?
S
existence
will retard
retard growth?
growth ? These
These questions
questions remain
remain to
to be
be answered.
answered.
existence will
sThis
argument assumes that different
units of capital, which are
8Thjs argument assumes that different units of capital, which are
economically
indistinguishable
in our model, also are physically
economic11y indistinguishable
our could
model,bealso
are physically
Otherwise, inthere
bubbles
in the prices of
indistinguishable.
indistinguishable. Otherwise,
there
could
be
bubbles
in thethat
prices
One might say, in such a case,
the of
capital
specific units of capital.
specificunits
of
capital.
One
might
say,
in
such
a
case,
that
the
is priced at its fundamental value, but that the “names” of specific capital
pieces
is priced
at its
fundamental
value, butuseless
that the
"names"
of specific
pieces
of
equipment
(which
are intrinsically
assets)
acquire
value as
of equipment (which are intrinsically useless assets) acquire value as
bubbles.
bubbles.
- 16
16 A
References
D Ac A
Prederick van der Ploeg
Ploeg i99O)
1990)"EndogenousGrovh
“Endogenous Growh
Alogoskouf is,is,George
Alogoskouf
GeorgeS.S.and
andFrederickvander
and
Generations,” uicussion
Discussion raper
Paper I'u.
6o. 90/26, Birkbeck
D1KOCC
aim Overlapping
uveripping ,eiiiaiiuns,
College,
University
of
London.
College, University of London.
Arrow, Kenneth
J. (1962)
(1962) "The
“The Economic
Economic Implications
Implications of
of Learning
Learning by
by Doing,"
Doing,”
Arrow,
Kenneth J.
Review rofEcnnnm{c
Economic Studies
155-173.
Rview
Studies29:2 155-17.
Blanchard, Olivier
Olivier J.
J. and
and Stanley
Stanley Fischer
Fischer (1989)
(1989) Lectures
Lectures inin lacroeconomics.
Macroeconomics.
Blanchard,
Cambridge, IA:
%A: lIT
MIT Press.
Press.
Cambridge,
“National Debt
Debt in
in aa Neoclassical
Neoclassical Growth
Growth Jodel,"
Bodel,”
Diamond, Peter
Peter A.
A. (1965)
(1965 "National
Diamond,
American Economic
Economic Review
Beview 55:
55: 1126-1150.
1126-1150.
American
1991) Innovation
Innovation and
and Growth
Growth in
in the
the
Grossman, Gene
and Elhanan
Elhanan llelpman
Helpman 1991)
Grossman,
Gene H.
L and
.... rh..,l,,n
VA.IA:VM41T Press.
Cambridge,
JQdLItJLJ.U5, ft.
Global £iU1IVILI.
Economv.
UAUVi
('1,k..1
——
Convex
ModelofofRniiilihrinm
Equilibrium
JonesGri;-;y
and Rodolfo
Banuelli (l99O
(1990) "A“ACnnv
.Tnns
Larry E.
E and
Rndnfn anii11i
Icde1
,” Journal of Political
Economy 98: 1008-1038.
rowth"Journa1ofPo1itica1Ecnorny'98:1OO8-1O38.
Lucas, Robert
Robert E.,
“On the
the echanics
Hechanics ofof Economic
Economic Development,"
Development,”
Lucas,
E., Jr.
Jr. (1988)
(1988) "On
Journal
of
lonetarv
Economics
22:
2-42.
Journal of Monetary Economics 22: 2-42.
O’Connell,
Stephen and Stephen Zeldes (1988)) “Rational
Ponzi Games,I’
O'Connell, Stephen and Stephen Zeldes (1988), "Rational Ponzi Games,"
International
Economic Review 29: 431-450.
internationai rconom1c ieview z: iii-'iou.
D..A
t
Romer, LD...1
Paul
1986) “Increasing
Returns and Long-Run
of
V. I.LOLJ)
1flQt!
D.... Growth,” II Journal
UJ. 1.
.L&L..I. C4 i1I iLV IUi LI LU 1JUiI5 D.ULI UI VW bil, IVUL LII. Vi
Political
d
conomv
94:
10021037.
Political Economy 94: 1002-1037.
JV1U.L
Romer, Paul III.
1990)
“Endogenous Technological
Progress,”
Journal
of
Romer,
Paul L (1990)
"Endogenous
Technological Progress," Journal of
Political
dconomy
98: S71-S102.
PiItical Economy 98: S71-S102.
Rebelo, Ser io (1991)
“Long Run Policy Analysis and Long Run Growth,”
Rebelo,
Sergio
Run Policy
Analysis and Long Run Growth,"
Journa
f of (1991)
Political"LongEconomy
99: 500-521.
Journal of Political Economy 99: 500-521.
AL
Sheshinski,
•..
Eitan
(1967)
‘Optimal
Accumulation with Learning by Doing,’
in
nesninsici,
"uptimal.
Accumulation
witnEconomic
earning Growth.
Dy Iloing, in
K.
Shell,ritan
ed.,(ibi)
Essays
on the Theory
of Ontimal
K. Shell, ed., Essays on the Theory of ODtimal Economic Growth.
Cambridge,
MA:
BIT Press.
1IT'P
D....,,
U1UL.LU5,ilL.
A. Z.LL
ILC.
Tirole, .1n
Jean(IQR9\
(1982) "fln
“On fhc
the Pnihi1+v
Possibility
of Speculation under Rational
Tirn1
a ii... w J n cnri1i+inn nnrlpr flfinn1
v
Expectations,
’ Econometrica 50:
1163- 1181.
Va.
a
Expectations," Econometrica 50: 1163- 1181.
Tirole, Jean (1985) “Asset Bubbles and Overlapping Generations,”
Tirole,
Jean (1985)53:
'tAsset
Bubbles and Overlapping Generations,"
Econometrica
1499-1528.
Ecpnometrjca 53: 1499-1528.
Tirole,
Jean (1990) “Intertemporal
Efficiency,
Intergenerational
Transfers,
Tirole,
"Intertemporal
Efficiency,
andJean
Asset(1990)
Pricing:
An Introduction,”
in P.Intergenerational
Champsaur et al., Transfers,
eds.,
and
Asset
Pricing:
An
Introduction,"
in
P.
Chainpsaur
et al., eds.,
Essavs in Honor of Edmond Balinvaud, Volume 1: Microeconomics.
Essays
in Honor
of Press,
Edmond lalinvaud. Volume 1: icroeconomics.
Cambridge,
IIA: MIT
tamoriage, IA:
Ill i'ress.
-- 17
17 --
tT_11_
U1Lieu
IlflOA\
tt'T'L,.
.. 1J..
iof LIFiatULIJ,
Wallace,
(1980)
“The UvcuiapkmLb
Overlapping Generations
Money,”AU
in
ULtCLU Kodel ,-C
wajiace, Neil
uouj lltC
Kareken and
and N.
N. Vallace,
Vallace, eds.,
eds., Xodels
Hodels of
of Konetary
Monetary Economics.
Economics.
Kareken
Ninnnn1ic
ofoflinneanolis.
Minneapolis: Federal esrv
ReserveRank
Bank
Minneapolis.
Per1
Veil, Phillippe
Phillippe (1987)
(1987) "Confidence
“Confidence and
and the
the Real
Real Value
Value of
of honey
Moneyin
in
Veil.
Overlapping Generations
Generations kdels,"
Models,” Quarterly
Quarterly Journal
Journal ofof Economics
Economics 102:
102:
Overlapping
l-22.
1-22.
Yanagawa,
Noriyuki (1991)
(1991)
Yanagawa, Noriyuki
“Bubbles and
andEconomic
EconomicGrowth,"
Growth,” mimeo.
mimeo.
"Bubbles
</ref_section>
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