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Massachusetts Institute of Technology
Department of Economics
Working Paper Series
Transparency of Information and
Coordination in Economies
With Investment Complementarities
George-Marios Angeletos
Alessandro Pavan
Working Paper 04-07
January 2004
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50
E52-251
Memonal
Cambridge,
Drive
MA 021 42
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://ssrn.com/abstract=502642
oACHUSETTS INSTITUTE
OF TECHNOLOGY
Transparency of Information and Coordination
in
Economies with Investment Complementarities*
George-Marios Angeletos
MIT
and
Alessandro Pavan
NBER
Northwestern University
January 2004
Abstract
How
do public and private information
affect equilibrium allocations
economies with investment complementarities?
And what
is
and
social welfare in
the optimal transparency in the
information conveyed, for example, by economic statistics, policy announcements, or news in
the media?
equilibrium
We
is
first
consider an environment where the complementarities are
unique no matter the structure of information.
public information
as long as there
is
may have
no value to
An
is
lotteries, welfare
because more transparency
a social perspective.
increase in the precision of
unambiguously increases with an increase
facilitates
more
full
transparency
effective coordination,
which
more transparency permits the market to coordinate more
either the "bad" or the "good" equilibrium. In this case, constructive ambiguity
there
is
is
is
in either
optimal.
valuable from
On the other hand, when complementarities are strong enough that multiple
equilibria are possible,
if
so that the
the perverse effect of increasing aggregate volatility. Nevertheless,
the relative or the absolute precision of public information. Hence,
This
weak
effectively
on
becomes optimal
a high risk that more transparency will lead to coordination failures.
"This paper was prepared for the annual meeting of the American Economic Association and will appear in
American Economic Review 94:1 (Papers and Proceedings).
invitation. For useful
We
are grateful to
Narayana Kocherlakota
for the
comments, we thank Daron Acemoglu, Ricardo Caballero, Christian Hellwig, Bengt Holmstrom
and Ivan Werning. Email: angelet@mit.edu, alepavan@northvvestern.edu.
G.M. Angeletos and A. Pavan
2
Introduction
1
Economies with production
externalities,
demand
spillovers,
incomplete financial markets, and Key-
nesian frictions are only a few examples where macroeconomic complementarities play a prominent
Within
role.
how does
this class of economies,
the precision of publicly provided and privately
collected information affect equilibrium allocations
and
social welfare?
transparency in the information conveyed, for example, by economic
And what
is
the optimal
statistics, policy
announce-
ments, or news in the media? To answer these questions, we consider a simple real economy where
the individual return to investment
is
increasing in the aggregate level of investment and where
market participants have heterogenous expectations about the underlying economic fundamentals
(the exogenous productivity).
We
either as a reduction in the level of
(that
is,
interpret an increase in the transparency of public information
common
uncertainty for given level of idiosyncratic uncertainty
an increase in the absolute precision of public information), or as a reduction
in the het-
erogeneity of expectations across market participants for given level of overall uncertainty (that
an increase in the
We
first
is,
relative precision of public information)
consider an environment where complementarities are weak so that the equilibrium
is
unique no matter the structure of information. Like in Morris and Shin (2002), complementarities
increase the sensitivity of equilibrium allocations with respect to public information, which increases
the volatility generated by
common
noise in market expectations. Moreover,
may have
heterogeneous, an increase in the precision of public information
when information
the perverse effect of
common
increasing aggregate volatility, by increasing the sensitivity of economic activity to
On
is
noise.
the contrary, an increase in the precision of private information necessarily reduces aggregate
volatility. Nevertheless,
we show that,
as long as there is
no value to
lotteries, welfare
unambiguously
increases with an increase in either the relative or the absolute precision of public information.
Hence, policies that either disseminate more precise information about economic fundamentals,
or reduce the heterogeneous interpretation of economic statistics
boost welfare.
On
and policy measures, necessarily
the contrary, an increase in the precision of private information
may
reduce
welfare by increasing the heterogeneity of expectations and thereby obstructing coordination in the
market, in which case policies that discourage the private collection of private information
may
increase welfare.
Morris and Shin (2002) have recently argued that, in environments with strategic complementarities
and heterogeneous information, more precise public information can reduce
whereas more precise private information
is
always beneficial.
We
social welfare,
find rather the opposite.
The
G.M. Angeletos and A. Pavan
difference in the results
is
3
due to an important distinction between the environments
in the
two
models. Morris and Shin (2002) consider a kind of "beauty contest," where the payoff of a player
own
decreases with the distance between his
tance
irrelevant
is
action and the action of others, but where this dis-
from a social perspective.
at the private level
It
follows that the complementarity
and hence the attempt of the agents to align their actions
more transparent public information
In this case,
valued by the market but not by the society.
complementarity
is
facilitates
In contrast,
more
we
is
effective coordination,
As shown
in
is
what
is
socially optimal, for they
on the return to others.
more
As
effective coordination in the
network
spillovers,
Angeletos and Pavan (2003), market
do not internalize the positive externality of
a consequence,
is
socially valu-
participants use public information to align their investment choices, but not enough as
to
which
consider environments where the
be the case in economies with production and demand
externalities, or incomplete financial markets.
present only
socially wasteful.
present at the social level so that effective market coordination
able, as it is likely to
is
compared
their investment
more transparent public information, by permitting
market, necessarily increases welfare, despite the fact that
it
may
lead to higher volatility. 1
In the light of these results,
we
finally consider
enough that multiple equilibria emerge
effective coordination in the
cal threshold for the
the possibility that complementarities are strong
for certain structures of information, in
market need not always be
which case more
socially beneficial. Indeed, there
is
a
criti-
transparency of public information above which multiple equilibrium levels of
investment are possible. Above this threshold, the desirability of more effective market coordination
and thus the welfare
equilibrium
is
coordination
effect of
selected. If the
is beneficial,
more transparent public information depend
critically
market coordinates on the socially desirable equilibrium,
and welfare tends to be maximized
at
on which
facilitating
high levels of transparency.
If in-
stead the market coordinates on the undesirable equilibrium, impeding coordination by introducing
noise in public information can be welfare enhancing.
This
final result is related to
Angeletos, Hellwig and Pavan (2003).
dination environments where a privately-informed policy maker
outcomes, active policy intervention
may
self-fulfilling
'in independent parallel work, Hellwig (2003)
in
which complementarities
that, in coor-
interested in fashioning market
lead to policy traps, where the optimal policy and market
outcomes are dictated largely by arbitrary
monetary economies
is
They show
market expectations. In the present paper,
and Lorenzoni
(2003), building on
arise in pricing decisions.
They
Woodford
(2002),
also find that the Morris-Shin result
about the social value of public information can be reversed. However, they do not show how the welfare
public information depend on whether market coordination
is
socially desirable.
examine
effects of
G.M. Angeletos and A. Pavan
we do not consider
4
active policy intervention. Nevertheless, a similar trap emerges regarding the
information disseminated by government agencies and central bankers:
The optimal transparency
depends on the aggressiveness or leniency of market expectations.
We
conclude that, in the class of environments considered in this paper," noise in public
may be
information
socially desirable only
when
there
a high risk that
is
more transparency
will
introduce coordination failures. Otherwise, the timely and frequent provision of public information
seems warranted from a social perspective, even
Weak
2
i
The economy
is
may
lead to an increase in volatility.
populated by a continuum of measure one of agents,
and uniformly distributed over the
R
interpret ki 6
interval.
[0, 1]
= Ah -
Ui
We
that
Complementarities
Preferences and Technologies.
indexed by
if
We
let
K=
risk neutral
with
utility
\k\.
as individual investment (or effort),
as the cost of investment.
Agents are
(1)
A
as the return to investment,
fQ kidi denote the aggregate
and kf/2
level of investment.
Like in Bryant (1983), Cooper and John (1988), Acemoglu (1993), Benhabib and Farmer (1994),
and others, we introduce a complementarity by assuming that the individual return to investment
is
increasing in the aggregate level of investment:
A=
The random
(1
- a)9 + olK.
(2)
variable 6 parametrizes the exogenous return to investment (the underlying funda-
mentals of the economy) and the coefficient a
Finally, social welfare
is
>
captures the degree of complementarity.
given by a utilitarian aggregator,
w= L
Uidi.
Using
(1)
and
(2),
we
have that
w = AK where var
is
=
concave in
JQ
(ki
— K) 2 di
K for a <
1/2,
\
[
kfdi
=
(1
- a)6K -
(1
-
2a)
\K2 -
\yar,
Jo
measures the cross-sectional heterogeneity in investment. Note that
whereas
welfare increasing and volatility in
it is
convex
K would be
for
a >
1/2. In the latter case, lotteries
desirable. Since
we
w
would be
are interested in the canonical
2
Canzoneri (1985), Cukierman and Meltzer (1986), Atkeson and Kehoe (2001), Stokey (2002) and others consider
how
the transparency of policy instruments relates to the ability of the market to detect policy deviations in Barro-
Gordon environments where the government
research.
lacks
commitment. Our approach
is
clearly orthogonal to that line of
G.M. Angeletos and A. Pavan
case where welfare
5
decreasing in both volatility and heterogeneity,
is
also suffices for the equilibrium to
be unique.
we
restrict
Information and Transparency. The fundamentals
common
prior about 9 be uniform over R.
=
such that z
statistic z
9
+
where e
o~ z e,
We
=
9
+ ax £i,
where
£, is
1/2). This
is
9.
For simplicity, we
let
summarize the public information by a
sufficient
standard normal, independent of 9 and
common
across agents. Similarly, the private information of agent
Xi
[0,
&6R are not known at the time investment
decisions are made. Furthermore, agents have heterogenous beliefs about
the
a G
3
is
i
summarized by a
standard normal, independent of 9 and
sufficient statistic
across agents.
i.i.d.
a z and a x
parametrize the precision of public and private information, respectively.
= a~ 2 /(o~~ 2 + u~ 2 and a = (cr~ 2 + cr" 2 -1 / 2 the posterior belief of agent about 9
with mean E [9] = E[#|xj, z] = (1 — 8)x + 5z and variance Farj[0] = Var[9\xi, z] = a 2
Letting 6
is
normal
)
2
9.
dependence of E;
More generally, however,
the fundamentals and
of
commonly
may
az
(that
or an increase in S for given
a (an
we have
in the
in
for given
mind
is
media may
such information
xt
is
the result of the observation of private signals
market expectations about
In this sense, 6 measures the level of conformity in market
of available information.
is,
an increase
in the absolute precision of public information),
4
increase in the relative precision of public information ).
affect either the noise in publicly available information, or the extent to
is
What
that the transparency of public announcements, policy measures, and news
interpreted differently across market participants.
results are not very sensitive to
2.1
on
interpret an increase in the transparency of public information either as a
ax
reduction in
[9]
thus be read also as heterogeneity in the filtering and interpretation
a the quality
we
In the following,
.
Xi introduces idiosyncratic variation in
available information.
expectations, whereas
i
,
l
Literally interpreted, the
about
)
As
it
will
become
which
clear,
our
which of the two interpretations we adopt.
Equilibrium
Each agent chooses
hi
so as to maximize Ej
ki
Individual investment
expected
level of
The equilibrium
is
=
Ei[A]
[ui]
=
.
(1
It
follows that the optimal investment
-
a)Ei[6]
+ aEi[K].
is
given by
(3)
thus increasing in the expected level of the fundamentals and in the
aggregate investment.
is
unique
if
and only
if
a <
1.
The
case
a €
[1/2,1)
is
considered in Angeletos and Pavan
(2003). In that case, introducing noise in public information can be desirable to the extent that this substitutes for
the absence of socially valuable lotteries.
Note that
5
is
an increasing transformation of the relative precision of public information.
G.M. Angeletos and A. Pavan
Given the
and the normality
linearity of (3)
decisions are linear so that k{
K = 09 + jz
Then,
=
follows that
symmetric
this one.
5
+ jz,
and 7 are constants determined
where
in equilibrium.
(1
-
=
a)(l
= (l-a + aP)[(l-S)xi + 8z]+arfz.
Ei[A]
- 8)/[l - a (I - 8)] and 7 =
8/[l
- a(l - 5)].
Clearly, this
is
the unique
linear (rational expectations) equilibrium. Furthermore, as proved in Morris
when
(2002),
0X{
of posterior beliefs about 9, equilibrium investment
and thus
ki
It
=
6
best responses are linear in Ej[0] and
Ej[.K"],
and Shin
there do not exist equilibria other than
Hence,
Proposition
The equilibrium
1
= 1-8-
and
exists, is unique,
1
p,
= 8 + p,
is
given by
and
p
=
=
1
—
8
=
and 7
8 for
a =
Moreover, p
is
is
+ 72,
where
(1 ~
— a (1 — \0)
(4)
excess sensitivity
compared to the case where there are no com-
increasing in a. Stronger complementarities thus lead to a higher
This
sensitivity of investment to public information.
equilibrium, the public signal
0Xi
The term p thus measures the
0.
of equilibrium allocations to public information as
plementarities.
=
1
Note that
ki
is
a direct implication of the fact that, in
a relatively better predictor of aggregate behavior than the private
signal.
The equilibrium
(f3a x )
2
,
respectively,
Proposition 2
(i)
with a reduction in
and 7 are given by
where
ity.
may
However, we
(4). It follows
Volatility necessarily increases with
a z for given
cr x
an increase in 8 or a reduction in
This result
and heterogeneity are Var(K\9)
levels of volatility
if
o~ z
and only
if o~\
=
(jcr z )
2
and Var(ki\6,
=
that
an increase in 8 for given
>
z)
Tzix a x- iv)
and increases
a,
Heterogeneity falls with either
.
suggest that transparency can be socially undesirable
will see that welfare necessarily increases
when
it
increases volatil-
with an increase in either the relative
or the absolute precision of public information.
2.2
Welfare
We now
consider social welfare evaluated at equilibrium. This
ft
=
{0(T x )
2
+ {l-2a){ 1 a z f = Var(k
°Note that, although the two models are
equilibrium strategies.
l
\9,z)
is
+
=
2
— ^Q, where
identical
and so are the
given by w(6)
\8
(l-2a)Var(K\9).
different, the structure of the best responses
is
G.M. Angeletos and A. Pavan
Q
7
measures the welfare consequences of heterogeneity in individual investment and
aggregate investment.
Since
a <
coordination:
The
both heterogeneity and
1/2, welfare decreases with
Furthermore, the relative weight on heterogeneity
volatility in
volatility.
increasing in a. This reflects the social value of
is
stronger the complementarity, the
more important the alignment
in individual
investment decisions.
Using
(4)
a j\J\ — 8 and a z
=
and substituting a x
=
o~/V8,
(l-2 a ) + « 2 (l-<5)
2
[1 - a(l - S)}
It
a S
follows that
Proposition 3 Welfare
both
in
and heterogeneity.
sition 2,
an increase in 8 implies lower heterogeneity
derstand
why
=
((3o- x
)
On
from the
fact that
a.
an increase
in
a
the other hand, as shown in Propo-
expense of higher
volatility.
To un-
the effect of lower heterogeneity dominates, note that social welfare under a
util-
moment
that
=
there were no complementarity (a
fi
an increase in 5 or a reduction in
at the
itarian objective coincides with the expected utility of
2
2
for given 8 follows directly
volatility
get
and therefore
necessarily increases with either
That welfare decreases with a
means an increase
Q>
1/2) suffices for
[0,
we
+
(7C 2 )
=
2
only on a and not on
(1
8.
—
S)a
2
+
0), in
8a
2
= a
which case
2
Suppose
an agent.
/3
=
—
1
8 and
7
for a
=
5. It
follows that
so that the expected utility of an agent depends
,
An
This result should be expected:
increase in 8 given
a substitutes a
higher precision in public information for a lower precision in private information, without altering
When a =
the overall precision of information.
individual choices are not interdependent and
0,
the decomposition of information between private and public
is
irrelevant.
becomes more important than private information
public information
When
instead
a >
0,
in predicting the return to
investment, so that a substitution from private to public information raises the expected utility of
an agent. In other words, an increase
in 8 raises welfare
because
it
permits the agents to second
guess each others' actions better and therefore facilitates more coordination in the market.
We
next consider the comparative statics of
effects of 8
and
a.
To
this aim,
we
rewrite
first
o x2 o 2z
^=
fi
w
with respect to a x and
cr z
,
which combine the
as
- 2a)al + (1 2
[a 2 + (1 - a)a 2
[(1
a) 2 * 2 )
}
It
follows that
Proposition 4
(i)
A
welfare if and only if
reduction in
a >
^
and a
az
2
>
necessarily increases welfare,
^
~"^ a 2
3
.
(ii)
A
reduction in
o~ x
decreases
G.M. Angeletos and A. Pavan
8
Hence, more precise public information necessarily increases welfare. This
tion in
On
a).
az
a x implies both better coordination (higher
for given
the contrary,
more
because a reduction in
coordination (lower
coordination, or
if
the complementarity
If
is
sufficiently
the relative precision of public information
and lower uncertainty (lower
8)
ambiguous
a z means lower uncertainty
for given
cr x
8).
precise private information has an
because a reduc-
is
effect
on welfare. This
is
(lower a) at the expense of lower
weak, so that there
is little
value to
very low, so that volatility
is
high,
is
the benefit of lower uncertainty outweighs the cost of lower coordination. Otherwise, a reduction
in
a x reduces
One can
welfare.
ax
interpret
as the
amount
of information collected privately by market participants.
Given the precision of the information and the strategies of the other agents, an individual decision
maker always values more
On
private perspective.
precise information.
Hence, a lower a x
the other hand, an agent
private information, since this
may
is
always beneficial from a
prefer other agents to have less precise
would permit him to predict more accurately the aggregate
investment. In other words, the private collection of information
may
create a negative externality,
We
implying that a lower a x need not be beneficial from a social viewpoint.
market
failure in the
amount
level of
can thus have a
of private information collected by individual agents, in which case
government intervention that discourages the collection of private information
may
actually increase
welfare.
more transparency
Finally, our result that
may
also increase volatility, contrasts
instead, there
level.
To
is
is
due to the
of
L=
is
(8
w=
— A)K and suppose
f Uidi
=
f
(6ki
is
offsets the
individual payoffs
— hkf)di.
This
is
complementarity
is
Ui
=
Aki
J
^kf
+ L,
which
in
at the social level.
It
follows that the coordination
not warranted from a social perspective, in which case stronger complementarity or
coordination
likely to
—
at the social
the analogue of Morris and Shin (2002)
more transparent public information may decrease welfare by exacerbating
spillovers,
In our model, the
the externality that renders the social (gross) return to investment independent
K, thus removing the complementarity
motive
social value of coordination.
an additional externality that perfectly
case welfare reduces to
L
it
equally present at the private and the social level. 6 In Morris and Shin (2002),
see this, let
in our setting.
even though
with the result of Morris and Shin (2002). As we anticipated
in the introduction, the difference is
complementarity
in public information increases welfare
is
socially valuable, as
it is
this motive. If instead
probably the case in economies with production or demand
network externalities, or incomplete financial markets, then more transparency
boost welfare.
See also Angeletos and Pavan (2003) for further discussion.
is
most
G.M. Angeletos and A. Pavan
9
Strong Complementarities
3
we consider environments
In this section,
in
which the complementarity
To capture
induce multiple equilibria for some information structures.
sufficiently strong to
is
we now
this possibility,
let
A = 9 + l[K>r],
>
where 1[K
equals one
r]
if
K
>
and zero otherwise,
r
r
6
aggregate investment necessary for the complementarity to pay
we
=
r
let
we
1/2. For tractability,
and constrain
Let 9
6
ki
=
without serious
off;
also let the cost of investment
U{
=
AK{
represents the critical size of
(0, 1)
be
loss of generality,
linear, so that
Ki,
[0, 1].
=
and
£
1. If
were
[0, 0]
common
knowledge, both
would be an equilibrium; the former coincides with the
coordination failure.
With heterogeneous
first
=
fc,
and
1
whereas the
best,
fcj
=
for all
i
latter represents a
information, the possibility of multiple equilibria depends
on the transparency of public information, as we show next.
Equilibrium
3.1
An
agent finds
optimal to invest
it
=
ki
1 if
E^
>
[A]
1,
and
ki
=
We
otherwise.
restrict
attention to equilibria with monotonic strategies, in which case for every z there exists x*(z)
such that
K(9,z)
only
if
ki
=
&([9
>
8
=
1 j£ Xi
—
>
x*(z) and
x*(z)]/a x ) and
where 9*(z)
0*(z),
=
=
/c,
otherwise.
thus increasing in
is
x*(z),
and therefore
9.
Aggregate investment
This implies that
K
>
E [A\x u z] =E{9\x u z) +
is
then given by
r
(= 1/2)
Pr(#
>
if
and
9*\ Xi ,z), or
equivalently
= (l-S)x +
E[A\xi,z]
It
=
follows that ki
with 9*
this
=
x*
,
1 if
x
>
l
x*,
we conclude
az
F
>
is
a z be the unique
ct z
=
+
,
then
F
is
*
Sz ~ e
a
otherwise, where x* solves E[>l|x*,x;]
=
5(z
-
x*)
- a^~
l
[1
-
(1
-
8)x*
easy to check that the above always admits a solution.
It is
let
ki
~ 6)Xl
=
1.
Combining
that the equilibrium threshold x* must solve
F(x*;z,S,a)
and
and
,{1
Sz + ^'
positive solution to a^s/^/n
monotonic
in
x
for all z,
instead non-monotonic whenever 6
>
5,
-
=
5z]
Let 5
= o x \/ Ox + crJ
2
0.
=
If S
•
(5)
t/2ttct/(1
<
5,
a z < a z In
.
y/2na)
or equivalently
and thus the equilibrium threshold x*
or equivalently
+
is
unique.
this case, let z,z
=
G.M. Angeletos and A. Pavan
±{m- $^
1/2
<
that
z
<
1
(?n)cr(l
-
6)/5
<
1.
For z
1/2 <~z
<
three solutions, x^OU)
-
x*nedium
1/2}
m
where
,
>
(z,z), (5) has a
$.
1/2 solves (p($
equilibrium:
(ii)
A
the
3.2
The
is
If S
1 if
>
In the
> x *hih {z),
this
=
/c z
If instead S
equilibria:
Xi
(i)
<
< x*hih The two extreme
we
and only
S (equivalently,
first,
ki
=
>
if Xi
1
if
a z > a z ), or
x*(z), where x*(z)
a z < a z ) and
and only
>
But
<r(l
for z
disregard.
We
-
G
and note
5)/5,
admits
(z, z), (5)
conclude:
(z,z), there exists a unique threshold
z
^
is
the unique solution to F(x*; z,
xfow (z); in the second,
5,
a)
fcj
=
1 if
the case, the second equilibrium (x*hi
.
)
=
and only
where x^ow (z) and x*hih {z) are the lowest and highest solutions to F(x*;z,5,a)
high level of transparency (high S or low a z )
first
.
=
0.
z 6 (z, z), there exist exactly two stable threshold
Xi
if
(T7i))
solutions represent stable equilibria; the
.
S (eqmvalently,
_1
unique solution x*
intermediate represents an unstable equilibrium, which
Proposition 5
10
may
thus lead to multiple equilibria.
=
if
0.
When
characterized by less aggregate investment than
is
(x*low ).
Welfare
probability a coordination failure
is
possible depends on the transparency of information.
Indeed,
PT[ze(z,z)\6]
increases with z, decreases with z,
= $[-
'-)-$
_
and decreases with a z
for 6
G
(z, z).
Moreover, dz/dS
<
<
dz/dS. Hence,
Proposition 6
If 5
>
S (equivalently,
a z < a z ) and
9
6
(z,z), the probability of multiple equi-
librium levels of investment increases with either a higher 5 for given a, or a lower
o~ x
a z for given
.
An
increase in the level of transparency
bility that
the "bad" equilibrium
analytically.
The
We
is
may
thus decrease welfare by increasing the proba-
played. Unfortunately,
it is
impossible to characterize welfare
thus resort to numerical simulations.
effect of
o~ z
on w(9)
is
illustrated in Figure
1
for various values for 9.
The
solid lines
represent welfare along the high-investment equilibrium, whereas the dashed lines represent welfare
along the low-investment equilibrium. In general, the welfare effects of transparency are neither
monotonic nor homogeneous across
sufficiently high values of 9.
We
9.
However, the
effects
tend to be small
for sufficiently
thus choose to concentrate on intermediate fundamentals.
low or
G.M. Angeletos and A. Pavan
Since
under
az =
is
=
az
restores
common knowledge for any given
common knowledge
coincides with the
Therefore, provided that there
0.
0,
and since the "good" equilibrium
that welfare
a coordination
failure, full
beyond d z
,
which case welfare
in
revealed by the examples of Figure
1
We
to space limitations.
Proposition 7
welfare
is
is
maximized
at
and are omitted due
thus conclude
If the socially preferable equilibrium is selected with high probability
tiple equilibria are possible,
az
transparency
appear to be robust across a large number
of simulations. Also, simulations of the welfare effect of 5 give similar results
at
at
level of transparency.
The patterns
maximal
maximized
is
played whenever multiple equilibria are possible,
is
welfare tends to decrease with a reduction in a z
>
it is trivial
risk of
is little
desirable. If instead the "bad" equilibrium
an intermediate
best,
first
o~ x
11
=
robustly
welfare
for given
ox
maximized
at
is
8
<
or
5,
=
1
for given a, and necessarily
worse equilibrium
is
selected with high probability,
maximal
robustly
If instead the
.
o~ z
whenever mul-
> az
at 5
.
Concluding Remarks
4
This paper examined the welfare
investment complementarities.
more transparency
possible,
This
increases volatility.
the market, which
level.
On
is
is
If
effects of public
and private information
the complementarity
if
weak
an economy with
so that multiple equilibria are never
in public information increases welfare, despite the fact that
because more transparency
socially valuable given that the
the other hand,
is
in
the complementarity
for high levels of transparency,
more
is
facilitates
more
complementarity
is
it
effective coordination in
present at the aggregate
strong so that multiple equilibria are possible
precise public information facilitates
more
effective
market
coordination on either equilibrium. In that case, "constructive ambiguity" becomes optimal
there
is
a high risk that the undesirable equilibrium
In Angeletos and
optimal allocations
Pavan (2003), we examine
for
in
also
is
when
selected.
more
detail the properties of equilibrium
economies with investment complementarities.
We
and
expect our insights to
turn useful also in the analysis of other settings in which aggregate complementarities play an important
role,
externalities.
such as economies with incomplete financial markets, Keynesian
frictions, or
network
G.M. Angeletos and A. Pavan
12
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[4]
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Woodford, Michael (2003), "Imperfect
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13
and the Effects of Monetary Pol-
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S.
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and M. Woodford,
eds.).
e
.
2
.
=
o.5
-
1
6
Figure
The
effect of o,
1
on welfare.
.
4
3337 020
Date Due
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MIT LIBRARIES
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