ï»¿ WPS5929
Policy Research Working Paper 5929
Financial Distortions and the Distribution
of Global Volatility
Maya Eden
The World Bank
Development Research Group
Macroeconomics and Growth Team
January 2012
Policy Research Working Paper 5929
Abstract
Why are emerging economies excessively vulnerable a further divergence in volatility, thereby providing a
to shocks to external funding? What was the role of new and simple explanation for the divergent trends in
financial flows from emerging to developed economies output volatility up to the recent crisis. In the integrated
in setting the stage for the subprime crisis? This paper environment, cheap funding leads to an endogenous
addresses these questions in a simple general equilibrium deterioration of the financial system in developed
framework that emphasizes the aggregate implications economies. These predictions are consistent with a wide
of the misallocation of funds on the micro level. The variety of microfoundations, in which distortions cause
analysis shows that the misallocation of funds amplifies productive projects to be relatively more sensitive to
volatility even in a closed economy. Financial integration aggregate shocks. The paper provides some empirical
between relatively distorted emerging economies and evidence for these microfoundations.
relatively undistorted developed economies leads to
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Financial Distortions and the Distribution of
Global Volatility
Maya Edenâˆ—
The World Bank, DECMG
January 3, 2012
Abstract
Why are emerging economies excessively vulnerable to shocks to external
funding? What was the role of ï¬?nancial ï¬‚ows from emerging to developed
economies in setting the stage for the subprime crisis? This paper addresses
these questions in a simple general equilibrium framework that emphasizes
the aggregate implications of the misallocation of funds on the micro level.
The analysis shows that the misallocation of funds ampliï¬?es volatility even in
a closed economy. Financial integration between relatively distorted emerg-
ing economies and relatively undistorted developed economies leads to a
further divergence in volatility, thereby providing a new and simple expla-
nation for the divergent trends in output volatility up to the recent crisis.
In the integrated environment, cheap funding leads to an endogenous dete-
rioration of the ï¬?nancial system in developed economies. These predictions
are consistent with a wide variety of microfoundations, in which distortions
cause productive projects to be relatively more sensitive to aggregate shocks.
The paper provides some empirical evidence for these microfoundations.
JEL Classiï¬?cation: E44, F36, G01, G15 Sector Board: FSE
Keywords: ï¬?nancial distortions, log supermodularity, emerging market volatility,
the Great Moderation, ï¬?nancial crises, matching
âˆ—
This article is based on the ï¬?rst chapter of my thesis at MIT. I am very grateful to my advisors
Ricardo Caballero, Arnaud Costinot and Guido Lorenzoni for their invaluable input. I have also
beneï¬?ted from comments made by Daron Acemoglu, George-Marios Angeletos, Harjoat Bhamra,
Dave Donaldson, Ana Fostel, Veronica Guerrieri, Bengt Holmstrom, Leora Klapper, Aart Kraay,
Roberto Rigobon, Luis Serven, Jenny Simon, Ivan Werning, participants of the NBER Summer
Institute 2010 (IFM) as well as participants of various other conferences and seminars. I thank
the World Economy Laboratory (WEL) for ï¬?nancial support. All errors are mine. This paper
reï¬‚ects my own views and not necessarily those of the World Bank, its Executive Directors or
the countries they represent. Please send comments to meden@worldbank.org.
1
1 Introduction
The patterns of global volatility over the last few decades have raised many ques-
tions regarding the consequences of globalization. For emerging economies, ï¬?-
nancial integration was typically associated with episodes of extreme volatility,
often related to ï¬‚uctuations in the supply of external funding. At the same time,
for developed economies, ï¬‚uctuations in the supply of funds did not seem to be
an important source of volatility, at least not until the recent crisis1 . Further,
evidence suggests that the relative importance of non-technology shocks in devel-
oped economies was declining over the period of ï¬?nancial globalization, as many
attributed the â€œGreat Moderationâ€? trend in output volatility to a decline in non-
fundamental volatility2 . Why were the initial eï¬€ects of ï¬?nancial integration so
diï¬€erent for emerging and developed economies?
The picture is complicated further by the recent crisis, that suggests that the
consequences of ï¬?nancial integration on volatility in developed economies may
have been highly complex. While ï¬‚uctuations in external funding were not an
important driver of volatility during normal times, it seems that the magnitude
of ï¬‚ows towards developed economies may have led to an overï¬‚ow of the ï¬?nancial
system and a collapse from within. Many attribute the ampliï¬?cation of the crisis
to the incapacity of the ï¬?nancial system to withstand even relatively small shocks,
a fragility that was an equilibrium outcome of a global environment that ï¬‚ooded
the ï¬?nancial system with liquidity. Did the global supply of funds play a role in
setting the stage for the sub prime crisis?
This paper takes the view that the aggregate implications of ï¬?nancial distor-
tions are central to these questions. I consider a model in which funding is the single
input of production, and there are heterogenous projects. Distortions increase the
sensitivity of relatively productive projects to aggregate ï¬‚uctuations in the sup-
ply of funds. In reduced form, this type of misallocation can be represented as a
1
See Demirguc-Kunt and Detragiache [1999], Kose et al. [2003] and Bekaert et al. [2006] for an
empirical discussion of the diï¬€erential eï¬€ects of ï¬?nancial integration on emerging and developed
economies. For literature emphasizing the importance of shocks to external funding to volatility
in emerging markets, see Neumeyer and Perri [2005], Uribe and Yue [2006], Chang and Fernandez
[2010] and Broner and Ventura [2010], among others.
2
See Gali and Gambetti [2009] for a structural VAR decomposition of the components of the
â€œGreat Moderationâ€?.
2
Figure 1: The Standard Deviation of Output Growh
(a) Developed markets (b) Emerging markets
2.5 2.5
Output Volatility in Developed and Emerging
2 Economies
2
1.5 1.5
1 1
0.5 0.5
0 0
1980-1989 1990-2003 2004-2011 1980-1989 1990-2003 2004-2011
The calculations are based on data from the IMFâ€™s World Economic Outlook, September 2011.
The calculation for developed markets are based on the series â€œAdvanced Economiesâ€?, and the
calculation for emerging markets are based on the series â€œEmerging and Developing Economiesâ€?.
Growth rates are calculated based on the cumulative output produced by all countries in the
group.
This ï¬?gure plots the standard deviation of output growth in developed and emerg-
ing economies during three periods: the â€œpre-integrationâ€? period (1980-1989), the
â€œintegrationâ€? period (1990-2003) and the â€œpost-integrationâ€? period (2004-2011)
(see Chinn and Ito [2008] for a discussion of the timing of ï¬?nancial globalization).
Two stylized facts are illustrated: (i) the initial divergence in volatility between
emerging and developed economies upon ï¬?nancial integration, as illustrated by the
decline in output volatility in developed economies between the periods 1980-1989
and 1990-2003, and the increase in output volatility in emerging economies over
the same time; and (ii) the spike in volatility in both regions in the post integration
period, that includes the subprime crisis.
3
less steeply declining aggregate marginal return to funds: in eï¬ƒcient economies,
projects are implemented in an order decreasing in their returns. The aggregate
marginal return to funds is decreasing, as less and less productive projects are
funded as the supply of funds increases. In distorted economies, the order in
which projects are implemented is less correlated with their productivity. The
marginal return to funding declines less steeply, as relatively productive projects
are implemented with the marginal units of funding, while relatively unproductive
projects are implemented inframarginally.
I embed this reduced form representation of distortions in a stylized general
equilibrium model of ï¬?nancial integration. I begin by studying the closed economy
equilibrium, and illustrate a tight link between ï¬?nancial distortions and aggregate
output volatility. Shocks to the aggregate supply of funds are ampliï¬?ed by ï¬?nan-
cial distortions, as distortions increase the vulnerability of relatively productive
projects to aggregate ï¬‚uctuations.
Next, I consider a global environment with a â€œdistortedâ€? emerging market re-
gion and an â€œeï¬ƒcientâ€? developed market region, and characterize the integrated
equilibrium under the short run assumption that the levels of distortion remain
ï¬?xed. I show that ï¬?nancial integration leads to a further divergence in volatility
between the two regions. In equilibrium, ï¬‚uctuations in the global supply of funds
adjust disproportionately through changes in the amount of funding supplied to
emerging markets: an expansion in the supply of funds would lead to a larger
expansion in emerging economies, as the projects implemented at the margin yield
relatively higher returns. At the same time, a contraction in the supply of funds
would lead to a larger contraction in emerging economies, as the set of projects
funded inframarginally yield a relatively lower return. This presents a new and
simple explanation for the divergence in volatility trends up to the recent crisis,
based on an intuitive â€œconservation of volatilityâ€? law: the equilibrium counterpart
of the increase in volatility in emerging economies is a decline in volatility in devel-
oped economies, as shocks to the domestic liquidity supply in developed economies
adjust primarily through changes in the amount of funding supplied to emerging
markets.
Finally, I study the medium run equilibrium in which the quality of the ï¬?nancial
system in the developed world endogenously adjusts to the integrated environment.
4
I extend the model to allow banks to choose the level of distortion, where a higher
level of distortion is associated with a lower cost. When ï¬?nancial integration is
associated with a large drop in the price of funding, banks endogenously select
a higher level of distortion. Intuitively, when funding is cheap, most projects
should be implemented anyway; the returns to sustaining institutions that enable
the diï¬€erential contraction of productive and unproductive projects goes down.
Interestingly, these endogenous institutional changes have a mixed eï¬€ect on output
and output volatility. While the output response to large contractions in the
supply of funds is ampliï¬?ed, the deterioration in the ï¬?nancial system actually
serves to increase and stabilize output during normal times. In the extreme case,
the ï¬?nancial system implements all projects, regardless of small ï¬‚uctuations in the
price of funding, resulting in high and stable output. However, when the supply
of funds contracts so much that the economy can no longer aï¬€ord to run at full
capacity, there is an eï¬ƒciency loss resulting from the economyâ€™s inability to absorb
contractions through the discontinuation of the least productive projects.
The modelâ€™s predictions depend crucially on the assumption that the marginal
return to funding is declining less steeply in more distorted economies. Formally,
the key assumption is that the marginal return to funding is log supermodular in
funding and the level of distortion. To assess the relevance of this assumption,
one can ask (i) under which microfoundations it will hold and (ii) whether or
not these microfoundations are themselves empirically relevant. I show that this
assumption arises naturally in a wide variety of models in which the equilibrium
is characterized by a stochastic matching between funding priorities and projects.
Distortions create a mismatch, making better projects less likely to receive high
priority, and relatively worse projects relatively more likely to receive a higher
priority. I present empirical evidence for these properties using ï¬?rm level data from
emerging and developed economies. I ï¬?nd that in emerging economies, productive
ï¬?rms are relatively more sensitive to ï¬‚uctuations in the aggregate supply of funds,
and that the opposite is true for relatively less productive ï¬?rms. I show that this
type of mismatch can arise from many common sources of distortions, such as
incomplete information, ineï¬ƒcient government intervention, collateral constraints
and search frictions.
5
2 Related literature
The results concerning the divergence in volatility between emerging and devel-
oped economies are related to several strands of literature. The idea that ï¬?nancial
distortions exacerbate output volatility appears prominently in the context of col-
lateral constraints. Kiyotaki and Moore [1997], Fostel and Geanakoplos [2008] and
Caballero and Krishnamurthy [2001] are important examples, the latter two with
speciï¬?c applications to emerging market economies. The general formulation in
this paper suggests that the link between ï¬?nancial distortions and volatility is not
unique to collateral constraints, and is common to many forms of distortions. The
mechanism in this paper is closest to Kiyotaki and Moore [1997], as the ampli-
ï¬?cation of shocks is a result of a domestic ineï¬ƒcient allocation of resources that
causes relatively productive projects to be more sensitive to aggregate ï¬‚uctuations.
However, the role of external funding in explaining emerging market volatility is
closest to Fostel and Geanakoplos [2008]. In Fostel and Geanakoplos [2008], a
small group of constrained investors hold emerging market assets. Shocks to the
liquidity in the hands of these investors evidently translate into movements in the
liquidity supply for emerging market projects. The focus of this paper is comple-
mentary to the one in Fostel and Geanakoplos [2008]: while their starting point is
that emerging market projects are funded by a small group of â€œresidualâ€? investors,
this paper uses ï¬?nancial distortions to endogenize the assumption that emerging
market projects are â€œresidualâ€?.
Also related is the literature on volatility, development, and openness. The
result that economies in earlier stages of development become more volatile with ï¬?-
nancial integration is in line with Obstfeld [1994], Greenwood and Jovanovic [1990],
and Koren and Tenreyro [2009]. The focus in these papers is on the changes in
the sectoral composition induced by better consumption diversiï¬?cation opportu-
nities. If ï¬?nancial integration allows for better diversiï¬?cation, investors may be
more inclined to take on high-risk projects, potentially increasing the aggregate
riskiness of the economy. This mechanism is very diï¬€erent from the mechanism
discussed in this paper, which does not rely on changes in sectoral composition.
While sectoral composition seems like a plausible source for some shocks, partic-
ularly in lower stages of development, it seems like an unlikely explanation for
6
the heightened volatility of emerging markets associated with movements in ex-
ternal funds (such as sudden stops). Moreover, it provides a poor explanation for
the common movements in emerging market economies, which have very diï¬€erent
sectoral compositions.
Conceptually related is the work of Caballero et al. [2008], who study global
imbalances as an outcome of ï¬?nancial integration in a world with heterogenous
ï¬?nancial development. While the questions motivating these papers are diï¬€erent,
both share the view that integration with a ï¬?nancially underdeveloped region is an
important factor behind recent trends in the US economy. The work of Fogli and
Perri [2006] links the Great Moderation with global imbalances by arguing that
global imbalances are a natural artifact of the decline in volatility. In their model,
the decline in volatility (relative to the rest of the world) reduces householdsâ€™
relative incentives to accumulate precautionary savings. This paper proposes an
alternative link between ï¬?nancial integration and the Great Moderation. In this
model, ï¬?nancial integration decreases volatility in the developed world and in-
creases volatility in emerging markets; it could be that as a result, through the
mechanism in Fogli and Perri [2006], the external balance of the developed mar-
kets deteriorates. This combined mechanism demonstrates an additional channel
through which ï¬?nancial underdevelopment in emerging markets may translate into
global imbalances.
The results concerning the endogenous deterioration of the ï¬?nancial system in
the developed world are broadly related to the literature on bubbles. As shown in
Tirole [1985], environments in which the interest rate is low are fertile grounds for
the formation of bubbles, and the presence of bubbles may lead to an expansion in
output (as in Farhi and Tirole [2010] and Martin and Ventura [2010]). However, the
mechanisms through which a low interest rate leads to an expansion are diï¬€erent: in
the bubble literature, bubbles serve as additional sources of liquidity, which enable
more economic activity. In this paper, low interest rates are indicative of a situation
in which the global supply of liquidity is already high; the expansion results from
an endogenous decision of intermediaries to implement projects indiscriminately,
increasing the total amount of projects implemented.
Similar to the bubble-burst view of the crisis, this paper takes the view that the
root of the crisis is a sudden contraction in the supply of liquidity. The contraction
7
in the supply of liquidity is not modeled here explicitly, and may be thought of
as resulting from a burst of a bubble on an asset used for liquidity purposes (see
Holmstrom [2008]). However, unlike the bubble-burst view of the crisis, in this
model the burst of the bubble itself does not explain the full extent of the crisis.
Rather, the crisis is ampliï¬?ed by the structural changes that the ï¬?nancial system
underwent during the expansionary period. The emphasis on the role of ï¬?nancial
frictions as an ampliï¬?cation mechanism of the crisis is shared with Hall [2009],
Gertler and Kiyotaki [2010], and others. The view closest to this paper is the
one expressed in Brunnermeier [2009] and Gorton [2008]. These papers discuss
mechanisms through which a low interest rate environment led to a decline in
lending standards and institutional changes which evidently ampliï¬?ed the subprime
crisis. The model presented in this paper may be seen as a simple formalization
grouping these phenomena.
This paper is also related to the empirical literature on the macroeconomic
consequences of misallocation. Closest to this paper is Hsieh and Klenow [2009].
Similar to this paper, Hsieh and Klenow [2009] conduct an empirical study of
the aggregate consequences of misallocation, without taking a stance on the type
of distortion that causes resources to be allocated ineï¬ƒciently. However, Hsieh
and Klenow [2009] focus on the static productivity loss induced by misallocation,
whereas I focus on the volatility induced by misallocation, or the ampliï¬?cation of
contractions caused by the discontinuation of relatively productive projects.
Methodologically, this paper is related to the literature emphasizing the role
of supermodularity and log supermodularity conditions in various economic ï¬?elds.
Prominent examples include, among others, Milgrom and Weber [1982] in auction
theory; Bulow et al. [1985] in industrial organization; Jewitt [1987] and Athey
[2002] in monotone comparative statics under uncertainty; and Costinot [2009] in
international trade. Shimer and Smith [2000] consider a model in which heteroge-
neous agents search for partners for joint production, where the output produced by
the match depends positively on each type. They use log supermodularity condi-
tions on the joint production function to generate suï¬ƒcient conditions for positive
assortative matching. Broadly, the model in this paper is the inverse exercise: I
characterize conditions on the matching process that deliver log supermodularity
of the aggregate production function.
8
3 An aggregate representation of misallocation
There is a single consumption good and a single input of production called funding
and denoted F âˆˆ [0, 1]. Of course, this is a shortcut for a richer model in which
funding is used to hire workers, rent capital and buy intermediate inputs. Fluc-
tuations in F can therefore be interpreted as ï¬‚uctuations in employment; when
F = 1, all inputs are employed.
There is a set of projects indexed x âˆˆ [0, 1]. Each project requires one unit of
funding to implement. Projects are of heterogeneous productivity: if implemented,
the project indexed x produces Ag(x) units of output, where A is the aggregate
component of productivity and g(x) is the idiosyncratic component of productivity.
Without loss of generality, I assume that g (x) â‰¤ 0, so projects with lower indices
are more productive.
Whether or not a project is implemented depends on the whether the aggre-
gate supply of funding is high enough. For each project x, there is a threshold
p = p(x), such that the project is implemented if and only if F â‰¥ p. In princi-
ple, this threshold is an equilibrium object that is determined by a wide variety
of factors, including the projectâ€™s productivity, its collateral, its connections to
people in power, etc. Importantly for our purposes, this equilibrium object can be
summarized as a funding priority: when the aggregate supply of funds is F , all
projects with funding priorities p âˆˆ [0, F ] are implemented.
The ï¬?nancial system is represented by a stochastic matching between funding
priorities and projects. Let Ï† be a reduced form parameter capturing the level of
distortion. A higher Ï† corresponds to a more distorted allocation. In an economy
with distortion level Ï†, the probability that project x receives priority p is given
by ÏƒÏ† (x, p).
Aggregate output is denoted Y . I assume that the matching takes place si-
multaneously in many diï¬€erent sub-locations, so aggregate output is deterministic
and equal to the expected output produced by all implemented projects, that is,
all projects with priorities p â‰¤ F :
F 1
Y (A, F, Ï†) = ÏƒÏ† (x, p)Ag(x)dxdp (1)
0 0
9
The aggregate marginal return to funding, denoted y, is given by:
1
âˆ‚Y (A, F, Ï†)
y(A, F, Ï†) = Ay(F, Ï†) = = ÏƒÏ† (x, F )Ag(x)dx (2)
âˆ‚F 0
I assume that better projects are relatively more likely to receive high priorities,
so the marginal return to funding is weakly decreasing ( âˆ‚y(F,Ï†) â‰¤ 0).
âˆ‚F
The key ingredient in the model is the following property, that states that the
marginal return to funding is log supermodular3 in the level of funding and the
level of distortion:
Property 1 For any Ï† â‰¥ Ï† and for any F â‰¥ F ,
y(F, Ï† ) y(F, Ï†)
â‰¤ (3)
y(F , Ï† ) y(F , Ï†)
Property 1 can be understood as follows. Fix any two levels of funding, F and
F , such that F â‰¤ F . Property 1 requires that the ratio of the marginal returns to
funding at F and F is relatively lower in more eï¬ƒcient economies; loosely stated,
the (negative) slope of the marginal return to funding is relatively more steep in
more eï¬ƒcient economies.
This simple setup is suï¬ƒcient for producing all of the macroeconomic insights
that follow. To motivate Property 1, in section 7 I show that it is consistent with
a wide variety of standard microfoundations, including models of informational
frictions, collateral constraints, ineï¬ƒcient government intervention and search fric-
tions. The common feature of these microfoundations is that distortions cause rel-
atively more productive projects to receive lower funding priorities, making their
implementation outcome more sensitive to changes in F .
For the time being, consider the following stark microfoundation, that will be
used to illustrate the results throughout the paper:
3
Recall that a function f (x1 , x2 ) is log supermodular in x1 and x2 if for any x1 < x1 and x2 <
x2 , we have that f (x1 , x2 )f (x1 , x2 ) â‰¥ f (x1 , x2 )f (x1 , x2 ). If f is strictly positive, this condition
f (x ,x )
implies that f (x1 ,x2 ) â‰¤ f (x1 ,x2 ) . If f is strictly positive and diï¬€erentiable, this corresponds to
f (x ,x2 )
1 2 1
âˆ‚ 2 ln f (x1 ,x2 )
âˆ‚x1 âˆ‚x2 â‰¥ 0.
10
Random allocation example. There are two types of economies: eï¬ƒcient
(ef f ) and distorted (dis). In eï¬ƒcient economies, projects are implemented in
the order of their productivity; the funding priority of project x is p(x) = x. This
means that the probability of being assigned priority p = F is 0 for all x = F , and
1 for x = F :
x
0 If x < F ;
Ïƒef f (z, F )dz = (4)
0 1 If x â‰¥ F .
Given an aggregate supply of F units of funding, output is given by the cumu-
lative output produced by the F best projects:
F
Yef f (F ) = Ag(x)dx (5)
0
The marginal return to funding is given by the productivity of the marginal
project:
yef f (F ) = Ag(F ) (6)
In distorted economies, projects are implemented in an arbitrary order. The
probability that priority p = F is assigned to project x is constant:
x
Ïƒdis (z, F )dz = x (7)
0
This randomness can be thought of as resulting from a wide range of distor-
tions; for example, it could be that the ï¬?nancial sector lacks the expertise to
evaluate projects, and must implement projects arbitrarily. Alternatively, the ran-
domness could be indicative of an economy with extreme corruption, in which the
implementation outcome is orthogonal to productivity.
Output is equal to the expected cumulative output produced by F randomly
drawn projects:
1
Ydis (F ) = F Â· Ag(x)dx (8)
0
The marginal return to funding is constant and equal to the average return to
projects:
1
ydis (F ) = Ag(x)dx (9)
0
11
It is easy to see that this model is consistent with Property 1, as the marginal
return to funding is declining in eï¬ƒcient economies, but constant in distorted
economies. Formally, it is easy to check that for any F â‰¤ F :
1
yef f (F ) Ag(F ) 0
Ag(x)dx ydis (F )
= â‰¤1= 1 = (10)
yef f (F ) Ag(F ) Ag(x)dx ydis (F )
0
4 Closed economy equilibrium
In this section I characterize the eï¬€ects of ï¬?nancial distortions on volatility under
autarky, and show that more distorted economies are more sensitive to ï¬‚uctuations
in the aggregate supply of funding.
In the closed economy, the supply of funding is given by an exogenous domestic
liquidity supply, Q. Domestic households supply liquidity to the ï¬?nancial system,
in exchange for future returns. In this model, liquidity is deï¬?ned simply as the
supply side of funding. The market clearing condition is:
F =Q (11)
After production takes place, the ï¬?nancial system repays households at a rate
of r units of output per unit of liquidity. I assume that r is equated with the
marginal return to funding. This can be thought of as a result of a competitive
banking system in which banks compete for liquidity supply from households.
There are two sources of volatility: shocks to the domestic technology level A,
and shocks to the supply of liquidity, Q. I assume that these shocks are indepen-
dent4 . Appendix C presents a model of liquidity supply in which liquidity supply
ï¬‚uctuations are driven by three primitive shocks: shocks to the money supply,
shocks to risk aversion, and shocks to the ability of the private sector to generate
promises for future repayment.
It is straightforward to show that, in the closed economy, the sensitivity of
4
The assumption that shocks to A and to Q are independent is, of course, unrealistic, as
periods of high productivity may imply that it is easier for entrepreneurs to issue promises on
future returns, as in Kiyotaki and Moore [1997]. The independence of the two shocks is not
necessary for any of the results, however separating the two types of shocks is convenient for
expositional purposes.
12
output to productivity shocks is unrelated to the degree of ï¬?nancial distortions.
However, more distorted economies are more sensitive to shocks to liquidity supply:
Proposition 1 For any given processes of A and Q,
1. Output is more volatile in more distorted economies:
âˆ‚ ln Y (Q, Ï†)
is increasing in Ï† (12)
âˆ‚ ln Q
2. The average productivity of funded projects is more sensitive to liquidity sup-
ply shocks in less distorted economies:
âˆ‚ Y (Q,Ï†)
Q
is increasing in Ï† (13)
âˆ‚ ln Q
The proof of the above proposition, together with other omitted proofs, is in the
appendix. The intuition follows directly from Property 1. In eï¬ƒcient economies,
the decline in the average productivity of projects mitigates the eï¬€ect of an increase
in funding. In distorted economies, a suboptimal set of projects is implemented, so
some low-yield projects are implemented before higher-yield projects. This implies
two things. First, some projects that should have been implemented are not imple-
mented; their implementation takes place only when the supply of funding is higher,
intensifying the returns to funding. Second, some projects that should not have
been implemented are implemented, lowering the average productivity of funded
projects. These two facts put together imply that the ratio of the marginal return
to funding and the average return to funding is higher in distorted economies. In
other words, liquidity abundance increases the eï¬ƒciency of distorted economies
relative to eï¬ƒcient economies both by alleviating the ineï¬ƒciency caused by im-
plementing a suboptimal set of projects and by allowing for the implementation
of higher-yield projects. Using the random allocation example, ï¬?gure 2 illustrates
the properties of the closed economy equilibria in a distorted â€œemerging marketâ€?
economy and an eï¬ƒcient â€œdeveloped marketâ€? economy.
13
`
y (F)
d y (F)
em
Yd Yd Yem Y em
Q d Q d Fd Q em Q em F
em
(a) Developed markets (b) Emerging markets
Figure 2: The ï¬?gure on the left depicts the closed economy equilibrium in eï¬ƒcient
â€œdevelopedâ€? economies, and the ï¬?gure on the right depicts the closed economy equi-
librium in distorted â€œemergingâ€? economies. In both economies there is a positive
shock to liquidity supply. The average productivity declines in eï¬ƒcient economies
and remains constant in distorted economies. The output response is therefore
larger in distorted economies (in the sense that âˆ†Y is larger).
Y
5 Volatility divergence
In this section I present a set of results concerning the divergence of volatility
between emerging and developed economies following ï¬?nancial integration. I ï¬?rst
present the globally integrated equilibrium, and then discuss equilibrium implica-
tions for small open economies.
The setup of the model is as follows. There are two regions of equal size:
an emerging market region (em) and a developed market region (d). For the time
being, I assume that the only diï¬€erence between emerging and developed economies
is that emerging economies are more distorted than developed economies:
Ï†em > Ï†d (14)
For simplicity, I denote Yi = Y (Ai , Fi , Ï†i ) and yi = y(Ai , Fi , Ï†i ), for i âˆˆ {em, d}.
I assume that var(ln(Ad )) = var(ln(Aem ))5 and that liquidity supply Qi is
independent from both foreign and domestic technology, Ai and Aj .
5
The results trivially generalize to var(ln(Ad )) < var(ln(Aem )).
14
In order to isolate the eï¬€ects of ï¬?nancial heterogeneity on the global equi-
librium environment, it is convenient to assume that Qd and Qem are perfectly
correlated. Assuming that liquidity supplies are perfectly correlated isolates the
eï¬€ects of ï¬?nancial heterogeneity because, under this assumption, ï¬?nancial inte-
gration between two identical economies would have no eï¬€ect on liquidity-supply
driven output volatility. In contrast, independent liquidity supplies would imply
that ï¬?nancial integration between two identical regions has a moderating eï¬€ect
on output in both regions, as shocks to liquidity supply are shared across regions.
Replacing the assumption that Qd and Qem are perfectly correlated with the as-
sumption that they are independent would therefore decrease volatility in both
regions; however, the result that volatility induced by ï¬?nancial integration would
be relatively higher for emerging economies would still hold.
5.1 Integrated equilibrium
Assume that liquidity can move freely across regions. The global equilibrium is
characterized by two equations:
Fem + Fd = Qem + Qd = Qw (15)
yem (Fem ) = yd (Fd ) = r (16)
The ï¬?rst equation is a market clearing condition, stating that the total amount
of funding, Fem + Fd , must be equal the global supply of liquidity, Qw = Qem + Qd .
The second condition is the optimality condition of the ï¬?nancial system, requiring
that there is no gain from reallocating liquidity from one region to another6 .
I denote autarkic values with superscript a (F a , Y a , etc). Denote by âˆ† the
absolute value of the average change in funding levels induced by ï¬?nancial inte-
gration:
a a
âˆ† = |E(Fem ) âˆ’ E(Fem )| = |E(Fd ) âˆ’ E(Fd )| (17)
The value of âˆ† is determined in equilibrium as a function of the average sup-
6
The results easily generalize if there is a constant wedge in marginal returns, that is, the
second equilibrium condition is replaced with a condition of the form yd (Fd ) = wyem (Fem )
15
Ad
ply of liquidity, the ï¬?nancial distortions, and the relative productivities Aem . In
Ad
particular, there is always a value of Aem for which âˆ† = 0. For the purpose of
this exercise, I assume that âˆ† is small. The importance of this assumption is in
assuring that the sensitivity of output to funding remains similar to its autarkic
level. If this assumption is violated, the implications of ï¬?nancial integration on
macroeconomic volatility depend more speciï¬?cally on how the sensitivity of output
with respect to funding changes with the level of funding.
The main result is stated in the proposition below:
Proposition 2 For âˆ† suï¬ƒciently small, ï¬?nancial integration exacerbates the volatil-
ity diï¬€erences between emerging and developed markets:
a a
var(ln Fem ) âˆ’ var(ln Fd ) > var(ln Fem ) âˆ’ var(ln Fd ) = 0 (18)
a
var(ln Yem ) âˆ’ var(ln Yd ) > var(ln Yem ) âˆ’ var(ln Yda ) > 0 (19)
Financial integration leads to a divergence in volatility levels for two rea-
sons7 . First, ï¬?nancial integration is associated with a new source of ï¬‚uctuations
in funding, which is shocks to the relative productivity of emerging and developed
economies ( Aem ). These shocks lead to a substitution of funding across regions.
Ad
Since, by proposition 1, ï¬?nancially-distorted emerging markets are more sensitive
to ï¬‚uctuations in funding than developed markets, this works towards exacerbating
the diï¬€erences in output volatility across regions.
Second, it turns out that shocks to the global supply of liquidity adjust dis-
proportionately through changes in the supply of funding to emerging markets.
This equilibrium property is closely related to the feature of ï¬?nancial distortions
emphasized by Property 1. In developed markets, projects are implemented in
an order decreasing in their returns: most implemented projects generate returns
which well exceed r, while most unimplemented projects generate returns which
are well below r. Fluctuations in the implementation threshold therefore have
a relatively small impact on the amount of projects implemented in developed
7
Proposition 2 easily generalizes to an equilibrium with many countries with diï¬€erent levels of
distortions. In an integrated equilibrium, the sensitivity of each economy to shocks to the global
supply of liquidity or to TFP will be an increasing function of its level of ï¬?nancial distortions.
Diï¬€erences in volatility levels will magnify upon ï¬?nancial integration.
16
economies. In contrast, in emerging markets, the order in which projects are im-
plemented is more arbitrary; this implies that the return generated by the next
unit of funding is similar to the return generated by the previous unit. The same
ï¬‚uctuations in r therefore induce larger ï¬‚uctuations in the amount of implemented
projects. Figure 3 illustrates this equilibrium property in the random allocation
example8 .
Generically, abstracting from productivity shocks, ï¬?nancial integration leads to
less variation in r from the developed marketâ€™s perspective, and more variation in
r from the emerging marketâ€™s perspective. Consequently, there is a divergence in
liquidity-driven output volatility between emerging and developed economies.
y (F)
d
y (F)
em
r
Yd Y em Y
em
Fd Fem F em
Q w Q w
Figure 3: In this ï¬?gure, the origin of the developed economy is on the left cor-
ner, and the origin of the emerging economy is on the right corner. The market
clearing condition states that the distance between the two corners is equal to the
global liquidity supply, Qw . The intersection of the marginal returns to funding
determines r, and hence the division of Qw into Fd and Fem . Shocks to the global
liquidity supply adjust entirely through changes in the funding levels supplied to
emerging markets, Fem . An increase in Qw of size âˆ†Qw is illustrated as a shift of
the emerging economyâ€™s origin to the right.
The direction in which volatility levels change following ï¬?nancial integration is
8
In the random allocation example, the equilibrium level of r does not change following a
shock to global liquidity supply. Rather, the shock is adjusted entirely through changes in the
quantity of funding supplied to the emerging market region.
17
potentially diï¬€erent in emerging and developed economies. In emerging economies,
the volatility of funding necessarily increases upon integration. This is because
funding becomes vulnerable to two new shocks: shocks to foreign liquidity sup-
ply (Qd ) and shocks to relative technology levels ( Aem ). In developed economies,
Ad
funding also becomes vulnerable to shocks to relative technology, which works to-
wards increasing volatility. However, funding becomes less sensitive to shocks to
domestic liquidity supply (Qd ), since shocks to liquidity supply adjust primarily
through movements in the funding supplied to emerging markets. The net eï¬€ect
on volatility depends on the relative importance of technology shocks and liquidity
shocks. Speciï¬?cally, if movements in the level of funding result primarily from
variation in the supply of liquidity, ï¬?nancial integration will decrease the volatility
of output in developed economies.
Under stronger assumptions regarding the relative importance of liquidity and
technology shocks, it is possible to obtain stronger results concerning the direction
in which volatility levels change following ï¬?nancial integration:
Proposition 3 For âˆ† suï¬ƒciently small,
1. Financial integration increases the volatility of funding and the volatility of
output in emerging markets:
a
var(ln Fem ) > var(ln Fem ) (20)
a
var(ln Yem ) > var(ln Yem ) (21)
2. If the variance of liquidity supply is suï¬ƒciently large compared to the variance
of relative TFP, ï¬?nancial integration decreases the volatility of funding and
the volatility of output in developed markets:
a
var(ln Fd ) < var(ln Fd ) (22)
var(ln Yd ) < var(ln Yda ) (23)
These results provide some insight into the distinct behavior of emerging and
developed markets following globalization. The theory above suggests that the
18
divergence in liquidity-driven output ï¬‚uctuations may have been a result of devel-
oped markets eï¬€ectively exporting their liquidity shocks to emerging markets.
5.2 Small open economies
Given that much of the literature on the excess volatility of emerging markets has
focused on small open economies, it is useful to study small open economies in the
context of this global equilibrium environment.
I assume that each region is composed of a continuum of small open economies,
identical within regions. Small open economies are subject to idiosyncratic pro-
ductivity shocks, as well as to exogenous shocks to r which result from changes in
the global liquidity supply.
The ï¬?rst thing to note is that this model naturally implies comovements in
emerging market economies. Compared to their developed counterparts, small
open emerging markets are more severely aï¬€ected by shocks to the global liquidity
supply. The importance of global liquidity supply as a source of emerging market
ï¬‚uctuations naturally implies common movements in emerging market output lev-
els. Similar to Fostel and Geanakoplos [2008], comovements in emerging market
economies result from a common sensitivity to an external supply of funding.
Second, it is interesting to note that both in emerging and in developed markets,
funding responds similarly to idiosyncratic productivity shocks and to shocks to
the price of liquidity. This suggests a link between the heightened sensitivity
of emerging markets to interest rate shocks (as in Neumeyer and Perri [2005]
and Uribe and Yue [2006]) and the ampliï¬?cation of shocks to productivity (as in
Caballero et al. [2005]). To see this link, note that in a small open economy, the
level of funding is pinned down by a single indiï¬€erence condition, equating the
marginal product of funding with the world rate of return:
r
Ai yi (F ) = r â‡’ yi (F ) = (24)
Ai
From the formulation above, it is easy to see that funding is aï¬€ected similarly
by shocks to r and shocks to Ai . Essentially, in this model, the responsiveness
of funding to either type of shock captures the density of projects which are im-
plemented at the margin and collectively yield a return equal exactly to r. A
19
small shock to the returns of these projects will shift them above or below the
implementation threshold; similarly, small shocks to r will determine whether or
not the projects at the margin generate a return which justiï¬?es implementation.
The result that small open emerging markets are relatively more sensitive to both
shocks is closely tied to Property 1, as it guarantees that the density of projects
implemented at the margin is higher.
The model presented in this section suggests the following conclusions regarding
the role of ï¬?nancial institutions in determining the eï¬€ects of ï¬?nancial integration
on output volatility. Poor ï¬?nancial institutions in emerging markets exacerbate
their sensitivity to funding, as well as increase the volatility of funding supplied
to them. At times in which ï¬?nancial institutions are intact in developed markets,
their superior ability to implement projects diï¬€erentially serves both to stabilize
equilibrium funding levels and to mitigate the eï¬€ects of ï¬‚uctuations in funding on
output.
6 The endogenous deterioration of the ï¬?nancial
system
In section 5 it was assumed throughout that the quality of ï¬?nancial institutions
remains ï¬?xed upon ï¬?nancial integration. While this may be a valid short-run
assumption, the recent subprime crisis comes as a reminder that the quality of
ï¬?nancial institutions may evolve with changing circumstances.
In section 6.1 I consider a model in which the ï¬?nancial system in the developed
world deteriorates endogenously following ï¬?nancial integration. In section 6.2 I
discuss the implications of the deterioration during â€œnormal timesâ€?. I show that
in the absence of large shocks, the deterioration of the ï¬?nancial system actually
increases and stabilizes output in the developed world. In section 6.3 I show that
the deterioration in the ï¬?nancial system ampliï¬?es large adverse shocks.
20
6.1 Endogenous deterioration
I extend the setup to allow for an endogenous adjustment in the quality of the
ï¬?nancial system in the developed world. Banks can choose the level of ï¬?nancial
distortions out of some ï¬?nite set. There is a cost Î»(Ï†) associated with choosing
the level of distortions Ï†, where Î»(Â·) is decreasing. This cost should be thought of
as the cost of sorting projects and overcoming other obstacles which stand in the
way of an eï¬ƒcient allocation. For simplicity, I assume that banks consider only
the mean price of liquidity when choosing the level of ï¬?nancial distortions, and do
not take into account any uncertainty.
Given a price of liquidity r, the banks choose the level of funding, Fd , and the
level of distortion, Ï†d , to maximize proï¬?ts. The bankâ€™s proï¬?ts are given by:
Ï€(r) = max{Ï€(r, Fd , Ï†d )} = (25)
Ï†d ,Fd
Fd
max y(F , Ï†d )dF âˆ’ rFd âˆ’ Î»(Ï†d ) (26)
Ï†d ,Fd 0
The following proposition characterizes the equilibrium response of the ï¬?nancial
system to a global environment with the following two features: ï¬?rst, liquidity
supply is high. The role of this assumption can be understood as follows. At low
levels of funding, there is little incentive to invest in creating an eï¬ƒcient matching,
as the scale of activity does not justify the cost. A marginal increase in funds will
work towards countering this eï¬€ect: the beneï¬?ts of an eï¬ƒcient matching increase
as there is more funding to be allocated eï¬ƒciently. At some point, as we increase
the level of funding, this type of scale eï¬€ect works in the opposite direction: the
returns to knowing which projects to exclude go down, as there are less projects
to be excluded. The assumption that liquidity supply is suï¬ƒciently high restricts
attention to this region.
Ad
The second feature of the global equilibrium environment is that Aem is rela-
Ad
tively large. Note that Aem captures the relative returns generated by the same
project in developed and emerging economies. The presence of limited enforcement
in emerging economies would tend to imply a positive wedge between the produc-
tivity of a project and its return to investors. The role of the assumption that
Ad
Aem
is large is to generate a ï¬‚ow of funds from emerging to developed economies,
21
broadly consistent with the view of global imbalances expressed in Caballero et al.
[2008].
Ad
Proposition 4 For Qw and Aem suï¬ƒciently large, ï¬?nancial integration leads to
an endogenous deterioration of the ï¬?nancial system in the developed market region.
It is straightforward to show that the objective of banks in this model coincides
with the objective of a social planner trying to maximize domestic output minus
the costs of diï¬€erentiation (taking r as given). The deterioration in the ï¬?nancial
system can therefore be interpreted more broadly as an outcome of endogenous lax
regulation.
In the context of the recent crisis, the above proposition formalizes the popu-
lar claim according to which ï¬?nancial integration increased the equilibrium level
of ï¬?nancial distortions by lowering the price of liquidity from the developed mar-
ketâ€™s perspective9 . Intuitively, if liquidity is suï¬ƒciently cheap so that nearly all
projects are implemented anyway, the beneï¬?ts of diï¬€erentiating between projects
may not be worth the cost. Broadly interpreted, the ï¬?nancial system will grav-
itate towards various institutional arrangements that tie the implementation of
high quality projects with the implementation of low quality projects.
6.2 Normal ï¬‚uctuations
What are the implications of the deterioration of the ï¬?nancial system on output and
on output volatility? Under autarky, the implications would be fairly intuitive: a
weakening of the ï¬?nancial system would decrease output and increase subsequent
output volatility10 . However, these intuitive results breakdown under ï¬?nancial
integration. The following proposition states that the deterioration in the quality
9
A note is in order regarding the applicability of these results to emerging market economies.
The analysis in this section relies heavily on the assumption that ï¬?nancial integration is associated
with a decline in the price of liquidity from the domestic perspective. The results are therefore
not applicable for emerging markets. For emerging markets, the mirror image is the relevant one:
ï¬?nancial integration is associated with an increase in r, potentially leading to an endogenous
increase the the quality of ï¬?nancial institutions. The characterization of the long run general
equilibrium environment, in which ï¬?nancial institutions are allowed to adjust in both emerging
and developed economies, is beyond the scope of this paper. I leave this interesting issue for
future research.
10
To see this, note that by Lemma 7 in the Appendix, holding funding ï¬?xed, output is higher
when ï¬?nancial institutions are intact (because a superior set of projects are implemented). Thus,
22
of the ï¬?nancial system in the developed world will increase funding in that region,
and may increase and stabilize output as well:
Proposition 5 An endogenous weakening of the ï¬?nancial system in the developed
market will:
1. Increase the ï¬‚ow of funds from emerging to developed economies.
2. If the increase in ï¬‚ows is suï¬ƒciently large (which will be the case for a
Ad
suï¬ƒciently large Aem ), developed market output will increase and stabilize
conditional on small ï¬‚uctuations.
Abandoning the higher standard of diï¬€erentiation causes ineï¬ƒcient projects
that were implemented at the margin to be implemented inframarginally, while
more productive projects become marginal. This lowers the average return to
funding, but increases the marginal return to funding. In the integrated equi-
librium, this increase in domestic marginal returns leads to additional inï¬‚ows of
funding. If these ï¬‚ows are suï¬ƒciently large, domestic output will rise.
The increase in the marginal return also serves to stabilize output, as domes-
tic funding adjusts less to ï¬‚uctuations in the interest rate. Intuitively, when the
domestic marginal return is higher, a larger fraction of the economy becomes glob-
ally inframarginal. Of course, section 4 illustrates that the economy becomes more
sensitive to ï¬‚uctuations in domestic funding: so, while F becomes less volatile, the
economy becomes more sensitive to ï¬‚uctuations in F . Conditional on small global
ï¬‚uctuations, the ï¬?rst eï¬€ect dominates and volatility declines.
Proposition 5 can shed light on the seemingly â€œirrationalâ€? behavior that led up
to the subprime crisis, in which many bad loans were given to subprime borrowers,
and, while the ï¬?nancial system behaved â€œirresponsiblyâ€?, the demand for US assets
seemed only to increase. This result suggests that this type of indiscriminate lend-
ing raised the expected marginal return to funds in the US, leading to additional
inï¬‚ows.
Finally, does the fact that output in the developed world increases with the
deterioration of its ï¬?nancial system mean that such a deterioration is â€œgoodâ€??
a weakening of the ï¬?nancial system constitutes an adverse shock to output. The fact that
subsequent output volatility increases is immediate from the comparison between closed emerging
and developed economies in section 4.
23
y (F)
d
y (F)
em
r
Yd Y em
Fd F d Fem
Q w
Figure 4: The origin of the developed economy is on the left corner, and the origin
of the emerging economy is on the right corner. The market clearing condition
states that the distance between the two corners is equal to the global liquidity
supply, Qw . The intersection of the marginal products of funding determines r.
A deterioration of the ï¬?nancial system in the developed world causes funding to
ï¬‚ow towards that region. In this ï¬?gure, the deterioration of the ï¬?nancial system
is illustrated by the â€œï¬‚atteningâ€? of the marginal return to funding. The size of
the increase in Fd is given by âˆ†Fd , the distance between the intersection of the
autarkic (sloping) marginal return to funding and r, and the point of satiation
(Fd = 1).
24
From a global perspective, no. The generic adverse eï¬€ect of a deterioration in the
ï¬?nancial system is that it decreases world output, both under autarky and under
ï¬?nancial integration:
Lemma 1 A weakening of the ï¬?nancial system in the developed world decreases
world output.
This lemma is immediate from the fact that intact ï¬?nancial institutions allow
for a diï¬€erential implementation of projects based on their returns; the set of
projects implemented when diï¬€erentiation is not possible is necessarily inferior to
the set of projects implemented when some diï¬€erentiation is possible.
6.3 Large adverse shocks
In the global environment described in this paper, the deterioration of the ï¬?nancial
system in the developed world serves to increase and stabilize output in that region
during normal times. However, while the response to small shocks is mitigated,
the output response to large negative shocks is ampliï¬?ed:
Proposition 6 In the developed world, the weakening of the ï¬?nancial system am-
Ad
pliï¬?es the output response to large adverse shocks to Qw or Aem .
Intuitively, cheap liquidity leads to structural changes in the ï¬?nancial system
that disable the separation of high-quality projects from low-quality projects. Dur-
ing normal times, this increases the amount of low-quality projects being imple-
mented, and output increases as a result. However, suï¬ƒciently large contractions
in liquidity are ampliï¬?ed by the inability to separate the discontinuation of low-
quality projects from the discontinuation of high-quality projects.
This result suggests that the deterioration in the quality of ï¬?nancial institutions
preceding the sub-prime crisis may have indeed precipitated it by creating an
ampliï¬?cation mechanism for large adverse shocks. This ampliï¬?cation mechanism
is consistent with many ineï¬ƒciencies that seem important for understanding the
extent of the crisis. A straightforward interpretation is the mortgage market itself.
The creation of mortgage backed securities enabled the pooling of idiosyncratic
risk of subprime loans. Once housing prices declined, issuing new subprime loans
25
became diï¬ƒcult, perhaps in part because the process of issuing subprime loans did
not allow for diï¬€erentiation between relatively promising borrowers and relatively
unpromising borrowers. A more subtle interpretation is in balance sheet eï¬€ects (as
in Brunnermeier [2009]). The heavy reliance of banksâ€™ balance sheets on mortgage
backed securities forced them to disengage from productive lending activities once
the subprime crisis hit. This can be viewed as an additional mechanism that ties
the implementation of productive projects to the implementation of unproductive
projects.
Corollary 1 Financial integration may lead to the ampliï¬?cation of large adverse
shocks in the developed world.
Corollary 1 is immediate from the analysis in this section: by Proposition 4,
ï¬?nancial integration leads to the deterioration of the ï¬?nancial system. By Propo-
sition 6, the deterioration in the ï¬?nancial system ampliï¬?es the output response to
large adverse shocks.
Note that this analysis also suggests that the subprime crisis cannot be ex-
plained solely in terms of a breakdown in the ï¬?nancial system; rather, a complete
explanation would require either an additional large shock to TFP or to liquidity
supply.
The results in this section present a modiï¬?cation to the view presented in
section 5 according to which ï¬?nancial integration mitigates output ï¬‚uctuations in
the developed world. If ï¬?nancial integration with a distorted emerging market
region is coupled with a decline in the price of liquidity, ï¬?nancial institutions may
deteriorate in accordance with Proposition 4. As a result, the sensitivity of output
with respect to small shocks will decline, but large adverse shocks will be ampliï¬?ed.
7 The ï¬?nancial system as a matching mechanism
The results presented in the previous sections rely heavily on Property 1. In
this section, I derive Property 1 from two primitive assumptions on the eï¬€ect of
ï¬?nancial distortions on the matching between funding priorities and projects. I
present empirical evidence for these assumptions, and show that Property 1 can
be derived from a variety of microfoundations.
26
Before proceeding to the general case, it is useful to consider the following
simpliï¬?ed example. Assume that there are only two funding priorities, â€œhighâ€?
and â€œlowâ€?, and only two types of projects, â€œgoodâ€? and â€œbadâ€?. The good project
produces 3 if implemented, and the bad project only produces 1 if implemented
(g(good) = 3 and g(bad) = 1; for simplicity, Iâ€™ve assumed A = 1).
In an eï¬ƒcient economy, the good project would be prioritized higher than
the bad project. However, in a distorted economy, there may be frictions that
prevent the eï¬ƒcient matching between funding priorities and projects: with some
probability Ï†, the bad project will be prioritized higher than the good project:
ÏƒÏ† (bad project, high priority) = Ï†
ÏƒÏ† (bad project, low priority) = 1 âˆ’ Ï†
ÏƒÏ† (good project, high priority) = 1 âˆ’ Ï†
ÏƒÏ† (good project, low priority) = Ï†
Note that Ï† = 0 corresponds to the eï¬ƒcient case; a higher Ï† corresponds to a
more distorted economy, in which the probability of implementing the bad project
before the good project is higher. Given Ï†, the marginal return to the ï¬?rst unit of
funding is equal to the expected productivity of the project that receives the high
funding priority:
y(ï¬?rst unit of funding) = (1 âˆ’ Ï†) Â· 3 + Ï† Â· 1 = 3 âˆ’ 2Ï† (27)
The marginal return to the second unit of funding is the expected productivity
of the project that receives a low funding priority:
y(second unit of funding) = (1 âˆ’ Ï†) Â· 1 + Ï† Â· 3 = 1 + 2Ï† (28)
The ratio of the marginal return to the second unit of funding and the marginal
return to the ï¬?rst unit of funding is therefore increasing in Ï†, in accordance with
27
the log supermodularity condition in Property 1:
y(second unit of funding) 1 + 2Ï†
= (29)
y(ï¬?rst unit of funding) 3 âˆ’ 2Ï†
Note that the log supermodularity condition holds both because the return to
the second unit funding is increasing in Ï†, and because the return to the ï¬?rst unit
of funding is decreasing in Ï†. In other words, the ratio of the marginal returns
increases with Ï† both because good projects are more likely to receive a low priority,
and because bad projects are more likely to receive a high priority.
For the general case, I am going to present two assumptions on the set of match-
ing functions {ÏƒÏ† }Ï†âˆˆÎ¦ that loosely correspond to these conditions, which guarantee
that the resulting marginal return to funding is log supermodular, consistent with
Property 1.
For this purpose, it is convenient to ï¬?x two funding priorities, p and p â‰¥ p ,
and two levels of distortions, Ï† and Ï† â‰¥ Ï† . We will be interested in comparing
the two matching functions (ÏƒÏ† and ÏƒÏ† ) in terms of the relative likelihood that
projects of certain types are assigned funding priorities p and p . Given the choices
of p, p , Ï†, and Ï† , for a measurable subset X, let D(X) be a given by:
D(X) = ÏƒÏ† (x, p)dx ÏƒÏ† (x, p )dx âˆ’ ÏƒÏ† (x, p )dx ÏƒÏ† (x, p)dx (30)
X X X X
The measure D(X) compares Ï† and Ï† in terms of the relative likelihood that
projects of types x âˆˆ X receive higher funding priority. To develop intuition,
consider for example the statement D(X) < 0. Assuming that all measures are
strictly positive, this statement holds true if and only if:
X
ÏƒÏ† (x, p )dx X
ÏƒÏ† (x, p )dx
D(X) < 0 â‡” < (31)
Ïƒ (x, p)dx
X Ï†
Ïƒ (x, p)dx
X Ï†
In words, this means that the ratio of the likelihood that projects of types
x âˆˆ X receive priority p (a high priority) and the likelihood that they receive
priority p (a low priority) is relatively smaller in less distorted economies. This
statement seems reasonable for X that is composed of relatively â€œbadâ€? projects: in
an eï¬ƒcient economy, these projects are unlikely to receive a high funding priority.
In a distorted economy, this type of mistake can happen sometimes.
28
The above suggests that a reasonable assumption is that D(X) < 0 for a set
X that is composed of â€œbadâ€? projects. Similarly, it is reasonable to assume that
for a set X composed of â€œgoodâ€? projects, D(X) > 0:
X
ÏƒÏ† (x, p )dx X
ÏƒÏ† (x, p )dx
D(X) > 0 â‡” > (32)
X
ÏƒÏ† (x, p)dx Ïƒ (x, p)dx
X Ï†
In words, good projects are relatively more likely to receive higher priority in
less distorted economies.
But what is a set of â€œgoodâ€? projects? Given the restriction to a decreasing
g(Â·), we know that projects of types x âˆˆ [0, x] are relatively better than projects
Â¯
of types x âˆˆ [Â¯, 1]. A set of the form X = [0, x] is therefore a set of relatively good
x Â¯
projects. The ï¬?rst assumption is as follows:
Assumption 1 Let X be of the form X = [0, x]. Then, D(x) â‰¥ 0.
Â¯
For the purpose of the second assumption, it is convenient to impose a partial
Â¯
ordering on the set of subsets of the form X = [x, x]: it will be said that X > X
if all elements in X are larger than all elements in X (x â‰¥ x ).
Â¯
Assumption 2 For every two segments X and X > X , D(X ) â‰¥ D(X).
This assumption loosely implies that relatively better projects are relatively
more likely to receive higher funding priority in less distorted economies. As weâ€™ve
seen above, for X composed of â€œbadâ€? projects, we are likely to see D(X) < 0,
whereas for X composed of â€œgoodâ€? projects, we are likely to see D(X) > 0. This
assumption essentially states that D(X) is monotone; if all projects x âˆˆ X are
better than all projects x âˆˆ X, then D(X ) â‰¥ D(X).
Theorem 1 Assumptions 1 and 2 imply compliance with Property 1 for any pos-
itive and decreasing g(Â·).
Assumptions 1 and 2 essentially state that distortions make it less likely for
good projects to be matched with high funding priorities, and that as we de-
crease the quality of projects they become relatively more likely to be prioritized
higher in more distorted economies. The theorem then states that when funding
29
priorities are distorted in this fashion, the average quality of projects with high
funding priorities is relatively closer to the average quality of projects with low
funding priorities. As the aggregate marginal return to funds is equal to the av-
erage productivity of projects with marginal funding priority (equation 2), this
implies compliance with Property 1.
7.1 Empirical interpretation
How plausible are Assumptions 1 and 2? In this section I present empirical evidence
that is consistent with Assumptions 1 and 2, and is hence supportive of Property
1 (by Theorem 1) .
As illustrated in the previous sections, there are many general equilibrium
implications of Property 1 that are consistent with empirical regularities. However,
there are obvious problems with testing Property 1 directly. Essentially, it would
require an exogenous source of variation in the supply of funding that does not
also aï¬€ect the productivity of funding. This is problematic, as we would expect
that periods of high productivity would imply both that the returns to funding
are higher and that the supply of funding is larger. Using the standard small
open economy trick and restricting attention on global variation in the supply of
funding is not helpful here, as it may capture variation in global productivity that
also aï¬€ects the domestic marginal return to funds.
Appendix A presents an empirical investigation of Assumptions 1 and 2. I
use the AMADEUS data set11 , that includes balance sheet data for all formal
sector ï¬?rms for several European and Eastern European countries, between the
years 1990-2011. For each ï¬?rm, I construct a measure of the marginal productivity
of funding (Ai ). In the appendix I illustrate how this measure maps into the
productivity of projects (Ag(x)).
I divide the set of countries into â€œdistortedâ€? and â€œeï¬ƒcientâ€? based on the crude
measure of GDP per capita. I choose the cutoï¬€ to be the GDP per capita in Cyprus.
After removing countries with insuï¬ƒcient data, the list of â€œeï¬ƒcientâ€? economies
includes Austria, Belgium, Finland, France, Germany, Iceland, Italy, Luxembourg,
Netherlands, Norway, Spain, Sweden and Switzerland. The list of â€œdistortedâ€?
11
The AMADEUS database (Analyze Major Databases from European Sources) is published
by Bureau van Dijk Electronic Publishing.
30
economies includes Belarus, Bosnia and Herzegovina, Bulgaria, Croatia, Czech
Republic, Estonia, Greece, Hungary, Latvia, Lithuania, Malta, Moldova, Poland,
Portugal, Romania, Russia, Serbia, Slovakia, Slovenia and the Ukraine.
Testing Assumption 1. Assumption 1 states that in less distorted economies,
productive projects are more likely to receive higher funding priorities. Of course,
funding priorities are not observable so this assumption cannot be tested directly.
However, we can get a crude measure of funding priority by calculating the extent
to which the implementation of the project depends on the aggregate supply of
funding. If a project has high priority, its implementation will depend little on
the aggregate supply of funds. Projects with lower funding priorities will be more
vulnerable to shocks to the aggregate supply of funds (unless of course they are
not implemented at all; these projects, however, will not show up in the data).
I test whether in less distorted economies, relatively more productive projects
are less sensitive to ï¬‚uctuations in the aggregate supply of funds. For each coun-
try, I divide the set of projects in each year into â€œhigh productivityâ€? and â€œlow
productivityâ€? projects, depending on whether their productivity is in the top k
percentile. Denote the set of high productivity projects by X(k).
I regress the funding of ï¬?rm i on aggregate funding, adding an interaction
term for productive projects. I then test weather the coeï¬ƒcient on the interaction
term is smaller for less distorted economies, that is, for eï¬ƒcient economies the
implementation of productive projects depends less on the aggregate supply of
funds. I consider the following speciï¬?cation:
Fi = Î²agg Fagg + Î²high,k (Fagg Â· Ï‡{i âˆˆ X(k)}) (33)
I then calibrate the empirical counterpart of D(X(k)) as:
Ë† ef f icient distorted distorted ef f icient
D(X(k)) = âˆ’Î²high,k âˆ’ (âˆ’Î²high,k ) = Î²high,k âˆ’ Î²high,k (34)
Where the superscripts indicate the coeï¬ƒcients estimated on the eï¬ƒcient and
Ë†
distorted subsamples. I then test the hypothesis D(X(k)) â‰¥ 0.
I do this exercise for k = 25%, k = 50%, and k = 75%. In all three cases, I
ï¬?nd support for the hypothesis (at least at the 5% conï¬?dence level). The results
31
are summarized in ï¬?gure 5.
Estimates of D(X) with 95% Confidence Intervals
0.6
0.5
0.4
0.3
0.2
0.1
0
X=[0,0.25] X=[0,0.5] X=[0,0.75]
max 0.4107914 0.4472499 0.5569949
min 0.2232662 0.3292569 0.4780644
point 0.3170288 0.3882534 0.5175296
Figure 5: The estimated values of D(X(k)). The ï¬?gure illustrates that the data
is consistent with the assumption that D(X) â‰¥ 0 for all X of the form X = [0, x].
Â¯
24,026,371 observations; standard errors adjusted for 392 clusters representing
country-year pairs.
Testing Assumption 2. Assumption 2 loosely states that relatively better
projects are relatively more likely to receive high funding priority in more eï¬ƒcient
economies. In similar spirit, I divide the projects in each country and each year
into 4 (disjoint) groups based on the quartile of their productivity. The quartiles
correspond to the sets of projects X1 = [0, 0.25], X2 = [0.25, 0.5], X3 = [0.5, 0.75]
and X4 = [0.75, 1].
For each quartile q = 1, ..., 4, I run the following regression:
Fi = Î²agg Fagg + Î²q (Fagg Â· Ï‡{i âˆˆ Xq }) (35)
Similarly, the empirical counterpart of D(Xq ) is given by:
Ë† distorted
D(Xq ) = Î²q ef
âˆ’ Î²q f icient (36)
32
Assumption 2 would suggest that for X < X (or q < q),
Ë† Ë†
D(X ) â‰¥ D(X) (37)
The results are summarized in ï¬?gure 6. Consistent with the hypothesis, the
Ë†
estimates D(Xq ) are weakly monotone in the sense that for q < q, the 95% conï¬?-
Ë† Ë†
dence interval of D(Xq ) either overlaps with the 95% conï¬?dence interval of D(Xq )
or is strictly above it. As we would expect, the estimate is positive for the ï¬?rst
quartile but negative for the last quartile.
Estimates of D(Xq) with 95% Confidence Intervals
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
X=[0,0.25] X=[0.25,0.5] X=[0.5,0.75] X=[0.75,1]
max 0.4107914 0.2426918 0.0686512 -0.4781197
min 0.2232662 0.15859 -0.069732 -0.5570674
point 0.3170288 0.2006409 -0.0005404 -0.5175936
Figure 6: The estimated values of D(Xq ). The ï¬?gure illustrates that the data is
consistent with D(Xq ) being weakly monotone decreasing in q. 24,026,371 obser-
vations; standard errors adjusted for 392 clusters representing country-year pairs.
7.2 Microfoundations
In this section I present diï¬€erent microfoundations of distortions that comply with
Property 1. These microfoundations are intended to illustrate both the plausibil-
ity of compliance with Property 1, and the ï¬‚exibility that Property 1 allows in
specifying the sources of distortions.
33
Incomplete information. Projectsâ€™ types are unobservable; instead, implemen-
tation decisions are made based on a signal that is correlated with the projectâ€™s
quality, s(x). There are two signals: half the projects receive the signal G (â€œgoodâ€?)
and the other half receive the signal B (â€œbadâ€?). The average quality of projects
receiving the signal G is higher than the average quality of the projects receiving
the signal B; thus, all projects with G signals will be implemented before any
projects with B signals will be implemented.
The parameter Ï† governs the noisiness of the signal. If Ï† â‰¤ Ï†, the signal Ï† is
more informative in the sense that for every x: Â¯
P rÏ† (x â‰¤ x|s(x) = G) â‰¥ P rÏ† (x â‰¤ x|s(x) = G)
Â¯ Â¯ (38)
P rÏ† (x â‰¤ x|s(x) = B) â‰¤ P rÏ† (x â‰¤ x|s(x) = B)
Â¯ Â¯ (39)
In other words, the distribution of projects that receive a good signal under
Ï† stochastically dominates the distribution of projects that receive a good signal
under Ï†; the distribution of projects that receive a bad signal under Ï† stochastically
dominates the distribution of projects that receive a bad signal under Ï† .
Lemma 2 In this model of incomplete information, Assumptions 1 and 2 are
satisï¬?ed. Hence, Property 1 is satisï¬?ed for any g(Â·).
Government intervention. The government owns a fraction Ï† of the econ-
omy: a fraction Ï† of each project is owned by the government, and the government
controls a fraction Ï† of the funds. The government distributes its funds among
government-owned projects; I assume that it does so ineï¬ƒciently, and that the
likelihood that a project receives government funding is uncorrelated with its pro-
ductivity.
The private sector eï¬ƒciently distributes its funds among privately-owned projects,
ï¬?nancing the more productive projects before allocating funds to the less produc-
tive projects. The matching function ÏƒÏ† (Â·, Â·) therefore satisï¬?es:
x x
ÏƒÏ† (z, F )dz = (1 âˆ’ Ï†) Ïƒef f (z, F )dz + Ï†x (40)
0 0
Where Ïƒef f (Â·, Â·) is deï¬?ned by equation 4. Here, the value of Ï† determines the
34
level of distortion: a higher Ï† implies that the government runs a larger part of
the economy, so more funds are being allocated randomly.
Lemma 3 In this model of government intervention, Assumptions 1 and 2 are
satisï¬?ed. Hence, Property 1 is satisï¬?ed for any g(Â·).
Collateral constraints. Consider a model in which projects are characterized
by their type, x, and by their collateral type, b. Assume that collateral types
(b) are distributed independently from the project type (x). Conditional on any
project type, collateral is uniformly distributed on [0, Ï†]. The collateral level of
the project is given by the following decreasing function:
Îº(b) = g(min{b, 1}) (41)
That is, collateral is decreasing in b, and is bounded from below by the pro-
ductivity of the least productive project.
A project with features (x, b) is implemented if and only if both its return and
its collateral level exceed the price of funding:
g(x) â‰¥ r (42)
Îº(b) â‰¥ r (43)
The mismatch between the quality of projects and their collateral changes the
order in which projects are implemented. Note that a higher Ï† implies that the
aggregate collateral is lower. It is easy to see that Ï† â†’ 0 corresponds to the
eï¬ƒcient allocation, as all projects have suï¬ƒcient collateral to be implemented
when their return is high enough. The case Ï† â†’ âˆž corresponds to an extremely
distorted economy, in which essentially all projects are collateral constrained and
can be implemented only when the market return is equal to the productivity of
the least productive project; in this case, the marginal product of funding is close
to constant, as projects are implemented essentially in a random order (as in the
previous example).
Lemma 4 Assume that g(x) = Î±xâˆ’(1âˆ’Î±) . In this model of collateral constraints,
Property 1 is satisï¬?ed.
35
Note that in this model, Property 1 is guaranteed only for the given functional
form of g(Â·). I leave the question of generality for future exploration.
Search frictions. Consider a model in which economies diï¬€er in the search
technology available to their banks. In each economy there are Ï† local banks
indexed i = 0, ..., Ï† âˆ’ 1. Projects owners are unaware of their projectâ€™s type until
right before production decisions must be made. Local banks are modeled as risk
sharing arrangements among project owners. Each local bank shares risk among
1
Ï†
project owners. The bank indexed i is a risk sharing arrangement between the
i
owners of projects indexed x âˆˆ ( Ï† , i+1 ] (for i = 0, the segment of projects is the
Ï†
1
closed set [0, Ï† ]). The process of distributing funds from households to projects is
as follows:
1. Households supply funds to a large savings bank. The savings bank has direct
access to projects (but is unaï¬ƒliated with the local banks, and is unaware
of projectsâ€™ types).
2. The savings bank distributes funds randomly among projects owners.
3. Project owners handover their funds to their local bank. When the produc-
tivity of projects is revealed, the local bank uses the funds in its hands to
implement the best set of projects among those owned by the bankâ€™s mem-
bers.
The parameter Ï† can be thought of as a measure inversely related to the inte-
gration of the domestic ï¬?nancial system. A high Ï† captures a situation in which
there are some banks with access to highly productive projects that lack liquidity
to implement them, and some banks with high liquidity without access to good
projects. The case Ï† = 1 corresponds to the eï¬ƒcient allocation: there is only one
bank in charge of allocating the entire supply of funds, and the bank has access
to the entire set of projects. The optimal set of projects is therefore implemented.
The case Ï† â†’ âˆž corresponds to the random allocation example: project owners
are essentially in autarky, as they must use their own funds to implement their
own project. The implementation of projects is therefore random, as it does not
depend on the level of productivity.
36
Lemma 5 Assume that g(x) = eâˆ’x . In this model of search frictions, Property 1
is satisï¬?ed.
Similar to the model of collateral constraints, Property 1 is guaranteed only
for a given functional form of g(Â·). Similarly, I leave the question of generality for
future exploration.
8 Conclusion
This paper studies the eï¬€ects of ï¬?nancial distortions on the global equilibrium en-
vironment. I present a reduced form formulation of ï¬?nancial distortions according
to which the marginal return to funding is log supermodular in funding and the
level of distortion. This formulation is consistent with a class of microfoundations
in which the distortion creates a mismatch between projects and funding priorities,
in a way which results in an order of implementation which is less indicative of the
relative quality of projects.
Upon ï¬?nancial integration, ï¬?nancial distortions aï¬€ect global volatility patterns
through two related channels: ï¬?rst, ï¬?nancial distortions determine the sensitivity
of output to liquidity supply. Output in emerging markets is more sensitive to
liquidity supply, because the projects implemented at the margin have high returns
compared to the projects implemented infra-marginally. Second, in the integrated
economy, the higher level of distortion in emerging markets causes them to absorb
a larger fraction of the volatility of global liquidity supply. As a result, ï¬?nancial
integration increases liquidity-driven output volatility in emerging markets, and
decreases liquidity-driven output volatility in developed markets.
In the long run, a global environment in which liquidity is cheap is conducive
to a deterioration in the ï¬?nancial system in the developed world. In the integrated
economy, a deterioration in the quality of the ï¬?nancial system has a mixed eï¬€ect
on output in developed economies: in the absence of large liquidity or TFP shocks,
it serves to increase output and to reduce output volatility. However, the response
of output to large adverse liquidity shocks is ampliï¬?ed. This oï¬€ers a modiï¬?ed view
regarding the long run eï¬€ect of ï¬?nancial integration on developed market output
volatility. As the quality of ï¬?nancial institutions adjusts downward, the economy
37
becomes less sensitive to normal ï¬‚uctuations, but more adversely aï¬€ected by large
shocks.
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A An empirical interpretation of Assumptions 1
and 2
Let ï¬?rms be indexed by i âˆˆ I. A subscript i indicates a variable belonging to ï¬?rm
i, that is, Fi is the funding allocated to ï¬?rm i, Ai is the productivity of ï¬?rm i, etc.
Variables common to all ï¬?rms within a country in a given year will be denoted
with a subscript agg. Country variables are denoted with subscript j.
Estimating Fi . I interpret F to be the cost of production. I estimate it as the
maximum of the ï¬?rmâ€™s reported cost and its reported expenses on materials and
labor.
Why should F be interpreted as the entire cost of production, and not only the
part of it paid in advance of production? In a broad sense, all inputs must be paid
in advance of production, either with a claim on future consumption backed by
the government (money) or a claim on future consumption backed by some other
agent in the economy (for example producer or bank credit). The distinction is
immaterial for our purposes, especially as the recent crisis suggests that much of
the variation in the ability to employ inputs is a result of variation in the ability
of non-government entities to generate promises for future repayment.12 Appendix
C further develops the idea that shocks to the private sectorâ€™s ability to issue
promises for future repayment is similar to a shock to the money supply.
I deï¬‚ate Fi by the GDP deï¬‚ator and subtract the output trend (calculated from
the IMFâ€™s IFS database). The decision to subtract the output trend is motivated
by the idea that the trend in productivity translates into a trend costs, which is a
result in most standard models. I also allow for a country speciï¬?c time trend in
Fi to account for any other unobservable trends.
Estimating Ai . I assume that ï¬?rms have constant returns to funding. This is
consistent with any standard Cobb-Douglas production function, where funding
reï¬‚ects the cost of labor and capital (note that this assumption is consistent with
12
There are also technical issues in identifying the component of inputs that must be paid in
advance. The common practice of using working capital is lacking, as this assumes away both
other uses of cash and other sources of cash that can be used to purchase inputs.
42
diï¬€erent ï¬?rms having diï¬€erent capital and labor intensities, as long as constant
returns to scale is satisï¬?ed).
Given this assumption, the marginal product of funding (MPF) is given by the
ratio of output to funding:
Yi
Yi = Ai Fi â‡’ Ai = (44)
Fi
I use sales data as the empirical counterpart of Y 13 .
Mapping this measure of Ai into our model requires some structure. I augment
the model to allow for ï¬?rms. I assume that there is a measurable set i âˆˆ I of
ï¬?rms, and that each ï¬?rm i owns a discrete collection of projects xi âˆˆ Xi , where it
is assumed that for any xi âˆˆ Xi :
Ag(xi ) = Ai (45)
I assume that every ï¬?rm can expand, that is, no ï¬?rm has all projects imple-
mented in full; all producing ï¬?rms are responsive to some degree to aggregate
ï¬‚uctuations.
I assume that the sample distribution of xi is similar across countries. This
assumption is obviously not realistic: we would expect that in more distorted
economies, the marginal productivity of producing ï¬?rms would be more dispersed
as in Hsieh and Klenow [2009]. However, this would create a bias against the re-
sults: for example, if the top 25% of marginal projects in distorted economies are
(relatively) more productive than the top 25% of marginal projects in developed
economies, the fact that they are relatively more responsive to aggregate ï¬‚uctua-
tions is even more striking (as eï¬ƒciency would dictate that these projects should
be even more inframarginal on average). For notational convenience, I assume that
the set of marginal projects is randomly distributed on [0, 1] - that is, I label the
top 25% of marginal projects X = [0, 0.25].
13
Of course, there are problems with this measure as it abstracts from investment in inventory;
I am thus assuming that the share of investment in inventory is independent of productivity.
Ignoring investment in inventory does not bias the result as long as sales and productivity remain
positively correlated (within the same country and the same year).
43
Estimating Fagg . A naive way of estimating Fagg would be to sum up the amount
of funding of all ï¬?rms in a given country-year pair. However, this is problematic as,
after being cleaned, the data accounts only for a fraction of all production. Further,
this fraction ï¬‚uctuates considerably across years, as evident from the large variation
in observations across time. To account for this, I create a sampling constant that
represents the fraction of output produced by ï¬?rms in the dataset, assuming that
ï¬?rms are sampled randomly. I calculate this sampling constant as the fraction of
total sales in the sample divided by GDP in current prices14 . I then calibrate the
aggregate supply of F by summing up Fi and dividing by the sampling constant.
Of course, there is a concern that for some larger ï¬?rms, this variable is endoge-
nous as by construction it is highly correlated with Fi . I therefore remove any ï¬?rm
for which Fi > 0.01Fagg .
I drop all country-year pairs that have less than 40 observations.
Testing Assumption 1. Let Ï‡e be a dummy variable indicating whether the
ï¬?rm belongs to an â€œeï¬ƒcientâ€? economy (for a list of â€œeï¬ƒcientâ€? and â€œdistortedâ€?
economies, see the description in section 7.1).
For each country for each year, I create dummy variables indicating whether
a ï¬?rm is in the top k% in terms of its productivity (relative to other ï¬?rms in
that country-year). I do this for k = 25, k = 50 and k = 75. Denote by Ï‡k the
corresponding dummies sets of productive projects.
Let cj be country dummies and let tj be time interacted with country dummies
(to allow for country-speciï¬?c trends in Fi ).
I run the following regressions:
ef f
ln(Fi ) = Î²agg ln(Fagg ) + Î²agg (ln(Fagg ) Â· Ï‡e ) + Î²agg,k (ln(Fagg ) Â· Ï‡k )+ (46)
14
GDP data is taken from the IMFâ€™s World Economic Outlook (WEO) database. Note that the
underlying assumption in this calculation is that the ratio of aggregate sales to GDP is constant
across time (within a country, up to a time trend). Recall that GDP is deï¬?ned as the the total
amount of ï¬?nal sales. Total sales diï¬€ers from GDP in that it includes also sales of intermediate
inputs. Unfortunately, as many countries do not have data on costs of intermediate inputs, it is
impossible to construct a â€?sample GDPâ€? by subtracting the costs of intermediate inputs from
ï¬?nal sales. However the assumption that the ratio of sales to GDP is constant is reasonable if
the chain of production does not ï¬‚uctuate considerably across time.
44
ef f
Î²agg,k (ln(Fagg ) Â· Ï‡k Â· Ï‡e ) + Î³j cj + Î´j tj + const
j j
ef f
I test whether Î²agg,h < 0. If so, this means that more productive projects are
relatively less sensitive to aggregate ï¬‚uctuations (i.e., implemented with higher
priority) in eï¬ƒcient economies. To map this back to the model, we can write:
Ë† ef f
D(top k-th percentile) = âˆ’Î²agg,k (47)
Ë†
The variable D is a measure of how much more likely are the top k% of projects
to receive a higher funding priority in eï¬ƒcient economies, that is, be less sensitive
to aggregate ï¬‚uctuations.
The results of the regressions are summarized in ï¬?gure 5.
Testing Assumption 2. In each country-year, I divide the set of ï¬?rms into 4
disjoint groups based on their productivity quartile. Denote by Ï‡q the indicator
variable indicating whether the ï¬?rm belongs to the q-th quartile (here q = 1 is the
top quartile and q = 4 is the bottom quartile).
I run the following regressions:
ef f
ln(Fi ) = Î²agg ln(Fagg ) + Î²agg (ln(Fagg ) Â· Ï‡e ) + Î²agg,q (ln(Fagg ) Â· Ï‡q )+ (48)
ef f
Î²agg,q (ln(Fagg ) Â· Ï‡q Â· Ï‡e ) + Î³j cj + Î´j tj + const
j j
Similarly, we can deï¬?ne:
Ë† Ë† ef f
D(q) = D(q-th quartile) = âˆ’Î²agg,q (49)
Ë† Ë†
I test the hypothesis that the series D(1), D(2), ... is weakly monotone decreas-
ing. The results are summarized in ï¬?gure 6. As illustrated by the ï¬?gure, this
hypothesis cannot be rejected at the 5% conï¬?dence level, as the conï¬?dence in-
tervals of any consecutive âˆ’Î²q are either overlapping or strictly decreasing. As
evident from the ï¬?gure, there is a clear downward trend in âˆ’Î²q .
45
B Proofs
B.1 Proof of Proposition 1
To show that Y (F, Ï†) is log supermodular, write Y (F, Ï†) as:
âˆž
Y (F, Ï†) = 1[0,F ] (n)y(n, Ï†)dn (50)
0
Where 1[0,F ] denotes the indicator function which takes a value 1 over the
interval [0, F ] (and 0 elsewhere).
Recall the deï¬?nition of log supermodularity as it appears in Costinot [2009],
which allows for 0 values:
Deï¬?nition 1 For X âŠ‚ Rw , a function h : X â†’ R+ is log supermodular if for all
z, z âˆˆ X,
h(max(z1 , z1 ), ... max(zm , zm ))h(min(z1 , z1 ), ... min(zm , zm )) â‰¥ h(z)h(z ) (51)
Claim 1 The function h(F, n, Ï†) = 1[0,F ] (n) is log supermodular in F , n, and Ï†.
To see this, note that both sides of the inequality in 51 can be either 0 or 1,
and consider the case in which the left hand side of the inequality is 0:
h(max(F, F ), max(n, n ), max(Ï†, Ï† ))h(min(F, F ), min(F, F ), min(Ï†, Ï† )) = 0
(52)
1[0,max(F,F )] (max(n, n ))1[0,min(F,F )] (min(n, n )) = 0 (53)
Assume without loss of generality that max(n, n ) = n. From the above
equality, 1[0,max(F,F )] (max(n, n )) = 0 or 1[0,min(F,F )] (min(n, n )) = 0. Assume
1[0,max(F,F )] (max(n, n )) = 0. Thus,
n > max(F, F ) â‡’ n > F â‡’ 1[0,F ] (n) = 0 â‡’ 1[0,F ] (n)1[0,F ] (n ) = 0 (54)
Assume instead that 1[0,min(F,F )] (min(x, x )) = 0. There are two cases: if
min(F, F ) = F ,
46
n > F â‡’ 1[0,F ] (n ) = 0 â‡’ 1[0,F ] (n)1[0,F ] (n ) = 0 (55)
if, instead, min(F, F ) = F , since max(n, n ) = n,
n > F â‡’ n > F â‡’ 1[0,F ] (n) = 0 â‡’ 1[0,F ] (n)1[0,F ] (n ) = 0 (56)
Thus, log supermodularity is satisï¬?ed.
The assumption that y(n, Ï†) is log supermodular in (n, Ï†) implies trivially that
it is log supermodular as a function of (F, n, Ï†).
Since the product of two log supermodular functions is log supermodular, and
the integral of a log supermodular function is log supermodular15 , it follows that
Y (F, Ï†) is log supermodular. Thus, by log supermodularity, âˆ‚ ln Y (F,Ï†) is increasing
âˆ‚F
in Ï†.
The second part of the proposition builds on the ï¬?rst part:
Y (F, Ï†)
= Y (F, Ï†)F âˆ’1 (57)
F
Since Y (F, Ï†) is log supermodular, and F âˆ’1 is trivially log supermodular, it
follows that average productivity is log supermodular as a product of two log
Y (F,Ï†)
âˆ‚ ln( F )
supermodular functions. Thus, by log supermodularity, âˆ‚F
is increasing in
Ï†. Since the derivative is negative, this implies that the sensitivity of average
productivity to the level of funding is higher in less distorted economies.
B.2 Proof of Propositions 2 and 3
1. To show that ï¬?nancial integration exacerbates volatility diï¬€erences, I begin
by showing that (at autarkic funding levels) funding is more sensitive to the
price of liquidity in emerging markets. Since output is more sensitive to
funding (Proposition 1), and since, by assumption, mean levels of funding
remain unchanged following ï¬?nancial integration, the proposition follows.
In equilibrium, the marginal return to funding is equal to its market price r:
Ay(F, Ï†) = r (58)
15
For proof see Karlin and Rinott [1980].
47
It follows that the derivative of F with respect to r is:
âˆ‚F 1 1
= âˆ‚r = âˆ‚Ay(F,Ï†)
(59)
âˆ‚r âˆ‚F âˆ‚F
y(F,Ï†)
Recall that if y(F, Ï†) is log supermodular, âˆ‚ lnâˆ‚F is increasing in Ï† (see, for
example, Costinot [2009]). Property 1 therefore implies that:
âˆ‚Aem y(F,Ï†em ) âˆ‚y(F,Ï†em ) âˆ‚y(F,Ï†d ) âˆ‚Ad y(F,Ï†d )
âˆ‚F âˆ‚F âˆ‚F âˆ‚F
= > = (60)
Aem y(F, Ï†em ) y(F, Ï†em ) y(F, Ï†d ) Ad y(F, Ï†d )
Since equilibrium requires that Aem y(F, Ï†em ) = Ad y(F, Ï†d ) = r, it follows
that
âˆ‚Aem y(F, Ï†em ) âˆ‚Ad y(F, Ï†d )
> (61)
âˆ‚F âˆ‚F
It follows that:
âˆ‚Fd 1 1 âˆ‚Fem
= âˆ‚Ad y(F,Ï†d )
> âˆ‚Aem y(F,Ï†em )
= (62)
âˆ‚r âˆ‚r
âˆ‚F âˆ‚F
Since the response of F to r is negative, it follows that Fem is more sensitive to
changes in r. By construction, Fem and Fd are similarly aï¬€ected by shocks to
relative productivity (which cause a substitution between Fd and Fem ). Thus,
since these are the only two sources of variation in F , under the assumption
that Qi = Fia are identically distributed,
a a
var(ln Fem ) âˆ’ var(ln Fd ) > var(ln Fem ) âˆ’ var(ln Fd ) = 0 (63)
To see that ï¬?nancial integration exacerbates the diï¬€erence in output volatil-
ity, note that:
âˆ‚ ln Y
var(ln Y ) = var(ln F ) + var(ln A) (64)
âˆ‚ ln F
Decompose volatility in F into volatility conditional on Q shocks and volatil-
48
ity conditional on relative TFP shocks:
var(ln F ) = var(ln F |Q) + var(ln F |A) (65)
var(ln Yem ) âˆ’ var(ln Yd ) âˆ’ (var(ln Aem ) âˆ’ var(ln Ad )) = (66)
âˆ‚ ln Yem âˆ‚ ln Yd
(var(ln Fem |Q)+var(ln Fem |A))âˆ’ (var(ln Fd |Q)+var(ln Fd |A))
âˆ‚ ln F âˆ‚ ln F
(67)
âˆ‚ ln Yem âˆ‚ ln Yd
= var(ln Fem |A) âˆ’ var(ln Fd |A)+ (68)
âˆ‚ ln F âˆ‚ ln F
âˆ‚ ln Yem âˆ‚ ln Yd
var(ln F |Q)( âˆ’ ) (69)
âˆ‚ ln F âˆ‚ ln F
Since the last term is positive, we have that:
var(ln Yem ) âˆ’ var(ln Yd ) âˆ’ (var(ln Aem ) âˆ’ var(ln Ad ))
âˆ‚ ln Yem âˆ‚ ln Yd
> var(ln Fem |A) âˆ’ var(ln Fd |A) (70)
âˆ‚ ln F âˆ‚ ln F
The following lemma will be useful to conclude the proof:
a
Lemma 6 (a) var(ln Fem |A) > var(ln Fem )
a
(b) var(ln Fd |A) < var(ln Fd )
Proof: To see this, consider a benchmark in which economy i integrates
with an economy with an identical sensitivity to r shocks. In this
hypothetical case, shocks to domestic and foreign liquidity supply adjust
equally between the two countries. Using the assumption that Qi are
perfectly correlated, it follows that:
1 1
var(Fi ) = var( (Qi + Qj )) = (var(2Qi )) = var(Qi ) = var(Fia ) (71)
2 4
The lemma above is proved using comparative statics with this bench-
mark. Since shocks to liquidity supply have a greater eï¬€ect on emerging
markets, the volatility of var(Fem ) is greater than this benchmark, and
49
since shocks to liquidity supply have a smaller eï¬€ect on developed mar-
kets, the volatility of var(Fd ) is lower than this benchmark. As mean
liquidity levels stay the same, the lemma (as stated in logs) immediately
follows.
Using the above lemma, the expression in equation 70 is greater than the
expression below, in which var(ln Fi |A) are replaced with autarkic values:
âˆ‚ ln Yem a âˆ‚ ln Yd a
(70) > var(ln Fem ) âˆ’ var(ln Fd ) (72)
âˆ‚ ln F âˆ‚ ln F
a
= var(ln Yem ) âˆ’ var(ln Yda ) âˆ’ (var(ln Aem ) âˆ’ var(ln Ad )) (73)
a
â‡’ var(ln Yem ) âˆ’ var(ln Yd ) > var(ln Yem ) âˆ’ var(ln Yda ) (74)
Which concludes the proof.
2. (a) To see that ï¬?nancial integration increases volatility of funding in the
a
emerging market region, note that both var(Fem |A) > var(Fem |A) =
a
0, and var(Fem |Q) > var(Fem |Q). To see that ï¬?nancial integration
increases the volatility of output in the emerging market region, note
that since var(A) remains the same, and since the level F is unchanged,
from equation 64 output volatility increases as well.
(b) The eï¬€ect of ï¬?nancial integration on var(Fd ) is ambiguous: the volatility
of Fd conditional on holding technology levels constant is smaller, so
a
var(Fd |A) < var(Fd |A). However, through the standard RBC channel,
a
var(Fd |Q) > var(Fd |Q) = 0. If shocks to relative TFP are suï¬ƒciently
a
small, the ï¬?rst eï¬€ect dominates so var(Fd ) < var(Fd ). In this case, from
equation 64 (and the assumption that the mean level of F is unchanged),
it follows that output volatility decreases as well.
B.3 Proof of Proposition 4
The following lemma will be useful in various proofs:
50
Lemma 7 For every F and Ï† â‰¤ Ï†,
Y (F, Ï† ) â‰¥ Y (F, Ï†) (75)
To prove this lemma, let Ï† > Ï† and consider the function:
Y (F, Ï† ) âˆ’ Y (F, Ï†) (76)
Recall that this function is 0 for F = 0 and for F = 1. Taking a ï¬?rst order
condition yields:
y(F, Ï† ) âˆ’ y(F, Ï†) = 0 (77)
This point is a local maximum, as the second derivative is negative by Property 1.
To see this, using equation 77:
âˆ‚y(F,Ï† )
âˆ‚F
âˆ’ âˆ‚y(F,Ï†)
âˆ‚F
âˆ‚y(F,Ï† ) âˆ‚y(F,Ï†)
âˆ‚ ln y(F, Ï† ) âˆ‚ ln y(F, Ï†)
= âˆ‚F âˆ’ âˆ‚F = âˆ’ <0 (78)
y(F, Ï†) y(F, Ï† ) y(F, Ï†) âˆ‚F âˆ‚F
The inequality stems from Property 1.
Thus, the function reaches a maximum at the point y(F, Ï† ) = y(F, Ï†). The
minima or this function are therefore at F = 0 and F = 1, at which the function
takes the value of 0. It follows that the function is always weakly greater than 0:
Y (F, Ï† ) âˆ’ Y (F, Ï†) â‰¥ 0 (79)
Which concludes the proof.
Lemma 8 Consider the problem:
F
max y(F , Ï†)dF âˆ’ Î»(Ï†) (80)
Ï† 0
Ëœ
The solution Ï†âˆ— is increasing in F for some range F âˆˆ (F , 1].
Using the proof of Lemma 7, for each pair Ï†i > Ï†j there is a point 0 < Fi,j < 1
such that Y (F, Ï†) has increasing diï¬€erences for F > Fi,j and Ï† âˆˆ {Ï†i , Ï†j }. Let
Ëœ Ëœ
F denote the maximum of these Fi,j . In the region (F , 1], there are increasing
51
diï¬€erences for all Ï† within the set of possible values. By Sundaram (1996), Ï†âˆ— is
increasing in F on that region.
Note that, for any r, Ï†âˆ— is the solution to:
F
max y(F , Ï†)dF âˆ’ Î»(Ï†) âˆ’ rF (81)
Ï† 0
This is because rF is a constant in this problem.
Recall the assumption that E(Qd ) = E(Qem ) = Q. Now, assume that Q âˆˆ
Ëœ Ad
(F , 1]. In this range, a drop in r is associated with an increase in F âˆ— . If Aem is
suï¬ƒciently small, integration will be associated with a drop in r from the developed
marketâ€™s perspective. It follows that Ï†âˆ— increases.
B.4 Proof of Proposition 5
For what follows, denote by Ï†w the level of distortions in the deteriorated â€œweakâ€?
d
i
ï¬?nancial system, and by Ï†d the autarkic â€œintactâ€? level of ï¬?nancial distortions.
Normalize Î»(Ï†w ) = 0 and Î»(Ï†i ) = Î».
d d
I begin with the ï¬?rst part of the proposition. By equations 77 and 78, there is
a unique point F0 âˆˆ (0, 1) such that:
yd (F0 , Ï†i ) = yd (F0 , Ï†w )
d d (82)
For every F < F0 , y(F, Ï†i ) > y(F, Ï†w ) and for every F > F0 , y(F, Ï†i ) < y(F, Ï†w ).
d d d d
Recall that in this setup, prior to ï¬?nancial integration the ï¬?nancial system in
the developed world was endogenously intact, and it endogenously deteriorated
following a drop in r. It turns out that these dynamics are possible only if r is
such that funding levels exceed F0 (when the ï¬?nancial system is intact and the
economy is integrated):
Lemma 9 There is an endogenous weakening of the ï¬?nancial system (in the de-
veloped world) only if r â‰¤ y(F0 , Ï†i ) = y(F0 , Ï†w ).
d d
Here, r denotes the rate of return on funding when the ï¬?nancial system in the
developed world is intact.
52
Proof: Assume r > y(F0 , Ï†i ), and it will be shown that in this case there is no
d
endogenous ï¬?nancial deterioration. Denote by ra the return to funding under
autarky in the developed world. We know that given ra , the optimal choice
of ï¬?nancial quality is Ï†d = Ï†i :
d
Ï€(ra , Ï†i ) > Ï€(ra , Ï†w )
d d (83)
F F
â‡’ max y(F , Ï†i )dF âˆ’ ra F âˆ’ Î» > max
d y(F , Ï†w )dF âˆ’ ra F
d (84)
F 0 F 0
The standard optimality condition is y(F, Ï†d ) = ra . Denote this F by
F âˆ— (r, Ï†d ).
Thus, the inequality in equation 84 can be rewritten as:
âˆž
(y(F âˆ— (r , Ï†i ), Ï†i ) âˆ’ y(F âˆ— (r , Ï†w ), Ï†w ))dr > Î»
d d d d (85)
ra
From the assumption that r > y(F0 , Ï†i ), it follows that ra > y(F0 , Ï†d ),
d
a
because r > r (there is a drop in r upon ï¬?nancial integration). For r >
y(F0 , Ï†i ), it is also the case that:
d
F âˆ— (r, Ï†i ) > F âˆ— (r, Ï†w )
d d (86)
This is because, since F âˆ— (r, Ï†i ) < F0 ,
d
y(F âˆ— (r, Ï†i ), Ï†w ) < y(F âˆ— (r, Ï†i ), Ï†i )
d d d d (87)
Thus, since y is decreasing in F , the inequality in equation 86 holds true.
Note that equation 87 holds for any y(F0 , Ï†d ) < r < ra . Thus,
F âˆ— (r,Ï†i )
d F âˆ— (r,Ï†w )
d
âˆ—
y(F , Ï†i )dF
d âˆ’ rF (r, Ï†i )
d âˆ’ y(F , Ï†w )dF âˆ’ rF âˆ— (r, Ï†w ) =
d d
0 0
(88)
âˆž âˆž
y(F âˆ— (r , Ï†i ), Ï†i )dr âˆ’
d d y(F âˆ— (r , Ï†w ), Ï†w )dr =
d (89)
r r
âˆž
(y(F âˆ— (r , Ï†i ), Ï†i ) âˆ’ y(F âˆ— (r , Ï†w ), Ï†w ))dr +
d d d d (90)
ra
53
ra
(y(F âˆ— (r , Ï†i ), Ï†i ) âˆ’ y(F âˆ— (r , Ï†w ), Ï†w ))dr
d d d d (91)
r
By equation 85, the ï¬?rst term is greater than Î». The second term is positive
by equation 87. Thus, the sum above is greater than Î». It follows that
choosing Ï†d = Ï†i is still preferable to choosing Ï†d = Ï†w . I conclude that an
d d
endogenous ï¬?nancial deterioration is not possible if r > y(F0 , Ï†i ).
d
To conclude the proof, note that for r < y(F0 , Ï†i ),
d
F âˆ— (r, Ï†i ) < F âˆ— (r, Ï†w )
d d (92)
Thus, the deterioration in the quality of the ï¬?nancial system is associated with
an increase in F .
Ad
To see the second part of the proposition, note that for Aem suï¬ƒciently large,
yd (1, Ï†w ) > yem (1, Ï†em )
d (93)
From continuity, there exists > 0 such that for every 1 âˆ’ < F < 1,
yd (1, Ï†w ) > yem (F, Ï†em )
d (94)
It follows that for Qw > 2 âˆ’ , the developed market will be satiated with
funding. Output is weakly higher than in the intact case (note that the conditions
under which the weakened ï¬?nancial system is satiated with funding are weaker than
the conditions under which the intact economy is satiated with funding, because,
since F0 < 1, yd (1, Ï†w ) > yd (1, Ï†i )). Under satiation, the developed economy is
d d
stable with respect to small shocks to the global supply of funding, as the economy
remains satiated as long as Qw satisï¬?es:
yd (1, Ï†w ) > yem (Qw âˆ’ 1, Ï†em )
d (95)
Similarly, the level of funding is unaï¬€ected by shocks to relative TFP. The volatility
of output is therefore smaller both with respect to liquidity supply shocks and with
respect to shocks to relative TFP.
54
B.5 Proof of Lemma 1
Recall the notation from the proof of Proposition 5: Ï†w denotes the level of dis-
d
tortions in the deteriorated â€œweakâ€? ï¬?nancial system, and Ï†i denotes the autarkic
d
â€œintactâ€? level of ï¬?nancial distortions.
Given Ï†d , world output maximization solves:
Yw (Ï†d ) = max Yw (Ï†d , Fd , Fem ) = (96)
Fd ,Fem
Fd Fem
max Ad y(F , Ï†d )dF + Aem y(F , Ï†em )dF (97)
Fd ,Fem 0 0
s.t.
Fd + Fem = Qw (98)
Fi â‰¤ 1 (99)
Under autarky there is an additional constraint which is:
Fi = Qi (100)
It is easy to see that for any given couple (Fd , Fem ) which satisfy constraints 98-99
or 98-100, the output produced is higher when the ï¬?nancial system in the developed
market is intact:
Yw (Ï†i , Fd , Fem ) â‰¥ Yw (Ï†w , Fd , Fem )
d d (101)
âˆ— âˆ—
Denote by (Fd (Ï†d ), Fem (Ï†d )) the optimal allocation of funding given Ï†d . From the
optimality of Fiâˆ— (Ï†i ):
d
âˆ— âˆ— âˆ— âˆ—
Yw (Ï†i ) = Yw (Ï†i , Fd (Ï†i ), Fem (Ï†i )) â‰¥ Yw (Ï†i , Fd (Ï†w ), Fem (Ï†w ))
d d d d d d d (102)
And, from equation 101:
âˆ— âˆ— âˆ— âˆ—
Yw (Ï†i , Fd (Ï†w ), Fem (Ï†w )) â‰¥ Yw (Ï†w , Fd (Ï†w ), Fem (Ï†w )) = Yw (Ï†w )
d d d d d d d (103)
It follows that world output is higher when the ï¬?nancial system in the developed
55
market is intact:
â‡’ Yw (Ï†i ) â‰¥ Yw (Ï†w )
d d (104)
B.6 Proof of Proposition 6
Recall the notation from the proof of Proposition 5: Ï†w denotes the level of dis-
d
tortions in the deteriorated â€œweakâ€? ï¬?nancial system, and Ï†i denotes the autarkic
d
â€œintactâ€? level of ï¬?nancial distortions.
Let F0 be given by the condition in equation 77:
y(F0 , Ï†i ) = y(F0 , Ï†w )
d d (105)
Consider a shock to the global supply of liquidity such that Qw < F0 . In this
range, the marginal product of funding in the developed world is higher under
intact ï¬?nancial institutions. It follows that funding is higher:
âˆ— âˆ—
Fd (Qw , Ï†i ) > Fd (Qw , Ï†w )
d d (106)
Since output decreases with the level of distortion by Lemma 7,
âˆ— âˆ—
Yd (Fd (Qw , Ï†i ), Ï†i ) > Yd (Fd (Qw , Ï†i ), Ï†w )
d d d d (107)
Since output is increasing in the level of funding,
âˆ— âˆ—
Yd (Fd (Qw , Ï†i ), Ï†w ) > Yd (Fd (Qw , Ï†w ), Ï†w )
d d d d (108)
It follows that output is higher under intact ï¬?nancial institutions:
âˆ— âˆ—
Yd (Fd (Qw , Ï†i ), Ï†i ) > Yd (Fd (Qw , Ï†w ), Ï†w )
d d d d (109)
âˆ—
Similarly, a shock to relative TFP such that Fd (Qw , Ï†i ) < F0 is ampliï¬?ed by
d
lack of high quality ï¬?nancial institutions.
56
B.7 Proof of Theorem 1
As g(Â·) is positive and decreasing, it can be arbitrarily well approximated by a sum
of the form: n
g(x) = gi Ï‡[0,xi ] (x) (110)
i=0
Where Ï‡[0,xi ] (x) = 1 if x âˆˆ [0, xi ] and Ï‡[0,xi ] (x) = 0 otherwise. For convenience,
denote: xi
i
ÏƒÏ† (F ) = ÏƒÏ† (x, F )dx (111)
0
Note that: n
1
i
y(F, Ï†) = ÏƒÏ† (x, F )g(x)dx = ÏƒÏ† (F )gi (112)
0 i=1
Let Ï† â‰¥ Ï† and F â‰¥ F . To satisfy Property 1, I need to show that:
y(F, Ï†)y(F , Ï† ) âˆ’ y(F , Ï†)y(F, Ï† ) â‰¥ 0 (113)
Using the expression above, this can be rewritten as:
n n n n
i i i i
( ÏƒÏ† (F )gi )( ÏƒÏ† (F )gi ) âˆ’ (( ÏƒÏ† (F )gi ))( ÏƒÏ† (F )gi ) â‰¥ 0 (114)
i=1 i=1 i=1 i=1
The above righthand side is a some of expressions of the form:
i j j i i j j i
gi gj (ÏƒÏ† (F )ÏƒÏ† (F ) + ÏƒÏ† (F )ÏƒÏ† (F ) âˆ’ ÏƒÏ† (F )ÏƒÏ† (F ) âˆ’ ÏƒÏ† (F )ÏƒÏ† (F ))
I argue that each of these expressions is non-negative, implying the non-negativity
of the sum. To see this, assume by way of contradiction that for some i and i â‰¤ j,
the above expression is negative. Thus, neither gi nor gj can be 0; thus, they are
strictly positive, so dividing through by gi and gj we get:
i j j i i j j i
ÏƒÏ† (F )ÏƒÏ† (F ) + ÏƒÏ† (F )ÏƒÏ† (F ) âˆ’ ÏƒÏ† (F )ÏƒÏ† (F ) âˆ’ ÏƒÏ† (F )ÏƒÏ† (F ) < 0 (115)
57
Note that:
i j j i
ÏƒÏ† (F )ÏƒÏ† (F ) + ÏƒÏ† (F )ÏƒÏ† (F ) =
xj xj
i i j j
ÏƒÏ† (F )ÏƒÏ† (F ) + ÏƒÏ† (F )ÏƒÏ† (F ) + ÏƒÏ† (x, F )dx ÏƒÏ† (x, F )dx
xi xi
Let Xi = [0, xi ], Xj = [0, xj ] and Xi,j = [xi , xj ]. Using the above, the inequality
in equation B.7 can be rewritten as:
D(Xi ) + D(Xj ) âˆ’ D(Xi,j ) < 0 (116)
This implies that:
D(Xj ) < D(Xi,j ) âˆ’ D(Xi ) (117)
This is a contradiction, as by Assumption 1 the left hand side is greater than 0,
and by Assumption 2 the right hand side is less than 0.
B.8 Proof of Lemma 2
Note that, for F â‰¤ 0.5:
x
ÏƒÏ† (z, F )dz = P rÏ† (z â‰¤ x|s(z) = G) (118)
0
And for F > 0.5:
x
ÏƒÏ† (z, F )dz = P rÏ† (z â‰¤ x|s(z) = B) (119)
0
Assumptions 1 and 2 hold trivially if both F, F â‰¤ 0.5 or F, F > 0.5. It is left to
show that Assumptions 1 and 2 hold for F â‰¤ 0.5 and F > 0.5.
From the proof of Theorem 1, it is suï¬ƒcient to show that for any x and x :
x x x x
ÏƒÏ† (z, F )dz ÏƒÏ† (z, F )dz + ÏƒÏ† (z, F )dz ÏƒÏ† (z, F )dzâˆ’
0 0 0 0
x x x x
ÏƒÏ† (z, F )dz ÏƒÏ† (z, F )dz âˆ’ ÏƒÏ† (z, F )dz ÏƒÏ† (z, F )dz â‰¥ 0
0 0 0 0
58
Rewriting,
P rÏ† (z â‰¤ x|s(z) = B)P rÏ† (z â‰¤ x |s(z) = G)+P rÏ† (z â‰¤ x |s(z) = B)P rÏ† (z â‰¤ x|s(z) = G) â‰¥
P rÏ† (z â‰¤ x|s(z) = G)P rÏ† (z â‰¤ x |s(z) = B)+P rÏ† (z â‰¤ x |s(z) = G)P rÏ† (z â‰¤ x|s(z) = B)
This inequality holds, as:
P rÏ† (z â‰¤ x|s(z) = B)P rÏ† (z â‰¤ x |s(z) = G) â‰¥ P rÏ† (z â‰¤ x |s(z) = G)P rÏ† (z â‰¤ x|s(z) = B)
And
P rÏ† (z â‰¤ x |s(z) = B)P rÏ† (z â‰¤ x|s(z) = G) â‰¥ P rÏ† (z â‰¤ x|s(z) = G)P rÏ† (z â‰¤ x |s(z) = B)
This is the case because P rÏ† (z â‰¤ x|s(z) = B) â‰¥ P rÏ† (z â‰¤ x|s(z) = B) and
P rÏ† (z â‰¤ x|s(z) = G) â‰¥ P rÏ† (z â‰¤ x|s(z) = G) (both for x and x ).
B.9 Proof of Lemma 3
x
To simplify notation, I write Î¸(x, F ) = 0 Ïƒef f (z, F )dz. In this model, it is easy
to see that Assumptions 1 and 2 are satisï¬?ed if for any Ï† â‰¤ Ï†, F â‰¤ F , x and x :
((1 âˆ’ Ï† )Î¸(x , F ) + Ï† x )((1 âˆ’ Ï†)Î¸(x, F ) + Ï†x)+ (120)
((1 âˆ’ Ï† )Î¸(x, F ) + Ï† x)((1 âˆ’ Ï†)Î¸(x , F ) + Ï†x ) â‰¥
((1 âˆ’ Ï† )Î¸(x , F ) + Ï† x )((1 âˆ’ Ï†)Î¸(x, F ) + Ï†x)+
((1 âˆ’ Ï† )Î¸(x, F ) + Ï† x)((1 âˆ’ Ï†)Î¸(x , F ) + Ï†x )
Rewriting the condition:
(1 âˆ’ Ï† )(1 âˆ’ Ï†)Î¸(x , F )Î¸(x, F ) + Ï†x(1 âˆ’ Ï† )Î¸(x , F ) + Ï† x (1 âˆ’ Ï†)Î¸(x, F ) + Ï†Ï† xx +
(1 âˆ’ Ï† )(1 âˆ’ Ï†)Î¸(x, F )Î¸(x , F ) + Ï†x (1 âˆ’ Ï† )Î¸(x, F ) + Ï† x(1 âˆ’ Ï†)Î¸(x , F ) + Ï†Ï† xx â‰¥
(1 âˆ’ Ï† )(1 âˆ’ Ï†)Î¸(x , F )Î¸(x, F ) + Ï†x(1 âˆ’ Ï† )Î¸(x , F ) + Ï† x (1 âˆ’ Ï†)Î¸(x, F ) + Ï†Ï† xx +
59
(1 âˆ’ Ï† )(1 âˆ’ Ï†)Î¸(x, F )Î¸(x , F ) + Ï†x (1 âˆ’ Ï† )Î¸(x, F ) + Ï† x(1 âˆ’ Ï†)Î¸(x , F ) + Ï†Ï† xx
This condition simpliï¬?es to:
Ï†x(1 âˆ’ Ï† )Î¸(x , F ) + Ï† x (1 âˆ’ Ï†)Î¸(x, F ) + Ï†x (1 âˆ’ Ï† )Î¸(x, F ) + Ï† x(1 âˆ’ Ï†)Î¸(x , F ) â‰¥
Ï†x(1 âˆ’ Ï† )Î¸(x , F ) + Ï† x (1 âˆ’ Ï†)Î¸(x, F ) + Ï†x (1 âˆ’ Ï† )Î¸(x, F ) + Ï† x(1 âˆ’ Ï†)Î¸(x , F )
Or:
Ï†(1 âˆ’ Ï† )(xÎ¸(x , F ) + x Î¸(x, F )) + Ï† (1 âˆ’ Ï†)(x Î¸(x, F ) + xÎ¸(x , F )) â‰¥
Ï†(1 âˆ’ Ï† )(xÎ¸(x , F ) + x Î¸(x, F )) + Ï† (1 âˆ’ Ï†)(x Î¸(x, F ) + xÎ¸(x , F ))
Rearranging:
Ï†(1 âˆ’ Ï† )(x (Î¸(x, F ) âˆ’ Î¸(x, F )) + x(Î¸(x , F ) âˆ’ Î¸(x , F ))) â‰¥
Ï† (1 âˆ’ Ï†)(x (Î¸(x, F ) âˆ’ Î¸(x, F )) + x(Î¸(x , F ) âˆ’ Î¸(x , F )))
Note that, as Î¸(x, F ) â‰¥ Î¸(x, F ) for all x,
x (Î¸(x, F ) âˆ’ Î¸(x, F )) + x(Î¸(x , F ) âˆ’ Î¸(x , F )) â‰¥ 0 (121)
Thus, the inequality is satisï¬?ed if and only if:
Ï†(1 âˆ’ Ï† ) â‰¥ Ï† (1 âˆ’ Ï†) (122)
Which holds true as Ï† â‰¥ Ï† .
B.10 Proof of Lemma 4
Begin by considering the case Ï† â‰¤ 1. First, note that for every F , there is a
Ëœ Ëœ
threshold F such that project (x, b) is implemented if and only if x â‰¤ F and
Ëœ Ëœ
b â‰¤ F . For F < Ï†,
âˆš
Ëœ Ëœ Ëœ 1Ëœ 1Ëœ Ëœ
F = P r(x â‰¤ F , b â‰¤ F ) = F Â· F = F 2 â‡’ F = Ï† F (123)
Ï† Ï†
60
Ëœ Ëœ
Note that F < Ï† if and only if F < Ï†. For F > Ï†, it is easy to see that F = F .
For F < Ï†, output is given by the following expression:
Ëœ
F Ëœ
F
Ëœ Ëœ 1Ëœ A Ëœ 1+Î±
Y (F ) = P r(b â‰¤ F )Ag(x)dx = F Ag(x)dx = F (124)
0 Ï† 0 Ï†
It follows that, for F < Ï†:
Î±âˆ’1 1+Î±
Y (F, Ï†) = AÏ† 2 F 2 (125)
The derivative of Y with respect to F is therefore given by:
1+Î± Î±âˆ’1 Î±âˆ’1
y(F, Ï†) = AÏ† 2 F 2 (126)
2
1+Î± 1âˆ’Î± 1âˆ’Î±
â‡’ ln y(F, Ï†) = ln( A) âˆ’ ln Ï† âˆ’ ln F (127)
2 2 2
The derivative of above with respect to F is:
âˆ‚ ln y(F, Ï†) 1âˆ’Î±
=âˆ’ (128)
âˆ‚F 2F
The above does not depend on Ï† as long as F < Ï†; the log supermodularity
condition is trivially satisï¬?ed. However, Note that for a higher Ï†, there are more
values of F such that F < Ï†. Let there be Ï† and Ï† such that Ï† < F < Ï†. For Ï† , it
is easy to see that the derivative of ln y(F, Ï† ) is given by the following expression:
y(F, Ï† ) = AÎ±F âˆ’(1âˆ’Î±) â‡’ ln y(F, Ï† ) = ln(AÎ±) âˆ’ (1 âˆ’ Î±) ln F (129)
âˆ‚ ln y(F, Ï† ) 1âˆ’Î± 1âˆ’Î± âˆ‚ ln y(F, Ï†)
â‡’ =âˆ’ <âˆ’ = (130)
âˆ‚F F 2F âˆ‚F
Thus, the derivative of ln y with respect to F is higher in the more distorted
economy Ï†, consistent withProperty 1.
Ëœ
Consider now the range Ï† â‰¥ 1. In this range, for F < 1, F is given by equation
âˆ‚ ln y
123, output is given by equation 124 and âˆ‚F is given by equation 128. In this
ln
range, âˆ‚âˆ‚F y is constant with respect to Ï†, so the log supermodular condition is
trivially satisï¬?ed.
âˆš
Ëœ 1
Note that F < 1 if and only if Ï†F < 1, or F < Ï† . This condition is violated
61
1
for more values of F if Ï† is larger. For F > Ï† , the marginal product of funding is
constant; the collateral constraint is binding for all implemented projects, so the
productivity of the projects implemented with each unit of funding is the same.
1
Thus, in the range F > Ï† ,
âˆ‚ ln y(F, Ï†) 1âˆ’Î±
=0>âˆ’ (131)
âˆ‚F 2F
1
The right hand side is equal to the derivative of ln y for the case F < Ï† . It follows
1 1
that the log supermodularity condition is satisï¬?ed for Ï† < F < Ï† .
B.11 Proof of Lemma 5
Output is given by the following expression:
Ï† i
+F
Ï† Ï†
Y (F, Ï†) = Ag(x)dx (132)
i
i=0 Ï†
This is because each local bank has F units of liquidity to allocate, and uses it to
Ï†
implement the ï¬?rst F in the sample of projects available to it.
Ï†
The marginal product of funding is given by:
Ï† Ï†
1 i F A i F
y(F, Ï†) = Ag( + ) = eâˆ’( Ï† + Ï† ) (133)
Ï† i=0
Ï† Ï† Ï† i=0
F Ï†
Aeâˆ’ Ï† i
= eâˆ’ Ï† (134)
Ï† i=0
It follows that:
Ï†
A i F F
ln y(F, Ï†) = ln( eâˆ’ Ï† ) + ln eâˆ’ Ï† = c âˆ’ (135)
Ï† i=0
Ï†
1
The derivative of above with respect to F is âˆ’ Ï† , which is increasing in Ï†. The log
supermodularity condition is satisï¬?ed, in accordance with Property 1.
62
C A monetary model of liquidity supply
In this section, I develop a model of liquidity supply, in which liquidity supply ï¬‚uc-
tuations are caused by three primitive shocks: shocks to the money supply, shocks
to consumersâ€™ risk aversion16 and shocks to the private sectorâ€™s ability to generate
promises for future repayment. Recall that the model makes three assumptions
about the distribution of liquidity supply:
1. The distribution of liquidity supply is unchanged by ï¬?nancial integration.
2. Liquidity supply is independent from both domestic and foreign productivity,
Ai .
3. Liquidity supply is perfectly correlated across regions.
Consider a model in which labor (denoted L) is the only productive input.
Given Li hired units of labor, output in country i is given by:
Yi = Ai fi (Li ) (136)
In this model, liquidity is money used to hire labor; thus, in this formulation,
fi already captures the eï¬ƒciency of the ï¬?nancial system in allocating liquidity (in
other words, f is log supermodular in L and Ï†).
Assumption 3 1. The price of a unit of labor in terms of money, w, is deter-
mined at the beginning of the period, before all shocks are realized. Agents
agree to supply any amount of labor for the wage w.
2. The price of output is ï¬?xed within a period, and is normalized to one.
Agents live for one period and consume at the end of their lives. The preferences
of agents in region i are given by:
E(ui (ci ) âˆ’ vi (Li )) (137)
16
The analysis of Broner et al. [Forthcoming] suggests that shocks to the risk aversion of inter-
national investors is indeed an important driving source of supply driven volatility in emerging
markets.
63
I assume that ui (ci ) takes the following stark form:
ci if c â‰¥ c0,i ;
ui (ci ) = (138)
âˆ’âˆž otherwise.
In this formulation, c0,i captures the level of risk aversion of households in
region i. To see this, consider the comparison between two agents, one denoted h
with c0,h = c0,h and one denoted l with c0,l < c0,h .
Deï¬?nition 2 Agent h is more risk averse than agent l if the following condition
holds: for any certain consumption payment c, and any lottery q, if agent h prefers
q over c then so does agent l.
To see that, according to this standard deï¬?nition, the condition c0,h > c0,l
implies that agent h is more risk averse than agent l, note the following claim:
Claim 2 Agent i prefers a lottery q over a certainty payment of c if and only if
the lottery q never delivers a payment of less than c0,i , and E(q) > c.
Proof: Trivially, if the above condition holds, the agent will prefer the lottery: if
c > c0,i he is risk neutral between the two lotteries, and if c â‰¤ c0,i his utility
from consuming c is âˆ’âˆž whereas it is positive given the lottery. If the above
condition is violated, it means that one of the following holds: either E(q)
delivers a payment of less than c0,i with positive probability, or E(q) < c. If
E(q) delivers a payment of less than c0,i with positive probability, then the
agentâ€™s expected utility from the lottery is âˆ’âˆž, so it is not preferred over
anything. If E(q) < c, but q always delivers a payment of more than c0,i ,
then it follows that c > c0,i , so the agent is risk neutral with respect to q and
c and would prefer c.
Using this claim, it is easy to see that h is more risk averse than l, as the fact
that q never delivers a payment of less than c0,h implies that it never delivers a
payment of less than c0,l < c0,h , so the set of lotteries and certainty payments in
which h prefers the lottery is included in the set of lotteries and certainty payments
in which l prefers the lottery.
Thus, we will think of c0 as the level of risk aversion of the agents.
Corollary 2 A higher level of c0,i implies a higher level of risk aversion.
64
C.1 Liquidity supply in the closed economy
After wages are agreed upon and prices are set, the money supply, Mi , and the
level of risk aversion, c0,i , are realized. Agents can choose to hold their money in
a safe (Mh,i ) or buy stocks in the productive sector (Qi ):
Mi = Qi + Mh,i (139)
The level of Qi is also the level of liquidity supply which can be used to hire
workers. After the productivity shock Ai is realized, the ï¬?nancial system allocates
the liquidity Qi to domestic projects who use it to hire workers:
Qi = wi Li (140)
After production takes place but before workers are paid, there is a shock to
the ability of the productive sector to make monetary transfers. With probability
(1 âˆ’ Î¸), this ability is intact; in this case, wages are paid and two rounds of
consumption follow. In the ï¬?rst round, households use their money holdings (which
include wage payments, wi Li , and money from the safe, Mh,i ) to buy output and
consume. In the second round, monetary revenues from sales are redistributed to
households as dividends (denoted d per share), and are used for consumption. The
end of the period consumption is given by:
ci = Mh,i + wi Li + dQi (141)
With a small probability Î¸, the ability of the productive sector to make mon-
etary transfers collapses. This implies two things: ï¬?rst, wages are not paid to
workers. Second, revenues from sales cannot be redistributed back to households,
so no dividends are paid. There is only one round of consumption, in which house-
holds use the money which they had kept in the safe (Mh,i ) to buy consumption
goods. It follows that the end of the period consumption is given by:
ci = Mh,i (142)
Simplistically, the shock to the ability of the productive sector to make mone-
65
tary transfers can be thought of as a strike in the postal services: households who
receive wage payments and dividend payments by mail (and are subject to a cash
in advance constraint) do not receive these payments in time to consume before
they die. Realistically, this shock is meant to capture a shock to the money supply,
in which certain substitutes for money used by the productive sector are no longer
valued17 . For example, prior to the sub-prime crisis, mortgage backed securities
were accepted by all as means of payment. In the sub-prime crisis, these securities
turned into illiquid assets, and people were no longer willing to hold these assets
without understanding the value of their components. Thus, it became harder to
trade these assets for consumption goods, which made bonds and cash more de-
sired18 . In this model, agents hold bonds (â€œmoney in the safeâ€?) precisely to insure
against events of this kind19 .
In addition, I assume that the productive sector is endowed with an inventory of
K consumption goods, where K > Mi for any realization of Mi . This assumption
will allow a simple way to incorporate shocks to Î¸ that aï¬€ect liquidity supply.
Speciï¬?cally, I assume that Î¸ is small with some probability Ï? and Î¸ = 1 with
probability 1 âˆ’ Ï?. The value of Î¸ is revealed before agents decide on their portfolio.
To summarize, the timing within a period is as follows:
1. The economy is endowed with an inventory of K units of consumption goods.
The wage wi and the price of output (normalized to 1) is set.
2. The initial money supply, M0,i , and the level of risk aversion, c0,i , are realized.
In addition, the probability of a collapse Î¸ is revealed.
3. Agents use some of their money to buy stocks and eï¬€ectively supply liquidity
to the productive sector (and keep the rest in a safe).
4. The productivity shock, Ai , is realized.
17
See Eden [2009] for a complete development of this idea.
18
See Holmstrom [2008] for a complete development of this idea.
19
Results similar to those derived in this section can be derived in a more standard framework,
in which agents hold money to insure against unemployment risk; however, this motive for
hoarding liquidity seems less compelling as the mechanism through which shocks to risk aversion
aï¬€ect liquidity supply. Rather, in this formulation portfolio decisions are motivated by fear of
large aggregate disasters, consistent with the view expressed in Barro [2006].
66
5. The ï¬?nancial system allocates liquidity to projects, and production takes
place.
6. â€¢ With prob. (1 âˆ’ Î¸) (intact): wages are paid, followed by a ï¬?rst round of
consumption in which agents trade their wage earnings (wi Li ) and their
money holdings (Mh,i ) for consumption. The productive sector redis-
tributes revenues from sales back to households in the form of dividends.
A second round of consumption takes place in which the dividends are
traded for consumption.
â€¢ With prob. Î¸ (collapse): the productive sector loses its ability to make
monetary transfers. Wages are not paid and revenues from sales cannot
be redistributed back to households. There is therefore only one round
of consumption, in which households use their money holdings (Mh,i )
to buy consumption goods.
C.1.1 Equilibrium
The portfolio decision. Clearly, the agent will reserve at least enough money
to ï¬?nance c0,i units of consumption in case of a collapse (as otherwise his expected
utility is âˆ’âˆž):
Mh,i â‰¥ c0,i (143)
I begin with the case in which Î¸ is small. Denote by d the realized dividend
per share of the productive sector, and let Q0 be the equilibrium level of liquidity
i
supply, which the individual agent takes as given. Agents solve:
max E(ci âˆ’ vi (Li )) (144)
Qi ,Mh,i
s.t.:
Mi = Qi + Mh,i (145)
Mh,i + Qi d + wi Li with prob. (1 âˆ’ Î¸);
ci = (146)
Mh,i with prob. Î¸.
Mh,i â‰¥ c0,i (147)
67
Substituting in the ï¬?rst constraint, this problem can be rewritten as:
max(1 âˆ’ Î¸)(Mi âˆ’ Qi + Qi d + wi Li ) + Î¸(Mi âˆ’ Qi ) âˆ’ vi (Li ) (148)
Qi
s.t.
Mi âˆ’ Qi â‰¥ c0,i (149)
The derivative of the above with respect to Qi is:
(1 âˆ’ Î¸)d âˆ’ 1 (150)
Note that, in equilibrium, the dividends per share are given by:
Mi
d= (151)
Q0
i
Assumption 4 With probability Ï?, the value of Î¸ is suï¬ƒciently small so that, for
any realization of Mi and c0,i , the derivative of equation 148 with respect to Qi is
positive at Q0 = Mi âˆ’ c0,i :
i
Mi
(1 âˆ’ Î¸) âˆ’1>0 (152)
Mi âˆ’ c0,i
Result 1 Under Assumption 4, when Î¸ is small the optimal portfolio decision is
Mh,i = c0,i , Qi = Mi âˆ’ c0,i .
Proof: Under Assumption 4, the constraint in equation 149 is binding. Thus,
Mi âˆ’ Qi = c0,i .
Consider next the optimal portfolio under the realization Î¸ = 1 (that happens
with probability 1 âˆ’ Ï?). In this case, consumers have no reason to supply liquidity
to the ï¬?nancial sector, as they know for certainty that their returns to liquidity
will be 0. Hence, Mh,i = Mi and Qi = 020 .
20
Assuming a suï¬ƒciently large inventory guarantees that there is enough output to consume
Mi goods even in the absence of production.
68
To summarize, in the closed economy we have that:
Mi âˆ’ c0 with prob. Ï?;
Qi = (153)
Mi with prob. 1 âˆ’ Ï?.
Fluctuations in Qi therefore result from ï¬‚uctuations in Î¸ (captured by Ï?), ï¬‚uc-
tuations in the money supply and ï¬‚uctuations in risk aversion (captured by c0 ).
Next, I will show that liquidity supply takes the same form in the open economy.
C.2 Liquidity supply in the integrated economy
I assume that there is a single currency, so both labor and consumption can be
paid for in either domestic or foreign money. For simplicity, I assume that agents
consume foreign and domestic goods proportional to their shares in output (so
that, regardless of the realizations of money supplies, a unit of domestic output
has the same probability of being consumed as a unit of foreign output).
As in the closed economy, agents choose between keeping money in the safe
(Mh,i ) and buying stocks (Qi ). In the integrated economy, a stock is a claim on
the sales revenues of the global economy. After portfolio decisions are made, the
global ï¬?nancial system distributes liquidity between foreign and domestic projects
in an output maximizing way21 .
Assumption 5 1. The value of Î¸ is perfectly correlated across regions, that is,
with probability Ï? in both regions Î¸ is small, and with probability 1 âˆ’ Ï? in both
regions Î¸ = 1.
2. When Î¸ is small (with prob. Ï?), shocks to the ability of the productive sector
to make monetary transfers are i.i.d. across regions.
21
In this model, it is implicitly assumed that consumption is always less than output, and that
there are some units of output which are ex-post â€œwastedâ€?. A natural question is therefore why
the global ï¬?nancial system allocates liquidity between foreign and domestic projects in an output
maximizing way. If we think of the global ï¬?nancial system as a monopoly, this indeed need not be
the case; however, a more competitive structure (for example, one in which the ï¬?nancial system is
composed of many small banks competing for liquidity) would deliver this result, as the expected
real value of a unit of produced output is positive.
69
C.2.1 Equilibrium
I begin by characterizing the equilibrium in the case that Î¸ is small in both regions
(an event that occurs with probability Ï?).
The portfolio decision. Because there is a positive probability that both economies
suï¬€er a simultaneous collapse (an event that happens with probability Î¸2 ), simi-
larly to the closed economy case the agent will reserve at least enough money to
ï¬?nance c0,i units of consumption:
Mh,i â‰¥ c0,i (154)
Denote by d the realized dividend per share of the global productive sector,
and let Q0 be the equilibrium level of liquidity supplied by country i which the
i
individual agent takes as given. Similarly to the closed economy, agents solve:
max ci âˆ’ vi (Li ) (155)
Qi ,Mh,i
s.t.:
Mi = Qi + Mh,i (156)
ï£±
ï£´ Mh,i + Qi d + wi Li with prob. (1 âˆ’ Î¸);
ï£²
ci = M + Qi d with prob. (1 âˆ’ Î¸)Î¸; (157)
ï£´ h,i
Mh,i with prob. Î¸2 .
ï£³
Mh,i â‰¥ c0,i (158)
Substituting in the ï¬?rst constraint, this problem can be rewritten as:
max E(Qi d) + (1 âˆ’ Î¸)wi Li + (Mi âˆ’ Qi ) âˆ’ vi (Li ) (159)
Qi
s.t.
Mi âˆ’ Qi â‰¥ c0,i (160)
The derivative of the above with respect to Qi is:
E(d) âˆ’ 1 (161)
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To calculate E(d), note that positive dividends are paid unless both economies
suï¬€er a collapse. If neither suï¬€ers a collapse (an event which occurs with prob-
ability (1 âˆ’ Î¸)2 ), dividends per share are d = Md +M0em . If economy i suï¬€ers a
Q0 +Qem
d
collapse but economy j doesnâ€™t suï¬€er a collapse (events which occur with proba-
bility (1 âˆ’ Î¸)Î¸ each), the dividend per share is positive, as consumers in region i
receive some dividends from their stock holdings in region j. Expected dividends
per share are therefore bounded from below by:
Md + Mem
E(d) > (1 âˆ’ Î¸)2 (162)
Q0 + Q0
d em
Assumption 6 With probability Ï?, the value of Î¸ is suï¬ƒciently small so that for
any realization of Mi and c0,i , the following inequality holds:
Md + Mem
(1 âˆ’ Î¸)2 âˆ’1>0 (163)
(Md âˆ’ c0,d ) + (Mem âˆ’ c0,em )
Result 2 Under Assumption 6, the optimal portfolio decision when Î¸ is small is
Mh,i = c0,i , Qi = Mi âˆ’ c0,i .
Proof: Under Assumption 6, the derivative of equation 159 with respect to Qi is
positive at Q0 = Mi âˆ’ c0,i :
i
Md + Mem Md + Mem
E(d)âˆ’1 > (1âˆ’Î¸)2 0 0
âˆ’1 = (1âˆ’Î¸)2 âˆ’1 > 0
Qd + Qem (Md âˆ’ c0,d ) + (Mem âˆ’ c0,em )
(164)
Thus, the constraint in equation 160 is binding, so Mi âˆ’ Qi = c0,i .
Next, consider the equilibrium given the realization Î¸ = 1. In this case, there
are no returns from providing liquidity to either the domestic or foreign productive
sector. As in the autarkic case, Qi = 0,
Corollary 3 Both under autarky and under ï¬?nancial integration, the liquidity
supply of country i is given by:
Mi âˆ’ c0 with prob. Ï?;
Qi = (165)
Mi with prob. 1 âˆ’ Ï?.
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Assumption 7 The money supply, Mi , and the risk aversion parameter, c0,i , are
perfectly correlated across regions and follow time invariant distributions.
Since equilibrium liquidity supply takes the same form both in the integrated
economy and under autarky, and the shock to Î¸ is perfectly correlated, it follows
trivially that the assumptions I make on the distribution of liquidity supply are
satisï¬?ed.
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