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Policy Research Working Paper 6462
International Liquidity Rents
Maya Eden
The World Bank
Development Research Group
Macroeconomics and Growth Team
May 2013
Policy Research Working Paper 6462
Abstract
This paper presents a model of global liquidity shortages. that unrestricted liquidity flows are (a) welfare reducing
Liquid claims are enforceable promises that play a for emerging economies and (b) Pareto inefficient. The
transaction role. Since developed economies have a inefficiency results both from excessive investment for the
comparative advantage in creating liquidity, they export purpose of creating collateral-backed liquid claims, and
liquid claims to emerging economies, resulting in a from excessive global fragility with respect to collateral
permanent current account deficit. This model suggests shocks.
This paper is a product of the Macroeconomics and Growth Team, Development Research Group. It is part of a larger
effort by the World Bank to provide open access to its research and make a contribution to development policy discussions
around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author
may be contacted at meden@worldbank.org.
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of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
International Liquidity Rents
Maya Eden âˆ—
World Bank, DECMG
May 23, 2013
Abstract
This paper presents a model of global liquidity shortages. Liquid
claims are enforceable promises that play a transaction role. Since de-
veloped economies have a comparative advantage in creating liquidity,
they export liquid claims to emerging economies, resulting in a per-
manent current account deï¬?cit. This model suggests that unrestricted
liquidity ï¬‚ows are (a) welfare reducing for emerging economies and (b)
Pareto ineï¬ƒcient. The ineï¬ƒciency results both from excessive invest-
ment for the purpose of creating collateral-backed liquid claims, and
from excessive global fragility with respect to collateral shocks.
JEL Classiï¬?cation: E44, F30, G15
Keywords: Liquidity shortage, the welfare eï¬€ects of ï¬?nancial integration,
international liquidity ï¬‚ows, liquidity creation
Sector board: Economic Policy (EPOL)
âˆ—
I thank Alessandro Barattieri, Ricardo Caballero, Arnaud Costinot, John Duca, Ben
Eden, Anton Korinek, Ha Nguyen, Vincenzo Quadrini, Luis Serven and Christoph Steï¬€en
for helpful comments. I have also beneï¬?ted from comments made by seminar partici-
pants at MITâ€™s international breakfast and the World Bank and conference participants
at IGIDR, INFINITI and the NBER summer institute, IFM workshop. 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 behavior of international capital ï¬‚ows is puzzling from a neoclassi-
cal perspective: while standard considerations would suggest that capital
should ï¬‚ow from steady-state developed economies to converging emerging
economies, there are large net capital ï¬‚ows in the opposite direction (com-
monly referred to as â€œglobal imbalancesâ€?). The persistent decline in interest
rates in the US is also a puzzling trend, as, given the high returns to capital
in emerging economies, the neoclassical model would predict that ï¬?nancial
integration should increase the returns to savings in global markets.
In their seminal work, Caballero et al. [2008] present a highly stylized
model of global asset shortages that can help explain these puzzles. Their
model features overlapping generations with an inelastic demand for saving.
Developed economies have a comparative advantage in creating assets, and,
in equilibrium, export assets to emerging economies.
In this paper, I attempt to embed this stylized intuition in a standard
neoclassical growth model, generating a demand for assets from a need for
liquidity. This focus is in line with the ï¬?ndings in Gourinchas and Rey [2007]
who show that US external liabilities are predominantly composed of liquid
claims which carry a signiï¬?cant liquidity premium. I then use the model to
revisit the welfare implications of ï¬?nancial integration, as well as the implica-
tions for consumption, investment and volatility. The model illustrates that,
despite a growing consumption path and high returns to capital, emerging
economies may be net lenders in equilibrium; in this case, ï¬?nancial inte-
gration is welfare-reducing for emerging economies. In contrast, developed
economies are made better oï¬€ by ï¬?nancial integration as they enjoy rents
from liquidity supply. Even though developed economies gain from ï¬?nan-
cial integration, it is possible to show that ï¬?nancial integration is Pareto
ineï¬ƒcient, and, in some cases, welfare inferior to autarky. The ineï¬ƒciency
is a result of excessive capital accumulation in the developed economy and
unnecessary fragility with respect to collateral shocks.
2
The starting point of the model is the assumption that, compared to
emerging economies, developed economies have a comparative advantage in
creating liquid claims. This assumption is consistent with ï¬?gure 1, that shows
that the average level of broad money (M3) as a fraction of nominal GDP is
positively correlated with income. To generate a need for liquidity, I assume
a transaction role for liquid claims. In the spirit of Neumeyer and Perri
[2005], this transaction role is modeled as a â€œworking capitalâ€? constraint in
the labor market: labor is unable to enforce payment ex-post, and must be
paid in advance with liquid claims (which are easily enforceable).
In emerging economies, there is not enough liquidity to ï¬?nance the un-
constrained wage bill. Consequently, the autarkic wage is depressed relative
to the marginal product of labor. In the integrated equilibrium, this wedge
creates an incentive to buy liquid claims issued by foreigners. However, the
purchase of foreign-issued liquid claims is associated with a pecuniary exter-
nality, as â€œimportedâ€? liquidity bids up wages.1 Since liquidity is expensive,
the increase in labor income is not enough to oï¬€set the fall in ï¬?rmsâ€™ proï¬?ts.2
Aggregate domestic income is lower than in the autarkic counterfactual, as
payments for liquidity services are sent abroad.
These â€œliquidity rentsâ€? incentivize agents in developed economies to ex-
plore innovative ways to create more liquidity. A high liquidity premium
increases the private return to physical capital, as it can be used as collat-
eral to back liquid claims. This is Pareto ineï¬ƒcient for two reasons: ï¬?rst, it
leads to excessive capital accumulation in the developed economy. Second,
equilibrium reliance on collateral-backed liquid claims exposes the economy
to unnecessary fragility, as collateral shocks change the incentives to accu-
mulate physical capital.
1
This result is broadly consistent with the empirical ï¬?ndings in Chari et al. [2012], who
show that ï¬?nancial integration in emerging economies is associated with an increase in
wages.
2
The way that ï¬?nancial integration changes domestic income shares is in the spirit of
Antras and Caballero [2009]: the returns to liquidity decline, as liquidity can be imported
more cheaply from abroad, allowing labor to absorb a higher share of output.
3
M3 as a percent of GDP (log)
6
5
4
3
2
1
4 5 6 7 8 9 10 11
GDP per capita (log)
Source: World Development Indicators, 2013: Liquid liabilities (M3) as % of GDP, and
GDP per capita (constant 2000 US$).
Figure 1: A positive cross-country correlation between the ratio of M3 and
M3
nominal GDP ( P Y
) and income per capita (in the year 2000). A 1% increase
in income per capita is associated with a 0.3% increase in real balances.
The general principle underlying the welfare analysis in this paper is that
agents are willing to undertake costly measures to relax binding constraints,
even when doing so is socially ineï¬ƒcient. For emerging economies, this takes
the form of buying liquid claims issued by foreigners. Privately, each ï¬?rm
thinks it can increase its proï¬?ts by importing liquidity and increasing its
labor inputs. In general equilibrium, foreign-issued liquidity merely bids up
the wage rate, leaving ï¬?rms worse oï¬€ as they face higher wages and must
make payments to foreign liquidity suppliers. For developed economies, the
ineï¬ƒciency takes the form of accumulating collateral. Privately, each agent
stands to proï¬?t from creating collateral-backed liquid claims; however, in
general equilibrium, this merely reduces the liquidity premium and wastes
valuable resources.
4
2 Related literature
The global equilibrium view expressed in this paper is closely related to the
â€œasset shortageâ€? view, summarized in Caballero [2006] and Caballero et al.
[2008]. Subsequent work such as Caballero and Krishnamurthy [2009] and
Maggiori [2008] observe that the surplus of emerging economies is composed
primarily of treasuries and other safe assets, and relate the demand for assets
to a demand for safety. In this paper, safety is de-emphasized and replaced
with liquidity. Of course, the views are not mutually inconsistent as safety
and liquidity often go together (see Krishnamurthy and Vissing-Jorgensen
[2012] for the case of treasuries). However, the focus on liquidity is key for
the welfare implications explored here.
The welfare implications are conceptually related to the idea of inter-
national seigniorage, as in Matsuyama et al. [1993] and Eden [2009]. In the
monetary literature, the fact that foreigners use dollars allows the US central
bank to collect seigniorage payments from abroad. An implication of this is
that the foreigners would be better oï¬€ if using dollars were illegal, as the
only seigniorage payments would be collected by the domestic government
and consumed domestically. The results here are of similar ï¬‚avor: in the
autarkic emerging economy, there are rents to liquidity supply, but they are
consumed domestically. Under ï¬?nancial integration, the developed economy
extracts some liquidity rents, which reduces aggregate domestic income in
emerging economies.
This paper is related to others that emphasize ineï¬ƒcient pecuniary ex-
ternalities in constrained environments, including Korinek [2011], Lorenzoni
[2008] and Eden [2012]. Most closely related is Eden [2012], in which I con-
sider a closed economy with pledgeability constraints in which the price of
production inputs is determined in equilibrium. Producers are willing to
pay an â€œintermediation costâ€? to relax their pledgeability constraint, but in
equilibrium this only raises the price of inputs and generates an ineï¬ƒciency.
This pecuniary externality is the key ingredient in both models. The main
5
diï¬€erence between the papers is in their focus. Here, I focus on the welfare
implications of international liquidity ï¬‚ows and on the distribution of sur-
plus between emerging and developed economies, as well as the implications
of collateral shocks in this context. In Eden [2012] I focus on the general
equilibrium costs of ï¬?nancial intermediation in a closed economy context.
The idea that in liquidity-scarce environments collateral shocks can trans-
late into liquidity shocks appears also in Midrigan and Philippon [2011].
Midrigan and Philippon [2011] consider a general equilibrium monetary model,
in which the Friedman rule is not implemented and â€œcash in advanceâ€? con-
straints bind in equilibrium. The ability to borrow against housing wealth in
order to relax the â€œcash in advanceâ€? constraint increases the private return
to housing. Thus, shocks to the collateral value of housing reduce the incen-
tives to invest in new houses. The mechanism here is similar: the economy
can issue liquid claims against the â€œcollateralizableâ€? part of its capital stock.
Shocks to the collateral value of capital reduce the incentives for capital ac-
cumulation. While the mechanism is similar, the suggested interpretation is
somewhat diï¬€erent: capital-backed liquid claims are interpreted not only as
mortgage loans, but also as securities with favorable liquidity properties (for
example, MBS or ABS that can be used as collateral in the repo market).
This paper contributes to the theoretical literature on the welfare im-
plications of ï¬?nancial integration in emerging economies, including (among
others) Gourinchas and Jeanne [2006] and Levine [2001]. Mendoza et al.
[2007] similarly consider the welfare implications of ï¬?nancial integration for
a ï¬?nancially underdeveloped economy. Similarly, the conclusion is that ï¬?-
nancial integration is welfare reducing. However, the mechanism is very
diï¬€erent.3
3
In Mendoza et al. [2007], the welfare eï¬€ects operate through the domestic distribu-
tional implications. Relatively poor households are equilibrium borrowers that are made
worse oï¬€ by higher equilibrium interest rates. In this model, there is no household hetero-
geneity and all emerging market households are net lenders in equilibrium. The welfare
eï¬€ects operate through the pecuniary externality on wages, which makes it more diï¬ƒcult
for domestic producers to ï¬?nance production.
6
3 Setup
I consider a discrete time inï¬?nite horizon model, where time periods are
indexed by t = 0, 1, 2....
Technology. There is a unit measure of identical ï¬?rms indexed i âˆˆ [0, 1].
The production technology is time invariant and given by:
Î± 1âˆ’Î±
Fi (ki,t , li,t ) = Ai ki,t li,t (1)
Where Ai is the ï¬?rmâ€™s productivity, li,t is the labor employed by ï¬?rm i
and ki,t is ï¬?rm iâ€™s physical capital.
Physical capital. Physical capital is owned by ï¬?rms. The ï¬?nal good can
be invested and turned into physical capital, to be used in the next period.
Capital depreciates at the rate Î´ . This implies the standard capital accumu-
lation equation (where ii,t is investment):
ki,t+1 = (1 âˆ’ Î´ )ki,t + ii,t (2)
Paying labor. To generate a role for liquidity, I assume that ï¬?rms need
to pay labor with enforceable promises on post-production output, prior to
production. Enforceable promises are transferable â€œIOU notesâ€? which I will
refer to as liquid claims.4
There are two types of liquid claims: publicly-backed liquid claims and
collateral-backed liquid claims (which will also be referred to as privately-
backed liquid claims).
4
This simpliï¬?ed modeling of liquid claims captures two important aspects of liquidity.
First, it can easily be used for transaction purposes (here, purchasing labor). Second,
liquid claims can be enforced without any expertise or enforcement power, a property
that is necessary for liquid claims to be widely acceptable. See Holmstrom and Tirole
[2011], Holmstrom [2008] and Kurlat [2010] for a more rigorous discussion of the necessary
attributes of liquid claims.
7
Publicly backed liquid claims. The government can guarantee a ï¬?rmâ€™s
promises up to m units of output. Publicly guaranteed claims are tradable
IOU notes that are issued by the ï¬?rm, and enforced by the government.5 I
assume for simplicity that the limit on publicly backed claims is proportional
to output:
1
mt = Î¸ Fi (ki,t , li,t )di (3)
0
The proportion coeï¬ƒcient Î¸ captures the economyâ€™s aptitude for creating
publicly backed liquid claims. Publicly backed liquid claims should be inter-
preted as traditional forms of liquidity, such as government bonds or money.
A government bond is a claim on domestic output, backed by the govern-
mentâ€™s ability to collect tax revenues; similarly, money is a claim on output,
its purchasing power guaranteed by the the commitment of the central bank
not to inï¬‚ate the currency. The parameter Î¸ captures attributes such as the
governmentâ€™s ability to commit future tax revenues and the central bankâ€™s
commitment to low inï¬‚ation.
Collateral backed liquid claims. In addition, ï¬?rms can privately back
their promises against a fraction Î³ of their capital stock.6 These privately
backed liquid claims should be interpreted as less traditional forms of liquid-
ity, such as MBS or ABS.
There are two important diï¬€erences between publicly backed claims and
collateral backed claims. First, publicly backed claims are undistortive, in the
sense that the ï¬?rm does not internalize the eï¬€ect of its capital accumulation
decisions on the amount of publicly backed claims that it can issue; rather,
ï¬?rms take the amounts mt as exogenous. In contrast, the ability to use capital
to issue collateral backed claims is internalized by the ï¬?rm in its investment
5
These claims are in the spirit of â€œmoneyâ€? in Caballero and Krishnamurthy [2005].
6
The distinction between â€œpublicly backedâ€? and â€œprivately backedâ€? liquid claims is
in the spirit of Farhi and Tirole [2011], who similarly distinguish between â€œinsideâ€? and
â€œoutsideâ€? liquidity.
8
Firms enter with xt Labor market Production; Liquidity
~ ,~
i t, Bi,t
ki,t i t, bi,t
i t, Bi,t
i t bi,t
it revealed (
(wt)
): li,t
it ppaid p
consumption market; ; rt, ~
rt,
with bi,t (ci,t) and Bi,t+1, bi,t+1,
and xtb ~ investment (ki,t+1); ~ ,~
i,t B i,t+1 bi,t+1
~
firms repay Bi,t and xtBi,t
Figure 2: The within-period timing of the model.
decisions.
Second, unlike publicly backed claims, collateral backed claims are (po-
tentially) risky: there is a random variable xt âˆˆ [0, 1] that determines the
fraction of collateral backed claims can be enforced. The use of collateral
backed claims therefore may expose the economy to aggregate â€œenforceabil-
ityâ€? risk. Denote by S T the history of the realizations of xt up to time T
(S T = (x1 , x2 , ..., xT )). To simplify, this is the only source of uncertainty that
I will consider.
Realistically, there is a sense that collateral-backed claims are less liquid
than publicly-backed claims. To capture this, I will assume that collateral
backed claims are specialized, in the sense that they are not enforceable across
borders. While, in principle, wage bills in one country can be paid with
publicly backed claims issued in another country, collateral backed claims are
only enforceable domestically. This captures the idea that collateral backed
claims are more specialized, and, in some sense, serve as â€œinside moneyâ€?
within a domestic ï¬?nancial system. This assumption will not be essential for
any of the theoretical results, but will play a role in the numerical simulation.7
To summarize, let Bi,t denote the total amount of publicly backed liquid
Ëœi,t denote the total amount of privately
claims that ï¬?rm i can issue, and let B
7
In the numerical simulation, this assumption aï¬€ects the wage dynamics associated
with an enforceability shock. Speciï¬?cally, if emerging markets hold privately-backed liquid
claims issued by developed economies, part of the instantaneous adjustment in wages would
take place in emerging economies.
9
backed liquid claims that ï¬?rm i can issue. These amounts are bounded by:
Bi,t â‰¤ mt (4)
Ëœi,t â‰¤ Î³ki,t
B (5)
Liquidity markets. After production takes place and investment decisions
are made, ï¬?rms issue liquidity that can be used in period t + 1 (the choices of
Bt+1 and B Ëœi,t+1 are made at the end of period t). There is a liquidity market,
in which ï¬?rms can buy and sell liquid claims. The price of publicly backed
1
liquid claims in terms of goods is 1+ rt
: one good can purchase 1 + rt publicly
backed liquid claims, that can be used to hire labor for production in period
1
t + 1. Similarly, the price of collateral backed liquid claims is 1+Ëœ rt
.
Denote by bi,t the amount of publicly backed liquid claims that ï¬?rm i
holds at the beginning of period t, and let Ëœ bi,t denote the amount of collateral
backed liquid claims that ï¬?rm i holds at the beginning of period t (these
quantities are determined in the liquidity market at the end of period t âˆ’ 1).
The amount of labor that ï¬?rm i can hire is bounded by these quantities, and
the aggregate state x that determines the extent to which collateral-backed
claims are enforceable:
wt li,t â‰¤ bi,t + xtËœbi,t (6)
This constraint, which resembles a â€œcash in advanceâ€? constraint on labor
purchases, will be referred to as the liquidity constraint.
Households. There is a unit measure of households indexed i âˆˆ [0, 1]. For
simplicity, I assume that each household owns one ï¬?rm (but cannot supply
its own labor to its ï¬?rm). Household iâ€™s preferences over state-contingent
consumption sequences {ci,t (S t )}t,S t are represented by:
âˆž
t
U ({ci,t (S )} t,S t ) = E( Î² t u(ci,t (S t ))) (7)
t=0
10
Where u(Â·) satisï¬?es the standard assumptions: u (c) > 0, u (c) < 0.
Households supply li,t = l units of labor inelastically. As I will focus primarily
on steady state analysis, l should be interpreted as the long-run level of labor
supply; the assumption is consistent with the widely-held view that long-run
labor supply is inelastic.8
Household i (that owns ï¬?rm i) faces the following optimization problem:
âˆž
max E( Î² t u(ci,t (S t )))
{ci,t (S t ),ki,t+1 (S t ),li,t (S t ),bi,t+1 (S t ),Bi,t+1 (S t ),Ëœ Ëœi,t+1 (S t )} t
bi,t+1 (S t ),B t,S t=0
(8)
s.t. (for any S t ):
bi,t+1 Ëœ
bi,t+1
ci,t + ki,t+1 + + = Fi (ki,t , li,t ) âˆ’ wt li,t (9)
1 + rt 1 + r Ëœt
Ëœ
+(1 âˆ’ Î´ )ki,t + bi,t âˆ’ Bi,t + xt (Ëœ Ëœi,t ) + wt l + Bi,t+1 + Bi,t+1
bi,t âˆ’ B
1 + rt 1 + r Ëœt
ki,t+1 â‰¥ 0 (10)
And the inequalities in equations 4, 5 and 6.
The productivity parameters Ai and the initial conditions ki,0 , Bi,0 , bi,0 ,
Bi,0 , Ëœ
Ëœ bi,0 are identical across ï¬?rms within a country. As households are identi-
cal (and subject to the same aggregate risk), it follows that consumption and
capital accumulation are the same across households and ï¬?rms in all periods.
At time t, households have seven choice variables: household consumption
(ci,t ), labor demand (li,t ), next-period capital levels (ki,t+1 ), demand for next-
periodâ€™s publicly backed claims (bi,t+1 ), demand for next-periodâ€™s privately
backed claims (Ëœ bi,t+1 ), supply of next-periodâ€™s publicly backed claims (Bi,t+1 )
and supply of next-periodâ€™s privately backed claims (B Ëœi,t+1 ).
Equation 9 is the householdâ€™s budget constraint. The householdâ€™s income
8
Long run labor supply is typically thought of as being inelastic, as permanent changes
in the wage rate have both an income and substitution eï¬€ect that roughly cancel out. See,
for example, Basu and Kimball [2002].
11
is composed of dividend income, labor income, and revenue from selling liquid
claims (issued against next periodâ€™s output). This income is divided between
consumption, the accumulation of physical capital, and the purchase of liquid
claims. Equation 10 states that capital cannot be negative (this will not be
binding).
Wage setting. For simplicity, I assume that wt is set at time t so that the
labor market clears (there is no wage stickiness and no unemployment).
Timing. Figure 2 summarizes the timing of the model. The within-period
timing of the model is as follows:
1. Firms enter period t with ki,t units of physical capital, bi,t units of
publicly backed liquid claims and Ëœ bi,t units of collateral backed liquid
claims. They also enter with Bi,t publicly backed outstanding obliga-
tions and BËœi,t collateral backed outstanding obligations, that they are
to repay at the end of the period.
2. The aggregate enforceability state, xt , is revealed.
3. Firms use their enforceable liquid claims to hire labor (li,t ). The wage
(wt ) is set so that the labor market clears.
4. After production takes place, ï¬?rms repay their enforceable outstanding
Ëœi,t ). Households (who are shareholders) decide
obligations (Bi,t + xt B
how much to invest in next periodâ€™s physical capital (ki,t+1 ), and how
much to consume.
5. Firms issue liquid claims against next periodâ€™s output and capital (Bi,t+1
and BËœi,t+1 ) and sell them in the liquidity market. Firms buy liquid
claims to be used in the next period (bi,t+1 and Ëœbi,t+1 ).
12
3.1 Global environment
There are two countries: an emerging economy (em) and a developed econ-
omy (d). The size of the emerging economy relative to the developed econ-
omy is Ï? (in the emerging economy, there is a measure Ï? of households-ï¬?rms,
and in the developed economy there is a measure 1 of households-ï¬?rms). As
household-ï¬?rms are identical within a country, with a slight abuse of notation
I will use the subscript i to denote country variables (i = d, em).
The countries diï¬€er both in their ability to create publicly backed liquid
claims and in their ability to create collateral backed liquid claims. The
emerging economy is assumed to be unable to create collateral backed liquid
claims:
Î³ em = 0 (11)
The emerging economy is also not particularly good at creating pub-
licly backed liquid claims: the fraction of output that the government can
guarantee, Î¸, is such that the liquidity constraint is binding in equilibrium.
Recall that given the Cobb-Douglas production technology, the wage bill in
an unconstrained economy is a fraction 1 âˆ’ Î± of output. Thus, the following
restriction guarantees that in the autarkic emerging economy, the liquidity
constraint is binding in equilibrium:
Î¸em < 1 âˆ’ Î± (12)
The developed economy is superior to the emerging economy both in its
ability to create publicly backed liquid claims and in its ability to create
privately backed liquid claims. I assume that in the developed economy, a
positive fraction of capital can be used as collateral:
Î³d = Î³ > 0 (13)
In addition, the government is able to back enough claims to ï¬?nance the
13
autarkic wage bill:
Î¸d â‰¥ 1 âˆ’ Î± (14)
I also allow for cross country diï¬€erences in productivity levels and in
Ëœi,0 , bi,0 and Ëœ
initial conditions (Ai , ki,0 , Bi,0 , B bi,0 for i = d, em).
4 Eï¬ƒcient allocations
It is useful to consider the social plannerâ€™s problem. Consider a social planner,
facing the following problem:
maxt U ({cd,t (S t )}) + Î¨U ({cem,t (S t )}) (15)
{ci,t (S t ),k i,t+1 (S )}iâˆˆ{d,em}
s.t.:
cd,t (S t ) + Ï?cem,t (S t ) + kd,t+1 (S t ) + Ï?kem,t+1 (S t ) = (16)
Ï?Fem (kem,t (S tâˆ’1 ), l) + Fd (kd,t (S tâˆ’1 ), l) + (1 âˆ’ Î´ )(Ï?kem,t (S tâˆ’1 ) + kd,t (S tâˆ’1 ))
Where kem,0 and kd,0 are given.
The social planner chooses consumption and investment to maximize a
weighted sum of developed and emerging market utilities, given the aggregate
budget constraint. The parameter Î¨ is the Pareto weight that the planner
puts on emerging economies. Note that the standard equivalence applies here:
any Pareto eï¬ƒcient allocation corresponds to the solution to the plannerâ€™s
problem, for some value of Î¨. In other words, if an allocation does not
correspond to the plannerâ€™s solution for some value of Î¨, both emerging and
developed economies can be made better oï¬€ by switching to an allocation
that does.
While the plannerâ€™s problem allows for state-contingent consumption and
investment sequences, it is easy to see that the solution is deterministic.
This is because the shock xt only aï¬€ects the ability to issue collateral-backed
liquid claims against capital; as the planner is not subject to any liquidity
14
constraint, this shock is irrelevant. The plannerâ€™s solution corresponds to the
eï¬ƒcient allocation in a standard open economy neoclassical growth model.
Lemma 1 The solution to the plannerâ€™s problem satisï¬?es the following equa-
tions:
âˆ‚Fem (kem,t+1 , l) âˆ‚Fd (kd,t+1 , l)
= (17)
âˆ‚kem âˆ‚kd
u (cd,t ) = Î¨u (cem,t ) (18)
âˆ‚F (kd,t+1 , l)
u (cd,t ) = Î²u (cd,t+1 )( + 1 âˆ’ Î´) (19)
âˆ‚k
cd,t + kd,t+1 + Ï?(cem,t + kem,t+1 ) = (20)
Fd (kd,t , l) + (1 âˆ’ Î´ )kd,t + Ï?(Fem (kem,t , l) + (1 âˆ’ Î´ )kem,t )
The plannerâ€™s solution converges to a steady state in which:
ss ss
1 âˆ‚Fd (kd , l) âˆ‚Fem (kem , l)
= +1âˆ’Î´ = +1âˆ’Î´ (21)
Î² âˆ‚k âˆ‚k
css ss ss ss ss ss
d + Ï?cem = Fd (kd , l ) âˆ’ Î´kd + Ï?(Fem (kem , l ) âˆ’ Î´kem ) (22)
The proof of this lemma, together with other omitted proofs, is in the ap-
pendix.
5 Closed economy equilibrium
This section characterizes the autarkic equilibrium. In this economy, the
autarkic equilibrium is deï¬?ned as follows:
Deï¬?nition 1 An equilibrium of the closed economy is a sequence of inter-
est rates {rt (S t ), r Ëœt (S t )}t,S t , a sequence of wages {wt (S t )}t,S t , a sequence
of labor demands {{li,t (S t )}t,S t }iâˆˆ[0,1] , a sequence of physical capital stocks
{{ki,t+1 (S t )}t,S t }iâˆˆ[0,1] , a sequence of liquidity demands {{bi,t+1 (S t ), Ëœ bi,t+1 (S t )}t,S t }iâˆˆ[0,1] ,
a sequence of liquidity supplies {{Bi,t+1 (S t ), B Ëœi,t+1 (S t )}t,S t }iâˆˆ[0,1] and a set of
15
consumption paths {{ci,t (S t )}t,S t }iâˆˆ[0,1] that jointly satisfy the following con-
ditions:
1. Given the sequence of interest rates and the wage sequence, the con-
sumption sequences, the labor demand sequences, the sequences of liq-
uidity demands and liquidity supplies, and the capital sequences solve
the optimization problem of household i (owner of ï¬?rm i).
2. Given the wage wt (S t ), the labor market clears:
li,t (S t ) = l (23)
Ëœt (S t ), the liquidity market clears:
3. Given the interest rates rt (S t ) and r
bi,t+1 (S t ) = Bi,t+1 (S t ) (24)
Ëœ Ëœi,t+1 (S t )
bi,t+1 (S t ) = B (25)
The last condition states that the liquidity market clears domestically;
there is no international trade in publicly backed liquid claims, so the do-
mestic r may be diï¬€erent across countries. This implies that in an autarkic
equilibrium, the entire wage bill is ï¬?nanced by domestically issued claims.
Assume that initial conditions satisfy b0 = B0 = m0 and Ëœ Ëœ0 = Î³k0 .
b0 = B
The following lemma characterizes the closed economy equilibrium:
Lemma 2 1. The equilibrium is characterized by the following equations.
The consumption and capital sequences are given by:
âˆ‚Fi (ki,t+1 , l)
u (ci,t ) = Î²u (ci,t+1 )( + 1 âˆ’ Î´) (26)
âˆ‚k
ci,t + ki,t+1 = Fi (ki,t , l) + (1 âˆ’ Î´ )ki,t (27)
For i = em, d.
16
Equilibrium wages are given by:
âˆ‚Fd (kd,t , l)
wd,t = (28)
âˆ‚l
Î¸em Fem (kem,t , l)
wem,t = (29)
l
Equilibrium ri,t are given by:
u (cd,t ) = Î² (1 + rd,t )u (cd,t+1 ) (30)
âˆ‚F (kem,t+1 ,l)
âˆ‚l
u (cem,t ) = Î² (1 + rem,t ) u (cem,t+1 ) (31)
wem,t+1
Equilibrium r Ëœem,t = âˆ’1 and:
Ëœi,t are given by r
Ëœd,t )Et (xt+1 )u (cd,t+1 )
u (cd,t ) = Î² (1 + r (32)
2. The autarkic equilibrium converges to a steady state, in which r, k , w
and c are constant. Steady state consumption and capital are pinned
down by:
ss
1 âˆ‚Fi (ki , l)
= +1âˆ’Î´ (33)
Î² âˆ‚k
css ss ss
i = Fi (k , l ) âˆ’ Î´ki (34)
For i = em, d.
Steady state wages are:
ss
âˆ‚Fd (kd , l) ss
= wd (35)
âˆ‚l
ss
ss
Î¸em Fem (kem , l)
wem = (36)
l
17
Steady state ri are:
ss 1
1 + rd = (37)
Î²
ss
ss wem
1+ rem = ss (38)
(kem ,l)
Î² âˆ‚Femâˆ‚l
ss
As for r Ëœem
Ëœi , r Ëœd,t may depend on S t and need not converge
= âˆ’1 and r
to a steady state.
The developed economy has enough publicly backed claims so that the
liquidity constraint is never binding, and there is no liquidity premium. Con-
sequently, the return to investment is unaï¬€ected by liquidity motives, and
unchanged by the shock xt . Equilibrium capital accumulation is given by
equation 26, which is the standard Euler equation. Enforceability shocks
have no eï¬€ect on the equilibrium path.
Equation 28 states that, in the autarkic developed economy, the wage
is equated with the marginal product of labor. This standard equilibrium
condition implies that producers are indiï¬€erent with respect to hiring an ad-
ditional unit of labor: the marginal productivity of labor exactly oï¬€sets its
cost. This indiï¬€erence is evidence that the liquidity constraint is not bind-
ing: a producer endowed with another unit of liquidity would be indiï¬€erent
between using it or not.
The closed economy equilibrium of the emerging economy is diï¬€erent in
nature. In the autarkic emerging economy, there are not enough liquid claims
to ï¬?nance the unconstrained wage bill, and the liquidity constraint is binding.
The wage bill is constrained by the aggregate amount of liquidity, and thus
given by wl = Î¸em F (kem,t , l). At this equilibrium wage, the ï¬?rmâ€™s liquidity
1
constraint is binding: an additional liquid claim could purchase w units of
âˆ‚F (kem,t ,l)
labor, which, at the margin, produce âˆ‚l
> w units of output each.
The return to liquidity is positive, reï¬‚ected in a liquidity premium in r.
Importantly, while the liquidity constraint is binding from the ï¬?rmâ€™s per-
spective, it is not binding from an aggregate perspective: since labor is sup-
18
plied inelastically, even though each ï¬?rm would like to hire more workers
at the equilibrium wage, from an aggregate perspective, all labor is already
employed in its most eï¬ƒcient use.9 The shortage in liquidity changes the
distribution of surplus between labor and the ï¬?rmâ€™s proï¬?ts, but does not
change aggregate income.
Consequently, similar to the unconstrained developed economy, equations
26 and 27 fully characterize the consumption and capital sequences in the
emerging economy. The assumption that Î³ em = 0 implies that, even though
there is a liquidity premium, the binding liquidity constraint does not aï¬€ect
the incentive to accumulate physical capital; capital accumulation is undis-
torted and follows the same path as in the unconstrained equilibrium.
Corollary 1 When initial capital levels are given by their steady state values
ss
(ki,0 = ki, 0 for i = d, em), the closed economy equilibrium is Pareto eï¬ƒcient.
To see this, note that in this case, the autarkic equilibrium corresponds
u (css
d )
to the solution to the plannerâ€™s problem with Î¨ = u (css .
em )
ss
Of course, under the more realistic assumption of kem,0 < kem and kd,0 =
ss
kd , the autarkic equilibrium is not Pareto eï¬ƒcient, as there are gains from
intertemporal trade between the two countries. In particular, it is optimal
for the emerging economy to borrow from the developed economy in order
to smooth consumption and speed up capital accumulation.
6 Integrated equilibrium
In the open economy, it is no longer required that the market for liquidity
clears domestically: foreigners and domestic ï¬?rms can trade publicly-backed
9
The assumption that labor is supplied inelastically is important for the eï¬ƒciency
result: absent this assumption, the depressed wage would aï¬€ect labor supply and generate
an ineï¬ƒciency. The assumption that ï¬?rms are identical is not important: in the presence
of domestic liquidity markets, the wedge between the marginal product of labor and the
wage would be equated across ï¬?rms. Thus, the marginal product of labor would be equated
across ï¬?rms and labor would be allocated eï¬ƒciently.
19
liquid claims in a global liquidity market.
The deï¬?nition of an equilibrium in the integrated economy is analogous
to the deï¬?nition of the autarkic equilibrium, with a single departure: rather
than requiring that the market for publicly backed liquid claims clears do-
mestically, it requires that the rate of return on publicly backed claims is
equated across countries. Formally, the equilibrium condition in equation 24
is replaced with:
Ï?bem,t (S t ) + bd,t (S t ) = Ï?Bem,t (S t ) + Bd,t (S t ) (39)
The other equilibrium conditions remain unchanged.
The following parametric restriction guarantees that in the autarkic steady
state, the aggregate amount of liquidity is insuï¬ƒcient to ï¬?nance the uncon-
strained wage bill in the integrated economy:
ss
Assumption 1 Let ki denote the autarkic steady state capital level in coun-
try i, and assume the following parametric restriction:
d ss
Î¸i Fd (kd ss
, l)+ Ï?Î¸em Fem (kem ss
, l)+ Î³kd ss
< (1 âˆ’ Î±)(Fd (kd ss
, l)+ Ï?Fem (kem , l)) (40)
The left hand side is the aggregate amount of liquidity in the autarkic steady
state, given xt = 1. The right hand side is the aggregate unconstrained wage
bill at the autarkic steady state (which is a fraction 1 âˆ’ Î± of steady state
output in each country).
Characterizing the integrated equilibrium is less straightforward than
characterizing the autarkic equilibrium, because there may be occasionally
binding constraints. However, it is possible to prove the following key result:
Proposition 1 The integrated equilibrium is Pareto ineï¬ƒcient.
There are two sources of ineï¬ƒciency in the integrated equilibrium. First,
there is excessive capital accumulation in the developed economy, driven by
20
an incentive to create collateral backed liquid claims. To see this, note that
the householdâ€™s ï¬?rst order condition with respect to the accumulation of
physical capital (the Euler equation) is given by:
âˆ‚F (kd,t+1 , l)
u (cd,t ) = Î²Et (u (cd,t+1 )( + 1 âˆ’ Î´ )) + Î³Î»t+1,B
Ëœ (41)
âˆ‚k
Where Î»t,B Ëœ is the Lagrange multiplier on equation 5 (the constraint on
issuing collateral-backed liquid claims, B Ëœ ). Under autarky, the incentive to
create private liquidity is muted, since there are enough publicly backed liquid
claims to insure that the liquidity constraint never binds. Thus, Î»t+1,B Ëœ = 0
and the above condition amounts to the standard Euler equation. In the in-
tegrated equilibrium, there is a global liquidity shortage driven by the excess
demand for liquidity in emerging economies. This results in a liquidity pre-
mium on internationally traded publicly backed liquid claims; consequently,
there is also a liquidity premium on privately-backed liquid claims, that can
be used to substitute for publicly-backed claims domestically. Thus, in the in-
tegrated equilibrium, Î»t+1,B Ëœ > 0, and the incentive to create privately backed
liquid claims enters into the developed economyâ€™s capital accumulation deci-
sion. From the plannerâ€™s perspective, this is ineï¬ƒcient.
The second source of ineï¬ƒciency is that reliance on collateral-backed liq-
uid claims creates vulnerability with respect to enforceability shocks. In
the autarkic equilibrium, enforceability shocks have no eï¬€ect on the incen-
tive to accumulate capital: when Î»t+1,B Ëœ = 0, expectations regarding xt+1 do
not enter the condition in equation 41. However, when Î»t+1,B Ëœ > 0, expected
changes in enforceability can aï¬€ect the incentives to accumulate capital. The
value of Î»t+1,BËœ depends on the expected transformation of physical capital
into enforceable collateral-backed claims. Thus, changes in the expectation of
xt+1 will change the incentives to accumulate physical capital, which results
in ineï¬ƒcient volatility in capital accumulation.
Of course, the fact that the integrated equilibrium is Pareto ineï¬ƒcient
21
does not necessarily imply that it is welfare inferior to autarky, as given real-
ss ss
istic initial conditions (for example, kem,0 < kem and kd,0 = kd ), the autarkic
equilibrium is Pareto ineï¬ƒcient as well. Standard considerations would sug-
gest that ï¬?nancial integration can be associated with welfare gains: emerging
markets can borrow from developed economies to implement a smoother con-
sumption path and faster capital accumulation. A natural question is: in the
presence of liquidity motives for borrowing and lending, are these gains from
ï¬?nancial integration still relevant?
It turns out that these standard considerations are relevant only when
kem is suï¬ƒciently small. At this range, the emerging economy borrows from
the developed economy in order to increase investment and implement a
smoother consumption path. Given these eï¬ƒciency gains, ï¬?nancial integra-
tion may be welfare superior to autarky, and beneï¬?t both emerging and
developed economies.
However, when capital levels are close to their autarkic steady state lev-
els, this is no longer the case: in this range, the emerging economy starts to
ss ss
lend to the developed economy, even if kem < kem and kd â‰¥ kd . The reason
for lending has nothing to do with diï¬€erential returns to capital or consump-
tion smoothing, but rather with liquidity shortages. Recall that, faced with
binding liquidity constraints, producers in emerging economies stand to make
strictly positive proï¬?ts from additional units of liquidity: with an additional
1
liquid claim, producers can purchase w units of labor, which, at the mar-
âˆ‚F (kem,t ,l)
gin, produce a return of âˆ‚l
> w. Anticipating their constraint in the
next period, producers in emerging economies ï¬?nd it optimal to buy liquid
claims in global liquidity markets. Importantly, when producers decide to
buy foreign issued liquid claims, they do not internalize the pecuniary exter-
nality on wages. At the aggregate level, since labor is supplied inelastically,
â€œimportedâ€? liquidity does not increase employment but translates entirely
into higher wages. At this range, the emerging economy is made worse oï¬€
by ï¬?nancial integration, as the economy must spend resources on importing
22
foreign liquidity.
Proposition 2 Assume that there is no enforceability risk (xt = 1 for all t).
1. There exists a unique integrated equilibrium steady state in which:
(a) The capital level in the emerging economy is equal to its autarkic
steady state level;
(b) The capital level in the developed economy is higher than its au-
tarkic steady state level;
(c) The emerging economy lends to the developed economy (bss
em âˆ’
ss
Bem > 0).
2. For kem,0 and kd,0 suï¬ƒciently close to their autarkic steady state levels,
ï¬?nancial integration reduces equilibrium welfare for emerging economies.
Developed economies are made better oï¬€ by ï¬?nancial integration (re-
gardless of initial conditions).
The ï¬?rst part of the proposition describes the steady state of the inte-
grated equilibrium. The capital level in the emerging economy is the same
as its autarkic level; however, the incentive to create privately-backed liquid
claims implies a higher steady state capital level in the developed economy.
At the steady state, the emerging economy lends to the developed econ-
omy in every period. This is because the steady state wage bill in emerging
economies is too high to be ï¬?nanced with domestically issued liquid claims;
eï¬€ectively, emerging economies â€œimportâ€? liquidity in order to ï¬?nance inï¬‚ated
production expenses.
The second part of the proposition summarizes the discussion above:
when initial conditions in emerging economies are very diï¬€erent from ini-
tial conditions in developed economies, emerging economies may gain from
ï¬?nancial integration through standard channels. However, when initial con-
ditions are suï¬ƒciently close, ï¬?nancial integration reduces welfare for emerg-
ing economies, as it creates ineï¬ƒcient dependence on foreign liquidity. The
23
numerical example in the next section illustrates that, in this context, â€œsuf-
ï¬?ciently closeâ€? need not be very close: even when the initial capital stock
of the emerging economy is 15% of its steady state level (and kd,0 is at its
autarkic steady state), it is a net lender in every period and made worse oï¬€
by ï¬?nancial integration.
Interestingly, regardless of initial conditions, developed economies are al-
ways made weakly better oï¬€ by ï¬?nancial integration. In this model, this
conclusion holds true even in the presence of enforceability risk. For agents
in developed economies, the autarkic consumption sequence is always feasible
under ï¬?nancial integration, as they always have enough publicly backed liquid
claims to ï¬?nance the autarkic level of employment. For emerging economies
this is not the case, because given equilibrium wages, domestically issued
liquidity is insuï¬ƒcient to ï¬?nance autarkic production.
7 Numerical example
This section presents two quantitative exercises. First, abstracting away from
enforceability shocks, I compare the autarkic equilibrium with the integrated
equilibrium. Second, I consider the implications of a permanent enforceabil-
ity shock.
I assume that the intertemporal elasticity of substitution is 1, or u(c) =
ln(c). The choice of parameters is summarized in table 1. The ï¬?rst three
parameters, Î² , Î´ , and Î±, are standard. The choice of l = 1 and Ad = 1
are convenient normalizations. The productivity of the emerging market is
calibrated based on Hsieh and Klenow [2009], who estimate manufacturing
productivity in the US to be about 150% higher than in India and China.10
The value of Î¸d was chosen to match the value of M3 over GDP in the US.
The value of Î¸em was calibrated to roughly match M3 over GDP in emerging
10
I chose to calibrate TFP diï¬€erences based on the diï¬€erences in manufacturing pro-
ductivity, which are relatively small compared to current diï¬€erences in TFP levels. This
reï¬‚ects some expected convergence in TFP in the long run.
24
Table 1: Calibration parameters
Notation Variable Value
Î² Discount factor 0.97
Î´ Depreciation rate 0.1
Î± Capital share in production 0.33
Ad Productivity: developed economies 1
Aem Productivity: emerging economies 0.4
Ï? Size of emerging market (relative to developed) 10
l Labor supply 1
Î¸d Public backing as a share of output: developed economies 0.7
Î¸em Public backing as a share of output: emerging economies 0.35
Î³ Private liquidity as a share of capital: developed economies 0.078
kd,0 Initial capital level: developed economies 3.97
kem,0 Initial capital level: emerging economies 0.15
economies, in particular China and India.11 The value of Ï? was chosen to
roughly match the population of BRIC countries (Brazil, Russia, India and
China) relative to the US.
I use the following procedure to calibrate Î³ . According to Gorton et al.
[2012], privately backed claims (including MBS, ABS, corporate bonds and
loans) accounted for about 25% of the supply of liquid claims in the US in
2006. I choose Î³ to match this proportion in the integrated steady state.
Importantly, this proportion approaches its steady state level quite quickly:
at t = 4 (the timing of the calibrated â€œshockâ€?), this share is already 23%.
Thus, the calibration of Î³ would be roughly the same if I were to choose Î³
to match this proportion at t = 4.
11
For the US, the average value of M3 as a percent of nominal GDP is about 70%
M3
between 1960-2011. It is worth noting that P Y in the US is essentially trend-less in this
period, despite the fact that the US has experienced high GDP growth. This feature of the
data is consistent with the assumption that Î¸ is a time invariant parameter that does not
change with GDP. Unfortunately, data for China is available only for the years 1977-1982.
For these years, M3 was 30% of nominal GDP on average. More data is available for India.
Between 1977 and 1992, the average M3 over nominal GDP in India was 38%. Source:
World Development Indicators.
25
The initial capital level in the developed economy is chosen as the autarkic
steady state level. In the emerging economy, the initial capital level is chosen
to match a 10% growth rate (under autarky). The other initial conditions
are given by the autarkic equilibrium levels, Bi,0 = bi,0 = Î¸i Fi (ki,0 , l) and
BËœi,0 = Ëœ
bi,0 = Î³ i ki,0 .
7.1 Financial integration
To illustrate the workings of the model, I present a quantitative comparison
between the autarkic equilibrium and the integrated equilibrium, abstracting
away from any enforceability risk (xt = 1 for all t).
Given the chosen parameters, the model suggests that, in developed
economies, ï¬?nancial integration is associated with welfare gains equivalent
to a 12% permanent increase in consumption, while, in emerging economies,
ï¬?nancial integration is associated with a welfare loss equivalent to a 6.5%
permanent reduction in consumption.
Steady state analysis. The steady state values of the autakic and open
equilibria, given the calibrated parameters in table 1, are summarized in the
ï¬?rst two columns of table 2 (the third column presents steady state values
for a permanent enforceability shock studied in the next section).
In this numerical example, steady state consumption in emerging economies
is about 5.3% lower in the ï¬?nancially integrated equilibrium, while steady
state consumption in developed economies is about 16.1% higher.
The last two rows are net exports as a fraction of GDP. Notice that, in this
model, the trade balance is equal to the current account. These parameters
suggest that, in the steady state, the emerging market exports roughly 4.2%
of its GDP to the developed economy, as payment for liquidity services. At
the same time, the developed economy enjoys a steady state ï¬‚ow of imports
equal to 9.7% of its GDP.
26
Table 2: Steady state comparison
Open Shock
Variable Autarky Open Shock
Autarky No shock
cem 0.3 0.284 0.283 0.947 0.996
cd 1.179 1.369 1.357 1.161 0.991
kem 1.012 1.012 1.012 1 1
kd 3.974 5.188 3.974 1.305 0.766
wem 0.141 0.211 0.18 1.496 0.853
wd 1.056 0.905 0.707 0.857 0.781
rem -0.461 -0.191 -0.31 1.623
rd 0.031 -0.191 -0.31 1.623
nx
( y )em 0.042 0.044 1.048
( nx )
y d
-0.097 -0.113 1.165
Transitional dynamics. I solve for the equilibrium using Dynare. Figures
3 and 4 describe the transitional dynamics of the integrated equilibrium
compared to the autarkic counterfactual.
Upon ï¬?nancial integration, the developed economy starts accumulating
capital, until it converges to its new steady state. The incentive to accu-
mulate additional capital stems from the ability to create collateral-backed
liquid claims. This trend is broadly consistent with the pre-crisis boom in
the US, and especially with the view that the housing boom was driven by
the incentive to create MBS (which had favorable liquidity properties).
On impact, ï¬?nancial integration leads to a 6% increase in consumption in
the developed economy, reï¬‚ecting a higher permanent income due to inter-
national liquidity rents. Faced with higher private returns to capital, house-
holds in the developed economy initially sacriï¬?ce some consumption growth
in favor of investment. However, consumption growth quickly recovers as it
converges to its new steady state.
Interestingly, the wage rate in the developed economy falls, despite the
fact that it is accumulating capital. Capital accumulation raises the â€œun-
constrainedâ€? wage bill, as the marginal product of labor increases; however,
27
1.5 0.4
1.4 Integration Autarky
0.3
Integration
1.3
0.2
1.2
Autarky
0.1
1.1
1 0
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76
(a) Consumption: developed econ-(b) Consumption: emerging econ-
omy omy
6 1.2
Integration
5 1
Integration
4 0.8
Autarky Autarky
3 0.6
2 0.4
1 0.2
0 0
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76
(c) Capital: developed economy (d) Capital: emerging economy
1 0.12
0.1
0.8
Integration
0.08
0.6 Autarky
Integration
0.06
0.4
Autarky 0.04
0.2 0.02
0 0
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76
(e) Investment: developed economy (f) Investment: emerging economy
1.1 0.3
Autarky
Integration
1 0.2
Integration Autarky
0.9 0.1
0.8 0
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76
(g) Wage: developed economy (h) Wage: emerging economy
Figure 3: A comparison of the integrated and autarkic equilibria: consump-
tion, capital, investment and wages.
28
0.1
Autarky: d 0.2
0
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 0.1
-0.1 nx: em
0
-0.2
Integration 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76
-0.1
-0.3 nx: d
-0.4 -0.2
Autarky: em
-0.5 -0.3
(a) Interest rate (r) (b) Net exports (as a fraction of out-
put)
Figure 4: A comparison of the integrated and autarkic equilibria: the interest
rate on publicly backed claims and net exports (in the closed economy, net
exports are 0).
at the same time, the return to liquidity increases, and the option of selling
liquid claims abroad becomes more attractive relative to paying for domestic
labor. The widening gap between the marginal product of labor and the
wage is consistent with recent trends in the US.12
The interest rate (r) is declining over time. From the perspective of
developed economies, ï¬?nancial integration is associated with an initial drop
in r from its autarkic steady state level of 3% to around 0. During the
transition, the interest rate declines until reaching its steady state value of
-19%. In principle, there are two competing forces aï¬€ecting the interest rate
trend: on the one hand, capital accumulation in both the emerging and the
developed economies decreases the marginal return to capital, thus putting
downward pressure on r. In addition, as the emerging economy grows, its
excess demand for liquidity increases. This channel further contributes to the
decline in r and to the increase in liquidity premiums. On the other hand,
12
Calibrating the marginal product of labor as M P L = (1âˆ’lÎ±)Y with Î± = 0.33, the
â€œlabor wedgeâ€? Mw PL
has been increasing steadily in the US, from around 1.2 in 1990 to
1.3 in 2010. The calculations are based on the following data from the OECD, 2013. For
Y : B1 GA: Gross domestic product (output approach) National Currency, current prices.
For l: Annual Labor Force Statistics, Total Employment. For w: Average annual wages,
current prices in NCU.
29
capital accumulation in the developed economy increases the supply of both
public and private liquid claims, somewhat countering the increased demand
for liquidity; this channel puts some upward pressure on r. In equilibrium,
the ï¬?rst channels dominate and the path of r is steadily decreasing.
Though not detectable in the ï¬?gures, ï¬?nancial integration actually slows
down capital accumulation in the emerging economy. For example, after one
period, capital is 0.89 of what it would have been under autarky; by the ï¬?fth
period, capital is 0.96 of its autarkic counterfactual level, and by the tenth
period, it is 0.99 of its autarkic counterfactual level. This ï¬?nding suggests
that (contrary to popular beleifs in policy circles) high foreign savings does
not accelerate growth, but rather slows down growth. In this model, growth
is driven by standard convergence considerations, and, while a high saving
rate emerges in equilibrium, equilibrium output growth is slower compared
to the autarkic counterfactual.
Similarly, consumption in emerging economies initially drops by almost
13% (compared to the autarkic counterfactual). The gap gradually declines
until it converges to its steady state level of 5.6%. Both consumption and
investment are disproportionately aï¬€ected in the ï¬?rst periods. In later pe-
riods, the increase in liquidity supply in the developed economy somewhat
mitigates the strain on the budget constraint, as liquidity imports become
relatively cheaper.
On impact, net exports in the emerging economy increase to roughly 20%
of GDP, mirrored by net imports of around 25% of GDP in the developed
economy. This initial surge is due to the fact that, in the ï¬?rst period, the
emerging economy is buying foreign bonds but not redeeming foreign bonds;
in subsequent periods, the trade balances are more modest, as the emerging
economy is both buying and redeeming bonds.
30
7.2 A permanent enforceability shock
The second quantitative exercise illustrates the eï¬€ects of a permanent and
unexpected enforceability shock. In the benchmark economy, there are no
enforceability problems and xt = 1 for all t. At some t Â¯, enforceability breaks
down unexpectedly and xt = 0 for every t â‰¥ t Â¯. Notice that this shock is
equivalent to a shock to Î³ in the developed economy, that brings the value
of Î³ d permanently to Î³ = 0. This extreme scenario is meant to illustrate
how, in a global environment characterized by liquidity shortages, a shock to
enforceability - or, alternatively, a shock to the ability to use capital to create
collateral-backed liquid claims - can lead to a surge in liquidity premiums and
a reduction in investment.
Before presenting the results, it is useful to clarify how this type of â€œen-
forceability shockâ€? is related to other models of the recent crisis. Broadly,
theories attempting to explain the recent crisis fall into one of two categories:
the â€œcredit shockâ€? view (e.g., Jermann and Quadrini [2012]) and the â€œdemand
shockâ€? view (e.g., Mian and Suï¬? [2012]). The key diï¬€erence between the two
views is the implication for the investment wedge. According to the â€œcredit
shockâ€? view, the tightening of a ï¬?nancial constraint creates an investment
wedge that prevents agents from taking advantage of high-return investment
opportunities. In contrast, according to the â€œdemand shockâ€? view, the con-
traction in investment is voluntary, as low demand lowers the expected return
to capital.
This model falls somewhere in between. Mechanically, the shock is similar
to a credit shock, or a fall in the underlying collateral value of physical capital.
However, similar to the demand shock view, the contraction in investment is
voluntary: the incentive to accumulate physical capital is lower, as it can no
longer be used as collateral to back liquid claims.13
13
This feature of the model is similar to Midrigan and Philippon [2011].
31
Steady state analysis. The steady state variables associated with the
permanent enforceability shock are given by the third column of table 2.
In both economies, steady state capital is equal to its autarkic steady state
level. Compared to the no-shock trajectory, consumption is lower in both
economies. In the emerging economy, this reï¬‚ects higher liquidity rents. In
the developed economy this reï¬‚ects lower steady state capital and output.
The steady state interest rate is substantially lower compared to the no-
shock scenario, at -31%. With a higher liquidity premium, steady-state trade
balances become slightly more extreme: the emerging economy exports an
additional 0.2% of its GDP, and the ratio of imports to GDP in the developed
economy increases by 0.6%.
Transitional dynamics. Figures 5 and 6 present the transitional dynam-
ics associated with the enforceability shock, compared to the uninterrupted
equilibrium path. The timing of the shock was chosen as t Â¯ = 4, to match an
8% growth rate in the emerging market at t = 3 (in 2006, the average growth
rate of the BRIC economies was 8.55%14 ).
The dynamics of the model can qualitatively account for three interesting
features of the recent crisis. First, in the model, the shock is associated with
a sharp and permanent decline in interest rates and a surge in liquidity
premiums. This reï¬‚ects a shock to liquidity supply, as collateral-backed
claims cease to be liquid. This is qualitatively consistent with the decline in
the treasury rate following the 2007-2008 crisis.
Second, the model generates a decline in investment in the developed
economy, and an increase in investment in the emerging economy. The decline
in investment in the developed economy reï¬‚ects the lower private return to
capital. The increase in investment in the emerging economy is a result of the
developed economy running down its capital stock: in part, this is achieved
through saving in emerging economies, to smooth the declining consumption
14
Source: World Development Indicators.
32
1.45 0.3
1.4 0.25
No shock Shock
1.35 Shock 0.2 No shock
1.3 0.15
1.25 0.1
1.2 0.05
1.15 0
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76
(a) Consumption: d (b) Consumption: em
6 1.2
No shock
5 1
No shock
4 0.8 Shock
Shock
3 0.6
2 0.4
1 0.2
0 0
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76
(c) Capital: d (d) Capital: em
0.8 0.14
Shock
0.12
0.6
No shock 0.1
0.08 No shock
0.4
Shock 0.06
0.04
0.2
0.02
0 0
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76
(e) Investment: d (f) Investment: em
1.2 0.25
No shock
1
No shock 0.2
0.8 Shock
0.15
Shock
0.6
0.1
0.4
0.05
0.2
0 0
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76
(g) Wage: d (h) Wage: em
Figure 5: The equilibrium dynamics with and without the shock: consump-
tion, capital, investment and wages.
33
0.1 0.25 0.05
Shock 0
0.2
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76
0 No shock -0.05
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 0.15
-0.1
-0.1 0.1 -0.15
No shock
-0.2
0.05
-0.2 No shock -0.25
Shock
0 Shock
-0.3
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76
-0.3 -0.05 -0.35
NX NX
(a) Y : d (b) Y : em (c) Interest rate (r)
Figure 6: The equilibrium dynamics with and without the shock: net exports
and the interest rate.
path. These predictions are roughly consistent with the observed changes in
investment around the 2008-2009 crisis. The model predicts that the invest-
ment share of output in the developed economy should drop by 6.4% in the
period following the shock. In the US, the investment share dropped by 5.1%
between 2007-2009. The subsequent recovery is also of a similar magnitude:
the model predicts that after two (additional) periods, the investment share
in the developed economy should increase by 0.96%, which is roughly consis-
tent with the 0.8% increase in the investment share in the US between 2009
and 2011. For the emerging economy, the model predicts an increase in the
investment share of 3.7%, which is somewhat smaller that the increase in the
investment share in China between 2007-2009 of 6.5%.15
Third, the model predicts a temporary current account reversal: in the
period of the shock, the developed economy becomes a net exporter, and the
emerging economy becomes a net importer. While the magnitudes in the
model are large compared to the data, this result is qualitatively in line with
current account movements during the crisis: the current account surplus in
China dropped form 8.5% of GDP in 2006 to 4% of GDP in 2010, and the
current account deï¬?cit in the US dropped from 6% of GDP in 2006 to 3.3%
of GDP in 2010.16
15
Source: World Development Indicators, Gross Capital Formation (% of GDP).
16
Source: World Development Indicators, 2013: Current account balance (% of GDP).
34
In the model, this temporary reversal is driven by standard neoclassical
channels: as the developed economy runs down its capital stock, it ï¬?nds
it optimal to smooth consumption by lending to emerging economies. It
is worth emphasizing that, in this model, the current account reversal is
temporary: the steady state current account balances are even larger than
in the â€œno-shockâ€? trajectory.
While the model qualitatively accounts for some aspects of the crisis, it
misses the mark on others. Most notably, in the model, consumption in
the developed economy increases following the shock. Part of this is due to
mechanical aspects of the model: in a simple neoclassical framework, the only
way to reduce global investment is to increase global consumption. Given
that wages adjust instantaneously, the shock has no contemporaneous eï¬€ect
on output or employment. Standard â€œï¬?xesâ€? such as sticky wages would imply
a contemporaneous eï¬€ect on output, which would perhaps also translate into
lower consumption.
Part of the increase in consumption reï¬‚ects an increase in equilibrium
welfare which is potentially worth noting. Since the developed economy re-
mains a net exporter of liquid claims, the surge in liquidity premiums implies
a permanent increase in liquidity rents. Welfare calculations reveal that the
developed economy is made better oï¬€ by the shock.17 The intuition for the
welfare gain is one of standard â€œterms of tradeâ€? manipulation: as an exporter
of liquid claims, developed economies are made better oï¬€ by restricting the
supply of liquid claims and enjoying higher liquidity premiums. This mo-
nopolistic argument reveals a coordination failure among agents in developed
economies. Privately, each agent ï¬?nds it proï¬?table to create collateral-backed
claims, not internalizing the eï¬€ect that this will have on the equilibrium r.
From an aggregate perspective, developed economies are made better oï¬€ if
they refrain from creating and using privately backed liquid claims, as limited
17
The welfare improvement for the developed economy is equivalent to a permanent
increase in consumption of 1.75%, compared to the â€œuninterruptedâ€? integrated equilibrium.
35
supply hikes up the liquidity premium.
With the permanent enforceability shock, the steady state equilibrium is
Pareto eï¬ƒcient, as the incentive to create privately-backed liquid claims is
once again muted. However, the emerging market is made worse oï¬€ by the
shock: steady state consumption drops by about 0.38%, and, compared to
the no-shock counterfactual, consumption is lower in every period. Emerging
economies, who import liquid claims, are made worse oï¬€ by the permanent
increase in liquidity premiums. Their welfare loss is equivalent to a perma-
nent 1.23% reduction in consumption.
8 Concluding remarks
The presence of binding liquidity constraints implies a transfer of surplus
to liquidity suppliers. In the closed economy, liquidity is supplied domes-
tically so the â€œliquidity rentsâ€? (if any) are consumed domestically. In the
integrated equilibrium, â€œliquidity rentsâ€? are consumed disproportionately by
those who have a comparative advantage in creating liquidity. Under the
assumption that developed economies are better at creating liquidity than
emerging economies, this implies a transfer of surplus from emerging to de-
veloped economies.
Even in the presence of neoclassical motives for intertemporal trade, ï¬?-
nancial integration may be welfare reducing for emerging economies when
capital ï¬‚ows are primarily driven by liquidity motives. From the producerâ€™s
perspective, the liquidity constraint is binding, and there are strictly posi-
tive proï¬?ts to be made from getting hold of additional liquidity. However,
from a macro perspective, as the economy is in full employment, the binding
constraint is not the liquidity constraint but rather the resource constraint.
Importing liquidity is similar to importing money: in equilibrium, this does
not change output but merely inï¬‚ates domestic prices. Similarly, investing
in capital for the purpose of creating privately backed liquid claims is similar
36
to investing in private money-printing machines, in that it merely inï¬‚ates
nominal prices but does not contribute to economic eï¬ƒciency.
The monetary analogy is useful, also for pointing out potential avenues
for further analysis. Naturally, this paper emphasizes some aspects of liquid
claims, abstracting away from others. In this framework, a shortage in liq-
uid claims does not create any ineï¬ƒciency (as long as it does not increase
the incentives to accumulate capital or import liquidity from abroad). Of
course, there is a rich monetary literature suggesting various ineï¬ƒciencies
associated with the shortage of liquid claims (see, for example, Friedman
[1969] with respect to transaction costs). The welfare analysis in this pa-
per, by abstracting away from these channels, is of course incomplete. In
particular, international trade in liquid claims may have some beneï¬?ts if the
shortage in liquid claims in emerging economies generates large ineï¬ƒciencies.
I hope that in light of the relevance of liquidity motives in international cap-
ital ï¬‚ows, the stark welfare conclusions suggested by this paper will refocus
attention towards this important question.
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A Appendix
A.1 Proof of Lemma 1
Let Î»t be the Lagrange multiplier on the aggregate budget constraint of time
t (equation 16). The FOC of the Lagrangian with respect to kd,t+1 is:
âˆ‚F (kd,t+1 , l)
Î»t âˆ’ Î»t+1 ( + 1 âˆ’ Î´) = 0 (42)
âˆ‚k
40
Replacing kd,t+1 with kem,t+1 (and multiplying by Ï?) yields the ï¬?rst order
condition with respect to kem,t+1 . Thus,
âˆ‚F (kd,t+1 , l) âˆ‚F (kem,t+1 , l)
= â‡’ kd,t+1 = kem,t+1 (43)
âˆ‚k âˆ‚k
The FOC with respect to cd,t and cem,t yields:
Î² t u (cd,t ) = Î»t (44)
Î¨Î² t u (cd,t ) = Î»t (45)
It follows that Î² t u (cd,t ) = Î¨Î² t u (cd,t ), and by equation 42 the Euler
equation follows. By standard arguments, this system of equations converges
kss ,l)
to a steady state in which Î² 1
= âˆ‚F (âˆ‚k + 1 âˆ’ Î´ , and the budget constraint is
satisï¬?ed with equality.
A.2 Proof of Lemma 2
Denote the Lagrange multipliers on equations 9, 6, 4 and 5 by Î»1 2 3
t , Î»t , Î»t and
Î»4
t respectively (it is easy to see that the constraint in equation 10 is never
binding). Note that Î»3 4
t and Î»t are the constraints relevant at time t, when
the ï¬?rm is choosing Bi,t+1 and B Ëœi,t+1 .
The FOC of the Lagrangian are as follows:
â€¢ With respect to ct :
u (ct ) = Î»1
t (46)
â€¢ With respect to li,t :
âˆ‚F (ki,t , lt )
Î»1
t( âˆ’ wt ) âˆ’ Î»2
t wt = 0 (47)
âˆ‚l
41
â€¢ With respect to ki,t+1 :
âˆ‚F (kt+1 , lt+1 )
âˆ’ Î»1 1
t + Î²E (Î»t+1 ( + 1 âˆ’ Î´ )) + Î³Î»4
t = 0 (48)
âˆ‚k
â€¢ With respect to bi,t+1 :
Î»1
t
âˆ’ + Î²E (Î»2 1
t+1 + Î»t+1 ) = 0 (49)
1 + rt
â€¢ With respect to Bi,t+1 :
Î»1
t
âˆ’ Î²E (Î»1 3
t+1 ) âˆ’ Î»t = 0 (50)
1 + rt
â€¢ With respect to Ëœ
bi,t+1 :
Î»1
t
âˆ’ + Î²E (xt+1 (Î»2 1
t+1 + Î»t+1 )) = 0 (51)
1+r Ëœt
Ëœi,t+1 :
â€¢ With respect to B
Î»1
t
âˆ’ Î²E (xt+1 Î»1 4
t+1 ) âˆ’ Î»t = 0 (52)
1+r Ëœt
The autarkic equilibrium in the developed economy. To show that,
for the developed economy, the equilibrium satisï¬?es Î»3 4 2
t = Î»t = Î»t = 0
for every S t+1 , I solve for the equilibrium under this assumption and verify
that the constraints are satisï¬?ed. First, note that the assumption Î»2 t = 0
(for every realization of xt ) implies that consumption is deterministic; to
see this, note that xt enters only in the budget constraint (equation 9) and
the liquidity constraint (equation 6). Since the liquidity constraint is not
binding, the problem is equivalent to one in which xt appears only in the
budget constraint; however, by symmetry and market clearing, it must be
42
the case that Ëœ Ëœi,t ; it follows that the term xt (Ëœ
bi,t = B Ëœi,t ) = 0, thus there
bi,t âˆ’ B
is no consumption risk in equilibrium.
The equilibrium can be described by equation 46 and the following system
of equations:
âˆ‚F (kt , l)
= wt (53)
âˆ‚l
âˆ‚F (kt+1 , l)
Î»1 1
t = Î²Î»t+1 ( + 1 âˆ’ Î´) (54)
âˆ‚k
Î»1 1
t = Î²Î»t+1 (1 + rt ) (55)
Î»1 1
t = Î²Î»t+1 (1 + r
Ëœt )E (xt ) (56)
In equilibrium, the wage bill is given by âˆ‚F (k t+1 ,l)
âˆ‚l
l = wt+1 l; using the Cobb-
Douglas speciï¬?cation, the equilibrium wage bill is (1 âˆ’ Î±)F (kt+1 , l). Let
bi,t+1 = Bi,t+1 â‰¥ (1 âˆ’ Î±)F (kt+1 , l), such that Bi,t+1 â‰¤ mt+1 (the set of such B â€™s
is non-empty by the assumption Î¸d â‰¥ (1 âˆ’ Î±). Let Ëœ bi,t+1 = BËœi,t+1 â‰¤ Î³ki,t+1 .
Note that the solutions in this set satisfy the constraints in equations 6, 4
and 5.
The standard neoclassical growth model that we are left with converges to
a steady state, that can be computing by replacing time t and t + 1 variables
in the equilibrium equations with steady state values.
The autarkic equilibrium in the emerging economy. First, note that
the emerging economy is deterministic, as it lacks any ability to issue collat-
eral backed claims (Î³ em = 0).
Note that the liquidity constraint is binding: recall that to ï¬?nance the
unconstrained wage bill, the liquidity supply must be at least a fraction 1 âˆ’ Î±
of total output. In the emerging economy, there are only publicly backed
claims, and publicly backed claims as a fraction of output are assumed to be
less than 1 âˆ’ Î± (Î¸em < 1 âˆ’ Î±).
Thus, in equilibrium the liquidity constraint is binding for all ï¬?rms, and
43
Î»2
t+1 > 0:
wt li,t = bi,t (57)
Labor market clearing requires that li,t = l for all t, and thus wt l = bt . Using
the FOC with respect to li,t :
âˆ‚F (kt ,l)
Î»1
t(
âˆ‚l
âˆ’ 1) = Î»2
t (58)
wt
Substituting into the FOC with respect to bi,t+1 :
âˆ‚F (kt+1 ,l)
Î»1
t
Î»1
t+1 (
âˆ‚l
âˆ’ 1) = âˆ’ Î»1
t+1 (59)
wt+1 Î² (1 + rt )
âˆ‚F (kt+1 ,l)
Î»1
t
â‡’ Î»1
t+1
âˆ‚l
= (60)
wt+1 Î² (1 + rt )
âˆ‚F (kt+1 ,l)
â‡’ Î»1
t+1
âˆ‚l
Î² (1 + rt ) = Î»1
t (61)
wt+1
Using the FOC with respect to Bi,t+1 , note that:
âˆ‚F (k ,l) âˆ‚F (kt+1 ,l)
Î»1
t
t+1
Î»3
t = 1 1
âˆ’ Î²Î»t+1 = Î²Î»t+1 âˆ‚l
âˆ’ Î²Î»1
t+1 = Î²Î»1
t+1 (
âˆ‚l
âˆ’ 1) > 0
1 + rt wt+1 wt+1
(62)
It follows that Î»3
t
em
> 0 and thus bt = Bt = mt = Î¸ F (kt , l) for all t.
Since Î³ em = 0, the FOC of the household with respect to ki,t+1 can be
rewritten as the standard Euler equation:
âˆ‚F (kt+1 , l)
Î»1 1
t = Î²Î»t+1 ( + 1 âˆ’ Î´) (63)
âˆ‚k
Market clearing with respect to bt and bt+1 implies the aggregate budget
constraint. Furthermore, since there is no supply of collateral backed claims,
Ëœt = âˆ’1 (an inï¬?nite price for collateral backed claims in terms of current
r
goods) clears the market.
44
The rest of the proof follows trivially. The economy converges to a steady
state, as the evolution of kt and ct can be described by a standard neoclassical
growth model.
A.3 Proof of Proposition 1
Recall that by Lemma 1, any Pareto eï¬ƒcient allocation converges to a steady
kss ,l)
state in which kem = kd = k ss , and Î² 1
= âˆ‚F (âˆ‚k + 1 âˆ’ Î´.
I show that the steady state is not an equilibrium outcome of the inte-
grated economy. Using the householdâ€™s FOC with respect to ki,t+1 (equation
48), and equating Î»1 1
d,t+1 = Î»d,t , the autarkic steady state capital level im-
plies that Î»4 d = 0 at the steady state. In tern, using the developed economy
householdâ€™s FOC with respect to B Ëœi,t+1 , this implies that 1 + r
Ëœdss
= Î²E1 .
(xt )
Inserting this into the developed economyâ€™s householdâ€™s FOC with respect
to Ëœbi,t+1 yields Î»2
d = 0. Using the FOC with respect to bi,t+1 , this yields
ss 1
1 + r = Î² , and thus (using the same condition for the emerging economy),
Î»2em = 0.
Thus, for the Pareto eï¬ƒcient steady state to be an equilibrium outcome it
must be the case that Î»2 2
em = Î»d = 0; the liquidity constraint cannot bind in
equilibrium, and wages must be equal to the marginal product of labor (using
equation 47). Thus, the sum of wage bills are (1âˆ’Î±)F (k ss , l)(1+Ï?) (regardless
of xt+1 ). By assumption, this violates the aggregate liquidity constraint when
xt+1 = 1, as aggregate liquidity is given by F (k ss , l)(Î¸d + Ï?Î¸em ) + Î³k ss .
It follows that Î»4
d > 0 at the steady state, and the steady state capital level
in the developed economy is higher than in any Pareto eï¬ƒcient allocation.
A.4 Proof of Proposition 2
First, I solve for the integrated steady state in the riskless economy (p =
0). Using equations 49 and 47, and imposing steady state values for Î»1 , it
follows that the wedge between the marginal product of labor and the wage
45
is equated across regions:
âˆ‚F (ki , l)
wi = Î² (1 + r) (64)
âˆ‚l
If Î² (1 + r) = 1, the marginal product of labor is equated with the wage
in both countries. In this case, Î»2 = 0 in both countries. Using equations 51
and 52, it follows that Î»4 d = 0. Using equation 48, it then follows that the
steady state capital level in the developed economy is equal to its autarkic
steady state level.
Note that, as Î³ em = 0, by equation 48, the steady state capital level in
the emerging economy is the same as in the autarkic steady state.
Thus, (1 + r)Î² = 1 implies that both in emerging and in developed
economies the steady state capital levels are the same as under autarky, and
the liquidity constraint is not binding in either country. But this violates As-
sumption 1, according to which the aggregate liquidity issued in the autarkic
steady state is insuï¬ƒcient to ï¬?nance the unconstrained wage bill.
Thus, wi < âˆ‚F ( ki ,l)
âˆ‚l
in both countries, and Î² (1 + r) < 1.
âˆ‚F (ki ,l)
Since wd < âˆ‚l , it follows that the developed economy sells publicly
backed liquid claims in equilibrium: otherwise, since Î¸d > (1âˆ’Î±), there would
be enough domestically held publicly backed liquid claims to ï¬?nance the
unconstrained wage bill, and the liquidity constraint would not be binding.
It follows that in equilibrium, the emerging economy lends to the devel-
oped economy in every period (bss ss
em âˆ’ Bem > 0).
To show that when initial conditions are suï¬ƒciently similar, the emerging
market is better oï¬€ under autarky, I use the following reasoning: when initial
conditions are the same, autarky is Pareto eï¬ƒcient. I show that (regardless
of initial conditions) the developed economy is made strictly better oï¬€ by
ï¬?nancial integration; it follows that emerging economies are made worse oï¬€
by ï¬?nancial integration. By continuity, this comparison holds true for initial
conditions that are not identical but suï¬ƒciently close.
To show that the developed economy is made better oï¬€ by ï¬?nancial inte-
46
gration, it is suï¬ƒcient to show that, given equilibrium prices, the autarkic al-
location is feasible. To see this, note that an agent in the developed economy
can replicate his autarkic consumption sequence by excluding himself from
ï¬?nancial markets, and ï¬?nancing his wage bill with self-issued publicly backed
claims. Formally, consider the choice bi,t+1 = Bi,t+1 = (1 âˆ’ Î±)F (kd,t+1 , l) (for
an agent i in country d). Note that this choice is feasible as Î¸d > (1 âˆ’ Î±) (and
mt is the same for all ï¬?rms, regardless of their individual capital levels).
Since wt l â‰¤ (1 âˆ’ Î±)F (kd,t , l), the agent always has suï¬ƒcient liquidity to
choose to hire l units of labor (li,t = l).
The agent receives the market wage, so his labor income is wt+1 l. The
agentâ€™s budget constraint (under the assumptions bi,t = Bi,t and li,t = l) is
therefore reduced to:
ci,t + ki,t+1 = F (ki,t , l) + (1 âˆ’ Î´ )ki,t âˆ’ wt l + wt l = F (ki,t , l) + (1 âˆ’ Î´ )ki,t (65)
For t > 0. For t = 0, by assumption the wage is set (at time -1) such that
all agents have enough liquidity to hire l units of labor; the only diï¬€erence
is some â€œinitial wealthâ€?, bi,0 âˆ’ Bi,0 .
This sequence of budget constraints replicates the autarkic sequence of
budget constraints. It follows that agents in developed economies can repli-
cate the autarkic consumption sequence; the fact that they choose not to
implies that they are made strictly better oï¬€ by ï¬?nancial integration. As
the autarkic equilibrium is eï¬ƒcient when initial conditions are identical, it
follows that emerging economies are made strictly worse oï¬€.
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