Apoorva Javadekar - My comments on mendoza and quadrini 2010

Financial Integration, Financial Development and Global
Imbalances;
Mendoza, Quadrini, Rios -Rull
Presented by Apoorva Javadekar
Boston University, Class of EC 741
January 10, 2012
Presented by Apoorva Javadekar (Boston University, Class of EC 741)Global Imbalances January 10, 2012 1 / 32

Summary
Motivation: Empirical Evidence
Objective of the Paper in more detail
Model, Equilibrium and Analytical solution
Extensions of the Model
Literature review
Conclusions by Authors
Comments

Motivation: Empirical Evidence
Process of financial Integration started in 1980’s, but countries differ
in the degree of development of financial markets.
USA’s current account position is deteriorating for last decade.
USA had built a large international debt position and at the same
time increased it’s share of risky asset holdings abroad.
Emerging economies have become providers of debt to developed
countries

Questions the Evidence Raises and Objective of the Paper
Paper tries to answer following questions
How does financial Integration affects the global savings and
borrowing patterns?
How does heterogeneity in financial development amongst the
countries determine the composition of portfolios of countries?
Is financial integration welfare improving?
Paper finds following answers
Heterogeneous Financial Development + Financial Integration =⇒
Explains observed data on NFA
Adjustment process is a long lasting (around 30 years)
Moderate heterogeneity leads to large changes in NFA positions

Broad Story of the Model
Countries with differing degree of development of financial markets
integrate financially
Developed Country (D) reduces savings as better insurance
opportunities are available while underdeveloped country (U)
increases savings on precautionary motive. Interest rates adjust for
this process to work.
Basically U lends to D and D invests it back in to risky assets in U.
This creates huge debt position for D and at the same time higher
investments in risky assets.
This matches with broad pattern observed for USA from 1980’s.

Model Set Up
1 Countries
Two countries; i ∈ {1, 2}, each inhabited by continuum of agents of
mass 1.
Differ in terms of contract enforceability due to income verifiability. φi
is the proportionate cost of hiding the true state.
φi
denotes the index of verifiability. Higher φi
implies higher
verifiability or higher punishment for false reporting of income.
2 Production Technology
Each country has a unit supply of non reproducible, internationally
immobile production asset, traded at price Pi
t , in country i
Production requires managerial capital, which is in limited supply but
internationally mobile in exclusive fashion (domestic or foreign)
Individual production function: yt+1 = kν
t zt+1, with one period lag
zt+1: idiosyncratic productivity shock
ν < 1 =⇒ Decreasing returns to scale due to limited managerial
capital.

Model Set Up
1 Agents
Maximize E
∞
t=0 βt
U(ct), U > 0
Face sequence of idiosyncratic income process {wt} and productivity
shock {zt}
Buys contingent claims to insure against these shocks
2 States and Assets
state vector: st = (wt, zt) with transition function g(st, st+1)
Arrow security for each state; qi
t(st, st+1) = g(st ,st+1)
(1+ri
t )
Price follows this formula because of no aggregate risk
3 Shocks
No aggregate risk
Individual production and no aggregate capital
Productivity shocks are avoidable, while endowment shocks are not
=⇒ Non trivial portfolio choice problem for agents

Legal Set up and Heterogeneity
Nature of Financial Contract
Agent enter in to a contract with intermediary for contingent claims
As shock is private, it is not directly observable. Hence, agent declare
the state he is in. Intermediary pay accordingly
If agent gets good shock and report bad shock, he gets to keep (1-φi
)
of differential income in addition to full income of bad state together
with contingent claims payoff of bad state.
This requires that contracts be incentive compatible. or given φi
,
contracts should induce agents to tell truth. Else, pricing is
inconsistent with competitive intermediary markets.
Heterogeneity
low φi
=⇒ diversion is unstoppable =⇒ non state - contingent
securities only =⇒ Incomplete markets and poor risk sharing
high φi
=⇒ Incentive compatibility satisfied =⇒ State - contingent
securities =⇒ more complete markets and better risk sharing
Hence More development =⇒ More Risk Sharing (A good
index)

Agents Maximization Problem: Constraints
Period t Net worth before consumption
at = ct + ktPi
t +
st+1
b(st+1)qi
t(st, st+1) (1)
Evolution of wealth
a(st+1) = wt+1 + ktPi
t+1 + zt+1kν
t + b(st+1) (2)
Enforceability in country i with index φi
Vt(sj , a(sj )) ≥ Vt(sj , a(s1)+(1−φi
) [(wj + zj kν
t ) − (w1 + z1kν
t )]) (3)
or Value from truth telling ≥ Value from hiding
Limited Liability
a(sj ) ≥ 0 (4)
∀ possible j ∈ {1, 2, ..., J}, with s1 being the worst

Agents Maximization Problem
Agents solve
V i
t (s, a) = max
c,k,b(s )
U(c) + β
s
V i
t+1(s , a(s ))g(s, s ) (5)
s.t (1), (2), (3), (4) above
Optimal Decision rules given by ci
t(s, a), ki
t(s, a), bi
t(s, a, s )
Decision rules + Shock process =⇒ distribution of agents Mi
t(s, k, b)
As deterministic price sequence Pi
t, qi
t(st, st+1) is equalized across
countries because of capital mobility, agents are indiﬀerent about
domestic versus foreign productive asset.

Equilibrium Under Autarky
Given φi and initial Mi (.), a general equilibrium is a collection of
ci
t(s, a), ki
t(s, a), bi
t(s, a, s )
associated Value function V i
t (s, a)
Price sequences Pi
t, ri
t , qi
t(s, s )
Distribution sequence Mi
t(s, k, b) Induced by policy rules
such that
qi
t(st, st+1) = g(st ,st+1)
(1+ri
t )
s,k,b ki
t(s, a) Mi
t(s, k, b) = 1
s,k,b,s bi
t(s, a, s )Mi
t(s, k, b)g(st, st+1) = 0
∀i ∈ {1, 2}

Equilibrium Under Integration
Given φi and initial Mi (.), a general equilibrium is a collection of
ci
t(s, a), ki
t(s, a), bi
t(s, a, s )
associated Value function V i
t (s, a)
Price sequences {Pt, rt, qt(s, a, s )}
Distribution sequence Mi
t(s, k, b) Induced by policy rules
such that
r1
t = r2
t = rt and P1
t = P2
t
qt(st, st+1) = g(st ,st+1)
(1+rt )
2
i=1 s,k,b ki
t(s, a) Mi
t(s, k, b) = 2
2
i=1 s,k,b,s bi
t(s, a, s )Mi
t(s, k, b)g(s, s ) = 0

Diﬀerence between two equilibriums
Asset markets and contingent claims market clears internationally, as
against domestically when integration is allowed
Interest rates, and other prices equalizes in both the countries in
equilibrium
As managerial input is mobile, and asset markets clear globally, NFA
position is created which is simply
NFAi
t =
s,k,b,s
bi
t(.)Mi
t(.)g(.) +
s,k,b
(ki
t(.) − 1)PtMi
t(.) (6)
NFAi
t = Net contingent claims + Net Productive asset position (net
of available 1 unit)

Equilibrium: Endowment Shocks Only in Autarky
Case I: Developed Country
Euler equations with respect to state claims and capital
respectively;
U (c) = β(1 + rt)U (c(w )) + (1 + rt)λ(w ) ∀w (7)
U (c) = βRt+1(k, z)E(U (c(w ))) + Rt+1(k, z)E(λ(w )) (8)
Characteristics
1 Since 7 holds for all w’, U (c(w )) is same for all w’: Result of
complete markets
2 β(1 + rt) = 1: Else growth of ct is non zero for all agents, which can’t
be an equilibrium.
3 Rt+1(k, z) = (1 + rt): Equality of returns on claims and productive
assets
4 This implies no precautionary savings (even if U”’ > 0)

Equilibrium: Endowment Shocks Only in Autarky
Case II: Underdeveloped Markets φi = 0
Euler equations
U (c) = β(1 + rt)EU (c(w )) + (1 + rt)E(λ(w )) (9)
U (c) = βRt+1(k, z)E(U (c(w ))) + Rt+1(k, z)E(λ(w )) (10)
Characteristics:
Incomplete markets imply consumption is state dependent and
expectations enters the equation
Still Rt+1(k, z) = (1 + rt) holds
Convex MU implies β(1 + rt) < 1 =⇒ precautionary savings
Lower interest rates than developed markets (because of higher
demand for saving)

Financial Integration Under Endowment Shocks Only
Outcome after integration
Interest rates equalize in both countries; =⇒ fall in rates for D and rise
in rates for U
=⇒ U lends and D country builds negative debt position
Though D maintains zero net position in productive asset. (There is no
incentive for any country not to employ available productive resources)
Transition
As world rates are equal, both countries employ 1 unit of available
capital. At world equalized rates, β(1 + rw
t ) < 1 must hold, else world
consumption growth would be positive forever. But then for D ct
growth is negative, which implies at falls till the time it hits zero
celling. As kt = 1, budget equation is ct + Pt +
st+1
b(st+1)qi
t(st, st+1) = 0. This implies developed country
borrows. More intuitively, as underdeveloped markets has lower
interest rates to begin with, it ends up being positive NFA holder.

Equilibrium Analysis II: Investment Shocks Only Under
Autarky
Case I: Developed Markets
Euler Equations:
U (c) = β(1 + rt)U (c(z )) + (1 + rt)λ(z ), ∀z (11)
U (c) = βE(Rt+1(k, z ))U (c(z )) + Rt+1(k, z )E(λ(z )) (12)
Characteristics
Complete markets implies state wise optimization wrt claims. Hence
consumption is state independent
This also implies that E(Rt+1(k, z)) = (1 + rt) holds. (As we can take
out MU out of joint expectations)
β(1 + rt) = 1 is the only plausible equilibrium. =⇒ no precautionary
savings

Equilibrium Analysis: Investment Shocks Only Under
Autarky
Case II: Underdeveloped Markets φi = 0
Euler Equations
U (c) = β(1 + rt)EU (c(z )) + (1 + rt)Eλ(z ), ∀z (13)
U (c) = βE[Rt+1(k, z )U (c(z ))] + E[Rt+1(k, z )λ(z )] (14)
Characteristics
incomplete insurance =⇒ stochastic consumption, hence E(U’())
enters Euler equation
ERt+1(k, z ) = (1 + rt)
ERt+1(k, z ) − (1 + rt) = −
cov(Rt+1(k, z ), U (c(z )))
EU (c(z ))
(15)
This implies the risk premium for holding productive assets
having positive covariance with consumption

Financial Integration Under Investments Shocks
Impact of Integration
World rates rt are equalized on claims
D built negative NFA position and positive position in productive asset
At rw
t , β(1 + rw
t ) < 1.
Transition
Only plausible rates imply β(1 + rt) < 1. Same arguments imply that
developed world will have Negative NFA position. Also E(RU
t+1(k, z))
> E(RD
t+1(k, z)) = (1 + rw
t ) =⇒ k employed by agents in D is more
than that employed by U (As returns are decreasing in k)

General Model: Set Up
Extensions
International Risk Diversiﬁcation
Managerial capital can be allocated in multiple markets. Ai,t denote
managerial capital at time t in country i = 1,2,..., N, such that
N
i=1 Ai,t = 1
Population size or productivity diﬀerences
Heterogeneity in borrowing limits
Impact
If zi
shocks are imperfectly correlated, risk sharing is possible for
investment shocks
State variable vector is st = (wt, z1
t , ..., zN
t )

General Model: Optimization
Wealth before consumption
at = ct +
N
i=1
ki,tPi,t +
st+1
b(st+1)qi
t(st, st+1) (16)
Evolution of wealth
a(st+1) = wt=1 +
N
i=1
ki,tPi,t+1 + zi,t+1A1−ν
i,t kν
i,t + b(st+1) (17)
Incentive Compatibility
a(sj ) − a(s1) ≥ (1 − φi
) wj
− w1
+
N
i=1
(zj
1,t+1 − z1
1,t+1)A1−ν
i,t kν
i,t
(18)
Limited Liability Constraint
a(si ) ≥ ai
(19)

Equilibrium
Definition: Equilibrium is collection of sequence of
consumption and investment decision rules and associated policy
functions
Allocation of managerial inputs across countries
Resulting prices of assets, interest rates and claims
resulting distributions
such that
claims are priced as in original model
asset markets clear
contingent markets clears
Characteristics
Interest rates are equalized
Asset prices are not equalized as shocks are imperfectly correlated and
agents are not indifferent about which country to put managerial
capital into.
Same properties as in first model applies in equilibrium. (No
managerial premium required for developed country)

Calibration: Parameters
µ1 = 0.30; replicates the share of USA in world productivity
Process for Endowment: w = w (+/-) ∆w; w = 0.85 is the
average labor productivity before depreciation.
persistence probability = 0.95 and ∆ w = 0.6
Process for productivity shocks: z = z (+/-) ∆z; calibrate s.t y =
0.15. this requires z =0.15. Also ∆z = 2.5 and z shocks are taken to
be i.i.d
0 correlation of z shocks across countries
(φ1, φ2) = (0.35, 0) and (a1, a2) = (0,0) (this is an initial guess)
CRRA Utility function; RA parameter = 2
β = 0.925
ν = 0.75 (scale parameter)

Results: Individual Policies
Agents with higher wealth buy more Contingent claims.
For poor net position in claims in negative and for rich it is positive
Total risky investments rises with wealth
With higher wealth in D, proportion of investment in U grows: Price
is lower in that country implying higher returns.
Why not to invest fully in U? Imperfectly correlated shocks implies
diversiﬁcation gains from investing in both U and D

Results: Aggregate Variables
D develops large debt = -89 % of the domestic income and net
investment in risky assets = 37% domestic income
This implies net negative NFA = 51% of the domestic income; This
matches data on USA
Model also predicts the gross holdings of risky assets goes up
Average return on risky assets > interest rates: result of decreasing
returns + Investment risk
Only Investment shock: Net +ve holdings of risky assets but large
debt position is not generated
Only Endowment shocks: Large negative NFA is generated but no
compositional shifts
⇒ We require both the shocks to generate this asset holding pattern

Results: Transition
Decline in NFA for D is a slow process: around 30 years. But there
are immediate jumps after integration.
Current account drops immediately to around 4% of gdp
Net investments in productive assets by D increase immediately and
then remains constant.
Interest rates converge instantly.
Net contingent claims jumps down for D instantly but keeps on
adjusting downward in long run.
Why drastic portfolio adjustment? In the model, integration takes
place overnight and also other shocks such as oil price shocks are
ignored.

Results: Welfare Study
Poor borrows in both countries =⇒ poor in D gain and in U lose as
interest rates drop in D and rise in U
Rich Lenders in both countries =⇒ opposite impact
Diversiﬁcation implies gains for all the agents in both the countries
Net results: In D, poor gains, rich lose and opposite in U
Distribution is concentrated on left tail with majority agents being
poor =⇒ overall welfare impact dominated by how poor are aﬀected

Robustness tests
Sensitivity to Cross country Correlations: Less opportunity to
diversify. But Still D built large Negative NFA. But welfare is reduced
for agents in D and U both.
Alternative forms of Financial Development:
Differences in completeness: moderate negative NFA and positive risky
asset holdings
Differences in borrowing capacity: Negative NFA but no positive
position in asset holding:
why? Higher borrowing limits change propensity to save, not the
propensity to take risk
conclusion: Differences in both are required to match the data
Adding More Countries: Essential patterns remain the same, but
extent reduces to some extent.

Conclusions by Authors
Financial integration can cause large and persistent global imbalances
when financial development differs across countries
Deeper financial markets =⇒ Reduced savings and large debt
Deeper financial markets =⇒ Increased risky investments abroad
Model generates these facts with differences in financial development
as the only source of heterogeneity
Debt Imbalance is consistent with inter temporal solvency condition
and hence sustainable
Robust to many alternative specifications

Comparison with Literature
Wilen (2004): Studies only endowment economy. Model extends
this to production risks, thereby making compositional conclusions
Cabarello (2008): Heterogeneity measured by ability to supply
assets. Cabarello generates imbalances by differential productivity
growth. Model relies on financial integration as a reason for
imbalances
Hunt, Rebucci (2005), Faruqee, laxton, Pesenti (2007):
Exogenous shocks causes global imbalances. In the model, the
imbalances is endogenous after financial integration, which is much
well accepted than exogenous shocks to tastes and other features in
the model

Own Comments and Conclusions
Pros
Robust conclusions with closed form /analytical solution
Endogenous portfolio formation mechanism as against previous
literature
Elegant / intelligent way to capture risk sharing potential
Cons
Paper ignores the issue of increased correlation of shocks after financial
integration. In this case, risk premium will be low and rise in risky asset
position will be lower than what model predicts
No active modeling of current account deficit; Remainder view
Many results not applicable to intermediate values of financial
development (Negative NFA Position is not guaranteed). This feature
makes closed form solution as mysterious as any calibration exercise for
intermediate values of development

Thank you

Apoorva Javadekar - My comments on mendoza and quadrini 2010

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