Apoorva Javadekar - My comments on mendoza and quadrini 2010

Financial Integration, Financial Development and GlobalImbalances;

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 differin 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 sametime increased it’s share of risky asset holdings abroad.

Emerging economies have become providers of debt to developedcountries


Questions the Evidence Raises and Objective of the Paper

Paper tries to answer following questions

How does financial Integration affects the global savings andborrowing patterns?

How does heterogeneity in financial development amongst thecountries 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 marketsintegrate financially

Developed Country (D) reduces savings as better insuranceopportunities are available while underdeveloped country (U)increases savings on precautionary motive. Interest rates adjust forthis 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 higherinvestments in risky assets.

This matches with broad pattern observed for USA from 1980’s.


Model Set Up

1 CountriesTwo countries; i ∈ {1, 2}, each inhabited by continuum of agents ofmass 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 higherverifiability or higher punishment for false reporting of income.

2 Production TechnologyEach country has a unit supply of non reproducible, internationallyimmobile production asset, traded at price P i

t , in country iProduction requires managerial capital, which is in limited supply butinternationally mobile in exclusive fashion (domestic or foreign)Individual production function: yt+1 = kνt zt+1, with one period lagzt+1: idiosyncratic productivity shockν < 1 =⇒ Decreasing returns to scale due to limited managerialcapital.


Model Set Up

1 AgentsMaximize E

∑∞t=0 β

t U(ct), U ′′′ > 0Face sequence of idiosyncratic income process {wt} and productivityshock {zt}Buys contingent claims to insure against these shocks

2 States and Assetsstate vector: st = (wt , zt) with transition function g(st , st+1)

Arrow security for each state; qit(st , st+1) = g(st ,st+1)

(1+r it )

Price follows this formula because of no aggregate risk

3 ShocksNo aggregate riskIndividual production and no aggregate capitalProductivity shocks are avoidable, while endowment shocks are not=⇒ Non trivial portfolio choice problem for agents


Legal Set up and Heterogeneity

Nature of Financial ContractAgent enter in to a contract with intermediary for contingent claimsAs shock is private, it is not directly observable. Hence, agent declarethe state he is in. Intermediary pay accordinglyIf 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 togetherwith 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 isinconsistent with competitive intermediary markets.

Heterogeneitylow φi =⇒ diversion is unstoppable =⇒ non state - contingentsecurities only =⇒ Incomplete markets and poor risk sharinghigh φi =⇒ Incentive compatibility satisfied =⇒ State - contingentsecurities =⇒ more complete markets and better risk sharing

Hence More development =⇒ More Risk Sharing (A goodindex)


Agents Maximization Problem: Constraints

Period t Net worth before consumption

at = ct + ktPit +

∑st+1

b(st+1)qit(st , st+1) (1)

Evolution of wealth

a(st+1) = wt+1 + ktPit+1 + zt+1kνt + b(st+1) (2)

Enforceability in country i with index φi

Vt(sj , a(sj)) ≥ Vt(sj , a(s1)+(1−φi ) [(wj + zjkνt )− (w1 + z1kνt )]) (3)

or Value from truth telling ≥ Value from hiding

Limited Liabilitya(sj) ≥ 0 (4)

∀ possible j ∈ {1, 2, ..., J}, with s1 being the worst


Agents Maximization Problem

Agents solve

V it (s, a) = max

c,k,b(s′)

{U(c) + β

∑s′

V it+1(s ′, a(s ′))g(s, s ′)

}(5)

s.t (1), (2), (3), (4) above

Optimal Decision rules given by c it(s, a), k i

t(s, a), bit(s, a, s ′)

Decision rules + Shock process =⇒ distribution of agents M it(s, k , b)

As deterministic price sequence{

P it , q

it(st , st+1)

}is equalized across

countries because of capital mobility, agents are indifferent aboutdomestic versus foreign productive asset.


Equilibrium Under Autarky

Given φi and initial M i (.), a general equilibrium is a collection of{c it(s, a), k i

t(s, a), bit(s, a, s ′)

}associated Value function

{V it (s, a)

}Price sequences

{P it , r

it , q

it(s, s ′)

}Distribution sequence

{M i

t(s, k, b)}

Induced by policy rules

such that

qit(st , st+1) = g(st ,st+1)

(1+r it )∫s,k,b k i

t(s, a) M it(s, k, b) = 1∫

s,k,b,s′ bit(s, a, s ′)M i

t(s, k , b)g(st , st+1) = 0

∀i ∈ {1, 2}


Equilibrium Under Integration

Given φi and initial M i (.), a general equilibrium is a collection of{c it(s, a), k i

t(s, a), bit(s, a, s ′)

}associated Value function

{V it (s, a)

}Price sequences {Pt , rt , qt(s, a, s ′)}Distribution sequence

{M i

t(s, k, b)}

Induced by policy rules

such that

r1t = r2t = rt and P1t = P2

t

qt(st , st+1) = g(st ,st+1)(1+rt)∑2

i=1

∫s,k,b k i

t(s, a) M it(s, k , b) = 2∑2

i=1

∫s,k,b,s′ bi

t(s, a, s ′)M it(s, k , b)g(s, s ′) = 0


Difference between two equilibriums

Asset markets and contingent claims market clears internationally, asagainst domestically when integration is allowed

Interest rates, and other prices equalizes in both the countries inequilibrium

As managerial input is mobile, and asset markets clear globally, NFAposition is created which is simply

NFAit =

∫s,k,b,s′

bit(.)M i

t(.)g(.) +

∫s,k,b

(k it(.)− 1)PtM

it(.) (6)

NFAit = 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 capitalrespectively;

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)

Characteristics1 Since 7 holds for all w’, U ′(c(w ′)) is same for all w’: Result of

complete markets2 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

assets4 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 andexpectations enters the equationStill Rt+1(k , z) = (1 + rt) holdsConvex MU implies β(1 + rt) < 1 =⇒ precautionary savingsLower interest rates than developed markets (because of higherdemand for saving)


Financial Integration Under Endowment Shocks Only

Outcome after integrationInterest rates equalize in both countries; =⇒ fall in rates for D and risein rates for U=⇒ U lends and D country builds negative debt positionThough D maintains zero net position in productive asset. (There is noincentive for any country not to employ available productive resources)

TransitionAs world rates are equal, both countries employ 1 unit of availablecapital. At world equalized rates, β(1 + rwt ) < 1 must hold, else worldconsumption growth would be positive forever. But then for D ctgrowth is negative, which implies at falls till the time it hits zerocelling. As kt = 1, budget equation is ct + Pt +∑

st+1b(st+1)qi

t(st , st+1) = 0. This implies developed countryborrows. More intuitively, as underdeveloped markets has lowerinterest rates to begin with, it ends up being positive NFA holder.


Equilibrium Analysis II: Investment Shocks Only UnderAutarky

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)

CharacteristicsComplete markets implies state wise optimization wrt claims. Henceconsumption is state independentThis also implies that E (Rt+1(k , z)) = (1 + rt) holds. (As we can takeout MU out of joint expectations)β(1 + rt) = 1 is the only plausible equilibrium. =⇒ no precautionarysavings


Equilibrium Analysis: Investment Shocks Only UnderAutarky

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)

Characteristicsincomplete insurance =⇒ stochastic consumption, hence E(U’())enters Euler equationERt+1(k, z ′) 6= (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 assetshaving positive covariance with consumption


Financial Integration Under Investments Shocks

Impact of IntegrationWorld rates rt are equalized on claimsD built negative NFA position and positive position in productive assetAt rwt , β(1 + rwt ) < 1.

TransitionOnly plausible rates imply β(1 + rt) < 1. Same arguments imply thatdeveloped world will have Negative NFA position. Also E (RU

t+1(k , z))> E (RD

t+1(k , z)) = (1 + rwt ) =⇒ k employed by agents in D is morethan that employed by U (As returns are decreasing in k)


General Model: Set Up

ExtensionsInternational Risk DiversificationManagerial capital can be allocated in multiple markets. Ai,t denotemanagerial capital at time t in country i = 1,2,..., N, such that∑N

i=1 Ai,t = 1Population size or productivity differencesHeterogeneity in borrowing limits

ImpactIf z i shocks are imperfectly correlated, risk sharing is possible forinvestment shocksState variable vector is st = (wt , z

1t , ..., z

Nt )


General Model: Optimization

Wealth before consumption

at = ct +N∑i=1

ki ,tPi ,t +∑st+1

b(st+1)qit(st , st+1) (16)

Evolution of wealth

a(st+1) = wt=1 +N∑i=1

ki ,tPi ,t+1 + zi ,t+1A1−νi ,t kνi ,t + b(st+1) (17)

Incentive Compatibility

a(sj)− a(s1) ≥ (1− φi )

[w j − w1 +

N∑i=1

(z j1,t+1 − z1

1,t+1)A1−νi ,t kνi ,t

](18)

Limited Liability Constraint

a(si ) ≥ ai (19)


Equilibrium

Definition: Equilibrium is collection of sequence of

consumption and investment decision rules and associated policyfunctionsAllocation of managerial inputs across countriesResulting prices of assets, interest rates and claimsresulting distributions

such that

claims are priced as in original modelasset markets clearcontingent markets clears

CharacteristicsInterest rates are equalizedAsset prices are not equalized as shocks are imperfectly correlated andagents are not indifferent about which country to put managerialcapital into.Same properties as in first model applies in equilibrium. (Nomanagerial 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 theaverage 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 tobe 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: Priceis lower in that country implying higher returns.

Why not to invest fully in U? Imperfectly correlated shocks impliesdiversification gains from investing in both U and D


Results: Aggregate Variables

D develops large debt = -89 % of the domestic income and netinvestment in risky assets = 37% domestic income

This implies net negative NFA = 51% of the domestic income; Thismatches data on USA

Model also predicts the gross holdings of risky assets goes up

Average return on risky assets > interest rates: result of decreasingreturns + Investment risk

Only Investment shock: Net +ve holdings of risky assets but largedebt position is not generated

Only Endowment shocks: Large negative NFA is generated but nocompositional 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 thereare immediate jumps after integration.

Current account drops immediately to around 4% of gdp

Net investments in productive assets by D increase immediately andthen remains constant.

Interest rates converge instantly.

Net contingent claims jumps down for D instantly but keeps onadjusting downward in long run.

Why drastic portfolio adjustment? In the model, integration takesplace overnight and also other shocks such as oil price shocks areignored.


Results: Welfare Study

Poor borrows in both countries =⇒ poor in D gain and in U lose asinterest 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 beingpoor =⇒ overall welfare impact dominated by how poor are affected


Robustness tests

Sensitivity to Cross country Correlations: Less opportunity todiversify. But Still D built large Negative NFA. But welfare is reducedfor agents in D and U both.

Alternative forms of Financial Development:Differences in completeness: moderate negative NFA and positive riskyasset holdingsDifferences in borrowing capacity: Negative NFA but no positiveposition in asset holding:why? Higher borrowing limits change propensity to save, not thepropensity to take riskconclusion: Differences in both are required to match the data

Adding More Countries: Essential patterns remain the same, butextent reduces to some extent.


Conclusions by Authors

Financial integration can cause large and persistent global imbalanceswhen 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 developmentas the only source of heterogeneity

Debt Imbalance is consistent with inter temporal solvency conditionand hence sustainable

Robust to many alternative specifications


Comparison with Literature

Wilen (2004): Studies only endowment economy. Model extendsthis to production risks, thereby making compositional conclusions

Cabarello (2008): Heterogeneity measured by ability to supplyassets. Cabarello generates imbalances by differential productivitygrowth. Model relies on financial integration as a reason forimbalances

Hunt, Rebucci (2005), Faruqee, laxton, Pesenti (2007):Exogenous shocks causes global imbalances. In the model, theimbalances is endogenous after financial integration, which is muchwell accepted than exogenous shocks to tastes and other features inthe model


Own Comments and Conclusions

ProsRobust conclusions with closed form /analytical solutionEndogenous portfolio formation mechanism as against previousliteratureElegant / intelligent way to capture risk sharing potential

ConsPaper ignores the issue of increased correlation of shocks after financialintegration. In this case, risk premium will be low and rise in risky assetposition will be lower than what model predictsNo active modeling of current account deficit; Remainder viewMany results not applicable to intermediate values of financialdevelopment (Negative NFA Position is not guaranteed). This featuremakes closed form solution as mysterious as any calibration exercise forintermediate values of development


Thank you


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Apoorva Javadekar - My comments on mendoza and quadrini 2010