international liquidity and exchange rate dynamics liquidity and exchange rate ... international...

International Liquidity and Exchange RateDynamics

Xavier Gabaix and Matteo Maggiori

New York University, Stern School of Business, NBER, CEPR

May 30 2014Macro Financial Modeling Meeting

Introduction Basic Gamma Model Policy and Welfare Conclusions

Imperfect Finance and the Determination of Exchange Rates

“One very important and quite robust insight is that the nominal exchangerate must be viewed as an asset price” Obstfeld and Rogoff (1996)

I Exchange rates are disconnected from traditional macroeconomicfundamentals

I They are instead connected to financial forces: e.g. capital flows andfinancial conditions

I Demand and Supply of assets in different currencies is central toexchange rate determination

I Financial determination in imperfect capital markets is key for welfareanalysis: floating exchange rates do not move to absorb real shocks asin Mundellian analysis

Important issues: framework is desirable, but has proven elusive

Gabaix, Maggiori (2013) International Liquidity and Exchange Rate Dynamics


Imperfect Finance and the Determination of Exchange Rates

We provide a basic framework of capital flows and exchange rates:

I Capital flows alter balance sheet of financiers who intermediate flows

I Financiers’ balance sheets and risk bearing capacity determine therequired compensation for intermediating capital flows

I Such compensation determines both the level and dynamics ofexchange rates

I Practical Example:

US investors demand Brazilian Real bonds → Financiers provide thesebonds in the short-medium run, Short Real and Long Dollar → Tocompensate financiers, the Real appreciates on impact and is expectedto depreciate relative to the Dollar

I Our framework is a basic theory where a price, the exchange rate, hasto move to balance the demand/supply of assets in financial markets



Building up the Framework

I Basic exchange rate determination in an imperfect financial world

FINANCIERS

US HOUSEHOLDS JAPANESE HOUSEHOLDS

PROFITS PROFITS

TRADE IN GOODS

I Two important papers in 1976: Dornbusch’s “overshooting” model,and Kouri’s “portfolio balance” model

I Obstfeld, Rogoff (1995) brought Mundell-Fleming-Dornbusch model inmodern macroeconomics

I We provide a modern general equilibrium theory of the financial marketforces first sketched by Kouri



Related Open Macroeconomics Literature

I Portfolio Flows: Hau, Rey (2006); Bacchetta, Van Wincoop (2010);Jeanne and Rose (2002); Evans, Lyons (2002)

I Financial Intermediation: Maggiori (2011); Bruno and Shin (2012)

I Welfare and Policy Analysis: Farhi, Werning (2012a,b); Farhi,Gopinath, Itskhoki (2012); Magud, Reinhart, Rogoff (2012); Devereux,Engel (2003); Schmitt-Grohe, Uribe (2012a,b); Korinek (2011);Bianchi (2011)

I Complete Market Asset Pricing: Lucas (1982); Backus, Kehoe,Kydland (1992); Dumas (1992); Obstfeld, Rogoff (2001); Pavlova,Rigobon (2007); Verdelhan (2010); Farhi, Gabaix (2011); Hassan(2013); Colacito, Croce (2011)

I Incomplete Market Asset Pricing: Alvarez, Atkeson, Kehoe (2002,09)



Basic ModelWe present here the simplest model: real model, imperfect capital markets

I Two countries (US, Japan (*)). Two periods (t = 0, 1)

I Unit measure of households in each country

I Four goods: 1 non-tradable (NT) and 1 tradable good in each country

I NT are endowments, tradables produced with int. immobileinelastically supplied labor

I NT good is the numeraire in each economy

I Incomplete Markets: two “risk-free” bonds that pay for sure one unitof the domestic numeraire (the NT good) for each economy

I Households borrow/lend in domestic “risk-free” bonds with thefinanciers

I Financiers intermediate resulting global capital flows



The Household ProblemUS households’ consumption/saving decision:

maxc

E [θ0 lnC0 + βθ1 lnC1]

s.t.1∑

t=0

CNT ,t + pH,tCH,t + pF ,tCF ,t

Rt≤

1∑t=0

YNT ,t + pH,tYH,t

Rt

where Ct ≡ [(CNT ,t)χt (CH,t)

at (CF ,t)ιt ]

1θt , and θt = χt + at + ιt

Corresponding Japanese households’ problem:

maxc∗

E [θ∗0 lnC ∗0 + β∗θ∗1 lnC ∗1 ]

s.t.1∑

t=0

C ∗NT ,t + p∗H,tC∗H,t + p∗F ,tC

∗F ,t

R∗t≤

1∑t=0

Y ∗NT ,t + p∗F ,tY∗F ,t + πt

R∗t

where C ∗t ≡[(C ∗NT ,t)

χ∗t (C ∗H,t)

ξt (C ∗F ,t)a∗t] 1θ∗t ; and θ∗t = χ∗t + a∗t + ξt



Household Optimality Conditions

I Intra-temporal Optimality Conditions:

CNT ,t =χt

λt; pF ,tCF ,t =

ιtλt

Simplifying assumption: YNT = χt ⇒ λt = 1.

I US imports: pF ,tCF ,t = ιt ; Japan Imports: p∗H,tC∗H,t = ξt

I US net exports: NXt = ξtet − ιtI et : (real) Dollar per Yen exchange rate

I Inter-temporal Optimality Conditions:

1 = E

[βR

U ′1,CNT

U ′0,CNT

]= E

[βR

χ1/CNT ,1

χ0/CNT ,0

]= βR,



Financiers’ Asset Demand

I Unit measure of intermediaries, each financier runs one intermediary

I Agents are selected at random. Zero starting capital. Rebate all profitsto households

I Trade Dollar and Yen bonds. Balance sheet: q0 = −qF ,0e0

I Financiers maximize expected returns in dollars:

V0 = E[β

(R − R∗

e1

e0

)]q0

Intermediation Friction: After taking positions, but before uncertaintyis realized financiers can divert funds. If financiers divert, creditors

recover(

1− Γ∣∣∣q0e0

∣∣∣) of their claims∣∣∣q0e0

∣∣∣:V0

e0︸︷︷︸Intermediary Value

in Yen

≥∣∣∣∣q0

e0

∣∣∣∣︸︷︷︸Total

Claims

Γ

∣∣∣∣q0

e0

∣∣∣∣︸︷︷︸DivertedPortion

= Γ

(q0

e0

)2

︸︷︷︸Total divertable

Funds



Financiers’ Asset Demand: Micro-foundationsFinanciers’ problem:

maxq0 V0 = E[β(R − R∗ e1

e0

)]q0 s.t. V0 ≥ Γ

q20e0

Optimality ⇒ Constraint always binds ⇒ Financiers’ demand q0 dollar and−q0/e0 yen, according to:

q0 =1

ΓE[e0 −

R∗

Re1

]I Γ ↑ ∞: no amount of intermediation is possible ⇒ autarky

I Γ = 0: any amount of intermediation is possible ⇒ Uncovered InterestParity holds

This Γ demand function is key to the model: Basic Gamma model

Simplifying assumption: financiers pay all profits to Japanese householdsGabaix, Maggiori (2013) International Liquidity and Exchange Rate Dynamics


Financiers’ Asset Demand: Micro-foundationsFinanciers’ problem:

maxq0 V0 = E[β(R − R∗ e1

e0

)]q0 s.t. V0 ≥ Γ

q20e0

Optimality ⇒ Constraint always binds ⇒ Financiers’ demand q0 dollar and−q0/e0 yen, according to:

Q0 =1

ΓE[e0 −

R∗

Re1

]I Γ ↑ ∞: no amount of intermediation is possible ⇒ autarky

I Γ = 0: any amount of intermediation is possible ⇒ Uncovered InterestParity holds

This Γ demand function is key to the model: Basic Gamma model

Simplifying assumption: financiers pay all profits to Japanese householdsGabaix, Maggiori (2013) International Liquidity and Exchange Rate Dynamics


Equilibrium Exchange Rate

The flow equations in the US dollar market:

ξ0e0 − ι0 + Q0 = 0; ξ1e1 − ι1 − RQ0 = 0;

Q0 =1

ΓE[e0 −

R∗

Re1

]The equilibrium exchange rate follows (assume ξt = R = R∗ = 1):

e0 =(1 + Γ) ι0 + E[ι1]

2 + Γ; E

[e0 − e1

e0

]=

Γ (E [ι1]− ι0)

(1 + Γ) ι0 + E[ι1]

I Financial Autarky (Γ ↑ ∞): et = ιt

I UIP (Γ ↓ 0): e0 = E[e1] = ι0+E[ι1]2



Overview of Results

1. Exchange Rate Disconnect. Some Empirical Evidence

I Little connection between traditional fundamentals and exchange ratesMeese, Rogoff (1983)

I More evidence that exchange rates are connected to flows in themedium run

I Adrian, Etula, Groen (2011), Adrian, Etula, Shin (2013): financiers’balance sheet forecast USD FX

I Hau, Massa, Peress (2010): inflows cause currency appreciation. CleanIV approach

I Yogo, Hong (2012): CME speculators positions help predict currencyreturns

I Froot, Ramodorai (2005): flows are associated with most of thevariation in expected currency returns over medium horizons,fundamentals matter only at long horizon

2. Gross Capital Flows Matter3. Flows not just Stocks Matter4. External Debt and Currency Returns5. Carry Trade6. Welfare and Heterodox Financial Policies



Overview of Results

1. Exchange Rate Disconnect. Some Empirical Evidence2. Gross Capital Flows Matter

I For simplicity, assume that some Japanese households have a noisedemand f for Dollar bonds (financed in Yen bonds), then theequilibrium exchange rate follows:

e0 =(1 + Γ) ι0 + E[ι1]− f Γ

2 + Γ

I ∂e0

∂f = − Γ2+Γ : if Japanese households demand Dollar bonds (f > 0), then

the Dollar appreciates (↓ e0): supply and demand of assets matters!

I This effect is absent both in complete market models or in models thatassume UIP. Empirical support: Hau et al. (2010)

3. Flows not just Stocks Matter4. External Debt and Currency Returns5. Carry Trade6. Welfare and Heterodox Financial Policies



Overview of Results


2. Gross Capital Flows Matter

3. Flows not just Stocks Matter

I US has an exogenous Dollar-denominated debt toward Japan. D0 due attime zero, and D1 due at time one

e0 =(1 + Γ) ι0 + E [ι1]

2 + Γ+

(1 + Γ)D0 + D1

2 + Γ

I When finance is imperfect (Γ > 0):

I Timing of repayment (flow, D0D1

) matters, not just debt stock (D0 + D1)

I The higher Γ the more weight on early repayment

4. External Debt and Currency Returns

5. Carry Trade

6. Welfare and Heterodox Financial Policies



Overview of Results

1. Exchange Rate Disconnect. Some Empirical Evidence2. Gross Capital Flows Matter3. Flows not just Stocks Matter4. External Debt and Currency Returns

I US net foreign assets: N0+ = e0 − ι0 = E[ι1]−ι0

2+Γ

I Proposition: When there is a financial disruption (↑ Γ), countries thatare net external debtors (N0+ < 0) experience a currency depreciation(↑ e), while the opposite is true for net-creditor countries

I Suppose ι0 − E[ι1] > 0, US runs a trade deficit and borrows in dollars

I Financiers are long Dollar and short Yen (Q0 > 0)

I If financial conditions worsen (↑ Γ), the Dollar depreciates (↑ e0)

I Empirical support: Della Corte, Riddiough and Sarno (2013)

5. Carry Trade6. Welfare and Heterodox Financial Policies



Overview of Results

1. Exchange Rate Disconnect. Some Empirical Evidence2. Gross Capital Flows Matter3. Flows not just Stocks Matter4. External Debt and Currency Returns5. Carry Trade

I Model extension to 3 periods with Γ1 stochastic

I Carry trade return: Rc1 ≡ R∗ e1

e0− 1,with R∗ ≡ R∗

R

I Expected carry trade returns:

E[Rc1 ] =

R∗Γ0(Γ1 + 1 +R∗)

Γ1(Γ0 +R∗) + Γ0 + (R∗)2

Γ1

1+Γ1≡ E0

[Γ1

1+Γ1

]. Returns are higher:

I the higher is the interest rate differential R∗

I the worse financial conditions are today (↑ Γ0), the better they aretomorrow (↓ {Γ1, Γ1})

I CIP always holds, separate class of financiers does all arbitrages




Overview of Results


2. Gross Capital Flows Matter

3. Flows not just Stocks Matter

4. External Debt and Currency Returns

5. Carry Trade




Output Effects of Exchange Rates

I Output: Y = L; potential labor (L) is supplied inelastically

I Assume downwards rigid goods’ prices at pH , and producer currencypricing (PCP), then:

CH,t + C ∗H,t =at + etξt

pH⇒ YH,t = min

(at + etξt

pH, L

)I Output can be demand determined

I Intuitively: if Dollar prices are too high (↑ pH), or if the Dollar is toostrong (↓ et), output falls and there is unemployment (YH < L)

I Recall et = f (Γt ,QH,t): so financial determination of ER can have realeffects



FX Swaps and Currency Interventions: Welfare Consequences

I Recall: YH,0(e0) = min(a0+e0ξ0pH,0

, L)

I The government buys q yen and sells qeo dollars at time 0

I So e0(q) = 1 + Γ2+Γq +O(q2): Dollar depreciates, creating employment

I Welfare:

V (q) ≡ E[U0 + U1] = V FB + a0 lnYH,0(e0(q))

L+ O(q2)

I Proposition If Γ > 0 and YH,0(q = 0) < L, then welfare V (q) isincreasing in intervention q ∈ [0, qOpt ], where e(qOpt) generates fullemployment

I Note that under no taste shocks there are no private incentives tointervene



Take-Aways

We presented a basic model with:

I Imperfect capital markets: financial intermediation, supply and demandof assets matters!

I Production: real effects of ER fluctuations, unemployment

I (Potentially) sticky prices: PCP, LCP, incomplete pass-through

I Welfare analysis: monetary policy, heterodox financial policies

Key implications: Exchange rates are a financial phenomenon determinedby supply and demand of assets in different currencies. Financiers’ balancesheets and risk tolerance are important determinants of ER

Key take-away: Floating exchange rate regimes can be the source ofproblems. Heterodox policies (interventions, capital controls) make sensewhen imbalances are big and financial markets distressed



Coming Soon

The framework is quite flexible and can also accommodate:

I Trading in multiple assets

I Multiple countries

I Quantitative implications (numerically)

Testing the key empirical implications: work in progress

I Model is consistent with a number of facts: carry trade, debtor andcreditor countries’ currency risk, failure of PPP, exchange ratedisconnect, Backus and Smith condition

I Directly test channel ⇒ Financiers’ demand equation: relates balancesheet and risk tolerance to currency returns



FX and Bond Market Structure

I This paper is not about volume, turnover, and transaction costs:

I $5.3trn daily volume in FX market

I Turnover mostly associated with market-making and inventory trading(Lyons (1997))

I We abstracted away these microstructure effects via perfect-risk-sharingamong financiers

I This paper is about risk bearing capacity of key financial players overseveral months/quarters:

I International FX and bond markets are OTC ⇒ role for intermediation

I Relatively concentrated market in ultimate risk taking

I PIMCO, Blackrock, Goldman Sachs (GSAM), Soros take most of therisk ⇒ are the marginal player

I While large, these institutions have limited risk taking capacity


international liquidity and exchange rate dynamics liquidity and exchange rate ... international...

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