The International Medium of Exchange: Privilege and Duty
Ryan Chahrour (Boston College) Rosen Valchev (Boston College) June 29, 2017
1/23
The US’s “Exorbitant Privilege”
• Unique external position of US • world’s largest net debtor, but ... • negative net payments to rest of the world ,→ 3% excess return (GCR, 2010)
• Large transfer to US • could fund sizeable trade deficit indefinitely ,→ current positions/returns support ≈ 2.5% of GDP
• But what causes EP and is it sustainable? • hard to answer: no model where EP arises endogenously
2/23
Meanwhile, US Assets are special
• US assets the international medium of exchange • Trade in goods and services • USD invoicing 5 times US world trade share (EUR 1.2 trade share) • Japan: USD in 50% of EX, 71% of IM (rest Yen)
• Financial transactions • 85% of bilateral FX trade involves USD (40% EUR) • 60% of international debt securities issued in USD (20% EUR)
3/23
This Paper: A Model of Endogenous EP
• Originates in need for medium of exchange • Key friction: trade happens in decentralized matching markets • importing firms pay up-front • freely choose transaction currency, but currency mismatch costly ,→ coordination incentive • heterogeneous information ⇒ unique equilibrium
• Feedback between macro variables and currency choice • dominant currency earns premium ⇒ increases holdings of dominant currency ⇒ increases available funding in that currency
• We use the model to understand • What can cause a switch in the DC, consequences, welfare effects ...
4/23
Literature
• Exorbitant Privilege in the Data: Gourinchas and Rey (2007), Lane and Milesi-Ferretti (2007), Gourinchas, Rey and Gouvillot (2010) • The USD’s special international role: Portes and Rey (1998), Goldberg (2011), Gopinath (2015) • Exogenous Exorbitant Privilege: Caballero, Farhi, and Gourinchas (2008), Gourinchas, Rey and Gouvillot (2010), Canzoneri, Cumby, Diba and Lopez-Salido (2013), He and Krishnamurthy (2016) • Endogenous Exorbitant Privilege:
this paper
5/23
Model
Model Overview
assets and commodities goods
U.S. -
Households
-
Firms
-
Government
E.U. imports
exports
Imp./Exp.
Imp./Exp.
funding
fees
payments
6/23
Static game of Currency Coordination 1. Firm formation • zero-profit ⇒ measure µc trading firms • choose probability of being importer, pcim (exporter is 1 − pcim ). 2. Funding • choose currency • seek funding (letter of credit) in chosen currency • if successful, continue to stage 3 3. Search/match • discover if importer or exporter • US importers searches among EU exporters (visa versa) • if successful, continue to stage 4 4. Trade • importers purchase good from matched exporter, splitting surplus • transaction requires (partial) payment up front • costly if hold different currencies
⇓ ex-ante coordination game 7/23
Stage 4: Trade and Profits
Expected profits of US importer holding USD assets i α h $,im eu eu eu eu πus = match X˜eu (Pus − Peu ) + (1 − X˜eu )(Pus − Peu − χ) Pus Expected profits of US importer holding EUR assets i α h eu eu eu eu e,im − Peu ) + X˜eu (Pus − Peu − χ) πus = match (1 − X˜eu )(Pus Pus Notation: • X˜eu = fraction of EU trading firms holding dollars • χ = cost of currency mismatch eu • Peu = walrasian price of EU-produced good when sold in EU eu • Pus = walrasian price of EU-produced good when sold in US match • Pus = price paid by importer (affects imports-per-unit-funding)
• α = share surplus to importer
8/23
Stage 3: Importer-Exporter Matching
Expected profits of a USD-holding trading firm: im ie $,im im ei $,ex ˜ $us = pus Π pus πus + (1 − pus )pus πus Notation: im • pus = prob of US trade firm being an importer ie • pus = prob of a US importer matching with an EU exporter
ie pus =
im µ ˜ eu (1 − peu ) im ))1/ + (µ im )1/ (µ(1 ˜ − peu ˜ us pus
• µ ˜ eu = measure of funded EU trading firms • µ ˜ us = measure of funded US trading firms
9/23
Stage 2: Search for Funding
Expected profits of seeking USD funding $ ˜$ $ Π$us = pus (Πus − κrus ) Notation: $ • pus = probability of us firm finding funding in USD market
$ pus =
$ Bus exp(θ) $ exp(θ))1/ε + (µ X )1/ε (Bus us us
ε
$ • Bus = USD assets held by US households
• Xus = fraction of US firms seeking dollars • θ = liquidity “wiggle” that makes matching probs uncertain • (recall) X˜us = fraction of funded US firms holding dollars X˜us =
$ Xus pus
$ Xus pus e + (1 − Xus )pus
10/23
Stage 1: Formation
• Optimality condition in terms of importing/exporting ∂ max{Π$us , Πeus } =0 im ∂pus determines share of importers • Fixed cost of entry φ, and zero profit condition max{Π$us , Πeus } − φ = 0 determines µc – measure of trading firms
11/23
Equilibrium under Incomplete Info
• Let $ effective USD funding = Bus exp(θ) e effective EUR funding = Bus exp(−θ)
with θ ∼ N(0, σθ2 ) • before choosing currency, firms see signal s i = θ + vi • signal threshold s¯us and s¯eu that leave indifferent between currencies
12/23
Comparative Statics – θ
1
0.9
Share of USD-seekers
0.8
0.7 0.6
0.5 0.4 0.3 0.2 0.1 0 -0.15
-0.1
-0.05
0
0.05
0.1
0.15
13/23
Comparative Statics – θ
1
0.9
Share of USD-seekers
0.8
0.7 0.6
0.5 0.4 0.3 0.2 0.1 0 -0.15
-0.1
-0.05
0
0.05
0.1
0.15
14/23
$ Comparative Statics – Beu
1
0.9
Share of USD-seekers
0.8
0.7 0.6
0.5 0.4 0.3 0.2 0.1 0 0.1
0.15
0.2
0.25
0.3
0.35
Share of USD bonds in EU portfolio 15/23
Implications for Steady-State
Dynamic model: Summary
Standard open economy in which • trade occurs via trading firms • households save in domestic or foreign bonds • households “rent” bonds to trading firms within period
16/23
Steady-State
• Euler equation for dollar bonds (home and abroad): 1 1 = $ β Q − ∆$us 1 1 = e β Q − ∆eeu • Re-writing in terms of interest rates and solving 1 + i$ 1 − ∆$us = 1 + ie 1 − ∆eeu • We get exorbitant privilege (i $ < i e ) when ∆$us > ∆eeu
17/23
Characteristics of ∆’s
• Liquidity premia are endogenous equilibrium objects: ∆$us =
$h pct |{z}
rct$
Prob. HH finds lending partner
• Well defined, concave maximization problem over portfolio holdings ⇒ unique portfolio holdings given other aggregate states • Endogenous liq. premia gets around typical indeterminacy
• Feedback between HH and firm choice ⇒ multiple steady states $ $ • Higher Beu ⇒ higher Xeu ⇒ higher ∆$eu ⇒ higher Beu
18/23
Multiple Steady States
EUR Coordination
US Holdings of USD Bonds
USD Coordination
EU Holdings of USD Bonds
EU Holdings of EUR Bonds
US Holdings of EUR Bonds
19/23
Characteristics of Steady State • The asymmetric, coordinated equilibrium is associated with 1. 2. 3. 4.
Higher liquidity premium on coordinated asset Higher asset price (lower interest rate) Higher consumption supported by permanent trade deficit Lower labor effort
• If coordinating on the USD ∆$us > ∆eeu ⇒ i USD < i EUR • and thus $ e Beu (1 + i $ ) − Bus (1 + i e ) = Trade Deficit < 0 | {z } Financial Account Deficit
• Coord. on your currency is a positive wealth transfer from abroad • Trade deficit is not a symptom economic stress, just the opposite! 20/23
Dynamic Economy
EUR Coordination
US Holdings of USD Bonds
USD Coordination
EU Holdings of USD Bonds
EU Holdings of EUR Bonds
US Holdings of EUR Bonds
21/23
Dynamic Economy
EUR Coordination
US Holdings of USD Bonds
USD Coordination
EU Holdings of USD Bonds
EU Holdings of EUR Bonds
US Holdings of EUR Bonds
22/23
Conclusion
• Model where EP arises endogenously due to need for medium of exchange • Search friction ⇒ complementarity in portfolio holdings • Endogenous states ⇒ enforce coordination (absent shocks) • Model captures several long-run features of int. financial markets
• Future work • Shocks/policies capable of changing steady-state • Transition paths • Welfare effects • Still a lot more to be done...
23/23
