A Gravity Model of A Gravity Model of Sovereign Lending:Sovereign Lending:

Trade, Default and CreditTrade, Default and Credit

Andrew K. Rose and Mark M. SpiegelAndrew K. Rose and Mark M. Spiegel

44thth annual I.M.F. Research Conference annual I.M.F. Research Conference November 6, 2003November 6, 2003

Sovereign defaults Sovereign defaults are still exceptionalare still exceptional

Direct penalties are elusiveDirect penalties are elusive

““Gunboat diplomacy” no longer viableGunboat diplomacy” no longer viable

However, countries largely behave “as if” However, countries largely behave “as if” default penalties were perceiveddefault penalties were perceived

Motivation for sovereign debt service Motivation for sovereign debt service therefore remains an important issuetherefore remains an important issue

One posited penalty in literature One posited penalty in literature is loss in tradeis loss in trade

Bulow and Rogoff (1989): Trade sanctions Bulow and Rogoff (1989): Trade sanctions as potential penaltyas potential penalty• Also loss of trade creditAlso loss of trade credit• However, unclear whether creditors can levy However, unclear whether creditors can levy

such penaltiessuch penalties

Empirical questions about efficacy of Empirical questions about efficacy of default penaltydefault penalty• Creditors may be unable to levy such penaltiesCreditors may be unable to levy such penalties• Penalties may not be “renegotiation proof” Penalties may not be “renegotiation proof”

[Kletzer and Wright (2000)][Kletzer and Wright (2000)]

Some empirical evidence Some empirical evidence of trade default penaltiesof trade default penalties

Ozler (1993): Evidence of positive, but Ozler (1993): Evidence of positive, but small premia charged to countries with small premia charged to countries with default histories default histories

Cline (1987): Bolivia and Peru experienced Cline (1987): Bolivia and Peru experienced disruption in trade credits subsequent to disruption in trade credits subsequent to Paris Club renegotiationParis Club renegotiation

Rose (2002): Sovereign Paris Club Rose (2002): Sovereign Paris Club reschedulings followed by significant reschedulings followed by significant reductions in tradereductions in trade

We examine notion of lost trade We examine notion of lost trade as enforcement mechanismas enforcement mechanism

Harsher penalties in sovereign debt usually Harsher penalties in sovereign debt usually improve global welfare by moving closer to improve global welfare by moving closer to first-best outcomefirst-best outcome

Nations that can threaten heavier trade Nations that can threaten heavier trade disruptions therefore have a comparative disruptions therefore have a comparative advantage in lendingadvantage in lending

We explore that idea We explore that idea

Simple borrowing modelSimple borrowing model

Sovereign borrowing by small debtor Sovereign borrowing by small debtor country from two creditor countriescountry from two creditor countries

Creditors identical except for Creditors identical except for bi-lateral trade volumes with debtor countrybi-lateral trade volumes with debtor country

Model predicts that borrowing will be Model predicts that borrowing will be concentrated on country with greater bi-concentrated on country with greater bi-lateral tradelateral trade

Then confirm empiricallyThen confirm empirically

Model AssumptionsModel Assumptions

Three countries: borrower country, Three countries: borrower country, ii, and , and two creditor countries, two creditor countries, aa and and bb

is a random variable reflecting total is a random variable reflecting total trade between country trade between country ii and country and country jj in in the second period the second period

Expectations of are unbiasedExpectations of are unbiased

where is an i.i.d. disturbance term with where is an i.i.d. disturbance term with expected value 0 on the interval expected value 0 on the interval

ijT

ijT

1ij ij iT E T

i,i

Model Assumptions (2)Model Assumptions (2)

Bilateral gains from trade are exogenous and Bilateral gains from trade are exogenous and equal toequal to , where is a positive constant , where is a positive constant

rr is one plus the world risk-free interest rate, is one plus the world risk-free interest rate, which is exogenouswhich is exogenous

Lenders are risk-neutralLenders are risk-neutral

If the debtor defaults on country If the debtor defaults on country jj it suffers a it suffers a penalty equal to a fraction of its gains from penalty equal to a fraction of its gains from bilateral trade with country bilateral trade with country jj

ijT

Extensive formExtensive form

Model has two periodsModel has two periods

In first period, the representative lender in country In first period, the representative lender in country jj extends a loan of magnitude in return for the extends a loan of magnitude in return for the promise of a fixed payment in the second promise of a fixed payment in the second periodperiod

In the second period, is realized and the debtor In the second period, is realized and the debtor makes its default decisionsmakes its default decisions

If the debtor chooses to service its debt it pays If the debtor chooses to service its debt it pays

If it defaults, it suffers default penaltyIf it defaults, it suffers default penalty

ijLijD

ijT

ijD

Agent CharacteristicsAgent Characteristics

Creditor nations differ only in their expected trade Creditor nations differ only in their expected trade volume with the debtor volume with the debtor

Expected debtor utility satisfies Expected debtor utility satisfies

where where is exogenousis exogenous

1st-pd consumption satisfies1st-pd consumption satisfies

is exogenous in both periodsis exogenous in both periods

1 1ia ibE T E T

1 1 1 2i i iE U U C E C ,' 0 0 ,"U U

1 1 .i i ia ibC Y L L

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Default DecisionDefault Decision

Default decision based on maximizing second Default decision based on maximizing second period consumption period consumption

Conditional on debt service, satisfiesConditional on debt service, satisfies

where and represents cost of default where and represents cost of default decision on debt owed to country decision on debt owed to country kk

Debtor chooses default on country Debtor chooses default on country jj when when

2iC 2 2 ,i i ij ij ik iC Y T D g D

j k ,ik ig D

ij ijD T

EquilibriumEquilibrium

Define as minimum realization of that Define as minimum realization of that induces debt service. Satisfiesinduces debt service. Satisfies

Equilibrium is defined as a pair of debt Equilibrium is defined as a pair of debt obligations that maximize obligations that maximize expected debtor utility subject to both expected debtor utility subject to both creditors’ zero profit conditions creditors’ zero profit conditions

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*1 .ij

ij ij

DE T

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Borrowing decisionsBorrowing decisions

Two decisions: the overall borrowing level,Two decisions: the overall borrowing level,

and the allocation across countries and the allocation across countries Given allocation satisfiesGiven allocation satisfies

Debtor skews borrowing towards nation with lower Debtor skews borrowing towards nation with lower probability of default with equal borrowing probability of default with equal borrowing

Doing so increases the default probability in “safe” Doing so increases the default probability in “safe” nation and narrows this difference nation and narrows this difference

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ib ib ia

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Result 1: Lending SharesResult 1: Lending Shares

Demonstrate in text thatDemonstrate in text that

Holding total lending constant, the share of Holding total lending constant, the share of lending originating in country lending originating in country aa is is increasing in the expected volume of trade increasing in the expected volume of trade with country with country aa

0ia

ia

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Result 2: Overall borrowingResult 2: Overall borrowing

Maximizing expected utility over the choice Maximizing expected utility over the choice of and the optimal allocation rule, and of and the optimal allocation rule, and then totally differentiating with respect to then totally differentiating with respect to and yields and yields

which implies that total borrowing which implies that total borrowing increases with increases with

We next test these empiricallyWe next test these empirically

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Data SetData Set

Use annual panel data set of trade and Use annual panel data set of trade and lendinglending• 20 creditors, 149 debtors, 1986-199920 creditors, 149 debtors, 1986-1999• Bank claims from BISBank claims from BIS• Rest from Glick-RoseRest from Glick-Rose

MethodologyMethodology

Estimate “gravity” model of lending:Estimate “gravity” model of lending: ln(Cijt) = ln(Cijt) = ln(Xijt) + ln(Xijt) + Zijt + Zijt + ijtijt

• where Z are gravity variables (distance, GDP, where Z are gravity variables (distance, GDP, …)…)

IV critical because of simultaneityIV critical because of simultaneity• Use different instrumental variables from Use different instrumental variables from

gravity model, especially geographic gravity model, especially geographic (landlocked status …)(landlocked status …)

MiscellanyMiscellany

Robust standard errors (clustered by Robust standard errors (clustered by country-pairs) recorded in parentheses. country-pairs) recorded in parentheses.

Intercepts and year effects not recorded.Intercepts and year effects not recorded. Instrumental variables for trade are: Instrumental variables for trade are:

distance; land border; number landlocked; distance; land border; number landlocked; number island nations; log of area.number island nations; log of area.

Table 1: OLS Estimates of Effect Table 1: OLS Estimates of Effect of Trade on Claimsof Trade on Claims

Default Default .54 (.04).54 (.04)

Without controlsWithout controls .75 (.02).75 (.02)

LevelsLevels .0001 (.00003).0001 (.00003)

Levels without controlsLevels without controls .0001 (.00003).0001 (.00003)

19901990 .51 (.05).51 (.05)

19951995 .53 (.07).53 (.07)

Only industrial debtorsOnly industrial debtors .74 (.04).74 (.04)

Table 2a: IV Estimates of Effect Table 2a: IV Estimates of Effect of Trade on Claims, Geographic of Trade on Claims, Geographic

InstrumentsInstruments

Default Default .41 (.07).41 (.07)

Without controlsWithout controls .50 (.04).50 (.04)

LevelsLevels .00006 (.00001).00006 (.00001)

Levels without controlsLevels without controls .00007 (.00002).00007 (.00002)

19901990 .52 (.10).52 (.10)

19951995 .40 (.10).40 (.10)

Only industrial debtorsOnly industrial debtors 1.03 (.07)1.03 (.07)

Table 2b: IV Estimates of Effect Table 2b: IV Estimates of Effect of Trade on Claims, Excludable of Trade on Claims, Excludable

InstrumentsInstruments

Default Default .80 (.40).80 (.40)

Without controlsWithout controls .83 (.07).83 (.07)

LevelsLevels .00004 (.00001) .00004 (.00001)

Levels without controlsLevels without controls .00005 (.00001).00005 (.00001)

19901990 .59 (.37).59 (.37)

19951995 1.13 (.49)1.13 (.49)

Only industrial debtorsOnly industrial debtors .79 (.29).79 (.29)

Table 3: IV Estimates of Effect of Table 3: IV Estimates of Effect of Trade on Claims, Controlling for Trade on Claims, Controlling for

Total ClaimsTotal Claims

Default Default .40 (.07).40 (.07)

Without controlsWithout controls .42 (.04).42 (.04)

LevelsLevels .00005 (.000004).00005 (.000004)

Levels without controlsLevels without controls .00005 (.000006).00005 (.000006)

19901990 .47 (.10).47 (.10)

19951995 .37 (.10).37 (.10)

Only industrial debtorsOnly industrial debtors .48 (.23).48 (.23)

Table 3: IV Estimates of Effect of Table 3: IV Estimates of Effect of Trade on Claims, Controlling for Trade on Claims, Controlling for

Total DebtTotal Debt

Default Default .42 (.07).42 (.07)

Without controlsWithout controls .27 (.04).27 (.04)

LevelsLevels .00006 (.00002).00006 (.00002)

Levels without controlsLevels without controls .00006 (.00002).00006 (.00002)

19901990 .56 (.09).56 (.09)

19951995 .42 (.10).42 (.10)

Only industrial debtorsOnly industrial debtors 1.10 (.20)1.10 (.20)

Table 4: IV Estimates of Effect of Table 4: IV Estimates of Effect of Trade on Claims, PanelTrade on Claims, Panel

Estimator:Estimator: OLS, REOLS, RE OLS, FEOLS, FE IV, REIV, RE

DefaultDefault .31 (.01).31 (.01) .19 (.02).19 (.02) .52 (.06).52 (.06)

Without Without controlscontrols

.38 (.01).38 (.01) .19 (.01).19 (.01) .52 (.03).52 (.03)

LevelsLevels .00003 .00003 (.000001)(.000001)

.00002 .00002 (.000001)(.000001)

.00006 .00006 (.00001)(.00001)

Levels no Levels no controlscontrols

.00003 .00003 (.000001)(.000001)

.00002 .00002 (.000001)(.000001)

.00007 .00007 (.000003)(.000003)

industrial industrial debtorsdebtors

.46 (.06).46 (.06) .28 (.07).28 (.07) .96 (.19).96 (.19)