-19-

nontradables rises with the quantity of Mexico's nonwage "income" of trad-
able goods (Q), expressed as a proportion of the output of nontradables that
is foregone by employing labor in the tradables sectors.

The appendix also characterizes the values of B and B* that
maximize (25) subject to conditions on qi, EC) and varC}.
The necessary condition on B* is that the marginal return on loans to U.S.
entrepreneurs must equal the marginal rate of consumer time preference. The

necessary condition on B has the general form

(30) B= glvart,, VarVp, ET, EVp, ty dy a)
where the sign above each argument is the sign of the partial derivative of B
with respect to that argument under assumptions that are taken to describe
"the normal case." The signs of the partial derivatives with respect to
VarT,, VarVp, d and u are intuitively clear: under the assumption of
diminishing marginal productivity of the Mexican capital stock, it is optimal
to reduce B whenever the perceived variability of the return on B increases,
whenever future consumption becomes less desirable relative to current con-
sumption, or whenever consumers become more averse to the riskiness of future
consumption levels. The partial derivatives with respect to ET,, EVp,
and t reflect the fact that an increase in ET, or EVp or a decline in t
directly reduces the expected return on any given level of B after taxes and
wages 4/

Finally, the appendix shows that the conditions on B and B” lead
to an expression for the country risk premium (CRP), defined as the dif-
ference between the expected marginal return on loans to Mexican entre-
preneurs and the (certain) marginal return on loans to U.S. entrepreneurs

(31) CRP = mVarT, + mjVarVp


-13-

(14) Ch = (14e*)B* + (14ryB
where r and r* denote average "after-tax" yields on the two types of
claims.

A key assumption of the analysis is that U.S. creditors view their
returns on loans to Mexican entrepreneurs as uncertain, and view loans to
U.S. entrepreneurs as a "safe asset." This assumption helps simplify the
analytic framework to a model in which the implications of the different
sources and relative degrees of uncertainty can easily be isolated. A second
simplyfying assumption is that only U.S. residents lend internationally,
while Mexican residents do not hold claims on U.S. entrepreneurs, so that net
and gross U.S. lending to Mexico coincide. In addition, the analysis
abstracts completely from the effects of uncertainty on Mexican savings
behavior. Thus, attention is concentrated on how the sources and degrees of
uncertainty about the returns on claims on Mexican entrepreneurs influence
the aggregate savings and international lending decisions of U.S. residents,
and thereby influence the terms of trade.

With this orientation we now describe the aggregate levels and dis-
tributions of U.S. and Mexican domestic products, expressed as functions of
the amounts which U.S. creditors lend to U.S. and Mexican entrepreneurs. The
analysis is restricted to stationary-state solutions within the overlapping
generations framework, which is equivalent to assuming that population sizes
are constant and that each generation behaves identically over its two-period
lifespan. (Although the stationary-state is characterized by each generation
choosing the same values for its choice variables, certain outcomes can vary

from period to period, reflecting the variance of two stochastic exogenous


- 23-

Using the default option can be thought of as acting inconsis-
tently over time. The subject of time inconsistent policies has received
considerable attention in recent years, generally in the context of domestic
Policy rules. For example, a simple rule for monetary policy, such as
constant growth of a monetary aggregate, can be thought of as a policy
contract between the government and the private sector. Although policy
contracts are rarely specified in detail, implicit policy contracts have an
important bearing on the nature of explicit contracts that private economic
agents enter into, such as nominal wage agreements or debt contracts, the
usefulness of which depend in part on a consistent application of the
implicit policy contract. The government can in same circumstances achieve
important goals by violating a policy contract; for example, unemployment
might be reduced temporarily by increasing the growth of the monetary aggre-
gates above the rates specified in a policy contract. The effects of
violating a policy contract include a subsequent reduction in the usefulness
of contracts, as well as an immediate redistribution of income among debtors
and creditors. Trade offs between the immediate and long run benefits and
costs of breaking policy contracts are very difficult to quantify or
predict.

Several factors seem important in shaping our understanding of
default as a time inconsistent policy. The default tax is only one of the
many elements of time inconsistent behavior that the government is likely to
consider following an unusually bad draw from the economic environment.
Different groups have entered into contracts from which they expect to obtain
incame. These include wage contracts, taxes, and transfers denominated in

domestic currency; bond contracts denominated in both domestic and foreign


-4-

tradable and nontradable goods and leads to an adjustment in the terms of
trade. To the extent that the peso wage rate and the peso price of
nontradable goods are fixed or sticky, the terms of trade adjustment
corresponds to an adjustment in the dollar/peso exchange rate.

Two important points emerge from Section III. First, even when all
assets are denominated in a common currency, risk can have an important
influence on the values of the terms of trade and the nominal exchange rate
that are consistent with asset equilibrium. Second, to the extent that
credit risk reflects uncertainties about both exogenous economic outcomes and
political attitudes or outcomes (as relevant to the size of the gross product
and its distribution), the ex ante probability distribution of the exchange
rate will reflect the ex ante probability distributions of both exogenous
economic and political outcomes: exchange risk will reflect both exogenous
economic uncertainty and political uncertainty.

In the model of Section III, nonresident creditors are assumed to
predict the "taxes" on their earnings as an ad hoc function of real and
political outcomes, rather than on the basis of a convincing model of how the
Mexican government would rationally behave under alternative real and
Political outcomes. Section IV discusses some issues that seem critical for
developing a more sophisticated model. The default option is cast as one of
many time-inconsistent choices through which the government may arbitrate a
Set of mutually excessive claims to the aggregate domestic product, and it is
argued that in some circumstances all parties involved may become better off
if the government acts to alter the terms of financial contracts between

domestic debtors and nonresident creditors.


- 20 -

Under normal assumptions mM, and my are each positive and increasing
functions of B.

Conditions (29)~(31) allow a comparative static analysis of the
effects of various "shocks" on the level of U.S. credit to Mexico, the
exchange rate and the country risk premium. Subject to the usual caveats
about using comparative static frameworks to analyze responses to shocks, the
model suggests that an increase in uncertainty about either revenues from
primary product exports or political attitudes toward taxing nonresidents
(VarVp or VarT,) raises the country-risk premium associated with any
level of B, and leads U.S. residents to reduce their outstanding stocks of
financial claims on Mexican entrepreneurs, other things equal. For a given
peso wage rate this will depreciate the dollar value of the peso (since h(B)
and hence ew decline as B declines) .42/

These results illustrate several important points. First,
independently of the currency denomination of assets, risk can have an
important influence on the values of the terms of trade and nominal exchange
rate that are consistent with asset equilibrium. Second, to the extent that
credit risk reflects uncertainties about both exogenous economic outcomes and
political attitudes or outcomes, the ex ante probability distribution of the
exchange rate will reflect the ex ante probability distributions of both
exogenous economic and political outcomes: exchange risk will reflect both
exogenous economic uncertainty and political uncertainty.

In Section II the stationary-state analysis under certainty
emphasized that an unanticipated transitory decline in Mexico's export

revenues, unless offset by a matching reduction in domestic absorption to

prevent the trade balance from declining in the short run, might well require


- 26-

uncertainties about outcomes for both exogenous economic variables and
political factors. ‘Together these types of exogenous uncertainties translate
into uncertainties about both the size of the country's domestic product and
the distribution of income among competing groups of claimants, including
nonresident creditors.

The focus on credit supply behavior provides several insights about
the behavior of real and nominal exchange rates. Although this paper has
chosen to model the nominal exchange rate between the Mexican peso and the
U.S. dollar, and to focus on the terms of trade between (Mexican) nontrad-
ables and tradables as the relative price that best represents a real
exchange rate in that context, the basic insights extend to nominal exchange
rates between pairs of “hard" currencies when real exchange rates refer to
relative prices between composites of tradable goods distinguished by country
of origin. A creditor who lends (domestically or internationally) to a
private entrepreneur or government agency in a hard-currency country cannot
be certain that the real after-tax interest and repayment streams he will
receive are independent of the outcomes for macroeconomic variables and
political factors specific to the borrowing country. Every country faces
different and time-varying degrees of uncertainty about macroeconomic and
political prospects, which can be translated, by modelling the rational
behavior of credit suppliers, into time-varying degrees of uncertainty about
real and nominal exchange rates between pairs of currencies, whether hard or
soft. In turn, changes over time in degrees of uncertainty about future
exchange rates lead to whatever changes in observed exchange rates are
necessary to adjust the relative expected returns on different assets to

market-clearing levels.


- 22-

Iv. Credit Availability and the Default Option

The previous section has emphasized that the jointly determined
levels of U.S. credit to Mexico, the relative prices of Mexican and U.S.
goods, and the dollar/peso exchange rate depend critically on how U.S.
creditors perceive the nature of the Mexican "tax" structure and on the
manner in which contracts to Mexican factors of production are written. The
formal representation of Mexican taxes on nonresident earnings is an analyti-
cally convenient method of addressing default or rescheduling risk. In this
regard the uncertain level of the tax burden on nonresident creditors has
been viewed to depend both on purely political attitudes and on the uncertain
level of Mexico's domestic product. Beyond this, however, the specific
hypothesis about how nonresident creditors assess their tax burden is ad hoc,
rather than based on perceptions of rational Mexican behavior.

This section presents some perspectives on default issues that we
consider critical for improving the specification of the uncertainties per-
ceived by nonresident creditors. The term "default" is used to refer ina
general sense to any alteration of a financial contract between a domestic
debtor and a nonresident creditor. We discard the particular specification
of the Mexican tax structure used in the previous section but retain the
general notion that the domestic government has some degree of power to
reduce the income of nonresidents in order to mitigate the effects on
domestic income of "unusually" low levels of domestic output or the relative
price of exports. In particular, we view the domestic government to have a
"default option" to unilaterally adjust the terms of Mexico's financial

contracts with nonresident creditors.


-17-

stochastic component of @Pp) induce increases in taxes on nonresident
earnings. T, and Vp are the only two stochastic exogenous variables in
the model. Taxes are used by the Mexican authorities to purchase manu-
factured goods, which are distributed to Mexican consumers through public
expenditure and transfer programs. In the stationary-state, moreover,
Mexican capitalist income and hence all of Q is consumed. Thus, the
parameter (1-t) can be interpreted as the extent to which Mexico reduces its
aggregate stationary-state consumption of manufactures (given its production)
in proportion to any change in the value of its primary product exports.

Having characterized the uncertainties that influence the size and
distribution of aggregate income, we now argue that the influence of
uncertainty on both intertemporal allocations and the composition of lending
affects the relative availability of goods in each period, which in turn
affects the terms of trade (and, under certain conditions, the nominal
exchange rate). The illustration we provide to support this argument is one
in which U.S. residents make intertemporal consumption decisions involving
only the manufactured good, while Mexican residents make strictly intra-
temporal consumption decisions involving two goods and leisure. Although the
two Mexican consumption goods are taken to be nontradables and tradables,
with relatively minor modifications we could adapt the framework to the case
of two tradable goods distinguishable by country of production.

The intertemporal allocations and composition of lending are
characterized by assuming that U.S. creditors choose B and B* to maximize a
preference function of the form

1 *
(25) U = Cl + p-H{EC) - warc>)


-9-

In condition (12) the stationary-state trade balance is related
negatively to the terms of trade (p" = ep): other things equal, an
increase in the Mexican trade balance requires either a depreciation of the
peso or a reduction in the peso price of nontradables. Each of these
alternatives is associated with a reduction in the Mexican (real) wage rate
measured in terms of manufacturers (ew).

Conditions (2) and (12) represent the reduced-form model for com-
parative stationary-state analysis. Denote initial stationary-state values
of the variables entering these two conditions by B°, TB’, KR,
r°, x. i, p’°, and @'°. Now consider a shock in
the form of a transitory decline in q associated with an unanticipated
foreign recession. Figure 1 describes the shock and Figures 2-4 contrast two
of the many possible adjustment paths. The transitory shock to q is
shown to last from times tg to t;- Figures 2-4 are based on the case
in which outputs and the capital stock are maintained at their initial
stationary- state levels throughout. Figures 2a-4a illustrate an adjustment
path that maintains the trade balance and stock of debt at their initial
stationary-state levels thoughout; essentially, the transitory decline in
revenue from primary product exports is absorbed through a matching decline
in consumption of tradables that, in turn, is induced by a transitory decline
in the relative price of nontradables. Such adjustment does not require a
permanent change in the terms of trade; after time ty all of the
variables have returned to their initial values.

By contrast, Figures 2b-4b illustrate the case in which e

remains at its initial stationary-state value for a period of time after


- 32-
Footnotes

xy This paper represents the views of the authors and should not be inter-
preted as reflecting the view$of the Board of Governors of the Federal Reserve
System or other members of its staff.

J/ In discussing credit risk it has become natural to aggregate inter-
national indebtedness across the residents of individual debtor countries,
reflecting the fact that the country is. the fundamental unit for distinguish-
ing macroeconomic policies, financial regulations and legal jurisdictions.

2/ The separation of tradable-goods output into M and P does not greatly
complicate the analytic framework and is useful for differentiating the
effects of global activity shocks on the U.S. and Mexican economies.

3/ Material inputs to production are ignored.
4/ See Chipman (1974).

5/ The costs of default might include restrictions on exports (possibly
reflecting increased difficulties of obtaining export finance), confiscation
of property owned abroad, withdrawals or embargoes of essential foreign
inputs to domestic production, loss of foreign military and technical
assistance, etc. Notice that in this model the cost does not include
restriction of access to further net borrowing, which is ruled out by defini-
tion of the stationary state.

6/ These assumptions can be viewed to describe an economy with a "surplus"
of labor. Alternatively, unemployment can be viewed to reflect a voluntary
choice about the amount of leisure to transform into nontradables consumption
at the fixed labor/output ratio aye

V/ Xp and q* will be treated as predetermined throughout this paper,
and the particular form of condition (6) has little relevance to the of
analysis.

8/ One of the many difficulties of extending the analysis beyond the
stationary-state framework is the complication arising from immobility of
physical capital.

9/ As mentioned above, this treatment abstracts from the extent to which
Mexican savings behavior is affected by uncertainties analogous to those that
influence the behavior of U.S. creditors.

10/ Although labor has not been specified explicitly as an argument of
the U.S. production function, income distribution can be viewed as neo--
classical under the assumption that the fixed stock of labor is fully
employed. Other assumptions that are also consistent with distributing Y* to
labor include the assumption that labor receives a fixed dollar wage plus
(minus) transfers (taxes) from goverment that equal the excess of
over the sum of the wage bill and the marginal-product rewards to capital.


- 29 -

Accordingly, if Ty and Vp are each symmetrically and independently dis-

tributed, root will be symmetrically distributed with mean and variance

(A15) EC) (1+r*)B* + B+ £(K,+B) — (1+h)ET,

((1-t)h-t )EVp

(AL6) VarCS = (14h) ?varT, + ((1-t)h-t)*varv,

Attention now turns to characterizing the values of B* and B that
maximize (25) subject to conditions (13), (Al5), and (ale) 2/ Necessary
conditions are that B* must satisfy

(Al7) = ((1+r*)B*) = 1+d

while B must satisfy

(Al8) f'=d+ h'(ET,+(1-t)EVp) + mjVarT, + moVarVp

where m, = 2uh'(1+h) > 0

My = 2uh'(1-t)((1-t)h-t)

Condition (Al7) requires that the marginal return on loans to U.S. entrepre-
neurs must equal one plus the marginal rate of time preference. In condition
(A18), the second term on the right hand side is the expected marginal cost of
labor (per incremental unit of B), aS can be seen from conditions (All) and
(24). Thus, since labor is the only cost of production that varies at the
margin, condition (Al8) can be interpreted as requiring that the marginal
product of capital in Mexico must exceed the opportunity cost of lending to
U.S. entrepreneurs (d) by an amount that covers marginal cost and also com-
pensates the risk-averse creditors for the two sources of uncertainty (VarT,

and VarVp) « The value of B that solves (Al18) will be unique under the

assumptions that: (i) the marginal product of capital diminishes as K,+B


-6-

that repayment of international debts on schedule is not strictly enforce-
able. In this section, however, uncertainty about repayment streams is
ignored and the stationary-state framework provides an identity between the
Mexican trade surplus and the flow of net interest payments from Mexicans to
U.S. residents. Accordingly, when U.S. residents are treated as a single
aggregate creditor, it is appealing to assume that the stock of credit
supplied (BS) in the stationary-state will be an increasing function of
the stationary-state level of Mexican trade balance (TB).

(2) BS = B(TB) with B' > 0

The combination of this stationary-state "credit supply function"
with a reduced form relationship between the trade balance and the terms of
trade provides a relationship between the long-run value of the terms of
trade and the stock of assets (debts) outstanding in the long run. The
remainder of this section illustrates this result and several corrolaries,
under behavioral assumptions that lead to a particular reduced form relation-
ship between the trade balance and the terms of trade. Three important
points should be appreciated at the outset. First, the question of whether
the trade balance is positively or inversely related to the terms of trade
has been long debated and never resolved in the transfer problem litera-
ture.4/ Second, the analysis stops short of attempting to convert the
relationship between the terms of trade and stock of debt into a relation-
ship between the nominal exchange rate and stock of debt, which requires
assumptions that tie down some nominal magnitude. And third, the analysis

implicitly assumes that it is rational for Mexico to pay interest on its debt

in the stationary state; obversely, the analysis implicitly constrains the


-5-

II. A _Stationary-State Model Without Credit Risk

Although most of the analysis can be generalized to any pair of
countries or currencies, the model features a menu of assets and goods that
seems particularly appropriate for a world in which the two countries are
considered to be Mexico and the United States. All lending between the two
countries involves interest-bearing dollar-denominated claims. Mexico is
assumed to produce three types of composite goods: tradable manufactures (M)
that are perfect substitutes for manufactures produced in the United States,
nontradables (N) and primary products (P) wf Mexican residents divide
their consumption betwen M and N, while P is produced only for export.2/
It is convenient to treat tradable manufactures as the numeraire, with a
price of one dollar, and to describe the structure of relative prices in
terms of the dollar price of the peso (e), the peso price of nontradables (p)
and the dollar price of primary products (q"). The dollar-equivalent
price of nontradables (p’) will be referred to as the terms of trade:

a) pt sep
For the present, the model is concerned with explaining Pp, but not
with the absolute levels of e and p, so there is no need at this point to
complicate the analysis by introducing money markets, or by adopting other
assumptions that tie down some nominal magnitude. Under the choice of
numeraire, the dollar-denominated claims can be viewed as claims denominated
in real units of manufacturered goods.

A realistic specification of the extent to which and terms on which

U.S. (foreign) residents will lend to Mexico must take account of the fact


-18-

subject to conditions (13), (14), etc., where the perceived ex ante prob-
ability distribution of os is symmetric. The parameter d is a measure
of the rate of time preference, while u summarizes the trade-off between the
expected value and the variance of Ce Conditions (21)-(24) and (15)
can be shown to imply

(26) rB= £(K,+B) - ew(L,+bB) - Ty + tVp
Conditions (13) and (14) can be transformed, under conditions (16)-(20) and
(26), into

£*(B*) - (14n*)B* - B

*
(27) cy

(28) C> = £(K,+B) - ew(L,tbB) - T, + tv,
2 = £(Ky ly a + tVp

(14+r*)B* + B

+

The intratemporal decision of Mexican consumers is described in the
appendix under the assumption that preferences for consumption bundles of
manufactures, nontradables, and leisure have a Cobb-Douglas form. In
general, the intratemporal decision provides solutions for the terms of
trade, and hence ew, as a function of the two exogenous stochastic terms
(Ty and Vp) and the choice variables from the intertemporal problem (B
and B*). Under the rational expectations assumption that U.S. creditors
have knowledge of the solution form for ew, the problem of maximizing (25)
subject to their budget constraint reduces to a choice in the context of only
the two unknown exogenous variables: Ta, and Vp.

The solutions for the terms of trade (p*) and ew in the appendix
illustration are

(29) p* = eWay = h(B) [0/( (hgHB) /ay)
where h is a positive and increasing function of BL The inter-

pretation of the square~bracketed term is that the relative price of


-8-

Following the classical hypothesis, it is assumed that wage
income is entirely consumed while other income (net of interest payments to
nonresidents) is entirely saved. In contrast with the Dornbusch-Fischer
formulation, the value of Mexican debt is assumed to have no direct influence
on the Mexican savings decision; rather, the constraint that relates the
value of production minus absorption to the outstanding stock of debt is
viewed to be imposed by U.S. creditors, as represented by condition (2).
Mexican residents are assumed to spend a proportion (c) of their wage income
on consumption of manufactures, and the remainder on nontradables consump-
tion, where

(7) c= c(p’) with c'>0
Thus, the market clearing condition for nontradables requires

(8) Xy = (1 - ¢)wL/p
while the trade balance, measured in dollars, is

(9) TB = Xy + a'Xy ~ I ecwl

By substituting condition (8) into (3), the level of employment can
be expressed as

(10) L = Ly/(1 - ay(1 - c)w/p)
For the case in which labor is the only factor to which the value added in
nontradables production is distributed, as described by condition (4), con-
dition (10) collapses to

(11) L= Lye
Substitution of (4), (5), and (11) into (9) then yields

(12) TB = £(K) - 1 +4" Xp - (p*/ay) bp


- 24-

currencies, and held by both residents and nonresidents; and equity con-
tracts. The existing assortment of contracts reflects the expected level and
perceived variability of output, as well as attitudes toward bearing risk.
Some contracts, for example equity ownership, specialize in providing the
holder with a residual of income after prior claims have been settled. Other
contracts are protected from particular sources of uncertainty by indexing
their value explicitly to future outcomes for uncertain variables. In
"normal" times, all contracts can be jointly fulfilled. However, the event
of an unusually low outcome for aggregate real income may make it undesirable
for all claimants to exercise their contractual rights. Indeed, if the
outcome for aggregate income is sufficiently low, the simultaneous
satisfaction of all claims may become infeasible. ‘The government in this
event acts as an arbiter that allocates the shortfall in aggregate income
among competing groups. This function of government is crucial, since
without effective arbitration the attempt of one group to exercise its
individual rights may force other groups into bankruptcy or revolution. The
general decline in asset values that can follow would impose costs on
everyone without helping to allocate the loss of income.

Accordingly, when faced with the prospect of catastrophe, the use
of the default tax to break loan agreements along with other time incon-
sistent policies to break other claims on aggregate output may increase the
welfare of each group of claimants to the aggregate output. Alternatively
stated, in some circumstances the default tax should be compared to even more
disruptive alternatives. For this reason it is not valid to argue that a
debtor country would never default because it would suffer costs over time

through its reduced access to international credit markets. The alternative


International Finance Discussion Papers
Number 221
May 10, 1983

COUNTRY RISK, INTERNATIONAL LENDING, AND EXCHANGE RATE DETERMINATION

by

Michael P. Dooley and Peter Isard*

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an
acknowledgment by a writer that he has had access to unpublished
material) should be cleared with the author or authors.


-u-

to. During that period, the trade balance is less than sufficient to
meet scheduled interest payments on the initial stock of debt, so debt
increases. If it is assumed that new stationary-state values ep,

tl, and B! are reached at some time T, and that e and TB

approach their new stationary-state values monotonically, it must be that

pt < p? in order to be consistent with TB! > 78° in

order to meet payments on Bl > B?,

The illustration conveys the notion that an unanticipated transi-
tory decline in Mexico's export revenues, unless offset by a matching
reduction in absorption to prevent the trade balance from declining in the
short run, may well require a permanent reduction in the terms of trade to
restore portfolio equilibrium from the viewpoint of Mexico's creditors. The
illustration is based on the assumption that a reduction in the terms of
trade leads to an improvement in the trade balance, and it ignores the case
in which a transitory "overadjustment" of the terms of trade obviates the
need for a permanent reduction.

More generally, the illustration emphasizes that many stationary-
state equilibria can exist, consistent with different levels of the trade
balance and terms of trade. An important corrolary is that the path that a
country chooses to follow in adjusting to a "shock" is likely to influence
the long-run value of its terms of trade. The corrolary hinges, of course,
on whether the long-run elasticity of the trade balance to the terms of trade
is finite. And implicitly, the possibility of stationary-state equilibria
with non-zero stocks of debt outstanding is based on the assumption that

there are positive costs of default in the stationary-state, such that it


-10-

qv Figure 1
qv? i
{ 1
1 '
1 '
'
| \
l t are
7 ime
t 4
* Figure 2a * ig
P p Figure 2b
*o Fo fp
P f P T
, ?
' ' a ,
= > - T > t
( 1 ty
TB . TB
F
Figure 3a * Figure 3b
? i 1p!
°
a TB° i '
> LZ | .
+7 .
° T
B B Figure 4b 1
4 Figure 4a r ? B
Pe ) | OU |
B° B f
' |
‘ |
! }



-31-
References

Calvo, Guillermo A. and Carlos A. Rodriguez. "A Model of Exchange Rate
Deterimation Under Currency Substitution and Rational Expectations,"
Journal _of Political Economy, June 1977, 85, 617-26.

Chipman, John S. "The Transfer Problem Once Again." In George Horwich and
Paul A, Samuelson, eds., Economic Theory and Mathematical Analysis, New
York: Academic Press, 1974.

Dornbusch, Rudiger. "Expectations and Exchange Rate Dynamics," Journal of
Political Economy, December 1976, 84, 1161-76.

and Stanley Fischer. "Exchange Rates and the Current Account,"
~Aerican Economic Review, December 1980, 70, 960-71.

Eaton, Jonathan and Mark Gersovitz. "Debt With Potential Repudiation:
Theoretical and Empirical Analysis," Review of Economic Studies, April 1981
48, 289-309. OT

« “A Theory of Expropriation and Deviations from Perfect Capital
Mobility." NBER Working Paper No. 972, August 1982.

Hanson, James A. "Optimal International Borrowing and Lending," American
Economic Review, September 1974, 64, 616-30.

Mussa, Michael. "The Role of the Current Account in Exchange Rate
Dynamics," Discussion Paper, University of Chicago, June 1980.

+ "A Model of Exchange Rate Dynamics," Journal of Political
“Economy, February 1982, 90, 74-104.

Sachs, Jeffrey. "LDC Debt in the 1980's: Risk and Reforms," NBER Working
Paper No. 861, February 1982.

and Daniel Cohen. "LDC Borrowing With Default Risk," NBER Working
Paper No. 925, July 1982.


- 30-

increases (i.e., £"< 0); (ii) manufacturing employment is small relative to
the potential supply of labor such that the denominator of h is positive in
condition (Al2); (iii) the tax parameter t is sufficiently small such that
mM is non-negative in condition (A18); and (iv) ET,> 0. Under these
assumptions, which will henceforth be considered "the normal case," unique—
ness follows from the fact that the right hand side of condition (A18) is an
increasing function of B,L8/, while the left-hand side is a decreasing
function of B. the optimal level of B can be represented as having the

general form

(Al9) B= g(VarT,, VarVp, Ely, EVpy ty dy U)
where the sign above each argument describes the sign of the partial deriva-
tive of B with respect to that argument in the normal case .22/

Conditions (Al17) and (A18) can now be used to derive an expression
for the country risk premium (CRP), defined as the difference between the
expected marginal return on loans to Mexican entrepreneurs and the (certain)
marginal return on loans to U.S. entrepreneurs. ‘The expected marginal return
on loans to Mexican entrepreneurs, as a function of B, is obtained from sub-
stituting (All) and (24) into (26), which yields

(A20) rB=f - (1+h)T, - ((1-t)h-t)Vp
Differentiating (A20) leads to

(A21) eStre) = £' - h'ET, - (1-t)h'EVp

which can be combined with (A17) and (A18) to yield

(A22) CRP = m)VarT, + m2VarVp,


-7-

stock of debt outstanding in the stationary-state to be below the level at
which it would be rational for Mexico to default 2/

In the model we now consider, tradables consumption happens to be
More sensitive than tradables production to changes in the terms of trade,
such that the trade balance declines when the relative price of nontradables
increases. Denote the steady-state levels of Mexican outputs by Xy,
Xyr and Xpe Nontradables are assumed to be produced with a fixed
labor/output ratio aye while employment in the two tradable-goods sectors
(Lp) is represented as a general function of the levels of Xy and

Xp. Total employment is thus described as

(3) L = ayy + Lp(XyXp)
with labor in all three sectors assumed to earn a wage rate of w pesos per
unit labor. Labor is assumed to be the only factor in nontradables
production, and w is assumed to be consistent with distributing the entire
value of nontradables output to labor £/ Thus

(4) w= p/ay
Xy is assumed to be produced with labor and capital as a function of the
steady-state level of the capital stock (K).

(5) Xy = £(K) with £' > 0, £" <0
Xp is assumed to be non-negatively related to the relative price of
primary products/

(6) Xp = Xp(q") with x", > 0

Pp >
To the extent that the capital stock depreciates it must be maintained at its
stationary-state level through gross investment purchases of I units of

manufactured goods per period.


-21-

a permanent depreciation of the peso to restore portfolio equilibrium from
the viewpoint of Mexico's creditors. The companion argument developed in
this section is that an increase in uncertainty about Mexico's export
earnings (or political attitudes), unless compensated for by a reduction in
domestic absorption in order to raise the returns that nonresidents can
expect on their loans to Mexico, might also require a permanent depreciation
of the peso to restore asset equilibrium.

Although the stationary-state framework is inappropriate for
analyzing the impact. effects of shocks on the terms of trade, it seems clear
from historical experience that the response of domestic savers and foreign
creditors to shocks plays a major role in conveying pressures to exchange
rates. The "shock" of high real interest rates and the 1981-82 world
recession on the ability of Mexico to meet its debt payments has driven the
country risk premium for Mexico (as measured by spreads over LIBOR) from
levels of around 1/2 percentage point prior to the Autumn of 1981 to 2-1/4
percentage points on the $5 billion credit that the Mexican government
negotiated with international banks in March 1983. Considering the
associated increases in negotiating fees, the effective widening of the
spread has exceeded 2 percentage points. With LIBOR rates in the range of 3
to 5 percent in real terms (9 percent nominal), the addition of a 2
percentage point spread suggests a substantial decline in the desired stock
of claims on Mexico. (To the extent that the terms on loans at the margin
reveal the market price of existing debt, the decline in the desired stock of
nonresident claims on Mexico might be estimated as the fraction of lending at

5 to 7 percent that offers a payments stream with the same present discounted

value as a loan at 3 to 5 percent.)


-27-
Appendix

The first objective of this appendix is to illustrate the solu-
tions for the terms of trade and the dollar/peso exchange rate that clear the
Mexican markets for goods and labor. The goods and labor markets are linked
by the assumption that ay units of leisure can be transformed at constant
returns to scale into one unit of nontradables output and consumption

(AL) Cy = Lyng
Consumption of manufactures is constrained by the difference between the
value of Mexican production of tradables, Xy + Vp = £(K) + Vp, and
Payments to nonresidents, rB, which from conditions (21)-(23) can be
expressed as

(A2) Cy = ew(I,+bB) + Q
If L denotes the available combined supply of leisure and labor, consumption
of leisure can be expressed as

(A3) Cy = L - ayCy - bB- 1,

For purposes of illustration it is assumed that Mexican behavior
maximizes a Cobb-Douglas utility function

(A4) U(Cyr Cyr Cy) = CE CR
subject to constraints (Al) - (A3). One of the necessary optimization
conditions is that the marginal rate of substitution between leisure and
nontradables in consumption must equal the marginal rate of transformation
through production.

(AS) (2Cy/xCy) = ay
A second condition is that the marginal rate of sustitution between manufac-

tures and nontradables must equal the market clearing terms of trade


-3-

response to a shock that changes the stock of debt depends critically on
the elasticity of the trade balance to the terms of trade. These consid-
erations apply to whatever definition of the terms of trade is appropriate
for analyzing the trade balance, whether it is the relative price of domestic
and foreign goods or the relative price of nontradable and tradable goods.
It is important to emphasize, in addition, that a determinate relationship
between the terms of trade and the nominal exchange rate requires an
assumption that pins down some nominal variable in the model.

Section III introduces uncertainty and credit risk. A two-period
model is developed in which lending and investment decisions in period 1
determine the availability of goods and relative prices in period 2, up to
several stochastic components. The two-period framework is viewed as a
segment of a stationary-state overlapping-generations model, which enables
discussion of how the introduction of uncertainty alters the stationary-state
analysis of Section II. U.S. residents extend loans to Mexican entrepre-
neurs, who use the funds to purchase investment goods. The returns to U.S.
residents in the aggregate, measured in real terms, depend broadly on all
factors that may influence the gap between Mexican production and absorption.
The model characterizes ex ante uncertainty about the realized size of this
gap in terms of uncertainty about "taxes on nonresident creditors." A dis-
tinction is made between autonomous taxes whose variance reflects pure
political uncertainty, and induced taxes whose variance reflects uncertainty
about the size of the gross Mexican domestic product that is available for
distribution among the competing groups of resident and nonresident
claimants. Revisions in expectations (as in the first model) or changes in
perceived levels of uncertainty influence the level of credit that U.S.

residents extend to Mexico, which influences the relative availability of


-14-

variables.) Physical capital stocks remain constant from period to period,
with each generation desiring to sell in its old age the exact portfolio of
claims that the next generation desires to purchase.8/ Under these
assumptions the capital stocks residing in Mexico and the United States are,
respectively,

(15) K=K,+B

(16) x* =B*
where K, is the amount of the Mexican capital stock financed out of Mexican
savings.2/ These capital stocks are assumed to be employed in the
manufacturing sectors of the two countries, yielding the outputs

(17) %y = £(k) with £' > 0, £" <0

x"

(18) %q = £*(K") with £*' > 0, £*" <0
Each of these production relations is treated as nonstochastic, but uncer-
tainty about the aggregate Mexican domestic product is introduced by assuming
that Mexico's revenue from primary product exports is stochastic.

The distribution of the value added in the U.S. manufacturing
sector is known with certainty ex ante, with capital receiving its marginal
Product, to which entrepreneurs bid up the interest rate on debt.

(19) x* = £*'(x*)

The remainder of U.S. manufacturing output is the income of the younger
generation of laborers .L&/

(20) ¥* = xy - r*B*

The distribution to U.S. creditors of value added in the Mexican
manufacturing and primary-product sectors can be described as

(21) rB= @Prp - ewlp -Q+ 4B


-16-

suggested by Hanson (1974), the extent to which creditors believe that their
loans will finance investment in productive capacity has an important bear-
ing on the optimal choice of B. Moreover, as suggested by Eaton and
Gersovitz (1981, 1982), the extent to which taking a tax bite out of the
expected earnings of nonresident creditors would impose costs (in subsequent
time periods) on the debtor country has an important influence on the
creditor's assessment of how widely Q might vary, which in turn affects the
optimal level of B. And in general, assessments of price distortions, com
mercial policies, the monopsony power of labor, government corruption and a
myriad of other factors may influence creditor assessments of the probable
returns on their loans.

The analysis below abstracts from many of these considerations
under the simplifying assumptions

(22) G@DPp = £(K) + Vp

(23) Lp = Ly + bB

(24) Q= Vp + Ty - tVp

Here, Vp denotes the value of Mexico's primary product output and exports
(Vp = a*Xp), which will be treated as the stochastic component of

@P,p- Employment in the tradables sectors is assumed to increase with the
size of the manufacturing sector, which increases with the level of B, as
assumed in condition (15). Condition (24) includes Vp in the revenues of
the combined Mexican government/capitalist sector. T, denotes an
"autonomous" component of taxes on nonresidents, the variance of which
reflects pure political uncertainty, while the parameter t is treated as a

constant that reflects the extent to which shortfalls in Vp (i.e., the


-2-

able to borrow or lend freely at a fixed foreign interest rate. A second
limitation of these models is the lack of attention to credit risk, and in
Many cases to exchange risk as well. Needless to say, such abstractions
don't square well with a world in which debt rescheduling has become common-
Place and few countries can be found whose liabilities are either small or
riskless from the perspective of their international creditors.

The next two sections of the paper outline comparative static
models for analyzing the joint determination of international lending and
exchange rates when debts are large and risky. ‘The determination of the
country risk premium is also describea. LY The models are oriented
primarily toward analyzing credit flows between countries like the United
States and Mexico, and toward understanding the corresponding exchange rate
between the Mexican peso and the U.S. dollar. Section II relaxes the
small-country assumption but continues to abstract from uncertainty. The
analysis emphasizes the stationary-state identity between the Mexican trade
surplus and the stream of Mexico's net interest payments to U.S. creditors.
Together, the "credit supply function" and the reduced-form relationship
between the trade balance and terms of trade determine the long-run
stationary-state value of the terms of trade. In particular, the terms of
trade required to produce long-run equilibrium in the goods market must be
consistent with the balance of international goods flows required to pay
interest on the outstanding stock of debt. Thus, the path of adjustment that
a country follows in the short run may influence its terms of trade in the
long run, to the extent that it influences its stock of debt outstanding in
the long run. The extent to which debt can exist in a stationary-state
equilibrium, however, is constrained by the costs of default to the debtor

country. Moreover, the extent to which the terms of trade will shift in


-25-

to default can also involve major economic and political costs. An appeal-
ing assumption is that the government will choose a portfolio of "defaults"
on international and domestic contracts that does the least harm to the long
term interests of its constituents .26/

In the case of international debts, one of the claimants on income,
the foreign creditor, is not directly represented in the political process
that administers the default tax. The fact that the nonresident creditor is
more vulnerable than resident claimants on income provides an incentive for
the creditor to attempt to strengthen its claims by channeling its invest-
ments through financial intermediaries. In this respect an insured financial
sector, or one for which a failure would spread costs to a set of taxpayers
in a third country whose government has some influence over the political
process in the debtor country, would appear to be particularly likely to
emerge as an intermediary in the international lending process.

Vv. Conclusions

Much of the recent literature on exchange rate determination is
based on the unrealistic assumptions that international lending occurs on
a small scale (i.e., at a fixed foreign interest rate), with no uncertainty
about interest and repayment streams. Some models, while abstracting from
credit risk, have emphasized the role of exchange risk when assets are
denominated in different currencies. In our opinion, however, models with
exchange risk have not provided satisfactory explanations of the exogenous
factors that underlie the probability distribution of the exchange rate.

This paper has emphasized the importance of country-specific
degrees of credit risk in the joint determination of international lending

and exchange rates. Country risk has been described in terms of


COUNTRY RISK, INTERNATIONAL LENDING, AND EXCHANGE RATE DETERMINATION
Michael P. Dooley and Peter Isard*
April 1983

(substantially revised)

I. Introduction and Summary

The subject of international lending in the presence of default
risk has attracted renewed attention during recent years. Insightful papers
by Eaton and Gersovitz (1981, 1982), Sachs (1982), Sachs and Cohen (1982) and
others have emphasized that a debtor country's ability to attract or retain
capital in the short run depends on its creditors' perceptions of its ability
and desire to meet its debt payments in real terms by generating trade
surplusses over time. To date, this literature has developed within the
confines of a one-good framework in which there is no place for real or
nominal exchange rates.

The purpose of this paper is to emphasize the importance of credit
risk in a model that integrates the determination of international lending
and exchange rates. The literature on exchange rate determination contains a
number of models that integrate an equilibrium condition on stocks of assets
or debts with an equilibrium condition on goods flows or the international
trade balance; together, these conditions anchor the (long-run) level of the
real exchange rate, defined either as a relative price of domestic and
foreign goods or a relative price of nontradable and tradable goods. Models
of this type include Dornbusch (1976), Calvo and Rodriguez (1977), Dornbusch
and Fischer (1980), and Mussa (1980, 1982). A restrictive feature of these
models, however, is the small-country assumption that concentrates attention

on the portfolio-adjustment behavior of domestic residents, who are assumed


-33-

1l1/ Value added in the Mexican nontradable goods sector is distributed

4

entirely to Mexican workers.

12/ Condition (21) ignores stationary-state investment for purposes of
replacing depreciated capital.

13/ Since Q is a linear combjnation of Ty and Vpr it can be seen from
conditions (28) and (29) that C5 has a symmetric distribution, given B
and B*, whenever Ty and Vp are independently and symmetrically distri-
buted.

14/ These signs are clarified in the Appendix. An increase in ET, or a
decline in t directly reduces the expected return on any given level of B
after taxes (recall condition 26), and this effect is magnified by an induced
increase in the extent to which the wage bill is expected to cut into
earnings (recall conditions 29 and 24). An increase in EV, reduces the
expected tax bite, but in our particular model the associated effect on the
expected return on B is outweighed by the increase in the expected wage
bill.

15/ To the extent that the peso wage rate rises as the peso depreciates,
the depreciation will be magnified (in order to achieve the required change
in the terms of trade).

16/ An interesting possibility is that domestic money creation might be
one such time inconsistent policy. This would provide an alternative link
between unusually poor outcomes for economic activity and nominal exchange
rates.

17/ U.S. creditors take y* as given in the first period of their lives
and, accordingly, optimize (25) subject to (13), (Al5), and (Al6) rather than
(27), (Al5), and (Al6).

18/ ‘The proof involves showing that h(B) has positive first and second
derivatives.

19/ The signs can be derived by totally differentiating condition (A18)
and noting that f' is a positive and decreasing function of B while h', m,
and my are each positive and increasing functions of B.


- 28-

(A6) (2Cy/yCy) = p*

where

(A7) p* =ep= eWay
Together, conditions (A3) and (A5) imply

(A8) Cy = 2(L - bB - Ly) /(x + Z)ay

Substitution of (A8) into (A6) leads to

(A9) p® = (x+z)Cy/y( (L-L,-bB) /ay)
which states that the relative price of nontradables varies in direct propor-
tion to the quantity of tradables available for consumption relative to the
amount of nontradables that could potentially be consumed if all labor/
leisure not employed in the two tradables sectors were devoted to producing
nontradables. Substitution of (A2) into (A9), using (A7), leads to

(ALO) p* = hO/( (I 4B) /ay))

(All) e

hO/w( 1, #bB)
where

(Al2) 4h

(x+Z) (Lg+bB)/(yL — (x+y+z) (L+bB) )
It is assumed that the denominator of h is positive, in which case it is
easily shown that h is a positive and increasing function of B.

The next objective is to compute the mean and variance of Ch.
From conditions (28) and (All) it follows that

(A13) Ch = (1+r*)B* + B + £(K,#B) — Ty + tVp — hO
From conditions (Al13) and (24) it follows that

(Al4) root = (1+r*)B* + B+ £(K,+B) ~ (14h)T, - ((1-t)h-t)Vp


-12-

is rational for debtor countries to continue paying interest (and for
creditor countries to continue expecting interest receipts).
III. A Model With Credit Risk

We are now ready to relax the assumption that creditors are
certain of receiving the payments they expect. International lending
behavior is described in the context of an overlapping generations model in
which each generation of creditors solves a two-period intertemporal
consumption problem. Conclusions about the sensitivity of international
lending and the terms of trade to various Parameters are again restricted to
inferences drawn from comparative static analysis. The overlapping
generations paradigm is used in a very limited way, which does little to
enrich or complicate the two-period problem, but which facilitates com
parison of the uncertainty case with the previous stationary-state analysis
under certainty.

The paradigm is that each generation of U.S. residents lives for
two periods, working to earn an income al in the first period, which
must be divided between first-period consumption (Cy) and purchases
of financial claims that can be sold to finance consumption during their
retirement in the second period. ‘Two types of financial claims can be
purchased: dollar-denominated claims on U.S. entrepreneurs (B") and
dollar-denominated claims on Mexican entrepreneurs (B). Entrepreneurs use
the funds obtained from issuing claims to purchase investment goods, which
are employed in producing the U.S. and Mexican domestic products. Given
y, a choice of B and B" by the younger generation of U.S.
residents implies first and second-period consumption levels

*

(13) cl =y*-B*-B


-15-

Here, GDPp denotes the gross domestic product of the two tradable goods
Sectors, ewlmp represents the dollar value of the goods that must be sold to
pay workers employed in the tradable goods sectors, and Q includes returns to
all Mexican non-labor factors of production, as well as the tax revenues col-
lected by the Mexican government .L2/ The AB term on the right side of
condition (21) recognizes that interest payments can always be met by borrow-
ing more. The analysis below, however, will focus on stationary-state
solutions in which 4B is zero and rB corresponds to Mexico's trade surplus,
as in condition (9) of the previous section.22/

Although the return on U.S. loans to an individual Mexican entre-
Preneur may be subject to the risks associated with the particular projects
undertaken by the entrepreneur (depending on the nature of any guarantees
provided by the Mexican government), condition (21) emphasizes that returns
are also subject to macroeconomic risks associated with uncertainty about the
size of Mexico's gross domestic product and uncertainties about the extent to
which that product will be claimed by Mexican residents. Even with a pre-
specified peso wage rate, the dollar value of labor's claims to @Pp will
be uncertain ex ante to the extent that the dollar/peso exchange rate is
uncertain. Moreover, taxes are generally uncertain ex ante, reflecting both
political uncertainty about the parameters relating the level of taxes to GDP
and/or other economic magnitudes, and economic uncertainty about the levels
of GP and/or whatever other economic variables enter the tax function.

Broadly viewed, the calculation of an optimal level of B for U.S.
creditors in the aggregate requires an assessment of the probability distri-
bution of the right hand side of condition (21), conditional on B. (The dis-

cussion here is restricted to the stationary-state case with aB-=0.) As