We present a simple example to illustrate how, despite having a sound net debt position, a crisis could be triggered off by the presence of large gross debt. The model essentially follows Chang and Velasco (2001, *CV*) with minor modifications. We consider a small open economy with ex ante identical agents. There are three time periods in the economy denoted by *t* = 0,1,2. There exists a single good which is freely traded and whose price is fixed and is normalized at a dollar. The domestic agents are endowed with *e* dollars. At *t* = 0, goods can be invested in a foreign long-term technology such that each dollar invested yields *R* > 1 dollars at the end of period 2. However, if the technology is liquidated in period 1, the return from this investment is *r* < 1. On the other hand, there is a world capital market that is liquid and deep. One dollar lent at *t* = 0 yields a gross return of 1 dollar at either *t* = 1 or *t* = 2. Domestic agents can lend as much as they want but can borrow a maximum of *f* > 0.

As in *CV*, each domestic agent discovers her type at *t* = 1. Specifically, she discovers with probability *λ* that she is impatient and derives utility only from period 1 consumption, *c* _{1}, or with probability 1-*λ*, that she is patient and derives utility only from period 2 consumption *c* _{2}. Type realization is \(i.i.\dot{d}.\) across agents and there is no aggregate uncertainty. The ex ante expected utility of domestic agents is

$$ \lambda u( {{c}_{1}} )+( 1-\lambda)u( {{c}_{2}} ) $$

(1)

where *u*(*c*) is \( \frac{{{c}^{1-\sigma }}-1}{1-\sigma }. \) In such a setup with no aggregate uncertainty, *Home* agents can benefit from pooling their resources, which rationalizes the existence of a bank. The bank maximizes the utility of the representative depositor conditional on the realization of her type. The problem is solved using the Revelation Principle wherein the social optimum is obtained by maximizing (1) subject to

$$ \lambda {{c}_{1}}\le {{d}_{1}}+rl $$

(3)

$$ (1-\lambda ){{c}_{2}}+{{d}_{0}}+{{d}_{1}}\le R[k-l] $$

(4)

$$ {{d}_{0}}+{{d}_{1}}\le f $$

(6)

$$ {{c}_{1}}\le {{c}_{2}} $$

(7)

$$ {{c}_{1}},{{c}_{2}},k,l\ge 0 $$

(8)

where *k* denotes the amount invested in the long-term overseas project, *d* _{0} and *d* _{1} are the foreign debts at *t* = 0, 1, respectively, and *l* denotes the liquidation amount of the long-term project at *t* = 1. Equation (2) restricts the long-term investment to be less than the endowment plus borrowings. Equations (3) and (4) represent the feasibility constraints in periods 1 and 2. Equations (5) and (6) are the external feasibility constraints and (7) is the truth-telling constraint. Following *CV*, at the social optimum, there is no wastage of resources, leading to the following conditions:

$$ \lambda {{\tilde{c}}_{1}}={{\tilde{d}}_{1}} $$

(10)

$$ (1-\lambda ){{\tilde{c}}_{2}}+{{\tilde{d}}_{0}}+{{\tilde{d}}_{1}}=R\tilde{k} $$

(11)

$$ \tilde{k}={{\tilde{d}}_{0}}+e $$

(12)

$$ {{\tilde{d}}_{0}}+{{\tilde{d}}_{1}}=f $$

(13)

where the tilde denotes the social optimal values of the respective variables. Equations (9)–(13) can be reduced to a single equation:

$$ ( 1-\lambda){{\tilde{c}}_{2}}+R\lambda {{\tilde{c}}_{1}}=R\omega$$

(14)

where \( w\equiv e+f[R-1]/R \) and can be interpreted as the social wealth of the *Home* country. The social optimal is obtained by maximizing (1) subject to (14), which yields

$$ \lambda {{\tilde{c}}_{1}}=\theta \omega$$

(15)

$$ (1-\lambda ){{\tilde{c}}_{2}}=(1-\theta )R\omega$$

(16)

where \( \theta =1/\left[ 1+\frac{\left( 1-\lambda \right)}{\lambda }{{R}^{\frac{\sigma =1}{\sigma }}} \right]\in [0,1] \). Denoting the gross and net foreign debt flows^{1} at the end of *t* = 0 as*d* _{0} and \( {{n}_{0}}\equiv {{d}_{0}}-k \), respectively, it follows that

$$ {{\tilde{d}}_{0}}=\tilde{k}-e=(1-\theta )\omega +f/R-e $$

(17)

$$ {{\tilde{n}}_{0}}=-e $$

(18)