A. Basic Model Details

In our model, the aid-recipient country announces (L_t, i_t), where L_t is the amount of loan that the LIC wants to borrow, and i_t the interest rate it is willing to pay in a given period, t. Thus, in the model, the borrowing LIC chooses and announces (L_t, i_t) so as to maximize utility. Assume further that each lender supplies either one unit of credit or nothing. Let $E_t^s$ be the expected excess supply of credit, and r_j the lowest rate at which the lender j is willing to lend to the borrower. It is assumed that r_j is inversely related to expected excess supply, $E_t^s$:

We assume that the total supply of loans in period t, S_t, to the LIC is determined as:

where $\partial S_t/\partial E_t^S\ge 0$ and ∂S_t/∂i_t ≥ 0 Donors view an excess supply of loans as a positive sign. Thus, given the S-function in equation (2), aid donors regard the current-period excess supply of loans, $E_t^S$, as the sign of the LIC’s creditworthiness. The lenders (aid donors) then supply the amount of loans or credit on rational expectations, where_e is the expectations superscript relative to the information set held in period t-1:

where $Y_t^e$ is the expected supply of funds in the current period; L_t the demand for credit in the current period; and i_t the interest rate the aid recipient or borrower is willing to pay in period t. Aid donors will end up supplying Y units of credit only if this amount satisfies equation (3).

The lender’s expected return, ${\rho }_t^e$, in period t is given as:

S is now a function of the expected supply of funds, $Y_t^e$, and the lender’s expected return, (i_t - π_tθ - γ_tλ)^e. π_t is the default parameter for the borrowing LIC and it lies between 0 and 1. Judging from past performance of a LIC in terms of loan repayment, the donor community is assumed to hold some prior knowledge of the lender’s propensity to default. The closer this parameter is to 0 for a given value of θ, the higher will be the lender’s expected return. θ is a given constant. Thus, π_tθ is the value of the default costs of the debt to the lender or donor.

The parameter γ_t in the lender’s expected return, (i_t - π_tθ - γ_tλ)^e, represents cost of acquisition of information to the lender and it also lies between 0 and 1. As mentioned above, apart from observing what their peers are doing, donors also seek information about the LIC on their own. There is, however, a cost attached to acquiring this extra information. It should be noted that a lower value of γ_t will imply a higher expected return to the lender. The symbol λ stands for some given constant.

We rewrite the S-function, which assumes rational expectations, as follows:

In the loan-pushing model, the supply of loans in period t, S_t, depends positively on expected supply in period t, $Y_t^e$, and lender’s expected return in period t, ${\rho }_t^e={\left(i_t-{\pi }_t\theta -{\gamma }_t\lambda \right)}^e$. The supply of new loans can be expressed as follows:

In equation (6), $\overline{Y}$ is the threshold level of the supply of funds and ρ* is the threshold level of the lender’s return. If the expected supply in period t, $Y_t^e$, and the lender’s expected return in period t, (i_t - π_tθ - γ_tλ)^e, exceed their threshold levels, $\overline{Y}$ and ρ* respectively, the LIC receives foreign loans or aid. Otherwise, there is no supply of new loans. This means that the supply function becomes discontinuous at the threshold levels. However, the model presents an extreme case of herding behavior, since a small decrease in the lender’s return will cause a drop in the supply of loans to zero.³ The strength of the model is that the discontinuity and the reversal of aid flows are explained endogenously, even though the entire primitive behavioral functions—equations (1) and (2)—in the model are continuous.

B. Generating a Domestic Debt Crisis

We next show how a domestic debt crisis occurs in the event of n-successive-period simultaneous withdrawals of aid by aid-donors from the borrowing LIC. Suppose that, as a result of either bad governance and corruption or poor macroeconomic management, in period t, aid donors announce their intention to withdraw financial assistance to the LIC with effect from period t+1 until favorable conditions prevail in the country. If this situation leads the government to borrow from domestic creditors (other than adjusting its expenditures, for example, in the expectation of a reversal of donors’ decision), we can envisage a rise in real interest rates in every period after t+1.

We can formalize this scenario as follows. Consider a sequence of T-zero aid flows to the LIC, where T is the number of periods for which the LIC does not have aid inflows following donor herding. Thus, from period t+1 up to period T, there is no supply of new loans, namely S_t+1, S_t+2,…, S_t+T. From equation (6) above, we can see that starting from period t+1 the condition that ${\left(i_t-{\pi }_t\theta -{\gamma }_t\lambda \right)}^e<\rho *or{Y}_t^e<\overline{Y}$ must hold to satisfy the outcome. As a result of ensuing high real interest rates on the domestic financial market, the government will start to default on domestic debt as long as accumulated debt in each period is above some threshold level. In each period, we have three likely outcomes:

where ψ_t+k is the actual domestic debt accumulated in period t+k (k = 1, 2, …, T) and ${\varpi }_{t+k}^{*}$ is the level of accumulated domestic debt that the government is able to repay in every period. It is assumed that the actual domestic debt accumulated (ψt+k) is determined as follows:

where $r{i}_{t+k}^d$ is the real interest rate prevailing on the domestic financial market; DS_t+k is the dummy variable which takes the value of 1 if there is no supply of foreign aid in period t+k and 0 otherwise; and ${\left(D{S}_{t+k}xr{i}_{t+k}^d\right)}^2$ is the square of the interaction variable between DS_t+k and $r{i}_{t+k}^d$. In equation (7), the actual domestic debt accumulated in period t+k, ψ_t+k, is a strictly increasing function of the square of the interaction variable, ${\left(D{S}_{t+k}xr{i}_{t+k}^d\right)}^2$; that is, $\partial {\psi }_{t+k}/\partial (D{S}_{t+k}xr{i}_{t+k}^d)>0$, given that DS_t+k = 1. On the other hand, if DS_t+k = 0, ψ_t+k is a decreasing function of $r{i}_{t+k}^d$; that is, $\partial {\psi }_{t+k}/\partial r{i}_{t+k}^d\le 0$.

From equation (7), we can see that as long as ψ_t+k is equal to or less than ${\varpi }_{t+k}^{*}$, a debt crisis does not occur in the LIC. A debt crisis occurs once ψ_t+k is greater than ${\varpi }_{t+k}^{*}$. The first two outcomes will obtain if the government of the LIC responds to donor herding by simultaneously reducing its expenditures and borrowing a well-calculated sum of loans from the home financial market. If no reduction to fiscal expenditures is made, then the third outcome (domestic debt crisis) is likely to be faced by the LIC.