## I. Introduction

In this paper, we assume that aid donors follow herding behavior that determines aid flows in a low-income country (LIC). We modify a loan-pushing model by Basu (1991) to introduce the donor herding behavior that may trigger domestic debt crisis in a LIC. According to Devenow and Welch (1996), rational herding behavior is usually modeled for three reasons: payoff externalities, principal-agent problems, and information externalities. Our model focuses on rational herding behavior of donors due to payoff and information externalities. Although there are many theoretical models on herding behavior, these models have not formally considered the relationship between donor herding and domestic debt crisis in an LIC. This paper is an attempt to fill this gap.

Vives (1993) defines “herding” as behavior where one person (or agent) observes the action(s) of their predecessor(s), updates their prior belief, and then has more incentive to imitate their predecessor(s) knowing that their choice may *ex post* not be optimal. Thus, agents often infer information out of the actions of other agents. The tendency to base decisions largely on the observed decisions of other agents has been modeled as information externalities. Banerjee (1992); and Bikhchandani, Hirshleifer, and Welch (1992) (henceforth BHW) introduced the first models that emphasized the inefficiencies of these information externalities in a context of social learning. Each one of these models considers a population of agents endowed with a private, costless and imperfect signal concerning the desirability of a course of action. Chamley and Gale (1994) consider a setup similar to the BHW models, except that all players have the possibility to wait, in order to observe how many players invest in the current period and to make their investment decision in the next period based on superior information. Their analysis shows how bad outcomes and inefficient waiting may occur in equilibrium.

The rest of the paper proceeds as follows. Section II presents our model. In Section III, we conclude by offering suggestions for empirical analysis.

## II. The Model

In our modified loan-pushing model, aid donors base their strategies on what they see other aid donors doing, and they, themselves, are also searching for extra information. As a result of searching for this extra information, there are costs ensuing to donors. The loan-pushing theory is further based on the assumption that aid donors or lenders are supplying more credit to the borrowing LIC than the latter would voluntarily take at the prevailing interest rate.^{2} In practice, the assumption that countries are persuaded to take more loans than they are willing to take might not be realistic, as loans are typically given with conditionality, which may be (politically) costly to the borrower. In certain cases, political economy considerations can be an important factor in contracting loans. For instance, when the number of (new) loan-financed projects enters positively in the voting function, in the short term politicians could be inclined to borrow beyond what could be justified by economic return. This aspect is not explicitly modeled here. We also exclude cases of donors acting purely for humanitarian reasons, for example, due to a natural disaster.

### 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 *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,

We assume that the total supply of loans in period *t*, *S*_{t}, to the LIC is determined as:

where *∂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* is the expectations superscript relative to the information set held in period *t-1*:

where *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, *t* is given as:

*S* is now a function of the expected supply of funds, *(i*_{t} - π_{t}*θ* - *γ*_{t}*λ)*^{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_{t}θ 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_{t}*θ* - *γ*_{t}*λ)*^{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*, *t,*

In equation (6), *ρ** is the threshold level of the lender’s return. If the expected supply in period *t*, *t*, (*i*_{t} - π_{t}θ *- γ*_{t}*λ)*^{e}, exceed their threshold levels, *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

where *ψ*_{t+k} is the actual domestic debt accumulated in period *t+k* (*k = 1, 2, …, T*) and *ψt*+*k)* is determined as follows:

where *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 *DS*_{t+k} and *t+k, ψ*_{t+k}, is a strictly increasing function of the square of the interaction variable, *DS*_{t+k} = *1*. On the other hand, if *DS*_{t+k} = *0*, *ψ*_{t+k} is a decreasing function of

From equation (7), we can see that as long as *ψ*_{t+k} is equal to or less than *ψ*_{t+k} is greater than

## III. Conclusion

Based on the analysis presented above, the main empirical research question that arises, therefore, is whether the changes in domestic debt stocks are linked to sudden shifts in external aid inflows, exacerbated by donor herding. Subsequent empirical work will need to establish whether there has been donor herding; that is, whether changes in the flows of assistance by one donor have been heavily influenced by one or more other donors. Concretely, this could be done, for example, by determining whether the growth rate of domestic debt beyond a certain threshold is explained by a decline in donor aid below a certain threshold, after controlling for a number of macroeconomic environment variables. Empirical work would also need to determine why, when faced with imminent or actual cuts in donor assistance, the government did not cut expenditure or raise revenues.^{4} Finally, the empirical analysis could also usefully assess the consequences of the behavior of the government for domestic economic outcomes.

A major challenge of the empirical work will be to gather the data on individual donor financing commitments and disbursements with sufficient frequency (monthly or quarterly), and over a sufficiently long period. Finding adequate domestic debt data on stocks and flows by type and holder, while easier, is not a trivial exercise as most LICs do not have good domestic debt data beyond banking system credit, and on treasury bills and bonds.

Banerjee, A., 1992, “A Simple Model of Herd Behavior,” The Quarterly Journal of Economics, Vol. 57, No. 3, pp. 797–817.

Basu, K., 1991, Analytical Development Economics (Cambridge: MIT Press).

Bikhchandani, S., D.Hirshleifer, and I.Welch, 1992, “A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades,” Journal of Political Economy, Vol. 100, No. 5, pp. 992–1026.

Chamley, C. and D.Gale, 1994, “Information Revelation and Strategic Delay in a Model of Investment,” Econometrica, Vol. 62, No. 5, pp. 1065–85.

Devenow, A. and I.Welch, 1996, “Rational Herding in Financial Economics,” European Economic Review, Vol. 40.

Vives, X., 1993, “How Fast do Rational Agents Learn?” Review of Economic Studies, Vol. 60, No. 2, pp. 329–47.

Yohane Khamfula is at Stellenbosch University, South Africa, and Ephraim Chirwa is at the University of Malawi. An earlier version of this paper is forthcoming in *Applied Economics Letters.* The authors would like to thank, without implication, Robert Flood and Paul Cashin for stimulating discussions and useful suggestions, as well as Peter Fallon, Carlos Leite, and David O. Robinson for comments and suggestions.

Basu (1991) observes that the interest rate is not the only factor involved; debt maturity and default provisions are also important.

This is a corner solution. In practice, there may be a minimum level of donor inflows, for example, in the form of humanitarian aid. However, the results obtained in this case would not be qualitatively different from what follows in the rest of the paper.

A possible reason could be that the LIC government believes that donors will be faced with the “Good Samaritan’s” dilemma, and not walk away for a prolonged period.