A. Aid and Growth

Historically, the rationale for aid has its theoretical foundations in the Harrod-Domar model, in which the driving force of economic growth is physical capital formation. In low-income countries that may be unable to save enough to finance high investment, foreign aid provides an additional source of funds that closes the domestic savings gap, boosts investment, and ultimately leads to higher growth. A variant of this model incorporates the additional assumption that (most) capital goods are not produced domestically but are imported, thereby linking investment and imports. If exports are not sufficient to finance the necessary level of capital goods imports, investment and growth suffer. Again, foreign aid helps close this trade gap and leads to higher growth.

This so-called “aid-investment-growth” hypothesis provided the intellectual foundation on which a huge aid industry was built after World War II in developed countries. Unfortunately, despite extensive efforts to provide empirical support for this hypothesis—much of it expended by international organizations involved in the aid business—the results were disappointing: there does not seem to be conclusive evidence of a robust link between foreign aid and growth.

This empirical literature has followed two tracks (White, 1992; Hansen & Tarp, 2000; and Hjertholm et al., 2000 provide excellent surveys). A large number of studies attempted to measure directly the impact of aid on growth, typically through reduced-form regressions, with very poor results: aid is sometimes found to have a positive impact on growth, but very often its impact is insignificant or negative. A number of other studies tried to examine the indirect link between aid and growth through investment. Once again, the evidence is inconclusive. While earlier papers generally found a positive correlation between aid and investment, more recent studies were unable to establish such a link (see Easterly, 1999; Dollar & Easterly, 1999).⁵

Efforts to incorporate aid in a structural growth model had similarly ambiguous results. A number of studies (e.g., Obstfeld, 1999; Gong & Zou, 2001) introduce foreign aid in an optimal growth model, treating it as a lump-sum transfer that changes the representative agent’s budget constraint. As the representative agent maximizes intertemporal utility under the expanded budget constraint, the impact of aid on the optimal consumption and capital accumulation paths can be traced. In these studies, aid has generally been found to stimulate investment in the short term. In the long term, however, aid lowers the steady state capital stock, increases consumption, and reduces labor supply.

Against this background, the focus recently started shifting to the reasons behind the apparent ineffectiveness of foreign aid. One strand of this literature concentrates mainly on the interaction between foreign aid and the policy environment. Burnside & Dollar (2000) argued that aid is often disbursed in the presence of serious policy distortions that reduce the marginal productivity of capital and weaken the incentive to invest. In such environments, aid is more likely to be consumed than invested. Burnside & Dollar tested their hypothesis by including a range of institutional and policy indicators along with aid in a reduced-form growth regression, and found that aid is more effective in countries with good policy environments. In a similar vein, Dollar & Easterly (1999), while unable to detect a relationship between aid and investment in general, claimed that there is a statistically significant relationship between aid and investment in good policy environments. These papers were initially very influential: they were seen as the answer to the “paradox” of the ineffectiveness of foreign aid. But Hansen & Tarp (2000 and 2001) have undermined these results, showing that they are extremely data dependent and, on the basis of the available evidence, concluded that the policy environment in the recipient country does not affect the effectiveness of aid.

Even if the policy environment matters, it is just one of several determinants of the effectiveness of aid. Lensnik and Morrisey (2000) argued that aid instability adversely affects investment decisions. In countries where aid is a major source of public revenues, McGillivray & Morrissey (2001) showed that volatility of aid flows can induce fiscal behavior that hinders growth (directly through cuts in public investment and indirectly through the complementarities between public and private investment). Bulíř & Hamann (2001) confirmed these findings and, analyzing data for over 100 aid recipient countries, showed that uncertainty about aid disbursements is large and that the information content of donor commitments is very small indeed.

This extensive literature on the impact of aid on growth is based on the experience of developing economies. Aid is modeled as an income transfer that relaxes the budget constraint of the recipient. The characteristics of the recipient economy are not taken into account, and no attempt is made to distinguish between different kinds of aid. Furthermore, with very few exceptions, the aid flow is implicitly assumed to be permanent (or last indefinitely), and no attempt is made to model the impact of a temporary transfer that depends on the state of the recipient economy.⁶ As we saw earlier, however, the facts in post conflict economies are completely different. Post conflict aid typically includes large amounts of humanitarian assistance that is tied to the needs of the country and tends to lapse once the emergency is over; and funds for reconstruction of destroyed infrastructure and for institution-building contribute directly to the rehabilitation of the productive capacity. Taken together, these transfers can reach extraordinarily high levels in the early post-conflict years, but decline rapidly thereafter. These differences in the nature, size, composition, and time profile of aid between post conflict and developing countries suggest that the findings of the traditional aid literature may not apply in post conflict cases.

B. Aid and Resource Allocation

Another important strand of the aid literature examines the impact of foreign aid on the recipient economy. Michaely made one of the earliest contributions in this area (Michaely, 1981). He used a simple two-sector model with tradable and non-tradable goods, in which foreign aid is introduced as a transfer of tradable goods. As the relative price of non-tradables increases in order to restore equilibrium, resources move to that sector and the production of tradables falls while that of non-tradables increases. In this model, the impact of aid is similar to the so-called Dutch disease.⁷ In a similar vein, Van Wijnbergen (1986) pointed out that the contraction of the tradable goods sector caused by aid hinders the export promotion objectives of many aid programs (see also the surveys in Rattsø & Torvik, 1999, and Hjertholm et al., 2000). These results aggravated the consternation among aid advocates: not only did the link between aid and growth turned out to be at best tenuous, but aid could directly hamper the country’s ability to reach and maintain a sustainable external position.

To make matters worse, the Dutch disease literature seemed to suggest that the damage to the tradable goods sector may be permanent even if the aid flow is temporary. Krugman (1987) pointed out that in the presence of learning-by-doing effects (or more generally increasing returns to scale) in the tradable goods sector, the future productivity in this sector would depend on its cumulative output. Consequently, even a temporary contraction in the output of the tradable goods sector triggered by a lump-sum foreign exchange transfer—such as aid—could lead to a permanent reduction in the productivity of this sector.

As in the case of the literature on the impact of aid on growth, these studies do not quite fit the experience of post conflict economies. Aid is modeled simply as a transfer of tradable goods or foreign exchange—hence the affinity with the Dutch disease literature. While humanitarian aid falls in this category, reconstruction aid may case supply bottlenecks and increase productivity in the tradable goods sector, and thus affect the recipient economy in a very different way.

A. The Basic Model

Production in the post conflict economy is described by a production function that includes capital, labor, and recostruction aid.⁸ Reconstruction is akin to a public good: foreign aid for reconstruction and institution-building benefit all sectors, but not necessarily to the same extent.⁹

Reconstruction is not the only form of foreign aid. The other component is humanitarian aid, H. One of the distinguishing features of our analysis is the formulation of humanitarian aid. International donors set humanitarian aid according the following simple “graduation” rule:

At consumption levels below the donor-defined minimum acceptable consumption ĉ, the country receives humanitarian assistance. As consumption rises, aid falls until ĉ = c. At this point, the country stops receiving humanitarian aid and “graduates”. The parameter α is very important: it measures the short-run generosity of the donor community. Higher values of α represent higher rates of disbursement of humanitarian aid. If α = 1, donors are prepared to make immediately available all the necessary resources so that the consumer could consume ĉ.

Reconstruction aid is assumed to be disbursed at a fixed amount each period for as long as the reconstruction phase lasts. Therefore, in each period, total post conflict aid D is:

In line with other models of this family, the representative agent is assumed to have an infinite planning horizon and perfect foresight, and to maximize a utility function in terms of consumption c and labor supply l. The instantaneous utility function is strictly concave in consumption and labor. We further assume that the marginal utility of consumption is decreasing in labor supply.

The intertemporal optimization problem is set up as a Hamiltonian. The representative agent optimizes this objective function subject to her budget constraint. Derivation of the optimality conditions yields estimates of the instantaneous impact of changes in the exogenous variables such as labor supply, capital accumulation, and consumption. Solution of the dynamic system— provided it is stable—yields estimates of the impact of changes in the exogenous variables on the steady state equilibrium. In the next two sections, two variants of this basic model are developed and solved. Readers who are not interested in the technical details can skip to the final chapter, which summarizes the results and draws the policy implications.

B. The One-Good Variant

This variant concentrates on the impact of different forms of post conflict aid on capital accumulation, growth, and welfare. This can best be done in a simple, one-good model. Therefore, the production and utility functions are:

where R = reconstruction aid, l = labor, and k = capital. The parameter θ is the agent’s rate of time preference. The representative agent’s budget constraint is

The Hamiltonian problem in the one good model is:

where λ is the co-state variable associated with the budget constraint, and can be intuitively interpreted as the marginal utility of wealth. The first order conditions from optimizing (2.4) are:

and the transversality condition is:

First order conditions (2.5) and (2.6) can be solved for a consumption and a labor supply function:

Substituting equations (2.9) and (2.10) into equations (2.3) and (2.7) gives the following dynamic system:

This system describes the dynamic evolution of k and λ and determines the intertemporal evolution of the economy as a whole. The steady state is reached when $\dot{\lambda }=\dot{k}=0.$

Denoting the steady state values of k and λ as k^* and λ^* respectively, and linearizing equations (2.11) and (2.12) around these values gives:

where:

This system has a saddle point equilibrium (for proof, see Appendix I), and the general form of the solution is:

where ϕ₁ and ϕ₂ are the positive and negative eigenvalues, respectively, and A₁ and A₂ are constants determined by the initial conditions and the transversality condition. Substituting these into (2.15) gives:

As usual, there are two saddle paths, one stable $\lambda -{\lambda }^{*}=-\frac{{\lambda }^{*}{q}_{21}}{{\lambda }^{*}{q}_{22}+{\varphi }_1}(k-k^{*})$ and one unstable $\lambda -{\lambda }^{*}=-\frac{{\lambda }^{*}{q}_{21}}{{\lambda }^{*}{q}_{22}+{\varphi }_2}(k-k^{*}).$

C. The Two-Good Variant

This variant of our basic model focuses on the impact of post conflict aid on the real exchange rate and the allocation of resources in the recipient economy between tradable and non-tradable goods. Since humanitarian aid in post conflict economies is typically short-lived, we can simplify the model by setting H= 0 and concentrating on the effects of reconstruction aid. Because reconstruction aid improves directly productivity in the recipient economy, its effects on the steady state equilibrium are bound to be different than the traditional aid literature suggests. For simplicity, we also fix total labor supply and normalize to unity. Using T, N to denote tradables and non-tradables, respectively, the production and utility functions become:

For tractability, we assume a multiplicative separable form of the above neoclassical production function, and (3.1) is simplified to:

where k=k_T +k_N, l_T +l_N = 1, and A_i(R) (i = T, N) is a factor that captures the efficiency gains from post conflict reconstruction and institution-building. This is the standard form used in the endogenous growth literature to reflect the function of public goods in production. Note that reconstruction aid need not benefit both sectors equally. Indeed the difference between A_T and A_N is critical for the results of this variant of the model, and will inform the conclusions on the optimal design of reconstruction aid. We assume that the tradable goods sector is more capital intensive than the non-tradable goods sector $(\frac{k_T}{l_T}\rangle \frac{k_N}{l_N})$ and that capital is non-tradable. Finally, since this is an open economy model, we need to introduce an additional tradable asset (bonds b) so as to allow the domestic consumption of tradables to be different than the domestic production (in other words, for the current account deficit to be different than zero, at least temporarily).

With these simplifying assumptions, this variant of our model has become very close to the model used by Brock & Turnovsky (1994) and Brock (1996), and the solution henceforth follows their work. Recalling that H = 0, the Hamiltonian for this variant can be written as

where p is the real exchange rate (relative price of non-tradables).

The optimality conditions are:

It is assumed, as is common practice in the literature, that the marginal utility of wealth remains constant. Consequently $\frac{\dot{\lambda }}{\lambda }=0,$ and (3.11) implies that the rate of time preference is equal to the world real interest rate.

The market clearing conditions for tradable and non-tradable goods are:

Expression (3.12) states that the rate of accumulation of tradable bonds equals the domestic supply of tradable goods minus the domestic consumption of these goods plus the interest earned on the outstanding stock of the tradable bonds. In other words, (3.12) describes the economy’s balance of payments with the rest of the world. Expression (3.13) states that capital accumulation equals the excess of domestic production over domestic consumption of non-tradables plus reconstruction aid. Note that reconstruction aid is akin to a capital good and cannot be used to finance directly the consumption of tradable goods. The representative agent is, of course, able to allocate the extra income generated through reconstruction aid to the consumption of either good or to savings, thereby using reconstruction aid indirectly to achieve higher consumption. This formulation fits exactly the stylized facts in post conflict economies.

The transversality condition is:

Total differentiation of the optimality conditions (3.6) and (3.7) yields the following partial derivatives:

where ${\Psi }=u_{\mathit{\text{TT}}}{u}_{\mathit{\text{NN}}}-u_{\mathit{\text{TN}}}^2>0$

The sign of (3.15) depends on whether tradables and non-tradables are substitutes (u_TN < 0) or complements (u_TN > 0) in consumption. The signs of (3.17) and (3.18) are negative on the assumptions that (i) both goods are normal (i.e., a decline in the marginal utility of wealth, which is associated with an increase in wealth, leads to increased consumption of both goods); and (ii) even if T and N are complements, the size of the cross effect u_TN is smaller than u_TT or u_NN.

The optimality conditions can be manipulated to derive a number of standard microeconomic results. First, (3.8) and (3.9) can be solved for r(p) and w(p). It can be shown that a real appreciation (i.e., an increase in the price on non-tradables) leads to a decline in the rate of return to capital:

r_p 〈0 since we have assumed κ_T > κ_N

Second, totally differentiating the optimality conditions (3.8) and (3.9) yields the following partial derivatives:

Expressions (3.20) and (3.21) imply that a real exchange rate appreciation increases the capital intensity in both sectors. This is because a real appreciation shifts demand away from the more capital-intensive tradable goods toward the more labor-intensive non-tradable goods, thereby increasing the relative price of labor. Firms in both sectors substitute capital for labor, and the capital-labor ratio increases.

Third, it can be shown that an increase in total capital leads to an expansion of the tradable goods sector and a contraction of the non-tradable goods sector. Recalling that the production functions have been assumed to be separable and that k_T +k_N =k and l_T +l_N = 1, we can write

and therefore the partial derivatives of y_N and Y_T with respect to total capital k are

since κ_t > κ_n. This is the standard Rybszinski theorem: an increase in total capital leads to an expansion of the capital-intensive sector and, because labor is drawn out of the labor-intensive sector, a contraction of the latter.

The dynamics of the system are described by the differential equations (3.10), (3.11), (3.12), and (3.13). This system of equations is block recursive, so we can linearize and solve the system in terms of p and κ.

where q₁₁ =r – r_p, q₂₁ = y_Np – c_Np, and q₂₂=y_Nk and, as before, an asterisk denotes the steady state value of the variable.

The determinant of the coefficient matrix is

which is negative as long as κ_t > κ_n,¹⁰ and the system thus has a saddle point equilibrium. The two eigenvalues of this dynamic system are μ₁ = q₂₂ < 0, μ₂ =q₁₁ > 0 and the solution consistent with the initial conditions and the transversality condition is: