I. Model

To study the insurance potential of foreign aid in a recipient country, we build a model of aid flows between two endowment economies—a rich donor and a poor recipient. Each country’s endowment growth path is taken as exogenous. We abstract from modeling any impact that aid might have on GDP or on GDP growth.

Of course, development assistance is the largest component of foreign aid, and the welfare effects of even small improvements in growth prospects are generally very large. One might therefore worry that, by abstracting from the development objective of aid, we may underestimate the cost of reallocating funds from growth promotion and overestimate the net benefits from a reduction in consumption volatility. Such should not be the case, however, for the following reasons.

First, our approach reflects the fact that, after decades of empirical research, there is little consensus on whether foreign aid directly affects economic growth in practice (Easterly, 2003).⁷ Accordingly, we focus on another direct effect of aid flows on welfare, through consumption smoothing. That is, we ask whether foreign aid could have a first-order welfare impact on recipients in spite of the fact that the growth channel is weak. Still, we do not assume that poor countries will forever experience low levels of consumption; in view of the empirical evidence, we simply assume away the possibility that aid helps increase their growth rate.

Second, several recent papers (Epaulard and Pommeret, 2003; Krebs, 2003; and Barlevy, 2004) have shown that accounting for the deleterious effects of volatility on growth (Ramey and Ramey, 1995; and Mobarak, 2005) substantially raises estimates of the welfare cost of business cycles. If anything, by abstracting away from this indirect link between aid and growth, we may thus underestimate the net welfare effect of using aid to reduce the impact of macroeconomic volatility.

Ours, then, is a simple infinite horizon model of a donor country and a recipient country (respectively, i = D, R) with time-varying endowments of a single, non-storable consumption good. Each country’s harvest of the good at time t, y_i,t, is a random variable that follows a known stochastic process Φ_i. The donor country is strictly richer than the recipient country. We assume that Φ_R and Φ_D are independent processes, which reflects empirical evidence that there has been very little co-movement between consumption levels in rich and developing countries in any of the past four decades (Köse, Otrok, and Whiteman, 2003; and Köse, Prasad, and Terrones, 2003).

The representative agents in both countries are infinitely lived. Throughout the paper, we assume that they have constant relative risk averse (CRRA), time-separable preferences over their own consumptions, c_r and c_d. This assumption makes analytical solutions to the donor’s problem possible. Furthermore, because one would expect macroeconomic fluctuations to bring about massive welfare costs under the alternative assumption of time-nonseparable preferences (Otrok, 2001), this assumption guarantees that the large welfare gain estimates we obtain in Section IV are not merely due to our choice of utility functions. There is no evidence suggesting that residents of developing, emerging, and developed economies exhibit different intensities of relative risk aversion (Ostry and Reinhart, 1992), so we posit that the donor and recipient agents have the same constant level of risk aversion γ; that is,

The recipient country’s representative agent derives utility solely from his own total consumption C_R over time:

where ß_R ∈ [0,1] is that agent’s discount factor. In contrast, the donor country’s representative agent is altruistic in that he cares about both his own consumption C_D and that of the recipient country’s resident, C_R. We posit that this altruism takes the form:

where ß_D ∈ [0,1] is the donor agent’s discount factor and A ∈ (0,1) is the weight assigned by the donor agent to his own utility.⁸,⁹

The donor country can allocate part of its time t endowment y_D,t to foreign aid a_t. We approximate the fact that much of the aid to poor countries comes as outright grants by positing that aid is given with no expectation of repayment.¹⁰ We assume, as is typically the case in practice (Prati, Sahay, and Tressel, 2003; and Eifert and Gelb, 2006), that the recipient country cannot save any part of these aid flows. With no possibility of storage, the periodic consumption levels in each country are, respectively, c_D,t = y_D,t - a_t and c_R,t = y_R,t + a_t.

The donor’s generosity is financially constrained in two ways. First, for each period, 0 ≤ a_t ≤ y_D,t. Second, we shall calibrate the altruism parameter A in Section IV so that the lifetime average a_t/y_R,t ratio is in line with its empirically documented counterpart. This second restriction leads to the following remarks. One, by calibrating A to past data, we are in effect positing that the donor’s preferences are time-invariant. Two, our analysis may not apply in the long run to recipient countries that are growing at a much faster clip than the donor is. Accordingly, we shall assume that y_R,t grows at the same rate as does y_D,t. This simplification is without much loss of generality, in that our qualitative results are even stronger if we assume instead that the recipient’s growth rate is lower than the donor’s (which has been empirically true for most of the world’s poorest countries).

II. Optimal Aid Policy

The donor’s problem is recursive and can be written as follows:

Aid does not affect future realizations of y_D,t and y_R,t, so the optimal aid rule is straightforward:

Proposition 1: It is optimal for the donor to transfer to the recipient, each period, an amount as follows:

Proof: The first-order condition for an interior optimum to the donor’s problem (equation (3)) is

With logarithmic utility (γ= 1), equation (5) simplifies to \frac{\left(y_{D,t}-a_t\right)}{\left(y_{R,t}+a_t\right)}=\frac{A}{1-A}, which implies the following optimal rule for foreign aid disbursements: a_t^{*}=(1-A)y_{D,t}-A{y}_{R,t}. This is a special case of equation (4) with γ = 1. If y ≠ 1, then the first-order equation (5) becomes \left(\frac{y_{D,t}-a_t}{y_{R,t}+a_t}\right)=\frac{A}{1-A}, which, given the nonnegativity condition on a_t, again yields the predicted optimal aid rule (equation (4)). ■

In the remainder of the paper, we focus on aid-dependent countries, that is, countries for which aid flows are always positive (a_t^{*}>0\forall t). From equation (4), it is evident that aid is positive as long as a simple condition is met: the donor’s endowment must be sufficiently bigger than the recipient’s. Accordingly,

Definition 1 (Aid Dependency): We say that the recipient country is aid-dependent if

Corollary 1: For aid-dependent countries, the optimal aid policy is countercyclical from the recipient’s viewpoint.

Proof: By definition, an aid-dependent country has a_t^{*}>0\forall t. Because Φ_R and Φ_D are independent processes by assumption, it follows that \frac{\partial a_t^{*}}{\partial y_{R,t}}=-\frac{A^{\frac{1}{\text{γ}}}}{{(1-A)}^{\frac{1}{\text{γ}}}+A^{\frac{1}{\text{γ}}}}<0.■

Of particular relevance to our study is the extent to which the aid a*\equiv \left\{a_t^{*}\right\}t=1,2,\dots can reduce consumption volatility in the recipient country. Intuitively, the donor should provide insurance to the recipient to an extent that reflects the donor’s income (relative to the recipient’s), altruism, and risk aversion. Proposition 1 and Corollary 1 together confirm this intuition. Our next proposition goes further. It shows that, if the recipient is aid-dependent, then the optimal aid policy does not merely reduce the volatility of the recipient’s consumption stream, it goes as far as equalizing the variability of per capita consumption in the donor and recipient countries.

Precisely, Proposition 2 focuses on a logical volatility benchmark that is familiar from the literature on business cycles (kydland and Prescott, 1982, for example): the standard deviation of per capita consumption expressed as a percentage of its mean. Let μ[X_t|Ω_t-1] and σ[X_t|Ω_t-1] denote, respectively, the mean and standard deviation of any random variable X_t conditional on the donor’s and recipient’s common information set at time t-1, Ω_t_₁. Then,

Proposition 2: In aid-dependent countries, the optimal aid policy drives the conditional volatility of per capita consumption down to that in the donor country.

Proof: Again, by definition of an aid-dependent country, a_t^{*}>0\forall t. Given an optimal policy of strictly positive aid flows a_t^{*}

View Expanded

View Expanded

View Expanded

View Expanded

III. Discussion

Although intuitive, Proposition 2 sends a powerful message to policymakers. We know that the massive volatility of private consumption in developing countries has a deleterious effect on their residents’ welfare (Pallage and Robe, 2003). Proposition 2 states that, without changing the actual amounts of foreign aid given on average, a simple reallocation of these aid flows across time has the potential to bring this volatility down to the much smoother ride enjoyed by rich countries. Given that the percentage volatility of consumption in poor countries is three to six times that in their developed counterparts, there is scope for cutting the former by at least two-thirds. This rough estimate already suggests that one cannot overlook the insurance power of current foreign aid budgets. We provide more precise estimates in Section IV.

Because the volatility reduction is so massive, it is worth discussing the conditions under which Proposition 2 holds. The analysis in Section II assumes that the donor and recipient countries are of equal size and grow at the same rate. It is easy to show, however, that our results carry through as long as the recipient country is poor, its population is not huge, and its economy is growing at most at the same rate as the donor country’s. Much of Africa, plus most of the poor countries in other regions of the Southern Hemisphere, meet these three conditions. What is more, even if the recipient economy eventually started catching up with the donor’s, our proposed aid policy would remain optimal for any time interval in which that recipient remains aid-dependent.

Our results show that donors could use foreign aid to drastically reduce consumption volatility in developing countries. What if this volatility were caused by poor policy choices in the recipient country? Our results do not imply that residents in donor countries should subsidize policy mistakes by recipient governments. Whether aid should be conditioned on good recipient policies is beyond the scope of this paper, and our model is not appropriate to discuss this issue. However, in the poor countries for which our analysis is most relevant, our abstracting from aid conditionality is without much loss of generality in that most of the observed macroeconomic fluctuations are due to exogenous shocks, such as terms-of-trade or world-price changes.¹¹

It should be noted that adopting the aid policy a* has a negligible impact on the volatility of consumption in the donor country. If we focus on aid to African countries, to which our analysis plainly applies, the median ratio of foreign aid to donor GDP was less than 0.1 percent in the previous three decades (Pallage and Robe, 2001). Clearly, any change in the sequencing of aid disbursements while maintaining that ratio in the long run will have only a minimal impact on the volatility of consumption in the donor countries. We know from the literature on the welfare cost of business cycles that, in industrialized countries, larger changes in aggregate consumption volatility have only trivial consequences on local residents' welfare, regardless of the model economy used to assess these welfare effects (Lucas, 1987; and Dolmas, 1998). Thus, even if donors had purely selfish preferences (A = 0), adopting policy a* or sticking to their current aid policy would make no difference quantitatively.¹²

Finally, we assume that aid cannot be stored by the recipient. Arguably, if aid could be saved, then the welfare benefits from the donor’s changing the timing of aid flows would fall. We think that our abstracting from the possibility of storage is sensible. First, there are a good number of practical reasons why recipient governments may choose not to save any part of the aid. For example, recipients who do not spend all the aid they receive in any given period can expect to see future aid flows reduced, because they have just demonstrated a lack of absorption capacity (Prati, Sahay, and Tressel, 2003; and Eifert and Gelb, 2006). Second, and more important, if aid can indeed be saved in practice, then observed patterns of consumption (inclusive of aid) already account for storage. That is, whatever aid storage takes place in reality is already reflected in the observed volatility of consumption. Yet, as will become clear in Section IV, a policy such as the one identified in our paper (which assumes away the possibility of savings) yields substantial welfare gains over observed aid policies. We take this as further evidence that substantial amounts of aid are not being saved in practice.

IV. Computing the Welfare Implications of Aid Patterns

The optimal aid rule a* of Propositions 1 and 2 is obtained under the assumption that donors act as a single agency and can perfectly coordinate their efforts toward the sole objective of providing insurance to the recipient country. In contrast, aid is given out in practice by many imperfectly coordinated donor agencies with a variety of motives for providing aid. In most developing countries, the resulting mix of foreign aid strategies is associated with procyclical net foreign aid inflows. In this section, we measure the welfare gain that would accrue to a typical recipient country’s representative resident if the actual aid process, denoted ã, were replaced by the aid rule a*.

Clearly, the volatility of consumption in developing countries might have been much larger if foreign aid had not been received in the first place. We are not questioning the benefits of aid per se, but rather consider the insurance potential of current aid budgets. In other words, the question we ask is how much one can improve on current aid practices. Proposition 2 suggests that, under the aid policy derived in Proposition 1, the volatility of consumption in the recipient country would equal that in the donor country. The welfare gain we wish to capture is thus the percentage increase in consumption necessary for the representative agent in the recipient country to be indifferent between (1) a consumption stream inclusive of current aid, with volatility calibrated to the recipient’s observed consumption stream; and (2) another stream, with the volatility of donor consumption.

We follow the usual compensating variation approach and measure this welfare gain as the percentage consumption increase, in all states of the world and for all dates, that would make the recipient country’s representative agent indifferent between the two reference environments. In the context of our model, this computation amounts to computing the welfare effects of providing the agent with two alternative consumption series that have a similar mean but different volatilities: c_{R,t}^{*}=y_{R,t}+a_t^{*}(y_{D,t},y_{R,t}) at the optimum, versus C̃_R,t = y_R,t + ã_t in practice.

In order to carry out these computations, we must make some assumptions about the stochastic processes that govern each country’s consumption stream per capita, C̃_i,t (i = D, R). We consider in turn two processes that are familiar from the literature on the welfare costs of business cycles. Because we are interested in percentage deviations from trend, we work throughout with the logarithms of the relevant series.

In the first process, the natural logarithm of real per capita consumption fluctuates randomly, and shocks to consumption levels are temporary:

We parameterize {\sigma }_{z_i}^2 in equation (7) to the standard deviation of the cyclical component of the Hodrick-Prescott (HP)-filtered logarithms of real per capita private consumption. This approach is the same as that taken by Lucas (1987) and many others and provides a floor for the welfare cost of macroeconomic fluctuations in an economy (Dolmas, 1998). This first process, thus parameterized, likewise provides a lower-bound estimate of the welfare gains from using foreign aid as insurance.

Let λ_RtoD denote the welfare gain to the recipient agent of a change in the timing of aid flows that reduces the percentage volatility of his periodic consumption, σ_Zr, down to the donor’s consumption volatility, σ_ZD. Likewise, let λ denote the welfare gain to the same recipient of eliminating all macroeconomic fluctuation, that is, of getting σ_ZR down to zero. Given that our economies are characterized by isoelastic preferences and consumption equation (7), and given our parameterization of σz_D and σ_Zr, both λ_RtoD and λ have closed-form solutions (Lucas, 1987):

To the extent that the exogenous shocks that affect developing economies are persistent (Cashin, McDermott, and Pattillo, 2004) and that their impact on domestic consumption is not easily smoothed out (Köse, Prasad, and Terrones, 2003), equation (8) will significantly underestimate the welfare gain that could be achieved by using foreign aid to reduce consumption volatility in poor countries. A simple way to account for shock persistence is to consider an alternative consumption process, in which both the level and the growth rate of per capita consumption are stochastic:

where g_i is the mean growth rate of the series in country i. This second process assumes that shocks to consumption levels are persistent but shocks to the growth rate of consumption are not.

In a recipient economy characterized by CRRA utility and consumption equation (9), the aid policy a* effectively reduces the conditional standard deviation of shocks to per capita consumption from σ_∈R to ∈_∈d. Let η_RtoD and η denote the welfare gains to the recipient of reducing σ_∈R to σ_∈D or to zero, respectively. Both η_RtoD and η have closed-form expressions (Obstfeld, 1994):

Quantitative Results

Table 2 summarizes our quantitative findings for the central parameter values discussed in the calibration section: β = 0.96; γ= 1.5, 2.5, or 5; σ_ZR = σ_∈R = 5 percent; σ_∈D = 1.36 percent and σ_ZD = 1.35 percent. Table 2 has two panels, to differentiate between situations in which aggregate economic shocks are transitory (left panel) and cases in which these shocks are persistent (right panel).

^{Table 2.}

Consumption Volatility, Aid Timing, and Welfare

Source: Authors’ computations.

Notes: The first row shows the welfare costs of aggregate consumption volatility in a typical recipient country, expressed in terms of permanent consumption. The second row shows the welfare gain from replacing the actual foreign aid stream, ã_t, with the optimal aid process, a_t^{*} of Propositions 1 and 2 (that is, by foreign aid flows with the same mean but different cyclical properties). That gain is also measured in terms of permanent consumption in the recipient country. The third row gives the ratio of the previous two; that is, it shows the fraction of the welfare costs of aggregate consumption volatility that could be eliminated by replacing the actual foreign aid stream, ã_t with the optimal aid process, a_t^{*}. The data in all rows are provided for three levels of risk aversion in the recipient country (γ =1.5, 2.5, 5), under the assumption that the percentage annual volatility of consumption (σ_zi. If shocks are assumed temporary, or σ_∈i. If they are assumed persistent) is 5 percent in the recipient country (i=R) and 1.35 percent (σ_zD) or 1.36 percent (σ_∈D) in the donor country (i=D).

^{Table 2.}

Consumption Volatility, Aid Timing, and Welfare

		Temporary Shocks			Persistent Shocks
		γ=1.5	=2.5	γ=5	γ=1.5	γ=2.5	γ=5
Consumption volatility costs
	(percent of permanent consumption)	0.19	0.31	0.63	4.12	5.86	9.36
Gain from timing aid optimally
	(percent of permanent consumption)	0.17	0.29	0.58	3.82	5.44	8.76
Fraction of volatility costs eliminated
	by optimal aid timing (percent)	92.6	92.6	92.6	92.6	92.8	93.6

Source: Authors’ computations.

Notes: The first row shows the welfare costs of aggregate consumption volatility in a typical recipient country, expressed in terms of permanent consumption. The second row shows the welfare gain from replacing the actual foreign aid stream, ã_t, with the optimal aid process, a_t^{*} of Propositions 1 and 2 (that is, by foreign aid flows with the same mean but different cyclical properties). That gain is also measured in terms of permanent consumption in the recipient country. The third row gives the ratio of the previous two; that is, it shows the fraction of the welfare costs of aggregate consumption volatility that could be eliminated by replacing the actual foreign aid stream, ã_t with the optimal aid process, a_t^{*}. The data in all rows are provided for three levels of risk aversion in the recipient country (γ =1.5, 2.5, 5), under the assumption that the percentage annual volatility of consumption (σ_zi. If shocks are assumed temporary, or σ_∈i. If they are assumed persistent) is 5 percent in the recipient country (i=R) and 1.35 percent (σ_zD) or 1.36 percent (σ_∈D) in the donor country (i=D).

View Table

^{Table 2.}

Consumption Volatility, Aid Timing, and Welfare

		Temporary Shocks			Persistent Shocks
		γ=1.5	=2.5	γ=5	γ=1.5	γ=2.5	γ=5
Consumption volatility costs
	(percent of permanent consumption)	0.19	0.31	0.63	4.12	5.86	9.36
Gain from timing aid optimally
	(percent of permanent consumption)	0.17	0.29	0.58	3.82	5.44	8.76
Fraction of volatility costs eliminated
	by optimal aid timing (percent)	92.6	92.6	92.6	92.6	92.8	93.6

Source: Authors’ computations.

Notes: The first row shows the welfare costs of aggregate consumption volatility in a typical recipient country, expressed in terms of permanent consumption. The second row shows the welfare gain from replacing the actual foreign aid stream, ã_t, with the optimal aid process, a_t^{*} of Propositions 1 and 2 (that is, by foreign aid flows with the same mean but different cyclical properties). That gain is also measured in terms of permanent consumption in the recipient country. The third row gives the ratio of the previous two; that is, it shows the fraction of the welfare costs of aggregate consumption volatility that could be eliminated by replacing the actual foreign aid stream, ã_t with the optimal aid process, a_t^{*}. The data in all rows are provided for three levels of risk aversion in the recipient country (γ =1.5, 2.5, 5), under the assumption that the percentage annual volatility of consumption (σ_zi. If shocks are assumed temporary, or σ_∈i. If they are assumed persistent) is 5 percent in the recipient country (i=R) and 1.35 percent (σ_zD) or 1.36 percent (σ_∈D) in the donor country (i=D).

As other papers have shown (Obstfeld, 1994; Pemberton, 1996; Dolmas, 1998; Otrok, 2001; and Pallage and Robe, 2003), the welfare gains from reducing consumption volatility vary greatly depending on whether consumption shocks are temporary, as in equation (7), or persistent, as in equation (9). It is therefore useful to provide a benchmark for the maximum possible welfare gains from changing the pattern of aid flows in a typical recipient country by first quantifying, for each consumption process, the welfare gain that would accrue to the recipient country’s representative agent if all consumption volatility were eliminated.

The first row in Table 2 shows that, when the coefficient of risk aversion is γ= 2.5 [γ= 5], the cost of macroeconomic volatility is λ = 0.31 percent [λ = 0.63 percent] of permanent consumption in the first model economy (in which shocks to consumption levels are transitory) but that same cost skyrockets to η = 5.86 percent [η = 9.36 percent] of permanent consumption in the second model economy (in which shocks are persistent). Even when γ = 1.5, a low value for the risk-aversion coefficient, the cost η is still more than 4 percent of permanent consumption.

The second row in Table 2 gives the welfare gain from optimizing the timing of foreign aid flows (λ_RtoD and λ_RtoD), again expressed in terms of the recipient’s permanent consumption. The third row, which gives the ratio of the first two rows, shows that, in both model economies, more than nine-tenths (92 percent) of the costs of macroeconomic volatility could be eliminated by reallocating aid flows through time in a manner consistent with Propositions 1 and 2.

Taken together, the data in Table 2 establish that the cyclical properties of foreign aid flows are of first-order importance. Policymakers should be pleased to know that foreign aid has the potential to make a huge difference in at least one key aspect of life in developing countries—coping with the impact of strong aggregate shocks. Indeed, given empirical evidence that a less volatile economy has better growth prospects (Ramey and Ramey, 1995; and Mobarak, 2005), the welfare benefits of optimizing the timing of aid disbursement could be substantially bigger still.

Robustness Checks

The results from Table 2 are robust to a wide range of alternative values for the key parameters, σ_ZR, σ_∈R, and γ. Figures 2, 3, and 4 provide a concise illustration of this robustness.

View Full Size

Welfare Costs of Macroeconomic Volatility

(Fraction of recipient permanent consumption)

Citation: IMF Staff Papers 2006, 003; 10.5089/9781589065819.024.A005

Source: Authors' computations.Notes: The figure plots the welfare costs of macroeconomic volatility (λ in Figure 2(a) and η in Figure 2(b)) in the recipient country as a percentage of permanent consumption, for typical levels of risk aversion (γ) and consumption volatility (σ_ZR in Figure 2(a) and σεR in Figure 2(b)). A value of 0.01 (1%) on the vertical axis means that the country’s representative resident would be indifferent between seeing all consumption volatility removed and getting an extra 1 percent of consumption in all states and at all dates. Figure 2(a) plots the value taken by λ in equation (8), when consumption shocks are not persistent. Figure 2(b) plots the value taken by η in equation (10), when consumption shocks are persistent, for a mean growth rate of per capita real consumption gR = 1 %.

• Download Figure
• Download figure as PowerPoint slide

View Full Size

Fraction of Macroeconomic Volatility Costs Eliminated by Timing Aid Flows Optimally

Citation: IMF Staff Papers 2006, 003; 10.5089/9781589065819.024.A005

Source: Authors' computations.Notes: The figure plots, for typical levels of risk aversion and consumption volatility in recipient countries, the fraction of the welfare costs of macroeconomic volatility that could be eliminated by replacing the actual foreign aid stream ã_t with the optimal aid process a_t* of Propositions 1 and 2 (that is, by foreign aid flows with the same mean but different cyclical properties). A “drop” value of 0.8 on the vertical axis means that 80 percent of the cost λ (in Figure 3(a), when consumption follows equation (7)) or η (in Figure 3(b), when consumption follows equation (9)) could be eliminated by reallocating aid flows optimally through time. Figures 3(a) and 3(b) are drawn under the assumption that the percentage volatility of consumption in the donor country (respectively σ_ZD or σ_εD) is 1.36 percent. Figure 3(b) assumes a mean growth rate of per capita real consumption in the recipient country of g_R = 1 %.

• Download Figure
• Download figure as PowerPoint slide

View Full Size

What Is Improving the Timing of Aid Worth, Compared with Getting Aid in the First Place?

Citation: IMF Staff Papers 2006, 003; 10.5089/9781589065819.024.A005

Source: Authors' computations.Notes: The figure displays, for typical levels of risk aversion and consumption volatility in recipient countries, the welfare gain that would accrue to residents of a recipient country if the actual foreign aid stream ã_t were replaced by the optimal aid process a_t* of Propositions 1 and 2 (that is, by foreign aid flows with the same mean but different cyclical properties). A value of 1 on the vertical axis means that changing the timing of aid is worth as much as increasing the recipient’s per capita consumption by 5 percent at all dates and in all possible states of the world. Figure 4(a) plots the value taken by the ratio λ_RtoD/5% in equation (8), when consumption shocks are not persistent. Figure 4(b) plots the value taken by the ratio η_RtoD/5% in equation (10), when consumption shocks are permanent. Figures 4(a) and 4(b) are drawn under the assumption that the percentage volatility of consumption in the donor country (respectively σ_ZDor σ_εD) is 1.36 percent. Figure 4(b) assumes a mean growth rate of per capita real consumption in the recipient country of g_R = 1 %.

• Download Figure
• Download figure as PowerPoint slide

Figure 2.a plots λ and Figure 2.b plots η, for various values of the recipient agent’s risk aversion and of the volatility of his consumption (respectively, σ_ZR and σ_∈R). As anticipated, the cost estimates in Figure 2 are often substantial. They are especially large when macroeconomic shocks are persistent—reaching, for example, a massive η = 15 percent of permanent consumption when consumption volatility is σ_∈R = 6 percent and the level of risk aversion is γ= 5.

Across the entire range of parameter values considered, Figure 3 shows that typically well over four-fifths, and always more than three-fourths, of the large welfare costs of aggregate consumption volatility could be eliminated by replacing the actual foreign aid stream ã_t with the aid process a_t^{*} (that is, by a foreign aid stream of the same average magnitude but different intertemporal properties).

Figure 4 provides another benchmark for the potential costs of ignoring the insurance implications of foreign aid. It expresses the welfare gains from replacing the actual foreign aid stream ã with the aid process a* of Propositions 1 and 2 (that is, λ_RtoD in Figure 4.a or η_RtoD in Figure 4.b) as a fraction of the gain from providing ã in the first place. We conservatively assumed in the calibration section that ã is worth 5 percent of permanent real per capita consumption in the recipient country. Thus, a value of 1 on the vertical axes of Figures 4.a or 4.b means that changing the timing of aid is worth as much to the recipient as increasing its per capita consumption by 5 percent at all dates and in all possible states of the world. Figure 4.b shows that, when consumption shocks are persistent, improving the timing of foreign aid flows is often worth more to the recipient than receiving aid in the first place.

V. Conclusions

“Rich countries must [&] pay more attention to the sudden economic shocks to which poor countries are vulnerable. Sudden plunges in the price of coffee or cotton pluck fewer heartstrings than floods or earthquakes, but can be much more destabilising and [make civil war] more likely. Aid should take such shocks into account.”¹⁵

When designing its foreign aid policy, a donor must tackle two broad questions. The first, from which we abstract, is the optimal allocation of aid budgets across potential recipients. The second, on which we focus, is the optimal path of disbursement of a given aid budget to a given recipient country. Although the first issue is probably very important, we demonstrate that the second issue cannot be dismissed.

We show that, even ignoring the possibility that economic shocks may bring about political mayhem or worse, merely changing the timing of aid flows could provide recipient countries with substantial insurance against macroeconomic fluctuations. At least three-fourths of the large welfare costs of aggregate consumption volatility in developing countries could potentially be eliminated by using current aid budgets to smooth aggregate consumption in these countries.

In the context of the ongoing, vigorous debate about the apparent ineffectiveness of foreign aid in boosting growth and alleviating poverty, our results do not imply that donors should stop examining why some aid programs have worked and why many others have not. Neither do we suggest that donors should give up on growth and poverty altogether and instead focus on insurance. Rather, our results have three implications for policy and further research.

First, the insurance potential of current aid budgets is of first-order magnitude. Second, foreign aid is given out in practice by many donors, for many reasons. Chief among the latter are growth promotion and poverty reduction, plus political alliances and disaster relief. In most developing countries, the resulting mix of aid strategies is associated with procyclical net aid inflows. If the strategies that bring about aid procyclicality could be replaced by others that do not (for example, through better donor coordination), then the resulting welfare gains might be as large as the gains from receiving aid in the first place. Third, if the observed aid patterns are the outcome of aid contracts designed to alleviate conflicts between donors and recipients under asymmetric information, then our results give an estimate of the deadweight losses brought about by these agency conflicts.

In sum, our point is simple. We know that the welfare costs of consumption volatility are very large in developing countries. Most of that volatility is the direct consequence of exogenous macroeconomic shocks. Lucas (2003) rightly argues that, regardless of the size of its costs, one should care about consumption volatility only to the extent that it can be reduced by feasible policies. In this paper, we focus on a policy that is both feasible and widely used: foreign aid. We show that altering the timing of aid flows has the potential to eliminate between 75 percent and 95 percent of the welfare cost of the massive macroeconomic fluctuations that affect developing countries. The impact on consumption volatility in donor countries would be negligible. In light of these results, we submit that the role of foreign aid as an insurance device deserves to receive much consideration.

REFERENCES