B.1 The Model

In each period, the donor country planner solves a static utility maximization problem to determine how much ODA to transfer to each of the NR potential recipient countries. ODA disbursements need not be equal across the NR recipients. The donor derives utility from own-consumption and from ODA disbursements in a manner to be described precisely below. The baseline donor’s consumption is defined as income net of investment and it is assumed to be taken as given by the planner when the ODA decision is made. Government expenditures and net exports are assumed to be fully absorbed by consumers. Each dollar disbursed has an equal direct opportunity cost in donor own-consumption. To keep the analysis tractable we abstract from strategic interaction among donors. We first solve the problem of disbursement to a single representative recipient and then generalize this solution to the full disbursement problem.

Let ND be the total number of donors and d a representative donor. Denote the vector of ODA disbursements by donor d as A=[A1,A2,...ANR]. In what follows, variables are time series but the time indices are omitted for ease of notation; we will explicitly reintroduce time indices only when necessary.

The donor resource constraint links total absorption, Cd, to the ODA donations through the standard accounting relation

where Yd−Id is the donor’s income net of private investment. For later reference, we define Cd,0=Yd−Id as donor income when no ODA donations are made. Consistent with our discussion above, we will refer to this total absorption term as simply “consumption.” Finally, ODA disbursements must be non-negative Ar⩾0 for all r=1,2,..NR and cannot exceed Cd,0. This generates the second constraint of the optimization problem

In the baseline model we adopt a log-additive utility function

in which total utility W⋅ includes the standard own-consumption component, UCd, and a second component, G⋅, that represents the donor’s total gain from the full vector of ODA disbursements. We disaggregate the self-interest and altruism components of G⋅ below. This type of specification is not new to the ODA literature. Dudley and Montmarquette (1976) use a utility function component equivalent to G⋅ representing direct and subjective altruistic returns of ODA in a seminal early work. More recent work with similar modeling includes Younas (2008) , Chong and Gradstein (2008) , and Gravier-Rymaszewska (2012) .

We assume that the total gain function G⋅ can be expressed as the product of individual gain functions associated with the disbursements to each of the NR recipients

The gain from each individual transfer, Gr⋅, is decomposed in two distinct components

The first component, RrAr, is a direct egoistic return from an ODA transfer to recipient r (e. g., the supportive UN vote). The second term, DrAr, reflects purely altruistic preferences of the donor toward recipient r and it can be thought of as a mapping from the recipients own-consumption utility function that preserves the marginal utility properties of the recipient’s utility.^[29] It is reasonable to assume that there is no gain from either component if no ODA donation is made to a recipient. Therefore Gr0=Rr0=Dr0=1. This specification allows a donor to be motivated by pure self-interest, pure altruism, or any combination of the two. A similar type of utility decomposition has been largely used in the charitable donations literature and charitable auction theory (see, for instance, Andreoni 1989 and Andreoni 1990 ).^[30]

As implied above, we assume Rr′, Dr′≥0, and Rr′′,Dr′′≤0 for all r. In fact, it is only necessary to make this assumption in a small positive neighborhood of Ar=0, not for its entire dominion 0,Cd,0. Since all observed bilateral ODA transfers are very small relative to Cd,0 (typically smaller than .01% of GDP), it is not necessary to fully characterize the gain function to obtain our theoretical predictions. Hence, we impose only a minimal set of assumptions on GrAr for Ar close enough to 0 to ensure a solution near Ar=0. That is, we approximate the solution around Cd,Ar=Cd,0,0.

Empirically, we will also allow the gain functions components to be affected by pair-specific shift factors, Xρr and Xδr. Hence, RrAr;Xρr and DrAr;Xδr are more complete expressions of the gain components suitable for estimation. Examples of shifters for Rr (the egoistic “return” component) in the literature are the tightness of the trade relationship between donor and recipient, geopolitical factors, and colonial relationships. Potentially important shifters for Dr (the “altruism” component) are the recipient’s level of consumption without ODA, cultural and religious factors, the recipient’s population size, political efficiency, and corruption. In our estimation, we explicitly incorporate the recipient’s initial level of consumption in the altruistic component by making Dr⋅ proportional to the change in the recipient’s utility due to the ODA donation, while the other shifters are introduced as control variables at the estimation stage.

The donor’s maximization problem is completed with the budget constraint of the recipient as seen from the donor’s perspective:

Equation (A4) makes explicit the relationship between DrAr;Xδr and recipient consumption, Cr, for given Cr,0, since Ar=Cr−Cr,0. An implicit assumption here is that altruistic donors care about recipient country consumers, but do not explicitly consider firms in their altruistic decisions. The recipient constraint also implies that ODA is consumed instantaneously by the recipient government and/or consumers – that is, we maintain the full absorption assumption for recipient government expenditures as we did for donors.

Consistent with clear empirical reality, we assume that constraint (A2) is never binding for any donor. Therefore, the local interior first-order necessary conditions of the donors problem are satisfied where the marginal utility of donor “own-consumption” is equal to the marginal gain (from the total gain function) for each of the recipients. Indirect effects of transfers across recipients that would be conveyed by the shadow price of constraint (A2), were it binding, are absent. Hence, we can obtain the local qualitative theoretical signal of altruism utilizing the ODA decision to a single representative recipient, r, taking the donor’s ODA to the other NR−1 potential recipients as already optimally determined. Note that the predetermined ODA to any (or all) of the other NR−1 recipients may also be zero. Finally, we modify the utility function with two simplifications that do not affect the results. First, we explicitly account for a reference level by normalizing the arguments of the utility function by the donor’s trend income Yˉ. Second, we take a log-transformation of the total utility W⋅ which is now additive in the logs of the three components. This transformation imposes a restriction on the sign of the three components of total utility, which must be strictly positive.^[31] We can now re-write the utility function (A3) after substituting for constraint (A1) as

where, in order to simplify notation, let z=Z/Yˉ be variable Z normalized by donor trend GDP and let w⋅, u⋅, ρr⋅, and δr⋅ respectively indicate the log of W⋅, U⋅, Rr⋅, and Dr⋅.

The first-order condition with respect to the generic donation ar to recipient r is

which is eq. [2] in the main text.

B.2 Alternative Utility Functional Forms

This section describes more in detail the CARA version of the model used for the robustness exercise in Section D.1 and the results for the CRRA version. The basic assumptions and results of the paper hold for these two versions too with the only exception that we start directly from the additive functional form in (A5) instead of the log-additive function in (A3). In particular, the countercyclical-altruism condition [9] is not affected by the choice of the functional form. In eq. (A5), it is reasonable to assume in this case that ρr0=δr0=0 and ρr′, δr′≥0 and ρr′′, δr′′≤0 for any r in a positive neighborhood of ar=0.

In the CARA version of the econometric model, we assume negative exponential functional forms for the own-consumption utilities

where σd and σr are donors’ and recipients’ risk aversion parameters. This choice corresponds to constant absolute risk aversion in the preferences for own-consumption. This type of functional form is fairly common in literature because preferences are easily characterized by the curvature parameter only. We adopt the same type of negative exponential function for ρr⋅ as we used for ur⋅

where ρr,0 and σρ are the parameters representing a scale factor and the riskiness of the direct return to ODA respectively. Finally, the altruism function is

where δr,0 expresses the degree of altruism of the donor toward recipient r. Under these functional forms, the second and third regression equations of the model for a given calibration of the risk aversion, σd and σr, and return, σρ, parameters are (omitting the controls)

and

The CRRA version of the econometric model can be derived starting from constant relative risk aversion own-consumption utility functions

and following similar steps. As mentioned below, the CRRA specification is more troublesome than the CARA in the sense that the estimation of the model is more sensitive to the small variability of the ODA flows, especially when multiple controls are included in the regression equations. In particular, the number of pairs that empirically satisfy the countercyclical-altruism test drops to 3−4% when controls are added, making a comparison with the other two specifications improper. Without controls, the results from this specification are perfectly consistent with those from the baseline and the CARA model. However, as two control variables are added, the number of cases for which the last two equations of the model are indistinguishable increases to about 60% of the total pairs leaving very little to the analysis. The CRRA specification is unsuitable for the estimation exercise we conduct because it is incompatible with the small variability of the ODA series; this case definitely calls for some caution in the choice of the functional forms.

C.1 Dataset

Letting A be total ODA donations, the donor’s resource constraint (A1) can be written as Yd=Cd+Id+A. In national accounting, ODA disbursements are included in donors’ GDP as exports that generate a trade flow without the corresponding income flow. The actual income available to a donor for consumption and investment must be adjusted for those items. We measure income as GDP and take investment from national accounting. Our framework implies a definition of consumption corresponding to absorption by the private and public sectors, and also assumes government expenditure and net exports are, ultimately, fully absorbed by consumers. Symmetrically for recipient countries, ODA transfers increase the resources available for consumption. Hence, we construct total recipient consumption by adding the ODA disbursements from donors to the recipient’s GDP, net of investment.

National account data is drawn from the Penn World Tables dataset PWT 7.1 while ODA data is from the OECD DAC Aid Statistics dataset; PPP per-capita GDP is drawn from rgdpl in PWT. We use net ODA disbursements for 19 OECD donors and 137 recipients for the period 1970 to 2010.^[32] Appendix A lists the 156 countries in our sample. All analysis utilizes 2005 International Dollars per person – the reporting basis in the Penn World Tables and the data taken from OECD was mapped to PWT data. Therefore, all the variables used in our analysis are expressed in equivalent PPP per-capita terms. Since the ODA flows from donor d to recipient r reported by the OECD are in current USD, these are adjusted by multiplying the flows by the ratio between PWT GDP and the current USD GDP from the OECD. Figure A1 below illustrates total net ODA disbursements for the 19 donors in our sample as a share of donor GDP. The majority fall between .1−.5% and, interestingly, the stated OECD-DAC target of .7% of GDP is rarely achieved. Finally, we use four variables as controls in the empirical assessment of the model. These controls are transformations of population, price index, degree of openness (from PWT 7.1) and of life expectancy from the World Bank online dataset World Development Indicators (WDI).^[33] The population growth rate seems appropriate for our analysis since we focus on business cycle variations over a long time series. Inflation is used to control for the quality of monetary policy; other papers use money supply but the two variables normally overlap. The degree of openness is the ratio to GDP of the sum of imports and exports. The change in life expectancy at birth captures generic development. The trend GDP, Yˉd, necessary to compute the ratio variables is constructed by applying the HP filter to the GDP series with the smoothing parameter set to 100.

Figure A1:

Total ODA disbursements as a ratio of GDP for the 19 DAC donors – sample 1970−2010. Each color represents a unique donor.

Figure A2 shows ODA relative to GDP for all 137 recipient countries – again each line represents a specific country. Note that ODA receipts range from very little to over 20% of GDP for some recipients. The darker line in Figure A2 represents the average amount of aid received by the 137 recipient countries in our sample, which is between 2% and 4%. Both Figures illustrate that there is considerable variance of ODA as a share of GDP for some donors and recipients while others are relatively stable. As noted previously, each donor disburses ODA to a large set of recipients. However, most donors have a stronger systematic ODA relationship, in terms of GDP share, with a relatively small subset of total recipients. The remaining recipient countries receive aid in smaller amounts, and some only on an occasional basis. This characteristic will play an important role in our results. The US is an extreme example of this pattern, disbursing ODA to 130 out of 137 countries with half of the countries receiving on average less than 0.5% of the total US ODA, while the 10 largest US recipients together receive on average 53% of total US ODA disbursements. US ODA disbursements are presented in Figure A3.

Figure A2:

Total ODA Disbursements as a ratio of GDP for all recipients – sample 1970−2010. Each green line represents one of the recipients. The dark line is the mean ODA across recipients.

Figure A3:

Shares of US ODA disbursements by recipient from 1970 to 2010. Each line represents a unique recipient.

C.2 Estimation Details

In the GMM estimation, the optimal weighting matrix is computed using a Bartlett kernel with a Newey-West fixed bandwidth. The model is estimated in Matlab, using a modification of the toolbox developed by Cliff (2003) which accommodates equation-specific orthogonality conditions. One estimation issue is that, for some pairs, it may be difficult to distinguish eqs (18) and (19) when ar∗ does not exhibit sufficient time variation. This could be the case, for example, when a recipient receives only sporadic ODA donations from a particular donor. Such a pattern may not be compatible with the altruism signal identified in this paper since continuity in the donor–recipient relation is assumed in the theory. Therefore, we apply a weak pre-selection criterion to each pair before the estimation stage and classify those pairs where the recipient received a disbursement during less than 10% of the time periods and the standard deviation of ar∗ was less than 10−6 as not displaying the countercyclical-altruism signal. This criterion affects about 17% of the pairs, leaving the large majority of pairs to be classified as satisfying the countercyclical-altruism condition, or not. In addition to these two criteria, a further pre-selection criterion was used when ODA variability was insufficient to distinguish the two equations up to machine computational precision. This propensity increased with the number of control variables. Control variables magnify the problem since their variability could mask the very small variability in ODA in some cases. We prefer to adopt a conservative approach and classify these pairs as non-altruistic as well. With no controls this situation virtually never occurs; with one or two controls about 20% of the pairs approach computational precision; and with four controls another 20% approach the limit. This constraint reduces the number of pairs that pass the countercyclical-altruism test, though the number never drops below 10% of the total pairs. We pick a middle ground for addressing this issue and we adopt a baseline with the two controls most linked to our context: population growth and inflation. We discuss the other specifications in the robustness section of the Appendix. Finally, the sample used for estimation includes 35 observations from 1975 to 2010 for our 2603 pairs.

In the GMM, the asymptotic distribution of θˆ is Tθˆ−θ→N0,V, where T is the length of the sample andV is the covariance matrix of θˆ obtained from the inverse of the optimal weighting matrix obtained in the GMM procedure. Under the null hypothesis of the countercyclical-altruism test, the asymptotic distribution of βˆrδˆr,0−δˆr,0∗ is approximated by

where Lθˆ is the gradient of βrδr,0−δr,0∗ with respect to the components of θ evaluated at the estimated coefficient vector θˆ

in which 0z is a row vector with length equal to twice the number of controls included in the regression eqs [18] and [19].

D.1 Robustness to the Model Specification

Regarding the control variables we find that increasing the number of controls reduces the number of pairs displaying the countercyclical-altruism signal for all specifications explored. For instance, going from zero controls to two controls in our baseline specification reduces the altruistic pairs from 23.1% to 16.3%. Changing the set of control variables might also affect the parameter estimates and the composition of the countercyclical-altruistic donor–recipient set; however, this did not occur in our robustness checks. Rather, the contraction of the set of altruistic pairs is mostly due to an increase in the number of cases for which eqs [18] and [19] become statistically indistinguishable and the small variability of ODA is absorbed by the controls.^[34] Fortunately, even though the selection of the controls clearly matters for the numerical relevance of the altruism signal, the number of controls in the model does not seem to be that crucial for the determination of the intrinsic characteristics of the signal, as we see in the growth and logit regressions.

We now turn to the choice of the functional forms. As an alternative to our baseline model of eq. (A5) we consider constant absolute risk aversion (CARA) own-consumption utility functions. The full description of the model under this different set of assumptions is given in Appendix B.^[35] In order to avoid non-linear restrictions on the coefficients of the model, we keep the curvature parameters of the three functions separate from ρr,0 and δr,0, which requires a calibration of the risk aversion coefficients of the two countries, σd and σr, and of the riskiness parameter of the return function, σρ. The combination of the log-additivity property and power functions in (A5) is particularly convenient in this respect because it allows us to estimate the model independently of the calibration of any parameter of the functional forms. We estimate the alternative models for parameter calibrations ranging from σdσrσρ=222 to 888 and including different combinations of the controls in the regressions.^[36] We find that the CARA model generates results very similar to the baseline specification. The CARA model with σd=σr=σρ=2 and two controls, which we take as main alternative specification, returns 20.6% donor–recipient altruistic pairs (it is 16.3% the baseline); about 80.9% of the pairs identified by the baseline model are also included in this CARA specification. Increasing the number of controls reduces the number of altruistic pairs in the CARA model as in the baseline. For example, the altruistic share with CARA goes from 23.2% with no controls to 20.6% with two controls. The results for the basic CARA specification are very robust to the changes in the calibration vector and, in general, we find the intersection of the set of altruistic pairs greater than 80% between the basic CARA and the other calibrations with two controls.

The most interesting difference between the baseline model and the CARA specification is the higher number of countercyclical-altruistic pairs relative to the other countries for Luxembourg, Norway, and in part Finland as well. Our baseline specification reduces the Scandinavian countries’ signals and, in this sense, can be considered a more conservative choice. However, although the composition of the altruistic group changes somewhat with CARA, the output of the growth regressions for the basic CARA case reported in Table A1 and of the logit regressions reported in Table A3 does not differ from our baseline model. The fact that the quality of the signal is preserved across specifications provides further evidence that the theoretical model identifies a robust signal.

A final robustness feature worth noting concerns the theoretical model. In earlier stages of this work other versions of the theoretical model were explored. For instance, we developed models with linear direct returns from ODA in the donor’s budget constraint or returns proportional to the loss in utility of the donors. The basic countercyclical signal emerges from these formulations as well. The theoretical model presented herein is more general and more tightly linked to the estimation.

C.2 Robustness of the Results in Section 5

In this Appendix, we provide some robustness check of the two out-of-model exercises discussed in Section 5. We start estimating the growth regressions for two other specifications of our empirical altruism model, namely the baseline model with no controls and the CARA (with parameterization σd=σr=σρ=2) functional form. The results, illustrated in the two panels of Table A1, are broadly consistent with the baseline evidence discussed in Section 5.2. We then discuss the results of the growth validation exercise with the RS specification, reported in Table A2 for the models with only linear effects. In this case the partition between altruistic and non-altruistic donor sets does not provide clearcut evidence in support of our countercyclical-altruism signal. The estimates of the ODA effects on growth are generally positive, but never statistically significant. The coefficients of the altruistic set are bigger in some of the specifications, as for example in column (1), (2), (4), or (6); however, the results are not always consistent across models as columns (3) and (5) show, and we don’t find a clear endogeneity bias in the contemporaneous regressions. Using early impact aid widen the gap between the estimates of the two donor sets, yet significance at conventional confidence levels is not achieved.

The strength of the BD aid-growth relationship, compared to RS, is not surprising since the BD model generally yielded larger and more significant ODA-growth linkages. CL, for instance, can find significant effects of ODA on recipients’ growth only for early impact for the RS model. In our case, not even the early impact category provides particularly positive estimates. Finally, using quadratic ODA terms in the non-linear specification of the regression model does not improve the overall outlook of the results in Table A2. The coefficients change often sign across specifications with no particular regularity and the growth-ODA relation becomes convex with early impact aid. These results suggest that our signal effectively identify aid with more positive impact on growth only in the BD specification, which as we know estimates the effects of ODA conditional on the quality of the institutions of the recipient country.

In Table A3 we present some robustness checks for the logit regression discussed in Section 5.1. We consider two alternative specifications: The baseline model with no controls and the main CARA functional specification (with parameterization σd=σr=σρ=2). The overall outlook of effects estimated in Table 1 is fairly confirmed by these alternative specifications, with the exception of a few specific differences. The first is that the effect of the population size, which was small but significant, is now non-significant in the specifications for the baseline with no controls. However, consumption is now significant for the baseline with no controls even when multilateral ODA is significant in the level models. The second is that the formal colonial status dummy is less significant in Table A3 for the CARA model, while it survives in the baseline with no controls. Among the three ties dummies, then, only the EU dummy preserves its original significance, reinforcing our interpretation of the results for the colonial variable. Looking at the humanitarian variables, while the significance of the internal conflict dummy drastically drops, the mortality rate seems to replace it in the identification of the countercyclical-altruism pairs, especially for the specifications in columns f and f†. Recipients with higher mortality rates are now more likely to receive altruistic aid. Bilateral trade follows the same pattern, except for model (f) under the CARA case where it is significant now, and military expenditure preserves its negative and marginally significant effects. Finally, it is worth noticing that multilateral ODA is positively related to the countercyclical-altruism signal in a significant way, which indicates a complementarity of bilateral altruistic ODA with other forms of aid that are usually believed to reflect more altruistic donors’ motivations.