Cingranelli and Pasquarello (1985) offered a general conceptual model of U.S. foreign assistance. According to them, the allocation of U.S. foreign aid could be conceptualised as the result of a unilateral decision-making process in two stages. In the first stage of gatekeeping, the U.S. identifies the nations qualified to receive its assistance. In the second stage of distribution, the U.S. decides how much each qualified country will receive. Since its first appearance, this conceptual model has gained its popularity in the empirical literature to explore various possible determinants of U.S. foreign aid, and considerable efforts have been made to tackle the selection effect in the gatekeeping stage. Poe and Meernik (1995) exemplify the application of this conceptual model in studying U.S. military assistance. By applying the Heckman selection method, the authors argued that they could address the selection effect better and contributed to the literature at the time.

It is interesting to note that empirical studies on U.S. foreign aid often start with the Cingranelli-Pasquarello model without asking whether it provides an appropriate conceptualisation of the issue. The single most significant feature of the Cingranelli-Pasquarello model is that it describes U.S. foreign aid as the outcome of unilateral giving behaviour and thus assumes away any possible influence of aid-recipient countries over the issue. Although such a unilateral decision-making paradigm is quite common and helpful in modelling charitable behaviour, it is largely at odds with empirical observations that point to U.S. foreign aid as the outcome of transactions with aid-recipient countries rather than unilateral behaviour of giving (Rai, 1980; Conteh-Morgan, 1990; Raffer and Singer, 1996; Wang, 1999; Neumayer, 2003; Dreher, Nunnenkamp and Thiele, 2008; Fleck and Kilby, 2010).

Bueno de Mesquita and Smith (2007, 2009) are probably best at making the point. By grouping the various self-interest motivations into the rubric of seeking policy concessions from foreign nations, they conceptualised foreign assistance as the result of aid-for-policy deals. Their logic is straightforward. Foreign assistance as a means of resource transfer from the donor to the recipient incurs immediate costs to the former and benefits to the latter. As long as donors care about their interests, they should be rewarded in some way that is highly valued at home. Compared with donor countries, aid-recipient countries are relatively poor regarding material resources but rich regarding policy discretion. Aid-recipient countries value additional resources more than the policy concessions they make, while donor countries value the policy concessions of foreign countries more than the resources they transfer. As a result, aid-for-policy transactions naturally stand out as a focal point where governments in both donor and recipient countries can advance their interests. It is worth noting that when the resource being transferred is defence-related, the self-interest motivation of the donor might have an even more prominent role to play because the transfer has imminent security implications.

Conceptualising U.S. military aid as the outcome of aid-for-policy transactions immediately highlights the issue of bargaining power. It is useful to recall that in any successful transaction, the buyer’s reservation price must be higher than that of the seller. In other words, the consumer must value the object in transaction more than the provider. The gap between the two reservation prices then provides the range of a transaction surplus over which the trading parties can haggle. For the commodity or service in transaction, the seller bargains for a higher price while the buyer bargains for a lower price (Osborne and Rubinstein, 1990). These general rules should be applicable if U.S. military aid is the result of aid-for-policy deals. In the aid-for-policy scenario, the U.S. offers military assistance in exchange for a package of its favoured policy adjustments made by the aid-recipient government, which is not unlike a buyer on the economic market paying the seller for its desirable commodities or services. Specifically, aid-recipient countries, on the sale side, try to push up the volume of U.S. military aid for the policy concessions they offer to make, while the U.S., on the buy side, tries to push it down.

The current research adopts the following two-tiered stochastic frontier analysis (Polachek and Yoon, 1987; Gaynor and Polachek, 1994; Kumbhakar and Lovell, 2000) to gauge the effect of bargaining on U.S. military aid. A discussion on the validity of applying two-tiered stochastic frontier analysis (SFA) models to the bargaining effect on bilateral assistance can be found in Wang (2016, 2018).

where μx=xδ indicates how aid-recipient countries’ characteristics affect the baseline U.S. military assistance, w represents the effort of the aid-recipient government to push up the amount of U.S. military aid, urepresents the effort of the U.S. to push it down, and vis a normal noise.

By assuming that w~i.i.d.Exp(σw,σw2), u~i.i.d.Exp(σu,σu2), v~i.i.d.N(0,σv2), and the error components are independently distributed fromx, Kumbhakar and Parmeter (2009) derived the joint density function of the i-th residual εi as

where ai=εiσu+σv22σu2,ci=−εiσv−σvσu,bi=σv22σw2−εiσw,hi=εiσv−σvσw, and Φ is the cumulative distributing function of standard normal distribution. The estimates for {δ,σw,σu,σv} can be obtained by applying a maximum likelihood estimation (MLE) to the following log-likelihood function

where n is the number of observations of a data sample.

The bargaining impact of the donor U.S., that of aid-recipient countries, and the net surplus can be measured accordingly as

where λ=1/σu+1/σw. All these measures reflect the bargaining effect as a percentage change from the baseline military assistance (Kumbhakar and Parmeter, 2009).

In the previous section, the baseline volume of U.S. military assistance is assumed to be a linear function of a vector of recipient characteristics. This section specifies those recipient characteristics by reviewing previous research on the determinants of U.S. foreign assistance. Two critical points deserve our attention here. First, although existing studies tend to suggest similar determinants of U.S. foreign assistance, their conclusions often conflict with one another due to differences in time horizon, variable operation, and estimation technique. As a result, general agreement on the effect of any single determinant is more likely to be an exception rather than the norm. Second, the existing literature on the determination of U.S. foreign assistance focuses almost exclusively on economic aid. Although certain determinants might influence both economic and military aid, their impact on the two types of assistance could be considerably different. Given this, the following review suggests the recipient attributes relevant to the allocation of U.S. military assistance. In other words, a variable is included as long as there is reason to believe it could affect the allocation of U.S. military assistance, even if the exact effect is far from conclusive.

Following Poe and Meernik (1995), I divide the traditional determinants of U.S. military assistance into a socioeconomic group and a political-strategic group. The socioeconomic attributes of recipient countries include national income, income per capita, population, imports from the U.S., and the inflow of U.S. economic aid. Many studies of U.S. economic assistance have suggested that small and poor economies face more serious financial constraints than their larger and wealthier counterparts and thus have more robust demand for additional resources (Meernik, Krueger and Poe, 1998; Gibler, 2008; Demirel-Pegg and Moskowitz, 2009; Gibler and Miller, 2012). When military assistance is considered, the same logic may also apply. Unlike large and wealthy economies, small and poor economies have extremely limited resources to meet their security needs. Hence, they have a strong desire to offer policy concessions in exchange for military assistance.

Population is another often-included determinant of U.S. foreign assistance (Neumayer, 2003; Bueno de Mesquita and Smith, 2007; Demirel-Pegg and Moskowitz, 2009). A couple of studies have suggested that U.S. economic assistance is biased in favour of populous economies, which contradicts what we have learned from the comparative aid literature showing systematic bias against them. The security implications of population can further complicate the issue of military assistance. According to Dunne and Perlo-Freeman (2003), a larger population by itself provides a certain level of security because populous countries might rely on a large military force as a substitute for prohibitive weapon systems with cutting-edge technology. If that is the case, countries with a large population have considerably less demand for foreign military assistance and lack the incentive to make policy concessions in exchange.

Next, imports from the U.S. are included because it has long been argued that precious foreign markets constitute a major strategic interest that U.S. policymakers need to serve. Some empirical studies have also shown systematic evidence that the U.S. provides more economic (Neumayer, 2003; Bueno de Mesquita and Smith, 2007; Fleck and Kilby, 2010) and military assistance (Poe and Meernik, 1995) to its major export markets.

Lastly, I include the inflow of U.S. economic assistance in this category because studies have shown a strong positive connection between the two types of aid (Hook, 1995; Neumayer, 2003).

The political-strategic group includes voting consistency with the U.S. in the United Nations General Assembly (UNGA), U.S. military presence, the level of democracy, violation of citizens’ personal integrity, geographical location and the war on terrorism. First, some studies have identified votes in the UNGA as a major form of policy concession that developing countries make in exchange for U.S. economic assistance (Rai, 1980; Wang, 1999; Dreher, Nunnenkamp and Thiele, 2008). Thus, an aid-recipient country’s voting consistency with the U.S. in the UNGA is included to cover for this possibility.

Second, some studies have examined the relationship between U.S. military presence and the volume of U.S. economic aid (Meernik et al., 1998; Apodaca and Stohl, 1999). Little evidence has been found in support of a significant connection between the two. Given the solid logical tie between U.S. military presence and military aid, however, I still include a variable of U.S. military presence to account for a potential nexus.

Third, extensive empirical literature has investigated the relationship between respect for human rights by the governments of aid-recipient countries and inflows of U.S. foreign aid. The scholarship could be further divided into two strands of research. The first focuses on the respect for political rights or the level of democracy (Meernik et al., 1998; Demirel-Pegg and Moskowitz, 2009; Fleck and Kilby, 2010; Gibler and Miller, 2012), while the second focuses on the abuse of citizens’ personal integrity (Poe, 1991; Lai, 2003; Neumayer, 2003; Gibler, 2008; Fariss, 2010). This study takes both political rights and personal integrity abuse into account.

Next, studies on U.S. foreign aid have long noticed the strategic significance of aid-recipient countries due to their geographical location. Although previous studies paid particular attention to American countries (Poe and Meernik, 1995; Apodaca and Stohl, 1999), it should be noted that countries in other regions could also be of unique value to U.S. foreign policy (Balla and Reinhardt, 2008). Thus, the current study takes geographical location into account when predicting the baseline volume of U.S. military aid.

Finally, the terrorist attacks of Sept. 11, 2011 have increased academic interest in exploring how the war on terrorism has reshaped U.S. foreign and security policies. Regarding foreign assistance, recent studies show that the post-9/11 era has been characterised by an expansion of U.S. foreign assistance in order to contain the ongoing terrorist threat to U.S. security (Fleck and Kilby, 2010; Boutton and Carter, 2013). Given the epoch-making nature of the Sept. 11 attacks and their evident impact on U.S. foreign and security interests, this research addresses those concerns as well.

To examine the effect of bargaining power on U.S. military assistance in the post-Cold War era, I first take a benchmark analysis that involves two different specifications. The first includes only the recipient characteristics proposed to influence the baseline volume of U.S. military aid. This specification is estimated with ordinary least square (Model 1a) and maximum likelihood (Model 1b), respectively. The second specification takes into account the bargaining effect by operating the two-tiered SFA developed in Section 2.2. In particular, two variants of the two-tiered SFA are applied. The first (Model 2a) operates hypothesis testing based on regular standard error, while the second (Model 2b) operates it based on robust standard error. Table 2 contains the results.

The two model specifications reach the same conclusion regarding how the proposed attributes of an aid-recipient country influence the baseline volume of U.S. military aid. As for the socioeconomic attributes, GDP, imports from the U.S., and the inflow of U.S. economic assistance have a positive effect on baseline military aid, while GDP per capita and population have had a negative effect during the post-Cold War era. It is interesting to note that the result for the population-aid nexus is consistent with what we have learned from the comparative literature of aid and the Dunne and Perlo-Freeman (2003) argument that population itself can provide a certain level of security.

Interesting results also appear concerning the political-strategic attributes. First, higher voting consistency with the U.S. in the UNGA and a larger contingent of U.S. military personnel help a recipient gain more military aid. Second, the results also suggest that U.S. military aid is indiscriminate regarding a recipient’s level of democracy (respect for citizens’ political rights) but biased in favour of those that regularly abuse the personal integrity of their citizens. Finally, the U.S. provides more military assistance in the war on terrorism, and countries in Asia and Europe received more U.S. military aid.

The main objective of this research, however, is to evaluate the impact of bargaining power on the distribution of U.S. military assistance. According to the estimates of Models 2a and 2b, both σu and σw are statistically significant at the 0.01 level. Since Model 1b is nested in Model 2a, we can use a likelihood ratio (LR) test to evaluate whether a more complicated specification is preferable. The chi-squared value of 32.98 is highly significant and thus supports the inclusion of additional parameters modeling the bargaining effect.

To illustrate the overall contribution of the bargaining effect to the variation in U.S. military assistance, I operate a variance-decomposition analysis based on the two-tiered SFA specification. Table 3 presents the results. According to this analysis, the overall unexplained variation in U.S. military assistance is 3.32. Of this unexplained part, 93% can be explained by the bargaining effect. Within the bargaining-related variation, 46% can be further attributed to the bargaining effort of aid-recipient countries to push up the amount of aid. In comparison, the other 54% can be attributed to the bargaining effort of the donor U.S. to push it down. The figures suggest a significant bargaining effect on the distribution of post-Cold War U.S. military assistance.

To complete the discussion, I provide the mean and quartile values of the bargaining effect of the donor U.S., that of its military aid recipients and the net surplus in Table 4. They are calculated based on the point predictors introduced in Equations (4) through (6), respectively. The results indicate that on average, the bargaining effort of the donor U.S decreases the volume of military assistance by 56.07%. In comparison, the bargaining effort of aid-recipient countries increases it by 54.47%. In equilibrium, the volume of U.S. military assistance is lower than the baseline volume by 1.60% at the mean and by 2.73% at the median. Obviously, the donor U.S. extracts a slightly larger portion of the transaction surplus at these central points.

However, the game of surplus division is not always about equally strong hagglers as it may first appear. In fact, the quartile values show substantial variance in bargaining performance and, hence, the final outcome of surplus division across transactions. As reported in the last row of Table 4, the net surplus at the first quartile point is −30.72%. This means that for a quarter of the aid-for-policy transactions in our data sample, the policy concessions made by aid-recipient countries were traded for at least 30.72% less than their baseline price. At the same time, the net surplus at the third quartile point is 27.88%, meaning that for another quarter of transactions, policy concessions were traded for at least 27.88% more than their baseline price. The inter-quartile variance (the difference between the first and third quartile values) is 58.60%, demonstrating the massive influence of bargaining power over the allocation of U.S. military assistance.

The two-tiered SFA analysis in Section 4.1 assumes bargaining efficiency to be homogenous among aid recipients. A more realistic scenario, however, would allow it to be heterogeneous across different recipients. Previous studies in the two-tiered SFA literature have addressed this issue by allowing seller and buyer attributes to influence the means of wand u, respectively (Groot and Maassen van den Brink, 2007; Murphy and Strobl, 2008; Kumbhakar and Parmeter, 2009 Tomini, Groot and Pavlova, 2012). Using the same approach, I now allow aid-recipient attributes to influence the mean of w. In particular, σw is now assumed to be a linear function of all the recipient characteristics studied in the benchmark analysis except the regional dummies.

Results based on this extended model are provided in Table 5. For the sake of comparison, findings based on Model 2b are duplicated here. Several interesting patterns are identified and worth discussing in detail. As far as socioeconomic attributes are concerned, only imports from the U.S. are shown to have a significant effect on the bargaining capability of an aid-recipient country. Specifically, importing more from the U.S. not only promotes the baseline level of military assistance but also grants the importer bargaining advantage in surplus division. The other socioeconomic attributes show no significant effect on the bargaining capability of an aid-recipient country, and their influence over the baseline military aid is similar to those identified in the benchmark analysis. The results demonstrate that U.S. economic aid inflows, population, GDP, and GDP per capita of an aid-recipient country affect U.S. military assistance only by determining the baseline aid.

With regard to the political-strategic attributes of an aid recipient, the accommodation of heterogeneity in bargaining efficiency provides a complicated picture of the channels through which such characteristics influence U.S. military assistance in equilibrium. All political-strategic attributes, except the voting consistency with the U.S. in the UNGA and the war on terrorism, show a significant impact on an aid recipient’s bargaining capability. Specifically, personal integrity abuse and U.S. military presence increase bargaining capability. However, a higher level of democracy (or higher respect for citizens’ political rights) decreases it.

Allowing bargaining efficiency to vary across aid recipients also has considerable consequences for determining the baseline level of military assistance. Once the cross-recipient difference in bargaining efficiency is assumed, U.S. military presence and the war on terrorism lose their significance. At the same time, democracy gains importance in determining the baseline level of U.S. military aid. Violation of personal integrity is still a significant determinant of baseline aid but switches its coefficient sign from positive to negative.

From such changes, essential lessons can be drawn concerning how the political-strategic attributes of an aid-recipient country influence the U.S. military assistance it receives through two different channels. In particular, recipient attributes can affect either the portion of the transaction surplus grabbed by aid-recipient countries or the value of foreign policy concessions made to the U.S. as reflected in the baseline level of assistance. According to the extended model, countries that regularly abuse the personal integrity of their citizens provide less valuable policy concessions, which is reflected in the lower baseline level of aid. However, this disadvantage is largely compensated by their strong capability in negotiating deals with the U.S. On the other hand, more democratic states provide more valuable foreign policy concessions and earn more military assistance as reflected in the baseline volume. The advantage, however, can be negated by their considerable bargaining inefficiency. Finally, unlike what we learned from the benchmark results, the war on terrorism has no impact on military assistance through either mechanism once difference in bargaining capability is considered.

Does the accommodation of heterogeneity in bargaining efficiency affect our evaluation of the overall contribution of the bargaining effect to the variation in U.S. military assistance? To answer this, I operate a variance decomposition analysis for the extended model and report the results in Table 6. The overall unexplained variation in U.S. military assistance is now 3.08. Of this unexplained variation, 86% can still be attributed to the bargaining effect. Within the bargaining-related variation, 48% can be further attributed to the bargaining effort of the recipient countries to push up the amount of U.S. military aid, while the other 52% can be attributed to the bargaining effort of the donor U.S. to push it down. Compared with the benchmark results, the overall explanatory ability of the bargaining effect has decreased from 93% to 86% after taking cross-recipient heterogeneity in bargaining efficiency into account. The relative impacts of recipient and donor bargaining efforts in the extended model are close to those reported in the benchmark analysis.

Next, I inspect the mean and quartile values of the bargaining effect of the donor U.S., that of its military aid recipients and the net surplus based on the extended model. The results presented in Table 7 show that on average, the bargaining effort of the donor U.S. decreases the amount of military aid by 53.84%, while the bargaining efforts of recipient countries increase it by 49.46%. As a result, U.S. military assistance in equilibrium is 4.38% lower than the baseline level at the mean and 5.99% lower at the median. The quartile values again show colossal variation in bargaining performance on both the donor and recipient sides as well as in the net surplus. The net surplus at the first quartile point shows that for a quarter of the aid-for-policy transactions, policy concessions are traded for at least 32.25% less than their baseline price. At the same time, the net surplus at the third quartile point shows that for another quarter of transactions, policy concessions are traded for at least 20.91% more than their baseline price. The inter-quartile range of 53.16% illustrates the massive impact of bargaining power and its substantial variation across transactions.

A quick comparison with the results from our benchmark analysis (Table 4) immediately reveals three noticeable differences. First, ignoring cross-recipient heterogeneity in bargaining efficiency is likely to overstate the overall impact of bargaining power on U.S. military assistance, a point that holds at both the mean and different quartile points. Second, the bargaining advantage of the donor U.S. in the surplus division is underestimated in the benchmark analysis. Third, assuming the same bargaining efficiency across recipients exaggerates the variance in bargaining performance, which is best reflected by the interquartile ranges.

Despite these differences, it is critical to note that the extended model unequivocally reconfirmed two general themes established in our benchmark analysis. First, the U.S. enjoys a modicum of bargaining advantage at both the mean and the median. In other words, it can grab a larger portion of the transaction surplus at those central points. Second, policy concessions are not always traded under their baseline price. Though many aid recipients ended up with highly unfavourable deals with the U.S., many others managed to strike highly favourable ones.

Some curious readers might then be interested in knowing more about the bargaining performance of individual aid recipients. Before moving to the final section, Table 8 shows the 10 most successful ones in terms of average bargaining performance (out of 133 aid-recipient countries). All of these countries are long-term beneficiaries of U.S. military assistance. It is also interesting to note that countries from the Middle East and North Africa dominate the list.