The Determinants of Military Expenditure:
A Spatial Panel Approach
Author: Arjan Boudewijn Huizinga∗
Supervisor: Prof. Dr. J. Paul Elhorst
University of Groningen
31-08-2012
Abstract
This paper investigates the spatial dependency of military expenditures among countries. We use a neo-classical welfare model and a spatial panel data approach with spatial fixed effects of 120 countries for the years 1993-2007. By comparing the performance of different model specifications we find that a spatial Durbin model with a third order binary contiguity weight matrix best describes our data. The results of this model show positive spatial dependency for the military expenditure of countries. Furthermore, the direct and indirect effects of the explanatory variables also suggest spatial linkages with military expenditure.
Keywords: Military Expenditure, Spatial Dependency JEL: C23, H56
2 1. Introduction
Why would a country want to spend valuable government budget on a military force? Collier and Hoeffler (2007) explain that the most reasonable motivation is the need for security. Throughout history, the main threat to this security was external. A country may be forced to fight an international war. However, after the Cold War and a changing global environment with increasing globalization, international wars have dropped significantly (McGuire, 2007). Moreover, nowadays the main threat is internal. Civil wars are more common, due to conflicts over ethnicity, religion, and control over resources (Kaldor, 1999).
Like utility or welfare, security is hard to quantify. Therefore it is often replaced by variables which can be measured, such as the military expenditure of a country (Smith, 1995). Determinants of military expenditure have been a research area of interest for a long time. In this literature, and in accordance with the external threat to security described above, it is widely accepted that one reason for conflict is geographical proximity. See for instance Enterline (1998) and Bremer (1992). Continuing this line of thought, the literature suggests that military expenditure of other, neighboring countries imposes a threat to the security of country i. One possible reaction of country i is to increase its perceived level of security, by increasing its own level of military expenditure. This could instigate a classical Richardson (1960) type arms race.
Taking post-Cold War developments into account, for this paper we are interested in the relationship between geographical closeness and a country’s military expenditures. Our main interest is to research if and how there is a spatial dependency between countries’ military expenditures.
3 effects estimates for the explanatory variables are interesting as well as the main result itself.
The results of this model show a positive significant spatial interaction effect at a low value for military expenditures of countries. Following the reasoning of Goldsmith (2007) we conclude that this result points towards a situation in which countries are able to dissect other countries’ defensive from offensive arms build-ups. Because of this ability it is possible that a country can maintain minimum defensive efforts, as long as offensive action does not occur, or just because war is considered unthinkable. This result is in line with the observation of a decreasing number of international wars after the Cold War.
The paper proceeds as follows. Section 2 summarizes the literature in the field of determinants of military expenditure. Section 3 describes the neo-classical welfare model we use, and Section 4 provides theoretical insight in the use of other, explanatory variables. Section 5 presents the spatial econometric methodology, while Section 6 provides a description of the dataset and its sources. In Section 7 the results of the empirical analysis are discussed. Finally, Section 8 concludes.
2. Literature Review
In this section we provide an overview of articles which study the determinants of military expenditure and the interaction between neighboring countries. According to Dunne and Perlo-Freeman (2003a), these studies can be categorized in two broad groups of empirical studies. The first group of studies mainly makes use of an arms race model. Richardson (1960) had a large influence on this line of research. The second group of research focuses on a comprehensive approach, studying the economic, political, and strategic determinants of military spending. We will explain both these groups of research below. We focus on the second line of research, as our study can be categorized in this group. This is because the Richardson (1960) type model is better suited to study pairs of countries which are in conflict (Dunne and Perlo-Freeman, 2003a), while we focus on a group of 120 countries.
4 Smith, 2007). The arms race model presented by Richardson (1960) has been one of the key models in this area.
According to Richardson (1960), the change of a nation’s military expenditure is influenced by three factors. First of all, the military expenditure of the adversary, secondly the economic burden of previous purchases of military forces, and thirdly the level of ‘grievance’ towards the adversary (Glaser, 2000). The model describes the phenomenon of an arms race in a descriptive and mechanical way, and uses a coupled pair of differential equations to explain the change in levels of weapons in each of two nations as a function of the weapons held by both sides (Brito and Intriligator, 1995). The resulting action-reaction framework has been developed in various ways but it has been difficult to prove the existence of an arms race empirically1. Possible reasons
for the failure have been provided by Dunne and Smith (2007), who argue that structural instability and globalization cause this difficulty.
The second line of research employs a more comprehensive approach on the determinants of military expenditure. Including, for example, economic, political, and strategic factors which influence the demand for military expenditure. There are studies which use a more formal theoretical framework, but also studies that are more informal in their model specification. Studies which use a theoretical framework often make use of a neo-classical welfare approach in which a nation’s social welfare is maximized, and where security is an important factor represented by military spending (Smith 1989, 1995).
Our focus lies on panel data models, and especially spatial panel data models. We discuss articles that make use of these approaches in greater detail below.
First of all, in the two articles by Dunne and Perlo-Freeman (2003a/b), they study the demand for military spending in developing countries, and how this demand is formed. The first article makes a distinction between situations during and after the Cold War. The second article uses a dynamic panel data approach, including possible time effects the first study did not pick up. In order to analyze this, both papers use a neo-classical welfare approach similar to the model mentioned above. Besides this theoretical building block and including several economic and political control
1 For a theoretical overview of the Richardson arms race model and its development, see for example
5 variables, they use a so-called ‘Security Web’ (Rosh, 1988) in order to model strategic factors which can influence the demand for military spending. A country’s Security Web incorporates all other countries capable to significantly affect that country’s security. Dunne and Perlo-Freeman (2003a/b) make a distinction between Enemies, Potential Enemies, and Others.
To analyze their model they use a cross-section averaging approach in the first article and a dynamic panel data approach in the second. The results of the first article show no significant differences between the two time periods that are studied. This suggests that there have been little changes in the determinants of military spending, despite the fact that the strategic environment underwent a major change. Before as well as after the Cold War countries react in kind to military spending of other countries. This result is found for both non-hostile as well as hostile neighbors. However, the effect of hostile neighbors on military expenditure is larger.
The results of the second article show a positive and significant effect of the Security Web and Potential Enemies variables, suggesting that countries do react on the military spending of their neighbors. Furthermore, they use a structural break to test for changes in the demand equation during and after the Cold War. The results reject the hypothesis of equal coefficients in the two time periods; Dunne and Perlo-Freeman (2003b) find higher coefficient estimates for Civil War after the Cold War. This suggests that internal factors have become more important after the Cold War.
6 race. They conclude that the same level of external security can be reached on a wide range of military expenditure levels, as long as an entire neighborhood changes its policy and behavior.
The fourth article, by Nordhaus et al. (2010) considers the influence of countries’ external security environment on their military spending. Using a liberalist-realist theoretical model, they estimate the ex-ante probability that a country ends up involved in a militarized interstate dispute. They use a panel data model for 165 countries over the period 1950-2000 to estimate the determinants for military spending. Besides estimating these determinants as a function of the threat for armed conflict, they include other influences such as actual military conflict, democracy, and civil war. Their results show that a one percent increase in a country’s calculated probability of getting involved in a militarized dispute leads to a three percent increase in this country’s military expenditure. Furthermore, they find that autocratic regimes spend more on their defense than do democratic regimes. Also, external threat with the possibility of ending up in an arms race leads to more military expenditure than the threat of civil war.
7 Finally, the article by Flores (2011) makes use of a spatial econometric approach. They test for spatial effects with respect to military expenditures between countries in a cross-sectional study for 168 countries in the year 2000. In order to explore different sources of interdependence, Flores (2011) examines two potential sources of spatial dependency. First of all geographical proximity, and secondly alliance membership. In order to estimate these different sources they make use of two weight matrices. For the first scenario they make use of a Euclidian distance matrix. In the second case they build an alliance membership matrix. They find evidence of spatial dependency of military expenditures using the Euclidian distance matrix, as the spatial lag model shows positive and significant results. Likewise, the spatial lag estimation which makes use of the alliance membership matrix also shows positive and significant results. As Flores (2011) explains, there are different theories regarding the nature of alliances. Their result confirms the case where alliances are perceived as both public and private goods. In this case, the spatial dependency of military expenditures between alliance members depends on the consumption relationship of the jointly produced defense outputs. The result of Flores (2011) confirms the hypothesis which states that alliance membership increases military expenditures when the alliance is characterized by complementarity.
8 3. Theoretical Model
We base our econometric analysis for the determinants of military spending on a theoretical framework. This framework forms the foundation of our analysis such that it provides us with a specification of causality, functional form, and relevant variables (Dunne and Perlo-Freeman, 2003a).
In the literature this is commonly achieved by use of a standard neo-classical welfare model. In this model, nation states are represented as rational agents who maximize a welfare function depending on security and economic variables. This function is subject to a budget constraint which includes military spending, and a security function which determines security in terms of its own, and other countries military forces. The state then balances the welfare benefits of extra security derived from military expenditure against its opportunity costs in terms of foregone civilian output, and solves this optimization problem which gives a derived demand for military spending. (Smith 1989, 1995)
Besides this standard framework, we want to formalize the theory of spatial interaction effects regarding military expenditure across countries. In order to incorporate this theory into our framework, we introduce a spillover model of strategic interaction among governments as described by Brueckner (2003) in our security function. In this spillover model, the level of military expenditure for a given government depends on the choices of other governments, which indicates the presence of spillovers.
First, we describe the neo-classical welfare model.
We define social welfare , as a function of utility derived from security , and Civilian output .
, (1)
The maximization of this function is subject to a simple budget constraint and a security function.
9 In this budget constraint represents national income; and are the prices of
civilian output and real military spending . Next, we introduce our security function. According to Smith (1995) security, like utility or welfare, is unobservable to the econometrician. Instead, security is produced by military expenditure of the country and other countries, together with other strategic variables X. As explained above, we apply a spillover model to capture possible strategic interaction effects among countries.
In the spillover model, a given country i chooses the level of military expenditure . However, this country is also directly affected by the level of military expenditure in other countries .
The security function can then be written as follows:
, , (3)
where represents a vector of political and strategic variables.
Finally, maximizing the social welfare function (1) subject to the budget constraint (2) and the security function (3) yields a demand function for military expenditure (4):
, ,
, (4)
This demand function represents a reaction function, which gives country i the best response to the choices of other governments regarding military expenditures, conditioned on ,
, and . Due to data limitations we assume uniformity for the
10 considered. Also, our study investigates spatial interaction effects between countries. This is an example of horizontal interaction. Following Brueckner’s (2003) explanation, we expect a situation of strategic complements to occur and thus a positive slope of the reaction function.
Jervis (1978) provides us with an explanation as to why we can expect certain interaction effects to occur. He explains the concept of ‘security dilemma’. Many of the means by which a nation tries to increase its security, decrease the security of other nations and increase the level of threat such a nation experiences. When countries cannot properly interpret intentions of other countries, they could perceive any kind of arms build-up, even if purely defensive, as an increase to the level of threat they experience. As a consequence their level of security decreases. A logical response would be to try and increase this level of security again. One way to achieve this would be by building up one’s own stock of arms. Continuing this line of thought could mean the birth of an arms race. However, under certain circumstances this perception of threat and building up of the stock of arms can be avoided. When a country can properly distinguish between offense and defense behavior or weaponry of another country, different outcomes of the security dilemma are possible.
Goldsmith (2007) explains that it is plausible to expect several spatial patterns of defense effort among states based on arms racing and security dilemma dynamics.
First of all, a typical Richardson type arms race outcome. In this case nearby countries will respond to each other’s arms build-ups by increasing their own. Obviously, this will lead to higher levels of arms overall.
Secondly, a nation might be confident in their ability to protect the country with small investments in defense when nearby countries increase their stock of arms. In this case, even though some countries increase their stock of arms, their neighbors are not very worried and a spiraling arms race does not occur. Even more so, when several neighboring countries form an alliance it is possible that some countries do not make additional investments in defense at all or even lower their defense expenditures. This can lead to free-riding behavior (Sander & Hartley, 2001)
11 long as offensive action does not occur, or simply because war is considered unthinkable.
All three scenarios can be associated with a different form of spatial interaction. The first scenario of a classical Richardson (1960) type arms race corresponds to positive spatial correlation at high values. In other words, the higher a country’s stock of arms, the higher its neighbors’ level will be as well.
The second case can be linked with either negative or zero spatial correlation. A negative correlation is possible in case of an alliance: a state with a high stock has neighbors with low stocks of arms. In case of zero spatial correlation a state’s stock of arms has no effect on its neighbors’ level at all.
Finally, the third scenario resembles to positive correlation at low values. When a country’s stock of arms is low, its neighbors will also have low levels of defense effort.
This paper focuses on a time period after the Cold War. As mentioned before, this period is characterized by a decreasing number of international wars. Therefore we do not expect high positive spatial dependencies between countries regarding military expenditures. Instead, we expect situation three to occur. Thus, we expect a low positive value which means that countries do not expect international wars to occur.
4. Explanatory Variables
In this section we turn our attention towards our vector of explanatory variables .
These variables are split into three categories: Economic, political, and strategic variables. We provide a theoretical insight for each variable we consider.
The variables we use as economic factors are GDP and Population. First of all, national income is part of the neo-classical welfare model we use as our theoretical framework. Other studies have provided more insight as to why national income or income per capita influences military spending.
12 that a higher income can lead to structural changes and inequalities. In turn, Maizels and Nissanke (1986) explain that this effect can cause conflict, requiring higher military spending in order to keep internal control.
Furthermore, Rahman (2000) makes use of Wagner’s Law to provide an economic rationale, explaining that military expenditure of a country grows in tandem with its level of income per capita. This explanation implicitly assumes as positive income elasticity of military expenditure. Therefore, we expect a positive relationship between military expenditures and GDP, as both arguments point to this direction.
The next economic factor is the population of a country. There are multiple theoretical reasons for using population as an independent control variable in our study. First of all, Dunne and Perlo-Freeman (2003a) suggest that population can capture possible size effects. Countries with a higher population could experience so-called ‘intrinsic security’. Similarly, Collier and Hoeffler (2002) describe that countries with larger populations are potentially more secure from external threat as they are more difficult to conquer and control. This makes these countries less attractive targets for possible aggressors. Due to this effect the need for military expenditure is reduced. Therefore we can speak of possible scale economies (Groot and van den Berg, 2009).
Furthermore, countries with a larger population could possibly reduce military costs by relying more on larger military personnel and less on costly high-tech military equipment (Dunne and Perlo-Freeman, 2003a). Finally, defense can be considered a public good as it is both non-rivalrous and non-excludable. Dunne and Perlo-Freeman (2003a/b) suggest that because of this, a large population makes military spending more effective, as it benefits a larger number of people. Including population can therefore pick up public good effects. As Fordham and Walker (2005) explain, the non-rivalrous characteristic of national defense implies that a larger population does not necessarily require additional resources allocated to the military to provide the same level of defense to the population. It can reduce the military expenditure need as the population increases.
Although the explanation of all these theories is different, they all predict a negative relationship between the size of the population and military expenditure.
13 In many studies political regime is considered as a determinant for military expenditure. For example, Maizels and Nissanke (1986) suggest that the nature of the state itself is likely to be an important influence, since a military dictatorship can be expected to maintain a larger military establishment, ceteris paribus, than would a democracy.
There are quite a number of studies who follow this reasoning, such as Mulligan et al. (2004), Collier and Hoeffler (2007), Groot and van den Berg (2009), and Goldsmith (2007). However, the study of Fordham and Walker (2005) provides us with a thorough reasoning based on international relations theory and in particular on Kantian Liberalism.
According to Fordham and Walker (2005), Kant claims that liberal states will allocate fewer resources to their militaries than will autocratic states. The reasoning according to liberal theory is as follows. First of all, there are domestic political reasons. During peacetime, a country’s high military expenditure can put pressure on, and adversely affect, the nation as a whole. Liberalists argue that all resources allocated towards a military purpose come at the cost of high valued social goods, such as education. Furthermore, they argue that high levels of military spending may threaten civil liberties and political freedom. These are values which stand in high regard in democratic countries. Therefore it is expected that the majority of citizens in democratic countries are opposed to high military spending.
At the same time liberals acknowledge the fact that small groups of society could benefit from the preparations for war. And, that these groups might very well have the power to influence or control military decisions in autocratic states. Likewise, Groot and van den Berg (2009) argue that in a non-democratic state, the military can play an important role in order to suppress and eliminate potential competitors of the dictator. Therefore a more autocratic country might need the military. In this case it is in the best interest of the dictator to keep the army happy and allocate a large amount of resources to the military budget.
14 Finally there are strategic factors that affect military spending. These strategic factors involve relations between two or more countries. The most obvious one is international war. Ongoing wars highly increase the demand for military expenditure because fighting a war is costly. For example, the army will have to replenish stocks of arms and ammunition used.
Articles that find a significant relationship are for example Dunne and Perlo-Freeman (2003 a/b), Collier and Hoeffler (2002, 2007), and Goldsmith (2007).
Another, closely related variable is civil war. According to Collier and Hoeffler (2002) the incidence of a civil war is now ten times greater than an inter-state war. Therefore, one can argue that nowadays the risk of rebellion can be more influential on the level of military expenditure than the threat of an international war.
In this paper we make the distinction between international war and civil war. Therefore we treat them separately as well. The effects of internal and external wars might be different. Fordham and Walker (2005) describe that a civil war can split a nation’s military forces. Also it is possible that a civil war prevents a nation from extracting resources from society for military use. This could lead to a situation in which a lower military spending level is observed compared to an external war. Also, in the case of a civil war it is likely that not all military forces obtain their resources from military resources allocated by the state. This is another reason for a possible difference in effects between the types of war.
We expect a positive relation for both variables with respect to military expenditure. However, we expect the effect of an international war to be larger.
5. Data
This section explains the data used in this study and how the variables are defined. Our sample consists of 120 countries over the time-period 1993-2007. A list of the countries in the dataset can be found in the Appendix. Table 1 provides an overview of the dependent variable and the explanatory variables, the abbreviations used throughout the paper, and their sources.
15 The military expenditures data is obtained from a dataset provided by prof. dr. J.P. Elhorst. As Brzoska (1995) explains, at first military expenditure seems a straightforward measure: the cost of maintaining a military force in times of war and peace. However, there are various conceptual problems when it comes to defining it in data and using it in empirical research. Various arguments of Brzoska (1995) are described below.
First of all, in essence military expenditure is an input measure. It is an aggregate of payments, and goods and services, etc. purchased by a country over the time span of a year. However, often it is used as an output measure to measure military strength due to lack of a better indicator. Implicitly this is also valid for this study. We relate higher military expenditure to an increasing level of perceived security. The thought behind this argument is that higher military expenditures provide a better ability to protect a country. Brozska (1995) says that this is problematic as military strength is basically a stock variable dependent on available military equipment. Also, it is hard to measure fighting performance in war and the ability to prevent war as this depends on factors such as training, motivation, and leadership (Wiberg, 1983). Therefore, military expenditure and military strength are not necessarily equal.
Furthermore, countries differ in their approach for the function of the military. For example, in many countries it is the function of the military to provide meteorological services, air traffic control, etc. And, should pensions for veterans be regarded as a military expenditure? Also, in unstable developing countries, the military expenditures often do not equate to the budget of the ministry of Defense and expenses are spread throughout governmental institutions. Moreover, in many countries, even democracies, part of the military expenditures are state secrets and are not observable to the public eye. Additionally, there are standard definitions for military expenditure formed by for example the NATO and IMF, but countries are free to use their own definitions. This can lead to large discrepancies between national and standard definitions of military expenditure.
16 ratio of GDP2. Often the literature denotes this as the ‘military burden measure’.
Using this ratio allows easy comparison between small and large countries. Also, comparison between rich and poor countries becomes easier. One new problem that arises is the reliability of the GDP data. Especially for developing or centrally planned economies there are estimation problems. Other studies that make use of the military burden measure are for example Dunne and Perlo-Freeman (2003a/b), Collier and Hoeffler (2007), Groot and van den Berg (2009), and Goldsmith (2007).
Thus, although military expenditure may be the best indicator of military activity, there are limitations to its use and reliability.
For several other variables we also use data provided by prof. dr. J.P. Elhorst. First of all, GDP is measured in real terms. Secondly, the measurement for Population is represented in millions. Both variables are log-linearized.
To test the impact of International War and Civil War on military expenditures, we use data obtained from the Major Episodes of Political Violence (MEPV) dataset, provided by the Center of Systemic Peace (CSP). From this dataset we use the Inttot variable to describe the occurrence of International War, and we use the Civtot variable to represent Civil Wars. Data of the MEPV dataset is defined by the systematic and sustained use of lethal violence by organized groups that result in at least 500 directly-related deaths over the course of the episode (Marshall, 2010). The Inttot variable consists of the sum of the magnitude scores of International Violence and International Warfare. Scores for both these variables range from 1 (smallest) to 10 (greatest) and describe the impact an episode of violence has. A value of zero is used when no episode is observed. The Civtot variable is constructed by combining the magnitude scores for Civil Violence, Civil Warfare, Ethnic Violence, and Ethnic Warfare. We use the total sum, to avoid the arbitrary distinction between episodes categorized as ‘Violence’ and ‘Warfare’. Also, we avoid the distinction between ‘Civil’ and ‘Ethnic’ episodes and include both types. The characteristics of the scores for this variable are similar to the scores for Inttot.
To describe the Political Regime of a country, we use the Polity2 variable of the Polity IV project dataset. In this dataset both democracy and autocracy are measured and
17 combined to create the Polity2 variable3. This indicator has a range from -10 to +10,
where -10 is strongly autocratic and +10 strongly democratic.
Table 2 presents the descriptive statistics for both the dependent and the explanatory variables.
<< Table 2 here >>
6. Methodology
In this section the methodology used to test the economic model laid out in Section 3 is discussed. As mentioned, we use a spillover model in our theoretical model which represents the spatial dependence of military expenditure among different countries. The spatial econometrics methodology is aimed at detecting such spatial interaction effects. This section explains which kind of spatial interaction effects are possible and how to model these effects. Furthermore, we describe how to decide which specification best suites the data and how to determine the spatial weight matrix W we use. Finally, we shortly explain the partial derivative interpretation we use to test for the hypothesis of the existence of spatial spillover effects.
In general, there are three types of interaction effects that can explain why military expenditure of a country i may be dependent observations of other countries j (j = 1,…,n ; j ≠i) (Elhorst, 2010).
The first one is an endogenous interaction effect. This effect measures if the dependent variable of country i depends on the dependent variable of another country j (j≠ i) and vice versa. Secondly, exogenous interaction effects mean that the dependent variable of a country i depends on the explanatory variables of another country j (j ≠ i). If the number of explanatory variables is K, this means there are K exogenous interaction effects possible. Finally, an interaction effect among the error terms means that countries tend to behave similarly because they share similar unobserved characteristics, or face similar unobserved institutional environments. Summing up, this means there are a total of K+2 possible interaction effects.
3 For a detailed description of the democracy and autocracy indicators composition, see the Polity IV
18 Because there are three types of interaction effects, there are various ways to model spatial interaction effects. The best known examples of spatial econometric models are the spatial lag model, in which the endogenous interaction effect is taken into account. Secondly, the spatial error model, in which the interaction effect among the error term is used. These two models are introduced by Anselin (1988, 1996). Thirdly, the spatial Durbin model takes both the endogenous and exogenous interaction effects into account.4 This last model is advocated by LeSage and Page (2009).
We use a spatial panel data approach. In order to control for spatial heterogeneity, we include spatial fixed effects. The inclusion of these spatial fixed effects will control for the influence of underlying space-specific time-invariant factors. Time specific effects are also a possibility, but our model estimation in Section 7 shows that these effects are not necessary.
A full linear regression spatial panel model with all types of interaction effects and spatial fixed effects takes the following form:
(5a)
(5b)
where denotes an N×1 vector of military expenditures for every country (i=1,….n) in the sample during time-period t. denotes an N×K matrix of exogenous
explanatory variables, is the endogenous interaction effect among the
dependent variables, the exogenous interaction effect among the independent
variables, and the interaction effect among the error terms. ρ is the spatial
autoregressive coefficient, λ the spatial autocorrelation coefficient, while θ, just as β, represents a K×1 vector of fixed but unknown parameters. µ is a vector of spatial fixed effects, and is a vector of error terms. Finally, W is an N×N nonnegative spatial
weight matrix of known constants describing the arrangement of the units in the sample. Its diagonal elements are zero by assumption, as no country can be its own neighbor.
However, as Manski (1993) explains, if all K+2 interaction effects are taken into account, there is an identification problem as the parameters will be unidentified. Therefore, at least one of the K+2 interaction effects must be excluded in the final
19 spatial econometric model. Thus, in order to determine which spatial econometric model best suites our dataset we combine the specific-to-general approach and the general-to-specific approach as proposed by Elhorst (2010). First, we will estimate a pooled OLS model without spatial interaction effects, and test if the spatial lag or spatial error model better describes the data.
We do this by using the LM test (Anselin, 1988) and robust LM test (Anselin et al. 1996). Both the classic LM test and the robust LM test are based on the residuals of the OLS model and follow a chi-squared distribution with one degree of freedom and a critical value of 3.86. If the pooled OLS model is rejected in favor of one or both models, we will estimate the spatial Durbin model using maximum likelihood (ML) techniques. Next, using a likelihood ratio (LR) test we test if we can reduce the spatial Durbin model to either the spatial lag or spatial error model. If this is the case, and the (robust) LM test points towards the same model as the LR test (either the spatial lag or spatial error model), than this model best describes the data. If the (robust) LM test points towards a different model than the LR test we adopt the spatial Durbin model. We also adopt the spatial Durbin model if the LR test shows us that we cannot reduce the spatial Durbin model to the spatial lag or spatial error model.
Once we have determined the model which best describes our data, we will analyze the estimate of the autoregressive coefficient ρ and see if there is a spatial dependency between military expenditures among countries.
20 means every neighbor of a country i will have the same amount of influence on this country.
Leenders (2002) also explains that the specification of a weight matrix should be constructed in such a way that it follows from (economic) theory. However, most often economic theory has little to say about the specification of a weight matrix. Therefore, we will specify various weight matrices. In addition, we use Bayesian posterior likelihood probabilities to determine which weight matrix provides results closest to the true specification of the model (LeSage and Page, 2009). Furthermore, a weight matrix has to adhere to one out of two stationarity conditions (Lee, 2004): a) the row and column sums of the weight matrix W, should be uniformly bounded in absolute values as N goes to infinity. b) The row and column sums of the weight matrix , should not diverge to infinity at a rate equal to or faster than the rate of the sample size N. The matrices we use are mentioned in Section 7, and follow at least one of the stationarity conditions.
Finally, as Elhorst (2010) and LeSage and Page (2009) explain, many studies use point estimates of a spatial regression model to test whether or not spatial interaction effects exist. However, in the book of LeSage and Page (2009), they explain that this can lead to wrong conclusions and that a partial derivative interpretation of the impact from changes to the variables of the model specification represents a more valid basis for testing this hypothesis. Without going into technicalities, this partial derivative approach results into the following important properties5. First, if an
explanatory variable in country i changes, the military expenditure of this country i will change. This is called the direct effect. The indirect effects measures the impact on the military expenditure of country i from changing an explanatory variable in all other countries j (j≠i).
For the purpose of clarification, all spatial econometric models show direct and indirect effects. Only the OLS and spatial error model do not have indirect effects6.
Secondly, the direct and indirect effects are different for all the countries in the sample. In order to simplify the presentation of both effects, LeSage and Page (2009) suggest to present one average direct effect and one average indirect effect. The sum
5 For a mathmetical derivation and interpretation of the direct and indirect effects, see Elhorst (2010) 6 For an overview of the specification of direct and indirect effects of different model specifications, see
21 of direct and indirect effects is represented by the total effect. Finally, we will only show the direct and indirect effects of the spatial Durbin model.
7. Results
In this section we discuss and interpret the results of the analysis using the methodology laid out in Section 6. To start with this analysis we make use of a first order binary contiguity weight matrix. A binary contiguity matrix means that when two countries are considered neighbors of each other, this is depicted in the weight matrix, and the corresponding element in the matrix has value 1, and zero
otherwise. In the case of a first order binary matrix only direct neighbors are considered. The vector of explanatory variables corresponds to the variables discussed in Section 4 and use the data discussed in Section 5.
First of all, we carry out the specific-to-general approach. Simultaneously we determine if we need to incorporate spatial and/or time period fixed effects into our model specification. Table 3 reports the results.
<< Table 3 here>>
22 In the next step we want to find out if this model can be extended to the spatial lag or the spatial error model. We perform the classic LM test and the robust LM test in order to find out which model is more appropriate to describe the data. Looking at the classic LM test, both the null hypothesis of no spatial lagged dependent variable (16.44 > 3.86) and the null hypothesis of no spatial auto correlated error term (26.39 > 3.86) must be rejected. When we look at the robust LM tests, the results of the classic LM tests are confirmed (spatial lag: 9.90 > 3.86 and spatial error: 19.84 > 3.86). This indicates that both the spatial lag model and the spatial error model describe the data better than the pooled OLS model with spatial fixed effects. The results of the spatial lag model and the spatial error model are shown in column (1) and (2) of Table 4, respectively. However, using the specific-to-general approach only, we cannot make a distinction between these two models. As a result we do not know whether the spatial lag model outperforms the spatial error model or vice versa. Therefore we also utilize the general-to-specific approach.
<< Table 4 here>>
23 the variables in equation (6) are equal to the interpretation in equations (5a) and (5b).
(6)
Now we turn our attention to the interpretation of the results of the spatial Durbin model. Our main interest is to determine if there exist spatial spillover effects between the military expenditures of different countries. The spatial autoregressive coefficient ρ shows a significant and positive endogenous interaction effect of 0.108. This means the model shows us that the spatial spillover effect exists and military expenditures of countries do depend on each other. Also, Brueckner (2003) explained that a positive coefficient is a common feature of horizontal interaction and of strategic complements in studies which use a spatial spillover model. Our results confirm this common feature.
In our theoretical model we made a distinction between three possible scenarios for this interaction effect. When we look at the coefficient, we see that it is positive, but with a relatively low value. This confirms our expectation that the third scenario we describe in Section 3 applies to our model. In a post-Cold War and increasingly globalizing environment, countries (on average) seem to be able to make a distinction between offensive and defensive arms build-ups. For this reason countries can maintain minimal defensive forces, as long as they do not observe offensive actions from neighboring countries.
24 the claim that military expenditures are a ‘public bad’ is not always valid. Therefore, the result of Collier and Hoeffler (2007) should be adjusted for the case in which countries can make a distinction between different types of arms build-ups.
Next, we look at the direct effects estimates in column (3b). Note that the direct effects estimates are different from the X coefficient estimates in column (3a), due to feedback effects. These feedback effects arise as a result of impacts passing through neighboring countries and back to the countries themselves (Seldadyo et al, 2010). The numerical difference between the coefficient estimates and the direct effects reflect these feedback effects. For example, when we look at this difference for our GDP variable we see that this amounts to an underestimation of its effect by -0.021. Furthermore, when we compare the results of the direct effects to our benchmark model in Table 3, we see large differences for especially the GDP and Population variable.
Turning our attention to these direct effects, we observe that all our explanatory variables give a significant result, except for the Civil War variable. Also, all the explanatory variables show the expected sign. However, the sign of our real GDP variable Lnrgdp does not. We obtain a significant negative coefficient of -0.502 while we expected a positive sign. Hartley and MacDonald (2010) find a similar result. They do not offer a detailed interpretation of this result. Instead, they claim the result may simply reflect the sample period, with a period of relatively high GDP growth of the 1990s coinciding with a post-Cold War cool down of military expenditures. As explained, our dependent variable Mratio is the military burden measure, which is the ratio of military expenditures and GDP. Figure 1 shows the average development of this variable during our time-period 1993-2007.
<<Figure 1 here>>
The figure shows a decline of this ratio over time, which confirms the finding of Hartley and MacDonald (2010). However, to explain why we find a negative relationship between the dependent variable Mratio and the explanatory variable Lnrgdp we return our attention to Table 3.
25 and the (time-series) variation within countries over time. This results in a positive relationship between Mratio and Lnrgdp, as expected in Section 4. By including spatial fixed effects in column (2) we control for the (cross-sectional) variation between countries and only take into account the (time-series) variation within countries over time. When we compare column (1) and column (2) of Table 3, we see that the inclusion of spatial fixed effects has consequences for the sign of Lnrgdp. The negative relationship between Mratio and Lnrgdp in column (2) is caused by the use of spatial fixed effects. In this situation the variation between countries drops out and the focus lies on the variation within countries over time. As Figure 1 shows, the development of the military burden measure Mratio is negative over time. Also Figure 2 shows that the development of Lnrgdp over time is positive. Therefore, we find a negative relationship between the two variables when we use spatial fixed effects.
<<Figure 2 here>>
Secondly, we observe that the Population variable follows the expected sign. A higher population leads to lower military expenditures, possibly because of size effects. Other explanations are given in Section 3. Next the results of International War Inttot en Civil War Civtot also confirm our expectations. However, even though nowadays civil wars are more common than international wars, the direct effect of our Civil War variable Civtot is not significant. As mentioned in the theoretical section, we split these two types of war in different variables as their impact on military expenditures might be different. This is what our results show as well. International wars have dropped significantly after the Cold War. Still, the impact of International War on military expenditures is quite large, with a direct effect coefficient of 0.697 compared to the 0.047 of Civil War. This result confirms our hypothesis of a larger effect from International War on military expenditures, relative to Civil War.
26 autocratic regimes have higher military expenditures, and more democratic countries have relatively lower military expenditures.
Column (3c) of Table 4 shows the indirect effects estimates of our spatial Durbin model. Note that the indirect effects estimates are different than the WX point coefficient esitmates of column (3a), as explained in Section 6. Also note that in our theoretical model in Section 3, we only expected a spatial interaction effect between military expenditures of countries. The resulting spatial Durbin model shows us that there are also spatial interaction effects between several of our explanatory variables and military expenditures of countries.
We observe significant spatial spillover effects for GDP, International War, and Political Regime. Seldadyo et al. (2010) explain that the indirect effects measure the impact on the military expenditure of country i from changing an explanatory variable in all other countries j (j ≠ i). When we look at the indirect effect of GDP we see again that the sign is negative. This is for the same reason as the negative sign for the direct effect explained above, only now the positive development of Lnrgdp of other countries causes the negative effect.
Next, the sign of the indirect effect of International War is the opposite of its direct effect. Apparently, if other countries are at war with each other, military expenditures of country i drop. This could be because country i feels less threatened from countries that are already at war. It is possible that country i observes that these countries are focused on the war they are fighting and do not have the resources to start another war with country i. Finally, Political Regime shows a positive indirect effect. This result is interesting, as the direct effect shows that a country i will decrease its military expenditure when it is a democratic country itself. The opposite is true when we look at the indirect effect. A country will increase its military expenditures the more democratic other countries are. A possible interpretation for the positive indirect effect is as follows.
27 public good among the alliance, some countries could start to spend fewer resources on defense, but still enjoy the benefits of the expenditures of other allied countries. A common feature of alliances such as the NATO and the EU is that many of its members are democratic countries. Therefore, the positive indirect effect of the Polity2 variable reflects an effect as a result of alliances. It indicates that we find a complementary effect of military expenditures as a result of alliance membership. This result can be explained when military expenditures are considered to be both public and private goods in an alliance. Some ally-specific benefits are private among the alliance, but public within an ally (Sander and Hartley, 2001). In this case, interdependence between military expenditures of alliance members depends on the specific consumption relationship (i.e. complementarity, or substitutability) of the jointly produced defense outputs (Flores, 2011)7. Like Flores (2011) we find a positive
relationship. This suggests that allies cooperate and complement their military allocations and military expenditures. Thus, we do not find free-riding behavior with respect to military expenditures in an alliance. The result is also in accordance with Palmer (1990), who explains that solidarity between alliance members also contributes to a positive relationship between the military expenditures of alliance members.
Thus far, the presented and discussed results depend on the choice of our first order binary contiguity weight matrix. We want to investigate whether the conclusions of the model are sensitive to the choice of the spatial weight matrix we use. It is interesting to find out whether the model improves and/or the results of the model change. In Table 5 we present the results of four alternative spatial weight matrix specifications. This table only shows the direct and indirect effects.
<< Table 5 here>>
First of all, column (1) depicts an inverse distance matrix based on the physical distance between the capitals of every pair of countries. Column (2) presents the results of a border-length matrix which shows how many kilometers of border two countries share. Column (3) and column (4) show the results of a second and third order binary contiguity matrix, respectively. The use of these different weight matrices does not change the results of the analysis for the model specification that
7 A detailed explanation of this model goes beyond the scope of this paper. For a theoretical overview
28 most accurately describes the data. For these four matrices, this analysis also points towards a spatial Durbin model with spatial fixed effects. When we compare the results of these four models with the results of the model with a first order binary contiguity matrix, we see that the values of the estimates fluctuate somewhat, although no large differences are observed. Moreover, there is also no change in the significance of the explanatory variables.
Nevertheless, we want to determine which spatial weight matrix best describes the data and is the most appropriate for our spatial Durbin model. We use Bayesian posterior model probability techniques to determine this. The result of this test is shown in Table 5, with the probability for the first order binary contiguity matrix in the footnote of this table. The model which shows the highest probability is the model we rely on.
When we compare the results of the Bayesian posterior model probabilities, we notice that the first-order binary contiguity matrix has a probability of 0.0044. Next, the models with the inverse distance matrix and the border length matrix have probabilities of respectively 0.0001 and 0.0003. Finally, the second and third order binary contiguity matrices have probabilities of respectively 0.2609 and 0.7343. We therefore conclude that the model with a third order binary contiguity spatial weight matrix outperforms the models based on other weight matrices. This means that our results show that a country’s military expenditures are not only influenced by their direct neighbors. They are also influenced by countries which are located further away. Since the weight matrix with the best fit is a third order binary contiguity matrix, this means that a country is influenced by its three nearest neighbors.
29 As mentioned, the new value of the spatial autoregressive coefficient ρ is 0.184. This value is still relatively low. Therefore the interpretation of this coefficient does not change compared to the results discussed previously. In the post-Cold War time period, countries seem to be able to discern offensive weapon build-ups from defensive build-ups or are not very worried that a war will break out. For this reason countries can maintain minimal defensive forces.
Finally, the coefficients of our other variables are quite close to the estimates of the model with a first order binary contiguity matrix. Also, the significance of these coefficients does not change and their interpretation therefore remains the same as discussed above.
8. Conclusions
In this paper we investigate the determinants of military expenditure. We are particularly interested in spatial interaction effects between countries and their military expenditures. In the literature several methods and various groups of factors are discussed. See for example Richardson (1960), Smith (1989), Dunne and Perlo-Freeman (2003a/b), and Goldsmith (2007). To our knowledge, thus far Goldsmith (2007) and Flores (2011) are the only papers that also incorporate spatial econometric techniques to answer this question.
For our theoretical building block we choose to follow Smith (1989) and use a neo-classical welfare model. This model uses security as an integral component which is represented by military expenditures. In order to incorporate a spatial dependence in our theoretical model, we use a spillover model as suggested by Brueckner (2003). In this spillover model, the level of military expenditure for a given government depends on the choices for military expenditure of other governments, which indicates the presence of spillover effects. The theory of security dilemma (Jervis, 1978) as interpreted by Goldsmith (2007) gives us three explanations for different types of spatial dependencies that can occur.
30 for GDP and Population. Political factors are represented by the Political Regime of a country. Strategic factors include the presence of International and Civil War.
We use a static spatial panel data approach to analyze these determinants. The sample spans across a time period of 15 years, from 1993 to 2007 and includes data from 120 countries. First of all, we find that including spatial interaction effects improves the results of the model. After estimating a spatial lag model, a spatial error model, and a spatial Durbin model we conclude that the spatial Durbin model best describes the data. This means we include both endogenous and exogenous spatial interaction effects in our model specification. Next, our results show that a model specification which uses spatial fixed effects and a third order binary contiguity spatial weight matrix describes the model with the highest fit.
The main result of this paper indicates that there is a significant positive endogenous interaction effect. Therefore, we find spatial dependency between countries and the military expenditures of a country depend on the choices for military expenditures of other countries. When we interpret this spatial dependency, one of the explanations provided by Goldsmith (2007) matches our result. We observe a positive interaction effect at a relatively low value. This leads to the conclusion that countries are able to make a distinction between offensive and defensive arms build-ups of other countries. For this reason countries can maintain minimal defensive forces, as long as they do not observe offensive actions from neighboring countries. This result is also in accordance with the observation that international wars are decreasing which means countries have a low expectancy for the occurrence of a war.
For the interpretation of our explanatory variables we use a partial derivatives approach as suggested by LeSage and Page (2009). This approach yields two estimates. First, a direct effect. This effect reflects the impact of a change in an explanatory variable of country i, on the military expenditure of country i itself.
31 expenditure. However, the impact of an International War is much larger than a Civil War. Our Political Regime variable shows that an autocratic country will spend more on military than will a democratic country.
Secondly, the indirect effects. This effect measures the impact on the military expenditure of country i from changing an explanatory variable in all other countries j (j ≠ i). The main findings of the indirect effects estimates are as follows. We observe significant spatial spillover effects for GDP, International War, and Political Regime. GDP of other countries has negative effect on the military expenditure in country i. This is for the same reason as the negative effect of the direct effects estimate.
Next, if other countries are participants in an International War, country i feels less threatened by these countries and lowers its military expenditures. Perhaps country i can discern that countries at war do not have the resources to start a war with another country as well. Secondly, the indirect effect estimate of Political Regime shows a positive value. This means that even though country i will decrease its military expenditure when it is a democratic country itself, it will increase its military expenditures the more democratic other countries are. An explanation for this result is alliances, as many alliance members are democratic countries. We find a complementary effect of military expenditures within an alliance, due to the public and private good nature of military expenditure within an alliance.
Finally, this paper contributes to the literature by using a comprehensive spatial econometric approach combined with a neo-classical welfare model. We find a positive spatial dependency regarding the military expenditures of countries. Even though there is quite some literature on the determinants of military expenditure this is one of the first papers using spatial econometric techniques. Future research could expand this method by looking at the possibility of a dynamic spatial panel model. Potentially, the lag of military expenditure could very well be an important determinant of the model. However, its estimation goes beyond the scope of this paper. Furthermore, typical econometric tests for robustness such as tests for heteroskedasticity, autocorrelation, and endogeneity are not applied in this study. These tests are not (yet) readily available in spatial panel estimations.
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36 Appendix.
Table 1. Variable Description
Variable Abbreviation Source Dependent Variable
Military Burden Mratio Elhorst Explanatory Variables
GDP Lnrgdp Elhorst Population Lnpop Elhorst International War Inttot MEPV Civil War Civtot MEPV Political Regime Polity2 PolityIV
Table 2. Descriptive Statistics
37 Table 3. Estimation results using panel data models without spatial interaction effects.
Determinants (1) (2) (3) (4) Pooled OLS Spatial fixed effects Time-period
fixed effects
Spatial and time-period fixed effects Lnrgdp 0.407*** (13.71) -0.622*** (-5.10) 0.412*** (13.96) -0.603*** (-3.71) Lnpop -0.573*** (-13.53) -1.724** (-4.64) -0.569*** (-13.51) -1.526*** (-3.74) Inttot 0.918*** (6.26) 0.664*** (8.43) 0.905*** (6.19) 0.674*** (8.57) Civtot 0.296*** (8.65 ) 0.037 (1.15) 0.283*** (8.27) 0.029 (0.88) Polity2 -0.164*** (-21.89) -0.025*** (-2.48) -0.163*** (-21.89) -0.026*** (-2.60) Intercept 2.464*** (4.43) σ2 3.338 0.7515 3.2955 0.7431 R2 0.2632 0.8341 0.2724 0.8359 LogL -3636.3 -2294.4 -3624.9 -2284.3 LM spatial lag 352.19 16.44 342.87 12.09 LM spatial error 212.45 26.39 203.77 20.17 robust LM spatial lag 140.39 9.90 170.35 13.58 robust LM spatial error 0.65 19.84 31.25 21.66
