Page | 1 Rijksuniversiteit Groningen Faculty of Economics and Business
MSc Thesis Economics
Military Expenditure, Security, and Growth in Latin and Central America
By Reinder Riemersma
Name: Reinder Riemersma Student number: s1494872
Email: riemersmareinder@gmail.com Supervisor: Dr. G.H. Kuper
Date: Tuesday, June 5, 2012
Page | 2 Abstract
The purpose of this paper is to investigate the relationship between military expenditure and economic growth. The assumption made in this paper is that the relative size of a country’s military expenditure versus the military expenditure of neighboring countries, a country’s security web, defines the level of security and thereby influences economic growth. A
framework is presented to theoretically substantiate this conjecture. To test the outcomes of this framework, a Barro-type growth model is examined for the Latin and Central American region using a two-way fixed effects panel model. For the period 2000-2010, military expenditure is higher than the optimal expenditure level, resulting in a negative significant relationship between military expenditure and growth. The conjecture that neighboring countries can militarily
threaten each other is justified by showing a significant negative effect of a country’s security web on growth.
JEL classification codes: H56, O47, O54
Keywords: military expenditure, security, economic growth
Page | 3 1. Introduction
The recent global financial crisis has led to a dramatic increase in public deficits of many developed countries, enforcing governments to take deficit-reduction measures. One of the electorally most popular measures is to reduce the amount of military spending in a country. The reason explaining this popularity is the problem of measuring the effect on output. Military spending is generally seen as having opportunity costs, cutting back on military spending liberates billions of dollars that can be reinvested in other more direct growth enhancing investments. A political term referring to this reinvestment is “the peace dividend” introduced after the Cold War by former US president George H.W. Bush. The Cold War was a continuing arms race between the western and communist countries that started after the Second World War. It ended after the collapse of the Soviet Union in 1991, resulting in decreased military tension, and causing an overall downward trend in the worldwide military expenditure levels.
Figure 1, illustrates this trend. However, after 1998 the trend reversed. According to the SIPRI
Figure 1: world military expenditure 1988-2011, in constant 2010 US$ billions. Source: Stockholm International Peace Research Institute Military Expenditure Database 2011 (data for 1991 is unavailable).
Page | 4 Yearbook (2011), the upward trend is explained by a combination of factors. One of the most important factors is the rise in military spending of booming developing nations like China and India. China, for example, increased its military expenditure by a staggering 256 percent in the last ten years. Another important factor is the involvement of countries into armed conflicts that contributed to multilateral peacekeeping operations. For example, the US increased its military spending by 83 percent in the last ten years, as a result of the involvement in peacekeeping operations in Afghanistan and Iraq. The recent global financial crisis has left worldwide military spending essentially unchanged in 2011, breaking the 13-year trend of continuous military spending increases.
Figure 2 illustrates the rise of military spending in the US and gives a closer look on the military spending patterns of other regions. The size of each dot shows the size of military spending in each region, while the movement of each dot characterizes the percentage change of military expenditure (2002=100).
Figure 2: regional military spending 2002-2011, 2002=100. Source: Stockholm International Peace Research Institute Military Expenditure Database 2011.
Page | 5 Western countries (North America and Western & Central Europe) display a stable or even negative trend in their military expenditure levels after the start of the crisis in 2008. The US, for example, decreased its real military spending level in 2011 with 1.2 percent, indicating the first decrease since 1998. The notion that the recent global financial crisis has affected western countries the most gives rise to the idea that cutting back on military expenditure is a popular deficit-reduction measure in times of crisis. The question that arises is whether these military reductions are harmful to the economies of the countries adopting these cuts.
In fact, military expenditure can positively impact growth. One of the most important and straightforward effects is the indirect effect on growth via the security channel. In his Wealth of Nations (1776), Adam Smith stated the following:
“The first duty of the sovereign, that of protecting the society from the violence and invasion of other independent societies, can be performed only by means of a military force”
A country’s security is of vital importance to enhance economic development. To achieve a secure environment, a country needs to be protected against threats. In the sense that a military force can be obtained through military expenditure, the indirect effect of military expenditure on growth is the provision of defense via the military force.
However, some difficulties arise in determining the extent of this effect. According to Dunne (1990), defense can be shown as being a purely public good, incorporating two important market failures: non-rivalry and non-excludability. Another important characteristic of defense is the presence of externalities, increasing military expenditure in a country may result in positive externalities on allies or in negative externalities on adversaries. These three characteristics give rise to the difficulties in measuring the growth effect of defense.
Benoit (1973, 1978) was the first to investigate the link between military spending and economic growth. He found that military expenditure positively influences economic growth. After his study, the nexus has been examined more extensively. Section 2 of this paper will present a brief survey of the existing literature.
In the sense that military expenditure “produces” security, it is the perception of threat that is of
importance to find the indirect effect on growth. Without any forms of threat, the significance of
Page | 6 security is minimal. Aizenman and Glick (2003) were the first to ground this notion with a
theoretical growth model. They found a nonlinear function between military spending and militarized threat posed by foreign countries and other external forces. Military expenditure driven by threat enhances growth, whereas military expenditure driven by rent-seeking diminishes growth.
The model presented in this paper is built on the specifications of the Aizenman and Glick (2003) model. In their framework threat is approximated by incidences of conflict between a country and its foreign adversaries. The theoretical model outlined in this paper deviates from this approximation and proxies threat by the military spending levels of a country’s neighbors.
Defining threat in this manner enables neighboring countries to militarily threaten each other.
According to Rosh (1988), the biggest threat comes from foreign countries that are closest to the domestic country. The greater the distance between countries, the less effective their military action towards each other. Following this definition, the conjecture made in this paper is that the relative size of military expenditure of a country versus the size of military expenditures of its neighboring countries defines the level of security, and via this security channel military expenditure influences economic growth.
The defense economics literature shows large heterogeneity in the results of the effect of military expenditure on growth between regions. Therefore, to empirically test the conjecture, a panel analysis has been made for the Latin and Central American region, the region with the largest data availability on military spending. Figure 2 illustrates that the Latin American region is one of the regions with the smallest absolute level of defense expenditure. However, the region shows the most rapid growth in military spending in 2010, with a rise of 5.8 percent, versus 1.3 percent worldwide.
The remainder of this paper is structured as follows. Section 2 briefly summarizes the existing
literature on the nexus between military expenditure and growth, and highlights the most
important theoretical models. Section 3 gives an overview of the results on the nexus for the
Latin American region. Section 4 outlines the theoretical model. Section 5 introduces the two-
way fixed effects Barro-type growth model. Section 6 defines, and characterizes, the panel data
Page | 7 used. Section 7 presents the obtained results. Finally, section 8 will provide a conclusion and give some comments on possible future extensions of this study.
2. Literature Overview
Nowadays, a large number of empirical papers on the effects of military spending on economic growth exist. It all began, however, with the cross-country analysis made by Benoit (1973, 1978). He was the first one to investigate the possible linkage between military spending and economic growth using a cross-section analysis of 44 least developed countries (LDCs) for the period 1950-1965. He came to the surprising conclusion that countries having higher military expenditure as a percentage of GDP; a higher military burden, face higher growth rates. Since his findings were so unexpected, a majority of the following research has been on the validation of his results. The bulk of the literature, however, rejects Benoit’s findings. The two biggest criticisms on Benoit’s work were on his multiple regression growth models, being largely ad hoc; and on the heterogeneity of his sample of countries. Frederiksen and Looney (1983), for example, divided the countries in Benoit’s sample into financial constrained and financial unconstrained countries. They found a positive and statistically significant influence of military expenditure on growth for the financial unconstrained group of countries, and a significant negative influence for the financial constrained group of countries.
As a result of this diversity in results, a variety of economic and econometric models has been
created to further investigate the relationship between military expenditure and growth, all from
a different theoretical perspective. Dunne et al. (2005) divided these different perspectives into
three main channels: the demand channel, the supply channel, and the security channel.
Page | 8 2.1 Demand Channel
The first approach made in the literature is that military expenditure influences economic growth via the demand channel; the Keynesian approach. According to Dunne et al. (2005), aggregate demand is affected through the Keynesian multiplier. An increase in military expenditure increases aggregate demand; and if scarce capacity exists, it will increase the utilization of capital and reduce unemployment. Furthermore, in developing countries, defense is often deployed in social, demand enhancing infrastructural projects (e.g.: building roads, improving communication networks, etc). On the other hand, defense exhibits opportunity costs and crowds out other forms of investment. According to Dunne et al. (2005), the range and form of this crowding out effect depends on the prior utilization of resources, and on the way military expenses are financed. Given the government budget constraints, there are several ways to finance an increase in military expenditure: a decrease in other forms of public expenditure, an increase in taxes, an increase in the supply of money, or an increase in debt. Obviously, these different financing methods will all have different effects on economic growth. In addition, Dunne et al. (2005) mentioned that a change in military expenditure will alter the composition of industrial output via input-output effects.
The most influential papers that analyze the effect of military expenditure on growth via the
Keynesian approach are Deger and Smith (1983), and Faini et al. (1984). Deger and Smith
(1983) estimate a traditional 3 simultaneous-equations model for 50 LDCs for the period 1965-
1973. They find a small positive direct effect of defense spending on growth via resource
mobilization and modernization effects, and a larger negative indirect effect via the negative
effect on savings. As a result, they find that the total effect of military spending on growth is
negative. Faini et al. (1984) estimate a Keynesian growth model for 69 countries over the period
1952-1970. In accordance with Deger and Smith, they find a generally significant negative effect
of defense spending on economic growth.
Page | 9 2.2 Supply Channel
The second approach made in the literature is that military expenditure impacts economic growth via the supply channel; the neoclassical approach. Production factors deployed in the defense sector cannot be deployed elsewhere. In other words, the military sector competes with the civilian sector for the same pool of labor and capital. But according to Dunne (2005), the defense sector may also induce several forms of positive externalities. Military expenditure may enhance the level of human capital via training and education of the defense workforce, and military research and development may lead to commercial spin-offs (e.g. the internet, GPS systems, and Boeing’s 707).
2.2.1. The Feder-Ram Model
The most influential neoclassical model on the link between military expenditure and economic growth is an externalities model introduced by Biswas and Ram (1986), adapted from Feder’s (1983) model on export.
The Feder-Ram model allows one to examine the externality effect of the military on the civilian sector, and to examine the difference in factor productivity between these two sectors. They divide the economy into two sectors: the military ( ), and civilian ( ) sector. Both sectors have neoclassical production functions, with labor ( ) and capital ( ) as their inputs.
( ) ( ),
where the subscripts denote the level of each input to each sector.
The factor endowments constraints are given by:
.
Total output ( ) is represented as military output plus civilian output:
Page | 10 .
Furthermore, the assumption made is that the marginal productivity between civilian and military output differs by a value of .
,
where the subscripts denote the partial derivatives.
After taking time derivatives of the total output function, the total factor endowments and sectorial output functions, and using the difference in marginal productivity; the neoclassical growth function can be represented by:
̇ ̇ (
) ̇ ̇,
where the dot notation indicates the rate of growth of the variables (e.g.: ̇
) ; indicates
; indicates ; represents net investment, ; and represents the externality parameter.
Biswas and Ram (1986) investigate this equation using cross-sectional data of 58 LDCs between 1960-70 and 1970-77. However, they fail to find any significant effect of military expenditure on economic growth. After 1986, many others use variants of the Feder-Ram model to further investigate the link between military spending and economic growth. The results of these studies are mixed, both interregional and for single countries. Biswas (1993) uses the Feder-Ram model to examine the link for 74 LDCs over the period 1981-1989. He finds a positive and significant effect of defense spending on growth. Mint and Stevenson (1995) divide the economy into three sectors: the non-government, the military component of government, and the non-military component of government sector. They estimate a Feder-Ram 3-sector model for 104 countries, for the period 1950-1985. In most of their individual-country estimates, they fail to find a
significant relationship between defense spending and growth. Atesoglu and Mueller (1990), and Huang and Mintz (1991) estimate the Feder-Ram model for the US, using time-series data.
Making use of the Feder-Ram 2-sector model, Atesoglu and Mueller find a small positive effect
Page | 11 of defense spending on growth for the 1948-1990 period. On the other hand, Huang and Mintz use a Feder-Ram 3-sector model and fail to find a significant effect during 1952-1988.
2.2.2 The Augmented Solow-Swan Model
Besides the Feder-Ram model, there is another influential neoclassical approach in examining the relationship between military expenditure and economic growth. Knight et al. (1996) extend the Solow growth model of Mankiw et al. (1992) by including a linkage between military expenditure and economic growth.
Knight et al. (1996) assume a neoclassical Harrod-neutral production function:
( ) ( ) ( ) ( )
. In which:
( ) ( )
( ) ,
where ( ) equals the military burden , and influences labor-augmenting technological change; and represents the technological growth rate.
Given the standard Solow-Swan assumptions, the steady-state level of output per effective unit of labor is defined as:
[
]
( ),
where is the exogenous savings rate; the constant labor force growth rate; and the capital depreciation rate.
The transitory dynamics of the output per effective unit of labor around its steady-state are
represented by:
Page | 12 ( ) ( ) ( ) { ( )
( ) } ( )
( ) ( ( ) ) , where ( )( ).
According to the steady-state level and the dynamics around this level, a permanent change in the military burden does not alter the steady-state growth level. However, it does affect the transitory growth rates along the path towards the steady-state growth level.
In order to test this model empirically, Knight et al. (1996) use panel data of 79 countries for the period 1971-1985. They find that military spending has a large and negative effect on economic growth. The negative indirect impact, via the impact on productive investment, is also
statistically significant. Dunne and Nikolaidou (2011) investigate the augmented Solow-Swan model for 15 European Union countries over the period 1961-2007, using both panel and time- series methods. They reject a postive linkage between military expenditure and economic growth.
2.3. Security Channel
In 1776, Adam Smith already mentioned the importance of security for governments of countries. A more secure environment will tend to increase private investment and innovation, and therefore will increase economic output. Especially in developing countries, a lack of
security as a result of external and civil wars has led to lower levels of economic development. In the sense that military expenditure increases the security level via the military force, it will have a growth enhancing impact on an economy. However, in the absence of threat, military
expenditure is not grounded by security level improvements but by rent-seeking activities of the government, and will thereby decrease economic growth. The linkage between military
expenditure and security is one of the main explanations for the nonlinear relationship found in
the more recent literature between military expenditure and economic growth. For countries with
a relatively low level of security additional military spending positively influences growth,
Page | 13 whereas for countries with a relatively high level of security additional military spending
negatively influences economic growth.
Landau (1993) suggests that national security faces a higher level of threat when neighboring countries adopt higher military expenditure schedules. He finds empirical evidence that a greater level of threat imposed on a country stimulates policy makers of developing countries to adopt more economically efficient public sector policies. More specifically, a larger tax base is needed to finance an increase in military expenditure. In order to generate such a larger tax base, policy makers have a greater incentive to adopt more productive government policies. Using a sample of 71 countries, Landau finds support for a quadratic relationship between military expenditure and economic growth. This indicates that the effect of an increase of military spending on economic growth is positive for countries with a relatively low military burden, whereas a similar increase of military spending in countries with a high military burden elaborates a negative effect. However, for a subsample of 47 countries, Landau finds no significant evidence supporting the quadratic relationship.
Continuing on Landau’s research, using a Barro-type growth model to investigate panel data of 44 LDCs for the period 1975-1989, Stroup and Heckelmann (2001) find empirical results
supporting the suggested nonlinear link between military expenditure and economic growth. The effect on growth is positive for low levels of military spending and military labor use and turns negative for higher levels.
However, the most influential theoretical model implementing this nonlinear relationship
together with the notion that military expenditure increases national security is the model derived
by Aizenman and Glick (2003). They present an extended version of Barro and Sala-i-Martin
(1995), and incorporate nonlinearities in the model. Since the theoretical model outlined in this
study is based on the Aizenman and Glick model, their model specifications and underlying
assumptions are further discussed in Section 4 of this paper. They find that military spending by
itself does not impact economic growth. Military spending in the presence of external threat,
however, enhances economic growth. Specifically, in countries that face a relatively smaller
threat, an increase in military spending has a negative influence on economic growth. Whereas in
countries that face a relatively greater threat, military spending enhances economic growth.
Page | 14 In general, there is no formal consensus on the effect of military spending on economic growth.
Defense literature shows large differences in results between the different channel approaches of the studies. Also within each channel, the literature yields different outcomes.
3. Empirical evidence in Latin America
According to Section 2, throughout the history of defense economics, military expenditure influences economic growth via three channels: the demand channel, the supply channel, and the security channel. In the literature, no study empirically estimates the link for a sample of Central American countries; however, there are empirical estimates for the Latin American region. This section highlights these results via the three channels.
3.1 Demand Channel
Deger and Smith’s (1983) selection of 50 LDCs includes a sample of 12 Latin American countries. They obtained data from two different sources: the U.S. Arms Control Disarmament Agency (ACDA), and the Stockholm International Peace Research Institute (SIPRI). For the ACDA data, they find a negative influence of the military burden on economic growth for the Latin American sample. However, for the SIPRI data, they find a positive relationship.
Lim (1983) estimates a logarithmic cross-sectional regression with ordinary least squares, using
a Harrod-Domar growth model for 54 LDCs, subdivided into six different regions, for the period
1965-1973. He finds interregional differences in the relationship between the military burden and
economic growth. For the Latin American sample of 13 countries, the relationship between the
military burden and economic growth is negative and significant.
Page | 15 In line with Deger and Smith (1983) and Lim (1983), Faini et al. (1984) find an adverse
relationship for the period 1952-1970 between the military burden and economic growth in Latin American countries.
3.2 Supply Channel
In Knight’s (1996) analysis on the effect of military spending on investment and economic growth, a dummy variable for Latin American countries is incorporated, which has the expected significant negative sign. Indicating that military expenditure negatively influences investment and economic growth.
In contrast with Knight (1996), Murdoch et al. (1997) find evidence that defense spending is growth enhancing. They estimate a Feder-Ram 3-sector type growth model through a two-way fixed effects pooled model for 8 Asian and 16 Latin American countries over the period 1954- 1988. When using an ordinary least squares estimation technique, however, their results are inconclusive and insignificant.
3.3 Security Channel
Landau (1993) predicts a non-linear relationship between military spending and growth.
However, for the subsample of Latin American countries, he finds an insignificant relationship between military spending and growth.
Stroup and Heckelman (2001) make a distinction between African and Latin American countries in their panel data analysis. For the sample average levels of 21 Latin American countries, they find evidence that military expenditure negatively influences economic growth and that military labor use positively impacts economic growth. However, when the average level of male
educational attainment in a country increases, this positive effect diminishes considerably.
Page | 16 Concluding, the only study that finds empirical evidence on a postive relationship between
military spending and economic growth for the Latin American region is Murdoch et al. (1997).
The other studies support an adverse relationship.
4. Theoretical Model
The theoretical model is based on the extension Aizenman and Glick (2003) made on Barro’s (1990) economic growth model. They model the interaction between growth, military spending, and external threat. Their starting point is the assumption that national security, defined as the relation between military expenditure and external threat, influences the production function, where the production factors exhibit constant returns to scale, directly:
( )
( ) , (1)
in which is an exogenous productivity factor, is the capital/labor ratio, is the
infrastructure/labor ratio; the non-military expenditure, and represents the national security level in a country. They use the following mathematical form for the national security level of a country:
( )
( ) ( ) , (2)
where denotes the domestic military expenditure and is a proxy for the foreign level of threat from potential adversaries. The proxy for threat is defined as the number of years a
country was at war with each of its adversaries during a certain period summed over the set of its
adversaries. Note that given this definition of security, measures the output cost of the
external threat of the country’s potential adversaries.
Page | 17 However, Smith (1980) and others in the defense economics literature define national security as being dependent on the military expenditure of a country relative to the military expenditure of its opponent:
( ) ( )
in which denotes national security, military expenditure of a country, and military expenditure of a country’s opponent.
When defining national security in this manner, adversaries can militarily threaten each other.
Apparently, the biggest threat comes from countries that share a border with a certain developing country. According to Starr and Most (1976), the more borders a country has, the great the risk confronting the country, and thus the higher the need to protect itself against potential enemies.
As a result, a country with many neighbors has a higher likelihood of getting involved in a conflict, and is thus confronted with a higher perceived level of threat. Rosh (1988) states that in the Third World the distance between two countries is of utmost importance in determining the degree in which states can militarily threaten each other’s security. The greater the distance between countries, the less effective is their military action towards each other. Therefore, security of a country is highly dependent on the military burden relative the burdens of the potential adversaries.
To determine the perceived threat, Rosh (1988) adopts the concept of a country’s security web.
The security web of a developing country is the average military expenditure of countries that share a border, and therefore pose a potential threat. Military superpowers (USA, China, and Russia) are left out of these security webs, since their military is of such a size that developing countries cannot defend themselves against them. The security web is represented in the following functional form:
∑
, (3)
Page | 18 in which denotes a developing country’s security web, represents military expenditure of the potential adversaries as a percentage of gross domestic product (the military burden), and denotes the number of countries that are a potential threat to a developing country.
The relative size of a country’s military burden is used since a country can only spend a certain absolute amount of its resources on military, regardless of the absolute military expenditure of its neighbors. Therefore, a country is more concerned with the relative expenditure on military than with the absolute expenditure. A country with a relatively high military burden conceals a larger threat than a country with a relatively low military burden. In the same line of reasoning, the average of the military expenditure of potential adversaries is used instead of an additive
approach. Since more potential adversaries with relatively low military burdens impose a smaller threat than one potential adversary with a relatively high burden.
In Smith’s (1980) model, can be used as an estimate for ; the military expenditure of a developing country’s opponent
1. This results in:
( ) ( ) . (4)
Following this formulation, an increase in a country’s military burden together with an offsetting increase in the burden of its security web, leaves the national security unchanged. Furthermore, implies a decreasing rate of return of military burden increases on the level of national security.
From substituting Equation (4) for ( ) in the output function (1) and continuing to assume that the production factors exhibit constant returns to scale, Equation (1) can now be written as:
1 Note that given this functional form of national security, members of military alliances, such as the NATO are excluded from analyses. Members of such an alliance that share a border do not impose a threat towards each other. On the contrary, an increase in the military burden of a neighboring NATO member increases the security level of a NATO member, as a result of their principle of collective defense.
Page | 19
( ) ( ) . (5)
In line with Aizenman and Glick (2003), corruption is introduced into the model. Following Aizenman and Glick, the assumption is made that corruption enters the model as a leakage of tax revenue, ( ), in which the greater the leakage , the greater the level of
corruption. If , there is complete leakage of tax revenue; public expenditure cannot be financed by tax revenues, and if there is no leakage of tax revenue; the total tax revenue can be used to finance government’s public expenditure.
Therefore, Equation (5) becomes:
( ( )) (
( )) . (6)
Furthermore, represents the ratio of military to non-military expenditure:
. (7)
In line with Barro’s model (1990), the government divides its public expenditure between military and non-military expenditure, and finances it by means of a proportional income tax rate .
( ) . (8)
The representative agent chooses consumption, , and capital, , to maximize its future utility level given its preferences, which are represented by:
∫
. (9)
According to Barro’s (1990) model, given the utility function (9), the growth rate of consumption and output can be written as
2:
2 See also the Mathematical Appendix (A4) for the derivation.
Page | 20
(( )( ) ). (10)
In order to derive the maximal output growth rate, the optimal values for , ̃, and , ̃, are calculated
3. From the appendix it follows:
̃ ; (11)
̃ . (12)
Note that in the absence of military spending, Equation (12) becomes ̃ , which equals the productive-efficiency condition that determines the optimal size of the government that maximizes utility if the technology is Cobb-Douglas, as derived by Barro (1990).
From equations (11) and (12), both the optimal tax rate and the optimal ratio of military to non- military expenditure only depend on the output elasticity of non-military government
expenditure and security. This implies that they are independent of the security function, and thus of their security web. Stated differently, the military burden of a country’s adversaries has no impact on the optimal ratio of military to non-military expenditure, nor on the optimal
proportional tax rate. Also from Equation (11), ̃ , implying that the optimal ratio of military spending is a positive number.
The derived optimal value ̃ , is in line with Stroup and Heckelman (2001). If the military burden is lower than its optimal burden, indicating that the military burden positively influences economic growth. In this case, the direct and indirect benefits of military expenditure dominate its opportunity costs. Likewise, if : the military burden is higher than its optimal level, resulting in a negative impact on economic growth. The opportunity costs of military expenditure dominate its direct and indirect benefits.
3 See the Mathematical Appendix for the derivation of ̃ and ̃. Equations (11) and (12) are derived by solving the underlying first-order conditions, in order to maximize . Applying the properties that are given in equations (7) and (8), and the implicit function theorem with respect to ̃ and ̃ .
Page | 21 Note that Equation (12) also can be written as: ̃( ̃) ( ̃) (see Equation (A13) in
Appendix A4), which equals the outcome derived by Aizenman and Glick (2003). The optimal outcome of the ratio of military to non-military expenditure of this model is a special case of the Aizenman and Glick model
4, if both optimal outcomes coincide. In other words, if the output cost of the threat, as defined by Aizenman and Glick, equals the output elasticity of the national security function, both models yield the same outcome.
Given the outcomes for the optimal proportional tax rate, and the optimal military to non- military expenditure ratio; the optimal growth rate can be represented by
5:
̃ [( )
( )
(
( ))
] . (13)
And in the reduced form:
̃ ̃( ) ̃ ̃ ̃ . (14)
Following Equation (13), a higher productivity level increases the optimal growth rate of a country. Furthermore, a higher level of corruption and higher military burdens of the country’s adversaries (higher security web) reduce the optimal growth rate of a country.
4 From comparing the optimal military to non-military ratio with the optimal ratio as derived by Aizenman and Glick, ̃ it follows that .
5 Equation (13) is derived from inserting the optimal level of output ̃ into Equation (10).
Page | 22 5. Empirical Model
This section introduces a Barro-type growth model that is used to empirically test the robustness of the outcomes of the theoretical model outlined in the previous section for a group of 11 Latin American and 5 Central American countries. To allow for observed heterogeneity between countries and time periods, a two-way fixed-effect panel analysis has been made, incorporating both cross-sectional and period fixed-effects.
The statistical linear representation of the economic growth model (13) is represented by
6:
, (15) where represent the coefficients for n variables; the cross-section fixed effects; the period fixed effects;
the military burdens;
the security webs;
the levels of corruption;
the sets of control variables; and
the error terms.
From Equation (14), the theoretical model suggests the following outcomes:
̃ ̃ .
According to Equation (15), ̃ is represented by , and ̃ by .
Comparing these derived outcomes with the empirical model results in the following specifications:
- ̃ ;
- ̃ . (16)
6 Since the theoretical model suggests nonlinearities in the relationship between military expenditure and growth, the squared term of military expenditure is introduced in the statistical linear representation of the theoretical model. The results of this model are represented in Appendix A2. From Table A2, the squared term of military expenditure is insignificant. As a result, the rest of this paper focusses on the empirical model represented in Equation (15).
Page | 23 Equation (14) predicts negative coefficients for respectively the security web , and the level of corruption .
The most interesting coefficient, however, is . According to the theoretical model, the sign of depends only on the output elasticity of government expenditure and security. If the country is on its optimal growth path ̃ , military expenditure does not influence economic growth;
. However, if , military expenditure increases economic growth; . Otherwise, if military expenditure decreases economic growth; .
The majority of the results of previous studies on the nexus for the Latin American region, as discussed in sector three, indicate a negative relationship between military expenditure and economic growth. Considering the theoretical model and given the fact that the sample of countries consists for the largest part of Latin American countries, the prediction is that .
The expected signs of the slope coefficients of the standard set of control variables in Barro-type growth models are represented in Table 1.
Table 1: expected signs of the coefficients for the control variables.
Variables Coefficient Explanation
(
) - Conditional convergence hypothesis: countries with initially low gross domestic product levels tend to grow at higher rates than countries with initially high levels; the catch-up effect
- A higher growth of the population decreases economic per capita growth
+ An increase in educational attainment, increases human capital and thus growth
+ Investment has a positive relationship with growth
Page | 24 6. Data
The annual data on growth of real per capita GDP,
, is obtained from the World Development Indicators 2012 database (WDI) constructed by the World Bank.
Data on the military burdens of the Latin and Central American countries in the sample,
military expenditure as a percentage of GDP, is obtained from the SIPRI military expenditure database. Their security webs,
, are derived using Equation (3); the average of the military burdens of a country’s potential adversaries. Appendix A1 gives an outline of these security webs. The countries that are presented in parentheses are left out of the security webs, due to missing data on their military burdens. These countries include: Costa Rica, Suriname, French- Guinea, Guyana, and Panama. This, however, does not alter the results of
, since these countries are too small; their military burden is too low to be of any threat to their potential opponents. Take Costa Rica, for example, its military burden is less than 0.05 percent, and is therefore too small to be a threat to its potential opponents. Furthermore, there is only data available on the military burden of Honduras for the period 2000-2010. Since the military burden of Honduras is too large to be left out of the security webs of El Salvador, Guatemala, and
Nicaragua; data on their webs is also available for 2000-2010. This effectively restricts the length of the sample period.
The control variables used in the model are: the log of the level of real GDP of the previous year,
; the share of investment to GDP,
; population growth,
; and the level of education as a proxy for human capital,
. The share of total investment to GDP is
measured by using data on gross fixed capital formation for 2000-2010. The level of education is defined as the average years of total schooling of the population over 25 years.
Data on the initial real GDP levels, population growth, and gross fixed capital formation is obtained from the WDI 2012 database. The data on the level of education is constructed from the Barro-Lee dataset, provided by the World Bank. Barro-Lee built a dataset on educational
attainment for five-year periods. The data on educational attainment used in this model is
Page | 25 constructed by linearly interpolating these five-year periods into annual figures for the period 1999-2010.
Finally, in line with the Aizenman and Glick model (2003) corruption is introduced into the model. As a measure for the level of corruption, the control of corruption index (CCI) is used
7. This index is constructed by the Worldwide Governance Indicators (WGI) project, affiliated with the Word Bank Institute. According to the WGI, the CCI is an aggregation of various indicators that measure the extent to which public power is exercised for private gain, including both small and large forms of corruption, as well as “capture” of the state by elites and private interests. The CCI ranges from: -2.5 (total corruption) to +2.5 (no corruption). However, in order to implement the index into the model, the CCI is rescaled from 0 (no corruption) to 100 (total corruption). As a result, an increase in the CCI represents an increase in corruption, whereas a decrease
represents a decrease in corruption.
6.1 Data Characteristics
The descriptive statistics of the variables used in the model are presented in Table A6 in
Appendix A5. The military burdens range from 0.37 (Guatemala 2005) to 3.81 (Chile 2002); the security webs range from 0.40 (Belize 2005) to 2.89 (Peru 2009); and the country with the smallest level of corruption is Chile (19.01 in 2002), whereas the most corrupted country is Paraguay (79.05 in 2005).
Table A7 in Appendix A5 represents the correlations of the dependent, and independent variables. The correlation between
and
is 0.42, indicating that countries with a high level of military spending face a larger security web, face a higher threat level. Furthermore, the correlation between
and
is -0.44, implying that more corrupted countries have a smaller military burden. Note that all the correlation levels in Table A7 are relatively small, indicating that there is no direct evidence of multicollinearity between the independent variables.
7 The CCI is available for 2000, and 2002-2010. The index for 2001 is constructed by linearly interpolating the figures for 2000 and 2001.
Page | 26 Furthermore, Table A8 in Appendix A5 provides the results of the stationarity tests of the
variables. In order to examine the existence of stationarity in the data series, the Phillips-Peron unit-root test is used. According to Table A8, only the series of the initial level of gross domestic product and of the educational attainment have a unit-root. To overcome the non-stationarity of the educational attainment variable, the first difference (
) which is stationary, is
incorporated into the model.
7. Empirical Results
The two-way fixed effects Barro-type growth model (15) is estimated using the Least-Squares technique. The results of the regression for 11 Latin and 5 Central American countries in the sample are shown in Table 2
8.
According to Table 2, all control variables are highly significant, and their coefficients have the expected signs. The level of investment, as a percentage of GDP; and the average years of total schooling of the population over 25 years, stimulate economic growth. On the other hand, population growth and the initial level of GDP negatively influence economic growth. The negative impact on growth of the initial GDP level supports the conditional convergence hypothesis.
The parameter for
is negative and significant at a 5% level. This result supports the adverse relationship found in the majority of the studies between the military burden and economic growth in the Latin and Central American region. Indicating that : the military burden of the region is at a higher level than its optimum. The opportunity costs dominate the direct and indirect benefits of military spending in the Latin and Central American region such that a one percent increase in a country’s military burden decreases growth with 1.30 percent.
8 To test the robustness of the empirical model, a view tests have been conducted. The results of these robustness tests are represented in Appendix A3.
Page | 27
Table 2: estimation results for Latin and Central American countries, fixed effects are not reported.Variable Coefficient
-22.92***
(7.62)
-3.12*
(1.83)
(
) 12.95***
(4.26)
0.65***
(0.13)
-1.30**
(0.62)
-3.20***
(1.18)
-0.22***
(0.08)
Constant 212.05***
(63.79)
Observations 174
Period 2000-2010
Note: panel estimation by least squares, with White cross-section coefficient covariance method (d.f. corrected).
Standard errors are in parentheses. *** indicates significance at 1%, ** at 5%, * at 10%. The dependent variable is
.
Table 2 further indicates that the parameter for
is negative at a 1% significance level, and supports the derived outcome: ̃ . A country’s security web has an expected significant negative influence on economic growth. Quantitatively, the effect of a one percent increase in a country’s security web on growth is nearly 2.5 times as great as a similar one percent increase in a country’s military burden; -3.20 versus -1.30.
The results in Table 2 furthermore suggest that the parameter for
is negative at a 1%
significance level, indicating that a higher control of corruption Index (CCI); a higher level of
Page | 28 corruption, decreases economic growth. Which is in accordance with the derived specification:
̃ . In quantitative terms, if the index increases with one point on a scale of 0 to 100, economic growth decreases with 0.22 percent. This result supports Aizenman and Glick (2003) findings, who also found an adverse relationship between corruption and growth.
8. Conclusion
The purpose of this paper is to examine and measure the relationship between military
expenditure and economic growth via the security channel. The theoretical model outlined in this paper is a variation of the Aizenman and Glick model (2003). It differs from the Aizenman and Glick model in its definition of security. The hypothesis in this paper is that the relative size of military expenditure of a country versus military expenditure of its neighboring countries, a country’s security web, approximates security and thereby impacts economic growth. According to the theoretical model, a country’s optimal military expenditure is independent of military expenditure of its neighboring countries. The model furthermore suggests that the impact of military spending on economic growth depends on the magnitude of a country’s military burden versus the ratio of the output elasticity of non-military government expenditure to the output elasticity of security. The level of corruption and a country’s security web have a derived negative influence on the growth rate.
In order to empirically test the robustness of the derived outcomes, a Barro-type growth model has been examined for a sample of 11 Latin American and 5 Central American countries using a two-way fixed effects panel model. For the period 2000-2010, military expenditure has a
significant negative impact on economic growth. Following the theoretical model, this implies
that the military burdens of the Latin and Central American countries are higher than the optimal
burdens; are higher than the ratio of the output elasticity of non-military government expenditure
to the output elasticity of security. The opportunity costs of military expenditure dominate the
direct and indirect benefits in this region. Furthermore, the panel model also indicates a
significant negative influence of a country’s security web and of the level of corruption on
growth, supporting the theoretical model.
Page | 29 Although the Latin and Central American countries have relatively small defense expenditure levels, their military burdens are still at a higher level than the optimal burdens, suggested by the model. These empirical results imply that a decrease in the military burdens of the Latin and Central American countries will result in higher economic growth rates. Such a decrease yields positive economic growth effects until the optimal military burdens are reached.
When more data is available, this analysis can be further extended to other regions and longer
time periods. Another possible extension is the special case of a military alliance. Military
alliances have the principle of a collective defense. If two neighboring countries are both
members of a military alliance, an increase in the military expenditure of one country increases
the level of security in the other, instead of imposing a threat on that country. In other words,
when the countries in the security web are all members of a military alliance, the security web
positively influences the level of security and thus growth. As a result, the definition of security
being the ratio of domestic to foreign neighboring countries military expenditure is no longer
feasible.
Page | 30 9. References
Aizenman, J., and R. Glick (2003), “Military Expenditure, Threats and Growth,” National Bureau of Economic Research Working Paper, No. 9618.
Atesoglu, H.S., and M.J. Mueller (1990), “Defense Spending and Economic Growth,” Defense Economics, Vol. 2, No. 1, pp. 19-27.
Barro, R J. (1990), “Government Spending in a Simple Model of Endogenous Growth,” Journal of Political Economy, Vol. 98, No. 5, pp. 103-125.
Barro, R.J., and X. Sala-i-Martin (1995), Economic Growth, Mac Graw Hill, London.
Benoit, E. (1973), Defense and Economic Growth in Developing Countries, Lexington Books, Boston
Benoit, E. (1978), “Growth and Defense in Developing Countries,” Economic Development and Cultural Change, Vol. 26, No. 2, pp. 271-280.
Biswas, B. (1993), “Defense spending and economic growth in developing countries,” in J.E.
Payne and A.P. Sahu (eds.), Defense Spending and Economic Growth, Westview Press, Boulder, pp. 223-235.
Biswas, B., and R. Ram (1986), “Military Expenditures and Economic Growth in Less Developed Countries: An Augmented Model and Further Evidence,” Economic Development and Cultural Change, Vol. 34, No. 2, pp. 362-371.
Deger, S., and R. Smith (1983), “Military Expenditure and Growth in Less Developed Countries,” Journal of Conflict Resolution, Vol. 27, No. 2, pp. 335-353.
Deger, S., and S. Sen (1995), “Military Expenditure and Developing Countries,” in K. Hartley and T. Sandler (eds.), Handbook of Defense Economics, Elsevier, Amsterdam, pp. 275- 307.
Dunne, J.P. (1990), “The Political Economy of Military Expenditure: An Introduction,”
Cambridge Journal of Economics, Vol. 14, No. 4, pp. 395-404.
Dunne, J. P., R. P. Smith, and D. Willenbockel (2005), “Models of Military Expenditure and Growth: A Critical Review,” Defence and Peace Economics, Vol. 16, No. 6, pp. 449-461.
Dunne, J.P, and E. Nikolaidou (2011), “Defence Spending and Economic Growth in the EU15,”
University of the West of England Discussion Papers, No. 1102.
Page | 31 Faini, R., P. Annez, and L. Taylor (1984), “Defense spending, Economic Structure, and Growth:
Evidence among Countries and over Time,” Economic Development and Cultural Change, Vol. 32, No. 3, pp. 487-498.
Feder, G. (1983), “On Exports and Economic Growth,” Journal of Development Economics, Vol.
12, No. 1-2, pp. 59-73.
Frederiksen, P.C., and R.E. Looney (1983), “Defense Expenditures and Economic Growth in Developing Countries,” Armed Forces and Society, Vol. 9, No. 4, pp. 113-125.
Huang, C., and A. Mintz (1991), “Defense Expenditures and Economic Growth: The Externality Effect,” Defense Economics, Vol. 3, No. 1, pp. 35-40.
Knight, M., N. Loayza, and D. Villanueva (1996), “The Peace Dividend: Military Spending Cuts and Economic Growth,” International Monetary Fund Policy Research Working Paper, No. 1577.
Landau, D. (1993), “The Economic Impact of Military Expenditures,” The World Bank Working Paper, No. 1138.
Lim, D. (1983), “Another Look at Growth and Defense in Less Developed Countries,” Economic Development and Cultural Change, Vol. 31, No. 2, pp. 377-384.
Mintz, A., and R.T. Stevenson (1995), “Defense Expenditures, Economic Growth and the ‘Peace Dividend’: A Longitudinal Analysis of 103 Countries,” Journal of Conflict Resolution, Vol. 39, No. 2, pp. 283-305.
Murdoch, J.C., P. Chung-Ron, and T. Sandler (1997), “The Impact of Defense and Non-Defense Public Spending on Growth in Asia and Latin America,” Defence and Peace Economics, Vol. 8, No. 2, pp. 205-224.
Ram, R. (1995), “Defense Expenditure and Economic Growth,” in K. Hartley and T. Sandler (eds.), Handbook of Defense Economics, Elsevier, Amsterdam, pp. 251-273.
Rosh, R.M. (1988), “Third World Militarization,” Journal of Conflict Resolution, Vol. 32, No. 4, pp. 771-98.
Smith, A. (1776), The Wealth of Nations, Penguin Books, Harmondsworth.
Smith, R. (1980), “The Demand for Military Expenditure,” Economic Journal, Vol. 90, No. 360,
pp. 811-820.
Page | 32 Starr, H., and B.A. Most (1976), “The Substance and Study of Borders in International Relations
Research,” International Studies Quarterly, Vol. 20, No. 4, pp. 581-620.
SIPRI (2011), SIPRI Yearbook 2011: Armaments, Disarmament and International Security, Stockholm International Peace Research
Stroup, M. D., and J. C. Heckelman (2001), “Size of the Military Sector and Economic Growth:
a Panel Data Analysis of Africa and Latin America,” Journal of Applied Economics, Vol.
4, No. 2, pp. 329-360.
The Worldbank (2012), World Development Indicators, Washington DC, The World Bank.
Page | 33 Appendix A1: Security Web
Table A1: Latin and Central American countries in the sample.
Country Security Web
Argentina Bolivia, Brazil, Chile, Paraguay, Uruguay
Belize Guatemala, Mexico
Bolivia Argentina, Brazil, Chile, Paraguay, Peru
Brazil Argentina, Bolivia, Colombia, Paraguay, Peru,
Uruguay, Venezuela, (Guyana, Suriname, French Guiana)
Chile Argentina, Bolivia, Peru
Colombia Brazil, Ecuador, Peru, Venezuela, (Panama)
Ecuador Colombia, Peru
El Salvador Guatemala, Honduras
Guatemala Belize, El Salvador, Honduras, Mexico
Honduras El Salvador, Guatemala, Nicaragua
Mexico Belize, Guatemala
Nicaragua Honduras, (Costa Rica)
Paraguay Argentina, Bolivia, Brazil
Peru Bolivia, Brazil, Chile, Colombia, Ecuador
Uruguay Argentina, Brazil
Venezuela Brazil, Colombia, (Guyana)
Page | 34 Appendix A2: Nonlinear Empirical Model
The theoretical model outlined in this paper suggests a nonlinear relationship between military expenditure and growth. In order to test this nonlinearity, the squared term of military
expenditure,
is introduced in the model. Therefore, the statistical linear representation of the economic growth model (13) becomes:
, (A1)
This two-way fixed effects Barro-type growth model is estimated using the Least-Squares technique. The results of the regression are presented in Table A2.
According to Table A2 the coefficient for
is insignificant, rejecting the quadratic
relationship between military expenditure and growth. As a result of the high correlation between military expenditure and its square term, the coefficient for military expenditure is also
insignificant. To test whether economic growth depends on military expenditure, a Wald test is conducted. Table A3 represents the outcome of this test.
Table A3 indicates that the null hypothesis that the parameters for
and
are simultaneous equal to zero can be rejected at a 5% significance level, using the F-statistic and Chi-Square. Therefore, military expenditure has a significant influence on economic growth, and needs to be incorporated in the model.
Given the theoretical model, this result implies that the military expenditure levels of the Latin and Central American countries are located beyond their optimal levels for the period 2000- 2010. The data on the military expenditures during this period is on the downside of the concave down relationship between military expenditure and growth suggested by the theoretical model.
As a result, the impact of the squared term of military expenditure on growth is insignificant.
Page | 35
Table A2: estimation results for Latin and Central American countries (including the square of militaryexpenditure). Fixed effects are not reported.
Variable Coefficient
-23.97***
(7.55)
-2.79*
(1.54)
(
) 16.46*
(9.33)
0.68***
(0.14)
0.29
(0.62)
-0.38
(0.59)
-2.51**
(1.14)
-0.21***
(0.08)
Constant 218.23***
(60.98)
Observations 174
Period 2000-2010
Note: panel estimation by least squares, with White cross-section coefficient covariance method (d.f. corrected).
Standard errors are in parentheses. *** indicates significance at 1%, ** at 5%, * at 10%. The dependent variable is
.
Table A3: Wald test.
Test Statistic Value
F-statistic 3.69**
Chi-square 7.38**
Note: null hypothesis: the parameters for and are simultaneous equal to zero. *** significance at 1%,
**at 5%, * at 10%.
Page | 36 Appendix A3: Robustness
In order to test whether the assumption that the model should be corrected for both cross-section and period fixed effects is sound, a likelihood ratio fixed effect test has been taken.
Table A4: redundant fixed effects tests.
Fixed Effects Tests Statistic
Cross-section F 4.57***
Cross-section Chi-square 68.98***
Period F 6.11***
Period Chi-square 62.621***
Note: *** significance at 1%, **at 5%, * at 10%.
According to Table A4, the null hypothesis that both the cross-section and the period fixed effects are redundant can be rejected at a 1% significance level, using sum-of-squares (F-test) and the likelihood function (Chi-square test).
Additionally, Figure A1 illustrates the cross-country residuals of the regression. The White
cross-section coefficient covariance method is used to correct for heteroskedasticity. This
method is robust to cross-section correlation, as well as for different error variances in each
cross-section. Correcting with this method does not change the coefficients of the variables; it
only alters the standard errors.
Page | 37
Figure A1: residuals of the Barro-type growth model.The adjusted R-squared statistic in Table A5, indicating the goodness-of-fit test, implies that 0.54 percent of the variance in the data is explained by the model. To test the existence of
autocorrelation in the model, the Durbin-Watson test statistic is analyzed. Table A5 shows a DW-statistic of 1.59, indicating that there is no significant form of autocorrelation between the residuals of the regression.
Table A5: test statistics.
Test Statistic
Adjusted R-squared 0.54
Durbin-Watson 1.59
Page | 38 Appendix A4: Mathematical Appendix
To determine the optimal growth rate, ̃, one needs to find the optimal levels for the tax rate , and the military spending ratio . Following equations (7) and (8), output can be written as an implicit function of , and .
Rearranging terms in Equation (8) gives:
. (A2)
And Equation (7), gives:
. (A3)
Using equations (A2) and (A3) in the production function y, gives an implicit function in terms of , and :
( )
((
) ) (
()( )
) . (A4)
In order to derive the optimal output growth path, the following optimization problem needs to be solved,
max. ∫
, (9)
subject to the constraint ̇ ( ) . (A5)
This gives us the Hamiltonian function:
[
]
( ) , (A6)
in which represents the co-state variable.
Page | 39 The corresponding first-order conditions are:
⟹
⟹
̇ ( )
̇ ⟹ ( )
̇ ⟹
̇( )
.
Differentiating with respect to time:
̇ (
)
̇
̇
(
̇ )
̇
(
̇ ).
From the first-order conditions we know that,
,
̇ (
̇ )
̇
̇ .
Substitute into
̇( )
gives:
( )
̇
̇ ( )
.
This results in the consumption Euler equation:
̇ ( )
(( )
