Military Expenditures, External Threats and Economic Growth

Military Expenditures, External Threats and Economic
Growth
Ari Francisco de Araujo Junior Cláudio D. Shikida
Ibmec Minas Ibmec Minas
Abstract
Do military expenditures have impact on growth? Aizenman Glick (2006) found that this
impact is positive in countries with good governance, where the external threat is significant.
Our article shows that their results suffer from three limitations: (i) they are not robust to the
most recent main database used; (ii) small changes in the time period of some variables
change their results, and (iii) the authors’ econometric specification is not adequate to their
hypothesis. Using a 2SLS specification we reconfirm the authors' hypothesis.
Citation: Araujo Junior, Ari Francisco de and Cláudio D. Shikida, (2008) "Military Expenditures, External Threats and
Economic Growth." Economics Bulletin, Vol. 15, No. 16 pp. 1-7
Submitted: August 13, 2008. Accepted: September 16, 2008.
URL: http://economicsbulletin.vanderbilt.edu/2008/volume15/EB-08O10019A.pdf

1. Introduction1
The CIA World Factbook informed for the year 2006 that the Brazilian government had spent 2.5%
of GDP on military expenditures. The most recent estimate (for the year 2005) for some
neighbouring countries pointed to expenditures of 1.3% (Argentina) and 1.2% (Venezuela). For
another country that is important in the regional political and military play, Colombia, the estimate,
also for 2005, was of 3.4% of GDP, which can possibly be explained based on its internal political
instability.
The situation of each of those countries in other dimensions (social, economic or institutional), if
properly assessed, will reveal a certain diversity of results, which can eventually be related to the
military expenditures of each country. This is one of the topics studied by the so-called Defence
Economics, which concerns the application of Economics to problems related to the military
defence of a country or group of countries. Although it is one of the most interesting research areas
in the literature, it has been little explored in Brazil. Ironically, this occurs in spite of the fact that
one of the first economic problems taught in undergraduate programmes – perhaps the most famous
– is precisely the trade-off faced by an agent in deciding whether to produce an additional unit of
butter or of cannons.
Basic questions arise from that example, on “what, how and for whom” to produce goods in an
economy. However, those are only initial questions that could be answered by an engineer, as said
by Alchian and Demsetz (1973). Besides those, defence economics encompasses more interesting
questions, such as: (i) the types of contracts between the military and their civil suppliers, (ii) the
determinant factors of alliance formation, (iii) the determinant factors of arms races, (iv) the
relationship between institutional arrangements and defence economics, (v) the economics of
conflict (conventional and non-conventional, such as terrorism), and (vi) the influence of the
defence sector in economic growth.
This papers deals with the last of the items above, which could be summarised in the following
question: More guns, more butter? In other words, do military expenditures have any impact on
the economic growth of a country? If so, is it a positive impact? The question is of obvious
relevance, since military expenditures are made by the public sector, not by the private sector.
More recently, Aizenman and Glick (2006) found a nonlinear relationship between military
expenditures and growth, using national instead of regional data. The mechanism of transmission
between the two variables is mediated by an “external threats” proxy. Our paper explores this causal
nexus in growth models with military expenditures. We seek to know whether the results found in
Aizenman and Glick (2006) are robust and, if not, we suggest a better way to deal with the problem.
2. Methodology and data
The adopted methodology and the data used in this paper follow Aizenman & Glick (2006). The
authors found evidences for nonlinearity in the interaction between threats and military
expenditures on economic growth in a cross-section matrix for the period 1989–98. The conjecture
tested by Ainzenman and Glick (2006) affirms that the “impact of military expenditures on growth
is a non-linear function of military threats suffered by a certain country from foreign countries or
other external forces” (Ainzenman and Glick 2006, 130).
1 We thank Pedro Henrique C. Sant’anna for his help and the participants of the 1st National Meeting of the Brazilian
Association of Defence Studies (ABED) for their comments. We take responsibility for any errors or omissions.
١

In this context, tcy denotes real growth, gm the military expenditures and am the effective threats.
The specification below represents such conjecture:
( ) ( ) Xamgmamgmtcy Θ+++= 121 βαα (1)
where Θ is the series of control variables, α1, β1 < 0 and α2 > 0. The first derivatives yield
mathematically the expected effects:
amamtcy
amgmtcy
21
21
αβ
αα
+=∂∂
+=∂∂ (2)
That is, the direct effects of military expenditures and external threats are supposed to be negative,
whereas the interactive effect is positive. We will test it econometrically:
( ) ( ) εβααγ +Θ++++= Xamgmamgmtcy 121 (3)
in which γ is the constant and ε are the errors. Our database is slightly different from the one used
in Aizenman & Glick (2006). tcy was built as the mean annual growth rate of real GDP per capita
between the period 1988–2003 (this variable was calculated until 2000 for Haiti), the source of
which is version 6.2 of the Penn World Table2. gm was calculated as the average of annual military
expenditures between 1988 and 2003. The source, in this case, is the World Bank Economic
Indicator3 (2007). As a proxy for external threats (am), we calculated the number of years during
which a country was in war with each one of its adversaries in the period between 1970 and 2003
(adding the total of its adversaries) from data of version 2.0 of the Correlates of War Project (COW)
of University of Michigan. In this specific case, we used two definitions: a more restrictive one
(am1), which considers as ‘years of war’ those in which at least one of the disputers suffered more
than 1,000 casualties specifically related to the conflict, and a less restrictive one (am2), which
takes into account as ‘year of war’ even those when war caused less than 1,000 casualties.
The variables that are contained in X are traditional, such as in Barro and Sala-i-Martin (1995). In
order to control conditional convergence, we used the Neperian logarithm of real GDP per capita of
1998 (yi). The hypothesis is that, controlling for other growth determinants, richer countries tend to
grow at lower rates than those observed in poorer countries. The population growth rate (tcpop)
and the average investment rate as a proportion of the GDP (inv) between 1988 and 2003 are
control variables that were also used. tcpop shows the expected negative effect and inv should
capture the positive effect of physical capital on growth. Finally, to capture the potential positive
effect on human capital growth, we used the Neperian logarithm of the average schooling years of
the population older than 25 years in 1990 (educ). The variables yi, tcpop and inv stem from the
Penn World Table whereas educ comes from Barro-Lee’s4 database. Descriptive statistics and
correlations of the variables are reported in the Annex to the paper.
The main differences between the databases used in this work and those used by Aizenman and
Glick (2006) are: tcy calculated in Aizenman & Glick (2006) uses the period between 1989 and
1998; the year 1975 is used for yi and educ; inv is used in the period between 1984 and 1988; and
the proxy for educ is restricted to men at high school level or above. That is, our main criticism is
centred in the lack of homogeneity regarding the periods defined for each variable. It is necessary
2 <http://pwt.econ.upenn.edu>
3 <http://publications.worldbank.org/WDI>
4 <www2.cid.harvard.edu/ciddata/barrolee>
2

to verify, therefore, whether the results are maintained when using a database that is more
homogeneous in time.
It is worth remembering that, as in Aizenman and Glick (2006) as in this paper, only the variable
am starts in 1970, that is, below the lower limit of tcy, which is 1988. In this case the justification
resides, for both papers, in the reduced number of observations that could be used in case the
definition of the time interval was more restricted.
If the nonlinear relation between military expenditures and growth is robust to the extent that it
could be considered an important benchmark for economic policy-making, it is expected that up-to-
date versions of the databases used, if subjected to the same econometric treatment, would generate
similar results. As mentioned above, this paper uses more recent versions of the Penn World Table
(6.2) and of the COW (2.0). The authors used, respectively, versions 6.1 and 1.1 of those databases.
The robustness test estimates of Aizenman and Glick (2006) were done by Ordinary Least Squares
by means of the White estimator (the same used by the authors).
3. Is there any relationship between military expenditures and economic growth? Revisiting
Aizenman and Glick (2006)
Table 1 below shows the results for the tests a la Aizenman and Glick (2006) from a cross-section
matrix for a longer period (1988–2003). The sign and, in most cases, the statistical significance of
the control variables correspond to the expected, according to the neoclassical model of economic
growth (except for education). The education proxy coefficient is positive, as expected, but not
significant. Countries the population of which grow at high rates have lower economic growth.
The investment in physical capital increases the economic growth in the countries of the sample.
The initial income per capita is negative and significant, that is, controlling for other determinants
of economic growth, it statistically captures conditional convergence.
Table 1 – Determinants of Growth [robustness Aizenman & Glick (2006)]*
(1) (2)
gm 0.04
(0.40)
0.33
(0.45)
gm_am1 -0.10
(0.44)
---
gm_am2 --- -0.10
(0.04)
am1 0.55
(0.32)
---
am2 --- 0.54
(0.00)
yi -0.83
(0.03)
-0.68
(0.00)
educ 0.12
(0.82)
0.01
(0.99)
tcpop -1.02
(0.00)
-0.97
(0.00)
inv 0.11
(0.00)
0.11
(0.00)
constant 7.87
(0.00)
6.60
(0.02)
N 88 88
R2 0.36 0.39
* P-value in round brackets, below each estimated coefficient.
3

Military expenditures and external threats increase growth. Moreover, we note that, both for am1
and for am2, the linear interaction between military expenditures and external threats does not
present the expected positive sign (and it is not significant at 10% when am1 is used as a proxy for
external threats). This implies that the results by Aizenman and Glick (2006) are not maintained
when minor changes are made in the database, in the temporal definition of some variables and in
the use of updated or fixed versions of some of their databases. However, there can be other
problems, as showed below.
4. Rethinking the causal nexus between threat and military expenditures: the problem of
simultaneity
The results presented above raise doubts about the nonlinear relationship proposed by Aizenman
and Glick (2006). The problem is that the authors not only suppose that military expenditures
influence the growth rate of GDP per capita, but also that such expenditures are a function of
another variable, the ‘threat’. There clearly is a theoretical problem of simultaneity between the
variables, which was neglected by the authors. In this case, it seems to be a mistake to make
estimates using Ordinary Least Squares (OLS). The most adequate is, in this sense, to estimate the
exercise by means of an equations system using specifically the Two-Stage Least Squares method
(2SLS). The threats proxies that we used follow those authors’ methodology. Even so, the use of
2SLS can be justified by a supposed theoretical relationship: if threats affect military expenditures,
this effect occurs with some time lag. This way, one of the possible improvements for econometric
tests of this nature concerns the creation of other proxies for threats.
Therefore, the external threat proxies that were used (am1 and am2) will serve as instruments for
military expenditures (gm) in the following specification:
( )( )
23
121
εαφ
εααγ
++=
+Θ+++=
amgm
Xgmamgmtcy (4)
Table 2 presents the results obtained using 2SLS. It can be seen that the convergence hypothesis is
not rejected in either equation. The impact of investment on growth is positive, as expected. The
population growth rate has a negative impact on growth, although it is significant in only one of the
equations. Education has a positive sign but does not present adequate statistical significance.

Table 2 – Determinants of Growth [2SLS]*
(1) (2)
gm -0.40
(0.42)
-0.88
(0.11)
gm_am1 0.06
(0.19)
---
gm_am2 --- 0.10
(0.04)
yi -0.86
(0.04)
-0.70
(0.11)
educ 0.20
(0.75)
0.37
(0.58)
tcpop -0.79
(0.06)
-0.37
(0.53)
inv 0.14
(0.00)
0.18
(0.00)
4