Arms trade, military spending, and economic growth

Defence and Peace Economics, 2007, Vol. 18(4), August, pp. 317–338 ARMS TRADE, MILITARY SPENDING, AND ECONOMIC GROWTH PAVEL YAKOVLEV* Department of Economics, College of Business and Economics, West Virginia University, Morgantown, WV 26505-6025, USA There is a large literature on the relationship between economic growth and defense spending, but its findings are often contradictory and inconclusive. These results may be partly due to non-linear growth effects of military expenditure and incorrect model specifications. The literature also appears lacking an empirical analysis of interaction between military spending and the arms trade and the impact of these two on growth. This paper investigates this nonlinear interaction in the context of the Solow and Barro growth models recommended by Dunne et al.1 (2005). Using fixed effects, random effects, and Arellano–Bond GMM estimators, I examine the growth effects of military expenditure, arms trade, and their interaction in a balanced panel of 28 countries during 1965–2000. The augmented Solow growth model specified in Dunne et al. (2005) yields more robust estimates than the reformulated Barro model. I find that higher military spending and net arms exports separately lead to lower economic growth, but higher military spending is less detrimental to growth when a country is a net arms exporter. [email protected] Taylor Defence 10.1080/10242690601099679 GDPE_A_209909.sgm 1024-2694 0Original 00 PavelYakovlev 2006 000 2004 00 and &and Article Francis (print)/1476-8267 Francis Peace Ltd Economics(online) Keywords: Arms trade; Defense spending; Military expenditure; Economic growth JEL CODES: O30, O38, H50 INTRODUCTION Some people view military expenditure as a guarantee of peace and security, while others see it as a wasteful enterprise potentially leading to arms races or direct military confrontations. Regardless of one’s perspective, arms production and trade is a big business with nontrivial economic consequences worthy of study. While a considerable amount of research has been done on the economic effects of military spending, the economic consequences of arms production and trade continue to be relatively unexplored. As Anderton (1995: 558) puts it, ‘…the economics of arms trade is essentially an unexplored sub-field of defense economics, ripe for foundational theoretical and empirical contributions.’ To the best of my knowledge, this statement still holds true today and provides the motivation for this empirical analysis of how arms trade and military spending may affect economic growth. According to the latest SIPRI (Stockholm International Peace Research Institute) estimates, world military expenditure amounted to $975 billion in 2004 in constant prices, or $162 of military spending per capita and 2.6 percent of world GDP. The United States, for example, is the major determinant of the world trend in military expenditure with its 47% share. Some of *Email: [email protected] 1 I would like to thank Paul Dunne, Ron Smith, and Dirk Willenbockel (2004) for sharing their data. ISSN 1024-2694 print: ISSN 1476-8267 online © 2007 Taylor & Francis DOI: 10.1080/10242690601099679 318 P. YAKOVLEV the biggest military spenders in the word are also some of the biggest arms traders. France, Germany, Russia, the UK, and the USA were responsible for 81% of all arms deliveries during 2000–2004. The SIPRI estimates also show that the combined arms deliveries of all 25 EU states to non-EU states made up about 19% of all arms deliveries in 2000–2004, making the EU the third largest arms exporter. The world arms trade rose to $51.6 billion in 1999 with developing countries now capturing the bigger share of arms trade, thereby reversing the previous trend. Developed nations accounted for 96% of total arms exports in 1999 compared to 92% a decade earlier. These figures highlight the economic significance of the military sector and raise questions about the likely economic impacts of military expenditures and the arms trade. One of the most relevant and researched issues is the relationship between economic growth and military expenditure. However, the empirical estimates of this relationship are often contradictory or inconclusive. Some of this confusion might be due to the non-linear relationship between growth and military expenditure or incorrectly specified models. Aizenman and Glick (2003) argue that linear empirical models lead to inconsistent results when the relationship between economic growth and defense spending is non-linear, which is what they find to be the case. In their review of defense-growth models, Dunne et al. (2005) point out that the identification or reverse causality issues and small observed deviations in military spending as a share of GDP can further complicate the empirical analysis of the defense-growth nexus. In another paper, Dunne et al. (2004) examine the theoretical and empirical issues involved in estimating the impact of military spending on growth. They suggest that a simple neoclassical growth model with technology affecting military expenditure combined with panel data produce more promising results than the commonly used Feder-Ram model. Taking these arguments into consideration, I examine the growth effects of military expenditure, net arms exports, and their interaction in a balanced panel of 28 countries from 1965 to 2000. Using fixed effects, random effects, and Arellano–Bond GMM estimators, I investigate the non-linear effect of military spending on economic growth in the Solow and Barro style growth regressions. Controlling for panel-level heteroskedasticity and autocorrelation problems that typically plague panel data estimation, I find that the augmented Solow growth model specified in Dunne et al. (2005) is more robust across different estimators than the reformulated Barro growth model. The estimates indicate a significant non-linear relationship between growth and military spending, being conditional on net arms exports. THE DEFENSE-GROWTH NEXUS This section provides a brief review of the commonly referred channels through which military spending and arms trade may influence economic growth. Whereas Smith (2000) and Dunne (1996) offer a more detailed description of the various channels of influence from military spending, I shall provide only a brief summary of these channels. The defense-growth literature has accumulated a large number of papers analyzing a wide variety of different channels through which military expenditure may influence growth. These channels can be broadly grouped into three major categories as done by Dunne et al. (2005): demand, supply, and security channels. In the demand channel, military spending works through the Keynesian multiplier effect that depends on the level and composition of military expenditure. According to this channel, additional military spending increases aggregate demand in the presence of spare capacity, which reduces unemployment and increases capital utilization. Hence, military spending is often seen as having a growth enhancing effect in this specification. In many developing countries, military spending might be seen as being capable of enhancing social infrastructure ARMS TRADE, SPENDING & GROWTH 319 (roads, communication networks, etc) and human capital (military education and training) that are likely to contribute to future economic growth. However, military spending has an opportunity cost and may crowd-out investment in human and physical capital. The extent and form of crowding-out, as pointed out by Dunne et al. (2005), depends on prior utilization of resources and how the increase in military spending is financed. A constrained government budget requires that an increase in military expenditure must be financed by budget cuts in other government programs, higher taxes, higher debt, greater money supply, or some combination of these methods. Different ways of financing additional military expenditure might, obviously, have different effects on output and growth. Moreover, a change in military expenditure may change the composition of industrial output through input–output effects, according to Dunne et al. (2005). Clearly, it may not be possible to deduce whether the net effect of higher military spending on output and growth is positive or negative in this demand channel specification. In the supply channel, the military sector competes with the civilian sector for labor, physical capital, human capital, natural resources and, perhaps, technology. The resources used by the military are not available for civilian use; hence the opportunity cost of military spending. Mylonidis (2006) lists a number of opportunity costs associated with a higher military burden that include: crowded-out public and private investment, adverse balance of payments in arms importing countries, inefficient bureaucracies (i.e. extensive rent seeking), fewer civilian public sector services, depleted R&D activities, and skilled workforce in the civilian sector. On the other hand, it can be argued that military R&D spending can result in the development of new technology (i.e. radar, jet engine, nuclear energy) that can spill over into the civilian (private) sector. Dunne et al. (2005) point out that training in the armed forces can make workers more or less productive when they return to civilian employment, while military R&D may lead to commercial spin-offs. Some proponents of military spending argue that some research projects will not be carried out in the private sector due to the high-risk environment and public-good characteristics of the final product. If this is true, then military R&D can be a net producer of positive technological externalities. To complicate things further, consider the argument by Stroup and Heckelman (2001) that the net effect of military spending on growth is described by a non-linear, concave function if the military sector exhibits diminishing marginal productivity. This argument implies that at low levels of military spending the net effect on growth is positive, but after a certain maximum point, growth declines as military spending continues to expand and may even become negative. Moreover, Dunne et al. (2005) suggest that conscription and ideological fervor may increase the mobilization of factors of production, particularly during times of a perceived threat of war, potentially leading to greater output if these mobilized resources are not used exclusively for military purposes. In other words, mobilization efforts could have, at best, a positive effect on growth in the short run. In the case of the security channel, the provision of national defense fosters the security of persons and property rights from domestic or foreign threats, which is essential to the operation of markets and to the incentives to invest and innovate. This is a very old argument dating back to Adam Smith, who noted that the first two duties of the state were to protect its citizens from foreign and domestic oppression or violence. It has been often noted in the literature that wars and a lack of security are major obstacles to development in many poor countries. Defense expenditures, thus, can strengthen the incentives to accumulate capital and produce more output, leading to higher economic growth (Thompson, 1974). However, when military expenditures are not driven by basic security needs and are due to the rent-seeking activities, military expenditures may provoke arms races or damaging wars. Supportive of this argument is Aizenman and Glick’s (2003) finding, indicating that economic growth increases with higher military spending when a country faces higher military threats, and that economic 320 P. YAKOVLEV growth decreases with higher military spending when a country experiences high levels of corruption. In this case, less military spending would be desirable and could lead to positive security effects on economic growth. For instance, the disarmament process and dramatic cuts in defense budgets in many countries following the end of the Cold War have often been credited with generating the so called ‘peace dividend’ that resulted in better standards of living. THE ARMS-GROWTH NEXUS The arms trade may affect economic growth through a number of different channels. It could also affect economic growth in a non-linear way through an interaction with military expenditure similar, in principle, to the interaction between threats and military spending explored by Aizenman and Glick (2003). The diversity of possible arms-related growth effects motivates this study to explore different empirical specifications in two different growth models. Considering the tendency of developed or technologically advanced nations to dominate the arms trade market, one could argue that arms exports reflect a high level of technological development in arms exporting nations. Thus, developed nations could experience greater technological externalities or spillovers from higher military spending that arms exports might proxy for. This idea could be consistent with the non-linear growth effect from the interaction between military spending and arms exports. Another possible explanation for the non-linear growth effect is the existence of economies of scale in the defense industry that lead to lower average unit costs as the size of military output increases. Given that some of the biggest military spenders in the world are also some of the biggest arms exporters, then the interaction between arms exports and military spending could have a non-linear effect on growth. In the case of arms imports, a component of military spending has to be allocated to pay for these purchases. Arms purchases are not cheap, and some countries have to resort to external borrowing in order to pay for their arms imports or some portion of their military budget in general. Of course, foreign borrowing does not necessarily lead to slower economic growth. In fact, reasonable levels of foreign borrowing might even stimulate growth. Dunne et al. (2003) suggest that, in evaluating the impact of debt on growth, it is important to consider how the external debt is being used. If it is used to increase productive capacity, external borrowing may even facilitate development. However, if the scarce foreign exchange resources are spent on arms imports instead of investment goods that are essential for self-sustaining growth, then the effect of external borrowing on growth is likely to be negative. Looney (1989) investigates how military expenditures and arms imports affect debt in resource-constrained countries and unconstrained countries and finds arms imports to be a significant contributor to Third World indebtedness. In another empirical study, Looney and Frederiksen (1986) find that the unconstrained developing countries are able to support higher level of arms imports. GunlukSenesen and Sezgin (2002) find that the growth in arms imports has a significant positive effect on external debt, while no such effect is found for the growth in military spending. On the other hand, it could be argued that arms imports may help the importing countries to acquire new technology through reverse engineering or through the necessary training of military personnel required for operating high-tech weapons systems. In some instances, arms imports may result in direct technological transfers when they take the form of a licensed production of military weapons or some of their parts. India and Russia, for instance, signed a major defense deal for the purchase of 310 new Russian T-90 main battle tanks and their production under a Russian license in India. This agreement allows India to manufacture some critical components of the T-90 tanks. Between 1993 and 2005, China acquired the rights to produce 200 SU-27 and 250 SU-30 fighters domestically under a Russian license. This tendency toward more licensed production, rather than finished ARMS TRADE, SPENDING & GROWTH 321 arms imports, is becoming more and more prevalent in the international arms trade, which has become increasingly competitive in the last decade or so. Given this tendency, it would be worthwhile to hypothesize about the reasons that governments have for preferring domestic production of arms instead of arms imports. At least three arguments come to my mind. First, some countries may find themselves at risk when their defense capabilities depend on the supply of arms from other countries, especially from potential enemies. Second, some governments may believe that relying on arms imports instead of producing arms domestically is economically wasteful. Finally, arms imports might be politically unpopular. The purpose of this study is to examine whether or not there exists a systematic relationship between the arms trade and economic growth for a given level of military expenditure. In other words, would the empirical evidence support the argument that arms imports are necessarily detrimental and arms exports are necessarily beneficial for economic growth? While this question will be rigorously explored in the empirical section of this paper, some obvious parallels can already be drawn. Between 2000 and 2004, according to the Stockholm International Peace Research Institute (SIPRI), the top ten suppliers of arms in the world were Russia, USA, France, Germany, UK, Ukraine, Canada, China, Sweden, and Israel (descending order). In addition, the SIPRI records show that the world’s top military spenders in total dollar value in 2004 were USA, UK, France, Japan, China, Germany, Italy, Russia, Saudi Arabia, and South Korea. Clearly, the majority of these countries are not only some of the biggest military spenders but also some of the biggest arms exporters. Moreover, the majority of these countries, with the exception of current and former planned economies, are developed countries. According to the World Military Expenditures and Arms Transfers (WMEAT) report, developed countries were overall net arms exporters in every year between 1989 and 1999 (Figure 1), as well as in the decade before that, which implies that developing countries were net arms importers over the same period. FIGURE 1 Arms trade in developed countries: 1989–1999. Arms Exports Arms Imports 70,000 Millions of dollars (constant) 60,000 50,000 40,000 30,000 20,000 10,000 0 1989 1990 1991 FIGURE 1 1992 1993 1994 1995 1996 Arms trade in developed countries: 1989–1999 1997 1998 1999 322 P. YAKOVLEV These casual observations suggest that arms trade patterns are correlated with military expenditures and the level of economic development. Perhaps whether or not a country is a net arms exporter depends on the level of military spending and technology that, in turn, could be affected by the level of economic development and, perhaps, political institutions. Relevant to this idea is the finding by Goldsmith (2003) that economic growth, per capita income, and democracy are among the significant determinants of military spending. It is possible that arms exports depend on a country’s technological progress and income. Thus, it is also possible that arms exports could proxy for spill-over effects or positive technological externalities stemming from military R&D. According to the neoclassical trade theory, the arms trade could be thought of as being explained by differences in national tastes, technology and factor endowments. As Anderton (1995) notes, the Heckscher-Ohlin model can explain the ‘North-South’ arms trade between the United States and some Latin American countries where the capital abundant United States exports capital-intensive armaments to labor abundant Latin America in return for some laborintensive civilian goods. Specializing according to your comparative advantage, whether it is weapons production or something else, and trading would deliver the gains from trade. Yet, Anderton (1995) shows evidence in favor of prevalent intra-industry arms trade in the world economy that the neoclassical trade models cannot explain. Intra-industry trade is the domain of trade models with scale and learning economies, which also imply imperfect competition. If there are economies of scale in weapons production, then a larger domestic military production can reduce the average unit cost of weapons and create great potential for arms exports. This might explain why many rich countries that can afford large military budgets also end up being some of the world’s biggest net arms exporters. Thus, a country that spends a lot on weapons production might be able to alleviate some of the detrimental growth effects from its military spending through larger arms exports if economies of scale are present in its military industry. As is the case with military spending, the net effect of net arms exports is ambiguous in theory and would ultimately have to be examined empirically. It is difficult to hypothesize about the direction of the net effect, given that there is a plethora of channels through which military spending and the arms trade could impact economic growth. Since it is impossible to incorporate all the significant linkages from military spending within one model, researchers often choose to focus on cross-country growth models. They neglect these complex linkages in favor of a simple reduced form relationship between output and military spending, according to Dunne et al. (2005). The result of this approach is a variety of diverging empirical findings on the defense-growth nexus, which is not surprising considering the diversity of models, econometric techniques, time periods, and country samples used. Dunne et al. (2005) suggest that some of these contradictory findings are due to the severe econometric and theoretical problems of the Feder-Ram model (Ram, 1995). Moreover, they conclude that the Feder-Ram model should be abandoned in favor of the conventional Barro or Solow growth models, which are better suited for analyzing the defense-growth relationship. Following their advice, I proceed to analyze the growth effects of military spending and the arms trade within the context of the two commonly used models: the reformulated Barro and the augmented Solow growth models. THE AUGMENTED SOLOW GROWTH MODEL In 1956, Robert Solow developed a model that revolutionized the study of economic growth. He assumed an economy with a standard Cobb–Douglas production function, with decreasing marginal returns to capital and a fixed level of technology. The textbook Solow growth model ARMS TRADE, SPENDING & GROWTH 323 treats the rate of saving, population growth, and technological progress as exogenous. The model predicts that ‘poorer’ countries should be able to grow at faster rates than ‘richer’ countries, thereby leading to cross-country convergence, albeit a conditional one, in the standards of living over time. In their influential paper, Mankiw et al. (1992) augmented the textbook Solow growth model with human capital. They showed that it could explain as much as 80% of cross-country variation in output per worker, and that it could approximately predict crosscountry convergence in the standards of living. A variant of the augmented Solow growth model was used by Knight et al. (1996) and Dunne et al. (2004) in estimating the effect of military expenditure on growth. The effect of military spending on growth could be modeled in a number of ways. One way is to assume that military spending (as a share of aggregate output) affects factor productivity via a level effect on the efficiency parameter that controls labor-augmenting technical change as shown by Dunne et al. (2005). To see this, consider a concise exposition of the model with the aggregate neoclassical production function featuring the labor-augmenting technological progress with human capital as in Mankiw et al. (1992): Y (t ) = K (t )α H (t )β [ A(t ) L(t )]1−α −β (1) where Y denotes aggregate real income, H is the human capital stock, K is the real capital stock, L is labor, and A is the technology parameter. Technology parameter A evolves according to: A(t ) = A0 e gt m(t )θ (2) where g is the exogenous rate of Harrod-neutral technological progress and m is the share of military spending in aggregate output. According to this specification by Dunne et al. (2005), a permanent change in military spending share does not affect the long-run steady-state growth rate, but it might have a permanent level effect on per-capita income along the steady-state growth path. Military spending (m) also can affect transitory growth rates along the path to the new steady-state equilibrium. Provided with this specification, one could estimate the influence of military spending on growth using panel-level data as was done by Dunne et al. (2004). Continuing with a concise exposition of this model, one can now observe some of its dynamic properties. Given the standard assumptions of an exogenous saving rate s, a constant labor force growth rate n and capital depreciation d, the model exhibits conventional dynamics of capital accumulation where human capital per effective worker (he=H/AL) and physical capital per effective worker (ke=K/AL) evolve the following way: he (t ) = sh ye (t ) − (n + g + d )he (t ) and ke (t ) = sk ye (t ) − (n + g + d )ke (t ) (3) where sh and sk denote the shares of human and of physical capital investment in aggregate income. Human capital is assumed to depreciate at the same rate (d) as physical capital. The steady-state physical and human capital stock levels are: ke* é s b s1 - b ù =ê h k ú êë n + g + d úû 1 / (1 -a - b ) and he* é s1-a sa ù =ê h k ú ën + g + d û 1 / (1 -a - b ) ( 4) The transitory dynamics of income per effective worker near the steady state are approximated by: 324 P. YAKOVLEV ∂ ln ye = (α + β − 1)(n + g + d )[ln ye (t ) − ln ye* ] ∂t (5) Now, the transitory dynamics of output per effective worker near the steady state need to be made suitable for empirical analysis. For a more detailed exposition of the model please refer to Dunne et al. (2004) and (2005). The equation for income per actual worker is now: ln x y(t ) = e z ln y(t - 1) + (1 - e z ) a b a+b ì ü ln sk + ln sh ln( n + g + d ) ý íln A + 1 -a - b 1 -a - b 1 -a - b î þ + q ln m(t ) - e zq ln m(t - 1) + (t - (t - 1)e z )g 0 (6) where z≡(α−1)(n+g+d) and θ is the elasticity of steady-state income with respect to the long-run military expenditure share. While there is a distinction between models of the level of output and the growth rate, the distinction is less important in practice as shown in Dunne et al. (2005). It is common in the empirical analysis of economic growth to treat s and n as variant across countries and time, while g and d as uniform time-invariant constants and A0 as country-specific and time-invariant (see Knight et al., 1996; Islam, 1995 and Dunne et al., 2004). The conceptual equation shown above can be adapted for empirical analysis using the dynamic panel model specification of the following form: growthit = β 0 + β1 ln yit −1 + β 2 ln sit + β 3 ln(nit + g + d ) + β 4 ln hit + β 5 ln mit + β 6 ln mit −1 + ε it (7) This equation will serve as the basis for the forthcoming empirical analysis of how military spending and arms exports can affect economic growth in the Solow-style regressions. As discussed previously, arms exports could affect growth through a multitude of channels, which makes the task of modeling these channels within the neoclassical growth model ambiguous and difficult. However, one could observe that there seems to be a causal correlation between the level of development, military spending, and arms exports. This could serve as the basis for arguing that arms exports should enter the Solow growth model similarly to military spending. But the final answer would have to be found empirically through a theoretically guided, albeit loosely, testing of these channels. THE BARRO GROWTH MODEL In their review of theoretical models on military expenditure and growth, Dunne et al. (2005) conclude that the mainstream models of economic growth like the augmented Solow and the endogenous Barro growth models should be more suitable for analyzing the defense-growth nexus than the Feder-Ram model. The Barro (1990) growth model explicitly allows for different forms of tax financed government expenditures to influence output through the production function. This model also features the representative agent with an explicit utility function that the government maximizes. Barro’s (1990) model postulates that government expenditure has a non-linear effect on growth produced by the interaction between the productivity enhancing and tax distorting effects of government spending. The theoretical equation describing the relationship between economic growth and its determinants turns out to be rather too complex to be estimated explicitly. This problem is often circumvented in the so-called Barro-style ARMS TRADE, SPENDING & GROWTH 325 regressions, in which the theory suggests what variables should enter the unrestricted and ad hoc growth regression. The same approach is taken by Aizenman and Glick (2003) and Mylonidis (2006), from whom I borrow my Barro-style specified equation to examine the joint effect of arms trade and military spending on growth. The Barro-style regression could take the following form: growthit = β 0 + β1 yit −1 + β 2 sit + β 3 popgit + β 4 educit + β 5 mit + ε it (8) where traditional variables like the log of initial per capita GDP, share of investment in GDP, population growth, and the log of average years of schooling (human capital) are included in the regression in addition to the share of military spending in GDP. Other control variables could include institutional, demographic, and geographic characteristics or an interaction term between military spending and threats or corruption as in Aizenman and Glick (2003). In their paper, Aizenman and Glick (2003) attempt to clarify a common finding that military spending has an insignificant or negative impact on economic growth. They conjecture that this finding arises from non-linear interactions between military expenditure, external threats and corruption. Aizenman and Glick (2003) explain the presence of these non-linear interactions in an extended version of Barro and Sala-i-Martin (1995) by allowing growth to depend on the severity of external threats and the size of military expenditure associated with these threats. In this novel specification, national output is influenced by security or military expenditure relative to the threat. This might be a more plausible specification of the defense-growth nexus for many countries than the specification in which defense spending influences output through technology. Aizenman and Glick (2003) hypothesize that military expenditure induced by external threats should increase output by increasing security, while military expenditure induced by rent seeking and corruption should reduce growth by displacing productive activities. They suggest a basic growth equation specification of the following form: growth = a1m + a2 ( m)(threat ) + b1threat + βX + ε ( 9) where growth is the growth rate of real per capita GDP, m is the share of military spending in output, threat is the level of military threat faced by a country, and X is a set of control variables. In this specification, the direct effects of military spending and external threats on growth are assumed negative, while the interactive effect of military spending and threat is positive. Aizenman and Glick’s (2003) cross-country estimates over the period 1989–98 indicate that when the threat is low, military expenditure reduces output, especially in countries with a lot of corruption. However, when the threat is high, military expenditure increases output. Among the avenues for further empirical research, Aizenman and Glick (2003) suggest investigating the relationship between the arms trade and corruption as pertaining to growth. DATA DESCRIPTION The two Solow-style and Barro-style regressions used in this paper are based on the same balanced panel data set and are generally similar in terms of the chosen independent variables, but they differ in the dynamic specification and measurement of some regressors. Specifically, the Solow-style regression includes lagged net arms exports and lagged log of military spending, whereas the Barro-style regression does not. These lagged variables could make a significant difference in panel data estimation considering the dynamic aspect of the 326 P. YAKOVLEV data. All independent variables, except for net arms exports,2 are in the natural log form in the Solow-style regression, but only some are in the Barro-style regression. For instance, the military spending variable is in the log form in the Solow-style but not in the Barro-style regression. In the Solow-style regression, the dependent variable (growth) is the annual growth rate of real per capita GDP averaged over five-year intervals. The set of explanatory variables includes some typical control variables used in the empirical growth literature such as initial real per capita GDP (yit−1), the average number of years of schooling attained by both sexes 25 years old and over at all levels of education (hit) taken from the Barro-Lee data set,3 annual population growth rate4 (nit+g+d) averaged over five-year intervals, and real investment as a share of GDP (sit) averaged over five-year intervals. Military expenditure (mit) is measured as a share of GDP averaged over five-year intervals. A lagged value of military expenditure (mit− 1) preceding a five-year average is also included in the Solow-style regressions. Net arms exports (naxit) are measured as (arms exports – arms imports)/(arms exports + arms imports), averaged over five-year intervals (all in current dollars). The interaction term (naxit)(lnmit) is the product of net arms exports and the natural log of military spending. In the Barro-style regressions, the dependent variable (growth) and the explanatory variables like the initial real per capita GDP, the average number of years of schooling, military expenditure, and net arms exports are measured the same way, except that they may enter the Barro-style regression without logs (except for schooling and initial real per capita GDP), following Mylonidis (2006) and Aizenman and Glick (2003). Investment share, military expenditure share, and population growth enter Barro-style regressions without logarithms. The interaction terms in the Barro-style regressions are constructed in the same way as those in the Solow-style regressions. Data on GDP, population, and investment are obtained from the Penn World Tables, version 6.1. Education data for the human capital proxy are taken from the Barro and Lee (1994) dataset. Data on military spending5 come from various SIPRI Yearbooks (Stockholm International Peach Research Institute), while data on arms exports and imports are taken from various editions of WMEAT (World Military Expenditures and Arms Transfers), published by the US Department of State after integration with the US Arms Control and Disarmament Agency. Please refer to Table I for more detailed variable descriptions and sources. The value of each explanatory variable represents either the calculated average over the seven five-year periods of the dependent variable (1966–1970, 1971–1975, 1976–1980, 1981–1985, 1986– 1990, 1991–1995 and 1996–2000) or the lagged value that corresponds exactly to the base years 1965, 1970, 1975, 1980, 1985, 1990 and 1995 (like yit−1, mit−1, and naxit−1). Like Islam (1995), I use five-year averages instead of annual values to diminish the effects of business cycles and serial autocorrelation in the empirical analysis. Moreover, the human capital variable taken from the Barro–Lee data set is available only in five year intervals. The final data set contains seven five-year periods and a diverse sample of 28 countries listed in Table II. These countries include developed and developing countries representing Africa, Asia, Europe, Middle East, Oceania, North and South America. The countries in the 2 Net arms exports cannot be expressed in the log form due to the negative values that appear for the net arms importing countries. 3 Education data is taken from Barro and Lee (1994) dataset, which can be found at http://www.cid.harvard.edu/ ciddata/ciddata.html. 4 Given the difficulty of obtaining panel data on working age population, I resort to the common alternative of using population growth rates instead. Following Mankiw et al. (1992), I assume g+d=0.05 to be the same for all countries and years and add this value to population growth. 5 Military spending and GDP data missing from the PWT were taken from the data set kindly provided by Dunne et al. (2004). ARMS TRADE, SPENDING & GROWTH TABLE I Variable Description and Summary Statistics Variable Name growthit(2) yit−1(2) sit(2) nit+g+d(2) popgit(2) hit(6) mit(5) naxit(4) demit(1) popit(2) cincit(3) 327 Variable Description Non-overlapping five-year average growth rate of real per capita GDP (Laspeyres). Lagged real per capita GDP or real per capita GDP in the year preceding the five-year average period. Five-year average investment as a share of GDP (Laspeyres). Five-year average population growth rate nit + 0.05 (the assumed value for g+d) used in the Solow-style regressions. Five-year average population growth rate used in the Barro-style regressions. Average number of years of schooling for both sexes 25 years of age or older. Five-year average military expenditure as a share of GDP. Since some of the logged values became negative, I scaled the log of military spending up by 1 to convert all negative values into positive, which had no effect on the results. Lagged mit is mit−1. Five-year average of net arms exports computed as (arms exports − arms imports)/ (arms exports + arms imports), all in current values. Lagged naxit is naxit−1. Democracy score. Consists of the two indexes (DEMOC) and (AUTOC) taken from Polity IV database and combined according to the commonly used formula [(DEMOCi-AUTOCi)+10]/2. Natural log of total country population. Natural log of the Composite Index of National Capability (CINC). It is computed as the weighted average of a state’s total population, urban population, iron and steel production, energy consumption, military personnel, and military expenditure. Mean (Std. Dev.) 2.46 (2.17) 9.09 (0.80) 21.42 (6.36) 1.83 (0.15) 1.27 (0.94) 6.59 (2.63) 3.69 (3.13) −0.39 (0.63) 2.01 (0.63) 17.19 (1.23) −4.74 (1.14) (1) Polity IV Project. 2000. Political Regime Characteristics and Transition, 1800–2000. Electronic data. (version p4v2000). College Park, Md.: CIDCM, University of Maryland. (2) Alan Heston, Robert Summers and Bettina Aten, Penn World Table Version 6.1, Center for International Comparisons at the University of Pennsylvania (CICUP), October 2002. (3) Singer, J. David, Stuart Bremer, and John Stuckey. (1972). ‘Capability Distribution, Uncertainty, and Major Power War, 1820–1965.’ in Bruce Russett (ed) Peace, War, and Numbers, Beverly Hills: Sage, 19–8. (4) Compiled from various issues of World Military Expenditures and Arms Transfers (WMEAT) by the U.S. Arms Control and Disarmament Agency. (5) Compiled by Dunne et al. (2004) from Stockholm Peace Research Institute (SIPRI) Yearbooks. (6) Barro, Robert J. and Jong-Wha Lee, ‘International Data on Educational Attainment: Updates and Implications’ (CID Working Paper No. 42, April 2000). Available at http://www.cid.harvard.edu/cidwp/042.htm. data set were selected based on the availability of annual figures for military and economic variables. The total number of observations in this cross-sectional time-series data set is 196 (seven five-year periods for each of the 28 countries). ESTIMATION AND RESULTS The approach taken in this section consists of estimating and comparing the effects of military spending and net arms exports on economic growth in the Solow and Barro style regressions. The effects of military spending and arms trade on growth will be analyzed separately and together (via interaction terms) using different estimation techniques to judge the robustness of results. Considering the ambiguities in modeling the channels through which military spending and arms trade could affect growth, I choose to incorporate the arms trade component through an ad-hoc empirical extension of the Solow and Barro growth models. Dunne et al. (2005) 328 TABLE II P. YAKOVLEV Countries Featured in the Sample Country Argentina Australia Belgium Brazil Canada Chile Denmark France Germany Greece India Israel Italy Japan Korea, Republic of Malaysia Netherlands Norway Pakistan Philippines Portugal South Africa Spain Sweden Turkey United Kingdom United States Venezuela Total Frequency Percent Cumulative 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 196 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 100.00 3.57 7.14 10.71 14.29 17.86 21.43 25.00 28.57 32.14 35.71 39.29 42.86 46.43 50.00 53.57 57.14 60.71 64.29 67.86 71.43 75.00 78.57 82.14 85.71 89.29 92.86 96.43 100.00 suggest that if there is a robust relationship, then a thorough empirical analysis would be able to reveal it regardless of the chosen specification or theoretical model. Bleaney and Nishiyama (2002) test the three growth models from Barro (1997), Easterly and Levine (1997), and Sachs and Warner (1997), but fail to reject any of them. Moreover, they find that an encompassing model (a combination of all three) provides a significant improvement over any of the candidate models they tested. Analogously, I attempt to combine different specifications of military spending in Aizenman and Glick (2003), Dunne et al. (2004), and Mylonidis (2006) in an attempt to find a robust relationship between economic growth and military spending conditional on the arms trade. However, data restrictions prohibit me from adopting an all encompassing cross-sectional model of Bleaney and Nishiyama (2002) without abandoning the panel data analysis. Fitting the neoclassical growth model to panel data can provide a number of benefits. The assumption that s and n are constant, for example, is much easier to justify in panel rather than cross-sectional long-run growth regressions. Moreover, a panel data analysis of the defense–growth nexus may offer further insights by employing two-way fixed effects and endogenous treatment of independent variables in the Arellano–Bond dynamic GMM estimation utilized in this paper. While growth models have been most successful in cross-sectional empirical studies, panel data estimation can provide a number of significant advantages over cross-sectional analysis. ARMS TRADE, SPENDING & GROWTH 329 Given the availability of cross-country time-series data, the fixed effects estimator or the least squares dummy variable (LSDV) model seems like the appropriate choice. When the unobserved effects are correlated with the observed covariates, the standard estimator used to eliminate the potential bias caused by omitted heterogeneity is the fixed effects (within) estimator. The fixed effects estimator is popular because it is simple, easily understood, and makes robust standard errors readily available, according to Wooldridge (2001). When analyzing the fixed effects estimator, the standard assumptions are that the time-varying errors have zero means, constant variances and zero correlations. In the presence of omitted variable bias and unobserved country and time effects that often appear in country level panel data, the fixed effects estimator is preferred over the pooled or random effects estimators. Islam (1995) explores the suitability of the LSDV fixed effects estimator for growth estimation with panel data. He argues that the fixed effects estimator is a very suitable technique because of the individual country effects being correlated with the exogenous variables in the model. After conducting a Monte-Carlo study, Islam (1995) finds that the LSDV estimator, although being consistent in the direction of T only, performs very well. However, there are a number of problems that plague panel data models in general and the LSDV models in particular. Too many dummy variables, for example, may significantly deplete the degrees of freedom, while country-specific (groupwise) heteroskedasticity or autocorrelation over time would violate the normality and homogeneity of errors assumption. Outliers can bias regression slopes, and heteroskedasticity problems from groupwise differences can bias standard errors. Panel data may exhibit panel specific or general autocorrelation, requiring dynamic panel analysis. The fixed effects OLS estimator would be suitable for panel estimation as long as there are no heteroskedasticity and autocorrelation problems. However, these conditions are so rare that it is often unrealistic to expect that OLS will suffice for such models, notes Yaffee (2003). Under these conditions, the more suitable and commonly used estimator, according to Yaffee (2003), is the feasible generalized least squares (FGLS). Greene (2002) and Wooldridge (2002) also recommend using White’s heteroskedasticity consistent covariance estimator with OLS estimation in fixed effects models for it can produce standard errors robust to unequal variance along the predicted line. For robust estimation in the presence of heteroskedasticity, autocorrelation, and outliers Yaffee (2003) recommends using a generalized method of moment (GMM) estimation with robust (White, Newey-West) panel standard errors. Wooldridge (2001) also notes that some of the most interesting recent GMM applications have been done to panel data. According to Wooldridge (2001), if either heteroskedasticity or serial correlation is present, a GMM procedure can be more efficient than the fixed effects estimator, but the potential gains over standard applications are largely unknown. The generalized method of moments is applied more often to unobserved effects models when the explanatory variables are not strictly exogenous even after controlling for an unobserved effect. In Wooldridge’s (2001) opinion, GMM appears indispensable for more sophisticated applications such as dynamic unobserved effects panel data models. Although GMM estimators can be asymptotically normal, argues Yaffee (2003), they may not always be the most efficient ones. One of the concerns associated with using a dynamic GMM estimator is a loss of valuable observations in small samples. In light of the typical problems in panel data estimation, I perform the Breusch-Pagan heteroskedasticity and Arellano-Bond autocorrelation tests, which confirm the suspected heteroskedastic and AR (1) error structure. In light of this evidence, it is clear that the FGLS and Arellano-Bond GMM, with the correctly specified error structure, should be my preferred estimators. Considering the growing popularity of the fixed effects estimator and the preceding discussion of recommended panel estimators, I propose using the two-way fixed effects FGLS estimator with standard errors robust to groupwise heteroskedasticity and autocorrelation as a benchmark with which the GLS random effects and Arellano-Bond GMM estimators 330 P. YAKOVLEV are to be compared. The estimates from two-way fixed effects FGLS, or analogously FGLSDV (FGLS with dummy variables), can be compared to the random effects estimates using the Hausman specification test. The random effects model is very different from the fixed effects model and requires that the cross-sectional error must be uncorrelated with explanatory variables. One way to handle the error term is to assume that the intercept is a random effect (outcome) variable in the time-series cross-sectional regression model. The Hausman specification test is the commonly used method of deciding which model, fixed or random effects, is more appropriate for the chosen empirical analysis. The dynamic panel data estimation method, known as the Arellano-Bond GMM estimator, can be very useful in addressing the endogeneity of explanatory variables in growth regressions as noted in Dreher’s (2005) paper on globalization and growth. The GMM estimator is convenient for estimating interesting extensions of the basic unobserved effects model when unobserved heterogeneity interacts with observed covariates, according to Wooldridge (2001). The one and two step ArellanoBond GMM estimator can be robust to violations of heteroskedasticity, normality, and autocorrelation in errors. As suggested by Yaffee (2003), the Arellano-Bond GMM estimator with instrumental and first-differenced lagged variables may circumvent problems with correlations of errors and help obtain additional efficiency gains over other panel data estimators. Now is a good time to present and compare the estimates from the Solow-style and Barrostyle regressions. The basic Solow-style fixed effects regression equation can be specified as follows: growthit = α i + α t + β1 ln yit −1 + β 2 ln sit + β 3 ln(nit + g + d ) + β 4 ln hit + β 5 ln mit + β 6 ln mit −1 + β 7 naxit + β 8 naxit −1 + β 9 (naxit )(ln mit ) + ε it (10) where mit and naxit are the military spending and net arms exports variables and (naxit)(mit) is their interaction term.6 The basic Barro-style fixed effects regression equation is specified as follows: growthit = α i + α t + β1 ln yit −1 + β 2 sit + β 3 popgit + β 4 ln hit + β 5 mit + β 6 naxit + β 7 (naxit )( mit ) + ε it (11) where military spending, net arms exports, and the interaction term are defined as before. Beginning with the basic Solow-style regression results reported in Column 1 of Table III, current military spending appears to be negatively and significantly (at 1%) related to economic growth in the two-way fixed effects FGLS regression with groupwise heteroskedastic and panel-specific AR (1) adjusted standard errors. Using the same dataset, Dunne et al. (2004) also find the same negative and significant relationship between current military spending and economic growth using fixed effects and random coefficient estimators. Lagged military spending, however, is not statistically significant in this FGLS regression. Traditional growth regressors such as the lagged per capita GDP, investment share, population growth, and human capital (schooling) all have the expected signs and appear statistically significant (except for human capital). Adding net arms exports to a regression does not change the negative sign or significance level of current military spending, but it makes lagged military spending statistically significant and positively related to growth. This positive growth impact 6 There is no lagged interaction term in either Solow or Barro fixed effects regression. It is easier to rationalize how the current interaction of military spending and arms exports might contribute to growth through economies of scale or technological spillovers rather than lagged interactions. Nonetheless, the forthcoming Arellano-Bond dynamic GMM regressions automatically include the lagged interaction term that, unlike the current period interaction term, does not appear significant. ARMS TRADE, SPENDING & GROWTH TABLE III Model 331 The Growth Effects of Military Spending and Net Arms Exports in the Augmented Solow Growth 1 lnyit−1 lnsit ln(nit + g + d) lnhit lnmit lnmit−1 naxit −5.28*** (0.54) 4.51*** (0.31) −4.28*** (1.28) 0.23 (0.57) −1.53*** (0.48) 0.49 (0.44) – 5 −3.01*** (0.41) 4.65*** (0.57) −4.13*** (1.40) 1.25** (0.55) −0.96 (0.72) 0.78 (0.66) −0.15 (1.07) 0.46 (0.34) 0.01 (0.47) 22.41*** (4.91) GLS-RE 107.94 – 0.00 2.31 (2.04) – – 0.77*** (0.06) 0.29*** (0.05) −0.11 (0.14) 0.07 (0.07) −0.06** (0.03) −0.04 (0.03) −0.12*** (0.05) 0.05 (0.04) 0.04* (0.02) 0.01 (0.02) A-B GMM – 112.82 0.00 – 36.55*** (10.39) FGLS 1112.64 – 0.00 – – – – – – – (naxit)(lnmit) – Estimator Wald Chi-Square F-statistic P-value Baltagi-Wu LBI (Durbin-Watson stat.) Sargan test (p-level) Arellano-Bond autocorrelation test (p-level) Observations 4 35.54*** (7.78) FGLS 2021.62 – 0.00 – – 196 −5.32*** (0.56) 4.59*** (0.37) −2.96** (1.39) −0.12 (0.63) −2.16*** (0.51) 1.17*** (0.43) −0.32 (0.24) −0.33 (0.22) – 3 −5.51*** (0.56) 4.78*** (0.37) −2.17 (1.40) −0.17 (0.62) −1.71*** (0.54) 0.80* (0.45) −1.03*** (0.38) −0.28 (0.21) 0.63** (0.27) 35.80*** (11.19) FGLS 1202.65 – 0.00 – naxit−1 Constant 2 196 196 196 0.90 0.53 140 Notes: Dependent variable: five-year average growth rate of real per capita GDP from 1965 to 2000. Standard errors shown in parentheses. Significance levels: *** at 1%, ** at 5%, and * at 10%. FGLS uses errors corrected for panel-specific heteroskedasticity and AR (1) autocorrelation with adjusted Durbin–Watson computation. The random effects regression (GLS-RE) here is estimated with GLS. The Baltagi-Wu LBI statistic is equivalent to the Durbin-Watson statistic: if it is far below 2.00 then a correction for serial correlation is necessary. Here, the A-B GMM or Arellano–Bond one-step GMM estimator uses robust errors with Huber–White sandwich and time fixed effects. All independent variables were treated as endogenous and their lagged first-differences (lags 1–3) were used as instruments, which passed the Sargan over-identification test. The A-B GMM automatically uses lagged first-differenced dependent variable instead of lnyit−1. The null hypothesis in the Arellano–Bond test: no second-order autocorrelation in the residuals. from lagged military spending could be due to technological externalities or spill-over effects materializing from previous military expenditures. The current and lagged net arms exports are negatively related to growth, but they are not statistically significant and nor is human capital (Column 2, Table III). The human capital variable in this regression has a wrong sign: it is negatively related to growth. This anomalous result regarding the role of human capital in growth regressions is common, according to Islam (1995). He attributes this counter-intuitive finding to the discrepancy between the theoretical variable H used in the model and the actual variable used in regressions. Moreover, the true levels of human capital in some countries have not increased by much. Statistically, this leads to a negative temporal relationship between the human capital variable used in regressions and economic growth. A richer specification of production function with respect to human capital, writes Islam (1995), would allow the theoretical 332 TABLE IV growthit lnyit−1 lnsit ln(nit+g+d) lnhit lnmit naxit P. YAKOVLEV Pair-wise Correlations of Variables growth lnyit−1 lnsit ln(nit+g+d) lnhit lnmit naxit 1.0000 −0.2037* 0.3323* −0.0496 −0.0940 −0.0074 −0.0830 1.0000 0.5713* −0.6735* 0.8257* −0.0006 0.4461* 1.0000 −0.4499* 0.4900* 0.0289 0.1480* 1.0000 −0.5208* 0.0969 −0.3872* 1.0000 0.1200 0.3651* 1.0000 0.0574 1.0000 Note: * Significant at 5%. properties of the human capital variable to be better reflected in the regression results. The negative coefficient for human capital in my regressions is most likely the result of it being highly correlated with lagged real per capita GDP, as pair-wise correlations statistics indicate in Table IV. This correlation coefficient is statistically significant at 5% and has the highest correlation of 0.83 for the variables shown in Table IV. The next step is to add an interaction term (military spending times net arms exports) in order to test for a significant nonlinear relationship between current military spending and economic growth that is contingent upon the level of net arms exports. This is the approach used by Aizenman and Glick (2003) in their study of the interaction between military spending and threats resulting in a nonlinear relationship between military spending and growth. The regression shown in Column 3 (Table III) reveals a significant positive relationship between the interaction term and growth and significant negative relationship between net arms exports and growth, while maintaining a significant and negative relationship between current military spending and growth. These estimates suggest that while current military spending and net arms exports have a negative effect on growth, the effect of military spending on growth becomes positive with higher net arms exports. In other words, military spending becomes less detrimental to growth with higher net arms exports. This finding is similar to the non-linear relationship between growth and military spending in the presence of military threats found by Aizenman and Glick (2003). At this point, one would probably want to compare the random effects estimator with the fixed effects estimator. The next regression utilizes the GLS random effects estimator with the AR (1) disturbance term (Column 4, Table 3). The random effects estimator produces notably different results and is rejected by the Hausman specification test7 in favor of the consistent fixed effects estimator, which shows that military spending and net arms exports impede growth. The negative and significant relationship between economic growth and net arms exports may seem counter-intuitive at first. Perhaps, the negative growth effects of military spending can be so pervasive as to carry over to arms exports. Another possible explanation for this negative relationship is a two-way causality where slower economic growth has a negative effect on military budgets, forcing more export sales in place of canceled domestic military contracts. In this case, there might be an identification problem for both military spending and net arms exports. This identification issue and the potentially endogenous nature of military spending and arms exports could be better addressed using the Arellano–Bond GMM estimator. 7 If several regressors are severely endogenous, then the Hausman random effects test is invalid. As the ArellanoBond GMM estimator will later show, the endogeneity problem must not be severe since the Arellano-Bond estimates are similar to fixed effects estimates. This suggests that the Hausman random effects test could be trusted. ARMS TRADE, SPENDING & GROWTH 333 As previous research has shown, some variables in growth regressions may also exhibit endogeneity problems. Fertility, for example, could be influenced by measures of wealth, according to Barro and Lee (1994). Similarly, the military spending variable could be subject to the same endogeneity problem. Using the Durbin-Wu-Hausman endogeneity test, I find that military spending is indeed significantly endogenous.8 Often, good instruments (those correlated with the included explanatory variables and uncorrelated with the error term) are hard to find. Goldsmith (2003) identifies several significant determinants of military spending that could aid in choosing the appropriate instruments. Goldsmith (2003) identifies the lagged military spending, economic growth, wealth, and political regime type as significant and robust determinants of military spending. Since economic growth and lagged wealth (per capita GDP) are already included in the model, I use the natural log of political regime type,9 natural log of total country population, and Composite Index of National Capability10 (CINC) as instruments. Among these three instruments, the natural log of political regime type was found to be negatively and significantly related to military spending in a separate 2SLS-IV regression (results not shown to save space). The same regression also picked up a significant negative relationship between military spending and net arms exports. The Hansen J statistic from the same 2SLS-IV regression showed that the instruments chosen to identify current military spending could not be rejected. To control for the potentially endogenous nature of military spending and other regressors, I use the one-step Arellano–Bond GMM estimator with robust standard errors. In the Arellano–Bond GMM estimation, the right-hand side variables can be instrumented with firstdifferenced lags and the validity of the exogeneity assumption can be tested. Sometimes, the lagged values of endogenous variables are their own best instruments. The Arellano–Bond GMM estimator boils down to first-differencing the estimated equation and using lags of the dependent variable and explanatory variables as their instruments. Due to first-differencing, this estimator also removes the individual country effects and first-order autocorrelation. I use the one-step Arellano–Bond GMM estimator with robust standard errors for coefficient inferences. However, I use the two-step Arellano–Bond GMM estimator for autocorrelation and validity of instruments inferences.11 The autocorrelation and over-identification tests from the two-step Arellano–Bond regression support those one-step tests reported in the tables. All Arellano–Bond regressions in this study treat the current period regressors as endogenous and being conventionally instrumented for with their own lags. The results from the one-step Arellano–Bond regression with time fixed effects are shown in Column 5, Table III. Like Dreher (2005), I use the natural logarithm of per capita GDP (five-year average) as a dependent variable instead of the growth rate because the Arellano–Bond estimator uses firstdifferencing that converts logs of levels into growth rates.12 The Arellano–Bond estimator 8 One interesting result that comes out of the endogeneity testing is that democracy (used as an instrument for military spending) appears negatively and significantly related to military spending suggesting that the apparent positive correlation between democratic regimes and income per capita can be partially attributed to lower military burdens in more democratic nations. 9 Political regime type is constructed according to this commonly used formula (DEMOC-AUTOC+10)/2. The democracy (DEMOC) and autocracy (AUTOC) measures come from Polity IV Project. 10 Using CINC as an instrument for military spending might be considered problematic since CINC already contains a measure of military expenditure, albeit in dollar terms rather than as a share of GDP. Regardless, the inclusion or exclusion of CINC as an instrument for military spending does not make a significant difference. 11 Arellano and Bond (1991) recommend using the one-step GMM estimator for coefficient inferences because in small samples like mine standard errors tend to be underestimated by the two-step estimator. The two-step estimator weighs the instruments asymptotically efficiently using the one-step estimates. The Arellano–Bond estimator, however, leads to a loss of observations from 196 to 140 since information from two periods is discarded by firstdifferencing. 12 First-differencing is also performed for all independent variables, which are treated as endogenous in Arellano– Bond regressions in this paper. 334 P. YAKOVLEV automatically uses lagged first-differenced dependent variable (per capita GDP) as an independent variable. The new lagged first-differenced per capita GDP no longer captures growth convergence, but rather growth momentum as indicated by its positive sign. All explanatory variables come out of the regression expressed in first-differences and lagged first-differences. In the Arellano–Bond regression (Column 5, Table III), lagged dependent variable, investment share, and population growth are all statistically significant and have the expected signs. Moreover, the human capital variable has the expected positive sign, but is not statistically significant. The military spending variable is negatively and significantly related to growth. The net arms exports variable is also negatively and significantly related to growth, while the interaction term is positively and significantly related to growth. The Sargan test of overidentifying restrictions (i.e. validity of instruments) shown in Column 5 (Table III) suggests that the instruments chosen to identify current military spending could not be rejected. This Arellano–Bond regression with endogenous regressors is in agreement with the previous findings obtained with the two-way fixed effects FGLS estimator for the augmented Solow growth model. Next, I will present the Barro-style regressions and compare their results with the abovementioned Solow-style regressions. Table V shows the estimates for the Barro-style regressions, which I believe perform worse than the Solow-style regressions in the context of this paper. The lagged per capita GDP, investment share, and population growth variables (but not human capital) exhibit robust and intuitive relationships with economic growth in the two way-way fixed effects Barro-style regressions as seen in Columns 6, 7, and 8 of Table V. Military spending is negatively and significantly related to growth in the first two of these regressions, which agrees with Mylonidis (2006) who also ran Barro-style FGLS regressions. However, the Barro-style regressions do worse than the Solow-style regressions when it comes to picking up statistical significance for military spending and net arms exports when the interaction term is included (Column 8, Table V). Although military spending, net arms exports, and the interaction term do not appear statistically significant at the 5% level, they at least turn out having the same signs as in the Solow-style regressions. Not very encouraging are the estimates in the next regression, which utilizes the GLS random effects estimator with the AR (1) disturbance term. Variables like lagged real per capita GDP, investment share, population growth, military spending, and even human capital come out statistically significant and have the expected signs (Column 9, Table V). However, military spending, net arms exports, and the interaction term are all insignificant. Ultimately, this random effects estimator is rejected by the Hausman specification test in favor of the two-way fixed effects FGLS estimator just as in the case with the Solow-style regressions. The Arellano–Bond GMM does not perform very well in the Barro-style specification with respect to military spending, although it shows net arms exports and the interaction term to be highly significant and appropriately signed (Column 10, Table V). The Sargan and Arellano– Bond autocorrelation tests fail to reject, respectively, the validity of instruments and absence of the second-order autocorrelation. Clearly, the estimates for military spending and net arms exports do not appear as robust in the Barro-style regressions as they do in the Solow-style regressions. Generally, increasing the number of lagged endogenous variables used as their own instruments in the Arellano-Bond regression could increase the amount of information being incorporated in the estimates. However, the benefit of incorporating more and more lags falls with higher order of lagged instruments since ‘older’ lags contain fewer and fewer useful information about current period variables. In this study, reducing the number of lagged endogenous variables used as instruments from three to two results in higher t-statistics for ARMS TRADE, SPENDING & GROWTH TABLE V Model 335 The Growth Effects of Military Spending and Net Arms Exports in the Reformulated Barro Growth 6 lnyit−1 sit popgit lnhit mit naxit −5.18*** (0.55) 0.25*** (0.02) −0.85*** (0.22) −1.01 (0.62) −0.08** (0.04) – Estimator Wald Chi-Square F-statistic P-value Baltagi-Wu LBI (Durbin-Watson stat.) Sargan test (p-level) Arellano-Bond autocorrelation test (p-level) Observations 8 9 10 −2.68*** (0.38) 0.22*** (0.03) −0.64*** (0.22) 1.01* (0.52) −0.02 (0.08) 0.22 (0.46) 0.04 (0.11) 21.28*** (2.95) GLS-RE 104.53 – 0.00 2.23 (1.95) – – 0.78*** (0.08) 0.014*** (0.002) −0.002 (0.022) 0.09 (0.07) −0.003 (0.007) −0.08** (0.03) 0.012*** (0.004) 0.03* (0.02) A-B GMM – 31.09 0.00 – 196 140 – −5.26*** (0.55) 0.25*** (0.02) −0.83*** (0.21) −0.76 (0.64) −0.09** (0.04) −0.36 (0.24) – 37.61*** (7.95) FGLS 870.10 – 0.00 – 38.47*** (7.95) FGLS 899.52 – 0.00 – −5.41*** (0.57) 0.26*** (0.02) −0.78*** (0.23) −0.82 (0.64) −0.05 (0.07) −0.51* (0.30) 0.04 (0.06) 38.82*** (8.34) FGLS 894.93 – 0.00 – – – – – – – (naxit)(mit) Constant 7 196 196 196 0.91 0.42 Notes: Dependent variable: five-year average growth rate of real per capita GDP from 1965 to 2000. Standard errors shown in parentheses. Significance levels: *** at 1%, ** at 5%, and * at 10%. FGLS uses errors corrected for panel-specific heteroskedasticity and AR (1) autocorrelation with adjusted Durbin–Watson computation. The random effects regression (GLS-RE) here is estimated with GLS. The Baltagi-Wu LBI statistic is equivalent to the Durbin–Watson statistic: if it is far below 2.00 then a correction for serial correlation is necessary. Here, the A-B GMM or Arellano–Bond one-step GMM estimator uses robust errors with Huber-White sandwich and time fixed effects. All independent variables were treated as endogenous and their lagged first-differences (lags 1–3) were used as instruments, which passed the Sargan over-identification test. The A-B GMM automatically uses lagged first-differenced dependent variable instead of lnyit−1. The null hypothesis in the Arellano–Bond test: no second-order autocorrelation in the residuals. military spending, net arms exports, and the interaction term in both Solow and Barro regressions. The estimates with two lags of instruments are not included in the paper in order to save space. This is a good time to summarize the results from the Solow and Barro-style regressions. There are two main conclusions that can be made from these results. First, the specification of the augmented Solow growth taken from Dunne et al. (2004, 2005) performs better empirically than the specification of the Barro growth model used in Mylonidis (2006) and Aizenman and Glick (2003). The estimates for the military spending variable are more robust in the Solow-style regressions in both fixed effects and Arellano–Bond estimators, compared to the Barro-style regressions. Throughout all Solow regressions, the Wald chi-square or F statistics are much higher than those in Barro regressions. Furthermore, the link specification test13 and 13 If a regression is properly specified, then the link test should show that no additional significant independent variables could be identified. It does so by refitting the model using y-hat and y-hatsq as predictors. While y-hat should be significant since it is the predicted value, y-hatsq should not be significant or have much explanatory power if the model is specified correctly. 336 TABLE VI P. YAKOVLEV Link and Omitted Variable Tests of the Solow and Barro Style Regressions Link test for model specification: Prob > F R-squared y-hat y-hatsq Ramsey RESET test—H0: model has no omitted variables: Prob > F Solow Barro 0.00 0.68 0.95*** (0.09) 0.01 (0.01) 0.00 0.65 0.91*** (0.10) 0.02 (0.02) 0.13 0.12 Notes: Standard errors are in parentheses. Significance levels: *** at 1%, ** at 5%, and * at 10%. If a regression is properly specified, then the link test should show that no additional significant independent variables could be identified. It does so by refitting the model using y-hat and y-hatsq as predictors. While y-hat should be significant since it is the predicted value, y-hatsq should not be significant or have much explanatory power if the model is specified correctly. omitted variable test (Table VI) pass the two models, but favor slightly the Solow specification described in Dunne et al. (2004, 2005) and implemented in this paper. The second important conclusion is that the two-way fixed effects FGLS estimator is probably better suited for estimating the Solow growth model than the Arellano–Bond GMM estimator when the number of observations is rather limited. Although both estimators produce compatible results in this paper, a fixed-effects estimator that controls for heteroskedasticity and autocorrelation might be even more efficient in my case than the Arellano–Bond estimator that ‘shoots you in the foot’ by reducing valuable observations. According to Wooldridge (2001), a generalized method of moments can improve, in large samples, over the standard panel data methods like ordinary, two-stage least squares or fixed effects when auxiliary assumptions fail. However, Wooldridge (2001) also notes that because these standard panel data methods can be used with robust inference techniques allowing for heteroskedasticity or serial correlation, the gains to practitioners from using GMM may be small, especially in small samples. Considering that the Arellano–Bond GMM estimator reduces my sample from 196 to 140 observations, it is a very valid concern. Moreover, the FGLS estimator includes both country and time fixed effects, whereas the Arellano–Bond GMM estimator includes only the time effects since first-differencing removes the country effects. Thus, I prefer the two-way fixed effects FGLS estimates of military spending, net arms exports, and their interaction with growth. The two-way fixed effects FGLS estimates based on the Solow growth model suggest that while higher military spending and net arms exports lead, on their own, to lower economic growth, higher military spending is less damaging to growth when a country is a large net arms exporter. CONCLUSION Using fixed effects, random effects, and Arellano–Bond GMM estimators I investigate the effect of military spending, net arms exports, and their interaction on economic growth in the Solow and Barro style regressions. The estimates suggest that the augmented Solow growth model with military spending as specified in Dunne et al. (2005) yields more robust estimates than the reformulated Barro model used by Aizenman and Glick (2003). According to the Solow-style regressions, military spending is negatively related to economic growth, net arms exports are negatively related to economic growth, and their interaction is positively related to ARMS TRADE, SPENDING & GROWTH 337 economic growth. This means that higher military spending and net arms exports separately lead to lower economic growth, but higher military spending is less damaging to growth when a country is a net arms exporter. In other words, if a country hopes to lose less in economic growth from an additional military spending, it better be a net arms exporter. For instance, the estimates in Column 3 of Table IV suggest that an average arms importing country with an average military spending would lose on average 3.7% in economic growth from military spending and arms imports. A country with zero net arms exports and average military spending would lose 3.6% in economic growth. In order for a country with average military spending to completely cancel out the negative effect of military spending, its net arms exports must significantly exceed the sum of its arms imports and arms exports, which is not possible by definition. In fact, no country for any given five-year period in the data set ever achieves a net positive effect on growth from military spending and arms exports. A number of potential avenues for future research should be suggested here. One could explore an interaction between military spending and internal threats as proxied by the degree of domestic unrest, civil wars, income inequality, and limited economic or political freedoms. A more precise study on the rule of law and how it relates to domestic security spending and growth would be warranted. A new insight might be gained by exploring how military alliance patterns (NATO, for instance) may affect the defense-growth relationship. Researchers might also want to look at the determinants of arms exports. References Aizenman, J. and Glick, R. (2003) Military expenditure, threats and growth. NBER Working Paper 9618. Anderton, C. H. (1995) Economics of arms trade. In Handbook of Defense Economics, edited by K. Hartley and T. Sandler. 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