Military spending and the growth-maximizing allocation of public capital: a cross-country empirical analysis.

Kalaitzidakis, Pantelis ; Tzouvelekas, Vangelis

I. INTRODUCTION

Public spending promotes economic growth by enhancing the productive capacity of private firms. The literature recognizes the possibility that different types of public spending (e.g., infrastructure, education, health, and military expenses) can exert different impacts on economic growth. Military spending is a case in point. Given its value in maintaining both internal and external security, military spending increases the incentives to accumulate private capital and attract foreign investment. The defense sector also provides a variety of public infrastructure (e.g., roads and communication networks), while also enhancing human capital accumulation through training and provision of educational services. On the other hand, military spending diverts resources that could be more productive for the economy in nonmilitary uses, In this sense, defense spending may degrade long-run economic growth. (1)

The characterization of the external effect of public spending on private firm decisions has focused on the context of a production function with the specification of the aggregate flow of public spending (Barro 1990) or the aggregate stock of public capital (Turnovsky 1997). A line of research takes care to break out different forms of public spending. Devarajan, Swaroop, and Zou (1996) recognize productive and unproductive public spending play distinct roles in an endogenous growth model using a production function. Kalaitzidakis and Kalyvitis (2004) break down public spending into infrastructure and maintenance expenditure, while Chen (2006) into productive and consumptive spending.

Benoit's (1973, 1978) seminal work decomposes growth rates to investigate defense expenditure rates on economic growth for a panel of 44 less developed nations between 1950 and 1965. With a view toward assessing the impact of different forms of public capital on economic growth, the production function approach has been undertaken to investigate the impact of government spending by type on growth (e.g., Baffes and Shah 1998, cross-country panel; Evans and Karras 1994, for a panel of states in the United States). Devarajan, Swaroop, and Zou (1996) investigate the impact of public capital types by focusing on growth rates and assume linear relations between the different types of government spending and the growth rate of real per capita gross domestic product (GDP). (2)

However, a theoretical growth model developed recently by Shieh, Lai, and Chang (2002) suggests that the effect of the budget share of military spending on GDP growth is nonlinear, following an inverse U-shaped pattern. Building upon theoretical construction in Shieh, Lai, and Chang (2002), this study derives the growth-maximizing values of the shares of public investment allocated to the two different types of public capital (i.e., military and nonmilitary spending), as well as the growth-maximizing tax rate. Focusing on a panel of both developed and developing economies, an empirical investigation is undertaken to assess the theoretical implications of the model that both the effect of the budget share of military spending and that of the tax rate on long-run growth are nonlinear, following an inverse U-shaped pattern.

The rest of the paper is organized as follows. Section II sets up a representative firm model and derives the growth-maximizing levels of the tax rate and the shares of public capital investment. Section III sets up the econometric procedures followed and presents an empirical investigation of the theoretical model in a sample of developed and developing economies. Finally, Section IV concludes the paper.

II. THEORETICAL FRAMEWORK

We consider a closed economy populated by identical agents consuming and producing a single commodity, Y, without population growth. The labor force is equal to the population, with labor supplied inelastically. On the production side, the representative firm j produces its output, using a conventional Cobb-Douglas technology, i.e., [Y.sub.j] = [K.sup.a.sub.j][([hL.sup.j]).sup.1-[alpha]] where 0 < [alpha] < 1, [K.sub.j] denotes the stock of private capital, and [L.sub.j] the labor used by firm j. The productivity of labor, h, is a function of the existing stock of public infrastructure (Z), and military capital (M), per worker so that: h = [Z.sup.[beta]][M.sup.1-[beta]]/L, where L is the total labor force, and 0 < [beta] < 1. The individual firm takes h as given. There are three types of capital in our economy: private, infrastructure, and military, which, for simplicity, depreciate at a common rate [delta]. If we let [G.sub.z] and [G.sub.M] denote gross public investment for infrastructure and military capital, respectively, then the net stock of each type of capital accumulates as follows:

[??] = 1 - [dekta]K, Z = [G.sub.z] - [delta]Z, M = [G.sub.M] - [delta]M. (1)

New output may be transformed to any type of capital, but in the case of private capital this process involves adjustment costs. The cost of investment faced by domestic firms is [psi](I, K) = (1 + [phi]/2 I/K)I where [phi] > 0 is the adjustment cost parameter. (3) The government finances its total expenditure through tax revenues collected via a tax rate [tau] imposed on total output produced by domestic firms. If the share of total government expenditure that goes toward military capital formation is denoted by [mu], then it holds that [G.sub.M] = [mu][tau]Y and [G.sub.z] = (1 - [mu])[tau]Y.

The representative firm j in our closed economy solves the following infinite horizon profit maximization problem:

max [[integral].sup.[infinity].sub.0] [e.sup.-rt] [(1 - [tau][Y.sub.i] - w [L.sub.j] (1 + [phi]/2 [I.sub.j/[K.sub.j]) [J.sub.j]]dt

(2) s.t. [[??].sub.j] = [I.sub.j], [delta][K.sub.j].

where r is the real interest rate, w is the real wage rate, while the price of Y is normalized to one. The corresponding first order conditions from the Hamiltonian upon aggregating across firms are:

(3) 1 + [phi] I/K = q [??] [??]/K = q - 1 / [phi] - [infinity]

(4) r = 1/q [[??] + (1 - [tau])[alpha] [(K/L).sup.[alpha]-1] [h.sup.1 - [alpha] + [phi]/2 [(1/K).sup.2]] - [delta],

where q is the shadow value of the private capital stock. Using relations (1), (3), and (4) we obtain:

(5) [??]/z = - q -1/[phi] + [tau] 1 - [mu]/z [z.sup.[beta](1 - [alpha])] [m.sup.(1-[beta])(1 - [alpha])]

(6) [??]/m = q - 1/[phi] + [tau] [mu]/m [z.sup.[beta](1 - [alpha])] [m.sup.(1-[beta])(1 - [alpha])]

(7) [??] = [r + [delta])q - (1 - [tau])[[alpha]z.sup.[beta](1 - [alpha]]) [m.sup.(1-[beta])(1 - [alpha])] - [(q - 1).sup.2]/2[phi],

where z [equivalent to] Z/K, and m [equivalent to] M/K. The stationary solution of the above system yields the equilibrium values of q and z, which are jointly determined by the following relations:

(8) q = 1 + [phi][tau][(1 - [mu]).sup.(1-[beta])(1 - [alpha])] [[mu].sup.1 - (1 - [beta])(1 - [alpha]) [Z.sup.-[alpha]

(9) (1 - [tau][alpha] [(1 - [mu]/[mu]).sup.(1 - [beta])(1 - [alpha])] [z.sup.1 - [alpha] = (r + [delta]) q - (q - [1.sup.2])/2[phi].

By totally differentiating the above equations with respect to [tau] and [mu], and taking into account the fact that the growth rate of the economy is an increasing function of the shadow price of private capital (see Equation (3)), yields:

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Following Shieh, Laim, and Chang (2002), the above relations indicate that the effects of both [tau] and [mu] on the growth rate are nonlinear, following an inverse U-shaped pattern. When these two policy variables are relatively small (large), an increase in their values raises (reduces) the growth rate of the economy.

III. EMPIRICAL SPECIFICATION, TESTING AND RESULTS

The quantitative assessment of the effect of the allocation of public investment on GDP growth employs a balanced data set of 17 Organization for Economic Co-operation and Development (OECD) and 38 non-OECD countries (4) covering the period from 1980 to 1995. The data for GDP at constant 1995 international prices, private and public investments and military expenditures are obtained from the Global Development Network Growth Database developed by the World Bank. The sample size over both countries and time was restricted by data availability on military spending by individual countries.

A. Specification

The econometric specification of the per capita growth equation is linearly related to (a) the share of private investment to GDP, which has been shown to be a robust explanatory variable of GDP growth, and (b) the real per capita-lagged GDP to capture any convergence process in the sampled countries. The allocation of public capital between military expenditures and public infrastructure enter the econometric specification quadratically to allow for a nonlinear pattern. The model is presented as:

(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [[??].sub.it] is the growth rate of real per capita GDP for country i = 1 ..., N at year t = 1, ..., T, [y.sub.it-1] is the one period-lagged real per capita GDP, [z.sub.it] = [I.sub.it]/[y.sub.it] is the share of private investment to GDP, [k.sub.it] = [G.sub.it]/[y.sub.it] is the share of total public spending to GDP and serves as a proxy to the tax rate [tau], [m.sub.it] = [M.sub.it]/[G.sub.it] is the share of military expenditures to total public spending, and 13s are the parameters to be estimated. The regression parameters, [beta]s, are all country specific allowing thus for intracountry heterogeneity on the effect of the explanatory variables on the growth rate of real per capita GDP.

B. Time Series Testing and Evaluations

Viewing Equation (12) as the long-run equilibrium relationship of optimal public capital allocation and GDP growth, we investigate if all variables in Equation (12) are integrated of order 1. To test this hypothesis, we employ the panel unit root tests of Im, Pesaran, and Shin (2003) and Maddala and Wu (1999). These tests have an advantage over earlier generation tests such as Breitung and Meyer (1994), Quah (1994), and Levin, Lin, and Chu (2002) in that they allow for greater flexibility under the alternative hypothesis. (5) First, Im, Pesaran, and Shin (2003, IPS hereafter) using the maximum likelihood framework suggest a procedure based on averaging individual unit root test statistics for panels. (6) Instead of averaging the individual Augmented Dickey Fuller (ADF) t-statistics, Maddala and Wu (1999, MW hereafter) suggest using the pooled values of the associated individual marginal significance levels. (7)

Upon establishing the existence of a unit root, the next step is to statistically examine the long-run relationship among GDP growth and the fight-hand side variables in Equation (12). This is accomplished with the panel cointegration test due to Levin, Lin, and Chu (2002). (8) With the long-run relationship established, the econometric estimation of relation (12) can be accomplished using Pedroni's (1996, 2000) between-dimension fully modified OLS estimator (FMOLS) which allows for the dynamic heterogeneity in cointegrated panels so that the transitional dynamics can be different among different countries in the sample. Thus, the FMOLS estimator addresses consistently the problem of nonstationary regressors as well as that of possible simultaneity bias. (9)

Pedroni (1999) develops a group p-statistic which is analogous to Philips-Perron rho-statistic based on the estimated autoregressive parameter, and both a nonparametric and parametric t-statistic analogous to the Phillips-Perron and ADF t-statistics well established in single time series literature. All these statistics are standardized by the means and variances so that they are distributed as N(0,1) under the null hypothesis. 10 These cointegration tests allow for considerable heterogeneity among countries in the sample, including heterogeneity in both the long-run cointegrating vectors as well as heterogeneity in the dynamics associated with short-run deviations from these cointegrating vectors.

The empirical analysis is carried out on the whole sample of developed and developing countries as well as OECD and non-OECD countries. We have also considered various country subgroupings according to the geographical location (i.e., Latin America, Africa, Europe, and Asia) to investigate the robustness of our results, but no clear pattern emerged. First, Table 1 summarizes the results of both IPS t-bar and MW Fischer statistics for all countries in the sample as well as for the two subgroups. (11) The lag truncations for the individual unit root regressions are allowed to vary by individual country in all three samples. The same procedure is followed also for the panel-based IPS and MW tests. The standard step down procedure applied in conventional time series analysis is employed to choose the lag length. This procedure involves starting with a sufficiently large number of lags and then eliminating a lag each time until one of them is statistically significant. For the initial starting value, with T = 15, we started with an initial lag value of 3, and then allowed the data-dependent procedure to choose the actual number of fitted lags. The actual number of fitted lags varied between 0 and 3 for each country in the sample.

The statistical testing results reported in Table 1 show that all series involved in each one of the three samples has a unit root at the 5% confidence interval. This is confirmed from both IPS t-bar and MW Fisher statistics. Given the short time span of our data, it is more likely that our data are coming from the early stages of the business cycle in the countries in the sample. However, when the first differences of that data series are used, the hypothesis of a unit root is rejected in all cases and for all variables.

The panel cointegration results for all subgroups of countries and the entire sample is reported in Table 2. In principle, the hypothesis of no cointegration is rejected for all countries and the hypothesis of one cointegrating vector is accepted. The Levin, Lin, and Chu (2002) test, with only fixed effects as well as with both fixed and time effects included, supports the hypothesis of a cointegrating relation between GDP growth and the explanatory variables included in Equation (12). On the other hand, the Maddala and Kim (1998) Fisher test supports the presence of one cointegrating vector in all subgroups of countries and the entire sample. Finally, Pedroni's (1999) test statistics in the context of between-dimension FMOLS estimator accept the hypothesis of a cointegrating relationship between GDP growth and all variables included in Equation (12). This is true only for the parametric ADF t-statistic, while both the rho and nonparametric Phillips-Perron t-statistic reject the hypothesis of cointegration for the sample of non-OECD countries.

All these tests employed so far are based on the analysis of possible cointegrated relations between GDP growth and the variables included in the empirical analysis. However, none of these tests takes into account the possibility of a cointegrating relationship that may exist between countries for any variable included in Equation (12). If this is the case then the between-dimension FMOLS estimator may yield biased results as the between transformation that is applied to the data before the estimation may destroy the cointegrating relationship that statistical testing confirmed previously. This may be true if military spending in individual countries is relative to each other so that each mit is cointegrated to one another. The ADF t-statistics of the mean normalized variables confirms that the between transformation does not render any of the series stationary. (12)

C. Econometric Results on the Growth Rate Estimation

Between-dimension FMOLS estimates of the cointegrating relationship for the entire sample of countries as well as for both OECD and non-OECD countries are reported in Tables 3-5. Regarding the entire sample estimates, the effect of both total public spending and military spending exhibits an inverse U-shaped pattern.

Private Investment. Private investment influences the growth rate of real per capita GDP positively, 0.238, while the GDP of the previous period negatively impacts the economic growth rate in countries in the sample at a lower but statistically significant rate, -0.058. The between-dimension FMOLS estimates for OECD countries are presented in Table 4. The results for the pooled sample (last row in Table 4) indicate that the share of private investment still impacts the growth rate of GDP positively with a higher magnitude 0.298, than in the case of the pooled sample. The individual country estimates, however, indicate significant variation. The highest impact is observed for United States followed by Ireland and United Kingdom, while Mexico, Greece, and Poland offer a much lower significance of private investment on economic growth. Finally, in Denmark, France, and Turkey, the relevant parameter estimates are statistically insignificant. The one period-lagged GDP still impacts the growth rate of per capita GDP negatively. The corresponding parameter estimate for the pooled data is -0.046 but again with a greater variation across OECD countries. In United States, Norway, Mexico, and Australia, the corresponding parameters are not statistically significant different than 0, implying that there is a structurally dependent permanent boost in their growth rates. In contrast, the GDP growth rate is highly dependent on their growth pace exhibiting the highest parameter estimates. Ireland, Luxemburg and Poland, Belgium, Canada, Denmark, and France exhibit the lowest impact with the corresponding parameter estimates being statistically significant on the order of -0.020.

Public Investment. For the pooled data, the share of public investment is monotonically decreasing. Both first- and second-order parameter estimates exhibit lower values compared with those obtained from the econometric estimation of the entire sample. Focusing on intercountry differences, the GDP share of total public spending appears to be at the optimal level in Belgium, Canada, Finland, and Ireland as both the associated first- and the second-order parameters turned to statistically not significant values. For the remaining 13 OECD countries in the sample, the inverse U-shaped pattern emerges in all cases but at a different magnitude. Military spending in Canada, Japan, and Luxemburg does not impact economic growth. In all three countries, the corresponding parameter estimates are not significant at the 5% level. Nevertheless, the impact of military spending is monotonically decreasing at a different rate for the remaining 14 countries. Using these parameter estimates, we have generated the respective marginal effects of total public spending and military spending on the growth rate of GDP and the results are presented in Table 6.

Marginal Value of Spending. The marginal effect of the GDP share of total public spending presented in Table 6 exhibits both negative and positive values which, however, are very close to their respective optimal levels. Similarly, the point estimate for the entire panel of the OECD countries exhibits a value close to zero, 0.0063, implying that public expenditures are rather close to their optimal level. In France, Greece, Luxemburg, and Norway, the marginal impact of the GDP share of total public spending is negative, implying that a relatively large portion of public budget, compared to the size of these economies, is allocated to public investment. On the other hand, the highest positive values are observed in United States (0.0477), United Kingdom (0.0436), Turkey (0.0318), and Poland (0.0301), implying public investment is below its optimal value. Finally, in Denmark and Korea, the relevant point estimates are closest to 0 and, thus, at their respective optimal levels.

The same nonuniform pattern emerges also for military spending. However, the individual point estimates exhibit a greater variation than those for spending on public infrastructure. The mean estimate for the whole panel is 0.1580, indicating that the allocation of public capital in military spending is far below its optimal level. In France, Greece, Turkey, United Kingdom, and United States, military spending is beyond its optimal allocation with the highest absolute values coming from France and United States with point estimates of -0.1261 and -0.1173, respectively. For the rest of the countries, the marginal impact of military spending is positive. The highest values are in Mexico (0.2502) and Norway (0.2189), indicating that these two countries are below the optimal allocation. In contrast, Australia and Belgium exhibit a point estimate very close to 0, implying that the allocation of public investment between infrastructure and military capital accumulation is growth maximizing.

Turning to the non-OECD countries, the corresponding parameter estimates are presented in Table 5. For the entire panel, the point estimates indicate that the lagged GDP is negatively impacting the current economic growth, that is, there is a lack of private investment in developing countries (see the last row in Table 5). Concerning the impact of the GDP share of total public spending and the share of military spending on economic growth, the estimates confirm the nonlinear relationship that emerges from the theoretical model. But the variation among developing countries is more intense than the sample of OECD countries. The intertemporal dependence of economic growth on the level of economic activity is consistently negative in all countries in the sample. The lowest impacts are observed in Brazil (-0.091), Guatemala (-0.088), Bangladesh (-0.087), South Africa (-0.079), and Paraguay (-0.078); the highest impacts are observed in Venezuela (-0.015), Egypt (-0.021), Colombia (-0.022), India (-0.031), Costa Rica (-0.031), and Peru (-0.031). The relative share of private domestic investment is higher in China (0.339), Argentina (0.301), India (0.289), Pakistan (0.276), and Philippines (0.269). In contrast, Iran, Madagascar, Ecuador, Namibia, Papua, and El Salvador present the lowest relative share of private investment in the sample. Finally, Bangladesh, Cote d'Ivoire, Dominican Republic, Guinea, Malawi, Malaysia, Trinidad-Tobago, and Tunisia present statistically significant values on this coefficient.

With regard to the GDP share of total public expenditures, Argentina, El Salvador, Guinea, Iran, Madagascar, Morocco, Pakistan, and Uruguay present statistically nonsignificant values, suggesting the GDP share of public spending is at its optimal level. For the remaining countries, the inverse U-shaped pattern is present in all but five countries (Colombia, Cote d'Ivoire, Dominican Republic, Ecuador, and Trinidad-Tobago). Table 7 presents the marginal impacts of military and total public spending using these point estimates. Bulgaria, China, and Romania present the GDP share of total public expenditures to be above its optimal level as the marginal impacts turned to a negative value very close to 0. In all other countries, the corresponding marginal impacts are positive indicating under provision of public investment. The highest value is observed in Costa Rica (0.3694) followed by Peru (0.3444), Mauritania (0.3428), Bolivia (0.3159), and Malaysia (0.3073). In all these countries, public investment is far below its optimal level. On the other hand, the lowest values are observed in Namibia (0.0570), Malawi (0.0818), Egypt (0.1008), Nicaragua (0.1095), Brazil (0.1278), and Kenya (0.1341) suggesting overprovision of public investment.

Finally, the parameter estimates presented in Table 5 indicate military spending in developing countries is not impacting the economic growth in Bulgaria, Cote d'Ivoire, Dominican Republic, El Salvador, Guinea, Madagascar, Morocco, Nicaragua, Pakistan, Papua, and Uruguay. The corresponding parameter estimates in these countries are all statistically nonsignificant than 0. The nonlinear relationship between military spending and GDP growth is not established in Bangladesh, Costa Rica, Guatemala, Malawi, Paraguay, Thailand, Trinidad-Tobago, and Tunisia, as the quadratic term turned to a statistically nonsignificant value. For the remaining 19 non-OECD countries, the inverse U-shaped pattern emerges. The corresponding marginal effects computed using the parameter estimates appearing in Table 5 are presented also in Table 7.

The mean effect of military spending for the entire panel is similar with that of public expenditures, 0.2674. However, individual country estimates exhibit both negative and positive values. Specifically, the marginal effect estimates are all negative in China, Chile, Colombia, India, and Iran, indicating that these countries allocate more than the optimal expenditures in military spending with respect to the relative size of their public investment. However, still these levels are not far from the optimal one. On the other hand, in Namibia, Mauritania, Malaysia, South Africa, and Ecuador, military spending is well below its optimal level. Specifically, Namibia exhibits a point estimate of 0.2990, the highest among all countries in the sample. Contrary, Egypt, Argentina, and India have achieved a better allocation of their public capital with respect to military spending as their marginal effects are very close to 0.

IV. CONCLUDING REMARKS

The main goal of this paper was to present an endogenous growth model to empirically address the growth maximizing allocation of public capital among expenditures on public infrastructure and military spending. Using this general model that draws from the theoretical framework developed by Shieh, Lai, and Chang (2002), we analyze the stability of the long-run equilibrium and we derive the growth-maximizing values of public capital allocated to its two different types, as well as the growth-maximizing tax rate. The model is applied to a panel of OECD and non-OECD nations to assess the implications of our theoretical model about the nonlinear effects of the tax rate and the allocation of public investment on the growth rate.

The empirical investigation carefully accounts for the nonstationarity in the data before estimating the long-run relationship between economic growth and the allocation of public capital. The empirical results strongly support the implication of our theoretical model by indicating the existence of an inverse U-shaped pattern between the share of military spending and the growth rate, as well as between the share of total public investment in GDP and the growth rate. This uniform pattern is more evident for the sample of OECD countries with some notable exceptions. In developing countries, the results also support the results implied by the theoretical model at a reduced level of intensity. However, the impact of public capital and military spending is not linear following an inverse U-shaped pattern for the majority of the developing countries in the sample.

ABBREVIATIONS

ADF: Augmented Dickey Fuller

OECD: Organization for Economic Co-operation and Development

FMOLS: Fully Modified OLS Estimator

GDP: Gross Domestic Product

IPS: Ira, Pesaran, and Shin

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(1.) Benoit (1973, 1978), using data from 44 developing countries, found that the net effect military spending on economic growth is positive. This result, which is known as the Benoit hypothesis, has been confirmed by a number of subsequent empirical studies (see Adams, Behrman, and Boldin 1991; Sandler and Hartley 1995; Ram 1995).

(2.) The Barro-type regression results usually indicate a nonsignificant or negative effect of public expenditure variables on economic growth interpreted as an overprovision of public capital.

(3.) The inclusion of adjustment costs allows the presence of transitional dynamics when analyzing the dynamic behavior of the model. Notice that we will not include adjustment costs for public capital formation, as this would only complicate the solution of the model without adding further insights.

(4.) The OECD countries included in the sample were Australia, Belgium, Canada, Denmark, Finland, France, Greece, Ireland, Japan, Korea, Luxemburg, Mexico, Norway, Poland, Turkey, United Kingdom, and United States. Accordingly the sample of non-OECD includes Argentina, Bangladesh, Bolivia, Brazil, Bulgaria, Chile, China, Colombia, Costa Rica, Cote d'Ivoire, Dominican Republic, Ecuador, Egypt, El Salvador, Guatemala, Guinea-Bissau, India, Iran, Kenya, Madagascar, Malawi, Malaysia, Mauritania. Morocco, Namibia, Nicaragua, Pakistan, Papua, Paraguay, Peru, Philippines, Romania, South Africa, Thailand, Trinidad-Tobago, Tunisia, Uruguay, and Venezuela.

(5.) Panel-based unit root tests have been initially suggested by Quah (1992, 1994). However the tests suggested by Quah do not accommodate heterogeneity across groups which is most likely the case with aggregate country data. On the other hand, the unit root test developed by Levin, Lin, and Chu (2002) and Breitung and Meyer (1994) allows for heterogeneity only in the constant term in the ADF regression equation.

(6.) Specifically, their t-bar test statistic is based on the average of ADF statistics computed for each cross-section unit in the panel. Their approach allows for residual serial correlation and heterogeneity of the dynamics and error variances across groups.

(7.) Breitung (1999) found that the IPS t-bar test statistic is sensitive to the specification of individual deterministic trends losing their respective explanatory power. On the one hand, the MW test statistic is not dependent on the lag lengths used in estimating the individual ADF tests, while on the other hand it takes into account the role of individual countries in contributing to the overall results for the panel. In particular, the MW Pearson-lambda statistic provides insight into whether the results for the panel are generally being driven by the strength of one or two outlier countries or whether it is a general tendency of all countries in the panel.

(8.) To deal with the heterogeneity among countries in the sample not accounted for by the test-statistic, we use Fisher's test to aggregate the individual p-values of Johansen's maximum likelihood cointegration test statistics as suggested by Maddala and Kim (1998, 137).

(9.) An important advantage of between-dimension FMOLS estimator compared to within dimension FMOLS is that it permits greater flexibility in the presence of heterogeneity of the cointegrating vectors. Specifically, the test statistics constructed to statistically examine the cointegrating slope parameters of the model are not constrained to be the same under the alternative hypothesis. In addition, the between-dimension point estimates are the mean values of the cointergating vectors when these are indeed heterogeneous (Pedroni, 2001, 728).

(10.) See Pedroni (1999) for more details on the FMOLS estimator and the exact formulas for calculating the corresponding test statistics.

(11.) In order to conserve space the individual ADF tests for each country in the sample are not reported but are available upon request.

(12.) The corresponding test statistics are not reported here but are available upon request.

PANTELIS KALAITZIDAKIS and VANGELIS TZOUVELEKAS *

* This research has been partly supported by a Marie Curie Transfer of Knowledge Fellowship of the European Community's Sixth Framework Programme under contract number MTKD-CT-014288. The authors thank Spiro Stefanou, Theofanis Mamuneas, and Thanasis Stengos for their useful comments and suggestions that materially improved the paper. The usual caveats apply.

Kalaitzidakis: Ass. Professor, Department of Economics, University of Crete, Crete, Greece. Phone +30-28310-77408, Fax: +30-28310-77406, E-mail kalaitz@econ.soc.uoc.gr.

Tzouvelekas: Ass. Professor, Department of Economics, Faculty of Social Sciences, University of Crete, University Campus, 74100 Rethymno, Crete, Greece. Phone +30-28310-77417, Fax +30-28310-77406, E-mail vangelis@econ.soc.uoc.g

doi: 10.1111/j.1465-7295.2009.00242.x

TABLE 1
Panel Unit Root Tests

 IPS t-Bar Test Statistic

Variable Levels First Difference

Whole sample (N = 55)

GDP growth -1.0712 -6.6072 *
Lagged GDP -0.7153 -2.3765 *
Share of private investment 0.3827 -3.3784 *
Share of total public spending -0.2281 -4.7781 *
Share of military spending -0.9573 -5.4429 *

OECD countries (N = 17)

GDP growth -0.2332 -2.3772 *
Lagged GDP -0.0883 -2.2009 *
Share of private investment 1.1288 -2.4069 *
Share of total public spending -0.7159 -2.3437 *
Share of military spending -1.2001 -3.3132 *

Non-OECD countries (N = 38)

GDP growth -1.1812 -2.3280 *
Lagged GDP -0.7943 -1.9206 *
Share of private investment 0.4649 -2.4686 *
Share of total public spending -1.5138 -4.8177 *
Share of military spending -0.6617 -5.1129 *

 MW Test Statistic

Variable Levels First Difference

Whole sample (N = 55)

GDP growth 114.23 135.43 *
Lagged GDP 102.17 149.32 *
Share of private investment 93.21 141.47 *
Share of total public spending 97.82 155.36 *
Share of military spending 99.34 153.42 *

OECD countries (N = 17)

GDP growth 41.54 51.36 *
Lagged GDP 37.98 48.92 *
Share of private investment 36.64 55.64 *
Share of total public spending 39.03 49.08 *
Share of military spending 36.55 53.21 *

Non-OECD countries (N = 38)

GDP growth 90.87 108.91 *
Lagged GDP 89.76 110.23 *
Share of private investment 92.34 107.56 *
Share of total public spending 88.03 111.35 *
Share of military spending 90.48 109.55 *

Note: The tabulated critical values for the MW tests at the 5%
significance level are 124.34 for the whole sample, 43.77 for the
sample of OECD countries, and 101.87 for the sample of non-OECD
countries.

* Rejection of the unit root hypothesis at the 5% level.

TABLE 2
Panel Cointegration Tests (the Dependent Variable is the GDP Growth
Rate)

Levin, Lin, and Chu (2002)

FE FTE

Whole sample (N = 55)

-11.76 * -18.00

OECD countries (N = 17)

-9.73 * -15.63

Non-OECD countries (N = 38)

-13.72 * -20.35

Fisher's Test

 r [less than r [less than
r = 0 or equal to] 1 or equal to] 2

Whole sample (N = 55)

139.6 * 111.2 93.8

OECD countries (N = 17)

54.8 * 40.2 35.7

Non-OECD countries (N = 38)

103.1 * 95.6 81.1

Pedroni (1999) BD Tests

rho pp adf

Whole sample (N = 55)

-1.89 * -2.04 * -2.75 *

OECD countries (N = 17)

-2.09 * -2.34 * -3.14 *

Non-OECD countries (N = 38)

-1.28 -1.48 -1.76 *

Note: FE denotes Levin, Lin, and Chu (2002) test with only fixed
effects, while FTE denote the existence of both fixed and time
effects. The tabulated critical values for the Fisher test at the 5%
significance level are 124.34 for the whole sample, 43.77 for the
sample of OECD countries, and 101.87 for the sample of non-OECD
countries. The critical value for Pedroni's (2000) between-dimension
test at the 5% significance level is -1.65.

* Rejection of the null hypothesis of no cointegration at 5%
significance level.

TABLE 3
Between-Dimension FMOLS for the Whole
Sample

Variable Estimate t-statistic

[GDP.sub.(-1)] -0.058 2.653 *
Share of private investment 0.238 3.293 *
Share of total public spending 0.198 2.981 *
[(Share of total public spending).sup.2] -0.103 2.334 *
Share of military spending 0.236 2.134 **
[(Share of military spending).sup.2] -0.102 1.942 **

* and ** indicate statistical significance at the 1 % and 5%
level. Only the panel estimates are reported in this table. The
individual country-specific parameter estimates are available
upon request.

TABLE 4
Between-Dimension FMOLS Estimates for the Sample of OECD Countries

 [GDP.sub.(-1)] Private Investment

Country Estimate t-statistic Estimate t-statistic

Australia -0.009 1.082 0.342 2.643 **
Belgium -0.022 1.982 ** 0.176 1.873 **
Canada -0.023 2.623 * 0.377 3.873 *
Denmark -0.022 1.751 ** 0.093 0.731
Finland -0.032 2.879 * 0.197 2.066 **
France -0.021 1.873 ** 0.211 1.163
Greece -0.044 3.098 * 0.123 1.837 **
Ireland -0.076 3.653 * 0.465 3.652 *
Japan -0.035 4.076 * 0.287 2.153 **
Korea -0.028 2.351 ** 0.212 3.231 *
Luxemburg -0.064 2.752 * 0.123 1.034
Mexico -0.017 1.531 0.098 1.829 **
Norway -0.012 0.763 0.164 2.580 *
Poland -0.056 3.423 * 0.103 2.203 **
Turkey -0.032 2.063 ** 0.132 1.429
United Kingdom -0.041 4.109 * 0.421 3.651 *
United States -0.007 1.112 0.541 2.963 *
Panel -0.046 2.095 ** 0.298 3.542 *

 Public Spending [(Public Spending).sup.2]

Country Estimate t-statistic Estimate t-statistic

Australia 0.034 2.127 ** -0.032 1.892 **
Belgium 0.019 1.123 -0.033 0.876
Canada 0.007 0.872 -0.008 0.951
Denmark 0.072 2.376 ** -0.140 2.351 **
Finland 0.004 0.153 -0.009 1.092
France 0.021 2.314 ** -0.063 2.253 **
Greece 0.033 3.098 * -0.151 2.897 *
Ireland 0.007 0.653 -0.009 0.809
Japan 0.042 2.125 ** -0.047 1.899 **
Korea 0.015 1.983 ** -0.033 1.820 **
Luxemburg 0.046 2.231 ** -0.129 2.213 **
Mexico 0.032 2.724 * -0.078 2.576 *
Norway 0.036 1.893 ** -0.116 2.341 **
Poland 0.066 2.673 * -0.117 3.133 *
Turkey 0.054 2.109 ** -0.122 2.783 *
United Kingdom 0.061 3.764 * -0.048 2.093 **
United States 0.053 3.093 * -0.021 1.793 **
Panel 0.033 1.894 ** -0.081 2.341 **

 [(Military
 Military Spending Spending).sup.2]

Country Estimate t-statistic Estimate t-statistic

Australia 0.143 2.624 * -0.075 2.352 **
Belgium 0.154 1.998 ** -0.088 1.813 **
Canada 0.131 1.212 -0.096 1.109
Denmark 0.321 2.724 * -0.125 2.672 *
Finland 0.193 2.377 ** -0.085 2.323 **
France 0.093 1.877 ** -0.187 2.614 *
Greece 0.125 1.798 ** -0.192 2.091 **
Ireland 0.209 2.841 * -0.055 2.104 **
Japan 0.062 0.745 -0.032 0.653
Korea 0.203 2.809 * -0.143 2.612 *
Luxemburg 0.091 1.212 -0.021 0.834
Mexico 0.432 3.651 * -0.198 3.124 *
Norway 0.321 2.746 * -0.113 2.578 *
Poland 0.194 2.585 * -0.064 2.314 **
Turkey 0.078 2.087 ** -0.135 1.893 **
United Kingdom 0.089 1.883 ** -0.176 2.798 *
United States 0.072 1.799 ** -0.184 2.913 *
Panel 0.158 2.764 * -0.109 2.412

* and ** indicate statistical significance at the 1% and 5% level.

TABLE 5
Between-Dimension FMOLS Estimates for the Sample of Non-OECD Countries

 [GDP.sub.(-1)] Private Investment

Country Estimate t-statistic Estimate t-statistic

Argentina -0.072 3.143 ** 0.301 2.913 **
Bangladesh -0.087 3.672 * 0.076 0.672
Bolivia -0.034 2.098 ** 0.254 3.287 *
Brazil -0.091 4.762 * 0.231 3.164 *
Bulgaria -0.063 2.965 * 0.176 2.872 *
Chile -0.032 2.134 ** 0.209 2.590 *
China -0.041 2.451 * 0.339 2.098 **
Colombia -0.022 1.097 0.183 1.980 **
Costa Rica -0.031 1.341 0.213 2.542 *
Cote d'Ivoire -0.036 1.513 0.097 1.364
Dominican R. -0.065 2.562 * 0.076 1.092
Ecuador -0.071 2.773 * 0.145 2.671 *
Egypt -0.021 0.791 0.175 2.154 **
El Salvador -0.076 3.098 * 0.160 1.963 **
Guatemala -0.088 2.960 * 0.219 2.672 *
Guinea -0.045 2.341 ** 0.118 1.451
India -0.031 1.451 0.289 2.352 **
Iran -0.069 2.673 * 0.102 2.009 **
Kenya -0.033 2.125 ** 0.176 2.608 **
Madagascar -0.076 2.798 * 0.112 1.907 **
Malawi -0.056 2.533 * 0.121 1.563
Malaysia -0.059 2.498 * 0.153 1.609
Mauritania -0.061 2.781 * 0.176 1.892 **
Morocco -0.043 2.124 ** 0.231 2.761 *
Namibia -0.037 1.563 0.124 2.341 **
Nicaragua -0.069 2.873 * 0.251 2.981 *
Pakistan -0.034 1.718 ** 0.276 3.082 *
Papua -0.066 2.901 * 0.121 1.913 **
Paraguay -0.078 3.092 * 0.208 2.123 **
Peru -0.031 1.321 0.217 2.542 *
Philippines -0.042 1.982 ** 0.269 2.823 *
Romania -0.061 2.314 ** 0.234 3.212 *
South Africa -0.079 3.245 * 0.179 2.124 **
Thailand -0.038 1.453 0.198 2.322 **
Trinidad -0.044 2.130 ** 0.089 1.331
Tunisia -0.060 2.983 * 0.161 1.412
Uruguay -0.071 3.415 * 0.192 2.613 *
Venezuela -0.015 0.679 0.214 2.761 *
Panel -0.061 2.761 * 0.334 2.871 *

 Public Spending [(Public Spending).sup.2]

Country Estimate t-statistic Estimate t-statistic

Argentina 0.142 1.435 -0.056 0.757
Bangladesh 0.223 2.341 ** -0.067 0.975
Bolivia 0.341 2.784 * -0.105 1.851 **
Brazil 0.298 2.590 * -0.368 3.247 *
Bulgaria 0.142 2.243 ** -0.524 3.574 *
Chile 0.304 3.222 * -0.465 2.412 **
China 0.085 1.982 ** -0.662 4.639 *
Colombia 0.365 2.748 * -0.084 0.936
Costa Rica 0.412 3.124 * -0.158 1.968 **
Cote d'Ivoire 0.213 1.898 ** -0.056 1.057
Dominican R. 0.189 1.754 ** -0.105 1.321
Ecuador 0.431 2.863 * -0.032 0.627
Egypt 0.142 2.173 * -0.214 2.236 **
El Salvador 0.134 1.482 -0.039 1.027
Guatemala 0.312 2.767 * -0.354 2.685 *
Guinea 0.152 1.376 -0.047 1.385
India 0.331 2.877 * -0.426 3.287 *
Iran 0.114 1.092 -0.012 0.365
Kenya 0.212 2.064 ** -0.325 2.933 *
Madagascar 0.109 0.982 -0.053 1.058
Malawi 0.223 2.231 ** -0.352 2.965 *
Malaysia 0.423 3.129 * -0.487 3.875 *
Mauritania 0.531 3.672 * -0.667 4.148 *
Morocco 0.112 1.176 -0.022 0.842
Namibia 0.312 2.898 * -0.445 2.421 **
Nicaragua 0.213 2.421 ** -0.321 2.796 *
Pakistan 0.112 0.917 -0.077 1.328
Papua 0.309 2.231 ** -0.412 3.596 *
Paraguay 0.341 2.314 ** -0.502 3.154 *
Peru 0.410 3.316 * -0.368 3.754 *
Philippines 0.275 2.773 * -0.326 3.165 *
Romania 0.074 1.715 ** -0.463 3.253 *
South Africa 0.412 3.129 * -0.524 4.875 *
Thailand 0.312 2.902 * -0.487 4.632 *
Trinidad 0.289 2.417 ** -0.217 1.258
Tunisia 0.308 3.325 * -0.372 2.985 *
Uruguay 0.123 1.143 -0.055 1.089
Venezuela 0.074 1.742 ** -0.645 3.822 *
Panel 0.337 2.981 * -0.285 2.857 *

 [(Military
 Military Spending Spending).sup.2]

Country Estimate t-statistic Estimate t-statistic

Argentina 0.104 1.785 ** -0.214 2.368 **
Bangladesh 0.215 2.058 ** 0.076 1.021
Bolivia 0.236 2.341 ** -0.174 1.985 **
Brazil 0.198 1.974 * -0.325 3.258 *
Bulgaria 0.085 1.102 -0.107 1.485
Chile 0.041 1.747 ** -0.164 1.685 **
China 0.187 2.132 ** -0.324 2.365 **
Colombia 0.121 2.025 ** -0.341 2.478 *
Costa Rica 0.365 3.141 * -0.089 1.239
Cote d'Ivoire 0.128 1.611 -0.033 0.857
Dominican R. 0.087 0.932 -0.017 0.635
Ecuador 0.111 1.854 ** -0.147 1.978 **
Egypt 0.117 1.814 ** -0.365 2.698 *
El Salvador 0.086 1.041 -0.034 0.748
Guatemala 0.305 3.321 * -0.117 1.236
Guinea 0.046 0.754 -0.014 0.658
India 0.124 2.285 ** -0.321 2.323 **
Iran 0.163 2.169 ** -0.458 3.852 *
Kenya 0.136 1.694 ** -0.214 2.478 *
Madagascar 0.041 0.789 -0.009 0.369
Malawi 0.168 1.874 ** -0.014 0.298
Malaysia 0.325 2.635 * -0.174 1.705 **
Mauritania 0.410 3.985 * -0.324 2.652 *
Morocco 0.082 0.285 -0.104 1.229
Namibia 0.321 2.638 * -0.121 1.675 **
Nicaragua 0.039 0.365 -0.089 1.109
Pakistan 0.074 0.795 -0.017 0.751
Papua 0.125 1.174 -0.008 0.228
Paraguay 0.312 2.985 * -0.104 1.365
Peru 0.236 2.457 * -0.177 2.074 **
Philippines 0.147 1.977 ** -0.214 2.298 **
Romania 0.214 2.074 ** -0.365 2.852 *
South Africa 0.325 2.695 * -0.415 3.625 *
Thailand 0.128 2.014 ** -0.027 0.852
Trinidad 0.225 2.852 * -0.063 0.985
Tunisia 0.207 3.285 * -0.038 0.795
Uruguay 0.085 1.188 -0.014 0.698
Venezuela 0.241 2.365 ** -0.342 2.985 *
Panel 0.298 2.385 ** -0.098 1.984 **

* and ** indicate statistical significance at the 1% and 5% level.

TABLE 6
Marginal Effects of Military Spending and
Total Public Spending on GDP Growth for the
Sample of OECD Countries

 Total Public
Country Spending Military Spending

Australia 0.0234 0.0382
Belgium 0 0.0321
Canada 0 0
Denmark 0.0034 0.1570
Finland 0 0.0876
France -0.0067 -0.1261
Greece -0.0063 -0.0886
Ireland 0 0.1498
Japan 0.0292 0
Korea 0.0093 0.0625
Luxemburg -0.0001 0
Mexico 0.0172 0.2502
Norway -0.0104 0.2189
Poland 0.0301 0.1352
Turkey 0.0318 -0.0525
United Kingdom 0.0436 -0.0874
United States 0.0477 -0.1173
Panel 0.0063 0.1580

TABLE 7
Marginal Effects of Military Spending and Total Public Spending on GDP
Growth for the Sample of Non-OECD Countries

 Total Public Military
Country Spending Spending

Argentina 0 0.0286
Bangladesh 0.2230 0.2150
Bolivia 0.3159 0.1804
Brazil 0.1278 0.0575
Bulgaria -0.0273 0
Chile 0.2216 -0.0319
China -0.0279 -0.0878
Colombia 0.3650 -0.0606
Costa Rica 0.3694 0.3650
Cote d'Ivoire 0.2130 0
Dominican Republic 0.1890 0
Ecuador 0.4310 0.2045
Egypt 0.1008 0.0158
El Salvador 0 0
Guatemala 0.2778 0.3050
Guinea-Bissau 0 0
India 0.2509 -0.0081
Iran 0 -0.0504
Kenya 0.1341 0.0854
Panel 0.2696 0.2674
Madagascar 0 0
Malawi 0.0818 0.1680
Malaysia 0.3073 0.2705
Mauritania 0.3428 0.2768
Morocco 0 0
Namibia 0.0570 0.2990
Nicaragua 0.1095 0
Pakistan 0 0
Papua 0.1436 0
Paraguay 0.2763 0.3120
Peru 0.3444 0.1750
Philippines 0.2094 0.0872
Romania -0.0374 0.1314
South Africa 0.2263 0.2281
Thailand 0.2215 0.1280
Trinidad 0.2890 0.2250
Tunisia 0.1932 0.2070
Uruguay 0 0
Venezuela -0.0138 0.0732