Distinct Asymmetric Effects of Military Spending on Economic Growth for Different Income Groups of Countries

ABSTRACT

Although possible asymmetries for univariate and multivariate dynamics have been the focus of interest in many areas of economic explorations, it seems that most of the research on military expenditure - economic growth nexus has tended to assume linear relationships. This paper aims to examine possible nonlinearities in military expenditure-economic growth nexus employing data for a sample of 103 countries covering the 1988-2019 period. For this purpose, Panel Smooth Transition Regression, PSTR, models are estimated not only for all countries’ sample but also for low income, middle income, and high-income countries’ subsamples to reveal possible distinct asymmetric relationships for country groups with different income levels. Empirical results for the whole sample, low income and middle income groups indicate that military expenditure not only governs the regime change, but also low and high levels of military expenditure have distinctive and rising negative effects on economic growth with dissimilar threshold effects. Moreover, empirical findings also indicate that net arms exports govern regime change for high income countries, and as net arms exports rise, the negative impacts of military expenditure on economic growth become deeper.

KEYWORDS:

• Military expenditure
• economic growth
• non-linear models
• panel smooth transition regression model

Acknowledgments

The authors thank the editor and anonymous referees who kindly provided valuable, constructive suggestions. The usual disclaimer applies.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. For a recent review of literature please see Yildirim and Öcal (2016), d’Agostino, Dunne, and Pieroni (2017), and Emmanouilidis and Karpetis (2020).

2. Model selection tests approve our choice and indicate LPSTR specifications, see next sections.

3. See Dunne, Smith., and Willenbockel (2005) for a critical review of models on the link between military expenditure and economic growth.

4. Ucar and Omay (2009) extend the test of non-stationarity versus exponential smooth transition type non-linearity proposed in Kapetanios, Shin, and Snell (2003) to the case of non-linear panel data. However, since the test specifically considers Exponential PSTR model as alternative hypothesis, application of it may lead to misleading conclusions if alternative specification is a Logistic PSTR one as in our case. Indeed, evaluations of the estimated LPSTR models, results of additive non-linearity tests in Step 5 and model selection tests in Step 6 given below seem to be strongly approving the use of LPSTR model.

5. However, to save space, we do not provide the results but they are available upon request.

6. Although Omay and Kan (2010) approach may seem a straightforward generalisation of Pesaran (2006)’s method to non-linear case, it is intuitively hard to justify changing cross-section dependencies across distinct regimes, particularly with changes in military expenditure. Moreover, the number of parameters to be estimated nearly doubles and consumes considerable degrees of freedom. Considering the number of variables in our specifications, this may pose problems especially for subsample of countries. We, therefore, applied the same procedure under the assumption that the CSD structure is fixed across two regimes. The results were again in line with the one presented here and available upon request.

7. The location parameter c is not identified under both null hypothesis, while ${\beta }_1$ is not identified under $H_0$ and $\gamma$ is not identified under $H_0^{\prime }$.

8. Employing different models for different samples, Cuaresma and Reitschuler (2006), Lee and Chen (2007), Stroup and Heckelman (2001), d’Agostino, Dunne, and Pieroni (2011) and Yolcu Karadam, Yildirim, and Öcal (2017) are among the studies that provide empirical support that defence-growth nexus is non-linear and depends on the level of defence expenditures.

9. Note that with a sharp change and growth rate as transition variable, the estimated Logistic PSTR model becomes a Momentum Panel Threshold model.

10. Since the majority of the world economies are arms importers and mostly high-income countries supply arms to the rest of the world, we introduce net arms exports as the transition variable only for the sample of high-income countries.

11. Two points are worth mentioning about the LM test. First, in its most general form, all variables appear as possible indicator variables, q_it, but this version of the test is impractical due to degrees of freedom considerations, and therefore each time, only one candidate variable is considered in the empirical application as in Equation (5)(5) $\mathrm{\Delta }{y}_{it}={\mu }_i+{\beta }_0^{\ast \prime }{X}_{it}+{\beta }_1^{\ast \prime }{X}_{it}{q}_{it}+{\beta }_2^{\ast \prime }{X}_{it}{q}_{it}^2+\dots ..+{\beta }_m^{\ast \prime }{X}_{it}{q}_{it}^m{u}_{it}$(5) . Teräsvirta (1994) argues that this may cause misleading results but claims that if the test wrongly indicates non-linear specification, it is highly likely that finding a plausible model implying inherent non-linearity will be very low. Second, if the data set contains outlying observations, it would not be surprising that this leads to the rejection of linearity hypothesis particularly against the logistic alternative, as LPSTR is very sensitive to capturing outliers. The scatter plot of estimated transition function with respect to ascendingly ordered values of transition variable, nevertheless, can be very informative in showing whether captured non-linearity is inherent or simply due to outliers. Here, we do elaborate models with transition functions clearly characterising two distinct regimes and do not discuss the ones capturing outliers.

12. It should be noted that endogeneity bias may appear as we use a dynamic Solow-type model. One advantage of employing Panel STR models, however, is that they are flexible enough to mitigate and/or bound the endogeneity bias since specification and estimation of these models produce estimates of infinite number of parameters sets identifying countless distinct regimes, as also pointed out in Fouquau, Hurlin, and Rabaud (2008), and Omay and Kan (2010).

13. These results are not surprising since it is unlikely to have same effects of low and high military expenditure on growth as implied by the EPSTR model.

14. As noted before, evidence of additive non-linearity for whole sample is most probably due to neglected asymmetries across separate income groups.

15. As explained earlier, logistic function is very sensitive to picking up outliers, in that case, we discard the model and attribute the test results to abnormal observations.

16. For the whole sample, we also estimated the PSTR model with the growth rate of military spending to GDP ratio being the transition variable but we were unable to estimate a plausible non-linear model. It seems that test results are due to outliers as the transition function does not clearly exhibit two separate regimes and seems to be capturing a few outliers. Therefore, we prefer not to elaborate empirical results in detail here but are available upon request.

17. Estimation results of LPSTR models with transition variables log of growth rate of military expenditure and momentum of this variable imply that there are no non-linearities in the estimated relationships since estimated transition functions take the value one only for a few values, most probably due to abnormal observations.

18. United States, Russia, France, U.K., Germany, China, Israel, Italy, Sweden, Canada, Spain, Netherlands, Ukraine, Switzerland and South Korea are the top 15 suppliers of arms in the world in 2017. Among them, only China and Russia are in the middle-income group, while Ukraine is categorised in the low-income group.

19. Nearly 52% of observations of middle-income countries fall below this threshold level.

20. Graph of the transition function in Figure 5 indicates that there are no values around the estimated threshold variable c and under these circumstances a precise estimation of smoothness and threshold parameters may be problematic (see Teräsvirta, Tjøstheim, and Granger 2010). Hence, a very large standard deviation of smoothness parameter estimate may be reflecting this.

Transition function with respect to the ascendingly ordered transition variable- Military spending to GDP for low-income countries.

21. https://www.sipri.org/research/armament-and-disarmament/arms-and-military-expenditure/military-expenditure