Nonlinear Dynamics of Militarization and Income Inequality Nexus in Post-Socialist Eastern Europe: A Panel Kink Regression Analysis (1990–2023)

1 Introduction

What is the relationship between income inequality and militarization? This paper explores this critical question in the context of Eastern European countries (EEC hereafter).

Since the Soviet Union’s collapse in 1991, democratization, economic reform, and integration with Western institutions have shaped post-communist states, exposing diverse authoritarian legacies and complicating transitions to market economies and democracy (Kollmorgen 2013; Ekiert and Hanson 2003). These challenges fostered social inequities, political patronage, and corruption (Hellman 1998). Scholars note uneven progress across EEC sub-regions, with varying reform success (Iammarino et al. 2019). Market transitions reshaped income distribution and inequality, with institutional and political factors playing a critical role in driving inequality throughout the twentieth century (Aristei and Perugini 2012; Nikolic et al. 2024). Within this context, militarization has emerged as a significant factor influencing income inequality, with recent studies showing that higher levels of militarization are generally associated with increased inequality in European countries (Biscione and Caruso 2021; Caruso and Biscione 2022). Meanwhile, new security threats – conflicts, border disputes, and arms proliferation – have heightened tensions between economic integration and security (Pop-Eleches 2007). Empirical evidence from European NATO countries shows that military expenditure influences inequality differently depending on country size and threat level, with higher military spending often reducing inequality in smaller states during heightened threats (Dudzevičiūtė and Česnuitytė 2024). Together, these dynamics make EEC a critical case for studying the complex links between militarization and income inequality.

Understanding how government spending mediates these effects is essential, aspublic transfers and subsidies directly raise household disposable income, improving nutrition, health, and education, while investments in these sectors enhance labour quality and productivity among poorer households (Heltberg et al. 2004). Although no unified theory explains the militarization-inequality nexus, three competing hypotheses suggest different dominant mechanisms at varying militarization levels (Elveren 2012). The inequality-widening hypothesis argues milex increases wage disparities, as defence workers often earn more than less-skilled workers elsewhere (Ali 2007; Lin and Ali 2009; Wolde-Rufael 2016a). Conversely, the inequality-narrowing hypothesis, aligned with Keynesian views, posits that higher milex boosts aggregate demand and employment, reducing inequality if military production is domestic and labour-intensive (Lin and Ali 2009). The neutrality hypothesis suggests defence spending has negligible effects on income distribution if it is a small budget share and employs few workers (Wolde-Rufael 2016a).

Building on the work of Biscione and Caruso (2021), Caruso and Biscione (2022) and Biyase et al. (2024), this paper reexamines the asymmetric militarization – as measured by the Global Militarization Index (GMI)^[1] – and income inequality nexus in EEC from 1990 to 2023. Unlike earlier studies relying on linear panel regressions, this study employs a Panel Kink Regression (PKR) model^[2] – (Card et al. 2015; Hansen 2017) to account for nonlinearities and threshold effects. The primary contribution of this study lies in its innovative application of the PKR framework to the militarization-inequality nexus, allowing identification of critical threshold points where the relationship between these variables undergoes structural changes. This advancement provides a deeper understanding of how militarization impacts inequality across different regimes. It enables the detection of kink points where militarization’s impact shifts, offering richer insights into heterogeneous dynamics over time and across the EEC. Consequently, it reveals how predictors influence outcomes across regimes more effectively than standard linear regression (Yamaka 2021).

Europe’s security landscape has become increasingly volatile since 2014. EEC countries raised defence spending even as GDP declined, largely due to Russia’s annexation of Crimea in 2014 and the escalation of the Ukraine conflict in 2022 (SIPRI 2024). Caruso and Biscione (2022) argue that rising militarization combined with shrinking GDP has intensified concerns about income distribution (see trends in Figure 1). However, militarization expansion competes with social spending, reducing resources for human capital development and equity initiatives, raising concerns about its distributive impact (Brooks 2025).

Figure 1:

Evolution (on average) of GMI & GINI in our sample, 1990–2023. Sources: Authors’ processing, based on data from: BICC for GMI and World bank poverty and inequality platform (2025) for GINI.

While prior studies (e.g. Biscione and Caruso 2021) examined militarization and inequality in European transition economies, Eastern Europe’s unique post-socialist transition, ongoing security challenges, and varying Western integration levels – alongside unprecedented militarization – warrant further investigation of nonlinear effects and thresholds. Scholarly debates remain divided: some argue military expenditure reduces inequality by stimulating demand, others contend it exacerbates inequality by increasing skilled labour wages, while some suggest a neutral effect (Elveren 2012; Wolde-Rufael 2016a). Extensive theoretical and empirical analyses on militarization and economic growth exist (e.g. Dunne and Tian 2020; Alptekin and Levine 2012; Yesilyurt and Yesilyurt 2019; Emmanouilidis and Karpetis 2021). Recent studies exploring nonlinear militarization effects on inequality (e.g. Shahbaz et al. 2016; Biyase et al. 2024) motivate this paper’s unique PKR application to identify threshold effects during heightened geopolitical tension in EEC.

The rest of the paper is as follows: Section 2 describes the data and sources; Section 3 details the methodology and analysis; Section 4 concludes the study.

2 Data

We use data from 15 EEC – Albania, Belarus, Bulgaria, Croatia, Hungary, Moldova, North Macedonia, Poland, Romania, Serbia, Slovakia, Slovenia, Czech Republic, Ukraine and Russia^[3] – covering 1990–2023. Data sources include the World Bank for GDP, government spending, population, investment, secondary school enrolment, trade openness, inflation, GINI and political stability (to capture socio-political risks); and bicc for GMI. Summary statistics are shown in Table 1.

3 Methodology and Analysis

This paper investigates the nonlinear and threshold effects of militarization on income inequality in EEC using the PKR model, following the approach of Hansen (2017). The PKR model captures structural breaks more flexibly than quadratic or standard threshold approaches (Zhang et al. 2017; Chen et al. 2024), making it well suited to detect asymmetries in the relationship between militarization and inequality. Unlike standard threshold models that impose abrupt level shifts at the threshold, PKR keeps the outcome variable continuous while allowing the slope to change (Hansen 2017; Card et al. 2015). This makes it particularly appropriate for contexts like ours, where the effect of militarization on inequality is expected to shift gradually across regimes rather than exhibit discrete jumps (Shahbaz et al. 2016; Biyase et al. 2024). Our study focuses on EEC countries with similar characteristics, and it is reasonable to assume that the same model is applicable across all countries, justifying the use of panel kink regression with fixed effects.^[4] We specify the model as follows:

Where: y_it is income inequality (GINI index) in country i at time t; x_it is the main regressor of interest – militarization (Global Militarization Index, GMI); κ: the unknown kink point (threshold); Ζ_it is the vector of control variables (GDP, investment, inflation, trade openness, population, government spending, political instability – based on a Barro-type growth specification following Dimitraki and Menla – Ali 2015); x it − κ −  = min (x_it − κ, 0), and x i t − κ +  = max (x_it − κ, 0); μ _i is the unobserved country fixed effects; and ε_it is the error term of country i at time t. In this framework, the kink point represents a threshold in militarization at which its effect on inequality changes. Identifying this threshold is crucial for understanding the regime-dependent dynamics between militarisation and inequality.

To remove the unobservable individual effects (μ _i ) we apply within transformation (demeaning each variable by its time-mean) and estimate the transformed equation using the Fixed Effects (FE) estimator (Zhang et al. 2017). The threshold κ is estimated through a grid search procedure that minimizes the residual sum of squares (RSS) across candidate values. This method allows the model to detect asymmetric responses of inequality to militarisation, depending on whether GMI lies above or below the kink point. Furthermore, we test for stationarity using IPS, Maddala-Wu, and CIPS panel unit root tests (Table 2).

The existence of a kink effect is tested using an F-type test for the null hypothesis H₀: α 1 −  =  α 1 + , with the bootstrap method applied to obtain valid p-values due to the nonstandard distribution of the test statistic (Hansen 2017). This approach enables an in-depth examination of how militarisation influences inequality across different regimes, capturing critical turning points in policy relevance. Our control variables were also included to ensure robustness and address the omitted variable bias. The bootstrapped F-test results are presented in Table 3.

The F-test strongly rejects the null hypothesis (F = 23.20, p < 0.001), confirming a significant kink effect in the militarisation–inequality relationship. Figure 2 visualises the residual sum of squares (RSS) across a grid of threshold values. The identified threshold marks a critical point where the relationship shifts regimes, highlighting its nonlinear, regime-dependent nature and the importance of such thresholds for effective policy design.

Figure 2:

Residual sum of squares (RSS) versus Kink grid. Source: Authors’ processing.

The main estimation results are presented in Table 4, which displays the panel kink regression estimates and highlights the asymmetric impact of militarisation on income inequality in the EEC. The estimated optimal kink point for the Global Militarisation Index (GMI) is 248, indicating a critical threshold in the militarisation-inequality relationship.^[5] Figure 3 visualizes this structural break, illustrating the piecewise relationship between militarisation and inequality.

Figure 3:

Marginal effects plot (piecewise slopes). Source: Authors’ processing.

Table 4 reveals asymmetric coefficients around the kink point: α₁⁻ = −0.0004*** and α₁⁺ = 0.0002. A coefficient of −0.0004 means that a 10-point increase in GMI below the threshold (GMI = 248) is associated with a 0.004 decrease in the GINI index. Given that the GINI typically ranges from 0.25 to 0.45 in EEC countries, this effect is modest in the short term but may become more meaningful when sustained over time or with larger changes in militarisation. This further indicates that militarisation below the threshold (GMI = 248) modestly reduces inequality, while higher levels may increase it, though with weaker evidence. These results align with Shahbaz et al. (2016) and Biyase et al. (2024), who found that excessive milex can widen inequality by crowding out social investment. Overall, the findings highlight the importance of accounting for nonlinear effects when assessing militarisation’s distributive impact, especially in fiscally constrained and geopolitically tense regions.

GDP per capita and political stability significantly reduce inequality, supporting the view that stable, growing economies better deliver redistributive outcomes (Aristei and Perugini 2012; Iammarino et al. 2019; Brooks 2025). Inflation is positively linked to inequality at the 1 % level, consistent with Hu et al. (2024), who note that rising prices disproportionately affect lower-income groups, especially where social safety nets are weak. Investment and government spending also correlate positively with inequality, possibly reflecting inefficiencies or biases favouring capital-intensive sectors or non-progressive expenditures like military budgets. This aligns with Biscione and Caruso (2021), who argue that public spending in many post-transition countries often fails to reduce inequality. Similarly, Caruso and Biscione (2022) find that militarisation in Europe may have regressive effects when defence priorities crowd out social investment. Trade openness is statistically insignificant, suggesting globalisation does not yield broad-based gains in the EEC, consistent with Meschi and Vivarelli (2009). Population size shows a positive effect on inequality at the 10 % level, potentially reflecting structural labour market challenges or regional disparities. The test for strict exogeneity shows no evidence of endogeneity, supporting the consistency of our panel kink regression estimates and aligning with exogeneity assumptions critical for valid inference in kink models (Yang et al. 2021).

Overall, the evidence supports balanced policies that safeguard security while promoting social equity and inclusive growth. Our findings echo recent warnings regarding the unequal effects of excessive militarisation in geopolitically tense regions (Brooks 2025). These nonlinear effects may arise through mechanisms such as defence wage premiums or the diversion of resources from social to military expenditure (Lin and Ali 2009; Caruso and Biscione 2022). Given variation across countries, those persistently above the threshold face greater risks of widening inequality, stressing the need to balance defence priorities with social cohesion. Figure 4 shows each country’s average deviation from the threshold during the sample period.

Figure 4:

Country-level deviation from kink point (average values). Source: Authors’ processing.

4 Conclusions

This study identifies a nonlinear relationship between militarisation and income inequality in the EEC, with a threshold beyond which militarisation exacerbates inequality. Applying a PKR framework, we reveal new regime-dependent insights: moderate militarisation reduces inequality below the GMI threshold (248) but increases it above this point. These findings align with recent evidence highlighting thresholds and nonlinearities in the militarisation–inequality nexus (Shahbaz et al. 2016; Biyase et al. 2024). These findings highlight the need for balanced defence and social policies in the region. Policymakers should prioritise defence efficiency and ensure that security objectives do not undermine social cohesion. In particular, governments should regularly monitor militarisation levels and adjust defence budgets to prevent surpassing critical thresholds, thereby safeguarding both national security and equitable development. Future research should examine the mechanisms – such as labour markets, social spending, and institutional factors – that might mediate these effects.