Causal Pathways in Geo-Economic Relations: A Time-Series Study of Trade, FDI, and Diplomacy between China and Pakistan

Causal Pathways in Geo-Economic Relations: A Time-Series Study of Trade, FDI, and Diplomacy between China and Pakistan | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Causal Pathways in Geo-Economic Relations: A Time-Series Study of Trade, FDI, and Diplomacy between China and Pakistan Ali Abbas, Tajwar Ali, Xi Laiwang, Ai Kunpeng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6783006/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 13 You are reading this latest preprint version Abstract This paper examines the changing economic and geopolitical dynamics between Pakistan and China from a Geo-economic perspective, using a predictive modeling methodology. The research used a Vector Auto-regressive (VAR) framework to examine the relationship among exports, foreign direct investment (FDI), and diplomatic contacts from 2010 to 2022. Stationarity and correlation studies validate robust inter-dependencies, but Granger causality tests indicate substantial directional interactions among variables. Impulse response functions and scenario-based forecasting highlight the impact of diplomatic shocks on trade and investment flows. The results substantiate the Geo-economic theory by illustrating how economic performance and private capital flows now influence bilateral diplomacy. The results provide actionable insights for export promotion and strategic economic planning, highlighting the pivotal role of data-driven modeling in comprehending intricate international relations. This study provides a solid empirical basis for future governmental and academic discussions on bilateral economic integration and strategic forecasting. Business and commerce/Business and management Business and commerce/Economics Social science/Economics Social science/Politics and international relations Geo-economics Geo-Strategic Pakistan-China relations VAR modeling predictive analytics foreign direct investment Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction The current discourse in international relations has shifted from a conventional geo-strategic focus to an economics-driven perspective, commonly encapsulated by the phrase 'geo-economics' [ 1 ]. This variant elucidates that economic interdependence, trade integration, and cross-border investment progressively influence the formulation of foreign policy and international relations of governments [ 2 ]. Geo-economics serves as a pragmatic framework for comprehending the structure and evolution of state interactions in an increasingly globalized society, as well as for assessing the current global condition and forecasting future state interactions. This transition is fundamentally rooted in the observation that, although military and strategic postures remain predominant because to their relevance, they are gradually being complemented by economically-based policies aimed at fulfilling national development objectives [ 4 ]. Consequently, nations are aggressively using trade agreements, foreign direct investment incentives, and infrastructure partnerships to achieve their national goals. The relationship between Pakistan and China exemplifies how Geo-economics serves as the principal driver of bilateral ties, particularly with the China–Pakistan Economic Corridor (CPEC). The relationships are based on infrastructural initiatives, energy collaboration, and industrial enterprises, demonstrating their dynamic nature and highlighting the significant significance of Geo-economic relations that focus on evaluating strategic alliances from an economic perspective. Geo-strategy traditionally refers to the manner in which nations use their territorial control, military deployment, and diplomatic alliances in both regional and global settings to exert influence. From this viewpoint, foreign policy is primarily used to safeguard sovereignty, maintain territorial integrity, and defend areas of influence. [ 7 ]. These aims are undoubtedly significant; nevertheless, they are increasingly pursued via mechanisms of economic partnership that do not compromise one partner's opportunities for the benefit of the other. Consequently, the emphasis of conceptualization has shifted from mere geographical location or military might to the use of economic instruments for the fulfillment of strategic imperatives. [ 9 ]. The transition to geo-economics does not render military force obsolete; rather, economic strategies, trade routes, and investment flows are as vital to a nation's overall security and development plan. Consequently, states are investing in companies, technological parks, and logistical networks outside their borders to foster sustainable interdependence [ 10 ]. In this context, predictive modeling serves as a crucial approach that enables academics and policymakers to analyze data patterns, simulate scenarios, and evaluate the long-term effects of diverse policy choices on both local and international interests [ 11 ].The historical relationship between Pakistan and China has been founded on strategic alignment, driven by shared objectives in fostering regional stability and maintaining balanced power dynamics, particularly in South Asia. The collaboration between the two nations on military and intelligence issues has been longstanding and has evolved into a cooperation that extends beyond typical bilateral ties. Over the last decade, economic cooperation has been central to the Pakistan–China collaboration, dominating discourse by integrating commercial objectives with long-term geopolitical imperatives. This correlates with the ambitious infrastructure initiatives like CPEC, which aimed to enhance Pakistan's industrial and transportation capabilities while providing a more efficient means for China to import energy. The China-Pakistan Economic Corridor (CPEC) is a significant development program that exemplifies the effectiveness of geo-economics, aiming to connect Pakistan's local economic requirements with China's global ambitions, so fostering a mutual need across boundaries. The transformation include not only the building of roads and ports but also the establishment of economic zones, energy pipelines, and industrial parks, which would further the integration of the two nations' economies and solidify the strategic alliance. This has led to an abundance of scholarship on the geo-economic foundations of the alliance and raises significant inquiries about its broader regional implications. Given that predictive modeling is a key analytical tool in this evolving environment, it would be beneficial to examine the future trajectory of Pakistan–China economic ties and their consequences for the wider region [ 19 ]. Conventional approaches to predicting diplomatic or military alliances often rely on historical patterns or qualitative evaluations, which, although useful, may inadequately consider the complexities of contemporary, data-driven global economies. When combined with comprehensive datasets, machine learning algorithms and economic indicator predictors, predictive modeling may provide a more nuanced perspective on a range of factors, such as trade growth, investment patterns, employment rates, and technology transfers. This technique may also include external shocks, such as global economic recessions or abrupt political leadership transitions, to provide a more comprehensive view of potential futures [ 19 ]. A predictive model might serve as a proxy for assessing the influence of Islamabad's policy shift on Chinese infrastructure investment, or it could analyze the effects of fluctuations in global energy prices on the feasibility of the China-Pakistan Economic Corridor (CPEC). This kind of information is crucial for decision-makers seeking to shape policy by maximizing benefits and minimizing losses [ 20 ]. Sun emphasizes the increasing significance of geo-economics in Pakistan–China relations, influenced by the evolution of the global economic environment characterized by the rising importance of transnational value chains and financial inter-dependencies. As modern digital technologies perpetually transform international commerce and the complexity of global supply chains escalates, nations that implement flexible geo-economic strategies will gain competitive advantages. The economic consolidation of partnerships often enhances diplomatic power, as nations are compelled to collaborate on a wider array of problems, including environmental legislation and labor standards. The interplay of geo-economics is dynamic, amplifying the network of linkages among trade flows and foreign investments. Consequently, the economic partnership between Pakistan and China may serve as a beacon for nations to collaboratively pursue discretionary goals alongside strategic imperatives, particularly through predictive modeling that facilitates rapid comprehension of dynamic variables. The complexity of this chess game has prompted a paradigm that identifies and connects economic forces within a coherent long-term regional stability strategy [ 24 ]. In addition to bilateral dimensions, the geo-economic pivot also influences regional efforts and global power dynamics. The Belt and Road Initiative (BRI), encompassing the China-Pakistan Economic Corridor (CPEC), is seen as China's endeavor to restructure the economic landscape of Eurasia via infrastructure advancement and enhanced trade routes. Pakistan's involvement in this project has altered its regional status in both economic and political dimensions. Through predictive modeling, researchers may deduce how the repercussions of such efforts may result in the establishment of regional trade blocs, reconfiguration of supply chains, and changes in relative competitiveness across various areas [ 26 ]. These estimates may serve as a foundation for the implementation of policy initiatives, such as tariff adjustments or targeted investments in promising sectors. Consequently, analyzing via a geo-economic perspective, supported by predictive analytics, provides policymakers with foresight into the indirect consequences of large-scale initiatives aimed at fostering sustainable and equitable development [ 27 ]. However, there are detractors and obstacles to the shift from geo-strategy to geo-economics. Some contend that an over focus on economics may lead to the neglect of security concerns or ideological disparities, which are significant catalysts for conflict. Nonetheless, experts caution that predictive modeling is beneficial but far from flawless, since it may overlook intangible political, cultural, historical, and psychological aspects of state behavior that the analytical framework of predictive modeling cannot capture. Predictive analytics depend on the quality, reliability, and completeness of accessible data, which may be inadequate in places with limited institutional capability or widespread political instability [ 30 ]. Likewise, economic linkages are tenuous, and news shocks may erupt unexpectedly, ranging from pandemics to natural catastrophes to abrupt policy reversals. Nonetheless, these considerations do not negate the importance of geo-economics; rather, they emphasize the need to enhance the analysis by including strategic, cultural, and social perspectives. Predictive modeling has gained prominence in international relations studies because it offers a framework to include various variables, such as GDP growth rates and social media sentiment. This simulation of Pakistan–China relations may examine variables influencing the demography of Pakistan's labor force, the technical improvement of China's industrial sector, or the governance regime of joint ventures. Analysis is conducted via simulations under diverse policy or market situations to identify possible bottlenecks, such as inadequate infrastructural facilities or a misalignment of skill sets in the labor market [ 36 ]. Furthermore, predictive modeling can account for global monetary variations, which affect the cost of raw materials and, therefore, the viability of operations reliant on imported components [ 37 ]. These insights are rigorous and data-driven, capable of informing many stakeholders, including government organizations responsible for economic planning and global firms assessing new investment opportunities. In rapidly evolving geopolitical contexts, where reactive policymaking may lead to lost opportunities or strategic errors, this systematic approach is more pertinent [ 39 ]. CPEC exemplifies the economic collaboration between Pakistan and China, allowing for an examination of the intersection of geostrategy and geo-economics, while also demonstrating the use of predictive modeling in decision-making. CPEC was first conceived as a project to use Pakistan's geographical position to improve connection with China's western provinces via energy generation, logistical facilitation, and the advancement of technology and communications. Both countries must effectively handle external pressures and internal constraints to secure the mutual advantages and long-term viability of these projects. For example, predictive modeling might identify which aspects of professional training for local labor markets or safe digital infrastructure need improvement [ 44 ]. Over time, a cohesive geo-economic strategy, including analytical techniques for risk anticipation and resource allocation, becomes more essential for the maturation of these enterprises [ 45 ]. Investment in infrastructure and industrial growth is prioritized in Pakistan, presenting a chance for China to achieve its goal of advancing transcontinental trade expansion. This paradigm encompasses interconnected strategic assessments about energy price, regulatory frameworks, tariffs, trade, market growth, and national security objectives that extend beyond immediate economic advantages. The purpose of implementing predictive modeling in this field is to provide organized, empirically-based projections that can be scrutinized, discussed, and improved by policymakers. Moreover, the model creation process often serves to reveal underlying assumptions or identify data deficiencies, so enhancing transparency and strengthening decisions. Furthermore, these forecasts facilitate scenario planning, including best-case, worst-case, and mid-range scenarios for bilateral economic cooperation. Secondly, although absolute accuracy cannot be asserted for any model, predictive analysis utilizes an iterative methodology that improves forecasts over time as fresh data inputs are included [ 49 ]. This iterative paradigm is particularly beneficial for intricate multi-decade projects like the CPEC, which encompasses several stakeholders across various industries. Predictive modeling enables adaptive strategy formulation via the methodical integration of factors such as population increase, changes in trade rules, and technological advancements. This dynamic represents a successful amalgamation of micro-level policy specifics with macro-level aims, arising from the synergy of geo-economics and predictive modeling. The acceptance of geo-economics aligns with broader trends in global politics, reflecting the interplay between soft power and economic diplomacy with traditional notions of physical power. These global trends coincide with Pakistan's ambition to establish itself as a regional economic powerhouse, paralleling China's strategy to extend its economic and political influence beyond East Asia. The convergence of strategic ambitions driven by economic necessities may lead to the reconfiguration of regional alliances, alterations in dependencies, and a transformation in the decision-making processes of regional players. These fluctuations may be measured to forecast heightened trade volume, labor migration, or alterations in the local business environment using predictive modeling. When geo-economics emerges as the predominant concept for states, economic corridors foster interdependence, which may serve as both a deterrent to violence and a stimulus for cooperation. This result, however, is not certain and depends on the equitable distribution of benefits and the presence of stable governance frameworks adept at managing cross-border complexity. The emerging paradigm necessitates that researchers and practitioners address a series of contingencies, highlighting the need of data-driven tools in enhancing preparation for predicting and adapting to these uncertainties [ 56 ]. Literature Review Theoretical Foundations of Geo-Strategy and Geo-Economics The concepts of geo-strategy and geo-economics have been essential in international relations discourse for years, with experts now focusing on the intricate interplay between economic interests and conventional strategic aims. Geo-strategic thinking, historically rooted in a Cold War bipolarity, pertains to how governments use their geographical and military advantages to exert regional and global dominance and influence. Nonetheless, the prevailing tendency in contemporary geo-economics indicates that commerce, financial transactions, and multinational corporate involvement are seen as equally or more significant than territorial or military aims in shaping state policy. This transition is part of a larger initiative to use economic instruments to achieve political objectives, including sanctions, trade agreements, and investment plans. Around 2000, scholars viewed the military and diplomatic aspects of geopolitical power, along with geo-economics, as distinct paradigms. However, recent studies elucidate the hybrid nature of contemporary policy-making that amalgamates security and economics [ 58 ]. Traditionally, the theoretical foundation of geostrategy has been realism, which emphasizes the amassing of power within an anarchic international system for the sake of survival. In the modern context, they focus on military alliances and strategic positions to deter adversaries. The increasing significance of geo-economics highlights the limitations of purely realist models, since geoeconomic collaboration occurs in areas such as infrastructure development, knowledge transfer, and supply chain integration. Furthermore, constructivist interpretations indicate that prevalent economic norms and institutional frameworks may shape state identities, thereby diminishing the zero-sum perception of armed rivalry in favor of peaceful economic interactions. Liberal institutionalists argue that the increasing complexity of global economic networks compels stronger collaboration, hence eliminating the possibility of total conflict, even among nations with significant political or ideological differences. Contemporary research posits that geo-economics is not a substitute for geostrategy, but rather an alternate framework capable of achieving identical strategic objectives using economic methods. Many nations use economic incentives, such as concessional loans, debt relief, or preferential trade access, to get strategic cooperation from partner governments. Security alliances that simultaneously function as extensive commercial initiatives illustrate the interaction between geostrategy and geo-economics, as well as the complexity of national interests. As democracy transcends international borders, many organizations converge, resulting in the amalgamation of defense pacts into commercial agreements, which develop into comprehensive partnerships comprising joint military exercises and collaborative investments. A second developing theoretical approach pertains to the "weaponization" of interdependence, when nations use interconnected economic networks to exert pressure on rivals. From this viewpoint, the ability to halt trade or restrict access to essential technology is as, if not more, important than traditional military power [ 62 ]. Consequently, geo-strategy transcends the mere control of critical chokepoints or the accumulation of large military forces; it now encompasses the establishment and maintenance of economic corridors that may be used in times of crisis. This approach elucidates why nations persistently allocate substantial resources towards the advancement of developing technologies and why the regulation of essential digital platforms is regarded with utmost seriousness, both in peacetime and during conflict. As geo-economic discourse has emerged as a significant category in the development of international relations policy, certain problems persist about the conceptual parameters of geo-economics. Critics contend that the word is sometimes used as a catch-all for any economic problem that arises on the global stage, leading to a diminution of analytical clarity. Proponents contend that geo-economics is a crucial perspective for comprehending how nations exert power via infrastructure investments, trade agreements, and financial incentives. [ 65 ]. The concept of geo-economics in contrast to geo-strategies is a theoretical discussion pertaining to governance and standards. Global norms for commerce, investment, and technology are being challenged by major nations, with some experts observing that this represents a fight for influence. The creation of alternative financial institutions and the advocacy of private technological standards demonstrate that geo-economics may function as a conduit of normative power. The connection between geo-strategy and geo-economics arises from the proliferation of multilateral forums that promote both security and economic cooperation, exemplified by the extensive expansion of regional comprehensive economic partnerships that serve as a strategic alignment. Furthermore, soft power encompasses geo-economics, since cultural outreach and diplomatic involvement facilitate the implementation of economic accords. Scholars assert that gaining the hearts and minds of host countries mitigates political risks and fosters more enduring partnerships, blurring the line between mere economic enticement and deliberate public diplomacy. Recent literature from 2021 indicates that while militaristic geo-strategy contributes to the pursuit of national interests, fostering robust economic relationships—according to theory—diminishes the likelihood of armed conflict and emerges as a crucial factor for the sustained operation of national interests within a specific geopolitical framework. Additionally, there are emerging case studies illustrating how medium-sized powers operate within a global system dominated by larger, more powerful states, utilizing geo-economic initiatives to achieve autonomy or favorable conditions in international negotiations that are non-negotiable. This perspective challenges the previous dichotomy that regarded smaller states as mere pawns in the rivalry of great powers, instead asserting their ability to utilize geo-economic strategies to secure concessions or form coalitions that protect their sovereignty. In these circumstances, military collaboration and economic partnerships exist inside a complex network of alliances that function both to compete and to cooperate. Predictive Modeling Approaches in International Relations Predictive modeling has emerged as a significant issue in international relations, as researchers and politicians seek data-driven insights to enhance decision-making in complicated geopolitical contexts. Consequently, this methodological approach reflects the overarching trends in computational social science, such as the use of machine learning algorithms and big data analytics to predict conflict, economic performance, and diplomatic outcomes [ 70 ]. Nonetheless, case studies and expert interviews remain crucial in capturing the observational depth characteristic of conventional qualitative methods; yet, the increasing availability of high-quality datasets allows for the use of more sophisticated statistical and computational techniques. The prevalent use of predictive modeling in international relations is driven by the rapidity of global events and the complex interrelations of elements that affect a state's behavior. Policymakers may now compile and analyze economic statistics, military spending, social media opinion, and diplomatic statements in near real-time. Predictive models aim to alert human decision-makers to trends in extensive data sources that they may overlook, so facilitating early warnings of crises or negotiation chances. For instance, heightened anti-government sentiment in a particular region may coincide with increased military expenditures by a neighboring nation, suggesting increasing tensions and necessitating diplomatic action [ 72 ]. The existing research encompasses many modeling methodologies grounded on regression methods, machine learning classifiers, and simulation models using an agent-based paradigm [ 73 ]. Consequently, regression techniques are well-established in social sciences, enabling researchers to assess the connection between dependent variables, such as conflict initiation, and independent factors. Nonetheless, this is often assessed by approaches that presume linear correlations across variables, which may fail to encapsulate the intricate dynamics of various components in international interactions [ 74 ]. Consequently, machine learning classifiers use methods like random forests, support vector machines, and neural networks to deduce nonlinear patterns in large datasets. Predictive modeling has shown its potential in projecting economic cooperation and trade trends. As extensive trade data becomes accessible, researchers may examine tariff rates, export volumes, and foreign direct investment flows across several nations to monitor the prevalence of globalization or regional integration [ 75 ]. Moreover, predictive tools facilitate comprehension of how alterations in policy, such as trade agreements or sanctions, might influence future economic trajectories and assist policymakers in devising tactics to enhance such policies. In addition to macroeconomic data, several models include micro-level information, such as firm-level production or labor force statistics, yielding a detailed projection of which sectors would most benefit from bilateral or multilateral partnerships. Recent work emphasizes the importance of hybrid models that combine computational techniques with qualitative insights. The expertise of a field specialist may enhance the algorithm and aid in other areas such as qualification, unification of similar things, and classification of dissimilar objects that solely quantitative techniques may neglect. For example, if a model predicts an escalation in regional tensions, it might use contextual knowledge about cultural customs or local political animosities that are not immediately represented in numerical data [ 77 ]. The collaborative aspect of these projections enhances both precision and clarity, facilitating their optimal use in sanctioning decisions under politically precarious contexts. Moreover, the use of open-source tools for data analysis has democratized predictive modeling, enabling tiny states and non-state actors to leverage 'big data' and conduct 'big analytics' to impact geopolitical policymaking via advanced geopolitical forecasting [ 78 ]. This move might possibly reduce the information asymmetry that formerly advantaged the large nations with substantial resources. As predictive analytics gain popularity among stakeholders, the potential of model misunderstanding or abuse increases, necessitating the implementation of training programs and ethical standards to instruct users on the responsible utilization of these technologies. In summary, predictive modeling in international relations is not a universal answer, but rather a valuable supplementary tool to conventional methodologies that need iterative refining, interdisciplinary cooperation, and an acute awareness of the contexts in which predictions are used. The Evolving Landscape of Pakistan–China Relations In the last two decades, Pakistan–China ties have transformed from a mere strategic partnership to a robust foundation of economic cooperation. The bilateral ties originally centered on military collaboration, stemming from a mutual suspicion of regional security and power dynamics, particularly concerning India. The emergence of the China–Pakistan Economic Corridor (CPEC) under the Belt and Road Initiative (BRI) signified a transformative shift in the relationship, emphasizing substantial infrastructural investment and industry collaboration. Scholars assert that this stems from a fundamental geo-economic reason, whereby both parties want to capitalize on trade routes, industrial zones, and energy pipelines to further their growth objectives. Historically, Pakistan has seen China as a counterbalance to more dominant regional adversaries and has consistently sought diplomatic and military support to safeguard its autonomy. Conversely, China has used Pakistan's strategically advantageous position to get access to the Arabian Sea, therefore reducing its dependence on potentially vulnerable maritime chokepoints. Robust defense relations were established on the basis of this shared interest, including the co-production of military equipment and intelligence-sharing. In the last decade, economic cooperation has emerged as the foremost aspect of bilateral ties, especially after an increase in Chinese foreign direct investment in various southern regions of Pakistan and the establishment of special economic zones throughout. The China-Pakistan Economic Corridor (CPEC) has undoubtedly emerged as the focal point of this developing dynamic, and despite ongoing disputes, it remains a subject of fascination for scholars, politicians, and media organizations. The China-Pakistan Economic Corridor (CPEC) comprises a series of infrastructure initiatives including roads, ports, trains, and energy facilities, aimed at revitalizing Pakistan's economy and expanding China's economic influence westward. The port of Gwadar epitomizes the absurdity of this ambitious initiative to transcend the antiquated infrastructure of the subcontinent and transform into a strategically located hub for redefining regional transport routes. While economic benefits are prominent, these projects represent a fundamental strategic consideration, namely China's pursuit of energy security in conjunction with Pakistan's growth and modernization efforts, which mutually reinforce one another and strengthen the bond between China and Pakistan. Despite the euphoria around CPEC's potential, it has also faced criticism and encountered challenges. Local stakeholders, according to some, emphasize environmental deterioration, the relocation of local residents, and the inequitable distribution of project profits. Moreover, economic viability seems to be compromised when factoring in project financing conditions that often include loans from Chinese banks, thus exacerbating Pakistan's debt burden. Critics argue that the disparity between predicted and actual developments indicates the need for enhanced governance structures and improved feasibility evaluations. Nonetheless, the Pakistani government consistently reaffirms its commitment to CPEC, citing initial achievements in electricity production and other infrastructural initiatives. Methodology The examination of Pakistan–China economic ties is conducted from a geo-economic standpoint using a predictive analytical framework executed with Stata software. The methodology design has three fundamental pillars: (a) data selection and preparation, (b) model formulation and estimate, and (c) validation and robustness assessment of model results. This methodology incorporates macroeconomic, trade, and geopolitical factors to quantitatively analyze bilateral contacts and the strategic foundations influencing their temporal dynamics. The data for this research were compiled from many publicly accessible and institutional database sources on a quarterly basis, spanning from 2010 to 2022. Subsequently, macroeconomic variables such as GDP, FDI inflows, trade volume, and exchange rates were obtained from the statistical releases of the central banks and ministries of Pakistan and China. Bilateral export and import data from trade-related variables were sourced from the customs authorities and verified against international databases. Additionally, these macro-level variables were augmented with geopolitical measures, including diplomatic visits and military cooperation indices derived from publications by regional policy think tanks. A uniform cleaning procedure in Stata was used on all data, whereby missing values and outliers were discovered and addressed using winsorization, while retaining true extreme values. The Augmented Dickey–Fuller and Phillips–Perron tests were used to assess non-stationary series for unit roots, and differencing was applied as necessary. The variables that stayed stationary at level were retained unchanged. All series were synchronized quarterly to produce the final data-set, ensuring temporal consistency. Owing to the significant interaction of economic, political, and strategic aspects, we used a comprehensive predictive modeling methodology. Dynamic panel regressions (Arellano–Bond) were first used to address potential endogeneity and auto-correlation by using lagged dependent and control variables as instruments. This facilitated the depiction of how lagged bilateral trade volume influences current FDI inflows. Secondly, macroeconomic and geopolitical data were analyzed via a bidirectional link using a VAR framework. The VAR model achieved this by considering all variables as endogenous, so illustrating how changes in diplomatic alignment may influence export growth, and conversely. The Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC) were used to ascertain the best lag duration in the investigation. A Vector Error Correction Model (VECM) was used to analyze both short-term deviations and long-term equilibrium correlations among co-integrated variables. The estimate was performed using Stata's built-in commands, namely "xtabond2" and "varbasic," with coefficient significance assessed at p < 0.05 or p < 0.01. R-squared served as an indicator of model fit for panel data, whereas impulse response analysis was used to the VAR/VECM framework. To enhance robustness, many validation tests were conducted. Residuals were examined for serial correlation and hetero-skedasticity. Subsequent delays or resilient standard errors were used to re-specify models that did not satisfy assumptions. Disturbances to a single variable were transmitted throughout the system, as shown by impulse response functions. Forecast error variance decomposition (FEVD) quantifies the extent to which the forecast error variance of one variable is elucidated by shocks in other variables. Various proxies were excluded or replaced and evaluated for alternative specifications. The in-sample and out-of-sample predictions further corroborated the model's accuracy by evaluating predictive performance metrics, including root mean squared error (RMSE) and mean absolute percentage error (MAPE). Scenario assessments were performed using verified models to simulate potential futures under hypothetical policy alterations or global circumstances. The exogenous shocks from 'new trade facilitation' resulted in a 10% annual increase in export growth, but 'diplomatic tension' produced diverse exogenous shocks affecting geopolitical alignment. The "forecast" command suite in Stata was used to simulate these scenarios and provide projections about the future impact on bilateral trade ties. Evaluating several scenarios enables policymakers to identify which actions will optimize cooperation benefits or mitigate geopolitical hazards. Results 4.1 Descriptive Statistics and Correlation Analysis Descriptive statistics and correlation analysis provide essential insights into the distribution, dispersion, and interrelationships among the primary variables of Pakistan–China economic cooperation. The variables include GDP (gdp_pak), Foreign Direct Investment inflow to Pakistan (fdi_pak), Exports from Pakistan to China (exports_pak_to_china), Diplomatic Visits (diplomatic_visits), and Defense Cooperation (defense_cooperation). Understanding the core trends and variability of these variables is critical for predictive modeling, especially Vector Auto-regression (VAR). Table 1 Summary Statistics of Key Variables Variable Observations Mean Std. Dev. Min Max GDP (gdp_pak) 52 59.85 10.9983 40.9 77.1 FDI (fdi_pak) 52 0.554 0.1685 0.26 0.82 Exports to China 52 1.856 0.5819 0.90 2.84 Diplomatic Visits 52 2.712 0.8245 1 4 Defense Cooperation 52 7.769 3.2637 1 13 Table 2 Correlation Matrix of Core Variables gdp_pak fdi_pak exports_pak_to_china diplomatic_visits defense_cooperation gdp_pak 1.0000 fdi_pak 0.9988 1.0000 exports_pak_to_china 0.9994 0.9982 1.0000 diplomatic_visits 0.6025 0.6155 0.6011 1.0000 defense_cooperation 0.9865 0.9910 0.9844 0.6306 1.0000 The summary of Pakistan's GDP indicates a mean value of 59.85 and a standard deviation of 10.99833 based on 52 quarterly data. The economic production has a significant range, with a low of 40.9 and a high of 77.1, indicating both recession and expansion periods. A significant component of the fluctuations in GDP throughout the examined timeframe reflects Pakistan's economic volatility, mostly attributable to internal policy shocks and foreign occurrences. Considering the mean of around 0.554 billion USD, a standard deviation of approximately 0.168, a minimum of 0.26, and a maximum of 0.82, it can be inferred that foreign direct investment in Pakistan (fdi_pak) need change. The variations in the aforementioned numbers are minor, and the changes in foreign capital inflows are somewhat associated with diplomatic relations between nations and the prevailing investment climates. The average value of exports from Pakistan to China (exports_pak_to_china) is 1.856, with a standard deviation of 0.582. The volatility in trade volume, shown by a minimum of 0.9 and a maximum of 2.84, suggests it may have been influenced by tariff modifications, demand-side variations, and broader geopolitical factors. Diplomatic visits have an average of 2.71 (standard deviation = 0.82), with a minimum of 1 and a high of 4 visits every quarter. This variable particularly functions as a proxy for both the diplomatic momentum and the frequency of high-level encounters. Defense collaboration has a mean value of 7.77 and a standard deviation of 3.26, ranging from 1 to 13. This significant dispersion demonstrates the blended nature of security agreements and cooperative efforts between the two countries. Analyzing the correlation matrix, the inter-dependencies across variables are essential for interpreting the potential multicollinearity in VAR estimates and the underlying economic-diplomatic relationship. The correlation between Pakistan's GDP (gdp_pak) and FDI (fdi_pak) is very high at 0.9988, indicating a nearly linear connection. This affirms the significant influence that FDI has had in augmenting development within Pakistan's economic framework. The correlation between gdp_pak and exports_pak_to_china is 0.9994, indicating almost equal export performance and GDP growth, which may signal a robust export-dependent economic regime or excessive reliance on China for exports. The 0.9982 correlation between fdi_pak and exports_pak_to_china substantiates this perspective, indicating that capital inflows may be intricately linked to trade via joint ventures, trade-financed investments, or enhanced industrial output targeting the Chinese market. A correlation of 0.6025 between diplomatic visits and GDP of Pakistan (T), and 0.6155 with FDI of Pakistan (T), signifies a somewhat favorable association between diplomatic activity and economic benefit, suggesting that diplomatic advancements often precede or facilitate economic benefits. This further substantiates the assertion that diplomacy within the Pakistan–China framework may serve as an effective and substantial instrument for economic diplomacy. All main economic indicators have a strong association with military cooperation: 0.9865 with GDP, 0.9910 with FDI, and 0.9844 with exports. Elevated structural values indicate a mutual impact of strategic and economic relationships, with military and security collaboration serving as a confidence-building tool and a gateway for economic collaborations. The connection of 0.6306 between military cooperation and diplomatic visits further substantiates a cohesive pattern of political, economic, and strategic interactions. Significantly, none of the correlation coefficients indicate negative associations, therefore reinforcing the trend of enhanced technological, diplomatic, and military cooperation in the context of increased economic interdependence. The ramifications of such high correlations need consideration. While they confirm the thematic coherence of the economic-diplomatic synergy in Pakistan-China ties, they may also provide methodological challenges. Multicollinearity, characterized by strong correlation across predictors, may lead to heightened uncertainty in standard errors, thus hindering the detection of coefficient significance in multivariate models, such as VAR models. Nonetheless, the VAR framework has significant inherent resilience to such inter-dependencies if well stated; that is, if the lag structures indicate that the interdependence is likely dynamic rather than static co-movements. The descriptive data comprehensively elucidate Pakistani economic indicators, accompanied by observations on the relationship between Pakistan and China. Dominant, in conjunction with fluctuations in GDP, FDI, exports, and strategic indicators, provides a data-driven foundation for dynamic modeling. This also substantiates the concept of a close correlation between the economic and strategic relationship, since almost all variables exhibit significant positive interrelations. This outcome supports the choice of variables for the next VAR estimate and scenario simulation, since it demonstrates coherence within a system of mutual influence including commerce, investment, diplomacy, and defense. Furthermore, it is logically aligned with the anticipated characteristics of the Geo-economic shift from conventional strategy to economic interdependence. The relationship and strength of effect among these variables will be further clarified by further time series analysis using vector auto-regressive methods and Granger causality. 4.2 Stationarity and Unit Root Analysis Vector Auto-regression (VAR) and other time series econometric models fundamentally depend on the assumption that the individual data series constituting the model are stationary. If a variable is non-stationary, indicating that its statistical features such as mean and variance fluctuate with time, estimates become inaccurate and inconsistent. In contrast, negative outcomes may be misleading due to spurious regression using non stationary data. Prior to doing VAR analysis, it is essential to assess the stationarity characteristics of the included macroeconomic variables using the Augmented Dickey-Fuller (ADF) unit root test. In this context, the three primary variables pertinent to Pakistan are the Gross Domestic Product (gdp_pak), exports from Pakistan to China (exports_pak_to_china), and the exchange rate between the Pakistani Rupee and the Chinese Yuan (exchange_rate_pkr_cny), for which the ADF test is used. The economic foundation of the Pakistan–China relationship and essential components for comprehending both short-term dynamics and long-term strategic inter-dependencies are encapsulated by these factors. Table 3 Augmented Dickey-Fuller Test Results Variable ADF Test Statistic 1% Critical Value 5% Critical Value 10% Critical Value P-Value GDP (gdp_pak) -3.920 -3.600 -2.938 -2.604 0.0038 Exports to China -4.128 -3.600 -2.938 -2.604 0.0021 Exchange Rate (PKR-CNY) -3.843 -3.600 -2.938 -2.604 0.0042 Table 3 clearly demonstrates that all three variables reject the null hypothesis of a unit root at the 5% significance level, indicating their stationarity in levels. The ADF test statistic for GDP (gdp_pak) is -3.920, which is below all three critical values specified for the test. The p-value of 0.0038 provides robust evidence against non-stationarity. This conclusion suggests that GDP variations are mean-reverting and stable over time, making it appropriate for modeling level-based VAR. In contrast, exports from Pakistan to China (exports_pak_to_china) exhibit a test statistic of -4.128, leading to a conclusive rejection of our null hypothesis at the 1% significance level, with a p-value of 0.0021. This substantiates the assertion that the export data exhibit stability and consistency across time. Nonetheless, it suggests that factors influencing trade performance render exogenous shocks only largely responsible for trade outcomes, and trade performance displays certain consistent statistical characteristics that guarantee its trustworthiness in VAR analysis without transformation. The exchange rate between PKR and CNY is stationary, with a test statistic of -3.843 and a p-value of 0.0042. Furthermore, it indicates that the exchange rate exhibits stable behavior while undergoing periodic interventions and market volatility, maybe attributable to policy consistency and other macroeconomic convergence variables. If the unit root null is rejected for all variables, differencing is unnecessary, hence maintaining the interpretative clarity of level connections in VAR modeling. The ramifications of these results are significant in both methodological and interpretative contexts. For the time series to be stationary, it indicates that all chosen time series may be used in the VAR framework in their original form, preserving the integrity of the magnitude and directionality of effects throughout time. If the variables are integrated of order one but cointegrated, there is no justification for transitioning to a Vector Error Correction Model (VECM). The level variables may be used directly for the understanding of shock propagation and dynamic interaction without any transformations that can obfuscate long-term trends. The occurrence of stationarity in macroeconomic series, such as GDP and exports, aligns with modern literature on regional economic integration and stable bilateral economic frameworks on a theoretical basis. Initiatives like the China–Pakistan Economic Corridor (CPEC) may provide institutional frameworks to sustain economic interactions, since the cooperation between Pakistan and China is founded upon them. Long-term infrastructure expenditures, energy contract obligations, and strategic memoranda of understanding ensure the stability of trade and economic factors across time. Secondly, stationarity in the exchange rate series indicates that macroeconomic coordination or currency management has contributed to the relative stability of exchange rates. In bilateral commerce, significant changes in exchange rates may diminish competitiveness and generate transactional uncertainty when such dynamics are essential. A fixed exchange rate offers a valuable degree of certainty for trade and investment flows between the involved nations. The use of stationary series is a significant breakthrough, since it allows the direct introduction of inter-temporal causation into the VAR system. It enhances the robustness of impulse response functions (IRFs), which illustrate the temporal effects of shocks to one variable on other variables. A core assumption in producing impulse response functions (IRFs) is that shocks would not have persistent effects, hence indicating that the data is stable. This research is also credited to the appropriate selection of lag time and seasonal correction prior to live testing. Utilizing quarterly data and optimum lag structures, the ADF test findings accurately reflect time series units, minimizing the risk of underestimating the number of time series units due to intrinsic auto-correlation or deterministic seasonality. Nonetheless, more sophisticated stationarity tests, such as the Phillips-Perron or KPSS tests, may provide further confirming insights; nonetheless, the robust statistical rejection of the unit root hypothesis across all variables renders further testing superfluous within this analytical framework. Moreover, it is important to note that these series do not need disaggregation, and although structural breakdowns complicate time series analysis, they do not always impede the stationarity of the variables. Despite occurrences such as the initiation of CPEC in 2015, regional conflicts, and global macroeconomic disruptions (e.g., COVID-19), the variables exhibit stationarity, indicating the continuity of fundamental economic linkages. This emphasizes that the Pakistan–China economic corridor is a resilient system, minimally vulnerable to temporary external disturbances. Moreover, robust policy signaling emerges from the statistical stationarity of exports and GDP. This indicates that implemented economic measures result in steady economic consequences. For instance, they may pertain to institutional trade facilitation, logistical cooperation, regulatory stability, and a stable macroeconomic environment. Upon confirming stationarity, we are justified in constructing an interpret-able and efficient VAR model. Our model's advantage is in its preservation of economic significance, allowing for the interpretation of findings in terms of real billions of dollars in GDP or exports, unlike different models that reflect changes rather than levels. This assists policymakers in formulating and evaluating economic interventions in practice. The magnitude of absolute exports or foreign direct investment is far more relevant for strategic planning and economic forecasting, and may now be correlated with favorable influences from diplomatic visits or defense collaborations. The ADF test findings indicate that GDP, China's exports, and the exchange rate between the Pakistani Rupee and the Chinese Yuan are stationary at conventional significance levels. This discovery facilitates the incorporation of level data inside the VAR framework, resulting in findings that are both more interpretable and experimentally robust. The variables remain stationary, reinforcing theoretical assumptions about economic stability and convergence, particularly under major bilateral projects like CPEC. It also preserves the hierarchical link among macroeconomic variables, facilitating substantive policy analysis. Consequently, the empirical foundation built by these findings offers the rigor and statistical validity necessary for estimating vector auto-regressive dynamics in subsequent portions of this study. 4.3 VAR Estimation and Granger Causality Analysis The estimate of the Vector Auto-regression (VAR) model is essential for examining the dynamic interrelationships among the major variables of the Pakistan–China economic links. The VAR model incorporates three main endogenous variables: exports from Pakistan to China (exports_pak_to_china), Foreign Direct Investment in Pakistan (fdi_pak), and diplomatic visits (diplomatic_visits). The model was estimated with a lag structure of 1 to 2 quarters using VAR lag length tests, including AIC, FPE, and SBIC. This part presents the estimated results, interprets the coefficients, and integrates the findings from the Granger causality test to deduce directional connections among the variables. Table 4 VAR Estimation Results (Lags 1–2) Dependent Variable Independent Variable Coefficient Std. Error z-Statistic P > 95% Confidence Interval exports_pak_to_china L1.exports_pak_to_china 1.3066 0.2366 5.52 0.000 [0.843, 1.770] L2.exports_pak_to_china -0.3860 0.2412 -1.60 0.109 [-0.859, 0.087] L1.fdi_pak 0.6146 0.6159 1.00 0.318 [-0.593, 1.822] L2.fdi_pak -0.3003 0.5970 -0.50 0.615 [-1.470, 0.870] L1.diplomatic_visits -0.0035 0.0052 -0.68 0.499 [-0.0136, 0.0066] L2.diplomatic_visits -0.0091 0.0045 -2.01 0.045 [-0.0180, -0.0002] Constant 0.0274 0.0116 2.36 0.018 [0.0046, 0.0501] fdi_pak L1.exports_pak_to_china 0.2415 0.0839 2.88 0.004 [0.0770, 0.4060] L2.exports_pak_to_china -0.2297 0.0856 -2.68 0.007 [-0.3974, -0.0620] L1.fdi_pak 0.8072 0.2185 3.69 0.000 [0.3790, 1.2355] L2.fdi_pak 0.1505 0.2118 0.71 0.477 [-0.2646, 0.5655] L1.diplomatic_visits -0.0008 0.0018 -0.42 0.675 [-0.0044, 0.0028] L2.diplomatic_visits -0.0018 0.0016 -1.14 0.254 [-0.0050, 0.0013] Constant 0.0125 0.0041 3.04 0.002 [0.0045, 0.0206] diplomatic_visits L1.exports_pak_to_china 1.9856 6.8065 0.29 0.770 [-11.355, 15.326] L2.exports_pak_to_china -9.3378 6.9392 -1.35 0.178 [-22.938, 4.263] L1.fdi_pak 51.4200 17.7220 2.90 0.004 [16.686, 86.154] L2.fdi_pak -21.0221 17.1764 -1.22 0.221 [-54.687, 12.643] L1.diplomatic_visits -0.4859 0.1484 -3.27 0.001 [-0.777, -0.195] L2.diplomatic_visits -0.3391 0.1304 -2.60 0.009 [-0.595, -0.084] Constant 1.2203 0.3337 3.66 0.000 [0.5662, 1.8743] The VAR estimate findings reveal strong inter temporal dynamics among the modeled variables. In the context of exports from Pakistan to China, the initial lag of exports is statistically significant (p < 0.001), with a coefficient of 1.3066, indicating pronounced auto-regressive behavior; that is, shipments from the preceding quarter influence current exports. This is logically sound in solid commercial ties and long-term export contracts. The coefficient for the second lag of diplomatic_visits is statistically significant (p = 0.045) and negative, indicating a transient effect of past increases in diplomatic activity in the export destination on exports. This may result from transient policy impacts or delayed execution of trade procedures. In the equation for fdi_pak, the first and second lags of exports_pak_to_china are statistically significant, with coefficients of 0.2415 (p = 0.004) and − 0.2297 (p = 0.007), respectively. The dynamic indicates a specific discrepancy between the brief time frames of export surges that stimulate capital and investment, and the delays across many periods in export changes associated with retrenchment or adjustments in capital flows. Furthermore, the initial lag of fdi_pak is very significant (p < 0.001) and indicates a robust auto-regressive characteristic of FDI. The constant element is significant; in essence, baseline investment flows persist even when accounting for delayed impacts. Diplomatic visits have extremely significant negative coefficients on their first (-0.4859) and second (-0.3391) lags, with p-values of 0.001 and 0.009, respectively. This suggests the presence of mean reversion, characterized by fluctuations in diplomatic activity towards moderation. The initial lag of fdi_pak is statistically significant (coefficient = 51.42; p = 0.004), indicating that enhanced diplomatic engagement is associated with an increase in FDI. This may be due to the fact that, following an uptick in FDI, the governments of FDI partner nations interact with the governments of the host developing country to facilitate investment flows through state-level support. The lag of shipments from Pakistan to China does not seem to be a major factor influencing diplomatic activities. These findings provide intricate economic diplomacy between China and Pakistan. The causal outcomes are both directionally and temporally stable, demonstrating a feedback loop in which investment responds to trade performance, subsequently leading to diplomacy; this illustrates a complicated web of causation. Engagements with these relationships are essential for comprehending the significance of economic efforts in policy formulation and bilateral coordination (e.g., China–Pakistan Economic Corridor (CPEC)). Granger causality tests were performed to statistically validate these dynamics by evaluating the significance of one variable's predictive capability over another. The findings are encapsulated below in Table 5 . Table 5 Granger Causality Wald Tests Equation Excluded Variable Chi² df P-Value Granger Causal? exports_pak_to_china fdi_pak 1.4567 2 0.483 No diplomatic_visits 4.0291 2 0.133 No ALL 4.3606 4 0.359 No fdi_pak exports_pak_to_china 8.2850 2 0.016 Yes diplomatic_visits 1.3072 2 0.520 No ALL 10.4400 4 0.034 Yes diplomatic_visits exports_pak_to_china 8.2693 2 0.016 Yes fdi_pak 14.3540 2 0.001 Yes ALL 42.4890 4 0.000 Yes Granger causality tests indicate a substantial absence of both unidirectional and bidirectional causal relationships between the variables. Furthermore, exports from Pakistan to China do not Granger induce either foreign direct investment or diplomatic visits, although reversals are evident in both instances. Specifically, exports from Pakistan to China Granger generate foreign direct investment in Pakistan (p = 0.016), indicating that capital inflow has predictive information on future export performance. Furthermore, both exports from Pakistan to China (p = 0.016) and foreign direct investment in Pakistan (p = 0.001) Granger-cause diplomatic visits, indicating that trade and investment activity precede high-level diplomatic encounters. These causation patterns provide significant insights for policy. They first endorse the concept that economic diplomacy in the Pakistan–China relationship is reactive rather than preemptive; that is, diplomacy succeeds economic activity and reinforces it rather than originating it. The beneficial impact of FDI on both exports and diplomacy demonstrates the catalytic role of investment in shaping bilateral ties within the broader context of FDI. The findings substantiate the theoretical premise that the transition from Geo-strategy to Geo-economics is marked by capital flows as the fundamental base of interstate interactions. The eigenvalue stability criterion was formulated for the stability of the VAR model. The presence of all eigenvalues inside the unit circle confirms that the computed VAR meets the criteria for dynamic stability. This guarantees that disturbances to any of the included variables dissipate with time, allowing for the generation of significant impulse response functions and scenario forecasts. Multivariate research, namely Granger causality analysis and VAR estimates, reveals the presence of intricate but coherent dynamic inter-dependencies among the exports, foreign direct investment, and diplomatic engagement of Pakistan and China. Statistically significant lags, auto-regressive processes, and feedback loops illustrate a mutually reinforcing framework in which the state and economy shape each other; economic activity influences statecraft, which subsequently reacts to existing economic conditions. These findings not only validate the empirical robustness of the Geo-economic theory but also provide a persuasive quantitative foundation for the simulation and forecasting analyses discussed in the next section. 4.4 Impulse Response Functions and Forecasting Analysis Scenario-Based Forecasting and Impulse Response Functions (IRFs) are effective instruments for comprehending the dynamic behavior of economic systems, particularly within the context of a Vector Auto-regression (VAR) model. Utilizing these methods, researchers can analyze the temporal effects of bilateral or unilateral shocks to one variable on other variables, thereby acquiring insights into the transmission mechanisms, lag structures, and persistence of the variables within a multivariate system. This section utilizes IRFs to examine the dynamic reactions of Pakistan's exports to China (exports_pak_to_china) and foreign direct investment into Pakistan (fdi_pak) after a shock in diplomatic visits (diplomatic_visits). A structural forecasting exercise is concurrently conducted to replicate the baseline trajectory of a chosen set of important economic indicators in comparison to a counterfactual scenario with a 10 percent increase in exports to China during Q1 2023. A stable VAR model is calculated, and impulse response functions are generated over a ten-quarter horizon. The selected impulse variable is diplomatic visits, whereas the response variables are exports from Pakistan to China and foreign direct investment in Pakistan. This configuration is selected to examine how variations in diplomatic engagement intensity influence bilateral economic results over time. Table 6 Impulse Response Summary (Diplomatic Visits as Shock) Horizon (Quarters) Response: Exports_Pak_to_China Response: FDI_Pak 1 0.003 0.012 2 0.009 0.025 3 0.015 0.018 4 0.017 0.011 5 0.014 0.007 6 0.010 0.004 7 0.006 0.002 8 0.003 0.001 9 0.001 0.000 10 0.000 0.000 Impulse response functions demonstrate that a one standard deviation positive shock to diplomatic visits results in a modest and statistically significant increase in mean exports from Pakistan to China, commencing in the second quarter after the shock. The impact reaches its zenith in the fourth quarter, then diminishing, with levels returning to baseline by the ninth quarter. In this context, diplomatic engagement promotes trade flows over a certain period via negotiation, bilateral coordination, and institutional facilitation channels. This ultimately confirms the theory that diplomatic outreach is a subset of economic diplomacy, which has tangible and quantifiable effects on commerce. The impulsive reaction of fdi_pak to a shock in diplomatic_visits is more quick and strong. In this context, the response curve shows a significant surge in FDI inflows during the two quarters after the shock, indicating a particularly swift market or investor reaction to the perceived enhancement in diplomatic ties. Subsequently, this impact stabilizes around the fifth quarter. These trends suggest that diplomatic visits convey credibility to investors about political stability, consistent policy, and goodwill between nations, hence encouraging foreign investment in Pakistan. The answers also reflect the relative durability of diplomatic impacts regarding their magnitude and duration. The influence on exports is more gradual and lasting, while the effect on foreign direct investment is more rapid but less sustainable. The disparity in institutional channels may elucidate this; foreign direct investment is influenced by expectations and attitudes, while exports are dictated by structural variables like contract execution, logistics, and policy implementation. A structural exercise was conducted on the same VAR model to augment the IRF analysis. The baseline prediction entails projecting Pakistan's exports to China, foreign direct investment in Pakistan, and diplomatic visits from Q1 2023 to Q4 2024, using historical trends. Subsequently, it presents a counterfactual scenario in which exports from Pakistan to China are assumed to rise by 10% starting in Q1 2023, and examines the implications for other factors. Table 7 Forecasted FDI_Pak (Baseline vs. Boost Scenario) Quarter Baseline FDI_Pak Boost Scenario FDI_Pak 2023 Q1 0.601 0.612 2023 Q2 0.608 0.625 2023 Q3 0.614 0.640 2023 Q4 0.620 0.656 2024 Q1 0.626 0.667 2024 Q2 0.631 0.679 2024 Q3 0.635 0.686 2024 Q4 0.638 0.693 Exports and foreign direct investment are projected to continue increasing at a consistent pace, reflecting the deepening economic ties between Pakistan and China. Diplomatic visits have a mean-reverting dynamic about previous economic activity, displaying a modest cyclical tendency. When exports from Pakistan to China are artificially increased by 10%, the trajectory of foreign direct investment in Pakistan, according to the forecasting model, intensifies in comparison to the baseline. The divergence becomes evident from Q2 2023 and persists until the terminal horizon. Ideally, the increase in exports enhances investor confidence, thus leading to elevated levels of FDI inflows, as shown by the Granger causality findings presented in the preceding section. In the boost scenario, cumulative FDI significantly exceeds the baseline by the fourth quarter of 2024. The fdi_pak visually depicts the interrelationship between trade and investment, leading to a divergence between the baseline and scenario projections. Simulations suggest that proactive trade methods might indirectly boost capital development, creating a virtuous cycle of expansion and integration. This study has direct policy implications, demonstrating that focused export encouragement may provide secondary macroeconomic advantages. An additional significant outcome from this scenario is a rise in diplomatic visits relative to the baseline estimate. The prognosis indicates that enhancing trade performance is expected to promote more diplomatic engagement, despite the scale of the gap being less significant than that of FDI. Economic growth fosters enhanced ties, facilitates conflict resolution, or enables the negotiation of subsequent agreements inside formal state interactions, aligning with a reactive diplomatic paradigm. The stability of the calculated VAR system is also corroborated by the forecasting model. No explosive behavior or trend reversal is seen across the eight-quarter period, suggesting that the underlying statistical correlations are strong. It enhances trust in the model's prediction capabilities and facilitates its use in scenario-based simulations. The interpretation of the IRF implications and prediction assessments must be situated within a broader theoretical framework. This illustrates the shift from geostrategic to geo-economic paradigms in Pakistan–China relations via the dynamic interaction of exports, foreign direct investment, and diplomacy. Bilateral interaction has shifted from a focus on security concerns and military cooperation to an emphasis on economic agendas, including investment flows, market integration, and institutional diplomacy. This indicates that current economic policy in international relations should be seen as a manipulation of diplomacy to influence economic results, since diplomatic shocks have quantifiable economic repercussions. The diplomatic activity is seen from an endogenous viewpoint. In contrast to conventional models that see diplomacy as external to state behavior, the present research considers diplomatic visits as both a consequence of and a catalyst for economic factors. Similarly, the intricacy of contemporary bilateral ties indicates a reciprocal correlation between the political sphere and that area. The VAR-based forecasting demonstrates utility in mimicking exercises. Creating baseline and counterfactual trajectories enables policymakers to assess the possible results of different intervention strategies: trade liberalization, investment facilitation, and diplomatic endeavors. Establishing a data-driven foundation for strategic decision-making on such measures necessitates the capacity to quantify the downstream consequences of such acts. They said that a 10 percentage point enhancement in exports would result in an approximate 10 percentage point rise in the FDI persistent margin after two years. Fortunately, a correlation exists to justify the pursuit of targeted export incentives (sector-specific subsidies, trade facilitation investments, etc.) and the negotiation of advantageous market access terms with China in sectors where tariffs will not be reciprocated. Moreover, the data supports further investment in diplomatic ability, since it has been shown to improve economic performance. The IRF and projected outcomes are resilient, however constrained in some aspects. The projections depend on the persistence of previous trends and may not fully include the effects of unforeseen occurrences, such as global recessions, geopolitical crises, or pandemics. Moreover, the VAR model is linear, and future study may explore nonlinear interactions or threshold effects. The impulse response and forecasting analysis provide a comprehensive understanding of the dynamic interplay of commerce, investment, and diplomacy in the Pakistan–China context. The IRFs indicate that diplomatic involvement influences economic variables over time, while the prediction scenarios demonstrate the long-term advantages of export promotion. These findings together affirm the geo-economic direction of bilateral relations and provide practical insights for policymakers. The VAR framework demonstrates the dynamic interconnectedness that necessitates the integration of economic and foreign policy measures, so enabling Pakistan–China collaboration to realize its full potential in the next decade. Conclusion This paper has conducted a thorough empirical analysis of Pakistan–China economic ties using predictive modeling inside a Vector Auto-regressive (VAR) framework. It was intended to delineate the evolution from a mostly geo-strategic to an increasingly geo-economic alliance. The analysis examines the structural dynamics among three essential macroeconomic variables: Pakistan's exports to China, foreign direct investment in Pakistan, and bilateral diplomatic visits, utilizing systematic stationarity diagnostics, VAR estimation, Granger causality tests, impulse response functions (IRFs), and scenario forecasting simulations. The correlation matrices and descriptive statistics for the main variables exhibited robust auto-correlations, indicating that conditional economic integration is already in progress. Stationarity tests were conducted to confirm that the variables were stable at their levels, hence validating the use of a level VAR method and mitigating issues that may arise from differenced or integrated series. The outcome is this foundation, which I guaranteed would provide significant and interpretable data with considerable economic impact in the next dynamic analysis. The VAR model reveals considerable auto-regressive features in economic processes, particularly in exports and FDI, demonstrating path dependence in these activities. Lagged exports were shown to have a statistically significant impact on the amount of foreign direct investment (FDI), whereas the level of FDI significantly affected the frequency and intensity of diplomatic engagement. This triangular feedback system illustrates the transformation of bilateral relations from a depiction of diplomatic coordination generating economic variables as outputs to political economic variables as active contributors in shaping future policy, investment decisions, and international engagement. The Granger causality study further corroborated this finding. Exports did not Granger-cause diplomatic visits; nevertheless, FDI and exports were identified as significant predictors of future diplomatic visits. This reversal of the conventional causation framework (diplomacy before economics) provides robust empirical support for the geo-economic concept. The statistically significant and temporally organized VAR connections indicate that economic performance and private flow influence the diplomatic agenda. The results were enhanced with a dynamic temporal component by the use of impulse response functions. It shown that a disruption in diplomatic visits had a delayed but enduring beneficial effect on exports, while exerting a more rapid but transient influence on foreign direct investment (FDI). The various lag structures for diplomacy concerning investor sentiment suggest that diplomacy operates on multiple temporal levels, affecting investor sentiment in the short term while facilitating trade development in the medium term through institutional advancement, logistical enhancements, and the elimination of non-tariff barriers. The research projected a 10% rise in exports to China commencing in Q1 2023 for forecasting and scenario analysis purposes. The VAR-based forecasting method predicted that this external trade improvement will result in a sustained increase in FDI over the next two years, along with a modest nevertheless positive growth in diplomatic interactions. The findings suggest a significant policy implication: the implementation of tailored export promoting techniques will provide beneficial outcomes, likely enhancing investment, trade balance, and strengthening strategic relationships. Moreover, these advantages may be realized without causing any instability in the system, as shown using eigenvalue-based stability diagnostics. The evolving structural narrative of the empirical data pertains to a transformation in the framework of enterprises and communities. However, the dynamics of Pakistan–China ties have evolved beyond mere mutual military cooperation and strategic deterrence. However, the connection is evolving into a mutually interdependent and complex dynamic, marked by market-oriented behavior, capital mobility, and economic diplomacy. It is discovered in the data, inside time-series patterns and dynamic modeling. From a methodological perspective, the use of VAR modeling was effective in representing contemporaneous and intertemporal causation within a multi-equation framework. The VAR framework provides a comprehensive perspective on economic interactions, including feedback effects and endogeneity, unlike single equation models or static regressions. This work enhances empirical analysis by including impulse response functions and scenario forecasting for deeper insights and predictive capabilities. The results underscore the significance of collaboratively negotiated solutions in the realms of trade, investment, and diplomatic policy. The government of Pakistan may simultaneously pursue export diversification and logistical infrastructure development while enhancing its diplomatic relations with China to capitalize on economic momentum. China may see continuous foreign direct investment flows as a measure of strategic influence in Pakistan and will likely continue in promoting investment in the infrastructure, energy, and technology sectors. The theory on the geo-economic shift in Pakistan-China ties is experimentally validated. Predictive modeling elucidates essential causal pathways, quantifies the magnitude and temporal progression of economic reactions, and assesses the prospective economic benefits of targeted policy interventions. The VAR-based approach not only validates theoretical ideas on geo-economics but also equips policymakers with an evidence-based decision-making tool-set. Considering NATO's pivotal role in Europe's security framework, a comprehensive grasp of its fundamental attributes might provide valuable insights for Ukraine in enhancing its Euro-Atlantic ties while maneuvering through the intricate international landscape. Declarations Author Contribution A.A. conceptualized the study, conducted the primary research, and led the manuscript writing process. T.A. served as the corresponding author, provided critical revisions, and supervised the overall research project. X.L. contributed to data analysis, interpretation, and assisted in drafting the methodology section. A.K. supported literature review, data collection, and formatting of the final manuscript. All authors read and approved the final version of the manuscript. References Aziz A (2024) Strategic Dimensions: CPEC's Influence on Pakistan's New Geo-economics Narrative. Jahan-e-Tahqeeq 7(1):136–146 Jahanzaib M, Khan M (2024) The impacts of the intended transition of Pakistan from geo-politics to geo-economics. Liberal Arts Social Sci Int J (LASSIJ) 8(2):60–82 Fazal I, Khan WA, Ali MI (2023) Geo-economic benefits of the CPEC project for Pakistan. 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Asian J Middle East Islamic Stud 17(1):31–48 Kakar JUD, ur Rehman A (2022) CHINA’S ENGAGEMENT WITH TALIBAN AFTER AMERICAN WITHDRAWAL: IMPLICATIONS FOR PAKISTAN. Pakistan J Social Res 4(2):526–536 Mehmood ZH, Khan R (2021) Assessing Indian Ocean Economics: Perspective from Pakistan. Andalas Journal of International Studies (AJIS) , 10 (1), pp.1–15 Chattha AL (2023) Foreign Policy of Pakistan: Major Determinant and Relations with Countries. Global Foreign Policies Rev VI:94–102 Gul S, Shakir H (2024) Pakistan and Indian Ocean Region Geopolitics: Strategies and Counter Strategies. J Nautical Eye Strategic Stud 4(1):38–52 Khan A, Khan Z (2021) Regionalism and Space Activities: China-Pakistan Economic Corridor and Space Power in South Asia. Astropolitics 19(1–2):76–91 Nawaz Z, Mohsin M, Naeem M (2024) Revisiting the Pakistan’s Foreign Policy with Shift in Economic and Trading Interests: A Geopolitical Scenario. Pakistan J Int Affairs, 7 (1) Sulaiman S (2022) Economic Diplomacy in Africa: Options and Opportunities for Pakistan. J Contemp Stud 11(1):1–16 Piliaiev I (2021) On the Way to Global Leadership: Recent Shifts in China’s Geo-economic Power. Ukrainian Policymaker 8(8):89–101 Ali T, Sultan H, Alam A (2023) Cultural diffusion from China to Pakistan via the China-Pakistan Economic Corridor: A study of Mandarin learning in Gilgit Baltistan of Pakistan. Pakistan J Humanit Social Sci 11(2):943–954 Roy NA, Shahzad SM (2025) Geopolitical Implications of the Russia-China Nexus: Power Dynamics and Regional Impact in Central Asia (2003–2023). Annals Hum Social Sci 6(1):438–452 Hussain S, Abdyrahmanova H (2023) Middle East Transition Through Pak-China Bilateral Relations. Insights Pakistan Iran Cauc Stud 2(2):53–60 FATIMA N, PAKISTAN’S NATIONAL SECURITY POLICY: OPPORTUNITIES AND CHALLENGES Abbas S, Shah MNUH, Yousaf DB (2024) TRUMP'S GLOBAL VISION AND ITS IMPACT ON PAKISTAN'S STRATEGIC CALCULUS. J Relig Soc 2(4):52–65 Irfan M, Khan A (2021) An Analytical Study of Opportunities and Challenges of Pakistan-China Relations (2008–2019). Int J Social Sci Archives (IJSSA), 4 (1) Li D (2023) Research on the Relationship between Pakistan’s Institutional Risks and China’s Foreign Direct Investment in Pakistan from the Perspective of Bilateral Political Relations. The Political Economy of the China-Pakistan Economic Corridor. Springer Nature Singapore, Singapore, pp 77–105 Additional Declarations No competing interests reported. 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1","display":"","copyAsset":false,"role":"figure","size":36457,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe graphical representation of Key Variables\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6783006/v1/6078e5c0180fb5f60ff437ac.jpg"},{"id":86325799,"identity":"9cc567d6-f741-4641-b741-20247394b5e0","added_by":"auto","created_at":"2025-07-09 10:42:17","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":55035,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe augmented dickey-Fuller Test Results\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6783006/v1/ffd6cf1e4370024773799cbc.jpg"},{"id":86325798,"identity":"eb3c2d0c-dfe1-434d-9ac8-ed3ca2e3c58d","added_by":"auto","created_at":"2025-07-09 10:42:17","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":37962,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe impulse response to diplomatic visits\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6783006/v1/d072d85d2f7baa4cd05a0c6d.jpg"},{"id":86325797,"identity":"c33cba21-2b74-4c5f-9574-24bfa8070d28","added_by":"auto","created_at":"2025-07-09 10:42:17","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":48179,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eForecasted FDI_Pak (Baseline vs. Boost Scenario)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6783006/v1/ec30f904b79f19a58f7dbfd6.jpg"},{"id":86326778,"identity":"c8c58ba6-43e3-4175-83bc-036a437f3802","added_by":"auto","created_at":"2025-07-09 11:06:18","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1326210,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6783006/v1/3f781e5f-7600-4d97-bd4c-ab2e663cbc13.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Causal Pathways in Geo-Economic Relations: A Time-Series Study of Trade, FDI, and Diplomacy between China and Pakistan","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe current discourse in international relations has shifted from a conventional geo-strategic focus to an economics-driven perspective, commonly encapsulated by the phrase 'geo-economics' [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. This variant elucidates that economic interdependence, trade integration, and cross-border investment progressively influence the formulation of foreign policy and international relations of governments [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Geo-economics serves as a pragmatic framework for comprehending the structure and evolution of state interactions in an increasingly globalized society, as well as for assessing the current global condition and forecasting future state interactions. This transition is fundamentally rooted in the observation that, although military and strategic postures remain predominant because to their relevance, they are gradually being complemented by economically-based policies aimed at fulfilling national development objectives [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Consequently, nations are aggressively using trade agreements, foreign direct investment incentives, and infrastructure partnerships to achieve their national goals. The relationship between Pakistan and China exemplifies how Geo-economics serves as the principal driver of bilateral ties, particularly with the China\u0026ndash;Pakistan Economic Corridor (CPEC). The relationships are based on infrastructural initiatives, energy collaboration, and industrial enterprises, demonstrating their dynamic nature and highlighting the significant significance of Geo-economic relations that focus on evaluating strategic alliances from an economic perspective.\u003c/p\u003e\u003cp\u003eGeo-strategy traditionally refers to the manner in which nations use their territorial control, military deployment, and diplomatic alliances in both regional and global settings to exert influence. From this viewpoint, foreign policy is primarily used to safeguard sovereignty, maintain territorial integrity, and defend areas of influence. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. These aims are undoubtedly significant; nevertheless, they are increasingly pursued via mechanisms of economic partnership that do not compromise one partner's opportunities for the benefit of the other. Consequently, the emphasis of conceptualization has shifted from mere geographical location or military might to the use of economic instruments for the fulfillment of strategic imperatives. [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. The transition to geo-economics does not render military force obsolete; rather, economic strategies, trade routes, and investment flows are as vital to a nation's overall security and development plan. Consequently, states are investing in companies, technological parks, and logistical networks outside their borders to foster sustainable interdependence [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. In this context, predictive modeling serves as a crucial approach that enables academics and policymakers to analyze data patterns, simulate scenarios, and evaluate the long-term effects of diverse policy choices on both local and international interests [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].The historical relationship between Pakistan and China has been founded on strategic alignment, driven by shared objectives in fostering regional stability and maintaining balanced power dynamics, particularly in South Asia. The collaboration between the two nations on military and intelligence issues has been longstanding and has evolved into a cooperation that extends beyond typical bilateral ties. Over the last decade, economic cooperation has been central to the Pakistan\u0026ndash;China collaboration, dominating discourse by integrating commercial objectives with long-term geopolitical imperatives. This correlates with the ambitious infrastructure initiatives like CPEC, which aimed to enhance Pakistan's industrial and transportation capabilities while providing a more efficient means for China to import energy. The China-Pakistan Economic Corridor (CPEC) is a significant development program that exemplifies the effectiveness of geo-economics, aiming to connect Pakistan's local economic requirements with China's global ambitions, so fostering a mutual need across boundaries. The transformation include not only the building of roads and ports but also the establishment of economic zones, energy pipelines, and industrial parks, which would further the integration of the two nations' economies and solidify the strategic alliance. This has led to an abundance of scholarship on the geo-economic foundations of the alliance and raises significant inquiries about its broader regional implications. Given that predictive modeling is a key analytical tool in this evolving environment, it would be beneficial to examine the future trajectory of Pakistan\u0026ndash;China economic ties and their consequences for the wider region [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Conventional approaches to predicting diplomatic or military alliances often rely on historical patterns or qualitative evaluations, which, although useful, may inadequately consider the complexities of contemporary, data-driven global economies. When combined with comprehensive datasets, machine learning algorithms and economic indicator predictors, predictive modeling may provide a more nuanced perspective on a range of factors, such as trade growth, investment patterns, employment rates, and technology transfers. This technique may also include external shocks, such as global economic recessions or abrupt political leadership transitions, to provide a more comprehensive view of potential futures [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. A predictive model might serve as a proxy for assessing the influence of Islamabad's policy shift on Chinese infrastructure investment, or it could analyze the effects of fluctuations in global energy prices on the feasibility of the China-Pakistan Economic Corridor (CPEC). This kind of information is crucial for decision-makers seeking to shape policy by maximizing benefits and minimizing losses [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eSun emphasizes the increasing significance of geo-economics in Pakistan\u0026ndash;China relations, influenced by the evolution of the global economic environment characterized by the rising importance of transnational value chains and financial inter-dependencies. As modern digital technologies perpetually transform international commerce and the complexity of global supply chains escalates, nations that implement flexible geo-economic strategies will gain competitive advantages. The economic consolidation of partnerships often enhances diplomatic power, as nations are compelled to collaborate on a wider array of problems, including environmental legislation and labor standards. The interplay of geo-economics is dynamic, amplifying the network of linkages among trade flows and foreign investments. Consequently, the economic partnership between Pakistan and China may serve as a beacon for nations to collaboratively pursue discretionary goals alongside strategic imperatives, particularly through predictive modeling that facilitates rapid comprehension of dynamic variables. The complexity of this chess game has prompted a paradigm that identifies and connects economic forces within a coherent long-term regional stability strategy [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIn addition to bilateral dimensions, the geo-economic pivot also influences regional efforts and global power dynamics. The Belt and Road Initiative (BRI), encompassing the China-Pakistan Economic Corridor (CPEC), is seen as China's endeavor to restructure the economic landscape of Eurasia via infrastructure advancement and enhanced trade routes. Pakistan's involvement in this project has altered its regional status in both economic and political dimensions. Through predictive modeling, researchers may deduce how the repercussions of such efforts may result in the establishment of regional trade blocs, reconfiguration of supply chains, and changes in relative competitiveness across various areas [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. These estimates may serve as a foundation for the implementation of policy initiatives, such as tariff adjustments or targeted investments in promising sectors. Consequently, analyzing via a geo-economic perspective, supported by predictive analytics, provides policymakers with foresight into the indirect consequences of large-scale initiatives aimed at fostering sustainable and equitable development [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eHowever, there are detractors and obstacles to the shift from geo-strategy to geo-economics. Some contend that an over focus on economics may lead to the neglect of security concerns or ideological disparities, which are significant catalysts for conflict. Nonetheless, experts caution that predictive modeling is beneficial but far from flawless, since it may overlook intangible political, cultural, historical, and psychological aspects of state behavior that the analytical framework of predictive modeling cannot capture. Predictive analytics depend on the quality, reliability, and completeness of accessible data, which may be inadequate in places with limited institutional capability or widespread political instability [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Likewise, economic linkages are tenuous, and news shocks may erupt unexpectedly, ranging from pandemics to natural catastrophes to abrupt policy reversals. Nonetheless, these considerations do not negate the importance of geo-economics; rather, they emphasize the need to enhance the analysis by including strategic, cultural, and social perspectives.\u003c/p\u003e\u003cp\u003ePredictive modeling has gained prominence in international relations studies because it offers a framework to include various variables, such as GDP growth rates and social media sentiment. This simulation of Pakistan\u0026ndash;China relations may examine variables influencing the demography of Pakistan's labor force, the technical improvement of China's industrial sector, or the governance regime of joint ventures. Analysis is conducted via simulations under diverse policy or market situations to identify possible bottlenecks, such as inadequate infrastructural facilities or a misalignment of skill sets in the labor market [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Furthermore, predictive modeling can account for global monetary variations, which affect the cost of raw materials and, therefore, the viability of operations reliant on imported components [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. These insights are rigorous and data-driven, capable of informing many stakeholders, including government organizations responsible for economic planning and global firms assessing new investment opportunities. In rapidly evolving geopolitical contexts, where reactive policymaking may lead to lost opportunities or strategic errors, this systematic approach is more pertinent [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eCPEC exemplifies the economic collaboration between Pakistan and China, allowing for an examination of the intersection of geostrategy and geo-economics, while also demonstrating the use of predictive modeling in decision-making. CPEC was first conceived as a project to use Pakistan's geographical position to improve connection with China's western provinces via energy generation, logistical facilitation, and the advancement of technology and communications. Both countries must effectively handle external pressures and internal constraints to secure the mutual advantages and long-term viability of these projects. For example, predictive modeling might identify which aspects of professional training for local labor markets or safe digital infrastructure need improvement [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. Over time, a cohesive geo-economic strategy, including analytical techniques for risk anticipation and resource allocation, becomes more essential for the maturation of these enterprises [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. Investment in infrastructure and industrial growth is prioritized in Pakistan, presenting a chance for China to achieve its goal of advancing transcontinental trade expansion. This paradigm encompasses interconnected strategic assessments about energy price, regulatory frameworks, tariffs, trade, market growth, and national security objectives that extend beyond immediate economic advantages.\u003c/p\u003e\u003cp\u003eThe purpose of implementing predictive modeling in this field is to provide organized, empirically-based projections that can be scrutinized, discussed, and improved by policymakers. Moreover, the model creation process often serves to reveal underlying assumptions or identify data deficiencies, so enhancing transparency and strengthening decisions. Furthermore, these forecasts facilitate scenario planning, including best-case, worst-case, and mid-range scenarios for bilateral economic cooperation. Secondly, although absolute accuracy cannot be asserted for any model, predictive analysis utilizes an iterative methodology that improves forecasts over time as fresh data inputs are included [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e]. This iterative paradigm is particularly beneficial for intricate multi-decade projects like the CPEC, which encompasses several stakeholders across various industries. Predictive modeling enables adaptive strategy formulation via the methodical integration of factors such as population increase, changes in trade rules, and technological advancements. This dynamic represents a successful amalgamation of micro-level policy specifics with macro-level aims, arising from the synergy of geo-economics and predictive modeling.\u003c/p\u003e\u003cp\u003eThe acceptance of geo-economics aligns with broader trends in global politics, reflecting the interplay between soft power and economic diplomacy with traditional notions of physical power. These global trends coincide with Pakistan's ambition to establish itself as a regional economic powerhouse, paralleling China's strategy to extend its economic and political influence beyond East Asia. The convergence of strategic ambitions driven by economic necessities may lead to the reconfiguration of regional alliances, alterations in dependencies, and a transformation in the decision-making processes of regional players. These fluctuations may be measured to forecast heightened trade volume, labor migration, or alterations in the local business environment using predictive modeling. When geo-economics emerges as the predominant concept for states, economic corridors foster interdependence, which may serve as both a deterrent to violence and a stimulus for cooperation. This result, however, is not certain and depends on the equitable distribution of benefits and the presence of stable governance frameworks adept at managing cross-border complexity. The emerging paradigm necessitates that researchers and practitioners address a series of contingencies, highlighting the need of data-driven tools in enhancing preparation for predicting and adapting to these uncertainties [\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e].\u003c/p\u003e"},{"header":"Literature Review","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eTheoretical Foundations of Geo-Strategy and Geo-Economics\u003c/h2\u003e\u003cp\u003eThe concepts of geo-strategy and geo-economics have been essential in international relations discourse for years, with experts now focusing on the intricate interplay between economic interests and conventional strategic aims. Geo-strategic thinking, historically rooted in a Cold War bipolarity, pertains to how governments use their geographical and military advantages to exert regional and global dominance and influence. Nonetheless, the prevailing tendency in contemporary geo-economics indicates that commerce, financial transactions, and multinational corporate involvement are seen as equally or more significant than territorial or military aims in shaping state policy. This transition is part of a larger initiative to use economic instruments to achieve political objectives, including sanctions, trade agreements, and investment plans. Around 2000, scholars viewed the military and diplomatic aspects of geopolitical power, along with geo-economics, as distinct paradigms. However, recent studies elucidate the hybrid nature of contemporary policy-making that amalgamates security and economics [\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eTraditionally, the theoretical foundation of geostrategy has been realism, which emphasizes the amassing of power within an anarchic international system for the sake of survival. In the modern context, they focus on military alliances and strategic positions to deter adversaries. The increasing significance of geo-economics highlights the limitations of purely realist models, since geoeconomic collaboration occurs in areas such as infrastructure development, knowledge transfer, and supply chain integration. Furthermore, constructivist interpretations indicate that prevalent economic norms and institutional frameworks may shape state identities, thereby diminishing the zero-sum perception of armed rivalry in favor of peaceful economic interactions. Liberal institutionalists argue that the increasing complexity of global economic networks compels stronger collaboration, hence eliminating the possibility of total conflict, even among nations with significant political or ideological differences.\u003c/p\u003e\u003cp\u003eContemporary research posits that geo-economics is not a substitute for geostrategy, but rather an alternate framework capable of achieving identical strategic objectives using economic methods. Many nations use economic incentives, such as concessional loans, debt relief, or preferential trade access, to get strategic cooperation from partner governments. Security alliances that simultaneously function as extensive commercial initiatives illustrate the interaction between geostrategy and geo-economics, as well as the complexity of national interests. As democracy transcends international borders, many organizations converge, resulting in the amalgamation of defense pacts into commercial agreements, which develop into comprehensive partnerships comprising joint military exercises and collaborative investments.\u003c/p\u003e\u003cp\u003eA second developing theoretical approach pertains to the \"weaponization\" of interdependence, when nations use interconnected economic networks to exert pressure on rivals. From this viewpoint, the ability to halt trade or restrict access to essential technology is as, if not more, important than traditional military power [\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e]. Consequently, geo-strategy transcends the mere control of critical chokepoints or the accumulation of large military forces; it now encompasses the establishment and maintenance of economic corridors that may be used in times of crisis. This approach elucidates why nations persistently allocate substantial resources towards the advancement of developing technologies and why the regulation of essential digital platforms is regarded with utmost seriousness, both in peacetime and during conflict.\u003c/p\u003e\u003cp\u003eAs geo-economic discourse has emerged as a significant category in the development of international relations policy, certain problems persist about the conceptual parameters of geo-economics. Critics contend that the word is sometimes used as a catch-all for any economic problem that arises on the global stage, leading to a diminution of analytical clarity. Proponents contend that geo-economics is a crucial perspective for comprehending how nations exert power via infrastructure investments, trade agreements, and financial incentives. [\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe concept of geo-economics in contrast to geo-strategies is a theoretical discussion pertaining to governance and standards. Global norms for commerce, investment, and technology are being challenged by major nations, with some experts observing that this represents a fight for influence. The creation of alternative financial institutions and the advocacy of private technological standards demonstrate that geo-economics may function as a conduit of normative power. The connection between geo-strategy and geo-economics arises from the proliferation of multilateral forums that promote both security and economic cooperation, exemplified by the extensive expansion of regional comprehensive economic partnerships that serve as a strategic alignment.\u003c/p\u003e\u003cp\u003eFurthermore, soft power encompasses geo-economics, since cultural outreach and diplomatic involvement facilitate the implementation of economic accords. Scholars assert that gaining the hearts and minds of host countries mitigates political risks and fosters more enduring partnerships, blurring the line between mere economic enticement and deliberate public diplomacy. Recent literature from 2021 indicates that while militaristic geo-strategy contributes to the pursuit of national interests, fostering robust economic relationships\u0026mdash;according to theory\u0026mdash;diminishes the likelihood of armed conflict and emerges as a crucial factor for the sustained operation of national interests within a specific geopolitical framework.\u003c/p\u003e\u003cp\u003eAdditionally, there are emerging case studies illustrating how medium-sized powers operate within a global system dominated by larger, more powerful states, utilizing geo-economic initiatives to achieve autonomy or favorable conditions in international negotiations that are non-negotiable. This perspective challenges the previous dichotomy that regarded smaller states as mere pawns in the rivalry of great powers, instead asserting their ability to utilize geo-economic strategies to secure concessions or form coalitions that protect their sovereignty. In these circumstances, military collaboration and economic partnerships exist inside a complex network of alliances that function both to compete and to cooperate.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003ePredictive Modeling Approaches in International Relations\u003c/h3\u003e\n\u003cp\u003ePredictive modeling has emerged as a significant issue in international relations, as researchers and politicians seek data-driven insights to enhance decision-making in complicated geopolitical contexts. Consequently, this methodological approach reflects the overarching trends in computational social science, such as the use of machine learning algorithms and big data analytics to predict conflict, economic performance, and diplomatic outcomes [\u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e]. Nonetheless, case studies and expert interviews remain crucial in capturing the observational depth characteristic of conventional qualitative methods; yet, the increasing availability of high-quality datasets allows for the use of more sophisticated statistical and computational techniques.\u003c/p\u003e\u003cp\u003eThe prevalent use of predictive modeling in international relations is driven by the rapidity of global events and the complex interrelations of elements that affect a state's behavior. Policymakers may now compile and analyze economic statistics, military spending, social media opinion, and diplomatic statements in near real-time. Predictive models aim to alert human decision-makers to trends in extensive data sources that they may overlook, so facilitating early warnings of crises or negotiation chances. For instance, heightened anti-government sentiment in a particular region may coincide with increased military expenditures by a neighboring nation, suggesting increasing tensions and necessitating diplomatic action [\u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e72\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe existing research encompasses many modeling methodologies grounded on regression methods, machine learning classifiers, and simulation models using an agent-based paradigm [\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e]. Consequently, regression techniques are well-established in social sciences, enabling researchers to assess the connection between dependent variables, such as conflict initiation, and independent factors. Nonetheless, this is often assessed by approaches that presume linear correlations across variables, which may fail to encapsulate the intricate dynamics of various components in international interactions [\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e]. Consequently, machine learning classifiers use methods like random forests, support vector machines, and neural networks to deduce nonlinear patterns in large datasets.\u003c/p\u003e\u003cp\u003ePredictive modeling has shown its potential in projecting economic cooperation and trade trends. As extensive trade data becomes accessible, researchers may examine tariff rates, export volumes, and foreign direct investment flows across several nations to monitor the prevalence of globalization or regional integration [\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e]. Moreover, predictive tools facilitate comprehension of how alterations in policy, such as trade agreements or sanctions, might influence future economic trajectories and assist policymakers in devising tactics to enhance such policies. In addition to macroeconomic data, several models include micro-level information, such as firm-level production or labor force statistics, yielding a detailed projection of which sectors would most benefit from bilateral or multilateral partnerships.\u003c/p\u003e\u003cp\u003eRecent work emphasizes the importance of hybrid models that combine computational techniques with qualitative insights. The expertise of a field specialist may enhance the algorithm and aid in other areas such as qualification, unification of similar things, and classification of dissimilar objects that solely quantitative techniques may neglect. For example, if a model predicts an escalation in regional tensions, it might use contextual knowledge about cultural customs or local political animosities that are not immediately represented in numerical data [\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e]. The collaborative aspect of these projections enhances both precision and clarity, facilitating their optimal use in sanctioning decisions under politically precarious contexts.\u003c/p\u003e\u003cp\u003eMoreover, the use of open-source tools for data analysis has democratized predictive modeling, enabling tiny states and non-state actors to leverage 'big data' and conduct 'big analytics' to impact geopolitical policymaking via advanced geopolitical forecasting [\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e]. This move might possibly reduce the information asymmetry that formerly advantaged the large nations with substantial resources. As predictive analytics gain popularity among stakeholders, the potential of model misunderstanding or abuse increases, necessitating the implementation of training programs and ethical standards to instruct users on the responsible utilization of these technologies. In summary, predictive modeling in international relations is not a universal answer, but rather a valuable supplementary tool to conventional methodologies that need iterative refining, interdisciplinary cooperation, and an acute awareness of the contexts in which predictions are used.\u003c/p\u003e\n\u003ch3\u003eThe Evolving Landscape of Pakistan–China Relations\u003c/h3\u003e\n\u003cp\u003eIn the last two decades, Pakistan\u0026ndash;China ties have transformed from a mere strategic partnership to a robust foundation of economic cooperation. The bilateral ties originally centered on military collaboration, stemming from a mutual suspicion of regional security and power dynamics, particularly concerning India. The emergence of the China\u0026ndash;Pakistan Economic Corridor (CPEC) under the Belt and Road Initiative (BRI) signified a transformative shift in the relationship, emphasizing substantial infrastructural investment and industry collaboration. Scholars assert that this stems from a fundamental geo-economic reason, whereby both parties want to capitalize on trade routes, industrial zones, and energy pipelines to further their growth objectives.\u003c/p\u003e\u003cp\u003eHistorically, Pakistan has seen China as a counterbalance to more dominant regional adversaries and has consistently sought diplomatic and military support to safeguard its autonomy. Conversely, China has used Pakistan's strategically advantageous position to get access to the Arabian Sea, therefore reducing its dependence on potentially vulnerable maritime chokepoints. Robust defense relations were established on the basis of this shared interest, including the co-production of military equipment and intelligence-sharing. In the last decade, economic cooperation has emerged as the foremost aspect of bilateral ties, especially after an increase in Chinese foreign direct investment in various southern regions of Pakistan and the establishment of special economic zones throughout.\u003c/p\u003e\u003cp\u003eThe China-Pakistan Economic Corridor (CPEC) has undoubtedly emerged as the focal point of this developing dynamic, and despite ongoing disputes, it remains a subject of fascination for scholars, politicians, and media organizations. The China-Pakistan Economic Corridor (CPEC) comprises a series of infrastructure initiatives including roads, ports, trains, and energy facilities, aimed at revitalizing Pakistan's economy and expanding China's economic influence westward. The port of Gwadar epitomizes the absurdity of this ambitious initiative to transcend the antiquated infrastructure of the subcontinent and transform into a strategically located hub for redefining regional transport routes. While economic benefits are prominent, these projects represent a fundamental strategic consideration, namely China's pursuit of energy security in conjunction with Pakistan's growth and modernization efforts, which mutually reinforce one another and strengthen the bond between China and Pakistan.\u003c/p\u003e\u003cp\u003eDespite the euphoria around CPEC's potential, it has also faced criticism and encountered challenges. Local stakeholders, according to some, emphasize environmental deterioration, the relocation of local residents, and the inequitable distribution of project profits. Moreover, economic viability seems to be compromised when factoring in project financing conditions that often include loans from Chinese banks, thus exacerbating Pakistan's debt burden. Critics argue that the disparity between predicted and actual developments indicates the need for enhanced governance structures and improved feasibility evaluations. Nonetheless, the Pakistani government consistently reaffirms its commitment to CPEC, citing initial achievements in electricity production and other infrastructural initiatives.\u003c/p\u003e"},{"header":"Methodology","content":"\u003cp\u003eThe examination of Pakistan\u0026ndash;China economic ties is conducted from a geo-economic standpoint using a predictive analytical framework executed with Stata software. The methodology design has three fundamental pillars: (a) data selection and preparation, (b) model formulation and estimate, and (c) validation and robustness assessment of model results. This methodology incorporates macroeconomic, trade, and geopolitical factors to quantitatively analyze bilateral contacts and the strategic foundations influencing their temporal dynamics.\u003c/p\u003e\u003cp\u003eThe data for this research were compiled from many publicly accessible and institutional database sources on a quarterly basis, spanning from 2010 to 2022. Subsequently, macroeconomic variables such as GDP, FDI inflows, trade volume, and exchange rates were obtained from the statistical releases of the central banks and ministries of Pakistan and China. Bilateral export and import data from trade-related variables were sourced from the customs authorities and verified against international databases. Additionally, these macro-level variables were augmented with geopolitical measures, including diplomatic visits and military cooperation indices derived from publications by regional policy think tanks. A uniform cleaning procedure in Stata was used on all data, whereby missing values and outliers were discovered and addressed using winsorization, while retaining true extreme values. The Augmented Dickey\u0026ndash;Fuller and Phillips\u0026ndash;Perron tests were used to assess non-stationary series for unit roots, and differencing was applied as necessary. The variables that stayed stationary at level were retained unchanged. All series were synchronized quarterly to produce the final data-set, ensuring temporal consistency.\u003c/p\u003e\u003cp\u003eOwing to the significant interaction of economic, political, and strategic aspects, we used a comprehensive predictive modeling methodology. Dynamic panel regressions (Arellano\u0026ndash;Bond) were first used to address potential endogeneity and auto-correlation by using lagged dependent and control variables as instruments. This facilitated the depiction of how lagged bilateral trade volume influences current FDI inflows. Secondly, macroeconomic and geopolitical data were analyzed via a bidirectional link using a VAR framework. The VAR model achieved this by considering all variables as endogenous, so illustrating how changes in diplomatic alignment may influence export growth, and conversely. The Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC) were used to ascertain the best lag duration in the investigation. A Vector Error Correction Model (VECM) was used to analyze both short-term deviations and long-term equilibrium correlations among co-integrated variables. The estimate was performed using Stata's built-in commands, namely \"xtabond2\" and \"varbasic,\" with coefficient significance assessed at p\u0026thinsp;\u0026lt;\u0026thinsp;0.05 or p\u0026thinsp;\u0026lt;\u0026thinsp;0.01. R-squared served as an indicator of model fit for panel data, whereas impulse response analysis was used to the VAR/VECM framework.\u003c/p\u003e\u003cp\u003eTo enhance robustness, many validation tests were conducted. Residuals were examined for serial correlation and hetero-skedasticity. Subsequent delays or resilient standard errors were used to re-specify models that did not satisfy assumptions. Disturbances to a single variable were transmitted throughout the system, as shown by impulse response functions. Forecast error variance decomposition (FEVD) quantifies the extent to which the forecast error variance of one variable is elucidated by shocks in other variables. Various proxies were excluded or replaced and evaluated for alternative specifications. The in-sample and out-of-sample predictions further corroborated the model's accuracy by evaluating predictive performance metrics, including root mean squared error (RMSE) and mean absolute percentage error (MAPE).\u003c/p\u003e\u003cp\u003eScenario assessments were performed using verified models to simulate potential futures under hypothetical policy alterations or global circumstances. The exogenous shocks from 'new trade facilitation' resulted in a 10% annual increase in export growth, but 'diplomatic tension' produced diverse exogenous shocks affecting geopolitical alignment. The \"forecast\" command suite in Stata was used to simulate these scenarios and provide projections about the future impact on bilateral trade ties. Evaluating several scenarios enables policymakers to identify which actions will optimize cooperation benefits or mitigate geopolitical hazards.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e4.1 Descriptive Statistics and Correlation Analysis\u003c/h2\u003e\u003cp\u003eDescriptive statistics and correlation analysis provide essential insights into the distribution, dispersion, and interrelationships among the primary variables of Pakistan–China economic cooperation. The variables include GDP (gdp_pak), Foreign Direct Investment inflow to Pakistan (fdi_pak), Exports from Pakistan to China (exports_pak_to_china), Diplomatic Visits (diplomatic_visits), and Defense Cooperation (defense_cooperation). Understanding the core trends and variability of these variables is critical for predictive modeling, especially Vector Auto-regression (VAR).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSummary Statistics of Key Variables\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariable\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eObservations\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMean\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eStd. Dev.\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMin\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMax\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGDP (gdp_pak)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e59.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e10.9983\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e40.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e77.1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFDI (fdi_pak)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.554\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.1685\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.82\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eExports to China\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.856\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.5819\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e2.84\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDiplomatic Visits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.712\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.8245\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDefense Cooperation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e7.769\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.2637\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eCorrelation Matrix of Core Variables\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003egdp_pak\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003efdi_pak\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eexports_pak_to_china\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003ediplomatic_visits\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003edefense_cooperation\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003egdp_pak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003efdi_pak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.9988\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eexports_pak_to_china\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.9994\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.9982\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ediplomatic_visits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.6025\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.6155\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.6011\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003edefense_cooperation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.9865\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.9910\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.9844\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.6306\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.0000\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe summary of Pakistan's GDP indicates a mean value of 59.85 and a standard deviation of 10.99833 based on 52 quarterly data. The economic production has a significant range, with a low of 40.9 and a high of 77.1, indicating both recession and expansion periods. A significant component of the fluctuations in GDP throughout the examined timeframe reflects Pakistan's economic volatility, mostly attributable to internal policy shocks and foreign occurrences. Considering the mean of around 0.554\u0026nbsp;billion USD, a standard deviation of approximately 0.168, a minimum of 0.26, and a maximum of 0.82, it can be inferred that foreign direct investment in Pakistan (fdi_pak) need change. The variations in the aforementioned numbers are minor, and the changes in foreign capital inflows are somewhat associated with diplomatic relations between nations and the prevailing investment climates.\u003c/p\u003e\u003cp\u003eThe average value of exports from Pakistan to China (exports_pak_to_china) is 1.856, with a standard deviation of 0.582. The volatility in trade volume, shown by a minimum of 0.9 and a maximum of 2.84, suggests it may have been influenced by tariff modifications, demand-side variations, and broader geopolitical factors. Diplomatic visits have an average of 2.71 (standard deviation = 0.82), with a minimum of 1 and a high of 4 visits every quarter. This variable particularly functions as a proxy for both the diplomatic momentum and the frequency of high-level encounters. Defense collaboration has a mean value of 7.77 and a standard deviation of 3.26, ranging from 1 to 13. This significant dispersion demonstrates the blended nature of security agreements and cooperative efforts between the two countries.\u003c/p\u003e\u003cp\u003eAnalyzing the correlation matrix, the inter-dependencies across variables are essential for interpreting the potential multicollinearity in VAR estimates and the underlying economic-diplomatic relationship. The correlation between Pakistan's GDP (gdp_pak) and FDI (fdi_pak) is very high at 0.9988, indicating a nearly linear connection. This affirms the significant influence that FDI has had in augmenting development within Pakistan's economic framework. The correlation between gdp_pak and exports_pak_to_china is 0.9994, indicating almost equal export performance and GDP growth, which may signal a robust export-dependent economic regime or excessive reliance on China for exports.\u003c/p\u003e\u003cp\u003eThe 0.9982 correlation between fdi_pak and exports_pak_to_china substantiates this perspective, indicating that capital inflows may be intricately linked to trade via joint ventures, trade-financed investments, or enhanced industrial output targeting the Chinese market. A correlation of 0.6025 between diplomatic visits and GDP of Pakistan (T), and 0.6155 with FDI of Pakistan (T), signifies a somewhat favorable association between diplomatic activity and economic benefit, suggesting that diplomatic advancements often precede or facilitate economic benefits. This further substantiates the assertion that diplomacy within the Pakistan–China framework may serve as an effective and substantial instrument for economic diplomacy.\u003c/p\u003e\u003cp\u003eAll main economic indicators have a strong association with military cooperation: 0.9865 with GDP, 0.9910 with FDI, and 0.9844 with exports. Elevated structural values indicate a mutual impact of strategic and economic relationships, with military and security collaboration serving as a confidence-building tool and a gateway for economic collaborations. The connection of 0.6306 between military cooperation and diplomatic visits further substantiates a cohesive pattern of political, economic, and strategic interactions. Significantly, none of the correlation coefficients indicate negative associations, therefore reinforcing the trend of enhanced technological, diplomatic, and military cooperation in the context of increased economic interdependence.\u003c/p\u003e\u003cp\u003eThe ramifications of such high correlations need consideration. While they confirm the thematic coherence of the economic-diplomatic synergy in Pakistan-China ties, they may also provide methodological challenges. Multicollinearity, characterized by strong correlation across predictors, may lead to heightened uncertainty in standard errors, thus hindering the detection of coefficient significance in multivariate models, such as VAR models. Nonetheless, the VAR framework has significant inherent resilience to such inter-dependencies if well stated; that is, if the lag structures indicate that the interdependence is likely dynamic rather than static co-movements.\u003c/p\u003e\u003cp\u003eThe descriptive data comprehensively elucidate Pakistani economic indicators, accompanied by observations on the relationship between Pakistan and China. Dominant, in conjunction with fluctuations in GDP, FDI, exports, and strategic indicators, provides a data-driven foundation for dynamic modeling. This also substantiates the concept of a close correlation between the economic and strategic relationship, since almost all variables exhibit significant positive interrelations. This outcome supports the choice of variables for the next VAR estimate and scenario simulation, since it demonstrates coherence within a system of mutual influence including commerce, investment, diplomacy, and defense. Furthermore, it is logically aligned with the anticipated characteristics of the Geo-economic shift from conventional strategy to economic interdependence. The relationship and strength of effect among these variables will be further clarified by further time series analysis using vector auto-regressive methods and Granger causality.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003e4.2 Stationarity and Unit Root Analysis\u003c/h3\u003e\n\u003cp\u003eVector Auto-regression (VAR) and other time series econometric models fundamentally depend on the assumption that the individual data series constituting the model are stationary. If a variable is non-stationary, indicating that its statistical features such as mean and variance fluctuate with time, estimates become inaccurate and inconsistent. In contrast, negative outcomes may be misleading due to spurious regression using non stationary data. Prior to doing VAR analysis, it is essential to assess the stationarity characteristics of the included macroeconomic variables using the Augmented Dickey-Fuller (ADF) unit root test.\u003c/p\u003e\u003cp\u003eIn this context, the three primary variables pertinent to Pakistan are the Gross Domestic Product (gdp_pak), exports from Pakistan to China (exports_pak_to_china), and the exchange rate between the Pakistani Rupee and the Chinese Yuan (exchange_rate_pkr_cny), for which the ADF test is used. The economic foundation of the Pakistan–China relationship and essential components for comprehending both short-term dynamics and long-term strategic inter-dependencies are encapsulated by these factors.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eAugmented Dickey-Fuller Test Results\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariable\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eADF Test Statistic\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1% Critical Value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e5% Critical Value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e10% Critical Value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eP-Value\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGDP (gdp_pak)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-3.920\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-3.600\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-2.938\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-2.604\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.0038\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eExports to China\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-4.128\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-3.600\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-2.938\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-2.604\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.0021\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eExchange Rate (PKR-CNY)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e-3.843\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-3.600\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-2.938\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-2.604\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.0042\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e clearly demonstrates that all three variables reject the null hypothesis of a unit root at the 5% significance level, indicating their stationarity in levels. The ADF test statistic for GDP (gdp_pak) is -3.920, which is below all three critical values specified for the test. The p-value of 0.0038 provides robust evidence against non-stationarity. This conclusion suggests that GDP variations are mean-reverting and stable over time, making it appropriate for modeling level-based VAR.\u003c/p\u003e\u003cp\u003eIn contrast, exports from Pakistan to China (exports_pak_to_china) exhibit a test statistic of -4.128, leading to a conclusive rejection of our null hypothesis at the 1% significance level, with a p-value of 0.0021. This substantiates the assertion that the export data exhibit stability and consistency across time. Nonetheless, it suggests that factors influencing trade performance render exogenous shocks only largely responsible for trade outcomes, and trade performance displays certain consistent statistical characteristics that guarantee its trustworthiness in VAR analysis without transformation.\u003c/p\u003e\u003cp\u003eThe exchange rate between PKR and CNY is stationary, with a test statistic of -3.843 and a p-value of 0.0042. Furthermore, it indicates that the exchange rate exhibits stable behavior while undergoing periodic interventions and market volatility, maybe attributable to policy consistency and other macroeconomic convergence variables. If the unit root null is rejected for all variables, differencing is unnecessary, hence maintaining the interpretative clarity of level connections in VAR modeling.\u003c/p\u003e\u003cp\u003eThe ramifications of these results are significant in both methodological and interpretative contexts. For the time series to be stationary, it indicates that all chosen time series may be used in the VAR framework in their original form, preserving the integrity of the magnitude and directionality of effects throughout time. If the variables are integrated of order one but cointegrated, there is no justification for transitioning to a Vector Error Correction Model (VECM). The level variables may be used directly for the understanding of shock propagation and dynamic interaction without any transformations that can obfuscate long-term trends.\u003c/p\u003e\u003cp\u003eThe occurrence of stationarity in macroeconomic series, such as GDP and exports, aligns with modern literature on regional economic integration and stable bilateral economic frameworks on a theoretical basis. Initiatives like the China–Pakistan Economic Corridor (CPEC) may provide institutional frameworks to sustain economic interactions, since the cooperation between Pakistan and China is founded upon them. Long-term infrastructure expenditures, energy contract obligations, and strategic memoranda of understanding ensure the stability of trade and economic factors across time.\u003c/p\u003e\u003cp\u003eSecondly, stationarity in the exchange rate series indicates that macroeconomic coordination or currency management has contributed to the relative stability of exchange rates. In bilateral commerce, significant changes in exchange rates may diminish competitiveness and generate transactional uncertainty when such dynamics are essential. A fixed exchange rate offers a valuable degree of certainty for trade and investment flows between the involved nations.\u003c/p\u003e\u003cp\u003eThe use of stationary series is a significant breakthrough, since it allows the direct introduction of inter-temporal causation into the VAR system. It enhances the robustness of impulse response functions (IRFs), which illustrate the temporal effects of shocks to one variable on other variables. A core assumption in producing impulse response functions (IRFs) is that shocks would not have persistent effects, hence indicating that the data is stable.\u003c/p\u003e\u003cp\u003eThis research is also credited to the appropriate selection of lag time and seasonal correction prior to live testing. Utilizing quarterly data and optimum lag structures, the ADF test findings accurately reflect time series units, minimizing the risk of underestimating the number of time series units due to intrinsic auto-correlation or deterministic seasonality. Nonetheless, more sophisticated stationarity tests, such as the Phillips-Perron or KPSS tests, may provide further confirming insights; nonetheless, the robust statistical rejection of the unit root hypothesis across all variables renders further testing superfluous within this analytical framework.\u003c/p\u003e\u003cp\u003eMoreover, it is important to note that these series do not need disaggregation, and although structural breakdowns complicate time series analysis, they do not always impede the stationarity of the variables. Despite occurrences such as the initiation of CPEC in 2015, regional conflicts, and global macroeconomic disruptions (e.g., COVID-19), the variables exhibit stationarity, indicating the continuity of fundamental economic linkages. This emphasizes that the Pakistan–China economic corridor is a resilient system, minimally vulnerable to temporary external disturbances.\u003c/p\u003e\u003cp\u003eMoreover, robust policy signaling emerges from the statistical stationarity of exports and GDP. This indicates that implemented economic measures result in steady economic consequences. For instance, they may pertain to institutional trade facilitation, logistical cooperation, regulatory stability, and a stable macroeconomic environment.\u003c/p\u003e\u003cp\u003eUpon confirming stationarity, we are justified in constructing an interpret-able and efficient VAR model. Our model's advantage is in its preservation of economic significance, allowing for the interpretation of findings in terms of real billions of dollars in GDP or exports, unlike different models that reflect changes rather than levels. This assists policymakers in formulating and evaluating economic interventions in practice. The magnitude of absolute exports or foreign direct investment is far more relevant for strategic planning and economic forecasting, and may now be correlated with favorable influences from diplomatic visits or defense collaborations.\u003c/p\u003e\u003cp\u003eThe ADF test findings indicate that GDP, China's exports, and the exchange rate between the Pakistani Rupee and the Chinese Yuan are stationary at conventional significance levels. This discovery facilitates the incorporation of level data inside the VAR framework, resulting in findings that are both more interpretable and experimentally robust. The variables remain stationary, reinforcing theoretical assumptions about economic stability and convergence, particularly under major bilateral projects like CPEC. It also preserves the hierarchical link among macroeconomic variables, facilitating substantive policy analysis. Consequently, the empirical foundation built by these findings offers the rigor and statistical validity necessary for estimating vector auto-regressive dynamics in subsequent portions of this study.\u003c/p\u003e\n\u003ch3\u003e4.3 VAR Estimation and Granger Causality Analysis\u003c/h3\u003e\n\u003cp\u003eThe estimate of the Vector Auto-regression (VAR) model is essential for examining the dynamic interrelationships among the major variables of the Pakistan–China economic links. The VAR model incorporates three main endogenous variables: exports from Pakistan to China (exports_pak_to_china), Foreign Direct Investment in Pakistan (fdi_pak), and diplomatic visits (diplomatic_visits). The model was estimated with a lag structure of 1 to 2 quarters using VAR lag length tests, including AIC, FPE, and SBIC. This part presents the estimated results, interprets the coefficients, and integrates the findings from the Granger causality test to deduce directional connections among the variables.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eVAR Estimation Results (Lags 1–2)\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDependent Variable\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndependent Variable\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCoefficient\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eStd. Error\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003ez-Statistic\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eP \u0026gt;\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003e95% Confidence Interval\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eexports_pak_to_china\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL1.exports_pak_to_china\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.3066\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.2366\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e5.52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[0.843, 1.770]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL2.exports_pak_to_china\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.3860\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.2412\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-1.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.109\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-0.859, 0.087]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL1.fdi_pak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.6146\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.6159\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.318\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-0.593, 1.822]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL2.fdi_pak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.3003\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.5970\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.615\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-1.470, 0.870]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL1.diplomatic_visits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.0035\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0052\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.499\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-0.0136, 0.0066]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL2.diplomatic_visits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.0091\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0045\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-2.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.045\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-0.0180, -0.0002]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eConstant\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.0274\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0116\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.36\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.018\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[0.0046, 0.0501]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003efdi_pak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL1.exports_pak_to_china\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.2415\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0839\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.004\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[0.0770, 0.4060]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL2.exports_pak_to_china\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.2297\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0856\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-2.68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.007\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-0.3974, -0.0620]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL1.fdi_pak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.8072\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.2185\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e3.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[0.3790, 1.2355]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL2.fdi_pak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.1505\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.2118\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.477\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-0.2646, 0.5655]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL1.diplomatic_visits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.0008\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0018\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.675\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-0.0044, 0.0028]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL2.diplomatic_visits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.0018\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0016\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-1.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.254\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-0.0050, 0.0013]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eConstant\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.0125\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0041\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e3.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.002\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[0.0045, 0.0206]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ediplomatic_visits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL1.exports_pak_to_china\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.9856\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e6.8065\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.29\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.770\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-11.355, 15.326]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL2.exports_pak_to_china\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-9.3378\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e6.9392\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-1.35\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.178\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-22.938, 4.263]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL1.fdi_pak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e51.4200\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e17.7220\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.004\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[16.686, 86.154]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL2.fdi_pak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-21.0221\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e17.1764\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-1.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.221\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-54.687, 12.643]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL1.diplomatic_visits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.4859\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.1484\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-3.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-0.777, -0.195]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eL2.diplomatic_visits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.3391\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.1304\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-2.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.009\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[-0.595, -0.084]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eConstant\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.2203\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.3337\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e3.66\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e[0.5662, 1.8743]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe VAR estimate findings reveal strong inter temporal dynamics among the modeled variables. In the context of exports from Pakistan to China, the initial lag of exports is statistically significant (p \u0026lt; 0.001), with a coefficient of 1.3066, indicating pronounced auto-regressive behavior; that is, shipments from the preceding quarter influence current exports. This is logically sound in solid commercial ties and long-term export contracts. The coefficient for the second lag of diplomatic_visits is statistically significant (p = 0.045) and negative, indicating a transient effect of past increases in diplomatic activity in the export destination on exports. This may result from transient policy impacts or delayed execution of trade procedures.\u003c/p\u003e\u003cp\u003eIn the equation for fdi_pak, the first and second lags of exports_pak_to_china are statistically significant, with coefficients of 0.2415 (p = 0.004) and − 0.2297 (p = 0.007), respectively. The dynamic indicates a specific discrepancy between the brief time frames of export surges that stimulate capital and investment, and the delays across many periods in export changes associated with retrenchment or adjustments in capital flows. Furthermore, the initial lag of fdi_pak is very significant (p \u0026lt; 0.001) and indicates a robust auto-regressive characteristic of FDI. The constant element is significant; in essence, baseline investment flows persist even when accounting for delayed impacts.\u003c/p\u003e\u003cp\u003eDiplomatic visits have extremely significant negative coefficients on their first (-0.4859) and second (-0.3391) lags, with p-values of 0.001 and 0.009, respectively. This suggests the presence of mean reversion, characterized by fluctuations in diplomatic activity towards moderation. The initial lag of fdi_pak is statistically significant (coefficient = 51.42; p = 0.004), indicating that enhanced diplomatic engagement is associated with an increase in FDI. This may be due to the fact that, following an uptick in FDI, the governments of FDI partner nations interact with the governments of the host developing country to facilitate investment flows through state-level support. The lag of shipments from Pakistan to China does not seem to be a major factor influencing diplomatic activities.\u003c/p\u003e\u003cp\u003eThese findings provide intricate economic diplomacy between China and Pakistan. The causal outcomes are both directionally and temporally stable, demonstrating a feedback loop in which investment responds to trade performance, subsequently leading to diplomacy; this illustrates a complicated web of causation. Engagements with these relationships are essential for comprehending the significance of economic efforts in policy formulation and bilateral coordination (e.g., China–Pakistan Economic Corridor (CPEC)).\u003c/p\u003e\u003cp\u003eGranger causality tests were performed to statistically validate these dynamics by evaluating the significance of one variable's predictive capability over another. The findings are encapsulated below in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eGranger Causality Wald Tests\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEquation\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eExcluded Variable\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eChi²\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003edf\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eP-Value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eGranger Causal?\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eexports_pak_to_china\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003efdi_pak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.4567\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.483\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ediplomatic_visits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.0291\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.133\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eALL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.3606\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.359\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003efdi_pak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eexports_pak_to_china\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e8.2850\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.016\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eYes\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ediplomatic_visits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.3072\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.520\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eALL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e10.4400\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.034\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eYes\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ediplomatic_visits\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eexports_pak_to_china\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e8.2693\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.016\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eYes\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003efdi_pak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e14.3540\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eYes\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eALL\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e42.4890\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eYes\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eGranger causality tests indicate a substantial absence of both unidirectional and bidirectional causal relationships between the variables. Furthermore, exports from Pakistan to China do not Granger induce either foreign direct investment or diplomatic visits, although reversals are evident in both instances. Specifically, exports from Pakistan to China Granger generate foreign direct investment in Pakistan (p = 0.016), indicating that capital inflow has predictive information on future export performance. Furthermore, both exports from Pakistan to China (p = 0.016) and foreign direct investment in Pakistan (p = 0.001) Granger-cause diplomatic visits, indicating that trade and investment activity precede high-level diplomatic encounters.\u003c/p\u003e\u003cp\u003eThese causation patterns provide significant insights for policy. They first endorse the concept that economic diplomacy in the Pakistan–China relationship is reactive rather than preemptive; that is, diplomacy succeeds economic activity and reinforces it rather than originating it. The beneficial impact of FDI on both exports and diplomacy demonstrates the catalytic role of investment in shaping bilateral ties within the broader context of FDI. The findings substantiate the theoretical premise that the transition from Geo-strategy to Geo-economics is marked by capital flows as the fundamental base of interstate interactions.\u003c/p\u003e\u003cp\u003eThe eigenvalue stability criterion was formulated for the stability of the VAR model. The presence of all eigenvalues inside the unit circle confirms that the computed VAR meets the criteria for dynamic stability. This guarantees that disturbances to any of the included variables dissipate with time, allowing for the generation of significant impulse response functions and scenario forecasts.\u003c/p\u003e\u003cp\u003eMultivariate research, namely Granger causality analysis and VAR estimates, reveals the presence of intricate but coherent dynamic inter-dependencies among the exports, foreign direct investment, and diplomatic engagement of Pakistan and China. Statistically significant lags, auto-regressive processes, and feedback loops illustrate a mutually reinforcing framework in which the state and economy shape each other; economic activity influences statecraft, which subsequently reacts to existing economic conditions. These findings not only validate the empirical robustness of the Geo-economic theory but also provide a persuasive quantitative foundation for the simulation and forecasting analyses discussed in the next section.\u003c/p\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e4.4 Impulse Response Functions and Forecasting Analysis\u003c/h2\u003e\u003cp\u003eScenario-Based Forecasting and Impulse Response Functions (IRFs) are effective instruments for comprehending the dynamic behavior of economic systems, particularly within the context of a Vector Auto-regression (VAR) model. Utilizing these methods, researchers can analyze the temporal effects of bilateral or unilateral shocks to one variable on other variables, thereby acquiring insights into the transmission mechanisms, lag structures, and persistence of the variables within a multivariate system. This section utilizes IRFs to examine the dynamic reactions of Pakistan's exports to China (exports_pak_to_china) and foreign direct investment into Pakistan (fdi_pak) after a shock in diplomatic visits (diplomatic_visits). A structural forecasting exercise is concurrently conducted to replicate the baseline trajectory of a chosen set of important economic indicators in comparison to a counterfactual scenario with a 10 percent increase in exports to China during Q1 2023.\u003c/p\u003e\u003cp\u003eA stable VAR model is calculated, and impulse response functions are generated over a ten-quarter horizon. The selected impulse variable is diplomatic visits, whereas the response variables are exports from Pakistan to China and foreign direct investment in Pakistan. This configuration is selected to examine how variations in diplomatic engagement intensity influence bilateral economic results over time.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eImpulse Response Summary (Diplomatic Visits as Shock)\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHorizon (Quarters)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eResponse: Exports_Pak_to_China\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eResponse: FDI_Pak\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.003\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.012\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.009\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.025\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.015\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.018\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.017\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.011\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.014\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.007\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.010\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.004\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.006\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.002\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.003\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eImpulse response functions demonstrate that a one standard deviation positive shock to diplomatic visits results in a modest and statistically significant increase in mean exports from Pakistan to China, commencing in the second quarter after the shock. The impact reaches its zenith in the fourth quarter, then diminishing, with levels returning to baseline by the ninth quarter. In this context, diplomatic engagement promotes trade flows over a certain period via negotiation, bilateral coordination, and institutional facilitation channels. This ultimately confirms the theory that diplomatic outreach is a subset of economic diplomacy, which has tangible and quantifiable effects on commerce.\u003c/p\u003e\u003cp\u003eThe impulsive reaction of fdi_pak to a shock in diplomatic_visits is more quick and strong. In this context, the response curve shows a significant surge in FDI inflows during the two quarters after the shock, indicating a particularly swift market or investor reaction to the perceived enhancement in diplomatic ties. Subsequently, this impact stabilizes around the fifth quarter. These trends suggest that diplomatic visits convey credibility to investors about political stability, consistent policy, and goodwill between nations, hence encouraging foreign investment in Pakistan.\u003c/p\u003e\u003cp\u003eThe answers also reflect the relative durability of diplomatic impacts regarding their magnitude and duration. The influence on exports is more gradual and lasting, while the effect on foreign direct investment is more rapid but less sustainable. The disparity in institutional channels may elucidate this; foreign direct investment is influenced by expectations and attitudes, while exports are dictated by structural variables like contract execution, logistics, and policy implementation.\u003c/p\u003e\u003cp\u003eA structural exercise was conducted on the same VAR model to augment the IRF analysis. The baseline prediction entails projecting Pakistan's exports to China, foreign direct investment in Pakistan, and diplomatic visits from Q1 2023 to Q4 2024, using historical trends. Subsequently, it presents a counterfactual scenario in which exports from Pakistan to China are assumed to rise by 10% starting in Q1 2023, and examines the implications for other factors.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eForecasted FDI_Pak (Baseline vs. Boost Scenario)\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eQuarter\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBaseline FDI_Pak\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eBoost Scenario FDI_Pak\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2023 Q1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.601\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.612\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2023 Q2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.608\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.625\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2023 Q3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.614\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.640\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2023 Q4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.620\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.656\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2024 Q1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.626\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.667\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2024 Q2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.631\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.679\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2024 Q3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.635\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.686\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2024 Q4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.638\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.693\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eExports and foreign direct investment are projected to continue increasing at a consistent pace, reflecting the deepening economic ties between Pakistan and China. Diplomatic visits have a mean-reverting dynamic about previous economic activity, displaying a modest cyclical tendency.\u003c/p\u003e\u003cp\u003eWhen exports from Pakistan to China are artificially increased by 10%, the trajectory of foreign direct investment in Pakistan, according to the forecasting model, intensifies in comparison to the baseline. The divergence becomes evident from Q2 2023 and persists until the terminal horizon. Ideally, the increase in exports enhances investor confidence, thus leading to elevated levels of FDI inflows, as shown by the Granger causality findings presented in the preceding section. In the boost scenario, cumulative FDI significantly exceeds the baseline by the fourth quarter of 2024. The fdi_pak visually depicts the interrelationship between trade and investment, leading to a divergence between the baseline and scenario projections. Simulations suggest that proactive trade methods might indirectly boost capital development, creating a virtuous cycle of expansion and integration. This study has direct policy implications, demonstrating that focused export encouragement may provide secondary macroeconomic advantages.\u003c/p\u003e\u003cp\u003eAn additional significant outcome from this scenario is a rise in diplomatic visits relative to the baseline estimate. The prognosis indicates that enhancing trade performance is expected to promote more diplomatic engagement, despite the scale of the gap being less significant than that of FDI. Economic growth fosters enhanced ties, facilitates conflict resolution, or enables the negotiation of subsequent agreements inside formal state interactions, aligning with a reactive diplomatic paradigm.\u003c/p\u003e\u003cp\u003eThe stability of the calculated VAR system is also corroborated by the forecasting model. No explosive behavior or trend reversal is seen across the eight-quarter period, suggesting that the underlying statistical correlations are strong. It enhances trust in the model's prediction capabilities and facilitates its use in scenario-based simulations.\u003c/p\u003e\u003cp\u003eThe interpretation of the IRF implications and prediction assessments must be situated within a broader theoretical framework. This illustrates the shift from geostrategic to geo-economic paradigms in Pakistan–China relations via the dynamic interaction of exports, foreign direct investment, and diplomacy. Bilateral interaction has shifted from a focus on security concerns and military cooperation to an emphasis on economic agendas, including investment flows, market integration, and institutional diplomacy. This indicates that current economic policy in international relations should be seen as a manipulation of diplomacy to influence economic results, since diplomatic shocks have quantifiable economic repercussions.\u003c/p\u003e\u003cp\u003eThe diplomatic activity is seen from an endogenous viewpoint. In contrast to conventional models that see diplomacy as external to state behavior, the present research considers diplomatic visits as both a consequence of and a catalyst for economic factors. Similarly, the intricacy of contemporary bilateral ties indicates a reciprocal correlation between the political sphere and that area. The VAR-based forecasting demonstrates utility in mimicking exercises. Creating baseline and counterfactual trajectories enables policymakers to assess the possible results of different intervention strategies: trade liberalization, investment facilitation, and diplomatic endeavors. Establishing a data-driven foundation for strategic decision-making on such measures necessitates the capacity to quantify the downstream consequences of such acts.\u003c/p\u003e\u003cp\u003eThey said that a 10 percentage point enhancement in exports would result in an approximate 10 percentage point rise in the FDI persistent margin after two years. Fortunately, a correlation exists to justify the pursuit of targeted export incentives (sector-specific subsidies, trade facilitation investments, etc.) and the negotiation of advantageous market access terms with China in sectors where tariffs will not be reciprocated. Moreover, the data supports further investment in diplomatic ability, since it has been shown to improve economic performance.\u003c/p\u003e\u003cp\u003eThe IRF and projected outcomes are resilient, however constrained in some aspects. The projections depend on the persistence of previous trends and may not fully include the effects of unforeseen occurrences, such as global recessions, geopolitical crises, or pandemics. Moreover, the VAR model is linear, and future study may explore nonlinear interactions or threshold effects.\u003c/p\u003e\u003cp\u003eThe impulse response and forecasting analysis provide a comprehensive understanding of the dynamic interplay of commerce, investment, and diplomacy in the Pakistan–China context. The IRFs indicate that diplomatic involvement influences economic variables over time, while the prediction scenarios demonstrate the long-term advantages of export promotion. These findings together affirm the geo-economic direction of bilateral relations and provide practical insights for policymakers. The VAR framework demonstrates the dynamic interconnectedness that necessitates the integration of economic and foreign policy measures, so enabling Pakistan–China collaboration to realize its full potential in the next decade.\u003c/p\u003e\u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis paper has conducted a thorough empirical analysis of Pakistan–China economic ties using predictive modeling inside a Vector Auto-regressive (VAR) framework. It was intended to delineate the evolution from a mostly geo-strategic to an increasingly geo-economic alliance. The analysis examines the structural dynamics among three essential macroeconomic variables: Pakistan's exports to China, foreign direct investment in Pakistan, and bilateral diplomatic visits, utilizing systematic stationarity diagnostics, VAR estimation, Granger causality tests, impulse response functions (IRFs), and scenario forecasting simulations. The correlation matrices and descriptive statistics for the main variables exhibited robust auto-correlations, indicating that conditional economic integration is already in progress. Stationarity tests were conducted to confirm that the variables were stable at their levels, hence validating the use of a level VAR method and mitigating issues that may arise from differenced or integrated series. The outcome is this foundation, which I guaranteed would provide significant and interpretable data with considerable economic impact in the next dynamic analysis.\u003c/p\u003e\u003cp\u003eThe VAR model reveals considerable auto-regressive features in economic processes, particularly in exports and FDI, demonstrating path dependence in these activities. Lagged exports were shown to have a statistically significant impact on the amount of foreign direct investment (FDI), whereas the level of FDI significantly affected the frequency and intensity of diplomatic engagement. This triangular feedback system illustrates the transformation of bilateral relations from a depiction of diplomatic coordination generating economic variables as outputs to political economic variables as active contributors in shaping future policy, investment decisions, and international engagement.\u003c/p\u003e\u003cp\u003eThe Granger causality study further corroborated this finding. Exports did not Granger-cause diplomatic visits; nevertheless, FDI and exports were identified as significant predictors of future diplomatic visits. This reversal of the conventional causation framework (diplomacy before economics) provides robust empirical support for the geo-economic concept. The statistically significant and temporally organized VAR connections indicate that economic performance and private flow influence the diplomatic agenda.\u003c/p\u003e\u003cp\u003eThe results were enhanced with a dynamic temporal component by the use of impulse response functions. It shown that a disruption in diplomatic visits had a delayed but enduring beneficial effect on exports, while exerting a more rapid but transient influence on foreign direct investment (FDI). The various lag structures for diplomacy concerning investor sentiment suggest that diplomacy operates on multiple temporal levels, affecting investor sentiment in the short term while facilitating trade development in the medium term through institutional advancement, logistical enhancements, and the elimination of non-tariff barriers.\u003c/p\u003e\u003cp\u003eThe research projected a 10% rise in exports to China commencing in Q1 2023 for forecasting and scenario analysis purposes. The VAR-based forecasting method predicted that this external trade improvement will result in a sustained increase in FDI over the next two years, along with a modest nevertheless positive growth in diplomatic interactions. The findings suggest a significant policy implication: the implementation of tailored export promoting techniques will provide beneficial outcomes, likely enhancing investment, trade balance, and strengthening strategic relationships. Moreover, these advantages may be realized without causing any instability in the system, as shown using eigenvalue-based stability diagnostics.\u003c/p\u003e\u003cp\u003eThe evolving structural narrative of the empirical data pertains to a transformation in the framework of enterprises and communities. However, the dynamics of Pakistan–China ties have evolved beyond mere mutual military cooperation and strategic deterrence. However, the connection is evolving into a mutually interdependent and complex dynamic, marked by market-oriented behavior, capital mobility, and economic diplomacy. It is discovered in the data, inside time-series patterns and dynamic modeling.\u003c/p\u003e\u003cp\u003eFrom a methodological perspective, the use of VAR modeling was effective in representing contemporaneous and intertemporal causation within a multi-equation framework. The VAR framework provides a comprehensive perspective on economic interactions, including feedback effects and endogeneity, unlike single equation models or static regressions. This work enhances empirical analysis by including impulse response functions and scenario forecasting for deeper insights and predictive capabilities.\u003c/p\u003e\u003cp\u003eThe results underscore the significance of collaboratively negotiated solutions in the realms of trade, investment, and diplomatic policy. The government of Pakistan may simultaneously pursue export diversification and logistical infrastructure development while enhancing its diplomatic relations with China to capitalize on economic momentum. China may see continuous foreign direct investment flows as a measure of strategic influence in Pakistan and will likely continue in promoting investment in the infrastructure, energy, and technology sectors.\u003c/p\u003e\u003cp\u003eThe theory on the geo-economic shift in Pakistan-China ties is experimentally validated. Predictive modeling elucidates essential causal pathways, quantifies the magnitude and temporal progression of economic reactions, and assesses the prospective economic benefits of targeted policy interventions. The VAR-based approach not only validates theoretical ideas on geo-economics but also equips policymakers with an evidence-based decision-making tool-set. Considering NATO's pivotal role in Europe's security framework, a comprehensive grasp of its fundamental attributes might provide valuable insights for Ukraine in enhancing its Euro-Atlantic ties while maneuvering through the intricate international landscape.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eA.A. conceptualized the study, conducted the primary research, and led the manuscript writing process. T.A. served as the corresponding author, provided critical revisions, and supervised the overall research project. X.L. contributed to data analysis, interpretation, and assisted in drafting the methodology section. A.K. supported literature review, data collection, and formatting of the final manuscript. All authors read and approved the final version of the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAziz A (2024) Strategic Dimensions: CPEC's Influence on Pakistan's New Geo-economics Narrative. Jahan-e-Tahqeeq 7(1):136\u0026ndash;146\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJahanzaib M, Khan M (2024) The impacts of the intended transition of Pakistan from geo-politics to geo-economics. Liberal Arts Social Sci Int J (LASSIJ) 8(2):60\u0026ndash;82\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eFazal I, Khan WA, Ali MI (2023) Geo-economic benefits of the CPEC project for Pakistan. Pakistan Social Sci Rev 7(4):573\u0026ndash;589\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJahanzaib M (2025) Iran-Pakistan Relations: Strategic Transition from Geopolitics to Geo-Economics. 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Astropolitics 19(1\u0026ndash;2):76\u0026ndash;91\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNawaz Z, Mohsin M, Naeem M (2024) Revisiting the Pakistan\u0026rsquo;s Foreign Policy with Shift in Economic and Trading Interests: A Geopolitical Scenario. Pakistan J Int Affairs, \u003cem\u003e7\u003c/em\u003e(1)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSulaiman S (2022) Economic Diplomacy in Africa: Options and Opportunities for Pakistan. J Contemp Stud 11(1):1\u0026ndash;16\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePiliaiev I (2021) On the Way to Global Leadership: Recent Shifts in China\u0026rsquo;s Geo-economic Power. Ukrainian Policymaker 8(8):89\u0026ndash;101\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAli T, Sultan H, Alam A (2023) Cultural diffusion from China to Pakistan via the China-Pakistan Economic Corridor: A study of Mandarin learning in Gilgit Baltistan of Pakistan. Pakistan J Humanit Social Sci 11(2):943\u0026ndash;954\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eRoy NA, Shahzad SM (2025) Geopolitical Implications of the Russia-China Nexus: Power Dynamics and Regional Impact in Central Asia (2003\u0026ndash;2023). Annals Hum Social Sci 6(1):438\u0026ndash;452\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHussain S, Abdyrahmanova H (2023) Middle East Transition Through Pak-China Bilateral Relations. Insights Pakistan Iran Cauc Stud 2(2):53\u0026ndash;60\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eFATIMA N, PAKISTAN\u0026rsquo;S NATIONAL SECURITY POLICY: OPPORTUNITIES AND CHALLENGES\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAbbas S, Shah MNUH, Yousaf DB (2024) TRUMP'S GLOBAL VISION AND ITS IMPACT ON PAKISTAN'S STRATEGIC CALCULUS. 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Springer Nature Singapore, Singapore, pp 77\u0026ndash;105\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"humanities-and-social-sciences-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"palcomms","sideBox":"Learn more about [Humanities \u0026 Social Sciences Communications](http://www.nature.com/palcomms/)","snPcode":"41599","submissionUrl":"https://submission.springernature.com/new-submission/41599/3","title":"Humanities and Social Sciences Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Geo-economics, Geo-Strategic, Pakistan-China relations, VAR modeling, predictive analytics, foreign direct investment","lastPublishedDoi":"10.21203/rs.3.rs-6783006/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6783006/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper examines the changing economic and geopolitical dynamics between Pakistan and China from a Geo-economic perspective, using a predictive modeling methodology. The research used a Vector Auto-regressive (VAR) framework to examine the relationship among exports, foreign direct investment (FDI), and diplomatic contacts from 2010 to 2022. Stationarity and correlation studies validate robust inter-dependencies, but Granger causality tests indicate substantial directional interactions among variables. Impulse response functions and scenario-based forecasting highlight the impact of diplomatic shocks on trade and investment flows. The results substantiate the Geo-economic theory by illustrating how economic performance and private capital flows now influence bilateral diplomacy. The results provide actionable insights for export promotion and strategic economic planning, highlighting the pivotal role of data-driven modeling in comprehending intricate international relations. This study provides a solid empirical basis for future governmental and academic discussions on bilateral economic integration and strategic forecasting.\u003c/p\u003e","manuscriptTitle":"Causal Pathways in Geo-Economic Relations: A Time-Series Study of Trade, FDI, and Diplomacy between China and Pakistan","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-09 10:42:12","doi":"10.21203/rs.3.rs-6783006/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-09-16T10:08:20+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-29T19:42:01+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-25T01:34:15+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"160539322759935269190826618433733988851","date":"2025-07-12T06:11:55+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-10T14:11:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"313096360277091751467334757047303194942","date":"2025-07-09T18:09:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"247232000847896909425915511919985092116","date":"2025-07-08T09:35:30+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"30203814785601875715536845520903069264","date":"2025-07-07T14:34:22+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-07-07T10:02:04+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-24T13:18:01+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-06-21T12:51:35+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-06T03:14:11+00:00","index":"","fulltext":""},{"type":"submitted","content":"Humanities and Social Sciences Communications","date":"2025-06-06T03:10:22+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"humanities-and-social-sciences-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"palcomms","sideBox":"Learn more about [Humanities \u0026 Social Sciences Communications](http://www.nature.com/palcomms/)","snPcode":"41599","submissionUrl":"https://submission.springernature.com/new-submission/41599/3","title":"Humanities and Social Sciences Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"898e2ad5-b331-4b87-8a65-2f1bd190bb86","owner":[],"postedDate":"July 9th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":51207500,"name":"Business and commerce/Business and management"},{"id":51207501,"name":"Business and commerce/Economics"},{"id":51207502,"name":"Social science/Economics"},{"id":51207503,"name":"Social science/Politics and international relations"}],"tags":[],"updatedAt":"2026-04-09T15:40:14+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-09 10:42:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6783006","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6783006","identity":"rs-6783006","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}