ssrn-5211826

Geopolitical Dynamics VERSION: APRIL 2025 SUGGESTIONS, COMMENTS, & FEEDBACK ARE WELCOMED GOING BEYOND THE DISTANCE: GEOPOLITICAL DYNAMICS Gianni De Bruyn University of South Carolina gdebruyn@email.sc.edu Ting Fung Ma University of South Carolina tingfung@mailbox.sc.edu ABSTRACT Research on institutional distance and geopolitics often implicitly acknowledges these concepts' dynamic and evolving nature. However, traditional approaches have relied on static variables, leading to a disconnect between theoretical frameworks and empirical testing. In this study, we introduce a novel methodology and measure capable of extracting dynamic components from time- series data, including panel time-series, and transforming them into straightforward and intuitive input variables. This innovative measure enables researchers to explore geopolitical dynamics by investigating trajectory-based research questions and hypotheses. We first detail the new methodology and validate its effectiveness. Following validation, we demonstrate how this measure can enhance theoretical development by facilitating more nuanced questions and potentially challenging existing findings. Additionally, we discuss several extensions and modifications. We conclude with examples of novel hypotheses that our methodology can address and highlight its utility in various research designs, extending beyond traditional large-N analyses. -- 1 of 41 -- Geopolitical Dynamics 1 INTRODUCTION International business and strategy researchers have long understood the importance of geopolitical relations between countries and their impact on the firms within the countries (Adarkwah et al., 2024; Albino-Pimentel et al., 2021; Bertrand et al., 2016; Hartmann et al., 2022; J. Li et al., 2018). The consensus is that positive country-dyadic relations have positive externalities to the firm, whereas hostile relations have the opposite effect (Arikan et al., 2020; Bertrand et al., 2016; Duanmu, 2014; Fieberg et al., 2021; Gartzke, 1998; C. Li et al., 2020). For example, positive geopolitical relations can reduce the political risk for foreign acquirers and increase foreign investment and alliances (Arikan et al., 2020; Arikan & Shenkar, 2013; Bertrand et al., 2016). In contrast, hostile relations can threaten legitimacy (Stevens et al., 2016) and enhance the risk of expropriation (Asiedu et al., 2009; Chan & Makino, 2007; Kostova & Zaheer, 1999; J. Li et al., 2017). Although significant and insightful progress has been made regarding the implications of geopolitical relations and firm internationalization strategies, extant research has predominantly focused on the level of distance between selected country-dyadic variables, such as political affinity (Bertrand et al., 2016; Fieberg et al., 2021)—the alignment of national interests (Gartzke, 1998), and recently also the volatility of this political affinity (Adarkwah et al., 2024). In contrast, scholars have paid less attention to the changes in geopolitical relations between countries over time, including changes in direction, magnitude, duration, variance, and structural breaks—geopolitical dynamics (GD). It is important to understand the dynamics of geopolitical relations because these country-dyadic connections are seldom stable over time (Adarkwah et al., 2024; Lindner & Puck, 2024; Yiu et al., 2023). In the past decade, we have witnessed an increasing trend in populism (Blake et al., 2022; Carballo Perez & Corina, 2023), deglobalization -- 2 of 41 -- Geopolitical Dynamics 2 (Witt, 2019b, 2019a), reversal of open market policies (Cuervo-Cazurra et al., 2019), and techno nationalism (Luo, 2022; Luo & Van Assche, 2023), as well as the breakdown of dyadic country relations (Bureau of Industry and Security, 2023; The White House, 2021). During these times of an evolving geopolitical landscape, where governments have to navigate numerous and often unstable country-dyadic relationships, multinational corporations (MNCs) must pay careful attention to the degree of political affinity between nations and the dynamic nature of these relations. Failure to do so may result in entanglement within these more significant geopolitical conflicts among nations with divergent interests. However, these dynamic concepts are often measured using static variables.1 We argue that GD will likely have crucial and novel implications for the MNC that are not fully described using a static distance perspective. Traditional political affinity measures capture the difference level between the two countries.2 Geopolitical dynamics, by contrast, capture additional information on the nature of this change or dynamism (i.e., direction, magnitude, variance, structural breakpoints, and duration) for a given country. This provides a different and complementary view, highlighting the manner in which these nations might be growing more alike (converge), further apart (diverge), or fluctuating between the two and the speed at which this occurs. 1 Outside of the international strategy literature, there has been more attention to country-dyadic relational dynamics in several fields, such as international political economy, macroeconomics, macrofinance, economics, and international relations. Collectively, this body of work emphasizes the dynamic nature of country-dyadic relations. 2 A common approach in the literature to investigating dynamics is using a shock as part of an event study or a difference-in-differences approach (Eden et al., 2022). Although this method provides many opportunities, it requires a known exogenous shock. The measure we develop does not. In fact, our measure can be used to identify unknown shocks in large quantities. In addition, methods such as the difference-in-differences approach often capture averages, not changes in trends, with some exceptions. -- 3 of 41 -- Geopolitical Dynamics 3 Therefore, in this study, we develop a novel measure and methodology to capture GD and its components allowing researchers to further investigate the implications of GD on firm strategy and, more broadly, institutional theory. Drawing from foundational works on political affinity (Bailey et al., 2017; Bertrand et al., 2016; Duanmu, 2014; Gartzke, 1998; Voeten, 2000), dynamic measurement techniques (Kim et al., 2022), and trend analyses (Davis et al., 2006; Ma & Yau, 2016), our study develops a robust approach for probing GD. We also discuss the measure’s validity, offering case study evidence, expert validation, and simulation results to support its robustness and accuracy. We also compare the newly developed measure with existing measures, highlighting the measure's contribution. In addition, we provide several examples of applications of how the measure can provide novel insights. We also briefly discuss how our code can be adjusted depending on data availability and how the measure can be extended to other measures and constructs, including those beyond the dyad level. Lastly, we provide an overview of the potentially new research questions that can be addressed using this measure. Our study makes several contributions. First, we introduce the novel concept of GD, which has often been theorized implicitly or confounded with other constructs (e.g., levels and distances). Second, we develop and provide a novel measure to capture this concept. The development of this measure not only allows scholars to test and refine prior theory more accurately but also allows future scholars to hypothesize different types of research questions, those questions rooted in change over time and trajectory changes (Gruber & Bliese, 2024; Langley et al., 2023). Third, although our measure of GD is rooted in theory, we show how it can be extrapolated to other fields and measures to capture dynamics similarly in the researcher’s field of interest, assuming the researcher has theoretical justification for doing so. This paper also directly addresses calls for the development of more sophisticated distance measures (Adarkwah -- 4 of 41 -- Geopolitical Dynamics 4 et al., 2024; Beugelsdijk et al., 2018) while spanning the boundaries between international business, international political economy, and political geography (Saittakari et al., 2023). A final methodological contribution is the algorithm developed to calculate GD. This methodology can be readily implemented to other time-series data at different units of analysis to extract a representative dynamic component, such as a firm’s patenting dynamics. MOTIVATION, LITERATURE REVIEW, AND THEORETICAL GROUNDING Motivation We motivate the need for our novel measure capturing GD using a stylized example. Consider two country pairs - AB and CD. Both pairs may have identical institutional distances, but if AB converges while CD remains static or diverges, their strategic implications differ vastly. A firm from country A venturing into country B could capitalize on this convergence, potentially establishing a first-mover advantage (Doh, 2000) or fostering robust governmental affiliations (Dau et al., 2021; García-Canal & Guillén, 2008), justifying the increased uncertainty associated with greater political distance. This would confer faster growth opportunities and a competitive edge over firms that are oblivious to this dynamic trend and join the “game” later (Luo, 1998). In contrast, a firm from country C venturing into country D that is rapidly diverging from C is at a higher risk of becoming less knowledgeable and familiar with the host environment in which it operates and less likely to use its experience acquired at home. Figure 1 below depicts four potential dynamics as a stylized example: fast diverging dyads, fast converging dyads, slow diverging dyads, and slow converging dyads. Specifically, looking at the two diverging dyads (i.e., fast and slow), we see that although both have a distance of 100 units at the end, they started at different distances. Fast divergers began at a relatively close distance of 10 units but -- 5 of 41 -- Geopolitical Dynamics 5 moved to a large distance of 100 units, a 10-fold increase. In contrast, the slow divergers started at an initial distance of 80 units, for a 0.25 increase in distance. *** Insert Figure 1 about here *** Consider the United States – South Korea (US-ROK) alliance further to illustrate the dynamic nature of country-dyadic political affinity. This alliance has a long history of strong support, with the ROK relying on US support for protection against the Democratic People's Republic of Korea (DPRK – North Korea). However, the strength of the US-ROK relations has fluctuated a lot in the past, depending on which administration is in power (e.g., Clinton, Carter, or Bush administration in the US, or Roh, Kim Young-Sam, or Kim Dae-Jung administration in South Korea) and their view of how to handle South Korea’s neighboring countries (Han et al., 2023; Lee, 2020), or the occurrence of outlier events that could shape country-dyadic relations.3 Literature Review and Theoretical Grounding Geopolitical dynamics Cuervo-Cazurra, Gaur, and Singh (2019) review several country-level pro-market reforms and reversals and their influence on global relations and strategy. The consensus is that institutions can evolve in ways that are independent and potentially counter to other nations' institutional development trajectories. For instance, the path of institutional development in China, and its Beijing Consensus and later Brazil, markedly contrasts with that of nations like South Korea, Singapore, India, and Hong Kong (Luo et al., 2019). By extension, these different developmental paths result in various and unique changes in political affinity for each country-dyad, resulting in 3 For example, the Yangju highway incident (June 13, 2002), when a U.S. Army armored vehicle struck and killed two 14-year-old South Korean girls in Yangju, South Korea. The American soldiers involved were acquitted of negligent homicide by a U.S. military court, which fueled anti-American protests in South Korea and led to calls for a revision of the U.S.-ROK Status of Forces Agreement (SOFA). https://www.nytimes.com/2002/07/31/news/road-accident-galvanizes-the-country-deaths-in-korea-ignite.html https://www.latimes.com/archives/la-xpm-2002-nov-27-fg-uskorea27-story.html -- 6 of 41 -- Geopolitical Dynamics 6 significant heterogeneity in political affinity affects how host countries treat foreign investors (Gartzke, 1998) and GD. Research highlights the significance of country-dyadic political relations between a firm's home and host countries. It emphasizes that political affinity impacts the risks of host government intervention, with higher affinity linked to reduced discrimination and interference (Bertrand et al., 2016). Host governments may selectively target firms based on specific objectives rather than applying uniform policy changes (Makhija, 1993). The political affinity between countries develops over time through economic, social, and political interactions and formal agreements (Crescenzi & Enterline, 2001). These interactions influence attitudes and behaviors between countries, shaped by their structural positions within global networks (Nahapiet & Ghoshal, 1998). The relational embeddedness perspective examines how historical interactions between countries affect the quality of their ties (Polidoro et al., 2011), complementing the structural perspective, which focuses on broader network configurations (Barden & Mitchell, 2007). Key components of geopolitical dynamics We build on recent efforts (e.g., Adarkwah et al., 2024) to develop the key components (direction, magnitude, variance, structural breakpoints, and duration) of our GD construct and measure. Geopolitical relations can vary in direction, being either positive (cooperative) or negative (conflictive) (Bilgili et al., 2023). Positive ties, characterized by mutual understanding, trust, and commitment (Dixon, 1986), promote social capital benefits such as timely access to resources and information (Granovetter, 1985). Cooperative interactions often aim for mutual benefits, such as alliances or economic aid, fostering trust and reciprocity (Uzzi, 1997), with -- 7 of 41 -- Geopolitical Dynamics 7 positive externalities for the firm (Makino & Tsang, 2011). Conversely, hostile relations arising from diverging interests or territorial disputes (Kastner, 2007) exhibit distrust, disagreement, and animosity (Dixon, 1986). These conflictive relations often have negative externalities to the firm (Cuervo-Cazurra et al., 2007), as firms might be seen as extensions of their home government (Bertrand et al., 2016). In addition to the direction of these relations, the magnitude of these relations also plays a role (Bilgili et al., 2023). The magnitude of the relations amplifies the effects of the direction with strongly positive relations enabling information and resource exchanges as well as cross- border collaborations (Dixon, 1986; Uzzi, 1997). In contrast, strong hostile relations increase opportunism and government resistance to foreign investment (Arikan & Shenkar, 2013; Godsell et al., 2023; Makino & Tsang, 2011). Lastly, given that these relations are formed over time (Arikan et al., 2020; Crescenzi & Enterline, 2001; C. Li et al., 2020), they have an inherent time component that captures the unique duration for each country-dyad. In addition to direction, magnitude, and duration, two more components – variance and structural breaks – capture the volatility of these GD. The variance component of GD captures the deviations from expected trends (i.e., direction and magnitude), representing unexplained fluctuations within the broader trajectory of country-dyadic relations. Additionally, structural breaks occur when there is a significant and enduring shift in the trajectory or trend of these relations, marking the end and beginning of a new duration component and altering their long- term trajectory. Shifts in domestic political values or external geopolitical pressures in the short term are often the source of this variance (Amenta et al., 2010). For instance, mobilization by activist groups or populist parties can shift domestic discourse, influencing governments to enact foreign -- 8 of 41 -- Geopolitical Dynamics 8 policies that deviate from historical patterns (Edelman, 2001). These deviations are inherently unpredictable, reflecting the reactive nature of political decision-making in response to dynamic public opinion or geopolitical events. In geopolitics, variance is amplified by a country’s recalibration of foreign policy stances. For example, the rise of China as a significant global power, coupled with the delegitimization of Western neoliberalism following the 2008 financial crisis and the 2017 US-China trade war, has introduced frequent and unexpected shifts in alliances and geopolitical strategies (Fisman et al., 2022; Luo & Van Assche, 2023; Witt, 2019a, 2019b). In contrast to variance, structural breaks represent profound and sustained changes in the trend of country-dyadic relations. A previously cooperative relationship may experience a significant rupture due to changes in governing elites or geopolitical alignments. For example, a realignment in national priorities, driven by ideological shifts or new leadership, can lead to a sharp decline in political affinity, disrupting long-term patterns of cooperation and economic exchange (Cuervo-Cazurra et al., 2019). Structural breaks often result from geopolitical realignments that reshape the international landscape. The changing dynamics of global power, particularly the interplay between Western and non-Western nations, have created new fault lines in international relations. These breaks alter the structural foundation of political relationships, marking a clear departure from prior trajectories and requiring firms and governments to recalibrate their expectations and strategies. Therefore, any measure that hopes to capture GD must account for the following five components: Direction, magnitude, variance, presence of structural breaks, and the duration of a given trend. MEASUREMENT DEVELOPMENT -- 9 of 41 -- Geopolitical Dynamics 9 We use the UN Voting data to capture political affinity (Bailey et al., 2017; Gartzke, 1998, 2000) as the source data to develop our GD measure. UN Voting measures the similarity of national interests in global affairs, which indicates alignment in a country’s values, world views, political agenda, and consensus on geopolitical issues (Gartzke, 1998), and has been used in the literature to measure country-dyadic relations (Adarkwah et al., 2024; Bertrand et al., 2016; Duanmu, 2014). High political affinity is associated with increased cooperation, whereas low political affinity indicates tensions between the two nations (Gartzke, 2000). Our measure is developed using a 4-step process. First, given a time series with total length, 𝑇 , and a minimum length for each segment, 𝜀𝜆. If we assume there are 𝑚 (unknown) changepoints, which segments the series into 𝑚 + 1 segments. we can then generate all possible configurations of potential changepoints, 𝑐𝑝𝑚,𝑇,𝜆𝜀 by 𝑐𝑝𝑚,𝑇,𝜀𝜆 = {(𝜆1, … , 𝜆𝑚), 1 < 𝜆1 < ⋯ < 𝜆𝑚 < 𝑇, 𝜆𝑖 − 𝜆𝑖−1 ≥ 𝜀𝜆, 𝑖 = 1, … , 𝑚 + 1}, where 𝜆0 = 1 and 𝜆𝑚+1 = 𝑇. Thus, the possible changepoint configuration when there are at most 𝑚𝑚𝑎𝑥 number of changepoints can be written as 𝐶𝑃𝑚𝑚𝑎𝑥,𝑇,𝜀𝜆 = ⋃ 𝑐𝑝𝑚,𝑇,𝜀𝜆 . 𝑚𝑚𝑎𝑥 𝑖=0 Within the 𝑗-th segment, the model is specified by the parameter 𝜃𝑗 . For our case, a linear model is adopted for each segment. Suppose there are 𝑚 + 1 segment (i.e. 𝑚 changepoints), we have, 𝑦𝑡 = { 𝛽0,1 + 𝛽1,1𝑡 + 𝜀1,𝑡, 1 ≤ 𝑡 ≤ 𝜆1 𝛽0,2 + 𝛽1,2𝑡 + 𝜀2,𝑡 𝜆1 + 1 ≤ 𝑡 ≤ 𝜆2 ⋮ ⋮ 𝛽0,𝑚+1 + 𝛽1,𝑚+1𝑡 + 𝜀𝑚+1,𝑡 𝜆𝑚 ≤ 𝑡 ≤ 𝑇, , -- 10 of 41 -- Geopolitical Dynamics 10 where 𝜀𝑗,𝑡 is a random sample from 𝑁(0, 𝜎𝑗2). Under the linear regression mode, we have 𝜃𝑗 = (𝛽0,𝑗, 𝛽1,𝑗, 𝜎𝑗2)𝑇, where 𝛽0,𝑗 is the intercept, 𝛽1,𝑗 is the slope, and 𝜎𝑗2 is the variance. Note that the number of changepoint 𝑚, parameters in segment (s), 𝜃𝑗 ′𝑠, and changepoint locations 𝜆𝑗𝑠 are unknown and have to be estimated, which is a strength of our methodology compared to other methodological tools that require a known shock or break (e.g., differences-in-difference, event studies, discontinuous growth models, regression discontinuity in time design). In the second step of the process, given the changepoint configuration, 𝝀∗ = (𝜆1 ∗ , … , 𝜆𝑚∗ ∗ )𝑇, we estimate the parameters 𝜽 = {𝜃1, … 𝜃𝑚∗+1} using the ordinary least square method. We then evaluate the Akaike’s information criterion (AIC) (Akaike, 1998; Konishi & Kitagawa, 2008) for the model, given the changepoint configuration. 𝐴𝐼𝐶(𝝀∗) = 2(𝑚∗ + 1)𝐾 + ∑ −2 log 𝐿(𝜃̂𝑗 , 𝜆𝑗−1 ∗ , 𝜆𝑗 ∗ ) 𝑚∗+1 𝑗=1 , where log 𝐿(𝜃̂𝑗 , 𝜆𝑗−1 ∗ , 𝜆𝑗 ∗ ) is the log-likelihood value evaluated at the ordinary least squares estimate for the 𝑗-th segment, and 𝐾 is the number of parameters for each segment. For our linear regression model, this further reduces to 𝐴𝐼𝐶(𝝀∗) = 6(𝑚∗ + 1) ∑ (𝜆𝑗 ∗ − 𝜆𝑗−1 ∗ + 1) log [ ∑ (𝑦𝑡 − 𝛽̂0,𝑗 − 𝛽̂1,𝑗𝑡)2 𝜆𝑗 ∗ 𝑡=𝜆𝑗−1 ∗ 𝜆𝑗 ∗ − 𝜆𝑗−1 ∗ + 1 ] 𝑚∗+1 𝑗=1 . The changepoint detection problem readily becomes selecting the “best” configuration among all candidates in 𝐶𝑃𝑚𝑚𝑎𝑥,𝑇,𝜀𝜆 , which can be treated as a statistical model selection problem with applications in economic time series (Ma & Yau, 2016). See Davis et. al (2006) for more details. -- 11 of 41 -- Geopolitical Dynamics 11 In the third step of the process, we estimate the number and locations of changepoints and other parameters by exhausting all possible configurations4 in 𝐶𝑃𝑚𝑚𝑎𝑥,𝑇,𝜀𝜆 , that is 𝝀̂ = argmin 𝝀∈𝐶𝑃𝑚𝑚𝑎𝑥,𝑇,𝜀𝜆 𝐴𝐼𝐶(𝝀), Moreover, given 𝝀̂, we have the corresponding ordinary least squares estimate 𝜽 ̂ = {𝜃̂1, … 𝜃̂𝑚̂ +1}. These estimates are stored in the model for later use. Figure 2 and Table 1 are examples of a single case (political affinity between the USA and Russia) where the parameters have been estimated. *** Insert Figure 2 about here *** *** Insert Table 1 about here *** Fourth, we repeat this process for all country dyads.5 Once all the models have been run and the parameters estimated, we combine all the results into a single dataset, which will be available on the authors’ GitHub page. Figure 3 depicts the entire process. *** Insert Figure 3 (Process) about here *** Ultimately, our methodology estimates five key parameters, as shown in Table 2 below, capturing the segmented nature of the GD's direction, magnitude, volatility, and duration. *** Insert Table 2 about here *** MEASUREMENT VALIDITY 4 Exhaustive search may become computationally infeasible when 𝑇 is large. Other algorithms, such as pruned dynamic programming (e.g., Killick et al., 2012 and Maidstone, et. al 2017) can be used. 5 Given the computational complexity and cost to estimate the parameters for all country-dyads, we used the Hyperion High Performance Computing (HPC) cluster available at the University. -- 12 of 41 -- Geopolitical Dynamics 12 Next, we validate and explore our measure. First, we use an illustrative historical example. Second, we use expert validation of our metric. Third, we run simulations to validate the methodology. Fourth, we explore the variance of the estimated parameters to validate that there is significant variance to be useful in future research. Fifth, we compare with other measures in the literature to highlight both conceptual and operational distinctiveness. Case Study: US-Brazil We will use the case of US-Brazil (Figure 2) to test the validity of our measures. This dyad was chosen for several reasons, including data availability, two nations that are familiar to most scholars, and both held different geopolitical views in terms of liberalist policies with significant fluctuations in their relations (Cuervo-Cazurra et al., 2019). After World War II and the early Cold War era, the diplomatic and geopolitical relations between the United States and Brazil were primarily shaped by their collaboration in the war effort against the Axis Powers. In 1942, Brazil declared war on the Axis Powers, becoming a crucial ally for the United States in South America. This declaration of war marked a significant shift in Brazil's foreign policy and established a foundation for future cooperation between the two nations. The alliance between the United States and Brazil during World War II laid the groundwork for their post-war relations and set the stage for increased U.S. influence in the region. The period from 1960 to 1975 was characterized by significant geopolitical changes and tensions globally and within Brazil. In 1964, the United States supported a military coup in Brazil that overthrew President João Goulart. This led to a shift in power towards a government perceived as more anti-communist and pro-American. Throughout this period, diplomatic ties -- 13 of 41 -- Geopolitical Dynamics 13 between the two countries remained strong, with the United States exerting considerable influence over Brazilian policies, particularly in the context of the Cold War. The years between 1975 and 1990 witnessed significant changes in the global geopolitical landscape, including the end of the Cold War and the transition to democracy in several countries. In Brazil, this period was marked by the gradual erosion of the military regime and the eventual transition to democracy in 1985. Diplomatic tensions between the United States and Brazil gradually rose over trade disputes and environmental policies, reflecting the complexities of their bilateral relationship. The period from 1990 to 2002 saw the consolidation of democracy in Brazil, and new challenges and opportunities emerged in the bilateral relationship between the United States and Brazil. Both countries worked closely on issues such as drug trafficking and trade, reflecting their shared interests and concerns. Their shared stances on global issues lead to an improvement in diplomatic relations. However, tensions occasionally flared over trade disputes and differences in environmental policies. Despite these challenges, diplomatic relations between the two countries kept improving gradually, with a continued emphasis on economic cooperation and environmental conservation. In contrast, the years from 2002 to 2016 were marked by fluctuations in US-Brazil relations, driven partly by changes in leadership and shifting geopolitical dynamics. Presidents Lula da Silva and Dilma Rousseff pursued a policy of South-South cooperation, focusing on regional integration and development. Their administrations often clashed with US policies, particularly in trade and regional influence. Tensions peaked in 2013 with the NSA spying scandal, revealing US surveillance on Brazilian officials, leading to significant diplomatic tension and a strained relationship between the two countries. -- 14 of 41 -- Geopolitical Dynamics 14 Despite these challenges, relations began to improve in 2016. The period from 2016 to 2021 witnessed significant shifts in US-Brazil relations under the leadership of Presidents Jair Bolsonaro and Donald Trump. Bolsonaro's presidency saw a notable improvement in relations with the United States, focusing on aligning Brazil more closely with US positions on international issues. This alignment was particularly evident in Venezuela, Israel, and trade. However, tensions resurfaced with the inauguration of President Joe Biden in 2021, as his administration emphasized environmental issues and human rights, leading to friction over Bolsonaro's policies and rhetoric, particularly regarding the Amazon rainforest. The brief description of US-Brazil diplomatic relations maps very well to the parameters produced by our methodology and measurements. It also highlights how dynamic country-dyadic diplomatic relations can be and that our measure can capture even very dynamic relations well. Expert Validation We asked experts to discuss the dyadic relations of two countries of their choice and, when possible, to draw a timeline. We did not prompt a specific dyad to give the expert full agency to decide on the dyad they are most familiar with. We then asked them to compare their discussion with our model and figures. Although all drawings were less nuanced than our models, they mapped well on the parameters produced by the models. We used four experts, including two consultants to Fortune 500 firms and two private equity specialists whose business model relied on identifying and using trends for real estate acquisitions. None of the experts disagreed with any of the results provided by the models. Simulation Two simulation settings were considered motivated by the Belgium-Qatar dyad. For the first setting, we estimated the parameters following the proposed procedure based on the real data. -- 15 of 41 -- Geopolitical Dynamics 15 The parameter estimates were used to simulate datasets. The mean function of the simulated dyad was computed by treating the estimated intercepts and slopes. Random errors were simulated from normal distribution using the estimated variance from the real data. For the second setting, the observed residuals were computed using real data. The new dataset was then generated by summing up the fitted values and resampling the residuals with replacement for the two segments. Owing to the relatively short dyad length, we set the minimum segment length at 15 in the simulation. We run 10,000 replicates for each simulation setting. Note that the two simulation settings could be viewed as parametric and non-parametric bootstrapping, respectively.6 Table 3 shows the results of the simulation under the two settings. The results for the two simulation settings were very similar. The percentages of the estimated number of changepoints equal to the true value (one) were both about 90%, indicating the procedure's accuracy. Moreover, the average and the standard deviation of the computation times were 0.17 and 0.04 seconds, respectively. Given the number of changepoints was correctly estimated, we considered the average bias and the standard deviation for the segment parameters. The average bias and standard deviation were slight for the slope and variance parameters but larger for the intercepts, as is expected due to their larger magnitudes. Conditional to the number of changepoints being correct, we visualized the empirical distribution of the estimated location of changepoint as histograms in Figure 4 with a red dotted line indicating the true value. The empirical distributions showed a non-standard distribution, which matched the time-series theoretical 6 See Davison & Hinkley (1997) for more details about bootstrapping. -- 16 of 41 -- Geopolitical Dynamics 16 results (Bai, 1994; Ling, 2016; Ma & Yau, 2016; Zhao et al., 2024). Overall, the simulation results aligned with those of Ma and Yau (2016). *** Insert Figure 4 about here *** *** Insert Table 3 about here *** Exploring Variance A critical feature of a variable is the presence of meaningful variance in the underlying data and estimated parameters that accurately represent the real world. Therefore, we explore the variance of our construct and parameters in several ways. First, the heat plots in Figure 5 indicate considerable variation in the underlying source data on country-dyadic relations and that these relations are selective and asymmetric. We have chosen the US as the base country for several reasons. First, the US has a strong history of UN Voting and data recording and collection in general. Second, the US has been the post-WWII hegemon, although this power has weakened. Third, anchoring to a single country shows that even if an actor is given in the dyad, there is still variation in geopolitical distances between countries. Figure 5 depicts heat plots based on z- scores, where scores are calculated at the country-dyad level to capture variation in a single dyad. *** Insert Figure 5 about here *** We have used the US-Brazil relations as a running example in our study, which we will contrast with another well-known dyad, the US-Russia relations. Figure 6 plots the changepoints identified by our model. Table 4 compares the parameters of the US-Brazil dyad (panel A) with the US-Russia dyad (panel B). *** Insert Figure 6 about here *** -- 17 of 41 -- Geopolitical Dynamics 17 *** Insert Table 4 about here *** A second critical factor is to explore the variance in the algorithm’s estimated parameters. We do so by comparing top and bottom performers. Table 5 below compares the parameters for the top 10 friendliest and bottom 10 least friendly dyads and the remaining dyads. The selection criteria are made by taking the average diplomatic distance of each dyad, after which we identify the 10 friendliest and 10 least friendly dyads. The parameters are all as expected. A negative slope indicates convergence, while a positive slope indicates divergence. We see that the top 10 friendliest dyads have had, on average, a negative slope, indicating convergence between the two countries. The low values for variance also suggest that this convergence has been relatively stable, without much variance. In contrast, we see that the 10 least friendly dyads, on average, diverge from each other, meaning they become geopolitically more distant or polarized, and this divergence is also associated with a greater degree of variance. Looking at the remaining dyads, we find a slight negative slope. This suggests that, on average, dyads have been slowly converging at a relatively stable rate compared to the least friendly dyads. This means that, on average, the world has become more aligned or less geopolitically polarized for most countries, insinuating that deglobalization is still more risk than reality. These findings imply that perceived deglobalization trends will likely be concentrated in those unfriendly dyads. *** Insert Table 5 about here *** Both the comparison of the two selected dyads and the comparison of the friendliest and least friendly dyads suggest that there is sufficient and important variance in our parameters. Correlation with alternative approaches -- 18 of 41 -- Geopolitical Dynamics 18 Our measure is only meaningful and important if it can capture additional information not captured by existing measures. Given that no other measure captures GD, we compare it to the original underlying source data, other country-dyadic distance data, and country-dyadic sentiment data. Specifically, we compare the parameters against Berry et al. (2010) distance measures, the distance between national institutions, both in “absolute” terms and in “real” distance, accounting for the direction. These different measures are chosen as they originate in different institutional theories (Aguilera & Grøgaard, 2019; Kostova et al., 2020). We also look at the correlation with a news-based score that has been gaining traction in recent years, Global Database on Events, Location and Tone (GDELT) (Albino-Pimentel et al., 2022; Odziemkowska & Henisz, 2021; Wang et al., 2021). GDELT provides comprehensive data about the interactions of different types of actors worldwide with other actors, as reported in the media. For our purposes, we have focused on several different operationalizations, including overall government sentiment, negative government sentiment only, overall sentiment (all actors) towards the home country, and only negative sentiment toward the home country. In essence, we looked at combinations of government actors versus all actors and overall sentiment versus negative sentiment only. We compute estimated slope, segment length, and segment variance using the proposed procedure for all dyads from 1990-2020 as our data. Table 6 indicates the pairwise correlation between our parameter estimates and other measures. In addition, we also calculate the confidence interval of the (spearman rank) correlation to make sure it does not include 1.0 in order to demonstrate discriminant validity. None of the confidence intervals include 1.0. The most significant correlation reported is between Segment Variance and Rule of Law Distance – absolute (0.28). These correlations are promising because they indicate that they are conceptually different and -- 19 of 41 -- Geopolitical Dynamics 19 suggest numerous fruitful future research questions that can be addressed by looking at how these different concepts influence each other, for example, in a moderation model. *** Insert Table 6 about here *** However, it is important to note that we are not the first to investigate dynamics and motion. Recent trends incorporating more longitudinal and dynamic aspects into our theories (e.g., Adarkwah et al., 2024; Kim et al., 2022) have spurred several attempts to account for trajectories. For example, Kim et al. (2022) use a Bai-Perron-inspired approach (Bai & Perron, 1998, 2003) to propose an evolutionary view of industry clusters focusing on cluster motion rather than mass. However, the approaches fundamentally differ in their uses, capabilities, assumptions, minimum requirements (e.g., known shock), origin, limitations, and, most importantly, the theoretical problems they solve. APPLICATION We provide several examples of how our parameters can be used in practice, some with surprising results and some with results as expected but with opportunities for further theory development. This is done to highlight that our new measure can challenge conventional thinking, warranting a renewed focus on some old, established, taken-for-granted results. Our example highlights the ability to provide more nuance to prior known findings by proposing a potential new boundary condition. Specifically, we investigate ownership percentage decisions upon entering a country. We add our variables of interest in progression in Table 7, first looking at the slope (model 1) and variance (model 2) parameters separately, followed by model 3, which combines both. Model 5 introduces a selection of commonly used control variables in the literature. Model 6 introduces the interaction terms, and model 7 is the full model. Models 1 – 5 -- 20 of 41 -- Geopolitical Dynamics 20 show an interesting but expected pattern. As country dyads diverge, ownership percentage increases, supporting an ownership control argument rather than an autonomy argument. However, the sign on variance is negative indicating that firms are likely to be less committed to countries with which the home country has very volatile relations. Interpreting these together in model 5 insinuates that stability comes with a degree of predictability, so firms are willing to commit more extensive resources to maintain control as the environment is more predictable. Looking at the models with the interaction term, we report a positive sign on the interaction. These models indicate that converging or diverging has little effect on the percentage of ownership when political affinity is high. However, when political affinity is low, fast converging dyads have low ownership, while fast diverging dyads have high ownership. In simple terms, when political affinity is low and diverges even more, the acquirer wants to maintain as much control as possible. However, when political affinity is low but converging, the acquirer is willing to lower their ownership percentage to potentially “ride the wave” of convergence. Although we do not focus on theory building, this application has the potential to shed more light on the control versus autonomy argument in cross-border acquisition ownership decisions (Belenzon et al., 2019). *** Insert Table 7 about here *** The two examples above are simple applications of topics often studied in the field, although with novel predictors not yet studied to the same extent. However, we can also investigate questions less studied due to measurement limitations. For example, what is the relationship between variance and trajectories? Is this relationship linear and symmetric? To study this question, we use a kink regression discontinuity design (Card et al., 2015) with a slope of 0 as the cutoff. This cutoff captures the switch from converging to diverging. A negative value -- 21 of 41 -- Geopolitical Dynamics 21 means converging geopolitical relations, whereas positive values indicate divergence again. The change in sign acts as an explicit cutoff. Figure 7 below reports our results visually. We see a clear change in the relationship around the cutoff, where the further from the cutoff, the more volatile the geopolitical relations become. This indicates that the least volatile dyads maintain relationships that are slowly diverging or converging. However, increasing the slope of either divergence or convergence is associated with increased volatility. *** Insert Figure 7 about here *** We have selected two specific examples, one focusing on introducing more nuance and one focusing on a new research question, but many more novel research questions are possible. Especially questions involving the change points. For example, is fast or slow convergence better in terms of stability? Are fast-converging dyads bound to relapse? Can variance indicate future divergence even if the dyad had a horizontal trajectory before? Is there an optimal degree of variance that prevents fast divergence or convergence? For example, a minimum degree of stress in the relationship is needed to know how the partner country will act when stress or difficulties are present. If there never was any stress, the slightest hiccup could disrupt the relationship. MODIFICATIONS AND EXTENSIONS Methodology Modifications The methodology can be modified to include different models, selection criteria, and parameter requirements. We have used the AIC and a linear regression model for our main discussion for changepoint detection and inference. Note that the proposed process can be parallelized easily and that our proposed method is not limited to the use of AIC but any information criterion, such as the Bayesian information criterion (BIC) and the minimum description length (MDL), which -- 22 of 41 -- Geopolitical Dynamics 22 balances between model complexity and goodness of fit.7 However, BIC and MDL would empirically require more computational time and longer series for good statistical properties. Moreover, our proposed process allows the scholars to select other models, such as ARIMA (Davis et al., 2006), the general time series model (Ma & Yau, 2016), and the spatiotemporal model (Zhao et al., 2024). Table 8 below lists the modifications along with the advantages and disadvantages. Where 𝑂 represents big-O notation,8 𝑇 is the length of the time series, 𝐾 is the number of parameters, 𝑚𝑚𝑎𝑥 is the maximum number of changepoints, and 𝜀𝜆 is the minimum segment length. *** Insert Table 8 about here *** Measure Extensions Given our focus on GD, we have used political affinity as the source data. However, the method can also be applied to other source data as long as there is a time-series component. Below, in Figure 8 and Table 9, we show an application of the method to another commonly used dataset in the IB literature that captures the distance between two countries (Kostova et al., 2020), demographic distance (Berry et al., 2010). We see that the methodology extrapolates to this data as well. It is also important to note that given the same specifications, only four changepoints are detected rather than 5, providing confidence that the methodology finds the best fitting changepoints rather than always maximizing the number of changepoints. 7 Information criteria evaluate models by considering both the complexity of the model (number of parameters) and how well the model fits the data (error or residuals). More complicated models with many parameters can usually fit the data better but are penalized because they are harder to describe. Models that fit the data well will have smaller residuals, meaning they capture the underlying pattern effectively. Information criteria aim to find the model that provides the best trade-off between these two aspects, leading to a model that is neither too simple (underfitting) nor too complicated (overfitting). 8 Mathematical notation used in computer science to describe the order of the runtime complexity of an algorithm or operation. -- 23 of 41 -- Geopolitical Dynamics 23 *** Insert Figure 8 about here *** *** Insert Table 9 about here *** Both the political affinity data and demographic distance data are at the country-dyad level, but our methodology can be extrapolated to any level (e.g., firm, teams, alliances, networks). Figure 9 and Table 10 are examples of our methodology applied to firm patenting behavior, trying to capture patenting dynamics. Specifically, we show the patenting dynamic of Merck & Co, a quintessential firm in the pharmaceutical industry, an industry known for its high patenting behavior and long history of patenting. *** Insert Figure 9 about here *** *** Insert Table 10 about here *** RESEARCH APPLICATIONS In addition to traditional large sample data analysis, three research applications our methodology might be particularly applicable to are: Historical case studies, event studies, and policy studies (Langley et al., 2023). Historical Case Studies As shown in the historical example, this method is particularly useful for case studies and determining how relations change over time. Moreover, the decomposition into several parameters allows nuanced descriptions and effects. Specifically, the case study can focus on trajectories, changes in trajectories, the degree of trajectory change, and the volatility during these segments. Additionally, rather than using it as a predictor variable or descriptive, the methodology can also be used to identify attractive candidates for case studies, similar to the LIVA measure proposed by Wibbens and Siggelkow (2020) that assess firm performance in more extended time frames. A scholar could search for either a common or unique pattern and do a deep dive into these patterns or do a comparative case study between different patterns to -- 24 of 41 -- Geopolitical Dynamics 24 determine commonalities or unique, previously unidentified dynamics (e.g., Gatignon & Capron, 2020). A particular advantage of our methodology for case studies is that each parameter, trend, segment length, volatility, etc., can be given specific attention and might act as quantitative support when needed. Event Studies Event studies often focus on immediate effects in the short term within a specific time window (Eden et al., 2022). For example, Minefee, McDonnell, and Werner (2021) exploit a whistleblower’s leak of the American Legislative Exchange Council’s corporate sponsors to investigate investor’s reaction to covert corporate political activity. Godsell, Lell, and Miller (2023) examine the effects of CIFIUS on foreign acquisitions into the US. Our methodology answers a fundamentally different but equally important question: trajectory changes. In addition, event studies require a known exogenous shock. In contrast, our method does not require this and can detect the changepoint and magnitude. They provide an excellent input opportunity to conduct a staggered difference-in-difference design. The researcher can decide to examine multiple shocks, shocks above a certain magnitude, only shocks that change the sign, or less investigated, shocks that do not change the sign but are still a significant departure from previous trends (e.g., sudden acceleration or leveling off). Policy Studies Relatedly, the methodology's properties capture the change of direction and magnitude of a changepoint rather than a single dummy coded variable for a changepoint (although this can still be coded if needed). In essence, our methodology extracts the dynamic component of a time series, turning it into a usable variable for a regression. These different parameters can be helpful -- 25 of 41 -- Geopolitical Dynamics 25 when assessing the impact on growth trajectories or volatility before or after a discontinuity, such as policy changes. FUTURE RESEARCH Future research can leverage our measure and deepen our understanding of geopolitical and economic dynamics by addressing limitations in static or aggregate analyses. First, this approach allows for the retesting of established relationships by capturing the dynamic and time-varying nature of these interactions. Second, it provides greater nuance to known relations by identifying temporal shifts, volatility patterns, and structural breaks that reveal periods of intensified or diminished effects, potentially offering a more granular understanding of current topics of interest (e.g., cross-border acquisitions, foreign direct investment, patent litigation). Finally, this methodology opens new avenues for inquiry by uncovering emergent trajectories and trends within the data that static models might overlook, such as the association between variance and structural breaks or trajectory slopes and stability. Table 11 provides several exemplar questions. *** Insert Table 11 about here *** DISCUSSION AND CONCLUSION Our research makes several theoretical, empirical, and managerial contributions. First, we formalize a known idea, that of change and dynamics, into an applicable construct, geopolitical dynamics. By doing so, we address several calls in the literature for more focus on dynamics and recognizing temporal elements (Adarkwah et al., 2024; Lubinski & Wadhwani, 2020; Luo & Van Assche, 2023; Phan, 2019; Yiu et al., 2023). Second, the development of this measure allows and even pushes the researcher to propose novel hypotheses (Gruber & Bliese, 2024). More specifically, the researcher can now build theory that includes dynamics as a crucial component of the hypothesis, which is now readily testable. The future research opportunity section provides -- 26 of 41 -- Geopolitical Dynamics 26 several examples of different novel hypotheses that can be answered. Adding dynamics to the researcher’s toolbox will require a deeper understanding of the theory and relations and will ultimately improve theory by providing more nuance (Langley et al., 2023). Third, as an empirical contribution, we provide scholars with a methodology to extract dynamic components from any time series data into simple and intuitive variables. We also show how the dynamic and static components are conceptually and empirically different. This allows scholars to delve into the nuances of the relationships between country-dyadic distance and the convergence or divergence between the two countries. Fourth, our measure allows for retesting of prior findings that might have used dynamic logic in their theory building but used static measures to test their theory. It would be interesting to see if the result holds. Fifth, we provide an alternative, more flexible, and accurate methodology with less stringent initial assumptions than existing dynamic methodologies. However, this comes at the cost of 1) the need for more extensive data samples and sufficiently long-time frames and 2) higher computational complexity depending on the chosen specification. Given the recent growth in big data, AI, and computational power, these costs are less consequential using cutting-edge tools and algorithms. Still, the researcher should carefully weigh different approaches. From a managerial perspective, practitioners can gain both backward- and forward-looking insights. First, managers can identify crucial managerial changes and events around changepoints that caused a change in slopes (e.g., market entry of a competitor, economic downturns) and understand their impact. Managers can also identify potential strategic decisions that affect their performance variance. In addition, predictive insights from these models, especially the ARIMA models, can assist in making more accurate forecasts and anticipate future trends based on identified patterns in the past. The model can also be used for scenario planning. 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Journal of International Business Studies, 50(7), 1053–1077. Yiu, D. W., Wan, W. P., Chen, K. X., & Tian, X. (2023). A Theory of Host Country Sentiments: An Illustration In Cross-Border Acquisitions. Academy of Management Journal. Zhao, Z., Ma, T. F., Ng, W. L., & Yau, C. Y. (2024). A Composite Likelihood-Based Approach for Change-Point Detection in Spatio-Temporal Processes. Journal of the American Statistical Association, 1–15. -- 31 of 41 -- Geopolitical Dynamics 31 TABLES TABLE 01. USA – BRAZIL PARAMETER ESTIMATES Segment Years Intercept (𝛃𝟎) Slope (𝛃𝟏) Variance (𝛔𝒊 𝟐) 1 1946 – 1961 40.94 -0.02 0.17 2 1962 – 1973 24.18 -0.01 0.03 3 1974 – 1989 -179.68 0.09 0.04 4 1990 – 2002 167.55 -0.08 0.01 5 2003 – 2012 -20.27 0.01 0.01 6 2013 - 2022 253.06 -0.12 0.02 TABLE 02. PARAMETER DESCRIPTIONS Parameter What it captures Intercept (β0) The intercept represents the baseline level of geopolitical tension between the two countries at the start of each segment. It indicates the initial degree of tension before any changes in the trend within that segment. Direction and magnitude Slope (β1) The slope represents the rate of change in geopolitical tension over time within each segment. A positive slope indicates that geopolitical tension is increasing, while a negative slope indicates that geopolitical tension is decreasing during that period. Variance Variance of the error term (σ𝑖 2) The variance of the error term measures the variability or fluctuations in geopolitical tension that are not explained by the linear trend. It captures the degree of unpredictability or instability in the tension levels during each segment. Structural breaks Location of changepoints (𝑐𝑝𝑖) The location of the changepoints identifies the specific times when there is a significant shift in the pattern or trend of geopolitical tension. These points mark the moments when the nature of the tension changes, such as during major diplomatic events or incidents. Duration Length of the segments (𝑐𝑝𝑖+1 − 𝑐𝑝𝑖 ) The length of the segments represents the duration of time during which the diplomatic tension follows a consistent trend. It indicates how long a particular level or trend of tension persists before a significant change occurs. -- 32 of 41 -- Geopolitical Dynamics 32 TABLE 03. SIMULATION Normal noise Estimated number of changepoints (percentage %) Computational time (second) 0 1 2 ≥ 𝟑 Average SD 0 86.82 13.18 0 0.1732 0.0394 Estimated number of changepoint = 1 True Mean SD Changepoint location (𝝀𝟏) 26 24.5298 3.6800 Segment 1 Segment 2 Intercept (𝛃𝟎) Slope (𝛃𝟏) Variance (𝛔𝒊 𝟐) Intercept (𝛃𝟎) Slope (𝛃𝟏) Variance (𝛔𝒊 𝟐) True -51.2099 0.0269 0.0222 57.5934 -0.0276 0.0239 Mean bias 2.1718 -0.0011 -0.0011 -1.9562 0.0010 -0.0008 SD 10.9147 0.0055 0.0071 9.0309 0.0045 0.0071 Resampling residuals Estimated number of changepoints (percentage %) Computational time (second) 0 1 2 ≥ 𝟑 Average SD 0 87.59 12.41 0 0.1762 0.0410 Estimated number of changepoint = 1 True Mean SD Changepoint location (𝝀𝟏) 26 24.5204 3.4878 Segment 1 Segment 2 Intercept (𝛃𝟎) Slope (𝛃𝟏) Variance (𝛔𝒊 𝟐) Intercept (𝛃𝟎) Slope (𝛃𝟏) Variance (𝛔𝒊 𝟐) True -51.2099 0.0269 0.0222 57.5934 -0.0276 0.0239 Mean bias 2.2882 -0.0012 -0.0020 -1.8150 0.0009 -0.0029 SD 10.7124 0.0054 0.0063 8.6414 0.0043 0.0056 TABLE 04. BRAZIL VERUS RUSSIA PARAMETER ESTIMATES Segment Years Intercept (𝛃𝟎) Slope (𝛃𝟏) Variance (𝛔𝒊 𝟐) Panel A: USA - Brazil 1 1946 – 1961 40.94 -0.02 0.17 2 1962 – 1973 24.18 -0.01 0.03 3 1974 – 1989 -179.68 0.09 0.04 4 1990 – 2002 167.55 -0.08 0.01 5 2003 – 2012 -20.27 0.01 0.01 6 2013 - 2022 253.06 -0.12 0.02 Panel B: USA - Russia 1 1946 – 1955 -149.00 0.079 0.18 2 1956 – 1974 -35.62 0.021 0.07 3 1975 – 1984 106.24 -0.051 0.02 4 1985 – 1994 641.81 -0.321 0.14 5 1995 – 2008 -121.87 0.06 0.01 6 2009 – 2022 -21.30 0.012 0.03 -- 33 of 41 -- Geopolitical Dynamics 33 TABLE 05. CONTRASTING PARAMETER ESTIMATES Top 10 Friendliest Remaining dyads Bottom 10 Friendliest Diplomatic Distance Mean 0.05 1.02 3.64 Min 0.04 0.06 3.70 Max 0.06 3.71 4.63 SD 0.00 0.23 0.67 Slope Mean -0.02 -0.01 0.01 Min -0.70 -0.39 -0.03 Max 0.01 0.35 0.56 SD 0.00 0.06 0.16 Variance Mean 0.00 0.05 0.17 Min 0.00 0.00 0.01 Max 0.01 0.73 1.41 SD 0.00 0.08 0.17 TABLE 06. CORRELATION WITH ALTERNATIVE MEASURES Slope Segment Length Segment Variance Segment Length 0.05 Segment Variance -0.04 -0.11 UN Voting Distance -0.15 -0.13 0.26 Administrative Distance 0.00 0.04 0.03 Demographic Distance -0.09 0.00 0.17 Cultural Distance -0.06 0.04 0.11 Economic Distance -0.04 -0.04 0.03 Geographic Distance -0.07 -0.16 0.15 Political Distance 0.02 0.01 0.01 Average Berry et al. (2010) Distance -0.04 0.03 0.09 Political Constraints Index Distance 0.02 0.03 -0.07 Political Constraints Index Distance - Absolute -0.04 -0.06 0.12 Rule of Law Distance 0.04 0.04 -0.03 Rule of Law Distance - Absolute -0.04 -0.09 0.28 Government Sentiment (GDELT) 0.00 -0.01 -0.01 Government Negative Sentiment (GDELT) 0.00 -0.02 -0.02 *None of the (spearman rank) correlation confidence intervals include 1.0, demonstrating discriminant validity -- 34 of 41 -- Geopolitical Dynamics 34 TABLE 07. APPLICATION: CROSS BORDER ACQUISITION OWNERSHIP (1) (2) (3) (4) (5) (6) (7) Ownership (%) Ownership (%) Ownership (%) Ownership (%) Ownership (%) Ownership (%) Ownership (%) Slope 25.405 20.215 16.693 19.160 1.224 -4.022 (0.000) (0.000) (0.000) (0.005) (0.868) (0.764) Variance -84.035 -77.002 -63.929 -74.608 -62.719 -72.804 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Slope * Political Affinity 10.873 17.409 (0.013) (0.045) Political Affinity -1.722 -2.618 -1.586 -2.377 (0.000) (0.000) (0.000) (0.000) Divestment 13.790 13.782 (0.000) (0.000) Deal Value ($mil) 0.001 0.001 (0.000) (0.000) Host Financial Advisor 3.682 3.676 (0.000) (0.000) Host Inflation -0.014 -0.014 (0.101) (0.109) Host GDP Growth -0.329 -0.327 (0.006) (0.007) Constant 81.230 82.567 82.549 84.211 82.348 84.092 82.141 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) R-sq 0.526 0.527 0.527 0.528 0.534 0.528 0.534 N 41685 41685 41685 41675 11627 41675 11627 p-values in parentheses -- 35 of 41 -- Geopolitical Dynamics 35 TABLE 08. MODIFICATIONS AND EXTENSIONS Modification Advantages Disadvantages Time to Compute ARIMA models • Better at capturing complex temporal dependencies and seasonality. More accurate modeling of trends and patterns. • Can generate more realistic counterfactual scenarios due to its capacity to model autocorrelation. • Error terms are modeled explicitly, allowing for a better understanding of residuals. • More computationally intensive and may require more data for accurate parameter estimation. • Assumes that past values and error terms are sufficient to predict future values, which may not hold in all cases. • Error terms may be autocorrelated, which can complicate interpretation. 𝑂(𝑇) for fitting one ARIMA model based on some suitable log- likelihood approximation BIC • Penalizes model complexity more than AIC, preventing overfitting in large sample. Provides a more parsimonious model. • Enjoy more statistical properties under large sample size • Fail to detect changepoint when sample size is moderate/small • May miss subtle changes due to higher penalty on additional parameters. Less sensitive to smaller variations. 𝑂(1) for calculating the penalty term MDL • Can handle model complexity and goodness of fit, providing a balance. Adaptable to various model complexities. • Enjoy more statistical properties under large sample size • Relate to information theory • Complex to compute and understand, may not be as intuitive. • Error terms might still present challenges in terms of interpretation due to the complexity of the model. 𝑂(1) for calculating the penalty term Maximum number of changepoints 𝑚𝑚𝑎𝑥 • Increasing the number of changepoints allows for more flexibility in identifying changepoints, capturing more nuance. • Error terms can be more finely analyzed within each segment, potentially improving model accuracy. • An increase in the number of maximum allowed changepoints increases computational complexity and may overfit if too many changepoints are allowed. Risk of identifying spurious changes. • Error terms might become more complex to interpret with increased changepoints. The total number of possible changepoint configuration: 𝑂(𝑇min(𝑚𝑚𝑎𝑥,⌊𝑇/𝜀𝜆⌋ )), where ⌊⋅⌋ is the floor function. Minimum segment length 𝜀𝜆 • Increasing length can ensure statistical robustness and meaningful segments, unadulterated by short term fluctuations. • Longer segments can lead to more stable and interpretable error terms. • May overlook short-term changes and reduce model sensitivity to abrupt shifts if length is too long. • Error terms might not capture short-term fluctuations adequately. -- 36 of 41 -- Geopolitical Dynamics 36 TABLE 9. EXTENSION: DEMOGRAPHIC DISTANCE Demographic Distance Berry et al. (2010) Segment Years Intercept (𝛃𝟎) Slope (𝛃𝟏) Variance (𝛔𝒊 𝟐) 1 1960 – 1976 175.48 -0.09 0.00 2 1977 – 1989 -1139.94 0.58 0.04 3 1990 – 1999 1349.03 -0.67 0.33 4 2000 – 2009 58.83 -0.03 0.08 5 2010 - 2018 184.93 -0.09 0.00 TABLE 10. EXTENSION: PATENTING DYNAMICS – MERCK & CO. Patenting Dynamics – Merck & Co. Segment Years Intercept (𝛃𝟎) Slope (𝛃𝟏) Variance (𝛔𝒊 𝟐) 1 1939 - 1980 -0.32 4.88 387.66 2 1981 - 1990 -170.50 7.64 300.12 3 1991 - 2004 -144.56 8.21 1140.54 4 2005 - 2021 1564.57 -18.26 2310.91 -- 37 of 41 -- Geopolitical Dynamics 37 TABLE 11. FUTURE RESEARCH Broad Field Research Question Direction and magnitude • Cross Border Acquisitions: How does the rate of increasing or decreasing geopolitical tensions influence cross-border acquisition decisions? Are firms willing to enter more “distant” nations if they are converging? • Patenting Strategy: Does the magnitude and direction of GD influence whether a firm is more or less likely to patent in the host nation? • Political Strategy: Are MNCs more likely to engage in corporate political strategies if they are “distant” but converging fast with the hopes of shaping the relationship and getting favorable treatments? Variance • Cross Border Acquisitions: How does the variance of the country-dyadic relationship influence the ownership decision? Are they more likely to take control, or do they leave autonomy with the target? • Patenting Strategy: Does instability in geopolitical relations affect a firm's R&D spending or patenting strategies in host countries? Is this interdependent with absolute levels of distance? • Political Strategy: Are firms more likely to adopt hedging political strategies (e.g., lobbying, insurance) in regions with high tension variance? • Industry: Do industries with high political sensitivity (e.g., defense, telecommunications) react differently to tension volatility compared to low-sensitivity industries? Structural Breaks • Cross Border Acquisitions: Are abrupt geopolitical shifts associated with changes in M&A ownership structures (e.g., from majority to minority ownership)? What is the minimum severity of change needed for a major change (i.e., is there a threshold that flips the decision between control and autonomy)? • Patenting Strategy: How do geopolitical shifts (e.g., trade wars, sudden conflicts) alter patent application collaborations between countries? • Supply Chain Strategy: How do major structural breaks in global political alliances impact global supply chain decisions? • Foreign Direct Investment: How do structural breaks in diplomatic relations between countries influence foreign direct investment decisions? Is there a trade that follows the flag dynamic? Or is it reversed? Duration • Cross Border Acquisitions: Does the duration of diplomatic stability between countries influence the probability of long-term acquisitions versus short-term ventures? (This would also be an interesting question in relation to variance) • Patenting Strategy: Are longer periods of stable or improving relations more likely to result in collaborative patenting? Does it influence the likelihood of trust in a nation’s IP laws? • Innovation Strategy: How does the length of stable political conditions impact the scale of R&D investments in host countries? Is the innovation produced more novel and radical as there is more confidence that the relationships are long-term, meaning that partners are willing to collaborate on long-term projects? • Foreign Investment Strategy: How does the persistence of tension reduction between countries affect decisions about greenfield investments versus acquisitions? Combination • What is the relation between magnitude and variance? Do faster converging or diverging relations lead to more or less variance? • What is the relation between magnitude and structural breaks? Are stronger converging and diverging relations bound to change (flip sign or plateau)? What is the importance of variance in this relation? Fast, but stable diverging are less likely to exhibit a structural break compared to fast divergence with a large degree of variance? • What is the association between duration and variance? • What is the association between duration and magnitude once a structural break does occur? Meaning, if there is a structural break in a long-lasting relation, it means that this is a severe topic of contention and the magnitude of change is large. Or does their history mitigate some of this effect, making it a change of smaller magnitude? -- 38 of 41 -- Geopolitical Dynamics 38 FIGURES FIGURE 01. GEOPOLITICAL DYNAMICS FIGURE 02. USA – BRAZIL GEOPOLITICAL TENSIONS FIGURE 03: PROCESS -- 39 of 41 -- Geopolitical Dynamics 39 FIGURE 04. SIMULATION: FIGURE 05. HEATMAP GEOPOLITICAL DYNAMICS FIGURE 06. USA – RUSSIA GEOPOLITICAL DYNAMICS -- 40 of 41 -- Geopolitical Dynamics 40 FIGURE 07. APPLICATION: RD – SLOPE & VARIANCE FIGURE 08. EXTENSION: DEMOGRAPHIC DISTANCE DYNAMICS FIGURE 09. EXTENSION: PATENTING DYNAMICS – MERCK & CO. -- 41 of 41 --