arXiv subjects

Viktor Stojkoski

Publications and source records attributed to Viktor Stojkoski.

At least 19 recordsLinked to original sources

arXiv2026

Geometric Brownian motion with intermittent entries and exits

We study a generalized geometric Brownian motion framework that incorporates both entries of new units and exit mechanisms for the current population, extending earlier stochastic resetting models where these rates are treated as identical. The model captures realistic features observed in many economic observables, which can be explained as market-driven firm entries/exits, worker inflow/outflow, and income growth/loss. This model is not conservative and, despite the asymmetry in the entry and exit rates, we find that the system eventually relaxes to a stationary distribution. Moreover, our analysis reveals three distinct dynamical regimes in the moments of the distribution, arising from the interplay between volatility, drift, entry, and exit rates. We further derive the survival probability and the mean first-passage time associated with the observed variable reaching certain threshold under the competing entry-exit processes. Interestingly, we identify an optimal exit rate that minimizes the mean first-passage time, providing insights into how entry and exit policies can influence the outcome of the system. These results should be useful for understanding the long-run behavior of economic systems in which growth, volatility, entry, and exit jointly shape the evolution of heterogeneous units.

econ.GN↗

arXiv2026

Business cycle synchronization between the EU and Western Balkan candidate economies: A Wavelet Analysis

Business cycle synchronization between EU and Western Balkan candidate economies is usually modeled with aggregate time-domain correlations that mix short-run and long-run dynamics. This paper addresses that limitation by combining wavelet-based time-frequency decomposition with Bayesian zero-inflated beta regression. Using annual dyad-year data for 2001--2021, we estimate synchronization separately at shorter (1.5--4.5 years) and longer (4.5--8.5 years) horizons and relate each horizon to its correlates. The results show that EU--WB dyads are less synchronized than EU--EU dyads in the short run, and that trade deepening over time is more positively associated with short-run synchronization in EU--WB pairs. At longer horizons, the positive association between shared EU/EMU membership and synchronization weakens or reverses when the same country pair moves into deeper institutional integration, while differences across country pairs in average EU/EMU status become negligible. Over the same horizon, trade deepening within a pair is more consistently associated with synchronization, and more persistent structural dissimilarity is associated with lower synchronization. EU--WB dyads are no longer clearly less synchronized at these frequencies, and the remaining convergence pattern is more consistent with sectoral differences narrowing over time than with trade. These findings indicate that synchronization channels are horizon-dependent and that conclusions based on single-horizon correlation measures can obscure the distinction between short-term coupling and structural convergence.

econ.GN↗

arXiv2025

Capability Accumulation and Conditional Convergence: Towards a Dynamic Theory of Economic Complexity

We develop a dynamic model of economic complexity that endogenously generates a transition between unconditional and conditional convergence. In this model, convergence turns conditional as the capability intensity of activities rises. We solve the model analytically, deriving closed-form solutions for the boundary separating unconditional from conditional convergence and show that this model also explains the path-dependent diversification process known as the principle of relatedness. This model provides an explanation for transitions between conditional and unconditional convergence and path-dependent diversification.

econ.GN↗

arXiv2025

Optimizing Economic Complexity

Efforts to apply economic complexity to identify diversification opportunities often rely on diagrams comparing the relatedness and complexity or products, technologies, or industries. Yer, the use of these diagrams is not based on empirical or theoretidal evidence supporting some notion of optimality. Here, we introduce an optimization-based framework that identifies diversification opportunities by minimizing a cost function capturing the constraints imposed by an economy's pattern of specialization. We show that the resulting portfolios often differ from those implied by relatedness-complexity diagrams, providing a target-oriented optimization layer to the economic complexity toolkit.

econ.GN↗

arXiv2025

The Theory of Economic Complexity

We provide a mechanistic foundation for economic complexity methods. In our model, an economy's ability to produce an activity depends on the joint presence of required capabilities. We analytically derive the Economic Complexity Index (ECI) for this model and show that it is a monotonic function of the stock of capabilities in an economy. We then explore the family of functions and conditions that are compatible with economic complexity estimates and show that multiplicatively separable production functions are incompatible with economic complexity estimates. By contrast, additive non-separable functions are sufficient regardless of whether they are log super-modular. We also show that this model explains differences in the shape of networks of related activities, such as the product space or research space. These findings solve long standing puzzles in the literature on economic complexity.

econ.GN↗

arXiv2025

Augmenting the availability of historical GDP per capita estimates through machine learning

Can we use data on the biographies of historical figures to estimate the GDP per capita of countries and regions? Here we introduce a machine learning method to estimate the GDP per capita of dozens of countries and hundreds of regions in Europe and North America for the past 700 years starting from data on the places of birth, death, and occupations of hundreds of thousands of historical figures. We build an elastic net regression model to perform feature selection and generate out-of-sample estimates that explain 90% of the variance in known historical income levels. We use this model to generate GDP per capita estimates for countries, regions, and time periods for which this data is not available and externally validate our estimates by comparing them with four proxies of economic output: urbanization rates in the past 500 years, body height in the 18th century, wellbeing in 1850, and church building activity in the 14th and 15th century. Additionally, we show our estimates reproduce the well-known reversal of fortune between southwestern and northwestern Europe between 1300 and 1800 and find this is largely driven by countries and regions engaged in Atlantic trade. These findings validate the use of fine-grained biographical data as a method to produce historical GDP per capita estimates. We publish our estimates with confidence intervals together with all collected source data in a comprehensive dataset.

econ.GN↗

arXiv2025

Network-based diversification of stock and cryptocurrency portfolios

Maintaining a balance between returns and volatility is a common strategy for portfolio diversification, whether investing in traditional equities or digital assets like cryptocurrencies. One approach for diversification is the application of community detection or clustering, using a network representing the relationships between assets. We examine two network representations, one based on a standard distance matrix based on correlation, and another based on mutual information. The Louvain and Affinity propagation algorithms were employed for finding the network communities (clusters) based on annual data. Furthermore, we examine building assets' co-occurrence networks, where communities are detected for each month throughout a whole year and then the links represent how often assets belong to the same community. Portfolios are then constructed by selecting several assets from each community based on local properties (degree centrality), global properties (closeness centrality), or explained variance (Principal component analysis), with three value ranges (max, med, min), calculated on a maximal spanning tree or a fully connected community sub-graph. We explored these various strategies on data from the S\&P 500 and the Top 203 cryptocurrencies with a market cap above 2M USD in the period from Jan 2019 to Sep 2022. Moreover, we study into more details the periods of the beginning of the COVID-19 outbreak and the start of the war in Ukraine. The results confirm some of the previous findings already known for traditional stock markets and provide some further insights, while they reveal an opposing trend in the crypto-assets market.

econ.GN↗

arXiv2024

The impact of stochastic resetting on resource allocation: The case of Reallocating geometric Brownian motion

We study the effects of stochastic resetting on the Reallocating geometric Brownian motion (RGBM), an established model for resource redistribution relevant to systems such as population dynamics, evolutionary processes, economic activity, and even cosmology. The RGBM model is inherently non-stationary and non-ergodic, leading to complex resource redistribution dynamics. By introducing stochastic resetting, which periodically returns the system to a predetermined state, we examine how this mechanism modifies RGBM behavior. Our analysis uncovers distinct long-term regimes determined by the interplay between the resetting rate, the strength of resource redistribution, and standard geometric Brownian motion parameters: the drift and the noise amplitude. Notably, we identify a critical resetting rate beyond which the self-averaging time becomes effectively infinite. In this regime, the first two moments are stationary, indicating a stabilized distribution of an initially unstable, mean-repulsive process. We demonstrate that optimal resetting can effectively balance growth and redistribution, reducing inequality in the resource distribution. These findings help us understand better the management of resource dynamics in uncertain environments.

cond-mat.stat-mech↗

arXiv2024

Multidimensional Economic Complexity and Fiscal Crises

Recent studies highlight economic complexity's role in mitigating fiscal crises, often measured via an economy's trade structure. Trade, however, is just one facet of an economy's structure and omits critical innovative activities like research. Here, we investigate how a multidimensional approach to economic complexity-including both trade and research structures-relates to fiscal instability. By using data on over 230 national fiscal crises from 1995 to 2021 and hazard duration analysis, we assess how measures of trade and research complexity combine to explain crisis likelihood. We find that the interaction of complexity dimensions significantly reduces crisis probability, whereas individual indexes alone are not robust predictors. This suggests that economies focusing on a single dimension may be more vulnerable, thus highlighting the importance of balanced development across multiple areas. These findings offer valuable insights for policymakers aiming to enhance economic resilience and mitigate fiscal risks.

econ.GN↗

arXiv2024

Mapping Election Polarization and Competitiveness using Election Results

The simplified hypothesis that an election is polarized as an explanation of recent electoral outcomes worldwide is centered on perceptions of voting patterns rather than ideological data from the electorate. While the literature focuses on measuring polarization using ideological-like data from electoral studies-which are limited to economically advantageous countries and are representative mostly to national scales-we argue that, in fact, voting patterns can lead to mapping effective proxies of citizen divisions on election day. This paper perspectives two complementary concepts, Election Polarization (EP) and Election Competitiveness (EC), as a means to understand voting patterns on Election Day. We present an agnostic approach that relies solely on election data and validate it using synthetic and real-world election data across 13 countries in the Eurozone, North America, Latin America, and New Zealand. Overall, we find that we can label and distinguish expectations of polarized and competitive elections in these countries, and we report that EP positively correlates with a metric of political polarization in the U.S., unlocking opportunities for studies of polarization at the regional level and for lower/middle-income countries where electoral studies are available, but surveys are limited.

cs.CY↗

arXiv2024

Measures of physical mixing evaluate the economic mobility of the typical individual

Measures of economic mobility represent aggregate values for how individual wealth changes over time. As such, these measures may not describe the feasibility of a typical individual to change their wealth. To address this limitation, we introduce mixing, a concept from statistical physics, as a relevant phenomenon for quantifying how individuals move across the wealth distribution. We display the relationship between mixing and mobility both theoretically and using data. By studying the properties of an established model of wealth dynamics, we show that some individuals can move across the distribution when wealth is a non-mixing observable. Only in the mixing case every individual is able to move across the whole wealth distribution. There is also a direct equivalence between measures of mixing and the magnitude of the standard measures of economic mobility, but the opposite is not true. We then describe an empirical method for estimating the mixing properties of wealth dynamics in practice. We use this method to present a pedagogical application using the USA longitudinal data. This, approach, even though limited in data availability, leads to results suggesting that wealth in the USA is either non-mixing or that it takes a very long time for the individuals to mix within the distribution. These results showcase how mixing can be used in tandem with measures of mobility for drawing conclusions about the extent of mobility across the whole distribution.

econ.GN↗

arXiv2024

Estimating Digital Product Trade through Corporate Revenue Data

Despite global efforts to harmonize international trade statistics, our understanding of digital trade and its implications remains limited. Here, we introduce a method to estimate bilateral exports and imports for dozens of sectors starting from the corporate revenue data of large digital firms. This method allows us to provide estimates for digitally ordered and delivered trade involving digital goods (e.g. video games), productized services (e.g. digital advertising), and digital intermediation fees (e.g. hotel rental), which together we call digital products. We use these estimates to study five key aspects of digital trade. We find that, compared to trade in physical goods, digital product exports are more spatially concentrated, have been growing faster, and can offset trade balance estimates, like the United States trade deficit on physical goods. We also find that countries that have decoupled economic growth from greenhouse gas emissions tend to have larger digital exports and that digital products exports contribute positively to the complexity of economies. This method, dataset, and findings provide a new lens to understand the impact of international trade in digital products.

econ.GN↗

arXiv2023

The Role of Immigrants, Emigrants, and Locals in the Historical Formation of European Knowledge Agglomerations

Did migrants make Paris a Mecca for the arts and Vienna a beacon of classical music? Or was their rise a pure consequence of local actors? Here, we use data on more than 22,000 historical individuals born between the years 1000 and 2000 to estimate the contribution of famous immigrants, emigrants, and locals to the knowledge specializations of European regions. We find that the probability that a region develops or keeps specialization in an activity (based on the birth of famous physicists, painters, etc.) grows with both, the presence of immigrants with knowledge on that activity and immigrants with knowledge in related activities. In contrast, we do not find robust evidence that the presence of locals with related knowledge explains entries and/or exits. We address some endogeneity concerns using fixed-effects models considering any location-period-activity specific factors (e.g. the presence of a new university attracting scientists).

econ.GN↗

arXiv2023

Random resetting in search problems

By periodically returning a search process to a known or random state, random resetting possesses the potential to unveil new trajectories, sidestep potential obstacles, and consequently enhance the efficiency of locating desired targets. In this chapter, we highlight the pivotal theoretical contributions that have enriched our understanding of random resetting within an abundance of stochastic processes, ranging from standard diffusion to its fractional counterpart. We also touch upon the general criteria required for resetting to improve the search process, particularly when distribution describing the time needed to reach the target is broader compared to a normal one. Building on this foundation, we delve into real-world applications where resetting optimizes the efficiency of reaching the desired outcome, spanning topics from home range search, ion transport to the intricate dynamics of income. Conclusively, the results presented in this chapter offer a cohesive perspective on the multifaceted influence of random resetting across diverse fields.

cond-mat.stat-mech↗

arXiv2023

Income Mobility and Mixing in North Macedonia

This study presents the inaugural analysis of income mobility in North Macedonia from 1995-2021 using the Mixing Time and Mean First Passage Time (MFPT) metrics. We document larger mobility (in terms of Mixing Time) during the '90s, with and decreasing trend (in terms of mobility) until 1999. After this year the Mixing time has been consistent with a value of around 4 years. Using the MFPT, we highlight the evolving challenges individuals face when aspiring to higher income tiers. Namely, we show that there was a noticeable upward trend in MFPT from 1995 to 2006, a subsequent decline until 2017, and then an ascent again, peaking in 2021. These findings provide a foundational perspective on the income mobility in North Macedonia.

econ.GN↗

arXiv2023

Multidimensional Economic Complexity and Inclusive Green Growth

To achieve inclusive green growth, countries need to consider a multiplicity of economic, social, and environmental factors. These are often captured by metrics of economic complexity derived from the geography of trade, thus missing key information on innovative activities. To bridge this gap, we combine trade data with data on patent applications and research publications to build models that significantly and robustly improve the ability of economic complexity metrics to explain international variations in inclusive green growth. We show that measures of complexity built on trade and patent data combine to explain future economic growth and income inequality and that countries that score high in all three metrics tend to exhibit lower emission intensities. These findings illustrate how the geography of trade, technology, and research combine to explain inclusive green growth.

econ.GN↗

arXiv2022

The fate of the American dream: A first passage under resetting approach to income dynamics

Detailed knowledge of individual income dynamics is crucial for investigating the existence of the American dream: Are we able to improve our income status during our working life? This key question simply boils down to observing individual status and how it moves between two thresholds: the current income and the desired income. Yet, our knowledge of these temporal properties of income remains limited since we rely on estimates coming from transition matrices which simplify income dynamics by aggregating the individual changes into quantiles and thus overlooking significant microscopic variations. Here, we bridge this gap by employing First Passage Time concepts in a baseline stochastic process with resetting used for modeling income dynamics and developing a framework that is able to crucially disaggregate the temporal properties of income to the level of an individual worker. We find analytically and illustrate numerically that our framework is orthogonal to the transition matrix approach and leads to improved and more granular estimates. Moreover, to facilitate empirical applications of the framework, we introduce a publicly available statistical methodology, and showcase the application using the USA income dynamics data. These results help to improve our understanding on the temporal properties of income in real economies and provide a set of tools for designing policy interventions.

econ.GN↗

arXiv2022

Ergodicity breaking in wealth dynamics: The case of reallocating geometric Brownian motion

A growing body of empirical evidence suggests that the dynamics of wealth within a population tends to be non-ergodic, even after rescaling the individual wealth with the population average. Despite these discoveries, the way in which non-ergodicity manifests itself in models of economic interactions remains an open issue. Here, we shed valuable insight on these properties by studying the non-ergodicity of the population average wealth in a simple model for wealth dynamics in a growing and reallocating economy called Reallocating geometric Brownian motion (RGBM). When the effective wealth reallocation in the economy is from the poor to the rich, the model allows for the existence of negative wealth within the population. We show that then, in RGBM ergodicity breaks as the difference between the time-average and the ensemble growth rate of the average wealth in the population. In particular, the ensemble average wealth grows exponentially whereas the time-average growth rate is non-existent. Moreover, we find that the system is characterized with a critical self-averaging time period. Before this time period, the ensemble average is a fair approximation for the population average wealth. Afterwards, the non-ergodicity forces the population average to oscillate between positive and negative values since then the magnitude of this observable is determined by the most extreme wealth values in the population. This implies that the dynamics of the population average is an unstable phenomenon in a non-ergodic economy. We use this result to argue that one should be cautious when interpreting economic well-being measures that are based on the population average wealth in non-ergodic economies.

cond-mat.stat-mech↗