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 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.

Correlates of the country differences in the infection and mortality rates during the first wave of the COVID-19 pandemic: evidence from Bayesian model averaging.

The COVID-19 pandemic resulted in great discrepancies in both infection and mortality rates between countries. Besides the biological and epidemiological factors, a multitude of social and economic criteria also influenced the extent to which these discrepancies appeared. Consequently, there is an active debate regarding the critical socio-economic and health factors that correlate with the infection and mortality rates outcome of the pandemic. Here, we leverage Bayesian model averaging techniques and country level data to investigate whether 28 variables, which describe a diverse set of health and socio-economic characteristics, correlate with the final number of infections and deaths during the first wave of the coronavirus pandemic. We show that only a few variables are able to robustly correlate with these outcomes. To understand the relationship between the potential correlates in explaining the infection and death rates, we create a Jointness Space. Using this space, we conclude that the extent to which each variable is able to provide a credible explanation for the COVID-19 infections/mortality outcome varies between countries because of their heterogeneous features.

Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity.

We explore the role of non-ergodicity in the relationship between income inequality, the extent of concentration in the income distribution, and income mobility, the feasibility of an individual to change their position in the income rankings. For this purpose, we use the properties of an established model for income growth that includes 'resetting' as a stabilizing force to ensure stationary dynamics. We find that the dynamics of inequality is regime-dependent: it may range from a strictly non-ergodic state where this phenomenon has an increasing trend, up to a stable regime where inequality is steady and the system efficiently mimics ergodicity. Mobility measures, conversely, are always stable over time, but suggest that economies become less mobile in non-ergodic regimes. By fitting the model to empirical data for the income share of the top earners in the USA, we provide evidence that the income dynamics in this country is consistently in a regime in which non-ergodicity characterizes inequality and immobility. Our results can serve as a simple rationale for the observed real-world income dynamics and as such aid in addressing non-ergodicity in various empirical settings across the globe. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

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 nonergodic, even after rescaling the individual wealth with the population average. Despite these discoveries, the way in which nonergodicity manifests itself in models of economic interactions remains an open issue. Here we shed valuable insight on these properties by studying the nonergodicity 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. In this work, we show that in the negative reallocation regime of 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 nonexistent. 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 nonergodicity forces the population average to oscillate between positive and negative values since 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 nonergodic 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 nonergodic economies.

The impact of state capacity on the cross-country variations in COVID-19 vaccination rates.

The initial period of vaccination shows strong heterogeneity between countries' vaccinations rollout, both in the terms of the start of the vaccination process and in the dynamics of the number of people that are vaccinated. A predominant thesis for this observation is that a key determinant of the swift and extensive vaccine rollout is state capacity. Here, we utilize two measures that quantify different aspects of the state capacity: (i) the external capacity (measured through the soft power of the country) and (ii) the internal capacity (measured via the country's government effectiveness) and provide an empirical test for their relationship with the coronavirus vaccination outcome in the initial period (up to 31st March 2021). By using data on 128 countries and a two-step Heckman approach, we find that the soft power is a robust determinant of whether a country has started with the vaccination process. In addition, the government effectiveness is a key factor that determines vaccine roll-out. Altogether, our findings are in line with the hypothesis that state capacity determines the observed heterogeneity between countries in the initial period of COVID-19 vaccines rollout. As such, they are a stark reminder for the need for transparent and fair global response regarding fair and equitable availability of vaccines to every country.

The short-run impact of COVID-19 on the activity in the insurance industry in the Republic of North Macedonia.

Recent studies suggest that the COVID-19 pandemic will induce drastic changes in the business models of the insurance industry. However, despite an abundance of predictions, the literature still lacks empirical investigations of the impact of the pandemic. In this paper, we perform a first of a kind analysis and investigate the short-run impact of COVID-19 on the activity in the insurance in one country-North Macedonia. By utilizing a seasonal autoregressive model, we find that during the first half of 2020, the activity in the insurance industry shrank by more than 10% to what was expected. The total loss in the industry amounted to approximately 8.2 million euros. This was much less than the volume of reserves that the Insurance Supervision Agency made available as funds for dealing with the potential crisis. In addition, the pandemic induced changes in the insurance activity structure-the share of motor vehicles class in the total industry activity fell at the expense of the property classes. Our results suggest that the insurance industry in North Macedonia was well prepared to tackle the consequences of the pandemic and that automatic stabilizers had a major influence on weakening the overall negative impact.

Geometric Brownian motion under stochastic resetting: A stationary yet nonergodic process.

We study the effects of stochastic resetting on geometric Brownian motion with drift (GBM), a canonical stochastic multiplicative process for nonstationary and nonergodic dynamics. Resetting is a sudden interruption of a process, which consecutively renews its dynamics. We show that, although resetting renders GBM stationary, the resulting process remains nonergodic. Quite surprisingly, the effect of resetting is pivotal in manifesting the nonergodic behavior. In particular, we observe three different long-time regimes: a quenched state, an unstable state, and a stable annealed state depending on the resetting strength. Notably, in the last regime, the system is self-averaging and thus the sample average will always mimic ergodic behavior establishing a stand-alone feature for GBM under resetting. Crucially, the above-mentioned regimes are well separated by a self-averaging time period which can be minimized by an optimal resetting rate. Our results can be useful to interpret data emanating from stock market collapse or reconstitution of investment portfolios.

Generalised Geometric Brownian Motion: Theory and Applications to Option Pricing.

Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset dynamics, due to irregularities found when comparing its properties with empirical distributions. As a solution, we investigate a generalisation of GBM where the introduction of a memory kernel critically determines the behaviour of the stochastic process. We find the general expressions for the moments, log-moments, and the expectation of the periodic log returns, and then obtain the corresponding probability density functions using the subordination approach. Particularly, we consider subdiffusive GBM (sGBM), tempered sGBM, a mix of GBM and sGBM, and a mix of sGBMs. We utilise the resulting generalised GBM (gGBM) in order to examine the empirical performance of a selected group of kernels in the pricing of European call options. Our results indicate that the performance of a kernel ultimately depends on the maturity of the option and its moneyness.

On the Structure of the World Economy: An Absorbing Markov Chain Approach.

The expansion of global production networks has raised many important questions about the interdependence among countries and how future changes in the world economy are likely to affect the countries' positioning in global value chains. We are approaching the structure and lengths of value chains from a completely different perspective than has been available so far. By assigning a random endogenous variable to a network linkage representing the number of intermediate sales/purchases before absorption (final use or value added), the discrete-time absorbing Markov chains proposed here shed new light on the world input/output networks. The variance of this variable can help assess the risk when shaping the chain length and optimize the level of production. Contrary to what might be expected simply on the basis of comparative advantage, the results reveal that both the input and output chains exhibit the same quasi-stationary product distribution. Put differently, the expected proportion of time spent in a state before absorption is invariant to changes of the network type. Finally, the several global metrics proposed here, including the probability distribution of global value added/final output, provide guidance for policy makers when estimating the resilience of world trading system and forecasting the macroeconomic developments.

Design of pH Responsive Textile as a Sensor Material for Acid Rain.

The chemical composition of rainwater can serve as an indicator of the excess of acidifying air pollutants. The pH value of rainwater in the presence of sulphur dioxide and nitrogen oxides, the precursors of acid rain, falls below pH 5.6, which is the limit value for acid rain. In this research, the tailoring of halochromic textile was examined for the design of a functional textile that can serve as a sensor and inform the wearer about the presence of pollutants in the air by means of an immediate colour change. For this purpose, a polyamide 6 fabric was dyed with the pH-sensitive Bromocresol green dye, which causes a colour change below pH 3.6 (yellow) and above pH 5.4 (blue). In addition, the dyed polyamide 6 fabric was treated with a water and oil repellent finish. Colour and colour change before and after immersion of unfinished and finished dyed samples in buffer solutions with different pH values were evaluated spectrophotometrically using the CIELAB colour space. The colour fastness to rubbing, washing, and light, and the water and oil repellency of the dyed fabrics were determined according to valid SIST EN ISO standards. The results showed that the unfinished dyed polyamide 6 fabric undergoes a reversible colour change faster and more clearly than the finished dyed polyamide 6 fabric. The dyed polyamide 6 fabric had good colour fastness to rubbing and domestic and commercial laundering, while the colour fastness to light was poor. In addition, the dyed polyamide 6 fabric was pH-sensitive, despite dye degradation under xenon light, regardless of whether it was finished.

Cooperation dynamics in networked geometric Brownian motion.

Recent works suggest that pooling and sharing may constitute a fundamental mechanism for the evolution of cooperation in well-mixed fluctuating environments. The rationale is that, by reducing the amplitude of fluctuations, pooling and sharing increases the steady-state growth rate at which individuals self-reproduce. However, in reality interactions are seldom realized in a well-mixed structure, and the underlying topology is in general described by a complex network. Motivated by this observation, we investigate the role of the network structure on the cooperative dynamics in fluctuating environments, by developing a model for networked pooling and sharing of resources undergoing a geometric Brownian motion. The study reveals that, while in general cooperation increases the individual steady state growth rates (i.e., is evolutionary advantageous), the interplay with the network structure may yield large discrepancies in the observed individual resource endowments. We comment possible biological and social implications and discuss relations to econophysics.

Economic complexity unfolded: Interpretable model for the productive structure of economies.

Economic complexity reflects the amount of knowledge that is embedded in the productive structure of an economy. It resides on the premise of hidden capabilities-fundamental endowments underlying the productive structure. In general, measuring the capabilities behind economic complexity directly is difficult, and indirect measures have been suggested which exploit the fact that the presence of the capabilities is expressed in a country's mix of products. We complement these studies by introducing a probabilistic framework which leverages Bayesian non-parametric techniques to extract the dominant features behind the comparative advantage in exported products. Based on economic evidence and trade data, we place a restricted Indian Buffet Process on the distribution of countries' capability endowment, appealing to a culinary metaphor to model the process of capability acquisition. The approach comes with a unique level of interpretability, as it produces a concise and economically plausible description of the instantiated capabilities.

Cooperation dynamics of generalized reciprocity in state-based social dilemmas.

We introduce a framework for studying social dilemmas in networked societies where individuals follow a simple state-based behavioral mechanism based on generalized reciprocity, which is rooted in the principle "help anyone if helped by someone." Within this general framework, which applies to a wide range of social dilemmas including, among others, public goods, donation, and snowdrift games, we study the cooperation dynamics on a variety of complex network examples. By interpreting the studied model through the lenses of nonlinear dynamical systems, we show that cooperation through generalized reciprocity always emerges as the unique attractor in which the overall level of cooperation is maximized, while simultaneously exploitation of the participating individuals is prevented. The analysis elucidates the role of the network structure, here captured by a local centrality measure which uniquely quantifies the propensity of the network structure to cooperation by dictating the degree of cooperation displayed both at the microscopic and macroscopic level. We demonstrate the applicability of the analysis on a practical example by considering an interaction structure that couples a donation process with a public goods game.

Promoting cooperation by preventing exploitation: The role of network structure.

A growing body of empirical evidence indicates that social and cooperative behavior can be affected by cognitive and neurological factors, suggesting the existence of state-based decision-making mechanisms that may have emerged by evolution. Motivated by these observations, we propose a simple mechanism of anonymous network interactions identified as a form of generalized reciprocity-a concept organized around the premise "help anyone if helped by someone'-and study its dynamics on random graphs. In the presence of such a mechanism, the evolution of cooperation is related to the dynamics of the levels of investments (i.e., probabilities of cooperation) of the individual nodes engaging in interactions. We demonstrate that the propensity for cooperation is determined by a network centrality measure here referred to as neighborhood importance index and discuss relevant implications to natural and artificial systems. To address the robustness of the state-based strategies to an invasion of defectors, we additionally provide an analysis which redefines the results for the case when a fraction of the nodes behave as unconditional defectors.

The Impact of Services on Economic Complexity: Service Sophistication as Route for Economic Growth.

Economic complexity reflects the amount of knowledge that is embedded in the productive structure of an economy. By combining tools from network science and econometrics, a robust and stable relationship between a country's productive structure and its economic growth has been established. Here we report that not only goods but also services are important for predicting the rate at which countries will grow. By adopting a terminology which classifies manufactured goods and delivered services as products, we investigate the influence of services on the country's productive structure. In particular, we provide evidence that complexity indices for services are in general higher than those for goods, which is reflected in a general tendency to rank countries with developed service sector higher than countries with economy centred on manufacturing of goods. By focusing on country dynamics based on experimental data, we investigate the impact of services on the economic complexity of countries measured in the product space (consisting of both goods and services). Importantly, we show that diversification of service exports and its sophistication can provide an additional route for economic growth in both developing and developed countries.