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'.

Ornstein-Uhlenbeck process and generalizations: Particle dynamics under comb constraints and stochastic resetting.

The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It also tends to a drift towards its mean function, and such a process is called mean reverting. Two examples of the generalized Ornstein-Uhlenbeck process are considered. In the first one, we study the Ornstein-Uhlenbeck process on a comb model, as an example of the harmonically bounded random motion in the topologically constrained geometry. The main dynamical characteristics (as the first and the second moments) and the probability density function are studied in the framework of both the Langevin stochastic equation and the Fokker-Planck equation. The second example is devoted to the study of the effects of stochastic resetting on the Ornstein-Uhlenbeck process, including stochastic resetting in the comb geometry. Here the nonequilibrium stationary state is the main question in task, where the two divergent forces, namely, the resetting and the drift towards the mean, lead to compelling results in the cases of both the Ornstein-Uhlenbeck process with resetting and its generalization on the two-dimensional comb structure.

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.

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.

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.