We address the problem of clearing mutual obligations among agents when a financial network collapses. To do so, we adopt an axiomatic approach and provide the first comprehensive characterization of the rules based on the principle of proportionality, covering the entire domain of financial systems. While a previous attempt by Csóka and Herings (2021) tackled this issue in a context where agents have strictly positive initial endowments, we show that their properties do not fully capture the set of proportional rules when extended to the full financial systems' domain. To overcome this limitation, we introduce new properties that emphasize the value of equity of the firms in the network. We show that a clearing mechanism satisfies compatibility, limited liability, absolute priority, equity continuity, and non-manipulability by clones if and only if each agent receives a payment proportional to the value of their claims. This characterization holds in the framework studied by Csóka and Herings (2021)

Economic globalization has led to production increasingly becoming concentrated in certain re- gions and countries of the world.

This article develops an accounting framework to provide the trends for the contribution of countries to global gross domestic production (GDP). In particular, the method transforms the multiregional input-output model to quantify the relative importance of individual economies to world GDP. The proposal uses a world input-output database that distinguishes between three main economic areas: China, the United States of America and the European Union.

In today's financial markets traders have access to competing trading venues with different levels of transparency for buying or selling assets. In addition to transparent exchanges, market participants can also trade in opaque trading venues such as dark pools. In December 2022, dark pools accounted for 13.75% of the US equity volume in the United States, and 7.50% of the total value traded in European markets. Dark pools often foster price improvement in relation to exchanges, but pose execution risks. In this context, information asymmetries play a fundamental role in investors' decision of where to trade and in the price discovery process. Therefore, a better understanding of the competition between an exchange and a dark pool with the presence of asymmetric information is essential.

In this note, we investigate the relationship between non-manipulability via merging (splitting) and strong non-manipulability via merging (splitting). Our analysis reveals that while these two non- manipulability axioms are generally not equivalent, they do coincide when the principle of solidarity is satisfied. This principle is fulfilled by a wide range of bankruptcy rules, including parametric rules. It remains open to investigate if there are rules satisfying non-manipulability via merging (splitting) and consistency but neither strong non-manipulability via merging (splitting) nor resource monotonicity. Although our intuition is that it is, this is a challenging problem since most classical bankruptcy rules exhibit resource monotonicity.

Productivity and High Growth Enterprises: resilience and recovery from the COVID-19 pandemic

The impact of crises on firm performance has been studied widely. This paper explores the relationship between firms' reaction to COVID-19 (in employment) and the adoption of digital technologies, taking into account their productivity, digitalisation level and high-growth episodes before the crisis. We match the EIB Group Survey of Investment and Investment Finance with ORBIS database for 27 EU Member States and the United Kingdom. We find that firms with higher productivity levels are less prone to decrease the number of employees in the short and long term due to the pandemic.

High-growth enterprises are less likely to expect a reduction in the number of employees in the long term. Moreover, firms in highly digitalised sectors have a lower probability to reduce the number of employees. Finally, our results suggest that COVID-19 leads firms to increase their use of digital technologies, especially those that were already more digitalised.