This paper aims at investigating empirically whether and to what extent the containment measures adopted in Italy had an impact in reducing the diffusion of the COVID-19 disease across provinces. For this purpose, we extend the multivariate time-series model for infection counts proposed in Paul and Held (Stat Med 30(10):118–1136, 2011) by augmenting the model specification with B-spline regressors in order to account for complex nonlinear spatio-temporal dynamics in the propagation of the disease. The results of the model estimated on the time series of the number of infections for the Italian provinces show that the containment measures, despite being globally effective in reducing both the spread of contagion and its self-sustaining dynamics, have had nonlinear impacts across provinces. The impact has been relatively stronger in the northern local areas, where the disease occurred earlier and with a greater incidence. This evidence may be explained by the shared popular belief that the contagion was not a close-to-home problem but rather restricted to a few distant northern areas, which, in turn, might have led individuals to adhere less strictly to containment measures and lockdown rules.

Many studies have analyzed empirically the determinants of survival for innovative startup companies using data about the characteristics of entrepreneurs and management or focusing on firm- and industry-specific variables. However, no attempts have been made so far to assess the role of the environmental sustainability of the production process. Based on data describing the characteristics of the Italian innovative startups in the period 2009–2018, this article studies the differences in survival between green and non-green companies. We show that, while controlling for other confounding factors, startups characterized by a green production process tend to survive longer than their counterparts. In particular, we estimate that a green innovative startup is more than twice as likely to survive than a non-green one. This evidence may support the idea that environmental sustainability can help economic development.

The spatial concentration of firms has long been a central issue in economics under both the theoretical and the applied point of view mainly due to the important policy implications. A popular approach to its measurement, which does not suffer from the problem of the arbitrariness of the regional boundaries, makes use of micro data and looks at the firms as if they were dimensionless points distributed in the economic space. However, in practical circumstances the points (firms) observed in the economic space are far from being dimensionless and are conversely characterized by different dimension in terms of the number of employees, the product, the capital, and so on. In the literature, the works that originally introduce such an approach disregard the aspect of the different firm dimension and ignore the fact that a high degree of spatial concentration may result from the case of both many small points clustering in definite portions of space and only few large points clustering together (e.g., few large firms). We refer to this phenomenon as clustering of firms and clustering of economic activities. The present article aims at tackling this problem by adapting the popular K-function to account for the point dimension using the framework of marked point process theory.