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The paper introduces an approach to identify a set of spatially constrained homogeneous areas maximally homogeneous in terms of epidemic trends. The proposed hierarchical algorithm is based on the Dynamic TimeWarping distances between epidemic time trends where units are constrained by a spatial proximity graph. The paper includes two different applications of this approach to Italy, based on different data (number of positive test and number of differential deaths, with respect to the previous years) and on different observational units (provinces and Labour Market Areas). Both applications, above all the one related to Labour Market Areas, show the existence of well-defined areas, where the dynamics of growth of the infection have been strongly differentiated. The adoption of the same lock-down policy throughout the entire national territory has been therefore sub-optimal, showing once again the urgent need for local data-driven policies., Comment: Preliminary version

Sampling from very large spatial populations is challenging. The solutions suggested in recent literature on this subject often require that the randomly selected units are well distributed across the study region by using complex algorithms that have the feature, essential in a design-based framework, to respect the fixed first-order inclusion probabilities for every unit of the population. The size of the frame, $N$, often causes some problems to these algorithms since, being based on the distance matrix between the units of the population, have at least a computational cost of order $N^2$. In this paper we propose a draw-by-draw algorithm that randomly selects a sample of size $n$ in exactly $n$ steps, updating at each step the selection probability of not-selected units depending on their distance from the units already selected in the previous steps. The performance of this solution is compared with those of other methods derived from the {\it spatially balanced sampling} literature in terms of their root mean squared error (RMSE) using the simple random sampling (SRS) without replacement as benchmark. The fundamental interest is not only to evaluate the efficiency of a such different procedure, but also to understand if similar results can be obtained even with a notable reduction in the computational burden needed to obtain more efficient sampling designs. Repeated sample selections on real and simulated populations support this perspective. An application to the Land Use and Land Cover Survey (LUCAS) 2012 data-set in an Italian region is presented as a concrete and practical illustration of the capabilities of the proposed sample selection method.

Empirical analysis in economics often faces the difficulty that the data is correlated and heterogeneous in some unknown form. Spatial parametric approaches have been widely used to account for dependence structures, but the problem of directly deal with spatially varying parameters has been largely unexplored. The problem can be serious in all those cases in which we have no prior information justified by the economic theory. In this paper we propose an algorithm-based procedure which is able to endogenously identify structural breaks in space. The proposed algorithm is illustrated by using two well known house price data sets.

We exploit the information derived from geographical coordinates to endogenously identify spatial regimes in technologies that are the result of a variety of complex, dynamic interactions among site-specific environmental variables and farmer decision making about technology, which are often not observed at the farm level. Controlling for unobserved heterogeneity is a fundamental challenge in empirical research, as failing to do so can produce model misspecification and preclude causal inference. In this article, we adopt a two-step procedure to deal with unobserved spatial heterogeneity, while accounting for spatial dependence in a cross-sectional setting. The first step of the procedure takes explicitly unobserved spatial heterogeneity into account to endogenously identify subsets of farms that follow a similar local production econometric model, i.e. spatial production regimes. The second step consists in the specification of a spatial autoregressive model with autoregressive disturbances and spatial regimes. The method is applied to two regional samples of olive growing farms in Italy. The main finding is that the identification of spatial regimes can help drawing a more detailed picture of the production environment and provide more accurate information to guide extension services and policy makers.