Three essays on econometrics: Network estimators with applications and assessment of the effects of Covid-19 pandemic

This thesis is a collection of the three research papers that I developed during my PhD. The first part, which includes the first two of them, aims to develop estimators of network structures from observations of a random vector whose components represent the variables of interest and are the nodes in a network. The goal is to reconstruct a (weighted) graph when we are not able to directly observe connections among variables. The first paper focuses on random vectors with multivariate Gaussian distribution. In this specific case, a graph embedding the conditional dependencies can be obtained from the precision matrix, which is the inverse of the covariance matrix. Furthermore, by a proper re-scaling of this matrix, it is possible to derive a weighted network of partial correlations. Three estimators are proposed and their performances are compared using simulations by looking at two performance measures, F1-score and Frobenius distance. They use elastic net penalty to shrink, possibly to 0, the parameters that must be estimated, which are the elements in the precision matrix, thus allowing to obtain a sparse graph. Simulations results suggest that the best estimator may depend on the sample size and on the underlying network structure. Furthermore, elastic net penalty seems to have some advantage with respect to LASSO, another well-known penalty, in highly correlated scenarios. Finally, one of the three estimators is used to reconstruct the set of relations among economic sectors in United States using market data, which is then studied using network analysis tools. In the second paper, the multivariate Gaussian assumption is relaxed considering instead the multivariate t-Student distribution as the joint distribution with heavier tails. A new estimator of a partial correlations network is introduced as a combination of a well-known estimator in the literature and one of the three estimators based on elastic penalty studied in the first paper. Using again a simulation approach, several estimators are compared testing both different underlying distributions of data and several underlying network structures. Results show that the proposed estimator has relatively good performance and it is robust to various distributional misspecifications. Then, it is used to reconstruct the network among a set of large European banks using stock prices. Possibly, this network has an important role for better understanding systemic risk in the banking sector, and more broadly, in the financial system. The second part focuses on the assessment of the impact of the Covid-19 pandemic in Trentino using electricity consumption data. Two methods are proposed: the first one models the trend and seasonality and looks at the deviations during pandemic periods, while the second one employs a difference-in-difference approach to estimate the variations with respect to a non-pandemic scenario. The impact is analyzed both at the aggregated and at macro-sectoral level. Results suggest heterogeneous effects both in terms of magnitude and in terms of dynamic response to the pandemic by the different macro-sectors, with the majority of statistically significant effects being negative.