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Policy evaluation studies, which intend to assess the effect of anintervention, face some statistical challenges: in real-world settingstreatments are not randomly assigned and the analysis might be furthercomplicated by the presence of interference between units. Researchers havestarted to develop novel methods that allow to manage spillover mechanisms inobservational studies; recent works focus primarily on binary treatments.However, many policy evaluation studies deal with more complex interventions.For instance, in political science, evaluating the impact of policiesimplemented by administrative entities often implies a multivariate approach,as a policy towards a specific issue operates at many different levels and canbe defined along a number of dimensions. In this work, we extend thestatistical framework about causal inference under network interference inobservational studies, allowing for a multi-valued individual treatment and aninterference structure shaped by a weighted network. The estimation strategy isbased on a joint multiple generalized propensity score and allows one toestimate direct effects, controlling for both individual and networkcovariates. We follow the proposed methodology to analyze the impact of thenational immigration policy on the crime rate. We define a multi-valuedcharacterization of political attitudes towards migrants and we assume that theextent to which each country can be influenced by another country is modeled byan appropriate indicator, summarizing their cultural and geographicalproximity. Results suggest that implementing a highly restrictive immigrationpolicy leads to an increase of the crime rate and the estimated effects islarger if we take into account interference from other countries.

Modelling Network Interference with Multi-valued Treatments: the Causal Effect of Immigration Policy on Crime Rates