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

Policy evaluation studies, which intend to assess the effect of an intervention, face some statistical challenges: in real-world settings treatments are not randomly assigned and the analysis might be further complicated by the presence of interference between units. Researchers have started to develop novel methods that allow to manage spillover mechanisms in observational 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 policies implemented by administrative entities often implies a multivariate approach, as a policy towards a specific issue operates at many different levels and can be defined along a number of dimensions. In this work, we extend the statistical framework about causal inference under network interference in observational studies, allowing for a multi-valued individual treatment and an interference structure shaped by a weighted network. The estimation strategy is based on a joint multiple generalized propensity score and allows one to estimate direct effects, controlling for both individual and network covariates. We follow the proposed methodology to analyze the impact of the national immigration policy on the crime rate. We define a multi-valued characterization of political attitudes towards migrants and we assume that the extent to which each country can be influenced by another country is modeled by an appropriate indicator, summarizing their cultural and geographical proximity. Results suggest that implementing a highly restrictive immigration policy leads to an increase of the crime rate and the estimated effects is larger if we take into account interference from other countries.