Estimating Causal Effects of Multi-Valued Treatments Accounting for Network Interference: Immigration Policies and Crime Rates

Policy evaluation studies, which assess the effect of an intervention, face statistical challenges: in real-world settings treatments are not randomly assigned and the analysis might be complicated by the presence of interference among units. Researchers have started to develop methods that allow to manage spillovers in observational studies; recent works focus primarily on binary treatments. However, many studies deal with more complex interventions. For instance, in political science, evaluating the impact of policies implemented by administrative entities often implies a multi-valued approach, as a policy towards a specific issue operates at many levels and can be defined along multiple 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 relies on a joint multiple generalized propensity score and allows one to estimate direct effects, controlling for both individual and network covariates. We follow this methodology to analyze the impact of the national immigration policy on the crime rate, analyzing data of 22 OECD countries over a thirty-years time frame. We define a multi-valued characterization of political attitude towards migrants and we assume that the extent to which each country can be influenced by another country is modeled by an 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 effect is larger if we account for interference.