Policy evaluation studies, which aim to assess the effect of an intervention, imply some statistical challenges:  real-world scenarios provide treatments which have not been assigned randomly 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 , under binary treatments. But many policy evaluation studies require complex treatments, such as multi-valued treatments . For instance, in political sciences , evaluating the impact of policies implemented by administrative entities often implies a multi-valued approach, as the general political stance towards a specific issue varies over many 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. Under multi-valued treatment, each unit is exposed to all levels of the treatment, due to the influence of his neighbors, according to the network weights. The estimation strategy is based on a joint multiple generalized propensity score and allows  to estimate direct effects, controlling for both individual and network covariates. We follow the proposed methodology to analyze the impact of  national immigration policy on crime rates . 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  is modeled by an appropriate indicator, that we call Interference Compound Index (ICI) . Results suggest that implementing  highly restrictive immigration policies leads to an increase of crime rates and the magnitude of estimated effects is stronger if we take into account multi-valued interference .
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 .
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scenarios provide treatments which have not been assigned randomly
settings treatments are not randomly assigned
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, under
; recent works focus primarily on
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However,
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require complex treatments, such as multi-valued treatments
deal with more complex interventions
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sciences
science
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multi-valued
multivariate
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the general political stance
a policy
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varies over many
operates at many different levels and can be defined along a number of
D
Under multi-valued treatment, each unit is exposed to all levels of the treatment, due to the influence of his neighbors, according to the network weights.
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one
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the
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crime rates
the crime rate
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country
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that we call Interference Compound Index (ICI)
summarizing their cultural and geographical proximity
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a
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policies
policy
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crime rates and the magnitude of
the crime rate and the
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stronger
larger
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multi-valued interference
interference from other countries