Fiscal decentralization as an instrument to reduce poverty is an open debate that still takes place with little and contradictory empirical evidence regarding whether or not it has served the poor. This paper focuses on analyzing the impact of municipalities’ per capita property tax revenues on multidimensional poverty in the Colombian case. This locally raised tax is used as an indicator of the state capacity that municipalities exercise when fiscal decentralization takes place. To estimate its impact on poverty, we control for the possible endogeneity biases that might affect this relationship while taking into account that multidimensional poverty exhibits strong spatial correlation among Colombian municipalities. We find statistically significant results that demonstrate a causal and diminishing effect of property tax revenues on the poverty headcount ratio and gap. We also find that this effect has substantial spillovers across municipalities. The findings of the paper highlight the need to strengthen subnational revenue systems through policy designs to increase locally raised revenues. We simulate four different counterfactual scenarios to evaluate the potential effect of alternative policy designs on multidimensional poverty. The results of these policy scenarios demonstrate that spatially differentiated policy schemes have greater effectiveness in reducing multidimensional poverty than geographically mute designs.