For each source sector, we estimate exposure impacts from emissions originating outside of each city by subtracting population-weighted concentrations caused by emissions within the city from total population-weighted concentrations. In this manner we obtain the fraction of total PM2.5 concentrations caused by within-city emissions as well as the fraction of total PM2.5 concentrations caused by different emission sources located either within or outside of the city. However, because the individual city simulations are typically at higher spatial resolution (as described above), in ~3% of the 1152 city-sector combinations the simulated concentrations caused by within-city emissions are greater than the simulated concentrations caused by all emissions, resulting in a negative contribution from out-of-city emissions. The median of those negative values is -0.0098 μg m -3 , and the largest value is -1.7 μg m -3 . In these cases, we set the concentrations caused by all emissions equal to the concentrations caused by within-city emissions, so that the contribution from out-of-city emissions equals zero.