Substitution Bias and the Construction of a Spatial Cost of Living Index

We estimate the spatial substitution bias based on the difference between a price index and the true cost of living. We estimate the substitution bias for several different geographical scales, using different base baskets and across several spending quartiles. Our results show a significant substitution bias for small geographic units. The choice of the base basket is relevant for the estimation of the bias. Finally, the spatial substitution bias is higher for higher level quartiles due to the heterogeneity in the consumption basket. This exercise shows how the spatial dimension modifies the construction of a price index. Moreover, the approach of fixed baskets (the axiomatic approach) should be carefully considered in the estimation of spatial price differentials.