What is an appropriate welfare measure for efficiency of local public policies inducing migration?

We demonstrate what welfare measure should be used for local public policies inducing migration. We show that the two conventional definitions of welfare measures having equivalency with compensation testing in a single-location economy without externalities have inconsistencies with compensation testing in a spatial economy: one definition has no equivalency with compensation testing even without externalities, and the other definition has difficulties arising from a problem in which the measure before a project has a non-zero value. Finally, we demonstrate that a specific welfare measure defined by Wheaton (1977) has appropriate properties with compensation testing in both cases with and without externalities.