W

In spatial econometrics, W refers to the matrix that weights the value of the spatially lagged variable of other units. As unimportant as it may appear, W specifies, or at least ought to specify, why and how other units of analysis affect the unit under observation. We show that theory must inform five crucial specification choices taken by researchers. Specifically, the connectivity variable employed in W must capture the causal mechanism of spatial dependence. The specification of W further determines the relative relevance of source units from which spatial dependence emanates and whether receiving units are assumed identically or differentially exposed to spatial stimulus. Multiple dimensions of spatial dependence can be modelled as independent, substitutive or conditional links. Finally, spatial effects need not go exclusively in one direction, but can be bi-directional instead, with recipients simultaneously experiencing positive spatial dependence from some sources and negative dependence from others. The importance of W stands in stark contrast to applied researchers typically employing crude proxy variables for true connectivity such as geographical proximity and adopting standard modelling convention for specifying W rather than substantive theory. We demonstrate which assumptions convention imposes on specification choices and argue that theories of spatial dependence will often conflict with them