W

In spatial econometrics,Wrefers to the matrix that weights the value of the spatially lagged variable of other units. As unimportant as it may appear,Wspecifies, or at least ought to specify, why and how other units of analysis affect the unit under observation. This article shows that theory must inform five crucial specification choices taken by researchers. Specifically, the connectivity variable employed inWmust capture the causal mechanism of spatial dependence. The specification ofWfurther determines the relative relevance of source units from which spatial dependence emanates, and whether receiving units are assumed to be identically or differentially exposed to spatial stimulus. Multiple dimensions of spatial dependence can be modeled as independent, substitutive or conditional links. Finally, spatial effects need not go exclusively in one direction, but can be bi-directional; recipients can simultaneously experience positive spatial dependence from some sources and negative dependence from others. The importance ofWstands in stark contrast to applied researchers’ typical use of crude proxy variables (such as geographical proximity) to measure true connectivity, and the practice of adopting standard modeling conventions rather than substantive theory to specifyW. This study demonstrates which assumptions these conventions impose on specification choices, and argues that theories of spatial dependence will often conflict with them.