On the Use and Abuse of Spatial Instruments

Instruments based on realizations of the endogenous variable in other units—for instance, regional or global weighted averages—are commonly used in political science. Such spatial instruments have proved attractive: they are convenient to obtain, typically have power, and are plausibly exogenous. We argue that the assumptions underlying spatial instruments remain poorly understood and challenge whether spatial instruments can satisfy the conditions required for valid instruments. First, when cross-unit dependence exists in the endogenous predictor, other cross-unit relationships—spillovers and interdependence—likely exist as well and risk violations of the exclusion restriction. Second, spatial instruments produce simultaneity in the first-stage equation, as left-hand side outcomes are included as right-hand side predictors. Because the instrument and the endogenous variable are simultaneously determined, the exclusion restriction is, necessarily and by construction, violated. Taken together, these concerns lead us to conclude that spatial instruments are rarely, if ever, valid.