On the Use and Abuse of Spatial Instruments

Abstract

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.

Spatial interdependence and instrumental variable models

“…Our discussion adds to growing concerns over spatially dependent instruments (Cooperman 2017; Betz, Cook and Hollenbach 2018). While we have identified challenges to credible inference using observational data, we emphasize that we do not discourage analyses using these data.…”

A Monte Carlo analysis of false inference in spatial conflict event studies

“…Answering this question adds to a continuously growing literature on the abilities and limitations of spatial methods in the social sciences [ 16 , 17 ]. This paper proceeds as follows: First, we briefly document the prevalence of high-profile studies that rely on SEA designs.…”

Revisiting firm flexibility and efficiency: evidence from the EU dairy processing industry

“…The relevance of selected instruments is assessed using the minimum eigenvalue statistic (Cragg and Donald, 1993) which in all cases rejects the null hypothesis of weak instruments. Note that using lagged explanatory variables as instruments only mitigates endogeneity in the case of no first-order autocorrelation in the residuals (e.g., Bellemare et al, 2017;Betz et al, 2018) and if lagged variables are themselves not relevant explanatory factors in the main equation (e.g., Reed, 2015). We, therefore, use the Arellano and Bond (1991) AR test which is particularly suited to detect autocorrelation in the residuals of 2SLS regressions.…”