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 -e.g., 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. * Thanks to Vincent Arel-Bundock and Michael Ward for their helpful comments. All remaining errors are ours alone. Authors are listed in alphabetical order, equal authorship is implied.

Spatial interdependence and instrumental variable models

“…Finally, our results add to growing concerns over spatially dependent instruments. Cooperman (2017), for example, focuses on the difficulties in obtaining appropriate variance estimates, while Betz, Cook and Hollenbach (2018) highlights the tenuous identification assumptions underlying some of these instruments. Yet, while we have identified challenges to credible inference when using observational data -where spatial interdependence and endogeneity concerns often coincidence -we want to emphasize that we do not discourage analyses using these data.…”

“…If, for instance, the instrument is based on regional political or institutional shocks, such as waves of democratization (Stasavage, 2005) or membership in international institutions in neighboring countries (Büthe and Milner, 2008), the instrument is by construction measured at a higher level of aggregation than the endogenous predictor: the value of the instrument is identical or nearly identical for each of the observations within the cluster. At the same time, because these instruments rely on the argument that units are connected to each other, the resulting model is a strong contender for spatial interdependence in the outcome: it is difficult to argue convincingly for spatial patterns in the instrument while ruling out the same for the outcome variable (Betz, Cook and Hollenbach, 2018). 10 Similarly, many of the outcome variables of interest to political scientists cluster in regional patterns, such as democratization, economic growth, or policy choices.…”

Determinants of downside risk exposure of dairy farms

“…This implies that lagged values of scc, nal, ndb as well as the lagged values of the first calving age and veterinary expenditure constitute valid and relevant instruments. Note that the inclusion of lagged explanatory variables, or the use of these variables as instruments in a 2SLS framework, only purges estimates of endogeneity if i) autocorrelation among the residuals is not present (e.g., Ansell, 2008;Bellemare et al, 2017;Betz et al, 2018) and ii) if the lagged values are themselves not present as explanatory factors in the main equation (e.g., Reed, 2015). We therefore apply Arellano and Bond`s (1991) AR test which is particularly suited to assess the presence of autocorrelation in the residuals of 2SLS estimations.…”

On the Use and Abuse of Spatial Instruments

“…3We list the articles in the Online Appendix (Betz, Cook, and Hollenbach 2017). The use of spatial instruments is positively correlated ( ) with a time trend.…”