When Space is Just a Nuisance: A Simple Solution for Spatial Dependence

(with Laron K. Williams)

Spatial autocorrelation is a ubiquitous phenomenon in cross-sectional data that poses notable challenges for statistical inference since unmodeled spatial dependence can cause common econometric methods to produce biased and inconsistent param- eter estimates. While political scientists so far predominantly rely on parametric spatial regression models, semiparametric spatial filtering techniques constitute a valuable alternative. By using the eigenfunction decomposition of a transformed connectivity matrix, the filtering approach generates a synthetic proxy variable from a linear combination of judiciously selected eigenvectors. Eigenvector selection is performed in a supervised or unsupervised fashion and different selection criteria can be employed. This synthetic variable acts as a surrogate for omitted spatial effects and removes spatial autocorrelation from the model residuals. This study introduces eigenvector-based spatial filtering to political science and discusses its strengths and limitations in comparison to parametric spatial models. Analyti- cal results and Monte Carlo simulations show that spatial filtering resolves spatial misspecification problems in regression models. Overall, this study concludes that this semiparametric approach constitutes a very flexible and intuitive strategy that requires only few assumptions. Given the widespread use of cross-sectional data, spatial filtering is applicable to a great variety of empirical analyses when space is just a nuisance. A new R package facilitates the application of this technique.

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