Network Structure and the Estimation of Spatial Autoregressive Parameters

Despite a well-known overlap and common origins between spatial econometrics and statistical network modelling, the two literatures have developed separately such that core concerns in one tend to be ignored in the other. While spatial econometrics focuses on node features, taking the network as exogenous, statistical network modelling focuses on tie features and network structure. This study focuses on the importance of network structure for the performance of estimators for the spatial autoregressive and the spatial error model. In Monte Carlo studies of the relative performance of different estimators in spatial econometrics (e.g. Calabrese and Elkink, 2014), the spatial contiguity matrix is typically based on highly regular network structures, with low variation in degree between nodes and high connectivity, for example by using a random geometric network (Dall and Christensen, 2002). I argue that the structure of the network affects the amount of information available in the estimation of the spatial coefficient. Using simulated networks (Morris, Handcock and Hunter, 2008), I construct random networks that vary in terms of levels of clustering, connectedness, density of ties, degree distribution, and other common characteristic statistics on network structures, and generate data assuming varying levels of spatial clustering in the node features. I then evaluate through simulation the performance of standard linear and binary spatial econometric models in terms of the estimation of spatial autoregressive and spatial error coefficients, as well as coefficients on covariates. Calabrese, Raffaella and Johan A. Elkink. 2014. "Estimators of binary spatial autoregressive models: A Monte Carlo study." Journal of Regional Science 54(4):664–687. Dall, Jesper and Michael Christensen. 2002. "Random Geometric Graphs." Physical Review E. Statistical, Nonlinear, and Soft Matter Physics 66(1). Morris, Martina, Mark S. Handcock and David R. Hunter. 2008. "Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects." Journal of Statistical Software 24(4).