A Two‐Stage Approach to Spatio‐Temporal Analysis with Strong and Weak Cross‐Sectional Dependence

Abstract

An understanding of the spatial dimension of economic and social activity requires methods that can separate out the relationship between spatial units that is due to the e¤ect of common factors from that which is purely spatial even in an abstract sense. The same applies to the empirical analysis of networks in general. We are able to distinguish between cross-sectional strong dependence and weak dependence. Strong dependence in turn suggests that there are common factors. We use cross unit averages to extract common factors and contrast this to a principal components approach widely used in the literature. We then use a multiple testing procedure to determine signi…cant bilateral correlations (signifying connections) between spatial units and compare this to an approach that just uses distance to determine units that are neighbours. We apply these methods to real house price changes at the level of Metropolitan Statistical Areas in the USA, and estimate a heterogeneous spatiotemporal model for the de-factored real house price changes and obtain signi…cant evidence of spatial connections, both positive and negative.

Causal ordering and inference on acyclic networks

“…The causal effects are positive in many cases, but negative in others. This feature of negative spillovers is also reported in other current research; see, for example, Bhattacharjee and Jensen-Butler (2013) and Bailey et al (2016). Further, Bhattacharjee and Holly (2013) suggest a measure for the influence of each unit within a network.…”

“…Bhattacharjee et al (2012) extend the above methods to pure cross section (spatial) data setting, and Bhattacharjee and Holly (2013) propose estimation under moment conditions drawing upon connections with the system GMM literature (Arellano and Bond 1991;Blundell and Bond 1998). Finally, Ahrens and Bhattacharjee (2015) and Bailey et al (2016) propose estimation under the assumption of a sparse spatial weights matrix. Most of the above inference methods are based on sample moments.…”

Advances in Spatial Econometrics: Parametric vs. Semiparametric Spatial Autoregressive Models

“…Using slightly different frameworks, Bai and Li (2015); Bailey et al (2016); Shi and Lee (2016); Vega and Elhorst (2016) consider a joint modeling of spatial interaction effects and common-shocks effects:…”

“…Bai and Li (2015); Shi and Lee (2016) use principle components to estimate common factors, while Bailey et al (2016); Vega and Elhorst (2016) follow Pesaran (2006) in using cross-sectional averages of y it and x it as observable proxies for f t . Bailey et al (2016) propose a two-stage estimation and inference strategy, whereby in the first step strong cross-sectional dependence is modeled by means of a factor model. Residuals from such factor models, referred to as de-factored observations, are then used to model the remaining weak cross dependencies, making use of spatial econometrics techniques.…”

“…Thus, the PS-ANOVA-SAR model works as an alternative to the models proposed by Bai and Li (2015); Bailey et al (2016); Pesaran and Tosetti (2011);Shi and Lee (2016); Vega and Elhorst (2016) based on extensions of common factor models to accommodate both strong crosssectional dependence (through the estimation of the spatio-temporal trend) and weak cross-sectional dependence (through the estimation of the ρ parameter). The advantage of the PS-ANOVA-SAR model lies in the fact that its ability to fully control for the residual cross-sectional dependence and to assess the presence of network effects net of common factor effects, is not crucially affected by the set of covariates included in the model.…”