Estimation of the spatial weights matrix under structural constraints

Abstract

While estimates of models with spatial interaction are very sensitive to the choice of spatial weights, considerable uncertainty surrounds de…nition of spatial weights in most studies with cross-section dependence. We show that, in the spatial error model the spatial weights matrix is only partially identi…ed, and is fully identi…ed under the structural constraint of symmetry. For the spatial error model, we propose a new methodology for estimation of spatial weights under the assumption of symmetric spatial weights, with extensions to other important spatial models. The methodology is applied to regional housing markets in the UK, providing an estimated spatial weights matrix that generates several new hypotheses about the economic and socio-cultural drivers of spatial di¤usion in housing demand.

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.…”

“…In comparison with (1.1), there are no regressors X . Further, since W is unknown in the current context, λ and W are not separately identified, and therefore without loss of generality, we set λ ≡ 1 (Bhattacharjee and Jensen-Butler 2013). The reduced form of (2.1) is Y t = (I − W ) −1 t .…”

“…In this context, estimation of spatial weights can be particularly useful. Bhattacharjee and Jensen-Butler (2013) show that, in a spatial lag or spatial error model, W is only partially identified from an estimated spatial variance-covariance matrix. Hence, additional structural assumptions are required for inference, and empirical verification of these assumptions is an important research question.…”

“…Hence, additional structural assumptions are required for inference, and empirical verification of these assumptions is an important research question. Beenstock and Felsenstein (2012) and Bhattacharjee and Jensen-Butler (2013) proposed estimation of W in a spatial panel setting under the assumption of symmetric spatial weights. Bhattacharjee and Holly (2011) and Pesaran and Tosetti (2011) discuss estimation in contexts where there is, in addition to stationary W -based spatial dependence, also spatial strong dependence modelled through a factor structure.…”

Land Bank 2.0: An Empirical Evaluation

“…A home's own price is excluded from the calculation by setting all values in the matrix diagonal to zero. The optimal specification of spatial weight matrices is an active area of research (Bhattacharjee and Jensen-Butler, 2013;Seya, Yamagata, and Tsutsumi, 2013;Gerkman and Ahlgren, 2014;Qu and Lee, 2015). Stakhovych and Bijmolt (2009) found that in simulated data, where the true data-generating process is known, selecting W using the Akaike information criterion (AIC) could reliably lead to models that accurately estimated regression coefficients.…”