A0570
Title: Endogenous weights in spatial autoregression with unit root
Authors: Francesca Rossi - University of Verona (Italy)
Offer Lieberman - Bar-Ilan Univesity (Israel)
Jungyoon Lee - Royal Holloway, University of London (United Kingdom) [presenting]
Abstract: Spatial models are generally specified in terms of exogenous weighting matrices. When the exogeneity assumption is not satisfied, typical model specifications and conventional estimation procedures are no longer valid. In this paper we establish asymptotic theory for a spatial autoregressive (SAR) model where the network structure is possibly endogenous and the spatial parameter can be less than or equal to unity. We extend the work in Qu and Lee (2015) along the lines in Johnsson and Moon (2021). Importantly, we verify that the widely used spatial instrument variable (IV), of e.g. Kelejian and Prucha (1998), no longer works asymptotically for the spatial unit root case and provide a novel IV that can offer a unified approach to estimation over the extended parameter range. Consistency of the two stage least squares estimators is proven and the asymptotic distribution is derived, including in the case of the spatial unit root. We also provide a test of exogeneity of the weight matrix. Simulations verify the analytical results. Finally, an empirical application based on Airbnb data is also presented
