Abstract
Spatial autoregressive (SAR) and related models offer flexible yet parsimonious ways to model spatial and network interactions. SAR specifications typically rely on a particular parametric functional form and an exogenous choice of the so-called spatial weight matrix with only limited guidance from theory in making these specifications. The choice of a SAR model over other alternatives, such as spatial Durbin (SD) or spatial lagged X (SLX) models, is often arbitrary, raising issues of potential specification error. To address such issues, this paper develops a new specification test within the SAR framework that can detect general forms of misspecification including that of the spatial weight matrix, the functional form and the model itself. Our approach relates to the conditional moment test framework of Bierens (1982, 1990) but introduces modifications needed by the spatial setting to achieve test consistency. A central element in spatial matrix specification testing is the infinite dimensional endogeneity induced by spatial linkages. This complexity is addressed by introducing a new component to the omnibus test that captures the effects of potential spatial matrix misspecification. With this modification the approach leads to a simple pivotal test procedure with standard critical values. We derive the asymptotic distribution of our test statistic under the null hypothesis of correct SAR specification and show consistency of the test. A Monte Carlo study is conducted to study finite sample performance of the test. An empirical illustration on the performance of our test in the modelling of tax competition in Finland and Switzerland is included.
Replication Files