Publication Date: August 2020
Spatial autoregressive (SAR) and related models oﬀer flexible yet parsimonious ways to model spatial or network interaction. 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 an omnibus speciﬁcation test within the SAR framework that can detect general forms of misspeciﬁcation including that of the spatial weight matrix, functional form and the model itself. The approach extends the framework of conditional moment testing of Bierens (1982, 1990) to the general spatial setting. 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.
Keywords: Conditional moment test, Misspecification test, Omnibus testing, Spatial AR, Weight matrix misspecification
JEL Classification Codes: C21, C23