Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models

This paper investigates a simultaneous equations spatial autoregressive model which incorporates simultaneity effects, own-variable spatial lags and cross-variable spatial lags as explanatory variables, and allows for correlation between disturbances across equations. In exposition, we also discuss a multivariate spatial autoregressive model that can be treated as a reduced form of the simultaneous equations model. We study parameter spaces, parameter identification, asymptotic properties of the quasi-maximum likelihood estimation, and computational issues. Monte Carlo experiments illustrate the advantages of the QML, broader applicability and efficiency, compared to instrumental variables based estimation methods in the existing literature.