This paper develops limited and full information estimators for a simultaneous panel data model with spatial lags on the dependent variables and spatially autocorrelated error processes in the form of spatial autoregressive or spatial moving average processes. The spatial error components are estimated with various generalized moment procedures. Monte Carlo experiments show that the proposed estimators outperform traditional estimators and also provide results on the impact of misspecifying the error process. We illustrate the various estimators on an empirical example pertaining to competition in current and capital expenditure between French municipalities in the capital region of Ile-de-France.