Maximum Likelihood Estimation of Spatially and Serially Correlated Panels With Random Effects: An Estimation Framework and a Software Implementation

I describe maximum likelihood estimation of panel models incorporating: random effects and spatial dependence in the error terms; and/or a spatially lagged dependent variable; and possibly also a serial dependence structure in the remainder of the error term. I derive an operational version of Anselin’s general estimation framework, discuss the computational challenges of estimation and describe an open source implementation in the R system for statistical computing. Applications of spatial panel models in the literature are usually restricted to the standard spatially autoregressive (SAR) and spa- tial error (SEM) models, possibly with random or fixed individual effects. While a combination as well as extensions of these models to richer correlation structures have been considered by methodologists, starting with Anselin who described a general estimation procedure, practical feasibility has been hampered by computational difficulties. This implementation allows estimating a complete taxonomy of panel models with a combination of spatial lags, spatial errors, serially correlated errors and random individual effects, distinguishing between two different specifications for the random effects (spatially correlated or not). Likelihood ratio and Wald tests for significance of the spatial lag and of any error covariance component are also available. I validate the estimation routines by means of Montecarlo simulations and finally illustrate the package functionalities by applying them to some well-known datasets from the literature.