The method of computing the Log-Jacobian of the variable transformation for spatial models - test and comments

Abstract

One of the most important problems in spatial econometrics is the compu- tation of the log of the Jacobian of variable transformations in models with spatial inter- actions. The computation is necessary in ML estimation and Bayesian analysis of models with spatial dependence (Smirnov and Anselin 2009). The effectiveness of the implementation of ML depends on computing effectiveness of the log-determinant of a matrix, especially for sparse and large matrices. The second problem is the numerical accuracy of computation of the log-determinant using different methods as it was shown by Walde et al. (2008). These issues provoked a search of new methods of estimation for spatial models. One of them is GMM being easier but more restrictive for computation than ML (Lee 2004, 2007). Another solution is to make some simplifications based on regular grids or band matrices (Rue, Held 2005). In the paper we test and comment the method of computing the log-Jacobian of the variable transformation for models with spatial interactions, suggested by Smirnov and Anselin (2009), for some practical case studies.