Оценка пространственных моделей с переменными коэффициентами пространственной чувствительности методом максимального правдоподобия и обобщенным методом наименьших квадратов

The traditional spatial lag model assumes that all regions in the sample exhibit the same degree of sensitivity to spatial external effects. This may not always be the case, however, especially with highly heterogeneous regions like those in Russia. Therefore, a model has been suggested that views spatial coefficients as being endogenously defined by regions’ intrinsic characteristics. We generalize this model, describe approaches to its estimation based on maximum likelihood and generalized least squares, and perform a Monte Carlo simulation of these two estimation methods in small samples. We find that the maximum likelihood estimator is preferable due to the lower biases and variances of the estimates it yields, although the generalized least squares estimator can also be useful in small samples for robustness checks and as a first approximation tool. In larger samples, results of the generalized least squares estimator are very close to those of the maximum likelihood estimator, so the former may be preferred because of its simplicity and less strict computational power requirements.