Comparison of Maximum Likelihood and Generalized
Method of Moments in Spatial Autoregressive Model
with Heteroskedasticity
Rohimatul Anwar
1
, Anik Djuraidah
2
, Aji Hamim Wigena
3
{rohimatul_anwar@apps.ipb.ac.id
1
, anikdjuraidah@apps.ipb.ac.id
2,
aji_hw@apps.ipb.ac.id
3
}
Student of DepartementStatistics, IPB University, Bogor, 16680, Indonesia
1
Lecturer of DepartementStatistics, IPB University, Bogor, 16680, Indonesia
2,3
Abstract.Spatial dependence and spatial heteroskedasticity are problems in spatial
regression. Spatial autoregressive regression (SAR) concerns only to the dependence on
lag. The estimation of SAR parameters containingheteroskedasticityusing the maximum
likelihood estimation (MLE) method provides biased and inconsistent. The alternative
method is the generalized method of moments (GMM). GMM uses a combination of
linear and quadratic moment functions simultaneously so that the computation is easier
than MLE. The bias is used to evaluate the GMM in estimating parameters of SAR
model with heteroskedasticity disturbances in simulation data. The results show that
GMM provides the bias of parameter estimates relatively consistent and smaller
compared to the MLE method.
Keywords: Heteroskedasticity, spatial autoregressive, maximum likelihood, generalized
moment method.
1 Introduction
Spatial dependence and spatial heteroskedasticity are problems inspatial data [1]. Lesage
[2] stated that spatial dependence can be described in regression models, such as
autoregressive response, error, or both. Models with dependencies in response are called
spatial autoregressive models (SAR).Fotheringham[3] stated that spatial heteroskedasticity can
be described using geographically weighted regression (GWR).
Ord [4] considered the maximum likelihood (ML) for the estimation of the regression
model. Kelejian and Prucha [5]extended that the MLE estimator is inconsistent in
heteroskedasticity disturbances. Anselin[1] introduced the two-stage least squares (S2SLS)
method. Kelejian and Prucha [6] introduced the generalized method of moments (GMM).
GMM does not require a distribution assumption of the disturbance andcomputationally easier
than the ML methods [7].
The results of Kelejian and Prucha’s research [5] showed that the estimation method is
valid if the assumption of errors is stochastic and identical normal. However,
heteroscedasticitycan occur in aggregation data. In this case,heteroskedasticity originates from
a data averaging process with many different observations at the time of aggregation [6].
Kelejian and Prucha [7]developed the GMM method into a robust form that has been proven
to be consistent if there is heteroskedasticity. Combination of linear and quadratic in moment
functionsare simultaneously assumed by GMM.
ICSA 2019, August 02-03, Bogor, Indonesia
Copyright © 2020 EAI
DOI 10.4108/eai.2-8-2019.2290489