Computational Issues in the Estimation of the Spatial Probit Model: A Comparison of Various Estimators.

Saved in:

Bibliographic Details
Title:	Computational Issues in the Estimation of the Spatial Probit Model: A Comparison of Various Estimators.
Authors:	Billé, Anna Gloria¹ ag.bille@unich.it
Source:	Review of Regional Studies. 2013, Vol. 43 Issue 2/3, p131-152. 22p. 1 Diagram, 6 Charts, 2 Graphs.
Subject Terms:	*Algorithms, Sparse matrices, Social aspects, Mathematical statistics, Parameter estimation, Quantitative research
Abstract:	In spatial discrete choice models the spatial dependent structure adds complexity in the estimation of parameters. Appropriate general method of moments (GMM) estimation needs inverses of n-by-n matrices and an optimization complexity of the moment conditions for moderate to large samples makes practical applications more difficult. Recently, Klier and McMillen (2008) have proposed a linearized version of the GMM estimator that avoids the infeasible problem of inverting n-by-n matrices when employing large samples. They show that standard GMM reduces to a nonlinear two-stage least squares problem. On the other hand, when we deal with full maximum likelihood (FML) estimation, a multidimensional integration problem arises and a viable computational solution needs to be found. Although it remains somewhat computationally burdensome, since the inverses of matrices dimensioned by the number of observations have to be computed, the ML estimator yields the potential advantage of efficiency. Therefore, through Monte Carlo experiments we compare GMM-based approaches with ML estimation in terms of their computation times and statistical properties. Furthermore, a comparison in terms of the marginal effects also is included. Finally, we recommend an algorithm based on sparse matrices that enables more efficient use of both ML and GMM estimators. [ABSTRACT FROM AUTHOR]
	Copyright of Review of Regional Studies is the property of Southern Regional Science Association Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database:	Education Research Complete

Description
Abstract:	In spatial discrete choice models the spatial dependent structure adds complexity in the estimation of parameters. Appropriate general method of moments (GMM) estimation needs inverses of n-by-n matrices and an optimization complexity of the moment conditions for moderate to large samples makes practical applications more difficult. Recently, Klier and McMillen (2008) have proposed a linearized version of the GMM estimator that avoids the infeasible problem of inverting n-by-n matrices when employing large samples. They show that standard GMM reduces to a nonlinear two-stage least squares problem. On the other hand, when we deal with full maximum likelihood (FML) estimation, a multidimensional integration problem arises and a viable computational solution needs to be found. Although it remains somewhat computationally burdensome, since the inverses of matrices dimensioned by the number of observations have to be computed, the ML estimator yields the potential advantage of efficiency. Therefore, through Monte Carlo experiments we compare GMM-based approaches with ML estimation in terms of their computation times and statistical properties. Furthermore, a comparison in terms of the marginal effects also is included. Finally, we recommend an algorithm based on sparse matrices that enables more efficient use of both ML and GMM estimators. [ABSTRACT FROM AUTHOR]
ISSN:	0048749X
DOI:	10.52324/001c.8088