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A Primer for Spatial EconometricsAlternative Model Specifications for Big Datasets

A Primer for Spatial Econometrics: Alternative Model Specifications for Big Datasets [In Chapters 3 and 4 we have presented a series of estimation techniques for the general spatial econometric linear model which can basically be traced back to the two paradigms of the Maximum Likelihood and the Generalized Two-Stage Least Squares. In particular, when discussing the Maximum Likelihood approach we pointed out that the likelihood functions cannot be maximized analytically due to a high degree of non-linearity in the parameters and so we have to use numerical approximations. However, the likelihood function involves the calculation of the determinant of a matrix whose dimension depends on the sample size and that has to be evaluated repeatedly for each trial value of the spatial correlation parameter in a numerical search. If n is very large, as often happens in many empirical applications with a massive quantity of data, this operation may be highly demanding, if not prohibitive. The eigenvalues decomposition suggested by Ord (1975) and used for many years in the literature (see section 3.4.3) also has some limitations. Indeed, Kelejian and Prucha (1998) report that the computation of eigenvalues by standard subroutines for general non-symmetric matrices, are also approximate and may already be highly inaccurate for W matrices that are of the order 400-by-400, that is, for relatively small sample sizes.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Primer for Spatial EconometricsAlternative Model Specifications for Big Datasets

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References (29)

Publisher
Palgrave Macmillan UK
Copyright
© Palgrave Macmillan, a division of Macmillan Publishers Limited 2014
ISBN
978-1-137-42816-5
Pages
167 –201
DOI
10.1057/9781137317940_5
Publisher site
See Chapter on Publisher Site

Abstract

[In Chapters 3 and 4 we have presented a series of estimation techniques for the general spatial econometric linear model which can basically be traced back to the two paradigms of the Maximum Likelihood and the Generalized Two-Stage Least Squares. In particular, when discussing the Maximum Likelihood approach we pointed out that the likelihood functions cannot be maximized analytically due to a high degree of non-linearity in the parameters and so we have to use numerical approximations. However, the likelihood function involves the calculation of the determinant of a matrix whose dimension depends on the sample size and that has to be evaluated repeatedly for each trial value of the spatial correlation parameter in a numerical search. If n is very large, as often happens in many empirical applications with a massive quantity of data, this operation may be highly demanding, if not prohibitive. The eigenvalues decomposition suggested by Ord (1975) and used for many years in the literature (see section 3.4.3) also has some limitations. Indeed, Kelejian and Prucha (1998) report that the computation of eigenvalues by standard subroutines for general non-symmetric matrices, are also approximate and may already be highly inaccurate for W matrices that are of the order 400-by-400, that is, for relatively small sample sizes.]

Published: Nov 9, 2015

Keywords: Directional Bias; Spatial Error Model; Spatial Econometric; Spatial Spillover; Lattice Grid

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