Efficiency of the OLS estimator in the vicinity of a spatial unit root

Martellosio, Federico

doi:10.1016/j.spl.2011.03.030

Cited by 10 publications

(5 citation statements)

References 28 publications

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“…Note that s does not depend on ρ except for a finite number of values of ρ (see Kato, 1995, p. 64). By Lemma A.1 in Martellosio (2011), the eigenspace of Σ −1 (λ −1 max ) associated to γ 1 (λ −1 max ) = 0 is equal to the eigenspace, say E λmax , of W associated to λ max . Assume now that g max = 1.…”

Section: Appendix a Proofsmentioning

confidence: 98%

The Correlation Structure of Spatial Autoregressions

Martellosio

2012

Econom. Theory

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This paper investigates how the correlations implied by a first-order simultaneous autoregressive (SAR(1)) process are affected by the weights matrix and the autocorrelation parameter. A graph theoretic representation of the covariances in terms of walks connecting the spatial units helps to clarify a number of correlation properties of the processes. In particular, we study some implications of row-standardizing the weights matrix, the dependence of the correlations on graph distance, and the behavior of the correlations at the extremes of the parameter space. Throughout the analysis differences between directed and undirected networks are emphasized. The graph theoretic representation also clarifies why it is difficult to relate properties of W to correlation properties of SAR(1) models defined on irregular lattices.

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Section: Appendix a Proofsmentioning

confidence: 98%

The Correlation Structure of Spatial Autoregressions

Martellosio

2012

Econom. Theory

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“…The efficiency of the OLS estimator was considered by Krämer and Donninger [40], Tilke [41] for the symmetric spatial weight matrices, and generalized by Krämer and Baltagi [42] with a broader covariance matrix. But the symmetry of the weight matrix is too restrictive to be used in practice, so Martellosio [43] generalizes this to nonsymmetric weights matrices. The efficiency of the OLS estimator is defined as η := .…”

Section: Estimation and Inferencementioning

confidence: 99%

A Survey of Spatial Unit Roots

Baltagi,

Shu

2024

Mathematics

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This paper conducts a brief survey of spatial unit roots within the context of spatial econometrics. We summarize important concepts and assumptions in this area and study the parameter space of the spatial autoregressive coefficient, which leads to the idea of spatial unit roots. Like the case in time series, the spatial unit roots lead to spurious regression because the system cannot achieve equilibrium. This phenomenon undermines the power of the usual Ordinary Least Squares (OLS) method, so various estimation methods such as Quasi-maximum Likelihood Estimate (QMLE), Two Stage Least Squares (2SLS), and Generalized Spatial Two Stage Least Squares (GS2SLS) are explored. This paper considers the assumptions needed to guarantee the identification and asymptotic properties of these methods. Because of the potential damage of spatial unit roots, we study some test procedures to detect them. Lastly, we offer insights into how to relax the compactness assumption to avoid spatial unit roots, as well as the relationship between spatial unit roots and other models, such as the Spatial Dynamic Panel Data (SDPD) model and Lévy–Brownian motion.

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“…In particular, OLS is considered to have unique advantages in exploring or modeling the relationship between multiple variables (Zhang et al, 2019). According to the existing research, OLS regression analysis can be used in the following three scenarios (Ceccato & Oberwittler, 2008;Martellosio, 2011;Yue et al, 2018):…”

Section: Ordinary Least Squares (Ols) Analysismentioning

confidence: 99%

Spatial Patterns and Development Characteristics of China's Postgraduate Education

Zhong

Zhang

2022

International Journal on Semantic Web and Information Systems

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Using four types of publicly available datasets and ArcGIS software, the authors identify the spatial characteristics of postgraduate education in China at three scales: comprehensive economic zone, provincial, and city. They also employ geographically weighted regression and ordinary least squares to study the factors influencing the spatial pattern of postgraduate education in Gin at the city scale. The findings show that the number of postgraduate education institutions increases as the longitude of a city increases, but the number decreases from coast to inland. Second, postgraduate education institutions tend to group together in provincial capitals and megacities. Finally, GDP, per capita GDP, population size, local income, and total retail sales of consumer goods significantly impact postgraduate education development. The study contributes to the literature and provides insights for practitioners in promoting urban planning and infrastructure development.

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Efficiency of the OLS estimator in the vicinity of a spatial unit root

Cited by 10 publications

References 28 publications

The Correlation Structure of Spatial Autoregressions

The Correlation Structure of Spatial Autoregressions

A Survey of Spatial Unit Roots

Spatial Patterns and Development Characteristics of China's Postgraduate Education

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