Sensitivity analysis of SAR estimators: A numerical approximation

Arbeitspapier

Estimators of spatial autoregressive (SAR) models depend in a highly non-linear way on the spatial correlation parameter and least squares (LS) estimators cannot be computed in closed form. We first compare two simple LS estimators by distance and covariance properties and then we study the local sensitivity behavior of these estimators using matrix derivatives. These results allow us to calculate the Taylor approximation of the least squares estimator in the spatial autoregression (SAR) model up to the second order. Using Kantorovich inequalities, we compare the covariance structure of the two estimators and we derive efficiency comparisons by upper bounds. Finally, we demonstrate our approach by an example for GDP and employment in 239 European NUTS2 regions. We find a good approximation behavior of the SAR estimator, evaluated around the non-spatial LS estimators. These results can be used as a basis for diagnostic tools to explore the sensitivity of spatial estimators.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Reihe Ökonomie / Economics Series ; No. 262

Classification and Topics

• Classification: Wirtschaft ; Bayesian Analysis: General ; Statistical Simulation Methods: General ; Model Evaluation, Validation, and Selection ; General Aggregative Models: Forecasting and Simulation: Models and Applications ; Size and Spatial Distributions of Regional Economic Activity
• Subject: spatial autoregressive models ; least squares estimators ; sensitivity analysis ; Taylor approximations ; Kantorovich inequality

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Liu, Shuangzhe ; Polasek, Wolfgang ; Sellner, Richard
• Event: Veröffentlichung
• (who): Institute for Advanced Studies (IHS)
• (where): Vienna
• (when): 2011

Further information

• Handle: http://hdl.handle.net/10419/68524
• Last update: 10.03.2025, 11:44 AM CET