Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Generalized Bayes estimation for a SAR model with linear restrictions binding the coefficients

  • Received : 2020.10.25
  • Accepted : 2021.03.12
  • Published : 2021.07.31
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Abstract

The Spatial Autoregressive (SAR) models have drawn considerable attention in recent econometrics literature because of their capability to model the spatial spill overs in a feasible way. While considering the Bayesian analysis of these models, one may face the problem of lack of robustness with respect to underlying prior assumptions. The generalized Bayes estimators provide a viable alternative to incorporate prior belief and are more robust with respect to underlying prior assumptions. The present paper considers the SAR model with a set of linear restrictions binding the regression coefficients and derives restricted generalized Bayes estimator for the coefficients vector. The minimaxity of the restricted generalized Bayes estimator has been established. Using a simulation study, it has been demonstrated that the estimator dominates the restricted least squares as well as restricted Stein rule estimators.

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Acknowledgement

The authors are grateful to the Editor and three anonymous referees for their useful comments and suggestions.

References

  1. Anselin L (1988). Spatial Econometrics: Methods and Models, Kluwer Academic Publishers, Boston, USA.
  2. Anselin L, Le Gallo J, and Jayet H (2008). Spatial panel econometrics, The Econometrics of Panel Data, Fundamentals and Recent Developments in Theory and Practice(3rd ed), Springer, Berlin.
  3. Baltagi BH (2011). Spatial panels,The Handbook of Empirical Economics and Finance(pp.435-454), Chapman and Hall, New York.
  4. Berger JO (1980). Statistical Decision Theory: Foundations, Concepts and Methods, Springer, Berlin.
  5. Brown LD (1971). Admissible estimators, recurrent diffusions, and insoluble boundary value problems, Annals of Mathematical Statistics, 42, 85-90.
  6. Chaturvedi A, Tran VH, and Shukla G (1996). Improved estimation in the restricted regression model with non-spherical disturbances, Journal of Quantitative Economics, (12), 115-123.
  7. Chaturvedi A, Wan ATK, and Singh SP (2001). Stein-rule restricted regression estimator in a linear regression model with non-spherical disturbances, Communications in Statistics Theory & Methods, 30, 55-68. https://doi.org/10.1081/STA-100001558
  8. Chaturvedi A and Mishra S (2019). Generalized Bayes estimation of spatial autoregressive models, Statistics in Transition, 20.
  9. Elhorst JP (2003). Specification and estimation of spatial panel data models, International Regional Science Review, 26, 244-268. https://doi.org/10.1177/0160017603253791
  10. Elhorst JP (2010). Spatial panel data models, Handbook of Applied Spatial Analysis(377-407), Springer, Berlin.
  11. Elhorst JP (2014). Spatial Econometrics: from Cross-Sectional Data to Spatial Panels, Springer, Berlin.
  12. Glass AJ, Kenjegalieva K, and Sickles RC (2016). A spatial autoregressive stochastic frontier model for panel data with asymmetric efficiency spillovers, Journal of Econometrics, 190, 289-300. https://doi.org/10.1016/j.jeconom.2015.06.011
  13. Kubokawa T (1991). An approach to improving the James-Stein estimator, Journal of Multivariate Analysis, 36, 121-126. https://doi.org/10.1016/0047-259X(91)90096-K
  14. Kubokawa T (1994). A unified approach to improving equivariant estimators, Annals of Statistics, 22, 290-299. https://doi.org/10.1214/aos/1176325369
  15. Lee LF and Yu J(2015). Spatial panel data models, The Oxford Handbook of Panel Data(pp.363-401), Oxford University Press, New York.
  16. LeSage JP and Pace RK (2009). Introduction to Spatial Econometrics, Boca Raton, New York.
  17. Maruyama Y (1998). A unified and broadened class of admissible minimax estimators of a multivariate normal mean, Journal of Multivariate Analysis,64, 196-205. https://doi.org/10.1006/jmva.1997.1715
  18. Maruyama, Y (1999). Improving on the James-Stein estimator, Statistics & Decisions, 17, 137-140.
  19. Pal A, Dubey A and Chaturvedi A (2016). Shrinkage estimation in spatial autoregressive model, Journal of Multivariate Analysis,143, 362-373. https://doi.org/10.1016/j.jmva.2015.09.011
  20. Rao CR (1973) Linear Statistical Inference and Its Applications(2nd ed), Wiley, New York.
  21. Rubin H (1977). Robust Bayesian estimation. In Proceeding of the Statistical Decision Theory and Related Topics II, Indiana, USA.
  22. Srivastava VK and Srivastava AK (1983). Improved estimation of coefficients in regression models with incomplete prior information, Biometrical Journal, 25, 775-782. https://doi.org/10.1002/bimj.19830250807
  23. Srivastava VK and Srivastava AK (1984). Stein-rule estimators in restricted regression models, Estadistica, 36, 89-98.
  24. Srivastava AK and Chandra R (1991). Improved Estimation of Restricted Regression Model When Disturbances are not Necessarily Normal, Sankhya, B. 53, 119-133.
  25. Stein C (1973). Estimation of the mean of a multivariate normal distribution(pp 345-381), CA, USA.
  26. Tsukamoto T(2019). A spatial autoregressive stochastic frontier model for panel data incorporating a model of technical inefficiency, Japan & The World Economy, 50, 66-77. https://doi.org/10.1016/j.japwor.2018.11.003
  27. Toutenburg H and Shalabh (1996). Predictive performance of the methods of restricted and mixed regression estimators, Biometrical Journal, 38, 951-959. https://doi.org/10.1002/bimj.4710380807
  28. Toutenburg H and Shalabh (2000). Improved predictions in linear regression models with stochastic linear constraints, Biometrical Journal,42, 71-86. https://doi.org/10.1002/(SICI)1521-4036(200001)42:1<71::AID-BIMJ71>3.0.CO;2-H