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GMM estimation of social interaction models with centrality

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Author Info

  • Liu, Xiaodong
  • Lee, Lung-fei

Abstract

This paper considers the specification and estimation of social interaction models with network structures and the presence of endogenous, contextual, correlated, and group fixed effects. When the network structure in a group is captured by a graph in which the degrees of nodes are not all equal, the different positions of group members as measured by the Bonacich (1987) centrality provide additional information for identification and estimation. In this case, the Bonacich centrality measure for each group can be used as an instrument for the endogenous social effect, but the number of such instruments grows with the number of groups. We consider the 2SLS and GMM estimation for the model. The proposed estimators are asymptotically efficient, respectively, within the class of IV estimators and the class of GMM estimators based on linear and quadratic moments, when the sample size grows fast enough relative to the number of instruments.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 159 (2010)
Issue (Month): 1 (November)
Pages: 99-115

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Handle: RePEc:eee:econom:v:159:y:2010:i:1:p:99-115

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Social network Centrality Spatial autoregressive model GMM Efficiency;

References

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  1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-33, May.
  2. Lee, Lung-fei, 2007. "The method of elimination and substitution in the GMM estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 140(1), pages 155-189, September.
  3. repec:att:wimass:9127 is not listed on IDEAS
  4. John C. Chao & Norman Rasmus Swanson, 2004. "Alternative Approximations of the Bias and MSE of the IV Estimator Under Weak Identification with an Application to Bias Correction," Yale School of Management Working Papers ysm375, Yale School of Management.
  5. William A. Brock & Steven N. Durlauf, 2000. "Interactions-Based Models," Working Papers 00-05-028, Santa Fe Institute.
  6. Peter C. B. Phillips & Chirok Han, 2004. "GMM with Many Moment Conditions," Econometric Society 2004 Far Eastern Meetings 525, Econometric Society.
  7. Donald, Stephen G. & Whitney Newey, 1999. "Choosing the Number of Instruments," Working papers 99-05, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. Paul A. Bekker & Jan Ploeg, 2005. "Instrumental variable estimation based on grouped data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 239-267.
  9. Bernard Fingleton, 2008. "A Generalized Method of Moments Estimator for a Spatial Panel Model with an Endogenous Spatial Lag and Spatial Moving Average Errors," Spatial Economic Analysis, Taylor and Francis Journals, vol. 3(1), pages 27-44.
  10. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, 09.
  11. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
  12. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
  13. Hasselt, Martijn van, 2010. "Many Instruments Asymptotic Approximations Under Nonnormal Error Distributions," Econometric Theory, Cambridge University Press, vol. 26(02), pages 633-645, April.
  14. Alvarez, J. & Arellano, M., 1998. "The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators," Papers 9808, Centro de Estudios Monetarios Y Financieros-.
  15. Lee, Lung-fei, 2007. "Identification and estimation of econometric models with group interactions, contextual factors and fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 333-374, October.
  16. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
  17. Hansen, Christian & Hausman, Jerry & Newey, Whitney, 2008. "Estimation With Many Instrumental Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 398-422.
  18. repec:sae:pubfin:v:30:y:2002:i:1:p:41-55 is not listed on IDEAS
  19. Hsiao,Cheng, 2003. "Analysis of Panel Data," Cambridge Books, Cambridge University Press, number 9780521522717.
  20. Lee, Lung-fei & Liu, Xiaodong, 2010. "Efficient Gmm Estimation Of High Order Spatial Autoregressive Models With Autoregressive Disturbances," Econometric Theory, Cambridge University Press, vol. 26(01), pages 187-230, February.
  21. Lung-fei Lee, 2003. "Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances," Econometric Reviews, Taylor and Francis Journals, vol. 22(4), pages 307-335.
  22. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  23. Manski, Charles F, 1993. "Identification of Endogenous Social Effects: The Reflection Problem," Review of Economic Studies, Wiley Blackwell, vol. 60(3), pages 531-42, July.
  24. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
  25. Lee, Lung-Fei, 2002. "Consistency And Efficiency Of Least Squares Estimation For Mixed Regressive, Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 252-277, April.
  26. Lung-fei Lee & Xiaodong Liu & Xu Lin, 2010. "Specification and estimation of social interaction models with network structures," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 145-176, 07.
  27. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
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Citations

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Cited by:
  1. Sergio Currarini & Elena Fumagalli & Fabrizio Panebianco, 2013. "Games on Networks: Direct Complements and Indirect Substitutes," Working Papers 2013.04, Fondazione Eni Enrico Mattei.
  2. Martellosio, Federico, 2011. "Efficiency of the OLS estimator in the vicinity of a spatial unit root," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1285-1291, August.
  3. Patacchini, Eleonora & Rainone, Edoardo & Zenou, Yves, 2011. "Dynamic Aspects of Teenage Friendships and Educational Attainment," CEPR Discussion Papers 8223, C.E.P.R. Discussion Papers.
  4. Xiaodong Liu & Eleonora Patacchini & Yves Zenou & Lung-Fei Lee, 2012. "Criminal Networks: Who is the Key Player?," Working Papers 2012.39, Fondazione Eni Enrico Mattei.
  5. Liu, Xiaodong & Patacchini, Eleonora & Zenou, Yves, 2011. "Peer Effects in Education, Sport, and Screen Activities: Local Aggregate or Local Average?," CEPR Discussion Papers 8477, C.E.P.R. Discussion Papers.

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