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GMM estimation of social interaction models with centrality

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  • 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, 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.
  2. Lung-fei Lee, 2003. "Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 307-335.
  3. John C. Chao & Norman Rasmus Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Yale School of Management Working Papers ysm374, Yale School of Management.
  4. Chirok Han & Peter C.B. Phillips, 2005. "GMM with Many Moment Conditions," Cowles Foundation Discussion Papers 1515, Cowles Foundation for Research in Economics, Yale University.
  5. 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.
  6. Hasselt, Martijn van, 2010. "Many Instruments Asymptotic Approximations Under Nonnormal Error Distributions," Econometric Theory, Cambridge University Press, vol. 26(02), pages 633-645, April.
  7. 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.
  8. 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-.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. repec:att:wimass:9127 is not listed on IDEAS
  14. William Brock & Steven N. Durlauf, 2000. "Interactions-Based Models," NBER Technical Working Papers 0258, National Bureau of Economic Research, Inc.
  15. Hsiao,Cheng, 2003. "Analysis of Panel Data," Cambridge Books, Cambridge University Press, number 9780521522717, October.
  16. Donald, Stephen G. & Whitney Newey, 1999. "Choosing the Number of Instruments," Working papers 99-05, Massachusetts Institute of Technology (MIT), Department of Economics.
  17. Jeffrey P. Cohen, 2002. "Reciprocal State and Local Airport Spending Spillovers and Symmetric Responses to Cuts and Increases in Federal Airport Grants," Public Finance Review, , vol. 30(1), pages 41-55, January.
  18. 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.
  19. 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.
  20. 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.
  21. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
  22. 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.
  23. 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.
  24. 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.
  25. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  26. 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 & Francis Journals, vol. 3(1), pages 27-44.
  27. 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.
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Citations

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Cited by:
  1. Patacchini, Eleonora & Rainone, Edoardo & Zenou, Yves, 2011. "Dynamic Aspects of Teenage Friendships and Educational Attainment," Research Papers in Economics 2011:4, Stockholm University, Department of Economics.
  2. Lee, Lung-Fei & Liu, Xiaodong & Patacchini, Eleonora & Zenou, Yves, 2011. "Criminal Networks: Who is the Key Player?," CEPR Discussion Papers 8185, C.E.P.R. Discussion Papers.
  3. Sergio Currarini & Elena Fumagalli & Fabrizio Panebianco, 2013. "Games on Networks: Direct Complements and Indirect Substitutes," Working Papers 2013.04, Fondazione Eni Enrico Mattei.
  4. Liu, Xiaodong, 2013. "Estimation of a local-aggregate network model with sampled networks," Economics Letters, Elsevier, vol. 118(1), pages 243-246.
  5. Liu, Xiaodong, 2012. "On the consistency of the LIML estimator of a spatial autoregressive model with many instruments," Economics Letters, Elsevier, vol. 116(3), pages 472-475.
  6. 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.
  7. 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.
  8. Fei Jin & Lung-fei Lee, 2013. "Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments," Econometrics, MDPI, Open Access Journal, vol. 1(1), pages 71-114, May.
  9. Liu, Xiaodong & Patacchini, Eleonora & Zenou, Yves, 2014. "Endogenous peer effects: local aggregate or local average?," Journal of Economic Behavior & Organization, Elsevier, vol. 103(C), pages 39-59.
  10. Eleonora Patacchini & Giuseppe Venanzoni, 2013. "Peer Effects in the Demand for Housing Quality," Center for Policy Research Working Papers 158, Center for Policy Research, Maxwell School, Syracuse University.

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