IDEAS home Printed from https://ideas.repec.org/p/eie/wpaper/1509.html

Parametric and Semiparametric IV Estimation of Network Models with Selectivity

Author

Listed:
  • Tiziano Arduini

    (Sapienza University of Rome)

  • Eleonora Patacchini

    (Cornell University, Sapienza University of Rome, EIEF, IZA and CEPR)

  • Edoardo Rainone

    (Bank of Italy)

Abstract

We propose parametric and semiparametric IV estimators for spatial autoregressive models with network data where the network structure is endogenous. We embed a dyadic network formation process in the control function approach as in Heckman and Robb (1985). In the semiparametric case, we use power series to approximate the correction terms. We establish the consistency and asymptotic normality for both parametric and semiparametric cases. We also investigate their finite sample properties via Monte Carlo simulation.

Suggested Citation

  • Tiziano Arduini & Eleonora Patacchini & Edoardo Rainone, 2015. "Parametric and Semiparametric IV Estimation of Network Models with Selectivity," EIEF Working Papers Series 1509, Einaudi Institute for Economics and Finance (EIEF), revised Oct 2015.
    • Handle: RePEc:eie:wpaper:1509
    as

    Download full text from publisher

    File URL: http://www.eief.it/files/2015/10/wp-09-parametric-and-semiparametric-iv-estimation-of-network-models-with-selectivity.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:dau:papers:123456789/10840 is not listed on IDEAS
    2. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
    3. Angelo Mele, 2010. "A structural model of segregation in social networks," CeMMAP working papers CWP32/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Paul Goldsmith-Pinkham & Guido W. Imbens, 2013. "Social Networks and the Identification of Peer Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 253-264, July.
    5. Yann Bramoullé & Bernard Fortin, 2009. "The Econometrics of Social Networks," Cahiers de recherche 0913, CIRPEE.
    6. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    7. Horrace, William C. & Liu, Xiaodong & Patacchini, Eleonora, 2016. "Endogenous network production functions with selectivity," Journal of Econometrics, Elsevier, vol. 190(2), pages 222-232.
    8. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    9. Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
    10. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    11. Takeshi Amemiya, 1975. "Qualitative Response Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 4, number 3, pages 363-372, National Bureau of Economic Research, Inc.
    12. Orazio Attanasio & Abigail Barr & Juan Camilo Cardenas & Garance Genicot & Costas Meghir, 2012. "Risk Pooling, Risk Preferences, and Social Networks," American Economic Journal: Applied Economics, American Economic Association, vol. 4(2), pages 134-167, April.
    13. Bramoullé, Yann & Djebbari, Habiba & Fortin, Bernard, 2009. "Identification of peer effects through social networks," Journal of Econometrics, Elsevier, vol. 150(1), pages 41-55, May.
    14. Lung-Fei Lee, 1982. "Some Approaches to the Correction of Selectivity Bias," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(3), pages 355-372.
    15. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    16. Áureo de Paula & Seth Richards-Shubik & Elie Tamer, 2015. "Identification of preferences in network formation games," CeMMAP working papers 29/15, Institute for Fiscal Studies.
    17. Coren L. Apicella & Frank W. Marlowe & James H. Fowler & Nicholas A. Christakis, 2012. "Social networks and cooperation in hunter-gatherers," Nature, Nature, vol. 481(7382), pages 497-501, January.
    18. Khan, Shakeeb, 2013. "Distribution free estimation of heteroskedastic binary response models using Probit/Logit criterion functions," Journal of Econometrics, Elsevier, vol. 172(1), pages 168-182.
    19. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    20. Gordon B. Dahl, 2002. "Mobility and the Return to Education: Testing a Roy Model with Multiple Markets," Econometrica, Econometric Society, vol. 70(6), pages 2367-2420, November.
    21. Marcel Fafchamps & Flore Gubert, 2007. "Risk Sharing and Network Formation," American Economic Review, American Economic Association, vol. 97(2), pages 75-79, May.
    22. Lei, J., 2013. "Smoothed Spatial Maximum Score Estimation of Spatial Autoregressive Binary Choice Panel Models," Discussion Paper 2013-061, Tilburg University, Center for Economic Research.
    23. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
    24. Francis Vella, 1998. "Estimating Models with Sample Selection Bias: A Survey," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 127-169.
    25. Heckman, James J. & Robb, Richard Jr., 1985. "Alternative methods for evaluating the impact of interventions : An overview," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 239-267.
    26. Nicholas Christakis & James Fowler & Guido Imbens & Karthik Kalyanaraman, 2010. "An empirical model for strategic network formation," CeMMAP working papers CWP16/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    27. Liu, Xiaodong & Lee, Lung-fei, 2010. "GMM estimation of social interaction models with centrality," Journal of Econometrics, Elsevier, vol. 159(1), pages 99-115, November.
    28. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    29. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, September.
    30. Jason R. Blevins & Shakeeb Khan, 2013. "Distribution-free estimation of heteroskedastic binary response models in Stata," Stata Journal, StataCorp LLC, vol. 13(3), pages 588-602, September.
    31. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
    32. Schmertmann, Carl P., 1994. "Selectivity bias correction methods in polychotomous sample selection models," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 101-132.
    33. Antoni Calvó-Armengol & Eleonora Patacchini & Yves Zenou, 2009. "Peer Effects and Social Networks in Education," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(4), pages 1239-1267.
    34. 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.
    35. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    36. Joris Pinkse & Margaret E. Slade, 2010. "The Future Of Spatial Econometrics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 103-117, February.
    37. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    38. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    39. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 170(1), pages 178-190.
    40. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    41. Lei, J., 2013. "Smoothed Spatial Maximum Score Estimation of Spatial Autoregressive Binary Choice Panel Models," Other publications TiSEM d63bf400-7ff2-4a1c-8067-1, Tilburg University, School of Economics and Management.
    42. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-782, May.
    43. Chih‐Sheng Hsieh & Lung Fei Lee, 2016. "A Social Interactions Model with Endogenous Friendship Formation and Selectivity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(2), pages 301-319, March.
    44. 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, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lopera, Maria Adelaida & Marchand, Steeve, 2018. "Peer effects and risk-taking among entrepreneurs: Lab-in-the-field evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 150(C), pages 182-201.
    2. Yann Bramoullé & Habiba Djebbari & Bernard Fortin, 2020. "Peer Effects in Networks: A Survey," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 603-629, August.
    3. Jochmans, Koen, 2023. "Peer effects and endogenous social interactions," Journal of Econometrics, Elsevier, vol. 235(2), pages 1203-1214.
    4. Brice Romuald Gueyap Kounga, 2023. "Identification and Estimation of a Semiparametric Logit Model using Network Data," Papers 2310.07151, arXiv.org, revised Jan 2026.
    5. Gao, Wayne Yuan & Li, Ming & Xu, Sheng, 2023. "Logical differencing in dyadic network formation models with nontransferable utilities," Journal of Econometrics, Elsevier, vol. 235(1), pages 302-324.
    6. Eric Auerbach, 2021. "Identification and Estimation of a Partially Linear Regression Model using Network Data: Inference and an Application to Network Peer Effects," Papers 2105.10002, arXiv.org.
    7. Ida Johnsson & Hyungsik Roger Moon, 2017. "Estimation of Peer Effects in Endogenous Social Networks: Control Function Approach," Papers 1709.10024, arXiv.org, revised Jul 2019.
    8. Arun Advani & Bansi Malde, 2018. "Credibly Identifying Social Effects: Accounting For Network Formation And Measurement Error," Journal of Economic Surveys, Wiley Blackwell, vol. 32(4), pages 1016-1044, September.
    9. Wayne Yuan Gao, 2017. "Nonparametric Identification in Index Models of Link Formation," Papers 1710.11230, arXiv.org, revised May 2018.
    10. Arun Advani & Bansi Malde, 2018. "Methods to identify linear network models: a review," Swiss Journal of Economics and Statistics, Springer;Swiss Society of Economics and Statistics, vol. 154(1), pages 1-16, December.
    11. Eric Auerbach, 2022. "Identification and Estimation of a Partially Linear Regression Model Using Network Data," Econometrica, Econometric Society, vol. 90(1), pages 347-365, January.
    12. Rainone, Edoardo, 2020. "The network nature of over-the-counter interest rates," Journal of Financial Markets, Elsevier, vol. 47(C).
    13. Diemer, Andreas, 2022. "Endogenous peer effects in diverse friendship networks: Evidence from Swedish classrooms," Economics of Education Review, Elsevier, vol. 89(C).
    14. Gao, Wayne Yuan, 2020. "Nonparametric identification in index models of link formation," Journal of Econometrics, Elsevier, vol. 215(2), pages 399-413.
    15. Eric Auerbach, 2019. "Identification and Estimation of a Partially Linear Regression Model using Network Data," Papers 1903.09679, arXiv.org, revised Jun 2021.
    16. Guido M. Kuersteiner & Ingmar R. Prucha, 2020. "Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity," Econometrica, Econometric Society, vol. 88(5), pages 2109-2146, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vincent Boucher & Bernard Fortin, 2015. "Some Challenges in the Empirics of the Effects of Networks," Cahiers de recherche 1504, CIRPEE.
    2. Rainone, Edoardo, 2020. "The network nature of over-the-counter interest rates," Journal of Financial Markets, Elsevier, vol. 47(C).
    3. Matthew O. Jackson & Brian W. Rogers & Yves Zenou, 2016. "Networks: An Economic Perspective," Papers 1608.07901, arXiv.org.
    4. Áureo de Paula, 2015. "Econometrics of network models," CeMMAP working papers 52/15, Institute for Fiscal Studies.
    5. William C. Horrace & Hyunseok Jung & Shane Sanders, 2022. "Network Competition and Team Chemistry in the NBA," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 35-49, January.
    6. Bryan S. Graham, 2015. "Methods of Identification in Social Networks," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 465-485, August.
    7. Topa, Giorgio & Zenou, Yves, 2015. "Neighborhood and Network Effects," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 561-624, Elsevier.
    8. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    9. Horrace, William C. & Liu, Xiaodong & Patacchini, Eleonora, 2016. "Endogenous network production functions with selectivity," Journal of Econometrics, Elsevier, vol. 190(2), pages 222-232.
    10. Arun Advani & Bansi Malde, 2014. "Empirical methods for networks data: social effects, network formation and measurement error," IFS Working Papers W14/34, Institute for Fiscal Studies.
    11. Gibbons, Steve & Overman, Henry G. & Patacchini, Eleonora, 2015. "Spatial Methods," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 115-168, Elsevier.
    12. Bryan S. Graham, 2017. "An econometric model of network formation with degree heterogeneity," CeMMAP working papers 08/17, Institute for Fiscal Studies.
    13. Edoardo Rainone, 2017. "Pairwise trading in the money market during the European sovereign debt crisis," Temi di discussione (Economic working papers) 1160, Bank of Italy, Economic Research and International Relations Area.
    14. Edoardo Rainone, 2015. "Testing information diffusion in the decentralized unsecured market for euro funds," Temi di discussione (Economic working papers) 1022, Bank of Italy, Economic Research and International Relations Area.
    15. Chih‐Sheng Hsieh & Lung‐Fei Lee & Vincent Boucher, 2020. "Specification and estimation of network formation and network interaction models with the exponential probability distribution," Quantitative Economics, Econometric Society, vol. 11(4), pages 1349-1390, November.
    16. Yingyao Hu & Zhongjian Lin, 2018. "Misclassification and the hidden silent rivalry," CeMMAP working papers CWP12/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Patacchini, Eleonora & Hsieh, Chih-Sheng & Lin, Xu, 2019. "Social Interaction Methods," CEPR Discussion Papers 14141, C.E.P.R. Discussion Papers.
    18. T. Arduini, 2016. "Distribution Free Estimation of Spatial Autoregressive Binary Choice Panel Data Models," Working Papers wp1052, Dipartimento Scienze Economiche, Universita' di Bologna.
    19. Bryan S. Graham, 2014. "An econometric model of link formation with degree heterogeneity," NBER Working Papers 20341, National Bureau of Economic Research, Inc.
    20. Yann Bramoullé & Habiba Djebbari & Bernard Fortin, 2020. "Peer Effects in Networks: A Survey," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 603-629, August.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eie:wpaper:1509. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Facundo Piguillem (email available below). General contact details of provider: https://edirc.repec.org/data/einauit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.