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Estimation and Inference in Dyadic Network Formation Models with Nontransferable Utilities

Published 31 Oct 2024 in econ.EM | (2410.23852v1)

Abstract: This paper studies estimation and inference in a dyadic network formation model with observed covariates, unobserved heterogeneity, and nontransferable utilities. With the presence of the high dimensional fixed effects, the maximum likelihood estimator is numerically difficult to compute and suffers from the incidental parameter bias. We propose an easy-to-compute one-step estimator for the homophily parameter of interest, which is further refined to achieve $\sqrt{N}$-consistency via split-network jackknife and efficiency by the bootstrap aggregating (bagging) technique. We establish consistency for the estimator of the fixed effects and prove asymptotic normality for the unconditional average partial effects. Simulation studies show that our method works well with finite samples, and an empirical application using the risk-sharing data from Nyakatoke highlights the importance of employing proper statistical inferential procedures.

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References (65)
  1. Acemoglu, D., A. Ozdaglar, and A. Tahbaz-Salehi (2015): “Systemic risk and stability in financial networks,” American Economic Review, 105, 564–608.
  2. Auerbach, E. (2022): “Identification and estimation of a partially linear regression model using network data,” Econometrica, 90, 347–365.
  3. Banerjee, A., A. G. Chandrasekhar, E. Duflo, and M. O. Jackson (2013): “The diffusion of microfinance,” Science, 341, 1236498.
  4. Battaglini, M., E. Patacchini, and E. Rainone (2022): “Endogenous social interactions with unobserved networks,” The Review of Economic Studies, 89, 1694–1747.
  5. Blitzstein, J. and P. Diaconis (2011): “A sequential importance sampling algorithm for generating random graphs with prescribed degrees,” Internet Mathematics, 6, 489–522.
  6. Boucher, V. and I. Mourifié (2017): “My friend far, far away: a random field approach to exponential random graph models,” The Econometrics Journal, 20, S14–S46.
  7. Breiman, L. (1996): “Bagging predictors,” Machine learning, 24, 123–140.
  8. Candelaria, L. E. (2024): “A semiparametric network formation model with unobserved linear heterogeneity,” arXiv preprint arXiv:2007.05403.
  9. Chandrasekhar, A. G. and M. O. Jackson (2023): “A network formation model based on subgraphs,” arXiv preprint arXiv:1611.07658.
  10. Charbonneau, K. B. (2017): “Multiple fixed effects in binary response panel data models,” The Econometrics Journal, 20, S1–S13.
  11. Chatterjee, S., P. Diaconis, and A. Sly (2011): “Random graphs with a given degree sequence,” The Annals of Applied Probability, 1400–1435.
  12. Chen, M., I. Fernández-Val, and M. Weidner (2021): “Nonlinear factor models for network and panel data,” Journal of Econometrics, 220, 296–324.
  13. Chen, X. (2007): “Large sample sieve estimation of semi-nonparametric models,” in Handbook of Econometrics, Elsevier B.V., vol. 6B.
  14. Chen, X., V. Chernozhukov, S. Lee, and W. K. Newey (2014): “Local identification of nonparametric and semiparametric models,” Econometrica, 82, 785–809.
  15. de Paula, Á., S. Richards-Shubik, and E. Tamer (2018): “Identifying preferences in networks with bounded degree,” Econometrica, 86, 263–288.
  16. de Paula, Áureo (2020): “Strategic network formation,” in The Econometric Analysis of Network Data, Elsevier, 41–61.
  17. De Weerdt, J. (2004): “Risk-sharing and endogenous group formation,” in Insurance against Poverty, ed. by S. Dercon, Oxford University Press, chap. 10.
  18. De Weerdt, J. and S. Dercon (2006): “Risk-sharing networks and insurance against illness,” Journal of Development Economics, 81, 337–356.
  19. De Weerdt, J. and M. Fafchamps (2011): “Social identity and the formation of health insurance networks,” Journal of Development Studies, 47, 1152–1177.
  20. Dhaene, G. and K. Jochmans (2015): “Split-panel jackknife estimation of fixed-effect models,” The Review of Economic Studies, 82, 991–1030.
  21. Dzemski, A. (2019): “An empirical model of dyadic link formation in a network with unobserved heterogeneity,” Review of Economics and Statistics, 101, 763–776.
  22. Fernández-Val, I. and M. Weidner (2016): “Individual and time effects in nonlinear panel models with large N, T,” Journal of Econometrics, 192, 291–312.
  23. ——— (2018): “Fixed effects estimation of large-T panel data models,” Annual Review of Economics, 10, 109–138.
  24. Gao, W. Y. (2020): “Nonparametric identification in index models of link formation,” Journal of Econometrics, 215, 399–413.
  25. Gao, W. Y., M. Li, and S. Xu (2023): “Logical differencing in dyadic network formation models with nontransferable utilities,” Journal of Econometrics, 235, 302–324.
  26. Goldsmith-Pinkham, P. and G. W. Imbens (2013): “Social networks and the identification of peer effects,” Journal of Business & Economic Statistics, 31, 253–264.
  27. Graham, B. S. (2017): “An econometric model of network formation with degree heterogeneity,” Econometrica, 85, 1033–1063.
  28. ——— (2020): “Network data,” in Handbook of Econometrics, Elsevier, vol. 7, 111–218.
  29. Gualdani, C. (2021): “An econometric model of network formation with an application to board interlocks between firms,” Journal of Econometrics, 224, 345–370.
  30. Hahn, J. and G. Kuersteiner (2011): “Bias reduction for dynamic nonlinear panel models with fixed effects,” Econometric Theory, 27, 1152–1191.
  31. Hahn, J., H. R. Moon, and C. Snider (2017): “LM test of neglected correlated random effects and its application,” Journal of Business & Economic Statistics, 35, 359–370.
  32. Hahn, J. and W. Newey (2004): “Jackknife and analytical bias reduction for nonlinear panel models,” Econometrica, 72, 1295–1319.
  33. Hirano, K. and J. H. Wright (2017): “Forecasting with model uncertainty: Representations and risk reduction,” Econometrica, 85, 617–643.
  34. Hsieh, C.-S. and L. F. Lee (2016): “A social interactions model with endogenous friendship formation and selectivity,” Journal of Applied Econometrics, 31, 301–319.
  35. Hughes, D. W. (2023): “Estimating nonlinear network data models with fixed effects,” arXiv preprint arXiv:2203.15603.
  36. Jackson, M. O., Z. Lin, and N. N. Yu (2024): “Adjusting for peer-influence in propensity scoring when estimating treatment effects,” Working Paper.
  37. Jackson, M. O. and A. Wolinsky (1996): “A strategic model of social and economic networks,” Journal of Economic Theory, 71, 44–74.
  38. Jochmans, K. (2017): “Semiparametric analysis of network formation,” Journal of Business & Economic Statistics, 1–9.
  39. Jochmans, K. and M. Weidner (2019): “Fixed-effect regressions on network data,” Econometrica, 87, 1543–1560.
  40. Johnsson, I. and H. R. Moon (2021): “Estimation of peer effects in endogenous social networks: Control function approach,” Review of Economics and Statistics, 103, 328–345.
  41. König, M. D., D. Rohner, M. Thoenig, and F. Zilibotti (2017): “Networks in conflict: Theory and evidence from the great war of africa,” Econometrica, 85, 1093–1132.
  42. Le Cam, L. M. (1969): “Théorie asymptotique de la décision statistique,” Les Presses de l’Universitede Montreal, Montreal.
  43. Leung, M. P. (2019): “A weak law for moments of pairwise stable networks,” Journal of Econometrics, 210, 310–326.
  44. Leung, M. P. and H. R. Moon (2019): “Normal approximation in large network models,” arXiv preprint arXiv:1904.11060.
  45. Lewbel, A., X. Qu, and X. Tang (2023): “Social networks with unobserved links,” Journal of Political Economy, 131, 898–946.
  46. Mei, Z., L. Sheng, and Z. Shi (2024): “Nickell bias in panel local projection: Financial crises are worse than you think,” arXiv preprint arXiv:2302.13455.
  47. Mele, A. (2017): “A structural model of dense network formation,” Econometrica, 85, 825–850.
  48. ——— (2022): “A structural model of homophily and clustering in social networks,” Journal of Business & Economic Statistics, 40, 1377–1389.
  49. Menzel, K. (2024): “Strategic network formation with many agents,” Working Paper.
  50. Miyauchi, Y. (2016): “Structural estimation of pairwise stable networks with nonnegative externality,” Journal of Econometrics, 195, 224–235.
  51. Moreira, M. J. (2009): “A maximum likelihood method for the incidental parameter problem,” The Annals of Statistics, 37, 3660 – 3696.
  52. Neyman, J. and E. L. Scott (1948): “Consistent estimates based on partially consistent observations,” Econometrica, 1–32.
  53. Qu, L., L. Chen, T. Yan, and Y. Chen (2024): “Inference in semiparametric formation models for directed networks,” arXiv preprint arXiv:2405.19637.
  54. Ridder, G. and S. Sheng (2020): “Two-step estimation of a strategic network formation model with clustering,” arXiv preprint arXiv:2001.03838.
  55. Robbins, H. and S. Monro (1951): “A stochastic approximation method,” The Annals of Mathematical Statistics, 400–407.
  56. Shen, X. (1997): “On methods of sieves and penalization,” The Annals of Statistics, 25, 2555–2591.
  57. Sheng, S. (2020): “A structural econometric analysis of network formation games through subnetworks,” Econometrica, 88, 1829–1858.
  58. Toth, P. (2017): “Semiparametric estimation in network formation models with homophily and degree heterogeneity,” SSRN 2988698.
  59. White, H. (1982): “Maximum likelihood estimation of misspecified models,” Econometrica, 1–25.
  60. Yan, T. (2019): “Approximating the inverse of a diagonally dominant matrix with positive elements,” arXiv preprint arXiv:1902.00668.
  61. Yan, T., B. Jiang, S. E. Fienberg, and C. Leng (2019): “Statistical inference in a directed network model with covariates,” Journal of the American Statistical Association, 114, 857–868.
  62. Yan, T., C. Leng, and J. Zhu (2016a): “Asymptotics in directed exponential random graph models with an increasing bi-degree sequence,” The Annals of Statistics, 44, 31–57.
  63. Yan, T., H. Qin, and H. Wang (2016b): “Asymptotics in undirected random graph models parameterized by the strengths of vertices,” Statistica Sinica, 273–293.
  64. Yan, T. and J. Xu (2013): “A central limit theorem in the β𝛽\betaitalic_β-model for undirected random graphs with a diverging number of vertices,” Biometrika, 100, 519–524.
  65. Zeleneev, A. (2020): “Identification and estimation of network models with nonparametric unobserved heterogeneity,” Department of Economics, Princeton University.

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Authors (3)

  1. Ming Li 
  2. Zhentao Shi 
  3. Yapeng Zheng 

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