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Weak Identification and Estimation of Social Interaction Models

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  • Guy Tchuente

Abstract

The identification of the network effect is based on either group size variation, the structure of the network or the relative position in the network. I provide easy-to-verify necessary conditions for identification of undirected network models based on the number of distinct eigenvalues of the adjacency matrix. Identification of network effects is possible; although in many empirical situations existing identification strategies may require the use of many instruments or instruments that could be strongly correlated with each other. The use of highly correlated instruments or many instruments may lead to weak identification or many instruments bias. This paper proposes regularized versions of the two-stage least squares (2SLS) estimators as a solution to these problems. The proposed estimators are consistent and asymptotically normal. A Monte Carlo study illustrates the properties of the regularized estimators. An empirical application, assessing a local government tax competition model, shows the empirical relevance of using regularization methods.

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  • Guy Tchuente, 2019. "Weak Identification and Estimation of Social Interaction Models," Papers 1902.06143, arXiv.org.
  • Handle: RePEc:arx:papers:1902.06143
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    References listed on IDEAS

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    1. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416-416.
    2. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    3. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
    4. Hansen, Christian & Kozbur, Damian, 2014. "Instrumental variables estimation with many weak instruments using regularized JIVE," Journal of Econometrics, Elsevier, vol. 182(2), pages 290-308.
    5. 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.
    6. 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.
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