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Variable Selection for Structural Equation with Endogeneity

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Abstract

This paper studies variable selection problem in structural equation of a two-stage least squares (2SLS) model in presence of endogeneity which is commonly encountered in empirical economic studies. Model uncertainty and variable selection in the structural equation is an important issue as described in Andrews and Lu (2001) and Caner (2009). The authors propose an adaptive Lasso 2SLS estimator for linear structural equation with endogeneity and show that it enjoys the oracle properties, i.e., the consistency in both estimation and model selection. In Monte Carlo simulations, the authors demonstrate that the proposed estimator has smaller bias and MSE compared with the bridge-type GMM estimator (Caner, 2009). In a case study, the authors revisit the classic returns to education problem (Angrist and Krueger, 1991) using the China Population census data. The authors find that the education level not only has strong effects on income but also shows heterogeneity in different age cohorts.

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Authors and Affiliations

  1. Wang Yanan Institute for Studies in Economics (WISE), Department of Statistics, School of Economics and Fujian Key Laboratory of Statistical Science, Xiamen University, Xiamen, 361005, China

    Qingliang Fan & Wei Zhong

Authors
  1. Qingliang Fan
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  2. Wei Zhong
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Corresponding author

Correspondence to Wei Zhong.

Additional information

Fan’s research was supported by the National Natural Science Foundation of China under Grant No. 71671149, the Fundamental Research Funds for the Central Universities under Grant No. 20720171042, and the Natural Science Foundation of Fujian Province of China under Grant No. 2016J01340; Zhong’s research was supported by the National Natural Science Foundation of China under Grant Nos. 11671334, 11301435, and 11401497.

This paper was recommended for publication by Editor SUN Liuquan.

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Fan, Q., Zhong, W. Variable Selection for Structural Equation with Endogeneity. J Syst Sci Complex 31, 787–803 (2018). https://doi.org/10.1007/s11424-017-6195-4

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  • DOI: https://doi.org/10.1007/s11424-017-6195-4

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