Sparse Linear Models and l1−Regularized 2SLS with High-Dimensional Endogenous Regressors and Instruments

Ying Zhu

MPRA Paper from University Library of Munich, Germany

Abstract: We explore the validity of the 2-stage least squares estimator with l_{1}-regularization in both stages, for linear regression models where the numbers of endogenous regressors in the main equation and instruments in the first-stage equations can exceed the sample size, and the regression coefficients are sufficiently sparse. For this l_{1}-regularized 2-stage least squares estimator, finite-sample performance bounds are established. We then provide a simple practical method (with asymptotic guarantees) for choosing the regularization parameter. We show that this practical method can produce an l_{2}-consistent 2SLS estimator whose rate of convergence can be made as arbitrarily close as the scaling of our finite-sample performance bounds under quite standard conditions.

Keywords: High-dimensional statistics; Lasso; sparse linear models; endogeneity; two-stage estimation (search for similar items in EconPapers)
JEL-codes: C1 C13 C31 C36 (search for similar items in EconPapers)
Date: 2015-07-20
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https://mpra.ub.uni-muenchen.de/82184/1/MPRA_paper_82184.pdf revised version (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:81217

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