Sparse linear models and -regularized 2SLS with high-dimensional endogenous regressors and instruments |
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Authors: | Ying Zhu |
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Institution: | Department of Economics, Michigan State University, 486 W. Circle Dr. Room 110, East Lansing, MI 48824, United States |
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Abstract: | We explore the validity of the 2-stage least squares estimator with -regularization in both stages, for linear triangular 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 -regularized 2-stage least squares estimator, we first establish finite-sample performance bounds and then provide a simple practical method (with asymptotic guarantees) for choosing the regularization parameter. We also sketch an inference strategy built upon this practical method. |
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Keywords: | C14 C31 C36 High-dimensional statistics Lasso Sparse linear models Endogeneity Two-stage least squares |
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