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We propose a two-stage penalized least squares method to build large systemsof structural equations based on the instrumental variables view of theclassical two-stage least squares method. We show that, with large numbers ofendogenous and exogenous variables, the system can be constructed viaconsistent estimation of a set of conditional expectations at the first stage,and consistent selection of regulatory effects at the second stage. While theconsistent estimation at the first stage can be obtained via the ridgeregression, the adaptive lasso is employed at the second stage to achieve theconsistent selection. The resultant estimates of regulatory effects enjoy theoracle properties. This method is computationally fast and allows for parallelimplementation. We demonstrate its effectiveness via simulation studies andreal data analysis.

A Two-Stage Penalized Least Squares Method for Constructing Large Systems of Structural Equations