  We propose a two-stage penalized least squares method to build large systems
of structural equations based on the instrumental variables view of the
classical two-stage least squares method. We show that, with large numbers of
endogenous and exogenous variables, the system can be constructed via
consistent estimation of a set of conditional expectations at the first stage,
and consistent selection of regulatory effects at the second stage. While the
consistent estimation at the first stage can be obtained via the ridge
regression, the adaptive lasso is employed at the second stage to achieve the
consistent selection. The resultant estimates of regulatory effects enjoy the
oracle properties. This method is computationally fast and allows for parallel
implementation. We demonstrate its effectiveness via simulation studies and
real data analysis.

Methodology