Regularization Methods for High-Dimensional Instrumental Variables Regression With an Application to Genetical Genomics

Motivated by such modern applications, we consider the problem of variable selection and estimation in high-dimensional sparse instrumental variables models.

To overcome the difficulty of high dimensionality and unknown optimal instruments, we propose a two-stage regularization framework for identifying and estimating important covariate effects while selecting and estimating optimal instruments. The methodology extends the classical two-stage least squares estimator to high dimensions by exploiting sparsity using sparsity-inducing penalty functions in both stages. The resulting procedure is efficiently implemented by coordinate descent optimization.