Conditional sparse boosting for high-dimensional instrumental variable estimation

We consider the structural equation models with both high-dimensional instrumental variables and observed exogenous covariates. To overcome the challenge of unknown optimal instruments and high-dimensional exogenous confounders, a novel two-stage sparse boosting approach is proposed to select the optimal instruments and important exogenous variables, as well as to estimate the causal parameter of interest. The methodology extends the classical two-stage least squares to high dimension settings by exploiting sparsity and integrating two versions of sparse boosting - the traditional unconditional sparse boosting and the newly developed conditional sparse boosting. The proposed method is illustrated through extensive simulations as well as an empirical example to estimate the effect of judicial eminent domain decisions on property price.