PDSLASSO: Stata module for post-selection and post-regularization OLS or IV estimation and inference

pdslasso and ivlasso are routines for estimating structural parameters in linear models with many controls and/or instruments. The routines use methods for estimating sparse high-dimensional models, specifically the lasso (Least Absolute Shrinkage and Selection Operator, Tibshirani 1996) and the square-root-lasso (Belloni et al. 2011, 2014). These estimators are used to select controls (pdslasso) and/or instruments (ivlasso) from a large set of variables (possibly numbering more than the number of observations), in a setting where the researcher is interested in estimating the causal impact of one or more (possibly endogenous) causal variables of interest. Two approaches are implemented in pdslasso and ivlasso: (1) The "post-double-selection" (PDS) methodology of Belloni et al. (2012, 2013, 2014, 2015, 2016). (2) The "post-regularization" (CHS) methodology of Chernozhukov, Hansen and Spindler (2015). For instrumental variable estimation, ivlasso implements weak-identification-robust hypothesis tests and confidence sets using the Chernozhukov et al. (2013) sup-score test. The implemention of these methods in pdslasso and ivlasso require the Stata program rlasso (available in the separate Stata module lassopack), which provides lasso and square root-lasso estimation with data-driven penalization.