rlassoIVselectZ: Instrumental Variable Estimation with Lasso

Description

This function selects the instrumental variables in the first stage by Lasso. First stage predictions are then used in the second stage as optimal instruments to estimate the parameter vector. The function returns an element of class rlassoIVselectZ

Usage

rlassoIVselectZ(x, ...)
# S3 method for default
rlassoIVselectZ(x, d, y, z, post = TRUE, intercept = TRUE, ...)
# S3 method for formula
rlassoIVselectZ(formula, data, post = TRUE, intercept = TRUE, ...)

Value

An object of class rlassoIVselectZ containing at least the following components:

coefficients: estimated parameter vector
vcov: variance-covariance matrix
residuals: residuals
samplesize: sample size
selection.matrix: matrix of selected variables in the first stage for each endogenous variable

Arguments

x: exogenous variables in the structural equation (matrix)
...: arguments passed to the function rlasso.
d: endogenous variables in the structural equation (vector or matrix)
y: outcome or dependent variable in the structural equation (vector or matrix)
z: set of potential instruments for the endogenous variables. Exogenous variables serve as their own instruments.
post: logical. If TRUE, post-lasso estimation is conducted.
intercept: logical. If TRUE, intercept is included in the second stage equation.
formula: An object of class Formula of the form " y ~ x + d | x + z" with y the outcome variable, d endogenous variable, z instrumental variables, and x exogenous variables.
data: An optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which rlassoIVselectZ is called.

Details

The implementation follows the procedure described in Belloni et al. (2012). Option post=TRUE conducts post-lasso estimation, i.e. a refit of the model with the selected variables, to estimate the optimal instruments. The parameter vector of the structural equation is then fitted by two-stage least square (tsls) estimation.

References

D. Belloni, D. Chen, V. Chernozhukov and C. Hansen (2012). Sparse models and methods for optimal instruments with an application to eminent domain. Econometrica 80 (6), 2369--2429.