lixiongyang/gmm-lasso

The scripts for simulation results in "Estimation of Sparse Structural Parameters with Many Endogenous Variables" (2016), Econometric Reviews.

This repository hosts functions that generate the simulation results in

Zhentao Shi (2016): "Estimation of Sparse Structural Parameters with Many Endogenous Variables", Econometric Reviews, 35(8-10): 1582-1608

Paper Abstract

We apply the generalized method of moments–least absolute shrinkage and selection operator (GMM-Lasso) (Caner, 2009) to a linear structural model with many endogenous regressors. If the true parameter is sufficiently sparse, we can establish a new oracle inequality, which implies that GMM-Lasso performs almost as well as if we knew a priori the identities of the relevant variables. Sparsity, meaning that most of the true coefficients are too small to matter, naturally arises in econometric applications where the model can be derived from economic theory. In addition, we propose to use a modified version of AIC or BIC to select the tuning parameter in practical implementation. Simulations provide supportive evidence concerning the finite sample properties of the GMM-Lasso.

Functionality of Scripts in v1.0

• master_DGP1.R is the master file.
• estimation.R is the main function for the estimation and the calculation of the summary statistics such as the MSE, squared-bias and variance. It also has many small functions to do the background work.
• DGP.R only contains functions that generate the data.

Works for future research

• solution_path_of_gmm_lasso.lyx contains idea to transform LARS for GMM_Lasso. I am interested in developing it into a note.
• super_master_inference.R is for another project for the asymptotic distribution of GMM-Lasso. func_inference.R contains the workhorse files.
• cv.lars.2sls is a modified version to implement cross-validation to choose the tuning parameter.