Estimation of Sparse Structural Parameters with Many Endogenous Variables
将GMM-Lasso方法应用于含多个内生变量的线性结构模型，在参数稀疏时建立新的Oracle不等式，并建议用修正的AIC或BIC选择调优参数，模拟验证了有限样本性质。
We apply the generalized method of moments--least absolute shinkage 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.