Adaptive Elastic Net for Generalized Methods of Moments

Area of Science:

• Econometrics
• Statistical Modeling

Background:

• Model selection and estimation are fundamental in econometrics.
• Generalized Method of Moments (GMM) is powerful for complex data like panel data.
• Existing methods may struggle with high dimensionality and collinearity.

Purpose of the Study:

• To develop a new technique for simultaneous model selection and estimation in GMM.
• To extend the adaptive elastic net estimator to nonlinear equation systems with endogenous variables.
• To address challenges of diverging parameters and collinearity in large-scale econometric models.

Main Methods:

• Extension of the least squares based adaptive elastic net estimator.
• Development of a new proof technique for estimators lacking closed-form solutions.
• A data-dependent technique for setting redundant parameters to zero.

Main Results:

• The proposed method achieves simultaneous estimation and selection in GMM.
• It handles an infinite number of diverging parameters and collinearity.
• The method demonstrates the oracle property, accurately estimating non-zero parameters and zeroing redundant ones.

Conclusions:

• The new GMM technique offers a robust approach to model selection and estimation.
• It outperforms existing methods like Bridge-GMM in handling complex scenarios.
• Numerical examples validate the method's effectiveness.