A Two-Stage Penalized Least Squares Method for Constructing Large Systems of Structural Equations.

Area of Science:

• Econometrics
• Statistical modeling
• Computational statistics

Background:

• Classical two-stage least squares (2SLS) is a standard method for estimating structural equations.
• Estimating large systems with many variables presents computational and statistical challenges.
• Instrumental variables (IV) provide a framework for addressing endogeneity in structural models.

Purpose of the Study:

• To propose a novel two-stage penalized least squares (2S-PLS) method for constructing large structural equation systems.
• To leverage the instrumental variables perspective for robust estimation.
• To develop a computationally efficient and scalable approach for complex models.

Main Methods:

• The proposed method employs a two-stage approach.
• Stage one utilizes ridge regression for consistent estimation of conditional expectations.
• Stage two employs the adaptive lasso for consistent selection of regulatory effects.

Main Results:

• The 2S-PLS method enables consistent estimation and selection in large-scale structural systems.
• Ridge regression ensures stable estimation in the first stage.
• Adaptive lasso provides efficient variable selection in the second stage.
• The method is computationally fast and amenable to parallel implementation.

Conclusions:

• The proposed 2S-PLS method offers an effective solution for building large structural equation systems.
• It combines consistent estimation and selection, outperforming traditional methods in high-dimensional settings.
• Simulation studies and real data analysis confirm the method's practical utility and efficiency.