Estimation of simultaneous equation models by backpropagation method using stochastic gradient descent

Area of Science:

• Econometrics
• Computational Statistics
• Artificial Intelligence

Background:

• Simultaneous Equation Models (SEMs) are crucial in econometrics and other sciences for analyzing bidirectional and simultaneous variable relationships.
• Traditional SEM estimation methods include Two-Stage Least Squares (2SLS), Three-Stage Least Squares (3SLS), and Indirect Least Squares (ILS).
• Existing research compares SEM estimators based on prediction error, computational cost, and statistical paradigms like classical and Bayesian statistics.

Purpose of the Study:

• To propose and investigate artificial neural networks (ANNs) as a novel framework for solving Simultaneous Equation Models (SEMs).
• To establish an analogy between SEM variables and ANN neurons, and SEM coefficients and neural network connection weights.
• To explore the efficacy of the backpropagation method with stochastic gradient descent (SGD) for estimating SEM coefficients.

Main Methods:

• Conceptualizing a Simultaneous Equation Model (SEM) as a specific architecture of an Artificial Neural Network (ANN).
• Mapping SEM variables to ANN neurons and SEM coefficients to the weights of neural network connections.
• Applying the backpropagation algorithm, powered by stochastic gradient descent (SGD), for the estimation of SEM coefficients.

Main Results:

• Demonstrates the feasibility of representing SEMs within an ANN framework.
• Successfully applies the backpropagation algorithm with SGD to estimate SEM coefficients.
• Establishes a new computational approach for solving SEMs.

Conclusions:

• Artificial neural networks offer a viable and innovative alternative for modeling simultaneous equations.
• The backpropagation method with SGD provides an effective technique for estimating coefficients in SEMs.
• This research bridges econometrics and machine learning, opening new avenues for SEM analysis.