Pérez-Sánchez Belén, Perea Carmen, Duran Ballester Guillem, López-Espín Jose J
Center of Operations Research, Universidad Miguel Hernández de Elche, Elche, Alicante, Spain.
Fragile Tech, Palma de Mallorca, Mallorca, Spain.
PeerJ Comput Sci. 2024 Oct 8;10:e2352. doi: 10.7717/peerj-cs.2352. eCollection 2024.
Simultaneous equation model (SEM) is an econometric technique traditionally used in economics but with many applications in other sciences. This model allows the bidirectional relationship between variables and a simultaneous relationship between the equation set. There are many estimators used for solving an SEM. Two-steps least squares (2SLS), three-steps least squares (3SLS), indirect least squares (ILS), . are some of the most used of them. These estimators let us obtain a value of the coefficient of an SEM showing the relationship between the variables. There are different works to study and compare the estimators of an SEM comparing the error in the prediction of the data, the computational cost, . Some of these works study the estimators from different paradigms such as classical statistics, Bayesian statistics, non-linear regression models, . This work proposes to assume an SEM as a particular case of an artificial neural networks (ANN), considering the neurons of the ANN as the variables of the SEM and the weight of the connections of the neurons the coefficients of the SEM. Thus, backpropagation method using stochastic gradient descent (SGD) is proposed and studied as a new method to obtain the coefficient of an SEM.
联立方程模型（SEM）是一种计量经济学技术，传统上用于经济学，但在其他科学领域也有许多应用。该模型允许变量之间存在双向关系以及方程组之间存在联立关系。有许多估计方法用于求解SEM。两阶段最小二乘法（2SLS）、三阶段最小二乘法（3SLS）、间接最小二乘法（ILS）等是其中最常用的一些方法。这些估计方法使我们能够获得一个SEM系数的值，该值显示了变量之间的关系。有不同的研究工作来研究和比较SEM的估计方法，比较数据预测中的误差、计算成本等。其中一些工作从不同的范式（如经典统计学、贝叶斯统计学、非线性回归模型等）来研究估计方法。本文提出将SEM视为人工神经网络（ANN）的一种特殊情况，将ANN的神经元视为SEM的变量，将神经元连接的权重视为SEM的系数。因此，提出并研究了使用随机梯度下降（SGD）的反向传播方法作为获得SEM系数的一种新方法。
