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

Abstract

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), etc. 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, etc. Some of these works study the estimators from different paradigms such as classical statistics, Bayesian statistics, non-linear regression models, etc. 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.