Unbiased Estimation Method for Coefficients of Simultaneous Equations with Stochasticity of Exogenous Variables

The paper addresses the problem of obtaining more statistically robust parameter estimates for simultaneous equation models compared to traditional methods, including Ordinary Least Squares, Instrumental Variables, Two-Stage Least Squares, Maximum Likelihood Estimation, and Generalized Method of Moments. Ordinary Least Squares, Instrumental Variables and Two-Stage Least Squares methods minimize the sum of squared errors between observed data and theoretical dependencies, but they tend to be compromised when errors are correlated with variables included in these expressions. This violation of the fundamental independence assumption undermines the desirable properties of coefficient estimation, such as unbiasedness, efficiency, and consistency. The paper establishes the efficiency of estimates obtained through proposed Method of Factorization of Simultaneous Equations, supporting these findings with theorem and lemma.