Instrumental Variables Estimation of Systems of Simultaneous Equations: Interrelation of Methods

Lyudmila O. Babeshko, Vera V. Ioudina, Maria Y. Mikhaleva, Irina V. Orlova


The article is devoted to the interrelation between methods of estimating parameters of simultaneous equations. Simultaneous equations model (SEM) is commonly used to model complex socio-economic phenomena. SEM is a set of linear simultaneous equations in which response variables are among explanatory variables in each equation of regression. This causes the problem of endogeneity and leads to biased and inconsistent estimation of parameters. There is a number of special methods to solve the problem of endogeneity of regressors: method of instrumental variables (IV), indirect least squares method (ILS), two-stage least squares method (2SLS), and three-stage least squares method (3SLS). In this article, the relationship between 2SLS and IV, ILS and 2SLS, ILS and OLS with restrictions on structural parameters, as well as the equivalence of point estimates of parameters and autocovariance matrices, is shown using empirical example.


System of simultaneous equations, instrumental variables method, parameter constraints, parameter estimates, autocovariance matrix of parameter estimates.

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ISSN: 1929-7092