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

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

doi:10.6000/1929-7092.2019.08.69

Abstract

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.

Highlights

Systems of Equations: Specification and Estimation MethodsIn Econometrics, different systems of equations are used to describe many complex economic problems:- Systems of independent equations.- Systems of seemingly unrelated equations, SUR.- Systems of simultaneous equations, Simultaneous equations model (SEM) [Greene 2011], [Eliseeva, Kurysheva, Kosteeva 2008].In economic systems, in general, changes in some variables cannot occur with the absolute immutability of others, when formalizing them, the SEM is used more often than other systems
Two special econometric methods were developed to estimate parameters of the system of simultaneous equations: indirect least square method (ILS) and two stage least square method (2SLS). They allow to solve the problem of endogeneity of variables that appears during the estimation of the structural parameters of the system
To increase the precision of 2SLS estimators of structural parameters, we use the three stage least square method (3SLS) that considers a correlation of disturbances of some of the equations in the system [Kleiber, Zeileis 2008]

Summary

INTRODUCTION

In Econometrics, different systems of equations are used to describe many complex economic problems:. Two special econometric methods were developed to estimate parameters of the system of simultaneous equations: indirect least square method (ILS) and two stage least square method (2SLS). They allow to solve the problem of endogeneity of variables that appears during the estimation of the structural parameters of the system. To increase the precision of 2SLS estimators of structural parameters, we use the three stage least square method (3SLS) that considers a correlation of disturbances of some of the equations in the system [Kleiber, Zeileis 2008]. The method of instrumental variables can be used to solve the endogeneity problem in SEM, which leads to biased and inconsistent estimation. Autocovariance matrix of parameter estimates is calculated according to the formula [Magnus, Katyshev, Peresetzkyi, Golovan 2007]

T PZ X

CONCLUSION