文档介绍：Chapter 15
Simultaneous Equation Models
Single equation regression models:
——The dependent variable, Y, is expressed as a linear function of one or more explanatory variables, the Xs.
Assumption the cause-and-effect relationship, if any, between Y and the Xs is unidirectional:
· explanatory variables are the cause;
· the dependent variable is the effect.
Simultaneous equation regression models:
——Regression models in which there is more than one equation in which there are feedback relationships among variables
The Nature of Simultaneous Equation Models
Ct=B1+B2Yt+ut Yt=Ct+It
Endogenous variable:
Variable that is an inherent part of the system being studied and that is determined within the system.
Variable that is caused by other variables in a causal system
Exogenous variable/predetermined variable:
Variable entering from and determined from outside the system being studied.
◆ If there are more endogenous variables, there will be more equations.
The Simultaneous Equation Bias: Inconsistency of OLS Estimators
Yt=Ct+It
=(B0+B1Yt+ut)+It
=B0+B1Yt+ut+It
The explanatory variable in a regression equation is correlated with the error term, this explanatory variable es a random, or stochastic variable.
In the presence of simultaneous problem, the OLS estimators are generally not BLUE. They are biased(in small sample)and inconsistent(in large sample)
Inconsistent estimator is the estimator which does not approach the true parameter value even if the sample size increases indefinitely.
. The Method of Indirect Least Squares(ILS)
1. Simplify the original model, and get the reduced form regression model
Ct=B1+B2Yt+ut
Ct=A1+A2I2+vt
A1=B1/(1-B2),A2=B2/(1-B2),andυt=ut/(1-B2).
2. Applying OLS to the reduced form of the model, get the OLS estimators of the reduced form model.
to the relationship between the parameters of the reduced form model and the parameters of the original model, obtain the estimators of the o