Chapter 15 Simultaneous Equation Models
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
• 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
• Simultaneous equation regression models: ——Regression models in which there is more than one equation in which there are feedback relationships among variables
15.1 The Nature of Simultaneous Equation Models C=B+B. Io YC+ 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 C If there are more endogenous variables, there will be more equations
15.1 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
15.2 The Simultaneous Equation Bias Inconsistency of ols Estimators C+ =(Bo+B1Y+u)+1 =B+B,Y+u+ B 1-B,1-B 1-B, The explanatory variable in a regression equation is correlated with the error term, this explanatory variable becomes a random, or stochastic variable
15.2 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 becomes a random, or stochastic variable. t t ut B I B B B Y 1 1 1 0 1 1 1 1 1 − + − + − =