第11章 联立方程模型共25页文档

Simultaneous-Equation Model
Because Pt and Qt are endogenous, applying ordinary least squares to the estimation of the supply (or the demand) equation will generate biased and inconsistent estimators.
The Pt-1 is determined within the system-by past values of the variables, thus, lagged endogenous variables are predetermined variables. The variable Yt is determined completely outside the model and is called an exogenous variable.
Simultaneous-Equation Model
SEM consists of a series of equations with each equation serving to explain one variable which is determined in the model. Consider a threeequation supply-demand model described as follows:
For this reason, the variables QtD, QtS, and Pt are often called endogenous variables; they are determined within the system of equations.
The model also contains two variables whose values are not determined directly within the system, which is often called predetermined variables. Pt-1 and Yt are both predetermined variables in the model.
If we solve the structural model for each of the endogenous variables as a function solely of the predetermined variables in the model. Then, the transformed model is called reduced form model.
– Supply:
QtS=a1+a2Pt+et
– Demand: QtD=b1+b2Pt+b3Yt+ut
– Equilibrium: QtS=QtD
The model is often called a structural model
because its form is given by the underlying theory.
Simultaneous-Equation Model
We can see the endogeneity of the Pt and Qt variables graphically in the figure.
SEM: structural model
Considering following supply-demand system
Supply: QtS=a1+a2Pt+a3Pt-1+et Demand: QtD=b1+b2Pt+b3Yt+ut Equilibrium: QtS=QtD
Simultaneous-Equation Model
The supply equation, demand equation, and equilibrium condition determine the market price and the quantity supplied (and demanded) when the market is in equilibrium.
A structural model contains endogenous variables
on the left-hand side(LHS) and contains
endogeneous as well as predetermined variables
on thຫໍສະໝຸດ Baidu RHS.
SEM: reduced model
Content
Introduction to simultaneous-equation systems
The indentification problem Indirect least-squares estimation (ILS) Two-stage least squares (2SLS)
Considering a supply-demand models, in which the price of a products is simultaneously determined by the interaction of producers and consumers in a market.
Introduction to simultaneous-equation systems
So far, we concerned ourselves primarily with single-equation models. In this chapter we turn our attention to models consisting of several equations, in which the behavior of the variables is jointly determined.