tailieunhanh - Lecture Advanced Econometrics (Part II) - Chapter 12: Simultaneous equations models

Lecture "Advanced Econometrics (Part II) - Chapter 12: Simultaneous equations models" presentation of content: Model, rank and order conditions for identification, estimation of a simultaneous equation system. | Advanced Econometrics Chapter 12 Simultaneous equations models Chapter 12 SIMULTANEOUS EQUATIONS MODELS I. MODEL Many economic problems involve the interaction of multiple endogenous variables within a system of equations. Estimating the parameters of such as system is typically not as simple as doing OLS equation-by-equation. Issues such as identification wether the parameters are even estimable and endogeneity bias are then primary topic in this chapter. 1. Example Demand and supply for peanuts at t qd t aPt S1t Vst pPt YRt 2t aPt S1t ppt rRt 2t a-ppt YRt 2t -su -1 R a-P t a-P qt quantity pt price Rt input price. Equilibrium qd t qs t qt The model is the joint determination of price and quantity qt and Pt are endogenous variables Rt is assume determined outside the model it is exogenous variable. All three equations are needed to determine the equilibrium price and quantity. Note The completeness of the system requires that the number of the equations equals the number of endogenous variables. 2. General model The simultaneous system can be written as Nam T. Hoang University of New England - Australia 1 University of Economics - HCMC - Vietnam Advanced Econometrics Chapter 12 Simultaneous equations models Where Yt Y1 Y2 . Ym t Yt r Xt B St 0 1xM M xM 1xK KxM 1xM X X1 X2 . Xm t é 1 2 M t 712 Ĩ1M r M xM Y21 YM1 YM 2 B M xM A 12 P22 Him P2M Jt a P11Pt P12 1 plP- 1t q a2 p21Pt 2t It Income P price of an alternative qt pt Endogenous determined within the model It Rt P Exogenous determined outside the model Matrix form q Pt ___v___ Y -1 -1 P1 P21 a u It Pt P12 P13 -V- X a2 0 1t 2t 0 0 Y 22 Y 2 M YMM M1 M 2 r B 0 1 3. Reduced form Each endogenous variable is expressed in terms of all exogenous variables Yt Xt n Vt Where n - B r-1 K xM K xM Nam T. Hoang University of New England - Australia 2 University of Economics - HCMC - Vietnam Advanced Econometrics Chapter 12 Simultaneous equations models V. st r- UM UM xM If the system is completeness r squared matrix is .