6-11 What determines whether an Equation is Identified or not? We could have three possible situations 1. An equation is unidentified like(12)or(13) we cannot get the structural coefficients from the reduced form estimates 2. An equation is exactly identified eg.(4)or(5) can get unique structural form coefficient estimates 3. An equation is over-identified Example given later More than one set of structura coefficients could be obtained from the reduced form C Chris brooks2002,陈磊204
© Chris Brooks 2002, 陈磊 2004 6-11 We could have three possible situations: 1. An equation is unidentified · like (12) or (13) · we cannot get the structural coefficients from the reduced form estimates 2. An equation is exactly identified · e.g. (4) or (5) · can get unique structural form coefficient estimates 3. An equation is over-identified · Example given later · More than one set of structural coefficients could be obtained from the reduced form. What Determines whether an Equation is Identified or not?
What determines whether an Equation is Identified or not? How do we tell if an equation is identified or not? There are two conditions we could look at The order Br condition- is a necessary but not sufficient condition for an equation to be identified The rank f condition-is a necessary and sufficient condition for identification 在G个内生变量、G个方程的联立方程组模型中,某一方程 是可识别的,当且仅当该方程没有包含的变量在其他方程中 对应系数组成的矩阵的秩为G-1 对于相对简单的方程系统,这两个规则将得到同样的结论。 ·事实上,大多数经济和金融方程系统都是过度识别的。 C Chris brooks2002,陈磊204
© Chris Brooks 2002, 陈磊 2004 6-12 • How do we tell if an equation is identified or not? • There are two conditions we could look at: - The order 阶condition - is a necessary but not sufficient condition for an equation to be identified. - The rank 秩 condition - is a necessary and sufficient condition for identification. 在G个内生变量、G个方程的联立方程组模型中，某一方程 是可识别的，当且仅当该方程没有包含的变量在其他方程中 对应系数组成的矩阵的秩为G -1。 • 对于相对简单的方程系统，这两个规则将得到同样的结论。 • 事实上，大多数经济和金融方程系统都是过度识别的。 What Determines whether an Equation is Identified or not?
6-13 Statement of the order condition Statement of the Order condition Let g denote the number of structural equations An equation is just identified if the number of variables excluded from an equation is G-1 If more than g-l are absent it is over-identified If less than g-1 are absent it is not identified Example the ys are endogenous. while the Xs are exogenous Determine whether each equation is over-, under-, or just- identified 1=a+ax1y2+33+a4X1+a5X2+l 12=A6+A13+A2X1+ (14)-(16) ro +ril2+ C Chris brooks2002,陈磊2004
© Chris Brooks 2002, 陈磊 2004 6-13 Statement of the Order Condition • Let G denote the number of structural equations. • An equation is just identified if the number of variables excluded from an equation is G-1. • If more than G-1 are absent, it is over-identified. • If less than G-1 are absent, it is not identified. Example • the Y’s are endogenous, while the X’s are exogenous. Determine whether each equation is over-, under-, or justidentified. (14)-(16) Statement of the order condition Y Y Y X X u Y Y X u Y Y u 1 0 1 2 3 3 4 1 5 2 1 2 0 1 3 2 1 2 3 0 1 2 3 = + + + + + = + + + = + +
6-14 Example of the order condition Solution G=3; If# excluded variables =2, the eqn is just identified If# excluded variables >2, the eqn is over-identified If# excluded variables <2, the eq" is not identified Equation 14: Not identified Equation 15: Just identified Equation 16: Over-identified 如果模型中每个结构方程都是可识别的,则称结构型联立方程 组模型是可识别的 C Chris brooks2002,陈磊204
© Chris Brooks 2002, 陈磊 2004 6-14 Solution G = 3; If # excluded variables = 2, the eqn is just identified If # excluded variables > 2, the eqn is over-identified If # excluded variables < 2, the eqn is not identified Equation 14: Not identified Equation 15: Just identified Equation 16: Over-identified 如果模型中每个结构方程都是可识别的，则称结构型联立方程 组模型是可识别的。 Example of the order condition
6-15 5外生性的定义 Leamer(1985): p310 变量X对变量Y是外生的,如果变量Y关于X的条件分布不随 产生X的过程的变化而改变。 外生性的两种形式: 前定变量:与方程中的当前和未来误差项独立。 ·严格外生变量:与方程中任何时期的误差项独立。 前定变量的通常定义:包括外生变量和滞后的内生变量 C Chris brooks2002,陈磊204
© Chris Brooks 2002, 陈磊 2004 6-15 5 外生性的定义 Leamer（1985）：p310 变量X对变量Y是外生的，如果变量Y关于X的条件分布不随 产生X的过程的变化而改变。 外生性的两种形式： • 前定变量：与方程中的当前和未来误差项独立。 • 严格外生变量：与方程中任何时期的误差项独立。 前定变量的通常定义：包括外生变量和滞后的内生变量