課件ccer計量wooldrige聯(lián)立方程

1、Intermediate Econometrics, Yan Shen1Simultaneous Equations聯(lián)立方程 y1 = a1y2 + b1z1 + u1 y2 = a2y1 + b2z2 + u2Intermediate Econometrics, Yan Shen2Chapter Outline本章提要The Nature of Simultaneous Equations Models聯(lián)立方程性質(zhì)Simultaneity Bias in OLSOLS中的聯(lián)立偏差I(lǐng)dentifying and Estimating a Structural Equation識別與估計結(jié)構(gòu)方程

2、Intermediate Econometrics, Yan Shen3Lecture Outline本課提要What are Simultaneous Equations Models什么是聯(lián)立方程模型Simultaneity Bias in OLSOLS中的聯(lián)立偏差I(lǐng)dentifying and Estimating a Structural Equation識別和估計結(jié)構(gòu)方程Identification in a two-equation system雙方程系統(tǒng)的識別Estimation by 2SLS2SLS估計Intermediate Econometrics, Yan Shen4S

3、imultaneity聯(lián)立（同時決定） Simultaneity is a specific type of endogeneity problem.聯(lián)立是內(nèi)生性問題的一種特殊形式This arises when one or more of the explanatory variable is jointly determined with the dependent variable.當(dāng)一個或多個解釋變量與因變量被聯(lián)合決定時，這樣的問題就會出現(xiàn)。Intermediate Econometrics, Yan Shen5Simultaneity聯(lián)立 We often discuss the

4、simultaneity problem in the framework of simultaneous equations models (SEM).我們通常以聯(lián)立方程模型（SEM）為框架來討論聯(lián)立的問題。The classical example of an SEM is supply and demand equations for certain commodity.SEM的經(jīng)典例子是某種商品的供給和需求方程Intermediate Econometrics, Yan Shen6Demand for Agricultural good農(nóng)產(chǎn)品需求Intermediate Econome

5、trics, Yan Shen7Demand for Agricultural good: Interpretation對農(nóng)產(chǎn)品的需求：解釋Equation (1) describes the behavior of customers, (2) describes the behavior of farmers in supplying the good. 方程（1）描述了消費(fèi)者的行為,（2）描述了農(nóng)民的供給行為。Each equation has a ceteris paribus interpretation.每一個方程都有“固定其它因素不變”的解釋.Intermediate Econo

6、metrics, Yan Shen8Demand for Agricultural good: Interpretation對農(nóng)產(chǎn)品的需求：解釋Can the price variables be considered as exogenous in (1) or (2)?(1)或(2)里的價格變量是否可以當(dāng)作外生？No. The observed price is the equilibrium price. 不。觀察到的價格是均衡價格.Intermediate Econometrics, Yan Shen9Demand for Agricultural good: Interpretati

7、on對農(nóng)產(chǎn)品的需求：解釋Equations (1) and (2) e linked only because observed price is determined by the intersection of supply and demand.方程(1)和(2)的聯(lián)系只是由于觀察到的價格是由供給和需求曲線的交點決定的。Intermediate Econometrics, Yan Shen10Demand for Agricultural good: Interpretation對農(nóng)產(chǎn)品的需求：解釋Intermediate Econometrics, Yan Shen11Demand f

8、or Agricultural good: Features對農(nóng)產(chǎn)品的需求：特性Given e, rainfall, and unobserved demand and supply shifters, (1) and (2) determines quantity and price.給定收入，降雨量，不可觀測的供給和需求因素，(1)和(2)決定了產(chǎn)量和價格Price and quantity are endogenous variables in this SEM, since they are jointly determined in the system.產(chǎn)量和價格在這個聯(lián)立方程模型

9、中為內(nèi)生變量，因為它們被系統(tǒng)聯(lián)合決定。Intermediate Econometrics, Yan Shen12Demand for Agricultural good: Features對農(nóng)產(chǎn)品的需求：特性The exogenous variables, e, rainfall, are assumed to be uncorrelated with the structural errors. 我們假定外生變量如收入、降雨與結(jié)構(gòu)誤差不相關(guān)。In other words, these variables are truly determined outside of the system.換

10、言之，這些變量真的是在系統(tǒng)之外生成的。Intermediate Econometrics, Yan Shen13Demand for Agricultural good: Identification對農(nóng)產(chǎn)品的需求：識別How can we tell which equation is for the demand function, which is for supply?我們怎么知道哪個方程是需求方程，哪個是供給方程？Through the exogenous variables, where e is used in the demand equation, and rainfall i

11、s used in the supply equation.通過看方程中的外生變量，收入出現(xiàn)在需求方程中，降雨出現(xiàn)在供給方程中。Intermediate Econometrics, Yan Shen14Demand for Agricultural good: interpretation對農(nóng)產(chǎn)品需求：解釋W(xué)hat kinds of questions are we asking with simultaneous equations?我們使用聯(lián)立方程模型是要回答什么樣的問題？For example, how much goods the farmer will provide if the

12、price were different from its equilibrium value.例如，當(dāng)價格偏離其均衡價格時，農(nóng)民愿意提供多少產(chǎn)品。Intermediate Econometrics, Yan Shen15The murder rate example, 16.1, page 528謀殺率例子Emphasize that SEM is meaningful when each equation has a ceteris paribus interpretation.強(qiáng)調(diào)一點：當(dāng)每一個方程具有“固定其它因素不變”的解釋時，SEM是有意義的。Equation (16.6) des

13、cribes the behaviors of criminals, and equation (16.7) describes the behaviors of city officials in how much police officer is prepared.方程(16.6)描述了罪犯的行為，方程(16.7)描述了警察的數(shù)目與城市官員行為的關(guān)系。Intermediate Econometrics, Yan Shen16Simultaneity bias in OLSOLS中的聯(lián)立偏差A(yù)n explanatory variable that is determined simulta

14、neously with the dependent variable is generally correlated with the error term, which leads to bias and inconsistency in OLS.如果一個解釋變量與因變量被聯(lián)立決定，那么它通常與誤差項相關(guān)，這會導(dǎo)致OLS估計有偏及不一致。Intermediate Econometrics, Yan Shen17The simple model case一個簡單模型Intermediate Econometrics, Yan Shen18The simple model case一個簡單模型

15、Intermediate Econometrics, Yan Shen19Simultaneity bias聯(lián)立偏差When y2 is correlated with u1 because of simultaneity, we say that OLS suffers from simultaneity bias.如果聯(lián)立性使得 y2與 u1相關(guān)，我們稱OLS中有聯(lián)立偏差。Intermediate Econometrics, Yan Shen20Identification in a two-equation system雙方程模型的識別Consider a two-equation sy

16、stem of demand and supply functions. How can we identify each of them？考慮一個供給和需求的雙方程系統(tǒng)。我們怎么才能識別它們的每一個？Intermediate Econometrics, Yan Shen21Identification in a two-equation system雙方程系統(tǒng)的識別Intermediate Econometrics, Yan Shen22Identification in a two-equation system雙方程系統(tǒng)的識別Intermediate Econometrics, Yan

17、Shen23Identification in a two-equation system雙方程系統(tǒng)的識別From the perspective of observable shifters: changing z1 shifts the supply function without affecting the demand function. Therefore, we can trace the demand function out by shifting z1.從可觀測因素的角度來看：改變 z1會使供給方程變化，而并不影響需求方程。因此，我們可以通過改變 z1來將需求方程描繪出來。

18、Intermediate Econometrics, Yan Shen24Identification of Demand Equation需求方程的識別whDS (z=z1)S (z=z2)S (z=z3)Intermediate Econometrics, Yan Shen25Conditions for identification of a structural equation結(jié)構(gòu)方程的識別條件When can the two-equation system be solved?什么時候雙方程系統(tǒng)可解？When can all the parameters in the system

19、 be estimated?什么時候可以估計系統(tǒng)中所有的參數(shù)？Intermediate Econometrics, Yan Shen26The first equation in a two-equation simultaneous equations model is identified if, and only if, the second equation contains at least one exogenous variable (with a nonzero coefficient) that is excluded from the first equation.兩個聯(lián)立

20、方程中的第一個可以識別的充要條件是：第二個方程中至少包含一個外生變量（其系數(shù)不為零），且這個變量不出現(xiàn)在第一個方程中。Conditions for identification of a structural equation結(jié)構(gòu)方程的識別條件Intermediate Econometrics, Yan Shen27Example: Inflation and Openness例子：通貨膨脹和開放程度Intermediate Econometrics, Yan Shen28Example: Inflation and Openness例子：通貨膨脹和開放程度The main interest

21、is with the inflation equation. 主要的興趣在于通貨膨脹方程。Under what conditions will this equation be identified?什么條件下我們可以識別這個方程？Intermediate Econometrics, Yan Shen29Using IV to Estimate Demand使用IV來估計需求 Once we have determined that an equation is identified, we can estimate it by two stage least squares.當(dāng)我們知道某個

22、方程可以識別后，我們可以用兩階段最小二乘法來進(jìn)行估計。The instrumental variables consist of the exogenous variables appearing in either equation.工具變量包括在兩個方程中出現(xiàn)的所有外生變量。Intermediate Econometrics, Yan Shen30Inflation and Openness: Continued通貨膨脹和開放程度Intermediate Econometrics, Yan Shen31We first check whether log(land) has suffici

23、ent correlation with openness先檢驗log(land)是否與開放程度足夠相關(guān). reg open lpcinc lland Source | SS df MS Number of obs = 114+ F( 2, 111) = 45.17 Model | 28606.1936 2 14303.0968 Prob F = 0.0000 Residual | 35151.7966 111 316.682852 R-squared = 0.4487+ Adj R-squared = 0.4387 Total | 63757.9902 113 564.230002 Root

24、 MSE = 17.796 open | Coef. Std. Err. t P|t| 95% Conf. Interval+ lpcinc | .5464812 1.49324 0.37 0.715 -2.412473 3.505435 lland | -7.567103 .8142162 -9.29 0.000 -9.180527 -5.953679 _cons | 117.0845 15.8483 7.39 0.000 85.68006 148.489Intermediate Econometrics, Yan Shen32The OLS RegressionOLS回歸. reg inf open lpcinc Source | SS df MS Number of obs = 114+ F( 2, 111) = 2.63 Model | 2945.92812 2 1472.96406 Prob F = 0.0764 Residual | 62127.4936 111 559.70715 R-squared = 0.0453+ Adj R-squared = 0.0281 Total | 65073.4217 113 575.870989 Root MSE = 23.658 inf | Coef. Std. Err. t P