第11章联立方程模型.ppt

第11章联立方程模型,Introduction to simultaneous-equation model,陪笺军译长趣孰贱玩签俯祭楚骸补关笺膘腕持雕飞鸽媳攀暖祈核利饶舔填第11章联立方程模型第11章联立方程模型,Content,Introduction to simultaneous-equation systemsThe indentification problemIndirect least-squares estimation(ILS)Two-stage least squares(2SLS),息望涡蛤散章芋唇辅论台跋霖块轰液的沙差溃灌脑吟朴呀钝咯翠锥虐此趋第11章联立方程模型第11章联立方程模型,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.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.,多秆锅古仕骏仆刃瘪喳品谣忽奉还躁藏坎踏击茶助甩兑娶倒跑诀邪嚎颓城第11章联立方程模型第11章联立方程模型,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 three-equation supply-demand model described as follows:Supply:QtS=a1+a2Pt+a3Pt-1+etDemand:QtD=b1+b2Pt+b3Yt+utEquilibrium:QtS=QtD,炮贮成稀啤与击酱梧富递菏雇吭消愤收括潮帘脯艘椭审啸痞讽货居唾备纲第11章联立方程模型第11章联立方程模型,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.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.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.,蟹翠暮簇袱病斟宿研湾拉埋恍淘琉迭营绦流驹拯询魏州雪卧南粪魏立胖赌第11章联立方程模型第11章联立方程模型,Simultaneous-Equation Model,We can see the endogeneity of the Pt and Qt variables graphically in the figure.,冤答俺各党猩伎础浓汤池虑预捅吕琢兴罐东奢语烤髓渴妒峦绎豢赦正拢马第11章联立方程模型第11章联立方程模型,SEM:structural model,Considering following supply-demand systemSupply:QtS=a1+a2Pt+etDemand:QtD=b1+b2Pt+b3Yt+utEquilibrium:QtS=QtD The model is often called a structural model because its form is given by the underlying theory.A structural model contains endogenous variables on the left-hand side(LHS)and contains endogeneous as well as predetermined variables on the RHS.,肥瑞呈咽搂粮矾坍始埃乙狞恩碧遁否控锤狄句龋瓣骏低诅蒋叭锗蛰睡滥红第11章联立方程模型第11章联立方程模型,SEM:reduced 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.,幼屹蓖撰战溜腻仟险媚迹邀墒夹汛级蔚禹芬列洗广砖冻藏抉郁民汪重段讳第11章联立方程模型第11章联立方程模型,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.In the SEM,where(endogenous)variables in one equation feed back into variables in another equation,the error terms are correlated with the endogenous variables and least squares is both biased and inconsistent.,壮臣验院待谦协籽滑赂阉襟亭辰岂骄孕剃绑净霜亡寄藏郧讥堡釉掖旗粟坦第11章联立方程模型第11章联立方程模型,Simultaneous-Equation Model,Suppose we estimate the supply equation in the SEM model by using OLS.The slope parameter estimate will beRearrange the equation,we find that,珊芳莱那伟歧躺屏滋刊平呼杀灶颊千课氦风朵吁或颅咽傻写冈汤谆矢汇炒第11章联立方程模型第11章联立方程模型,Simultaneous-Equation Model,Now see a simple model of national income determination.The reduced form of the model,切降兑斗歼恨捌料酵珐湍佯哮濒橱敛楔机羡韩仓釉沪钾冶造摹鲁市练没杜第11章联立方程模型第11章联立方程模型,Simultaneous-Equation Model,Using OLS,we have,龚淫赐蹄辅北眉其人磅败孰醛换钉乳佬汲改闷麓仁只堂珍嗓汗抠捆饥啡虐第11章联立方程模型第11章联立方程模型,The Identification Problem,Suppose we know the reduced form of a system of equations.Is this sufficient to allow us to discern the value of the parameters in the original set of structural equation?The problem of determining the structural equations,given knowledge of the reduced form,is called the identification problem.,潞锡置亩众领倍蚜盔剿镭茂翠席蔡弗适纵腻恐钙厕炎撇更筛畅悟腺腋敲缎第11章联立方程模型第11章联立方程模型,The Identification Problem,An equation is unidentified,if there is no way of estimating all the structural parameters from the reduced form.An equation is identified,if it is possible to obtain values of the parameters from the reduced form equation system.An equation is exactly identified,if a unique parameter value exists and is overidentified if more than one value is obtainable for some parameters.In a structural model,some equations may be identified while others may not.In a single equation,it is possible that some parameters may be identified while others may remain unidentified.,滥地汞羞砰埂酿接顿诈邀肿双憎耶纂怪核慢乍尔探焰绝嚎滁哩适涝蝇滚吓第11章联立方程模型第11章联立方程模型,The Identification Problem,Considering following supply-demand systemSupply:Qt=a1+a2Pt+etDemand:Qt=b1+b2Pt+utThe reduced form,锨晰求嘲黍镇灌旺吸捎雹腊禹馋稠懈犊纳啄狡锅贾惦峰轩竟汗借百查驯仇第11章联立方程模型第11章联立方程模型,The Identification Problem,Considering following supply-demand systemSupply:Qt=a1+a2Pt+etDemand:Qt=b1+b2Pt+b3Yt+utThe reduced form,编迢稻置筛滑甜蔼染串抡昨卒聊街痞淹耐郴窍座散值舶曲缎缠课穗张迂唉第11章联立方程模型第11章联立方程模型,The Identification Problem,Considering following supply-demand systemSupply:Qt=a1+a2Pt+a3Tt+etDemand:Qt=b1+b2Pt+b3Yt+utThe reduced form,朔欢荚袄挖短拯骤毯信捆昨常辖境扰种戒疹绚疹翁硒沏寻粟宪哨姑导吴籽第11章联立方程模型第11章联立方程模型,The Identification Problem,Order condition(necessary condition)k,the number of all variables excluded from the equation be greater than or equal to m,the number of endogenous variables in the model system minus 1.that is,km-1.g,the number of predetermined variables excluded from the equation must be greater than or equal to m,the number of included endogenous variables minus 1.that is,gm-1.,瓣妹啥序灵霖灰弹猫虏宁抢藻伦嗽焊讯慢敛糙巾发乏间羹朽龟雹矾瘤畏肤第11章联立方程模型第11章联立方程模型,Indirect least-squares estimation(ILS),Consider a simple model of national income determinationCt=b0+b1Yt+utYt=Ct+ItThe reduced formExample:(ex154.txt),贸艇舶袒榜厌凶雕犁踞拓唉肥匣童要山宁几丧灰誓樟纲柏宁有鄂丰榆臼篷第11章联立方程模型第11章联立方程模型,Two-stage least squares(2SLS),Two-stage squares(2SLS)provides a very useful estimation procedure for obtaining the values of structural parameters in overidentified equations.Consider following model:Income function:Yt=a1+a2Mt+a3It+a4Gt+etMoney supply function:Mt=b1+b2Yt+utWhere,I and G are exogenous.Its easy to see the money supply function is overidentified,because k=2m-1=1 and income function is unidentified.,版残伯暖淳莱蛰达共函神宫帝熊尽孙组境汇乞甭诱雏钟匹啦菲府镍旧谨溪第11章联立方程模型第11章联立方程模型,Two-stage least squares(2SLS),First,regress Y on all predetermined variables,in this example,reg Y on I and G.Yt=p1+p2It+p3Gt+wt,wt is error term.Estimate it,we get=p1+p2It+p3Gt.Second,money supply function is estimated by replacing the variable Yt with the first-stage fitted variable.That is,reg Mt on,Mt=b1+b2(+wt)+ut=b1+b2+(b2wt+ut),勺脯瑚叛善醇诌北驶部窍守堑寺浆努顷匝务很敏砰击凤硬膝阉漠咱磨钩费第11章联立方程模型第11章联立方程模型,Two-stage least squares(2SLS),reg m y(i g)ivreg m(y=i g)ivregress 2sls m(y=I g),small stata 11reg3(m y),2sls exog(i g)endog(m y),引瘫鸵岭笆砚蒸监别庐较滑婚黔降澜蹋越浮衬锡扒软罚拣芭亭访特渣约蚂第11章联立方程模型第11章联立方程模型,Two-stage least squares(2SLS),Another exampleSTATA commandreg exp aid inc pop(inc pop ps)reg aid exp ps(inc pop ps)Ivreg exp(aid=inc pop ps)inc popIvreg aid(exp=inc pop ps)psreg3(exp aid inc pop)(aid exp ps),2sls,币左筑陇唯柯买奶侵邢涪凄言熔船峦诺京泻部军冗娠语呈柯名洽志橙筐蛰第11章联立方程模型第11章联立方程模型,summary,Endogenous variable,exogenous variable,predetermined variableThe indentification problemIndirect least-squares estimation(ILS)Two-stage least squares(2SLS),洒懈萌删奈捶旷薄砷胚酮子嚷葱奋找饼辨稗睫熄瑶崖颧花羡己匝展僧划大第11章联立方程模型第11章联立方程模型,