联立方程估计

1、线性联立方程组估计线性联立方程组.PROC MODEL也可以达计线性联立方程.SY5UN过程提供 以下估计方法OLS. 2SLS. LIML.SCR. I ISLR, 3SLS, IBSLS.HMLa 不炎供 GMM 方 法（MODEL过程提供）.1介绍OLS Estimation加果不指定估il方法，默认用OLS.proc syslin data-in;demand: nodel q = p y 8； supply: nodel q p u;run;这相当于两个独立的OLS估计,但是由于联立性,估fl结果可能会有大的偏差.Two-Stage Least Squares Estimation价

2、格P足内生变量.外生变量为收入Y,单位成本U,替代品价格S.这时候用2SLS：proc syslin data-in 2sls； endogenous p;instruments y u a;demand： model q p y ; supply: nodel q = p u;run;这里告诉系狡p是内生变址.虽然q也是内生变色,但是q不作为解释变外,没 有必要列出来.往往所有前定受量都用作工具变量,这里Y,U,S都用作工具变量,用在第一步回 IQ中慎#IP.输出结果只有第二步.如果要看第一步结果,在MODEL语句中用FIRST选项。Analysis of VarianceSourceDFS

3、um ofSquaresMeanSquareF ValuePr FModel39.6708823.223627115.58 FModel29.6460984.823049253.96 |t|Variable LabelIntercept1-0.518780.490999-1.060.2952InterceptP11.3330800.05927122.49 0001Priceu1-1.146230.243491-4.71 |t|Variable LabelIntercept11.9802611.1691691.690.0959InterceptP1-1.176540.605012-1.940.0

4、568Pricey10.4041150.1171793.450.0011Incomes10.3592040 0850774.22 |t|Variable LabelIntercept1-0.518780.4909991.060.2952InterceptP11.3330800.05927122.49.0001Pncru1-1.146230.2434914.71 It|Variable SbelIntercept11.9885291.2336251.610.1126InterceptP1-1.181470.652274-1.810.0755Pricey10.4023100.1072693.750

5、.0004Incomes10.3613450.1038163.480.0010Price ofSubstitutesModelSUPPLYDependent VariableqLabelQuantityParameter EstimatesVariableDFPara meter EstimateStandardErrort ValuePr It|Variable LabelIntercept1-0.524430.479522-1.090.2787InterceptP11.3360830.05793923.06.0001Priceu11.148040.2377934.83.0001Unit C

6、ostFigure 19.7: FIML ResultsComputing Reduced Form Estimates可以用REDUCED选项输出帙型的REDUCED形式.proc ayalln dat*in 31ls reduced; endo9anouA p;inatrument， y u 8； demand: model q = p y s;supply: nodel qP U；Restricting Parameter Estimates可以用restrict语句和srestrict语句对赛数魄加线性约束。Restrict语句对 前面的nodel语句中的参数通加方程内的约率,而sre

7、strict用来谑加方程网的 ，数约束,这需要告诉摹统是哪个方程的冷数。有西种方法,如果方程有label, 直接用label.变最衣示相应的参数.如果没有label. E以用这个方程的因变量 作为labels输出加应拉格朗H乘数,proc ayalln data*in 3als;ndoganous p;insrrumnt y U |t|Variable LabelInterceptIntercept11.9802611.1691691.690.0959P1-1.176540.605012-1.940.0568PriceY10.4041150.1171793.450.0011Incomes10.

8、3592040.0850774.22 F11136790.0104Figure 19.10: TEST Statement Results跨方程的怆验要用proc syslln data*in 3als;endo9enoua p;instrumantfl y u s;demand: nodel q p y 0;supply: nodel q = p u;ateatl: atest demand.y .01 supply.u; run;The SYSUN Procedure Three-Stage Least Squares Estimation System Weighted MSEDegre

9、es of freedom|113System Weighted R-Square 0.9627ModelDEMANDDependent VariableqLabelQuanblyParameter EstimatesVariableDFParameter EstimateStandardErrort ValuePr a |t|Variable LabelIntercept11.9802611.1691691.690.0959InterceptP1-1.176540.605012-1.940.0568Pricey10.4041150.1171793.450.0011Incomenn COCC7

10、7a noSubstitutesModelSUPPLYDependent VariableqLabelQuantityParameter EstimatesVariableDFParameter EstimateStandard Errort ValuePr It|VHnble LabelIntercept1-0.518780.4909991.060.2952InterceptP11.3330800.05927122.49.0001Priceu11.146230.2434914.71 F111322.460.0001J以保存同测伯和殡希.在“Tin语句用。ut数融集,然后用在相应方程后血 用o

11、utput语句饰出要输出的变显和保存变显名.proc syslln dataln out*pred 3sls;endogenous p;inatrumontd y u s;demand: model q p y s;output predlctedqdcmand;supply: nodl q - p u；output predicted=1_suppLy;run;2语法:PROC SYSL1N options ；fiY variables;ENDOGENOUS variables;IDENTITY identities ;INSTRUMENTS variables ;MODEL respons

12、e = regressors / options ;OUTPUT PREDICTED= variable RESIDUAL= variable ;RESTRICT restrictions ;SRESTRICT restrictions ；SIESI equations ;TESY equations ；VAR variables ;WEIGHT vanable;PROC SYSLIN StatementPROC SYSLIN options；DATA= SAS-data-setOUT= SAS-data-set指定一个数据篥出及差和预色值.和后面3PW诲句配合使用.OUTEST= SAS-d

13、ata-set崎的叁数估计结果.OUTCOVCOVOUT纪参数方外矩内珈出H。心i= 里面.OUTCOV3COV3OUT使用3s1s.bg timl方出的时候,T而个方程的协方注矩田输出到ouy估计方法2SLS3SLSFIMLITSURIT3SLSLIMLOLSSUR出，REDUCED 抬出陵个的REDUCED FORM 必狈用IDENTITY lA句使俺解殳成方的ENDOGENOLIS StatementENDOGENOUS variables ;坦定第一步需要用，只交0件预知的内，殳S不一定是殳部的内牛女IDENTITY StatementIDEHTTrf equation ; 许出定义式

14、，怛等式.label: IDENTITY ;INSTRUMENTS StatementINSTRUMENTS variables ;MODEL StatementMODEL response = regressors / options ; 立力如下：CORRBCOVB DW NOINT OVERID过僮识别为奴检5ft.OUTPUT StatementOUTPUT PREDICTED= variable RESIDUAL=variable ;和SYSLIN中的OUT=数抠*配合隹用.PREDICTED= variableIRRECT-, PRFD- or I*-.RESIDUAL= vari

15、ableRESID-or R-proc syslln dataa outb; model y s xl x2;output p=yhat ryrsid; run;proc yslln data*in outbred; decaand: model q p y ;output p=q_demand rr_demand; supply: model q p u;output p*q_aupply rr_aupply; run;RESTRICT StatementRESTRICT equabon，.equation ;施加纹忖的虫.可以用NTERCEPT做板M1J配可以使用LABEL妇：label : RESTRICT 一 ;restrictreatriatinter8Pt x4 = 0;xl x2 , #3估。方法是加拉格朗H乘数.注意.RESTRICT语句不能用在FIML估讳方法中,SRESTRICT StatementSRESTRICT equation，.equation ;和RESTRICT爰不多.只是用于的方杵下数的七 用LARELSRIABLE讥加半缸 没书 LABEL的方程用该方程的因变件LAREL,只要没ff冲突.q以用LABEL 也不能在 FIML中用.label: SRESTRICT ;proc sydlln dataa 3sls