第十讲 受限因变量模型(Tobit)

第十一章受限因变量模型模型与方法BinaryChoiceModel(Logit或Probit)Multi-logitModelOrdered-logitModelCensoredModel(Tobit)审查模型TruncatedModel截断模型HeckmanModel(Incidentialtruncated)本章主要讲CensoredModel(Tobit)托宾(删失、审查)模型Tobit(Censored)Model*2***~(0,),00,0iiiiiiiiiiyxNyxyyy对yi0部分数据用OLS估计的结果iiiiiiiiiiiiixxExxxExyEyyE)|()|()|()0|(*0)|(iiixE∵-50-40-30-20-10010203040f(εi)εi00)|(iiixEixY*=-40+1.2X+uY=Y*ifY*0Y=0ifY*0Y*0ifu40-1.2X)10,0(~Nu例如：-40-30-20-100102030400102030405060uXY2.140*Y*XTOBIT模型的估计-40-30-20-100102030400102030405060YuXY2.140*XOLS：用全部实际观察到的数据-40-30-20-100102030400102030405060uXY2.140*YXOLS：用全部实际观察到的数据参数估计向下偏误Tobit模型问题：遗漏变量导致非零均值误差和内生问题*(|0)(|)(|)(|)iiiiiiiiiiiiiiiiiEyyEyxExxxExfxxmFiiiiiiiiimxFxfxEyE)/()/()|()0|(*0,00,),0(~***2*iiiiiiiiiiyyxyyNxy与Tobit模型相关的三个回归函数*1)[|]2)[|0,]3)[|][|0,]()iiiiiiiiiiiiiiEyxxfEyyxxFEyxFEyyxFxf0,00,),0(~***2*iiiiiiiiiiyyxyyNxy解释变量的边际效应jijiiiiiijjiijjiFxxyEFfFfxxxyyExxyE]|[)31],0|[)2]|[)12*调用奶牛数据库讲解度量了xj对E(y*/x)的偏效应，其中y*是潜变量。iiiiiiiiiiiiiifxFxyyEFxyEFfxxyyExxyE)(],0|[]|[)3],0|[)2]|[)1*条件期望无条件期望逆米尔斯比率InverseMillsratio2)和3)的关系jijiijiijiFxzFxyyExxyyEzFxxyE))((*],0|[],0|[*)(]|[Tobit模型的应用例：研究农户奶牛养殖头数的影响因素yijt=xijt+uijt或Yijt=f(Pj(t-3),Rjt,Yij2000,Hijt)1.模型：2.变量说明：上式中下标i和j分别代表农户和村；t代表年份，分别是2000年和2004年。被解释变量Y为农户养殖奶牛头数。在解释变量（x）中，P是衡量乳品加工企业的指标；R是当地交通条件，用村离县级以上公路的距离（公里）表示；Y表示家庭富裕程度，加入这变量是因为我们也关心贫困农户是否被排斥在外，Y用基期（2000年）农户家庭人均财产（元）表示，用基期的家庭财产而不用各年的收入，是为了避免收入的内生性问题；H是农户特征，包括户主年龄、受教育水平（年）、人均耕地面积（亩/人）﹑劳动力占总人口的比例（%），以及非农就业劳动力占总劳动力的比例。为待估计的系数。调用数据库：dairydata3.农户奶牛养殖与乳品加工企业的关系的简单描述分析表4北京周边地区25个奶牛村的奶牛养殖户的养殖情况与乳品加工企业之间的关系养奶牛户数（户）奶牛养殖户的户均养殖奶牛头数（头/户）前三年离村30公里内有乳品加工企业的村前三年离村30公里内无乳品加工企业的村2000744.53.420041457.73.6平均--6.73.5注：数据来源于25个奶牛养殖样本村的奶牛养殖农户的调查数据整理。TobitestimatesNumberofobs=480LRchi2(8)=29.35Probchi2=0.0003Loglikelihood=-956.95318PseudoR2=0.0151cownumberCoef.Std.Err.tPt[95%Conf.Interval]scaler303100.75293560.28788242.620.009.1872461.318625agehh-.13717040.0591357-2.320.021-.2533721-0.0209686eduhh.10531570.176140.60.550-.24079980.4514313labper2.9798652.6068251.140.254-2.1425528.102282offlab-5.1131921.78785-2.860.004-8.626323-1.600061pculti-.20073990.3599666-0.560.577-.90807530.5065954passet.00008620.00005161.670.096-.00001520.0001876roaddistant-.31939490.2355036-1.360.176-.78216010.1433702_cons1.2470273.45660.360.718-5.5452018.0392554.模型结果5.边际效应MarginalEffects:LatentVariablevariabledF/dxStd.Err.zPzX_at[95%C.I.]scaler303100.7529356.28788242.620.0091.35208.1886971.31717agehh-.1371704.0591357-2.320.02044.8083-.253074-.021267eduhh.1053157.176140.600.5506.7-.239912.450544labper2.9798652.6068251.140.253.707161-2.129428.08915offlab-5.1131921.78785-2.860.004.321513-8.61731-1.60907pculti-.2007399.3599666-0.560.5772.04953-.906262.504782passet.0000862.00005161.670.09510122.9-.000015.000187roaddistant-.3193949.2355036-1.360.1751.19687-.780973.142184_cons1.2470273.45660.360.7181-5.527788.02184MarginalEffects:UnconditionalExpectedValuevariabledF/dxStd.Err.zPzX_at[95%C.I.]scaler303100.2968965.11351742.620.0091.35208.074407.519386agehh-.0540888.0233183-2.320.02044.8083-.099792-.008386eduhh.041528.06945530.600.5506.7-.094602.177658labper1.1750161.0279191.140.253.707161-.8396693.1897offlab-2.016226.7049826-2.860.004.321513-3.39797-.634486pculti-.0791555.1419415-0.560.5772.04953-.357356.199045passet.000034.00002031.670.09510122.9-5.9e-06.000074roaddistant-.1259433.0928634-1.360.1751.19687-.307952.056066_cons.49172581.3630010.360.7181-2.179713.16316MarginalEffects:ConditionalonbeingUncensoredvariabledF/dxStd.Err.zPzX_at[95%C.I.]scaler303100.2326898.08896822.620.0091.35208.058315.407064agehh-.0423916.0182755-2.320.02044.8083-.078211-.006572eduhh.0325471.05443490.600.5506.7-.074143.139238labper.9209077.80562211.140.253.707161-.6580832.4999offlab-1.580199.5525235-2.860.004.321513-2.66312-.497272pculti-.0620374.1112453-0.560.5772.04953-.280074.155999passet.0000266.00001591.670.09510122.9-4.6e-06.000058roaddistant-.0987069.0727808-1.360.1751.19687-.241355.043941_cons.38538551.068240.360.7181-1.708332.4791MarginalEffects:ProbabilityUncensoredvariabledF/dxStd.Err.zPzX_at[95%C.I.]scaler303100.0294978.01127842.620.0091.35208.007393.051603agehh-.0053739.0023168-2.320.02044.8083-.009915-.000833eduhh.004126.00690060.600.5506.7-.009399.017651labper.1167423.10212771.140.253.707161-.083424.316909offlab-.2003198.0700427-2.860.004.321513-.337601-.063039pculti-.0078644.0141024-0.560.5772.04953-.035505.019776passet3.38e-062.02e-061.670.09510122.9-5.9e-077.3e-06roaddistant-.012513.0092263-1.360.1751.19687-.030596.00557_cons.0488548.13541940.360.7181-.216562.314272