个体随机效应模型

个体随机效应模型作者:日期:

个体随机效应模型在面板数据的计量分析中,如果解释变量对被解释变量的效应不随个体和时间变化，并且解释被解释变量的信息不够完整，即解释变量中不包含一些影响被解释变量的不可观测的确定性因素，可以将模型设定为固定效应模型，采用反映个体特征或时间特征的虚拟变量(即知随个体变化或只随时间变化)或者分解模型的截距项来描述这些缺失的确定性信息。但是，固定效应模型也存在一定的不足。例如固定效应模型模型中包含许多虚拟变量时，减少了模型估计的自由度；实际应用中，固定效应模型的随机误差项难以满足模型的基本假设，易于导致参数的非有效估计。更为重要的是,它只考虑了不完整的确定性信息对被解释变量的效应，而未包含不可观测的随机信息的效应。为了弥补这一不足,Maddala(1971)将混合数据回归的随机误差项分解为截面随机误差分量、时间随机误差分量和个体时间随机误差分量三部分，讨论如下随机效应模型或双分量误差分解模型(1):y=3+it 1 kkititit(1)k=2u〜N(0,b2)表示个体随机误差分量；TOC\o"1-5"\h\zi uv〜N(0,b2)表示时间随机误差分量；t vw〜N(0,b2)表示个体时间(或混合)随机误差分量。it w如果模型(1)中只存在截面随机误差分量u而不存在时间随机误差分量v，i t则称为个体随机效应模型,否则称为个体时间小于模型。或者称为但分了误差分解模型。下面来介绍这两种模型：1•个体随机效应模型当利用面板数据研究拥有拥有充分多个体的总体经济特征时，若利用总体数据的固定效应模型就会损失巨大的自由度，使得个体截距项的估计不具有有效性。这时，可以在总体中随机抽取N个样本，利用这N个样本的个体随机效应模型：y=3+it1 kkitiit (2)k=2推断总体的经济规律。其中，个体随机误差项U是属于第i个个体的随机干i扰分量，并在整个时间范围(t=1,2，•・・,!)保持不变，其反映了不随时间变化的不可观测随机信息的效应。检验：个体随机效应的原假设和备择假设分别是：H:b2=0(混合估计模型)0uH:b2丰0(个体随机效应模型)1 U个体随机效应的检验统计量:LM=NT2(LM=NT2(T-1)其中,E是混合模型OLS估计的残差。在零售下，统计量LM服从1个自由it度的X2分布，即LM〜X2（1）。2•个体时间随机效应模型实践：一、数据:已知1996—2002年中国东北、华北、华东15个省级地区的居民家庭人均消费（cp，不变价格）和人均收入（ip，不变价格）居民，利用数据（1）建立面板数据（paneldata）工作文件；（2）定义序列名并输入数据；（3）估计选择面板模型；（4）面板单位根检验。年人均消费（consume）和人均收入（income）数据以及消费者价格指数（p）分别见表1，2和3。表11996-2002年中国东北、华北、华东15个省级地区的居民家庭人均消费（元）数据人均消费19961997199819992CONSUMEAH3607.433693.553777.413901.84232.94514736.52187.65CONSUMEBJ5729.5656970.87498493.48910284.6231.8138.48922.72CONSUMEFJ4248.474935181.455266.695638.746015.116631.685.95CONSUMEHB3424.34003.713834.44026.34348.474475069.2539.758CONSUMEHLJ3110.923213.43303.13481.73824.44192.364462.082544CONSUMEJL3037.33408.033449.73664020.84337.224973.88241.687CONSUMEJS4057.54534889.435010.95323.185536042.63.5712.74CONSUMEJX2943199.613266.813482.333623894.54549.32.113.5612CONSUMELN3493.023719.913890.73989.94356.064655342.64434.42CONSUMENMG2767.83032.33103468.9394195.64859.8845.74927.752CONSUMESD3770.94040.634143.9645150225252.45596.95.05132CONSUMESH6763.126819.946866.418248868.19336.1104647.699CONSUMESX3033228.713267.3493941.874123.014710.965.5972.98CONSUMETJ4675204.15471.015851.56121.06987.7191.969.6153422CONSUMEZJ5764.276176216521.547020.227952.8710.147.93393.08表21996—2002年中国东北、华北、华东15个省级地区的居民家庭人均收入（元）数据人均收入19961997199819992INCOMEAH4512.774594770.475064.65293.555668.86032.49.27INCOMEBJ7332.07813.168471.989182.76103411577.7812463.9219.69INCOMEFJ516143.646486859.817432.268313.089189.3672.935.63INCOMEHB4442.814955084.65365.035661.165984.826679.688.674INCOMEHLJ3768.314090.4268.54595.144912.5425.876100.567288INCOMEJL3805.534190.584204480.0148105340.46260.16.6466INCOMEJS5185.795765.26017.856538.26800.237375.18177.64INCOMEJX3780.24071.324251.424720.585103.585506.026335.64INCOMELN4207.234518.14617.244898.65357.75797.016524.5219INCOMENMG3431.813944.674354770.535129.055535.8960513.02INCOMESD4890.25190.795380.085806489.977101.087614.3688.96INCOMESH8178438.898773.1109311718.0112883.413249.88.481.646INCOMESX3702.69394098.734342.614724.115391.056234.3689.92INCOMETJ5967.716608.397110.547649.838140.58958.79337.56INCOMEZJ697358.727836.768427.959279.1610464.6711715.655.79表31996—2002年中国东北、华北、华东15个省级地区的消费者物价指数物价指数19961997199819992PAH109.9101.310097.8100.7100.599PBJ111.6105.3102.4100.6103.5103.198.2PFJ105.9101.799.799.1102.198.799.5PHB107.1103.598.498.199.7100.599PHLJ107.1104.4100.496.898.3100.899.3PJL107.2103.799.29898.6101.399.5PJS109.3101.799.498.7100.1100.899.2PJX108.410210198.6100.399.5100.1PLN107.9103.199.398.699.910098.9PNMG107.6104.599.399.8101.3100.6100.2PSD109.6102.899.499.3100.2101.899.3PSH109.2102.8100101.5102.5100100.5PSX107.9103.198.699.6103.999.898.4PTJ109103.199.598.999.6101.299.6PZJ107.9102.899.798.810199.899.1二、1输入操作：步骤：(1)File——New——Workfi1e0FileEditObjectViewPro匚QuickOptionsAdd-insWindowHelpN.ewkWarkfilc...Ctrl+flO.penDatabase...SaveCtrl+5frograrnSaveAt...TextFileImport►步骤：（2）Startdate Enddate OK

srileEditObject|ViewProcQuickOptionsAdd-insWindowHelpNewObject...generateSe-ries...rManageLinks&.Formulae—FetchfromDR.UpdateselectedfromDB■…StoreselectedtoDB…r|w曰Copyseiectedc.BShowFetchS-toreDelete■RaiSarRenameselected.«... F2©0DeleteselectedP_riintSelected步骤：（4）Typeofobject Pool步骤：（5）输入所有序列名称rEPookPOOLMODIELWorkfile:UNTITLIED::Untitled\-口|View|ProcObjectPrintNameFreezeEstimateDefinePoolGenrSheetCrossSectian.IdentiEiere：（EnteridentiEierz"belowthisline）AHBJFJHBHLJ」LJSJXLhJNMGSDSHSXTJZJ步骤：（6）定义各变量点击sheet—输入consume?income?p?

EPool;POOLMODELWorkfile;UNTITLED;;Untitled\-nxViewProcObjectPrintNameFreezeEstimateDefinePoolGenrSheetCrossSec七1onIdentiAHBJFJHBHU」LJSJXLNNMGSDSHsxTJZJ步骤：(7)将表1、2、3中的数据复制到Eviews中obsC-ONSUME?INCOME?P?obsCONSUME?INCOME?P?AH-19963607.430451Z770109.9000AH-19973693.5504599.270101.3000AH-19983777.4104770.470100.0000AH-19993901.8105064.60097.80000AH-20004232.9S05293l5W100.7000AH-200-14517.6505663.S00100.5000AH-2002斗736.520603240099.QOOOOBJ-19965729.5207332.010111.6000BJ-19976531.8107B13L160105.3000BJ-199S6970.8308471.980102.4000BJ-19997498.4809132750100.6000BJ-20003493.49010349.69103.50002•估计操作：步骤：（1）点击poolmodel Estimate[ P「<jt]OR]上ufc] [P「[ P「<jt]OR]上ufc] [P「in+;|IMeaEt[ 上兀■][e日t:iE日1:上[DciFin上|Pcj口丨Gcei~Sh上壬七匸x-口口口Sacti^xb.工赳口i£云口X-□： C.Hxi'Lax-xdLaxi.-tifi^x-st<X?w 二Xxx~lqAMDJFJHBHLJTLJSJXLJJI4MGSDSH5XTTZJPoolEstimaticinSpecificationOptiori5口亡口endentvariable.；=Estin'iatioi-imrthQd・—：Fixe-djnidR.3ndorniEtffe-匚1t£Pcirjod；v*iNovva-ightcR■上口andAROterms-bi^,fDFnmbn匚i-i-e-ffi匚ie-ntt:EBtimationnettiri口日Lca?-t5quareo-CandARJSample-sI 1旦吕I眄n匚匕Sample-sSample!-耳史涟

对话框说明Dependentvariable:被解释变量;Common:系数相同部分Cross-sectionspecific:截面系数不同部分步骤:(2)将截距项选择区选Randomeffects(个体随机效应)Cross-section：Random备注：若是个体时间小于模型则选择cross-section:randomperiod：random

得到如下部分输出结果：□ependentVariatile:CONSUME^Method;PooledEGLS(Cross-sectionrandomeffects^□ate:07/24^14Time:16:18Sample:19962002Included!observations:7Cross-sectionsincluded:15Totalpool(balanced}observations:105SwamyandAroraestimatorofcomponentvariancesVariableCoefficientStd.Errort-StatisticProb.C367.974-379378914.635665o.aoooINCOME?0.7220000.01111864.93S44o.aoooRandamEffects(Crass}AH-C-6.747120BJ-C385.5398FJ-C-53.80761HB-C-109.92B3HU—C107.3301JL-C4837777-24.23240」H—0-2304927LN-C107.9779NhlG-C-138.3494SD-C-104.000BSH-C142.5914-SX-C-26.30302TJ-C12.27173ZJ-C114.3827相应的表达式是:

Consume=368.0+0.72Income-6.7D+385.6D+...+114.4DTOC\o"1-5"\h\zit it 1 2 15(64. 9 )R2二0.97,SSE=3066120其中虚拟变量D,D，…,D的定义是：1 2 15八［1,如果属于第i个个体,i=l,2,...,15i10,其他豪斯曼检验：接下来利用Hausman统计量检验应该建立个体随机效应回归模型还是个体固定效应回归模型。H:个体效应与回归变量(IP)无关(个体随机效应回归模型)0 itH:个体效应与回归变量（IP）相关（个体固定效应回归模型）1 it分析过程如下：步骤：（3）在上述输出结果选择：View—Fixed/RandomEffectsTesting—CorrelatedRandomEffects-HausmanTest0 EViews-EFileEditObjectViewPro匚QuickOptionsAdd-insWindo-wHelpViewProcObjectPrintNameFreezeEstimateID-efinePoolGenrSheetCro-ssSectionIdentifiersRe^recentationtbetimationUtitputq.Statistic Chi-Sq.d.f. ProbResiduals►CQ'ef匚^varianceMatrixIS.759161 1 0.0000Ca'effi