個(gè)體隨機(jī)效應(yīng)模型

1、個(gè)體隨機(jī)效應(yīng)模型在面板數(shù)據(jù)的計(jì)量分析中，如果解釋變量對(duì)被解釋變量的效應(yīng)不隨個(gè)體和時(shí) 間變化，并且解釋被解釋變量的信息不夠完整，即解釋變量中不包含一些影響被 解釋變量的不可觀測(cè)的確定性因素， 可以將模型設(shè)定為固定效應(yīng)模型，采用反映 個(gè)體特征或時(shí)間特征的虛擬變量(即知隨個(gè)體變化或只隨時(shí)間變化)或者分解模 型的截距項(xiàng)來(lái)描述這些缺失的確定性信息。但是，固定效應(yīng)模型也存在一定的不足。例如固定效應(yīng)模型模型中包含許 多虛擬變量時(shí)，減少了模型估計(jì)的自由度；實(shí)際應(yīng)用中，固定效應(yīng)模型的隨機(jī) 誤差項(xiàng)難以滿足模型的基本假設(shè)，易于導(dǎo)致參數(shù)的非有效估計(jì)。更為重要的是， 它只考慮了不完整的確定性信息對(duì)被解釋變量的效應(yīng)，而未

2、包含不可觀測(cè)的隨 機(jī)信息的效應(yīng)。為了彌補(bǔ)這一不足，Maddala(1971)將混合數(shù)據(jù)回歸的隨機(jī)誤差 項(xiàng)分解為截面隨機(jī)誤差分量、時(shí)間隨機(jī)誤差分量和個(gè)體時(shí)間隨機(jī)誤差分量三部 分，討論如下 隨機(jī)效應(yīng)模型或雙分量誤差分解模型(1):KyitikXkitUi v 代k 2UN(0, u2)表示個(gè)體隨機(jī)誤差分量；vt N(0, v2)表示時(shí)間隨機(jī)誤差分量；WitN(O, w2)表示個(gè)體時(shí)間(或混合)隨機(jī)誤差分量。如果模型(1)中只存在截面隨機(jī)誤差分量Ui而不存在時(shí)間隨機(jī)誤差分量vt， 則稱(chēng)為個(gè)體隨機(jī)效應(yīng)模型，否則稱(chēng)為個(gè)體時(shí)間小于模型?；蛘叻Q(chēng)為但分了誤差分 解模型。下面來(lái)介紹這兩種模型：1.個(gè)體隨機(jī)效應(yīng)模

3、型當(dāng)利用面板數(shù)據(jù)研究擁有擁有充分多個(gè)體的總體經(jīng)濟(jì)特征時(shí)，若利用總體數(shù)據(jù)的固定效應(yīng)模型就會(huì)損失巨大的自由度，使得個(gè)體截距項(xiàng)的估計(jì)不具有有效 性。這時(shí)，可以在總體中隨機(jī)抽取 N個(gè)樣本，利用這N個(gè)樣本的個(gè)體隨機(jī)效應(yīng) 模型：Kyit1kXkit Ui Wit(2)k 2推斷總體的經(jīng)濟(jì)規(guī)律。其中，個(gè)體隨機(jī)誤差項(xiàng) Ui是屬于第i個(gè)個(gè)體的隨機(jī)干擾分量，并在整個(gè)時(shí)間范圍(t=1,2,T)保持不變，其反映了不隨時(shí)間變化的 不可觀測(cè)隨機(jī)信息的效應(yīng)。檢驗(yàn)：個(gè)體隨機(jī)效應(yīng)的原假設(shè)和備擇假設(shè)分別是：H。： u20 (混合估計(jì)模型)0(個(gè)體隨機(jī)效應(yīng)模型)2個(gè)體隨機(jī)效應(yīng)的檢驗(yàn)統(tǒng)計(jì)量：LM =NT2 2NT2?iti 1 i

4、11N N1?22(T 1)iti 1 t 1其中，彳是混合模型OLS估計(jì)的殘差。在零售下，統(tǒng)計(jì)量 LM服從1個(gè)自 由度的2分布，即LM 2（1）。2.個(gè)體時(shí)間隨機(jī)效應(yīng)模型實(shí)踐：一、數(shù)據(jù)：已知19962002年中國(guó)東北、華北、華東15個(gè)省級(jí)地區(qū)的居民 家庭人均消費(fèi)（cp，不變價(jià)格）和人均收入（ip，不變價(jià)格）居民，利用數(shù)據(jù)（1）建立面板數(shù)據(jù)（panel data工作文件；（2）定義序列名并輸入數(shù)據(jù)；（3） 估計(jì)選擇面板模型；（4）面板單位根檢驗(yàn)。年人均消費(fèi)（consume和人均收入（income）數(shù)據(jù)以及消費(fèi)者價(jià)格指數(shù)（p）分別見(jiàn)表1，2和3。表1 1996 2002年中國(guó)東北、華北、華東 1

5、5個(gè)省級(jí)地區(qū)的居民家庭人均消費(fèi)（元）數(shù)據(jù)人均消費(fèi)1996199719981999200020012002CONSUMEAH3607.433693.553777.413901.814232.984517.654736.52CONSUMEBJ5729.526531.816970.837498.488493.498922.7210284.6CONSUMEFJ4248.474935.955181.455266.695638.746015.116631.68CONSUMEHB3424.354003.713834.434026.34348.474479.755069.28CONSUMEHLJ3110.92

6、3213.423303.153481.743824.444192.364462.08CONSUMEJL3037.323408.033449.743661.684020.874337.224973.88CONSUMEJS4057.54533.574889.435010.915323.185532.746042.6CONSUMEJX2942.113199.613266.813482.333623.563894.514549.32CONSUMELN3493.023719.913890.743989.934356.064654.425342.64CONSUMENMG2767.843032.33105.

7、743468.993927.754195.624859.88CONSUMESD3770.994040.634143.964515.0550225252.415596.32CONSUMESH6763.126819.946866.418247.698868.199336.110464CONSUMESX3035.593228.713267.73492.983941.874123.014710.96CONSUMETJ4679.615204.155471.015851.536121.046987.227191.96CONSUMEZJ5764.276170.146217.936521.547020.227

8、952.398713.08表2 1996 2002年中國(guó)東北、華北、華東15個(gè)省級(jí)地區(qū)的居民家庭人均收入（元）數(shù)據(jù)人均收入1996199719981999200020012002INCOMEAH4512.774599.274770.475064.65293.555668.86032.4INCOMEBJ7332.017813.168471.989182.7610349.6911577.7812463.92INCOMEFJ5172.936143.646485.636859.817432.268313.089189.36INCOMEHB4442.814958.675084.645365.035661

9、.165984.826679.68INCOMEHLJ3768.314090.724268.54595.144912.885425.876100.56INCOMEJL3805.534190.584206.644480.0148105340.466260.16INCOMEJS5185.795765.26017.856538.26800.237375.18177.64INCOMEJX3780.24071.324251.424720.585103.585506.026335.64INCOMELN4207.234518.14617.244898.615357.795797.016524.52INCOME

10、NMG3431.813944.674353.024770.535129.055535.896051INCOMESD4890.285190.795380.085808.966489.977101.087614.36INCOMESH8178.488438.898773.110931.6411718.0112883.4613249.8INCOMESX3702.693989.924098.734342.614724.115391.056234.36INCOMETJ5967.716608.397110.547649.838140.58958.79337.56INCOMEZJ6955.797358.727

11、836.768427.959279.1610464.6711715.6表3 19962002年中國(guó)東北、華北、華東15個(gè)省級(jí)地區(qū)的消費(fèi)者物價(jià)指數(shù)物價(jià)指數(shù)1996199719981999200020012002PAH109.9101.310097.8100.7100.599PBJ111.6105.3102.4100.6103.5103.198.2PFJ105.9101.799.799.1102.198.799.5PHB107.1103.598.498.199.7100.599PHLJ107.1104.4100.496.898.3100.899.3PJL107.2103.799.29898.610

12、1.399.5PJS109.3101.799.498.7100.1100.899.2PJX108.410210198.6100.399.5100.1PLN107.9103.199.398.699.910098.9PNMG107.6104.599.399.8101.3100.6100.2PSD109.6102.899.499.3100.2101.899.3PSH109.2102.8100101.5102.5100100.5PSX107.9103.198.699.6103.999.898.4PTJ109103.199.598.999.6101.299.6PZJ107.9102.899.798.81

13、0199.899.1二、1輸入操作：步驟：（1）FileNewWorkfile而亡 Edit Objec tView Proc Quick OpttansAdd-ins WindowHelporkfile.,Ctri亠忖O.pen.Database.SaveCtrl*5Prog ramSave As,h.led Fileflcis 亡Jmpartk步驟:(2) Start dateEnd dateOK步驟:(3) ObjectNew Object步驟:(4) Type of objectPool目 Workfile; New Objectsew嚴(yán)gjRange: 199Gample 1006c

14、百 rasid< > .Untitledr /r* nf nhjpctiMannF finr objectPoolpoolmodelEqualmnFactDfGraph Group logLMa trix-V ector -Coef ModelSampJp ScalarSerieE S#ri#s Link series Alpha Spwl SSpace Stririg svectoi System TabisTe)rt VdlMdtJ VAR步驟:步驟:將表1、2、3中的數(shù)據(jù)復(fù)制到Eviews中步驟：（5）輸入所有序列名稱(chēng)CE Pool: POOLMODEL Workfile:

15、UNT|TLED:Untitled - 口View | Proc Object | | Print | iNa m e Freeze Estimate D-elfine | PoolGenrj Sheet Cross Sac lien IderLti f rs： CEnt*!5 idaitii £i talow thi s lisn 呂0 AHBJFJHBHULJSJXlmMMGSDSHsxTJZJ(6) 定義各變量點(diǎn)擊 sheet輸入 con sume? in come ? p?E Pool: POOLMODEL Workfile: UNTITLED;:Untitled_ Q XV

16、iewProc Object |Print nameFreezeEstimateDefinePoolGenrSheetCross Sscti on Idsnti AHBJHB HLJl_X.LNNMGSDSH SX TJ ZJ(7)Ot)SCONSUME?INCOME?P?CONSUME?INCOME?p? rAH-19563607.4304512.770109 9000 nAh19Q73693.5504599.270101.3000AH-19S83777.4104770 470100 0000AH-19993901.810506460097.60000AH-2Q04232.9305293.5

17、501007000AH-20C14517.6505569.3001Q0.5000AH-20C2473b 5206032 40099.00000BJ-19965729 5207332 010111 6000BJ-19976531 8107813.160105.3000 0J-19986970.8308471 9801024000BJ-19997498.4809182.760100 50000J-2OOO049349010349 69103 50002.估計(jì)操作:步驟：（1）點(diǎn)擊 poolmodelEstimate 丹p 電 PzirlL Nieijniic F j«r»c&#

18、177;iel*iir w ta * £iL wl-i： AL L £1 «lr ta *(.Jif J.i4 wiir 山k L d li弘*X v4f Llhl. X1 inv JAH 燈 rmHUJLJSJXUTNMGSD£Wr=K丁丁ZTPool LstriimatiomOip-tidn-s-I尺上老上NOh弓 Oi-id AR0 tehrTi鼻鼻盯 SLornmc-ni co -effi ci« ntcih/l 斗 t bcBdlLoa<Cil 雯quufe* ac dridi AR)Sampll-e!-:1M6 2002n i

19、fifllffliTl'CeI 1 J SHBrnpl#Depe nden t variable:被解釋變量；Com mon ：系數(shù)相同部分Cross-section specific:截面系數(shù)不同部分步驟：（2）將截距項(xiàng)選擇區(qū)選 Random effects （個(gè)體隨機(jī)效應(yīng)）Cross-section： Random備注：若是個(gè)體時(shí)間小于模型貝U選擇cross-section random period random對(duì)話框說(shuō)明Poo EstimationSpedfkatHjnOptionsconsume?-Regressors and ARQ tEmns-,M,l5, Common

20、coefficients：c ineome?Estimation nethoc-jjFixed and Random tfteets% Hoel:Crc» Mctiori!Cross-section spe匚ifk toeffi匚館匱弓;Weights: No weight:Period specific coefficientsMethod LS - Leait Squares (and AR)1996 2002iiBallaixelSampleWja. L 得到如下部分輸出結(jié)果:Dependent Variable: CONSUME9Method; Pooled EGLS (Cr

21、oss-section random effects)Date: 07/24/14 Time: 16'1SSample: 1995 2002Includea obseivations. 7Cross-sections included: 15Total pool (balancec：: obserM'ations: 105Swamy and Arora eslimator of component variancesVariableCoefficieniStcL Error(-StatisticProbC367.974379.373914.635&ego.aoooINC

22、OM 匚;10 7220000.01111564.92844o.aoooRandam Effects (Crass)AH-C-6.747120BJ-C3B5.5898FJ-C-53.00761HB-C-109 9263HLJ-C-107.3301JLC4S.37777s-c-34 23240230.4027LN-C107 9779MMG-C-1383494SD-C-1040005SH-C1425914SX-G-2630302TJ-C1227173ZJ-C114 3927相應(yīng)的表達(dá)式是:(64.9)R20.97,SSE 3066120其中虛擬變量D1,D2,., D15的定義是:1,如果屬于第i個(gè)個(gè)體,i=1,2,.,150,其他豪斯曼檢驗(yàn)：接下來(lái)利用Hausman統(tǒng)計(jì)量檢驗(yàn)應(yīng)該建立個(gè)體隨機(jī)效應(yīng)回歸模型