實(shí)驗(yàn)二單一方程模型的其他估計(jì)方法

1、實(shí)驗(yàn)二 單一方程模型的其他估計(jì)方法異方差的檢驗(yàn)與修正一、實(shí)驗(yàn)?zāi)康模毫私猱惙讲?（heteroscedasticity） 、 Goldfeld-Quandt 檢驗(yàn)、 Spearman rank correlation 檢驗(yàn)、Park 檢驗(yàn)、 Glejser 檢驗(yàn)、 Breusch-Pagan 檢驗(yàn)、 White 檢驗(yàn)、加權(quán)最小二乘法（ weighted least squares簡(jiǎn)記WLS）、模型對(duì)數(shù)變換法等基本概念及異方差產(chǎn)生的原因和后果。掌握異方差的檢驗(yàn)與修正方法以及如何運(yùn)用 Eviews 軟件在實(shí)證研究中實(shí)現(xiàn)相關(guān)檢驗(yàn)與 修正。二、基本概念：異方差（heteroscedasticy）就是對(duì)同

2、方差彳K設(shè) （assumption of homoscedasticity）的違反。 經(jīng)典回歸中同方差是指隨著樣本觀察點(diǎn) X 的變化，線性模型中隨機(jī)誤差項(xiàng)的方差并不改變，保持為常數(shù)。異方差的檢驗(yàn)有圖示法及解析法， 檢驗(yàn)異方差的解析方法的共同思想是， 由于不同的觀察值隨機(jī)誤差項(xiàng)具有不同的方差， 因此檢驗(yàn)異方差的主要問題是判斷隨機(jī)誤差項(xiàng)的方差與解釋變量之間的相關(guān)性。異方差的修正方法有加權(quán)最小二乘法和模型對(duì)數(shù)變換法等， 其基本思路是變異方差為同方差，或者盡量緩解方差變異的程度。三、實(shí)驗(yàn)內(nèi)容及要求：內(nèi)容：根據(jù)北京市1978-2007 年人均儲(chǔ)蓄與人均收入的數(shù)據(jù)資料，若假定X 為人均收入（元） ， Y

3、為人均儲(chǔ)蓄（元） ，通過建立一元線性回歸模型分析人均儲(chǔ)蓄受人均收入的線性 影響，并討論異方差的檢驗(yàn)與修正過程。要求： （ 1）深刻理解上述基本概念（ 2）思考：異方差的各種檢驗(yàn)方法所適用的情況及如何運(yùn)用加權(quán)最小二乘法（WLS ）修正異方差？（ 3）熟練掌握相關(guān)Eviews 操作四、實(shí)驗(yàn)指導(dǎo)：1 .用 OLS 估計(jì)法估計(jì)參數(shù)（ 1）導(dǎo)入數(shù)據(jù)打開 Eviews 軟件， 選擇 “ File ” 菜單中的“ New-Workfile ” 選項(xiàng)， 出現(xiàn) “Workfile Range對(duì)話框，在"Workfile frequency "框中選擇"Annual"，在&

4、quot;Start date"和"End date”框中 分別輸入“ 1978”和“ 2007” ，如下圖：Wcrlcfil 曰 C reateV/orkfte structure typeDd led regular frequency ，Date spedficabonFrequenc/：Irregular Dated and Panel workfiies maybe made from Unstructured woclcfiles t>y latier specifying date and/or other identifier series.End d

5、ate:Start date:V/ortfiie names (optional)WF：Page:OK |Cancel |圖1建立新文件然后單擊“ OK”，彈出如下窗口：圖2建立新文件在命令窗口輸入創(chuàng)建數(shù)組的命令" data shouru chuxu”來創(chuàng)建變量shouru、chuxu。并輸 入數(shù)據(jù)。如圖所示圖7殘差序列的散點(diǎn)圖修彳EViewsFik Edit Objsrt ViM Proc Qiiek Optiorc Add-int Window H©lpCommandddiashuuiu cnuxuz- CommandI I Capturt國(guó) Group： UNTTTL

6、tD Worldllu； CNTTTLED：UntitedSHOUBUCHUXU1978305 4| 106,9954128197g414 95123.41137121900501.36159181415919D1514.1 4199 2274211igs2561 05232 56547011QB35904731247379451GG46g3740144777B61935907 725227502528IM，1067 52664 52453271QR71 1P1 R7P71n'iew Proc Object Print Nome Freeze Dei自金365. 4Sort Edit-

7、 - Smpl*/- Compare.-P5th = c：user5ldckumerts DB - nene WF = untitled圖 3 建立 shouru、chuxu(2)回歸數(shù)據(jù)估計(jì)方程設(shè)模型為Y 12X,在Eviews命令窗口中輸入"ls chuxu c shouru ”并回車,得到如下結(jié)果:回 Equation: UNITTLED WorkFih: UNTm.ED:Untitledrirn1/iew Proc Object Print Harm Fieeze Eat mate Forecast Stats ResidsDependentVariabie. CHUXU M

8、ethod. Least Squares Dat職 03/07/20 Time: 01:07 Sample: 1S7S 2007 Included observations： 30VariableCoefficientstd Error t-StatisticProb.G詼葩0375442136-5.2700570 0000SHOURU2 707139O.C6OB44 44 49296口。00。R-squared0.9B&Q53Mean dependentvar1043.75Adju&t&d R-&quared0 985555S.D. dependent var

9、17749.41S.E. of regression2133 250Akaike info criterion18 23202Sum squared resid1N7E+0RSchwarzcrilerion18 32643Log livelihood-271.4953Hannan Cuinn alter.伯262glF-statistic1979.622DurblivWateon stat。一416577Prob(F-statistic)0 0000002 .異方差檢驗(yàn)(1)圖示法首先通過"Equation”對(duì)話框中"Procs"菜單的"Make Res

10、idual Series”命令生成殘差 序列E,點(diǎn)擊OK”。圖5生成殘差序列Quick”菜單中選« Graph”選項(xiàng)，再在彈出的對(duì)話框中輸入« X E2”圖6殘差序列圖不法并單擊“ OK”即可得到：再在"Graph Options”框中選擇散點(diǎn)圖(Scatter),并單擊“OK”即可得至k(2) Goldfeld-Quandt 檢驗(yàn)首先將時(shí)間定義為1978-1988,方法如下：在“ Workfile”對(duì)話框中選擇“ Procs”菜單的“set sample”選項(xiàng)，彈出如下窗口并把期間改為“1978 1988”。圖8樣本范圍的設(shè)定再在Eviews命令區(qū)輸入命令&qu

11、ot; LS Y C X ”回車得到:回 Equation; UNTITLED Workfile： UNTmED;:UntitleclView Proc Object Print Name Fresie E由mate Forecast Stat.5Dependent Variable: CHUXU Mettiod: Least Squares Date: 03A37/20 Time. 0122 Sample. 1978 1393 Included observations: 1Jvanaoiecoefficientsw. Error t-siatisticFrobC*253 422127767

12、1S *9.1266730.0000SHOURU0 0991230.03307426.543100 0000R-squared0.987317Mean dependent 面4119.70&4Adjusted R-squared0.965985S.D. dependerit var316.5141S E. of regression37.50799Akaike info criterion10.24995Sum squared resid12861 65Schwarz criterion10.32230Lag likelihood-54.37473Hannan-Quinn enter1

13、0.20435F-slaUsUc704 5364urbin-Watson slat20760 3SProbfF-statiEtic)0 000000圖69 1978-1995年數(shù)據(jù)的回歸結(jié)果即用OLS方法可求得下列結(jié)果：Y=-253.4221+0.899123X(1978-1988)(-9.127)(26.543)22R =0.98780 =12661.65其次用相同的方法將時(shí)間定義為1997-2007,回歸得到如下結(jié)果:回 Equstiont UNTTTLED Workfile: UN TITLE D:Untitled 回View Proc ObjectPrint Name Freeze1

14、I Estimate Forecast Stats Resids/art ableCoefficientStd. Error t-StatisticProD.C-7804.9541875.46241616160.0024SHOURIJ3.0639840.13127523.340230.0000R-squared0.9S374SMean dependentvaf336S7.64Adjusted R-squared0.331942S.D. dependent var14715.33S.E. of regression1977462Akaike info entenon10 17953Sum squ

15、ared resid3=193203Schwarz enterion16 25233Log likelihood-97,98990Hannan-Quinn alter.tfi 12438F-statistic544.7664Durbin-1. Vats an stat1.412590Prob(F-statistic)0,000000Dependent variable: CHU/；UMethod: Least SquaresDate1 03/07/20 Time: 01:29Sample. 1997 2007included observations. 11即:圖610 1997-2007年數(shù)

16、據(jù)的回歸結(jié)果丫=-7804.954+3.064X(1997-2007)(-4.16)(23.34)22R =0.9837e2 =351932082e2求F統(tǒng)計(jì)量：F 4=2779.5,查F分布表，給定顯著性水平=0.05,得臨界值_ 22F0.05(6,6) =4.28,比較 F=2779.5> FO.05(6,6) =4.28 則拒絕 H。： 12 ,表明隨機(jī)誤差項(xiàng)顯著存在異方差。(3) White 檢驗(yàn)將樣本時(shí)間還原為19782007,擬合方程“ Ls y c x”，在方程擬合的結(jié)果窗口點(diǎn)擊鼠標(biāo)進(jìn)行選擇：view/Residual Diagnostics/Heteroskedasti

17、city Tests ,出現(xiàn)對(duì)話框HeteroskedasticityTests ,選擇 White，點(diǎn)擊 “ OK ”Meti9ro5<e-dlasticitji' Ted5brecrtcaron為比ndtrn f/dr tsLiv：Theiea胎值 te sauaredcsic-La 與 on the ctcss prodj zt af the ongrial regresscrE an£ a zorstert.金 lnddu /Vhtr crass LeitteTsL tyje；Ereuscn -Pagan -Godfrey harv-efiROjCus-:cin

18、ii Te±tV/iid .OCCancelrxn從中可知 Obs* R2 =6.823,2 .P值為0.033 ,nR大于2 、(2)表明模型隨機(jī)誤差項(xiàng)存在異方差性。3.異方差的修正(1) WLS估計(jì)法選擇"Equation”對(duì)話框中Equation EstimationEstimate"菜單的"Option”選項(xiàng)。出現(xiàn)下圖所示Sp«ci ficaticn OptionsLnf力 matrix: Hd. f.Cceffi ciezd Corari wc» Etihad;A.dj.ns tin en-Qptimi Ntionptimi

19、 區(qū)制tiu ' method. -Gaus tonSt好MarquardtHex i mum500Corner geiLeeI 0.0001ObJfCT 國(guó)即w- Fir*-7*-Fcnwa鼠口Ht&IOSKm：d!:LEH T=L Whrt；FBUEVCQtis*R-6quaje(iSeal。6>rlmriGn SB3 fl?45265噂M彷 + 043243/4t> F(2.27)ProU 54曄皿)pro 6 51-3 1但由 12，0 030T ?？?。tlJ326A Equation： UNTULED Wprkfilb： UMTJTLtgUEUgTBSt

20、 E4UOlMlDcrenaeTt vansb t Llcn&d: Least EqLara 口supamgQ Time：otJS sanw： 1"日 3 M irclJKd axr7HMM JOVariableCcelhaenlSid. Error t-StetistcPirDfi.c1 羽 HB9.14241.0，的跟0.44Q4白 HQURLT200320570.02221.44J34410.1613SHDURU914.37974351S092J025260.04&UR-sqi.isred0227447I4ear dpendlrrt4247374Ad|ust*c

21、JR-MU4rtd017322130泊r503S90S3 E ofrfrgftSAWi*5M2Mmfo criirian61053Sue sqinrtd 中艮時(shí)5 6BFt14nhwAi7 rHerion3375065Log likelihood-501.1579H三口昌昨出"nn rrter33 65535F-stafeticDubn界st5 0n stat1 ?64£00P” MF-紀(jì)劍 Stic)0033693圖11White檢驗(yàn)結(jié)果圖12異方差修正L Displ setiingr in 二 口口tpqt確相卵消Inverse std.發(fā)現(xiàn)當(dāng)權(quán)重View PtqcPr

22、int HsmeFreeie LstiimatiE Fore castResids其中Variance是方差；Std. deviation是標(biāo)準(zhǔn)差；Inverse Variance是方差倒數(shù); dev是標(biāo)準(zhǔn)差倒數(shù)。經(jīng)過試錯(cuò)，選擇 Std. deviation分別填入權(quán)重 shouru、shouruA2> shouruA(-0.5) > shouruA(-1)> shouruA(-2), 取shouruA(0.9),異方差情況得到比較大的改善：回 Equation; UNTITLEDV/orkfile： UUTITLED：;Un冊(cè)lrd_=_l且旦JYi ew ProcObje

23、ct PrintNameFreeze EstimateForecastStatsRe51d 二HetfiroskfidastidtyT«H WhIteF-statistc0 307994Prob. F3,26)08194CJ3s*R-squared1.029545Prob. Chi-Squaref3) 7941Scaled explained SS0.332497Prob, Chi-3quareC3)0.9536TestEqu ation:Dependent Yaria Die. WGT_RESIDA2Methods Least SquaresDate. 03/07/20 Time:

24、 02.13Sample. 197S2D07Included observatons：30VariableCoeffidantStd Errort-StatislicProb.c252&597879577.3Q.2B7479口 7750SHOURUA2*WGT20.0327940980530.0658450.9480SH0URU*WGTA2-155.5209556.2558-0 27976507819WGTA2,14Afi1A Hfl 4H07PRn Fwm圖13 WLS估計(jì)結(jié)果加權(quán)修正后的擬合結(jié)果如下圖回 Equations UNTITLED V/orlcfile; UNTITLED

25、;Untitled;Dependent Variable CHUXUMethod. L日&引 Squa esDale: 03/07/20 Time: 02:23Sample: 197B 2007Included obserations: 3。Weighting series: SHOURU*0.9Voight typo Standard dovistion (avorago scaling)VariableCo&ffidentStd Errort-StatisticProb.C-1019478118.26268 6204600.0000SHOURU2 2042680104117

26、21 17102nooooWeighted StatisticsR-squared0.941203Mean dependent'/ar1747 521Adjusted R-squ are d3 939103S.D. depeidenl var120f 524S.E of regression514.9502Akaike info criterion15 33035Sum square j resid7424864.Schwarz criterion15.4B377Log lik«lihocd-228 B5B4Hsnnan*Cuinn crrt«r.15 42024F

27、-statistic448 2122Dubin-Watson stat0144170Prob(F-statistic)0.000000lA'eigtited mean dep.499 3748Unweighted StatisticsR-aquared0.946540Mean d«psndentar1403.75AdjusledR-squared0 944S30S.D. dep&idenl var17749.41O.L. of rtgression4176.576Sun squared resid4 aaEtoaDurbin-Watson stat3.114163(2

28、)對(duì)數(shù)變換法在"Equation"窗口中"Estimate”菜單的對(duì)話框直接輸入“LOG(chuxu) C LOG(shouru)C.5T：lniate Forecast | 曰白 re si 口手1JL I再單擊“ OK”后，就可以得到線性模型對(duì)數(shù)變換后的結(jié)果如下圖：/lew Frot oti|eci尸nnt Name , Freeze囿 Equation: UNTITLED Workfile: UNTTTLED;Untitled>叵IDependent Variable: LOGCHLILI)Method: Leasi SquwrEmDale: 03/0

29、7/20 Time: 02:10Sample: 1978 2007Incliidea oastrvations: 30Varia lieCoefficientStd. Errpr t-聚曲stkFr血C-4.2641230.184583-2X10135o.ooocLOG(SHOURU)1 5479970 32271668.14 &770.0000R.-squared0 994-007Mean dependentwat0145064Adjusled R-scuaredi0 9937933.D. dependent var2099930S E ofr&gression0.165445Akaike into criterion-0.596018Sum squar«d resid0.765416Schwarz criterion-0.502605Log likelihood1244027Hannan*Quinn alter.*0.565134F-statlstlc4.643.992Durbin-Watson stat0 413675Prob(F-statistrc)0.000000圖14對(duì)數(shù)變換估計(jì)結(jié)果 懷特檢驗(yàn)的結(jié)果如下：ViewProt O