实验八模型设定偏误问题

1、实验八 模型设定偏误问题姓名：何健华 学号：2班级：13金融数学2班一实验目的：掌握模型设定偏误问题的估计与应用，熟悉EViews的基本操作。二实验要求：应用教材P183例子5.3.1的案例，利用RESE检验检验模型设定偏误问题; 应用教材P185例子5.3.2的案例，利用Box-Cox变换比较线性模型与双对数线 性模型的优劣。三实验原理：普通最小二乘法、阿尔蒙法、格兰杰因果关系检验、DW检验。四预备知识：普通最小二乘法，F检验，Box- Cox变换。五实验步骤一、下表列出了中国某年按行业分的全部制造业国有企业及规模以上制造业非 国有企业的工业总产值 Y,资产合计K及职工人数L。 序号工业总产

2、值Y（亿）序号工业总产值Y（亿元）资产合计K（亿元）职工人数L（万人）序号工业总产值Y（亿元）资产合计K（亿元）职工人数L（万人）13722.703078.2211317812.701118.814321442.521684.4367181899.702052.166131752.372742.7784193692.856113.1124041451.291973.8227204732.909228.2522255149.305917.232866.658062291.161758.77120222539.762545.639671345.17939.1058233046.954787.902

3、228656.77694.9431242192.633255.291639370.18363.4816255364.838129.68244101590.362511.9966264834.685260.2014511616.71973.7358277549.587518.7913812617.94516.012828867.91984.5246134429.193785.9161294611.3918626.94218145749.028688.0325430170.30610.9119151781.372798.908331325.531523.1945161243.071808.4433

4、假设有人不同意原幕函数模型是正确设定的模型，而下面的线性形式是正 确设定的模型，将如何检验哪一个模型设定更正确?Y 01心 2Li i1.建立工作工作文件并录入数据，得到图 1.16 Group: UNTITLED Workfile: P186:Untitled - = xView| Proc Otyert Print Mdme jbceele Del aultvSort Edit+/- Smpl4丨KLY1307fl.220113.00003722.700A21684.430&7 O0OW1442.52032742.77034.000001752 37041973.82027.000

5、001451.29055917.010327 0000M 49+3006175B770120.00002291.1607939.10005B.ODOOO1345 1708694.940031.00000656.77009363 480016 00000370 18D0102511.99066 0000011590.36011973750050QQOQO616 71Q012516.01002B 00000617 9400n3785.91061.000004429 1903688 030254 00005743 02015279&.90033.0000017& 1.37016180

6、8.44033 000001243070171118.81043.00000812,7000182052. ISO&1 000001899.700V19<>图1.12.采用RESET佥验来检验模型的设定偏误2.1对于原幕函数形式的模型，变换成双对数模型InY ° al nK lnL采用OLS进行估计，估计结果如图1.2。1= Equation: UNTITLED Workfile: P1$6:Untitld - 3 xV竝w | Proc.Piinl NdHit? Fftw” E、山Fm电3!it St也 盹讥血，spondent Variable LOGJY)

7、r.leihod: least Seuaresat«: 11Z2CP15 -ime: 00:42Sample: 1 31Included observations' 31GambleCoeff cientStd. Errort-StatisticPrnb.c1 153994 -727&111 58&aa4D.1240LOGK)0 5092360.1763793 4541490.0018LOG(L)0 360796-2015911.789741D.0843R-squared0 809925Mean dapandent var7.493997Adjusted R-

8、squared0 796346S.D. cependent rmir0 9429&QS.E of regressiar3 42553SAksnke info cmerion1.220839Sum squared res id5 070303Schwarz t ri：erion1.359612Log likelihood15 92300Hannan-Quiinn enter.1.2SG075F-statisti:59.S5501Ddbin-V/atson stat0 7932C-9PrDto-(F-statEtic0.000000图1.2在图 1.2 窗口选择“ Views'St

9、ability Test'Ramsey RESETTest. ”，在出现的 RESET Specification 窗口的 Number of fitted terms栏内输入“ T,点击“OK,得到检验结果如图1.3所示。Rflinsey RESET TestEqual ion: UNTITLEDSpecrficatipn LOG(Y) C LOGK) LOG L;Qmrlted Variables Squares of fitted valuerValuec*fProbabilitybslatistic1 472669270.1524F-statistic2J&8754(1

10、,27i0.15242.395098101217图1.3由F统计量的伴随概率知，在 5%勺显著性水平下，不拒绝原模型没有设定偏误的假设。2.2采用OLS对线性模型进行估计，估计结果如图1.4.=! Equation;UNTITLED Workfile； P106：Vntitled_ 5 XProc | QbjcclPrim Noth!EsiMndLo FcxkilOepantlAnt '.'fl r a bit: Y'.lethod: Leat Squaresate： ii：20 is Ine： 00:53Sarrpia: 1 31vanabieCosffc am St

11、d. Error t-StadstK Proo.c KL583.6173C.1S925B11.12021339 33341.7343420 0319362.4318763 6226713.0596160,0939D.D2170.004R-squared0 67147&Uean dt&endTl mZ54S.389Adjusted R-s(|ijarfidi0.648012SO. dependent var192SG395.E. of regression1143.Q77Akalke info criterion)17.O1：6CSurr squared resid3656S49

12、Scriterion17 15137Log tlkelih口od-MO 6953Mnn'Ouirifi true*17 057*4F-statistic28.61511Durbin-Watson stat1 40974CProb(F-5tamcOOOOM&图1.4同样地，选择“ Views'Stability Test'Ramsey RESET Test ”，在新出现的对话框中输入“ T,得如图1.5所示的RESET佥验结果Ramsey RESET TestEquation： UNTITLEDSpaclflcaflcn: Y C K LOmitted Varis

13、bles： Squares of fitted valuesValuedfProbability(-statistic4.414818270.0001Fatalistic19 49062(1.270.0001Likelihood ratio16 8453210.0000图1.5首先，尽管K与L的参数估计值的t统计量在5%勺显著性水平下都是显著 的，但拟合优度比原幕函数的模型低。由F统计量的伴随概率知，在 5%勺显著性水平下，拒绝原模型没有设定偏 误的假设。可见，相比较而言，线性模型确有设定偏误，而原幕函数模型没有设定偏误 问题。二、通过 Box-Cox变换检验中国居民总量消费函数的建立中，原线

14、性模型Y 0 1X与双对数线性模型哪一个最优？表263中国居民总量消费支出与收入资料单位：亿元年份GDPCONSCPITAXGDPCXY19783605.61759.146.21519.287802.56678.83806.719794092.62011.547.07537.828694.27551.64273.219804592.92331.250.62571.709073.77944.24605.519815008.82627.951.90629.899651.88438.05063.919825590.02902.952.95700.0210557.39235.25482.4198362

15、16.23231.154.00775.5911510.810074.65983.219847362.73742.055.47947.3513272.811565.06745.719859076.74687.460.652040.7914966.811601.77729.2198610508.55302.164.572090.3716273.713036.58210.9198712277.46126.169.302140.3617716.314627.78840.0198815388.67868.182.302390.4718698.715794.09560.5198917311.38812.6

16、97.002727.4017847.415035.59085.5199019347.89450.9100.002821.8619347.816525.99450.9199122577.410730.6103.422990.1721830.918939.610375.8199227565.213000.1110.033296.9125053.022056.511815.3199336938.116412.1126.204255.3029269.125897.313004.7199450217.421844.2156.655126.8832056.228783.413944.2199563216.

17、928369.7183.416038.0434467.531175.415467.9199674163.633955.9198.666909.8237331.933853.717092.5199781658.536921.5204.218234.0439988.535956.218080.6199886531.639229.3202.599262.8042713.138140.919364.1199991125.041920.4199.7210682.5845625.840277.020989.3200098749.045854.6200.5512581.5149238.042964.6228

18、63.92001108972.449213.2201.9415301.3853962.546385.424370.12002120350.352571.3200.3217636.4560078.051274.026243.22003136398.856834.4202.7320017.3167282.257408.128035.02004160280.463833.5210.6324165.6876096.364623.130306.22005188692.171217.5214.4228778.5488002.174580.433214.42006221170.580120.5217.653

19、4809.72101616.385623.136811.21.建立工作工作文件并录入数据，得到图 2.16 Group: UNTITLED Workfile: P. -View Frc| Object PrintNarre Freeze defaultvXY197S6678.8003806 700A19797551,6004273.20019807944.2004605 50019818438.00050&3.90D19829235.20054B2.400198310074.605983 200198411585.00674570019fi511601 707729.200198613

20、036.508210.900198714627.708840 ODO198815794.0095&0 500198915035.509005.500199016526 909450 900199118939.601037B.S0V1992<>图2.12.采用Box-Cox变换检验原线性模型与双对数线性模型的优劣 2.1对原线性模型采用OLS进行估计，估计结果如图2.2 o=Equation; UNTITLED Workfile: P187:Untitled 曰耳 丄flfl j1 twi#亠 FqiJU口单p»rc#fit麻 YMelhod leasl Squar

21、e*DMfr' 11CW1B Tlrre： 13 10SWfiplB 197B 2006 inclusad obtarval dm. 29V9fi4bl<9Errort-StatiilicProbc2091 295334.9BG96 2429UO.OOODX0.4375270.00929747.0635&O.OOODR-squaivd0987955Mean dspendenl var14355 72Adjusltd 良uqMrtd0.967509S.D. -d«p4Dd«<itVAr9472.076S.E. cf rvgnitiDn1090.63

22、3Ak« kt info crittnon16.833B2Sum tqbared rvsia30259014tri儈rion16S2B11Log likelihood-242 03D3Hamar-Otirn crter16 &6335F七茄sfic22U 596Durbift-Wstson ita:0 2_7155PrOh(F-StatiSliC).OOQODO图2.2由图中2.2的数据，可得：Y?=2091.295+0.437527X(6.242914) (47.05950)2R =0.987955 , F=2214.596 , RSS1 =302590142.2对双数线性

23、模型采用OLS进行估计，估计结果如图2.3Tl Equation; UNTITLED Workfile: P1S7:UntitledWiawlprac OtjKtj PriM| Name llEMimattlForMaitjStttiLRaidiDepencient Variably LOG(¥) Method; Lea&f Squar» Date 11/20/15 Trne：U：17 Sample： 1978 2006 included cb$ertitn$'variableCoe"icjentEmort-StatisticProb.C0,567

24、3060.880017Q 1427974.1128650Q1421361392350 00030 0000R-squared Adjured R-$quared S.E. qf regresaicr Sum squared raiaLog ikBlihcodF-stadscProt -statistic)0.9930010.99274： 0hD5G789 0.0B7076 43 070723330 664 o.ooooocMean dependent w S.D. dependent var Akaiks infc triterionSchwarz criTfirion Hanran-ajin

25、r criter. Durt n-Wa:son $：眸9.401236 0&W577 -2832453 -2 733167 -2 8029310 415281图2.3由图2.3的数据，可得：In Y?=0.587306+0.880017InX(4.112865)( 61.89235)R2=0.993001，F=3830.664，RSS2=0.087076虽然双对数线性模型的可决系数大于原线性模型，残差平方和小于原线性模 型，但不能就此认为双对数线性模型“优于”线性模型。2.3采用Box-Cox变换后再进行比较在主界面菜单选择 “Quick'Ge nerate Series ”

26、,在出现的 “ Gen erate Series by Equation ”窗口中输入“ LY=LOG(Y)，点击OK按钮即可生成Y的对数序列 LY。然后在主页的命令编辑区域中输入“ scalar 丫仁exp(sum(LY)/29” ,如图 2.4，点回车键生成一个标量 Y1。File Edit Object View Pro匚 Quick Options Add-ins Window Helpscalar Y1 =exp(3Uim(LY)/29图2.4选择 “ QuickGe nerate Series ”，在出现的 “ Gen erate Series by Equati on窗口中输入“

27、 丫2二丫/YT，点击OK按钮即可生成丫的对数序列丫2。作Y2关于X的线性OLS回归得如图2.5所示结果叵Equation: UNTITLED Workfile: P187;rUntitled| Vi#wPrccObjtc | PrjrtT | Nd苗亡ilEsTirriATeFOrKA5TResidsDeperd 的 t VariaW&： Y2Mettiod; Least SquaresDat« 11/20/15 Tim*; 1331Sample 1970 2006Inclu ded cbservati 口 " 2 9VariableCoefficientStd

28、Error t-StatlstlcProb.Cai727B70 0276776.242914oooooX3 61E-057.6SE-Q747.05950OOODOR->quired0987955Mean dependent var1.227408Adjusted R-squared0 907509S D. depeixlent var0.702601S.E. of regression0 067466Akakke Info enterian1 968655Sum squared resid0 2Q6559Sctiwarz criterion-1.B7435BLeg likelihood30.54550Hannan-Quinn crlter.-1.939123F-3UtiStiC2214 J96Durbin-Welaan $tat0,277155Prob(F-stntlstlc)O.OQOOOO图2.5由图2.5的回归结果可得：Y2=0.172787+0.0000361X(6.242914) (47.