基于多元回归分析方法的财政收入影响因素分析

1、 基于多元回归分析方法的财政收入影响因素分析一、问题提出及背景分析近年来，随着国家的财政收入保持高速增长的姿态。财政作为一个经济范畴，是一种以国家为主体的经济行为，是政府集中一部分国民收入用于满足公共需要的收支活动，以达到优化资源配置、公平分配及稳定和发展经济的目标,主要有资源配置、收入分配和稳定经济发展等职能。国家或地区政府为社会经济活动提供公益服务与公共物品的种类和范围，很大程度上取决于国家或地区财政收入的状况。所以，研究一国或地区的财政收入增长因素就显得尤为必要,这有助于政府认清现状,作出合理的决策.目前，财政输入的主要影响因素主要有各项税收、经济活动和国内生产总值等，因此，文章是通过前

2、人学者的基础之上，从国家统计局获取相关数据，采用多元线性回归分析方法对其进行分析。二、数据获取为探究国家财政收入的影响因素，从中国国家统计局（2014中国统计年鉴）中获得19782013年国家财政收入及各个影响因素的数据并采用多元回归分析法利用Eviews7.2对其进行分析，具体数据见表1：表119792013年财政收入及各项影响因素数据（单位：亿元）年份财政收入（Y）各项税收（X）1经济活动（X）2国内生产总值（X）319781132。26519。28406823645。219791146。38537。82415924062.619801159。93571.70429034545。61981

3、1175.79629.89441654889.519821212。33700.02456745330.519831366。95775。59467075985。619841642.86947.35484337243.819852004.822040。79501129040。719862122。012090。735154610274。419872199.352140。365306012050.619882357。242390。475463015036。819892664。902727.405570717000。919902937.102821。866532318718.319913149。4829

4、90.176609121826。219923483。373296.916678226937。319934348。954255.306746835260。019945218。105126。886813548108.519956242.206038。046885559810。519967407.996909。826976570142.519978651。148234。047080078060。919989875。959262。807208783024。3199911444。0810682。587279188479。2200013395。2312581.517399298000。5200116386

5、。0415301。3873884108068.2200218903.6417636.4574492119095.7200321715。2520017。3174911134977.0200426396。4724165.6875290159453o6200531649。2928778.5476120183617.4200638760。2034804.3576315215904.4200751321.7845621.9776531266422o0200861330.3554223.7977046316030o3200968518.3059521.5977510340320.0201083101.51

6、73210.7978388399759o52011103874。4389738.3978579468562o42012117253。52100614。2878894518214.72013129209。6411053007079300566130.2三、模型建立与求解设被解释变量为财政收入（Y）,解释变量分别为各项税收（X）、经济活动（X）2和国内生产总值（X），因此我们设定回归模型为3Y=0+0X+0X+0X+u011i22i33ii应用Eviews的最小二乘法程序，输出结果见表2：表2Eviews输出结果DependentVarisble:YMethod:LeastSquaresate:0

7、5/31/15Time:15:20Sainple:197820-13InducedcbservatiDns:36VariableCDEffiuiEntStdErrort-StatisticPrcb.C1666.459072.80402.47&S360.0187X11.J104290.04146131.606550.0000X2-0.0296290.012105-2.26092200307X3-0.0276710.0D9532-3.2433060.0020R-squared0.999865.leandependentvar240210BAdjust凶R-squaredSDdependentvar

8、35232.27G.E.cfreorescion42S.4-262.kaikeinfocriterion-15.06255Elinisquaredresld873559.Schwarzcriterion15.23B50Loalikelihood-267.1260Hannan-Quinnalter.15.12396F-statig1ic78883.15Durbin-.-Vatson?tst1.-176786Frob(F-&tatistiD0.000000由上表可知，得出估计的回归方程为Y=1666.459+1.310429X-0.029629X-0.02671Xi1i2i3i（2.48）（31.

9、61）（-2.26）（-3.24）1、回归方程显著性分析1）回归方程的显著性检验（F检验）原假设：H:0=0=.=0=0;012k备择假设：H:至少有一个0不等于零（j=12,k）。1j由上表可知：RSS/kESS/(n_k_1)=78889.15给定显著性水平0.05，查表可知F(3,32)=2.92criterion16.29100Sumsquaredresid22421560SchAi!arzcritsrian16.2789SLoclikeihocd-291.2380Hannan-Quinnciter.16.32171F-s:atlslc653475Durtiln-Watsonstat0

10、.332395ProhfF-statistic)0.000000b)Y关于X回归分析2Y=86513.21+1.704490X2(3.61)(4.70)R2=0.393637,R2=0.375803,DW=0.059435,F=22.07207表5Y关于X回归分析结果2DependentVariable:YMethod:LeastSquaresDate:OE/31-15Time:15:42Sample19732013Includedobser/stions:36/ariableCoefficientStd.Errort-StatisticProb.C-S6E13.2123930.52-3.60

11、76450.0010X21.7044300.3623054.6980920.0000R-squared0.393637.leandependentvar24-021.03AdjustedR-squared0.375803S.D.dependentvar3523227S.E.ofregression27935.65Akaikeinfocriterion23.95998Sumsquaredresid2.63E+WSchwarzcriterion23.44795Loglikeihood-4184796Hannan-Quiincriter.23.39068F-statistc22.0723?Durbi

12、n-Watso仃stat0.059斗35ProbfF-statistic;0.000042c)Y关于X回归分析3Y=3690.723+0.220517X3(4.17)(50.15)R2=0.999484,R2=0.999469,DW=0.332395,F=65847.35表6Y关于X回归分析结果2Dependsnt加怕bl圧YMethod:LeastSquaresDate:Q5B1/15Time:15:43Sample:19792012Includedobservations:36VariableCoefficientSid.Errort-StatisticProb.C-3690.723684

13、.6401-4.1710510.0002X30.2.205170.004-40950.015B10.0000R-squared0.985591r.eciidepeidertvar24D21.Q8AdjustedR-squared0.985196s.Ddependent.ap35232.27S.E.ofregression4139.336.aikEirfocriterion19.54844Sumsquaredresid5.83E08Schwarzcriterion19.63641LogIil3liiood-349.0718l-arnan-ClLimcitm.19.57914F-statistic

14、2501.582Durbiii-V/atscnstat0.101932ProbCF-slatistic)ooooooo根据经济理论和回归结果可知，易知各项税收X是最重要的解释变量，所以选取第1一个回归方程为基本回归方程。加入经济活动人口X，对Y关于X，X作最小二乘回归，得12Y=3320.839+1.176337X-0.064969X12(6.67)(333.71)(-7.86)R2二0.999820,R2二0.999809,DW二0.915509,F二91837.45表7Y关于X，X回归分析结果12DependentVariable:YLletliod:LeastSquaresate:05/

15、31.15Time:15:44Sample:19782013Inclndeg!obser日ticins:36VariableCoefficientStd.Errort-StatisticProb.C3320.339497.9804j.jjSSO?0.0000 x-i1.1763370.00352533370730.0000X2-0.0649690.003264-7.8617970.0000R-squared0.999820.leandependentvar2402-1.08AdjustedR-squared0.999B09S.D.dependentvar35232.27S.E.ofregres

16、sion486.3073Akaikeinfocriterion1529121Sun-!squaredresid7S04327.Schwarzcriterion15.42317Loglikelihood-272.2413Hannan-Quinncriter.15.33727F-statistic91037.45urhin-Watsonstat0.915509Prob(F-statistic;0.000000可以看出，加入X后，拟合优度R2和R2均有所增加，并没有影响x的显著性，所1以在模型中保留X.2加入国内生产总值X，对Y关于X，X作最小二乘回归，得13Y=167.5254+1.385650X

17、-0.043709X12(1.38)(52.81)(-8.70)R2二0.999843,R2二0.999834,DW二1.059547,F二105220.7表8Y关于X,X回归分析结果1DependentVariable:Y【ethod:LeastSquaresate:05/3115Time:15:45Sample:197820-13Includedobservations:363VariableCoefficientStdErrort-StatisticProb.C1G75254121.5277-1_37S4960.1773X11.3S56500.02623752.813jj0.0000X3

18、-0.0437090.005026-8.6960600.0000R-squared0.999043Meandependentvar24021.03AdjustedR-squared0.999834S.D.dependentvar352K27S.E.ofregression4543338Akaiheinfocriterion15.15520Sumsquaredresid6011035.Schwarzcriterion15.28716Loglikelihood2697935Hannan-Quinncriter.15.20125F-statistic105220.7urbin-V/atsonstat

19、1.05954?Prob(F-statistic:0.000000可以看出，加入X后，拟合优度R2和R2均有所增加，并没有影响X的显著性，1所以在模型中保留X.3综合以上分析，虽然根据相关系数矩阵回归方程存在部分的多重共线性，但是由逐步回归分析方法分析可知，多重共线性的存在不影响回归方程的评价结果，因此，回归方程不变。4、异方差检验采用White检验：先采用图示法，直观判别是否存在异方差Q20.000W.OCX)1OT.0CX)14O.C0OXI图1X，X，X对Y的散点图123图2残差与X的散点图1X2JC3图3残差与X的散点图2图4残差与X的散点图3由图1-4可知，随着X,X,X的增加，财政

20、收入Y随之也增加,表明存123在异方差性，但其异方差是否显著存在，还需要进一步验证.（2）White检验表9White检验输出结果HeteroskedastiDtyTaet:hiteF-引ctstic1375111Prob.Fit.2B)0.0027Cbs3R-gquared2DS4S48Pi-square(.gia0133Scaleds)qzlaindSS15.55036Pnob.Chi-Squara(D：0.0769TestEquation:DependentVariable:RESIDA2Method:LeastSquares日ta:口3B1/15Time-13:37Sample:197

21、82013Includedobsenatians:367a-iDieCoeflicientStd.Errort-StatisticProb.c-101374862993035.-3.403597D.Q0227D7661698.61301.1B2169247BX12-0.0371150.0152792.4292210009929-17479103.0923XI嗔30.0146650.0060382.42B760D.0224X2411.3263118.14013.481533D.QQ18X2屹-0.003910a.oomo-3.622575D.001SX2*X30.0

22、04947a.0017232.671540D.Q080K3-2S12009100.7034-2.5937S3DQ15iX2性-o.oo-mi0.000591-2.437411D.0219R-squaredor9125Mesndependentvar163154.7AjdjueiedR-squared0.433437s.DdspendentMsar227351.7S.E.ofregrsssiDn171136.0Akaikeinfocriterion27.16844Suinsquaredre3id7.61E+11Schwarz,criterion27.60030Loglllcellhoad-479

23、0319Hannari-Cuinnenter.2732196F-elatistic2.976111Durbin-Z/ateon5lat2181160Frob(Tstafiafic0.002730辅助回归式估计结果如下：u2=10187486+707.6616X-0.037115X2-0.01735563+411.3263X-0.003910X2t11122+0.004947X*X-261.2009X-0.001441X22333R2=0.579125,T=36因为TR2=36x0.579125=20.8485/2(9)=18.307，所以该回归方程存在异0.05方差.克服异方差性:采用加权最小

24、二乘法克服异方差。表10加权过后回归分析结果dependentfananiG：fk-letiodLeastSquaresDale:D5/311ETiire:23:02Sample:197&2013ncudsdobser；3tion36weiantingseries:uxz.heightt/pe.Inversestandarddeviaticn(E/ieA?3defaults匚mlirg)VariableCccffidGntStdErrortStatisticDpob.C2096.545536.80893.9055700.0005X11.275210O.D4070831.325790.0000K

25、200397710.31-065-3.5039690.0014X3-0C20J50.308200-24691r0.0131weiunt&dstatisticR.-squared0.9999+2Meandependentyar19569.2CAdjustedR-squaredo.gggs28S.D.dependentMar27477.Q7Sf.q1regression392.3060Akaikeinfo:nrenon14.86640sums口创nejid4924947.Sdiwaizalleilor15.05235Loglikelihood-263.9553卜1日仃仃an-Guinncriter

26、14.94761Fstatistic67H-.D9Durbin-V/atsonsta11.099977Dpcb(F-gtatitc;0.0000DOWeightedmeandep.15260.41nTigliledstatisticsR-squared0.999862Meandependentyar221.0&AdjustedR-squared0.999840S.D.dependentMar35.2：2.275f.oiregression433.2409Sumsnuaredresio6006326Durblii-watscnstat1.145433表11加权后White检验结果Heterosk

27、eda5ticityTest:WhiteF-staistic2683835ProbP9.26)0.0247Obs*R.-squared17.25695Prcb.Ghi-3quare(9；.0.C443Scaledexplained!SSD.279949Prob.CIi-SquarefD;0.4112TeetEquatiortDependenivariable:WGT_R.ESIDA2Method:LeastSquaresDate：oyi5Tiime:20:D6sample:19782013Includedobservalions:36Cullinaartestegresscrsdroppedf

28、romspecificationVariableCoafficiontEtd.Error:-StatisticProb.c-594770.25559S3.-2.18&8920.0378WGP2-3742D68.1678594.-2.2298230.0346工代吨卩2-0.0233630.016181-1?52S97009KX1*WGTA21214.570502.32782.4178B40.02291*X2*WQT2-D.021S0?0.008948-2.437191002201X3XWGF23.01097+0.00537217223590.0959X2*WGTZ2152.509760.6060

29、12.2240300.0350X2欣少0.0040420.00164524576B70.0210X陀VflJE-D.0010360.L00622-1.56&65001076X3*WGT;2231.701093.90467-2.+674D5002D5R-squaredD.479360r.ieandependeiinar1368D4.1AdjusledR-squaredD.299138S.D.dependentvar161073.1S.E.ofregrQEsion135516.1Akaikeinfol:riterian26.70170Sumsquaredresid477E+11曰匚hv?arzcr

30、i1erian.27.14157LoglilTlinood470.6306Hannan-Guinncriter.26.95523F-staistic2.659335DLrbiivjjatEonstat2.30913(1Fiob(F-5taii5ti)3.024G90根据TR2二36x0.47936二17.25695z2(9)二18.307，所以克服了异方差。0.055、自相关检验图5残差图(1)估计线性回归模型并计算残差Y二1666.459+1.310429X0.029629X0.02671X123(31.61)(2.26)(3.24)R2=0.999865R2=0.999852s.e.二42

31、8.4262DW二1.177?回归方程拟合较好，但DW较低。残差图见图5.分别用DW,LM统计量检验误差项u是否存在自相关t已知DW二1.177，若给定二0.05,查表得出，DW检验的临界值d二1.29,d二1.65。因为DW二1.1771.29，依据判别准则，认为误差项存在严LU重的正自相关。LM自相关检验辅助回归式估计结果是：e=137.4608+0.020205X+0.0029X0.0037X+0.37934e+0.1897e123t2R2=0.182478,DW=2.047,LM=TR2=6.57表12LM自相关检验估计结果Breusch-GodfreySeriaICorrelatio

32、nLTvITestF-stalsllc3.343127Prob.F(2.3(J)00斗盯Obs*R-squared6.569202Prob.ChSquare0.0375TestEquslian:DependentVariable:RESIDMethod:LeaslSquaresDat0：OaB1/15Time:20:26sample:13782013Includedobsenations:36F1resamplemissingu!aluelaggedresidualssettozero.VariableCoefficientSidErrort-Stato:icFroh.C-137.4608S3

33、0.7659-0.2179270.8290X10.020205D.0396850.6091210.6141X20.0029000.01229402358*508151X3-0.0037003.006122-0.4555770.6520RESID-1:0.37Q3d0O.1S62S42.03635200506RE3IDI-2)0.189775D.199739Q.9501150.3496R-squared0.182478Meanclependentvar173E-12AdjustedR-squared0.0452243.D.dependtiilvar+090530S.E.ofegression40

34、3.0739Akaikeinfocriterion14.97219Sumsquaredresid4SD1773.Schurzcriterian15.23611Leglikelihood-2634994Hannan-Quinn匚riter.15.00430Fstati&ti?1.3302E1Durbin-Watsonstata.0717-ProblF-statistr0.274896因为咒2(2)二5.991LM，所以lm检验结果也说明原回归方程的误差项存0.05在自相关。广义最小二乘法估计回归参数首先估计自相关系数，6=1-DW=0.412对原变量做广义差分变换。令TY二Y0.41Yttt-1TX=X-0.41X1t1t1t-1TX=X-0.41X2t212t-1TX=X-0.41X3t3t3t-1以TY,TX,TX,TX(1979-2013年)为样本进行再次回归，得t1t2t2tTY二939.5436+1.312407TX-0.028730TX-0.027836TXt1t2t3t(1.45)(22.57)