基于多元回歸分析方法的財(cái)政收入影響因素分析

1、 基于多元回歸分析方法的財(cái)政收入影響因素分析一、問題提出及背景分析近年來(lái)，隨著國(guó)家的財(cái)政收入保持高速增長(zhǎng)的姿態(tài)。財(cái)政作為一個(gè)經(jīng)濟(jì)范疇，是一種以國(guó)家為主體的經(jīng)濟(jì)行為，是政府集中一部分國(guó)民收入用于滿足公共需要的收支活動(dòng)，以達(dá)到優(yōu)化資源配置、公平分配及穩(wěn)定和發(fā)展經(jīng)濟(jì)的目標(biāo),主要有資源配置、收入分配和穩(wěn)定經(jīng)濟(jì)發(fā)展等職能。國(guó)家或地區(qū)政府為社會(huì)經(jīng)濟(jì)活動(dòng)提供公益服務(wù)與公共物品的種類和范圍，很大程度上取決于國(guó)家或地區(qū)財(cái)政收入的狀況。所以，研究一國(guó)或地區(qū)的財(cái)政收入增長(zhǎng)因素就顯得尤為必要,這有助于政府認(rèn)清現(xiàn)狀,作出合理的決策.目前，財(cái)政輸入的主要影響因素主要有各項(xiàng)稅收、經(jīng)濟(jì)活動(dòng)和國(guó)內(nèi)生產(chǎn)總值等，因此，文章是通過(guò)前

2、人學(xué)者的基礎(chǔ)之上，從國(guó)家統(tǒng)計(jì)局獲取相關(guān)數(shù)據(jù)，采用多元線性回歸分析方法對(duì)其進(jìn)行分析。二、數(shù)據(jù)獲取為探究國(guó)家財(cái)政收入的影響因素，從中國(guó)國(guó)家統(tǒng)計(jì)局（2014中國(guó)統(tǒng)計(jì)年鑒）中獲得19782013年國(guó)家財(cái)政收入及各個(gè)影響因素的數(shù)據(jù)并采用多元回歸分析法利用Eviews7.2對(duì)其進(jìn)行分析，具體數(shù)據(jù)見表1：表119792013年財(cái)政收入及各項(xiàng)影響因素?cái)?shù)據(jù)（單位：億元）年份財(cái)政收入（Y）各項(xiàng)稅收（X）1經(jīng)濟(jì)活動(dòng)（X）2國(guó)內(nèi)生產(chǎn)總值（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、模型建立與求解設(shè)被解釋變量為財(cái)政收入（Y）,解釋變量分別為各項(xiàng)稅收（X）、經(jīng)濟(jì)活動(dòng)（X）2和國(guó)內(nèi)生產(chǎn)總值（X），因此我們?cè)O(shè)定回歸模型為3Y=0+0X+0X+0X+u011i22i33ii應(yīng)用Eviews的最小二乘法程序，輸出結(jié)果見表2：表2Eviews輸出結(jié)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兇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，得出估計(jì)的回歸方程為Y=1666.459+1.310429X-0.029629X-0.02671Xi1i2i3i（2.48）（31.

9、61）（-2.26）（-3.24）1、回歸方程顯著性分析1）回歸方程的顯著性檢驗(yàn)（F檢驗(yàn)）原假設(shè)：H:0=0=.=0=0;012k備擇假設(shè)：H:至少有一個(gè)0不等于零（j=12,k）。1j由上表可知：RSS/kESS/(n_k_1)=78889.15給定顯著性水平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關(guān)于X回歸分析2Y=86513.21+1.704490X2(3.61)(4.70)R2=0.393637,R2=0.375803,DW=0.059435,F=22.07207表5Y關(guān)于X回歸分析結(jié)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關(guān)于X回歸分析3Y=3690.723+0.220517X3(4.17)(50.15)R2=0.999484,R2=0.999469,DW=0.332395,F=65847.35表6Y關(guān)于X回歸分析結(jié)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根據(jù)經(jīng)濟(jì)理論和回歸結(jié)果可知，易知各項(xiàng)稅收X是最重要的解釋變量，所以選取第1一個(gè)回歸方程為基本回歸方程。加入經(jīng)濟(jì)活動(dòng)人口X，對(duì)Y關(guān)于X，X作最小二乘回歸，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關(guān)于X，X回歸分析結(jié)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，擬合優(yōu)度R2和R2均有所增加，并沒有影響x的顯著性，所1以在模型中保留X.2加入國(guó)內(nèi)生產(chǎn)總值X，對(duì)Y關(guān)于X，X作最小二乘回歸，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關(guān)于X,X回歸分析結(jié)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，擬合優(yōu)度R2和R2均有所增加，并沒有影響X的顯著性，1所以在模型中保留X.3綜合以上分析，雖然根據(jù)相關(guān)系數(shù)矩陣回歸方程存在部分的多重共線性，但是由逐步回歸分析方法分析可知，多重共線性的存在不影響回歸方程的評(píng)價(jià)結(jié)果，因此，回歸方程不變。4、異方差檢驗(yàn)采用White檢驗(yàn)：先采用圖示法，直觀判別是否存在異方差Q20.000W.OCX)1OT.0CX)14O.C0OXI圖1X，X，X對(duì)Y的散點(diǎn)圖123圖2殘差與X的散點(diǎn)圖1X2JC3圖3殘差與X的散點(diǎn)圖2圖4殘差與X的散點(diǎn)圖3由圖1-4可知，隨著X,X,X的增加，財(cái)政

20、收入Y隨之也增加,表明存123在異方差性，但其異方差是否顯著存在，還需要進(jìn)一步驗(yàn)證.（2）White檢驗(yàn)表9White檢驗(yàn)輸出結(jié)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輔助回歸式估計(jì)結(jié)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?yàn)門R2=36x0.579125=20.8485/2(9)=18.307，所以該回歸方程存在異0.05方差.克服異方差性:采用加權(quán)最小

24、二乘法克服異方差。表10加權(quán)過(guò)后回歸分析結(jié)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口創(chuàng)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加權(quán)后White檢驗(yàn)結(jié)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工代噸卩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根據(jù)TR2二36x0.47936二17.25695z2(9)二18.307，所以克服了異方差。0.055、自相關(guān)檢驗(yàn)圖5殘差圖(1)估計(jì)線性回歸模型并計(jì)算殘差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?回歸方程擬合較好，但DW較低。殘差圖見圖5.分別用DW,LM統(tǒng)計(jì)量檢驗(yàn)誤差項(xiàng)u是否存在自相關(guān)t已知DW二1.177，若給定二0.05,查表得出，DW檢驗(yàn)的臨界值d二1.29,d二1.65。因?yàn)镈W二1.1771.29，依據(jù)判別準(zhǔn)則，認(rèn)為誤差項(xiàng)存在嚴(yán)LU重的正自相關(guān)。LM自相關(guān)檢驗(yàn)輔助回歸式估計(jì)結(jié)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自相關(guān)檢驗(yàn)估計(jì)結(jié)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?yàn)橹?(2)二5.991LM，所以lm檢驗(yàn)結(jié)果也說(shuō)明原回歸方程的誤差項(xiàng)存0.05在自相關(guān)。廣義最小二乘法估計(jì)回歸參數(shù)首先估計(jì)自相關(guān)系數(shù)，6=1-DW=0.412對(duì)原變量做廣義差分變換。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)為樣本進(jìn)行再次回歸，得t1t2t2tTY二939.5436+1.312407TX-0.028730TX-0.027836TXt1t2t3t(1.45)(22.57)