我國財(cái)政收入和國民生產(chǎn)總值的計(jì)量分析

我國財(cái)政收入和國民生產(chǎn)總值的計(jì)量分析前言1978年十一屆三中全會(huì)確立了改革開放的戰(zhàn)略決策，在這一戰(zhàn)略決策的指引下，我國的國民經(jīng)濟(jì)取得了飛速的進(jìn)展,我國的整體經(jīng)濟(jì)實(shí)力不斷增強(qiáng)，國民生產(chǎn)總值持續(xù)增加，總量已經(jīng)位居世界前列，我國已經(jīng)在經(jīng)濟(jì)進(jìn)展上取得了舉世注視的成績。隨著國民生產(chǎn)總值的增加，我國的財(cái)政收入也呈每一年增加的趨勢：一.成立模型咱們明白國民生產(chǎn)總值是影響財(cái)政收入的主要因素，國民生產(chǎn)總值X與財(cái)政收入Y之間存在緊密的關(guān)系，財(cái)政收入隨國民生產(chǎn)總值的增加而增加，但變更幅度相對(duì)較低，因此可設(shè)定財(cái)政收入Y與國民生產(chǎn)總值X之間的關(guān)系為Y=B1+B2X+U其中：Y為年財(cái)政收入（億元）；Xi為年國民生產(chǎn)總值（億元）。變量采用年度數(shù)據(jù)，樣本

期為1978—1997年。B1指當(dāng)國民生產(chǎn)總值為零時(shí)的最低財(cái)政收入。二．估量模型中的未知參數(shù)假定模型中的隨機(jī)誤差項(xiàng)U知足古典假設(shè)，運(yùn)用OLS方式估量模型的參數(shù)。1．成立文檔，輸入數(shù)據(jù)obsXY1S783624.1001132.2601S794038.200114G.3001順4517.0001159.93019B14860.300117579013B25301.8001212.3301S836957.40013EG.960720S.7001642.06019站0989.1002004.82019B610201.402122.01013B711954.502199.3501S8814922.302357.240196916917.802664.900W9018598.402937.100199121662.503149.480199226651.903483.3701S9334660.604348.950199446670.005218.100199557494.906242.200199666850.508651.140199773452.508651.1402．用OLS估量未知參數(shù)-[E?u.ation：EQO1Vorkfile：BD]FilegditIJbjecteViProcs卽lick0ptic-neWirnlowHelpV1ewlFroczlobjFtint|Mani@DeperdentVariable:VMethod:LeasiSquaresDate:05/12/C4Time:16:09Sample:19781997Includedobservations:20VariableCoefficieniStd.Errort-SiatisticProb.C858.310867.1201512787680.0000X0.1000310.00217246.047S80.0000R-squared0.9915B3Meandependentvar3081.158AdjustedR-squared0.991115S.D.dependentvar2212.591S.E.ofregression200.5600Akaikeinfocriterion13.61296Sumsquaredresid702956.0呂匚hwarzcriterion1371255Loglikelihaod-134.1290F-statistic2120.406Durbin-Watsonstat0.859457Prob(F-statistic)0.000000所以模型是Y=++U

三模型查驗(yàn)從估量結(jié)果、能夠看出，可決系數(shù)為，表面上看模型在擬合上超級(jí)好。系數(shù)顯著性查驗(yàn)：對(duì)于B2,t統(tǒng)計(jì)量為。給定a=,查t散布表，在自由度為n-2=18下，。。。。。得臨界值t(18)=,因?yàn)閠〉t(18),所以拒絕H。B2=0,A表明國民生產(chǎn)總值對(duì)財(cái)政收入有顯著影響。而且從經(jīng)濟(jì)意義上看，=,表面國民生產(chǎn)總值每增加1億元，財(cái)政收入平均增加億元。四，預(yù)測i……VS二i……VS二Actual:X-■I-：i；t!rril-!'V;:1TCIriluiJi.i：i：i■:v1-ji,/：）RootMeanS|JiredFrn-25112^'i"/l^nLr-j''；二LLJMeanAbs.PercentErrar755.6483uilnequalityCoefficientD.802532心卞「，，“「-「巧'i4=r：—7VarjnceProportionD.502053?ovaranceProportionO.QOOOOO若1998年的國民生產(chǎn)總值為億元，下面預(yù)測1998年的財(cái)政收入。通過Eviews計(jì)算得丫=元。通過下圖能夠看到

暫-[Series：IFlorkfile：ID]FileEditObjectsV^i肚ocwQuiukOp.^ionsWindowHeKi總啊|Ffjum|DljutMlFyint|lIsmGEdit+/-1￡mpH■/~~|L^b總1十「Lastupdated;05/12AJ4-15;42Modified:19701998//fltff^actual)yf19781220.8321S791262.26519B01310.23019S11344.49019521388.654畑1454.23419841579.20319B517574971SB61878.766196720M.12919682361.00019船2550.611愉0271B.72319913025.22719923524.321199343154241994552G.7471S956609.5701SS67545.4W19S78205.32119988662.491五，自相關(guān)性查驗(yàn)圖示法按照上述OLS估量。咱們暫把Y=++U作為模型。按照其取得殘差resid，運(yùn)用genr生成序列e,則在quick菜單當(dāng)選graph項(xiàng),在圖形對(duì)話框里鍵入：ee(-l),再點(diǎn)擊scatterdiogram。得輸出結(jié)果：從上圖能夠看出殘差E呈線性自回歸，表明隨機(jī)誤差U存在自相關(guān)查驗(yàn)按照Yi=++Ui的估量結(jié)果。由DW=，給定顯著性水平a二，查Durbin-Watson表,n=20,k'(解釋變量個(gè)數(shù))=1,得下限臨界值d=,上限臨界值d=,因?yàn)镈W統(tǒng)計(jì)量為＜dL=。按照判斷區(qū)域可知，這時(shí)隨機(jī)誤差項(xiàng)存在正的一階自相關(guān)。自相關(guān)的修正1.由DW=，按照P=l-DW/2，計(jì)算出P=。用GENR別離對(duì)X和Y作廣義差分。在Workfile框當(dāng)選GENR菜單，在對(duì)話框中直接輸入生成格式。即DX=*X(-1)DY=*Y(-1)然后再用OLS方式估量其參數(shù)，結(jié)果為■Equation:UNTITLED-l.nlxlVist)Froce|Otijecte|Frint|衛(wèi)ane|Trfseis|Estimaty|FurycaEt]StatslEpsids|DependentVariable:DYMethod:LeastSquaresDate;05/1BAJ4Time;21;52Sample(adjusted);19791997Includedobservations:19alteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C363.431061.197925.9386180.0000DX0.1019750.00372127.401930.0000R-squared0.9778S1Meandependentvar1593.874AdjustedR-squared0.976558S.D.dependentvar1183.759S.E.ofregression181.2411Akaikeinfocriterion13.33B83Sumsquaredresid55S421.9Schwarzcriteriori13.43B25Loglikelihood-124.6999F-siatistic750.8B58Durbin-Watsonstat1.076900Prob(F-statistic)0.000000DY=+t=可決系數(shù)為,F=,DW=.這時(shí)，咱們發(fā)覺用廣義差分法后，DW值有顯著提高，但仍然存在自相關(guān)。迭代法在Quick菜單中選EstimateEquation項(xiàng)，出現(xiàn)估計(jì)對(duì)話框，直接鍵入：YCXAR⑴,得如下結(jié)果：見下圖:-In]x|Wi-In]x|Wi|ObjEC|Ftint|IImm總|FmHe|EmtimatE|Forgc總弓11St總tm|Remidu|Equation:UNTITLEDWorkfile:DDDependentVariable:￥Method:LeastSquaresDate:05/18/04Time:22:09Sample(adjusted):19791997Includedobservations:19afteradjustingendpointsConvergenceachievedafter11iterationsVariableCoefficientStd.Errort-StatisticProb.C044.4010168.09975.0236970.0001X0.1022040.00409320.065450.0000AR⑴0.6135260.2637212.3264240.0335R-squared0.993740Meand已pendentvar3163731Adjust已dR-squar已d0.992958S.D.M已pend已ntvar2223.829S.E.oft■已gression186.6187Akaik已i門忙icriterion13.43995Sumsquar已dresid557224.3Schwarzcriterian13.58907Loglikelihood■124.6795F-statistic1270.013Durbin-Watsonstat1.087370Prob(F-statistic)0.000000InvertedARRoots.61從上表能夠看到DW=，繼續(xù)有所提高，但仍存在自相關(guān)性。利用對(duì)數(shù)線性回歸修正自相關(guān)。運(yùn)用GENR別離對(duì)X和Y生成logX和logY，即GENRLY=LOG(Y)GENRLX=LOG(X)在估量對(duì)話框中直接鍵入：LYCLX,即得相應(yīng)的輸出結(jié)果，見下表：UErievE-UlTITlJDTorkEile：DD]IIIEilwElit01'jsets蟲己,1*1,FreesQuickO^tiqilsWinlowHn：LpV~i日]F于竺|dbjec"|Ffint包|DependentVariable:LYMethod:LeastSquaresDate:05/13/04Time:10:03Sample(adjusted):19781997IncludEdohservations:20afteradjusting已ndpointsVariableCciEffieientStd.Errort-StatisticProb.C1.4897610.1551949.5993750.0000Di0.6624270.01616140.990180.0000R-squared0.9B9401Meandeperidentvar7.819392AdjustedR-squared0.9BBB12S.D.dependentvar0.655077S.E.ofregfEssiori0.069291Akaikeinfocriterior-2.406371Sumsquaredresid0.0B6422Schwarzcriterion-2.30679BLoglikelihood26.06371F-statistic1G80.195Durbin-Watsonstat0.602413ProL(F-staiistic)0.000000DW值不升反降,ViewViewIFreesIObjeelsFrintIlTaineIFreezeIEitimatalForecaztlstati|L@zidsI-Inix|再同時(shí)考慮迭代，在估量對(duì)話框里鍵入：LYCLXAR(1)-Inix|onZIIJITITLEDToi-lcfiLe：DependentVariable:LYMethod:LeastSquaresDate:05/18/04Time:19:50Sarriple(adjusted):19791997Includedobseivations:19afteradjustingendpointsConvergenceachiev/edafter14-iterationsVariableCoefficientStd.Error■t-StatisticProb.C0.0337520.E962131.1975530.2485DC□7270030.0G759710.766830.0000AR(1)□7161570.2102143.4020450.0036R-squared0.994045Meandependentvar7.B60B35AdjustedR-squared0.994201S.D.dependentvar0.645528S.E.ofregression0.049159Akaikeinfocriierion-3.043582Sumsquaredresid0.038665Schwarzcriterion-2.B94460Loglikelihood31.91403F-statistic1543.923Durbin-Watsonstat^^6O891|Prob(F-statistic)0.000000InvertedARRoots.72故可知該模型始終存在自相關(guān)性。咱們估量這是由于政府在制定財(cái)政預(yù)算時(shí)，總要按照上年乃至前幾年的財(cái)政收入數(shù)據(jù)進(jìn)行編制。這就是說今年的財(cái)政收入要受前幾年的財(cái)政收入的影響。異方差性查驗(yàn)先將時(shí)刻定為1978—1985，然后用OLS方式取得下列結(jié)果-[EQUAtiaik：UlTITLEDVarkfilczDD]FiletOT'jacViewProcsQuickOptions世in心HeljDependentVariable;YMethod;LeastSquaresDate;0e/U9/U4Time;14;14Sample:19781984Includedobservalions:7VariableCoefficientStd.Errort-StatisticProb.C535.6012119.74144.4729830.0066X0.1432790.0230446.2177130.0016R-sqjared0.886479Meandependentvar1262.367AdjustedR-squared0.862674S.D.dependentvar185.5669S.E.ofregression68.78738Akaikeinfocriterion11.53487Sumsquaredresid23658.52Schwarzcriterion11.51942Loglikelihood-38.37206F-statistic38.65996Durbin-Watsorstat0.844481Prob(F-statistic)0.001573Y=+(4.473)R'2=工e「2=然后將時(shí)刻概念為1991——1997，再用OLS方式取得如下結(jié)果EVieTs—[Eq_ua-tion.：:EQ03Torlzfile：DD]口FileEditObjects已HFrocs￡uichOjitiunsWiniovi'HelpView|Procs|Obj—Priitt|Nam11Freeze]DependentVariable:YMethod:LeastSquaresDate:05/16/04Time:15:1BSample:19911997Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.C773.861930S.57562.5078520.0540X0.1010690.00613316.400250.0000R-squared0.9B1923Meandependentvar5500.176AdjustedR-squared0.97B30BS.D.dependentvar2046.016S.E.ofregressian301.3419Akaikeinfocriterion14.48932Sumsquaredresid454034.8Schwarzcriterion14.47387Loglikelihood■48.71264F-statistic271.5988Durbin-Watsonstat1.198836Prob(F-statistic)0.000015Y=+R2=工e22=求F統(tǒng)計(jì)量：F==,查F散布表，給定顯著性水平a=，得臨界值(6,6)=,比較f=>,則拒絕原假設(shè)，表明隨機(jī)誤差存在異方差。異方差的修正1，WLS估量法。第一生成權(quán)數(shù)W=1/X，然后用OLS估量得出結(jié)果：View|PrView|Proce|Obje^cis|PtintIU：±itieIFreezeEs11m=ate|Jorec^Etts|肛1玉;I^fEVievs-[Elation：UITITLEDlorkEile：DD]IllFileEditObjsetsYie,i*i-Fi_qcs■:kOttiurLSWindoTi'HelpDependentVariable:YMethod:LeasiSquaresDate:05/10/04Time:17:54Sample(adjusted):19701997Includedcihservations:20afteradjusting已門日卩dintsWeightingseries:WVariableCoefficientStd.Errort-StatisticProb.c713.808639.0350918.286330.0000X0.1111150.00521721.299810.0000WeightedStatisticsR-squared0.948920Meandependentvar1772.688AdjustedR-squared0.94G0B2S.D.dependentvar592.8911S.E.ofregr&ssiciri137.6702Akaikeinfocriterion12.78224Sumsquaredresid341155.6Schwarzcriterion12.88181Loglikelihood-125.B224F-statisiic463.6820Durbir-Watsonstat0.4E04B6Prob(F-statistic)0.000000UnweightedStaiisticsR-squaredAdjustedR-squaredS.E.ofregressionDurbin-Watsonstat0.9771000.975912343.39750.336199MeandependentvarS.D.dependentvarSumsquaredresid3001.1502212.5912122594.2，對(duì)數(shù)變換法先用GENR生成序列LX和LYGENRLY=LOG(Y)GENRLX=LOG(X)然后用OLS法求LY對(duì)LX的回歸，其結(jié)果為:^IlEVi-[Ea-u&tiaik：U1TITLEDVorkfile：DD]l""lFileElitOljecIsViewFrQui0衛(wèi)ti皿wH?LpVi*w|Fyboe|dbj直ctM|Ffint|EMtimmt■總|f°f直cgMt|staAM|R$midT|DependentVariable:LYMethod:LeastSquaresDate:05718/04Time:1S:03Sample(adjusted):197S1997Includedobservations:20afteradjustingendpointsVari^bleCciEffic：ientStd.Errort-StatisticProb.C1.489761□.1551949.5993760.0000DC0.6S2427□.□1616140.990180.0000R-squared0.989401Meandeperidentvar7.819392AdjustedR-squared0.988812￡.D.dependentvar0.655077S.E.ofregression0.0E9291Akaikeinfocriterion-2.406371Sumsquaredresid0.086422Schwarzcriterion-2.306798Loglikelihood25.06371F-statisticleeo.wsDurbin-Watsonstat0.602413Prob[F-statistic)0.000000比較第一中方式與第二種方式，咱們發(fā)覺X與Y