計(jì)量經(jīng)濟(jì)學(xué)案例報(bào)告.doc

國(guó)民經(jīng)濟(jì)核算是反映國(guó)民經(jīng)濟(jì)運(yùn)行狀況的有效工具；國(guó)民經(jīng)濟(jì)核算是宏觀經(jīng)濟(jì)管理的重要依據(jù)；國(guó)民經(jīng)濟(jì)核算是制定和檢驗(yàn)國(guó)民經(jīng)濟(jì)計(jì)劃的科學(xué)方法；國(guó)民經(jīng)濟(jì)核算是微觀決策的重要依據(jù)。國(guó)民經(jīng)濟(jì)統(tǒng)計(jì)工作是國(guó)家整個(gè)統(tǒng)計(jì)工作的一個(gè)重要核心部分，而GNP又是國(guó)民經(jīng)濟(jì)生產(chǎn)統(tǒng)計(jì)中的一個(gè)重要目標(biāo)，GNP是按國(guó)民原則計(jì)算的國(guó)民經(jīng)濟(jì)核算中的重要的綜合指標(biāo)，等于國(guó)內(nèi)生產(chǎn)總值與國(guó)外凈要素之和。雖然GDP是國(guó)民經(jīng)濟(jì)的最核心指標(biāo)，但GNP又有其重要意義，比如，聯(lián)合國(guó)根據(jù)連續(xù)六年的國(guó)民生產(chǎn)總值和人均國(guó)民生產(chǎn)總值來(lái)決定一個(gè)國(guó)家的會(huì)費(fèi)；世界銀行根據(jù)人均國(guó)民生產(chǎn)總值來(lái)決定一個(gè)國(guó)家所能享受的硬貸款、軟貸款等優(yōu)惠待遇；國(guó)際貨幣基金組織根據(jù)國(guó)民生產(chǎn)總值、黃金與外匯儲(chǔ)備、進(jìn)出口額、出口額占國(guó)民生產(chǎn)總值的比例等因素來(lái)決定一個(gè)國(guó)家在基金的份額，進(jìn)而決定在基金的投票權(quán)、分配特別提款權(quán)的份額及向基金借款的份額等等，在這些方面直接影響到我國(guó)的經(jīng)濟(jì)利益和政治利益。所以，我們從中國(guó)統(tǒng)計(jì)年鑒(1999)上查找到1987-1998年的GNP，并找出一些變量建立多元線形回歸模型對(duì)GNP進(jìn)行研究。 我們選擇選擇人均主要產(chǎn)品產(chǎn)量作為影響GNP變化的變量，人均主要產(chǎn)品產(chǎn)量有糧食，棉花，油料，糖料，茶葉，水果，豬牛羊肉，水產(chǎn)品，布，機(jī)制紙及紙板，紗，原煤，原油，發(fā)電量，鋼，水泥等，經(jīng)過(guò)初步考慮，我們決定選用原煤，糧食和棉花作為建立模型所用的三個(gè)變量設(shè)為X2，X3，X4，設(shè)GNP為Y，數(shù)據(jù)如下： GNP與人均主要產(chǎn)品產(chǎn)量 年Y(GNP)/億元X2(原煤)/噸X3(糧食)/千克X4(棉花)/千克1987119550.86371.743.921988149220.89357.723.771989169180.94364.323.391990185980.95393.103.971991216630.94378.264.931992266520.96379.973.871993345610.98387.373.171994466701.04373.463.641995574951.13387.283.961996668511.15414.393.451997731431.12401.743.741998780181.01412.423.62（1） 確定樣本回歸方程：對(duì)于中國(guó)1987年至1998年國(guó)民生產(chǎn)總值及有關(guān)影響因素初步建立多元線形回歸模型。 Y=1+2*X2+3*X3+4*X4 假設(shè)模型中隨機(jī)誤差項(xiàng)ui滿足古典假設(shè)，運(yùn)用OLS方法估計(jì)模型的參數(shù)，利用Eviews計(jì)算得出如下輸入結(jié)果： Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 17:40Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C-306717.489148.80-3.4405110.0088X2142124.451901.062.7383720.0255X3570.9199271.56822.1023080.0687X4-4222.6768323.401-0.5073260.6256R-squared0.831636 Mean dependent var38953.65Adjusted R-squared0.768499 S.D. dependent var24406.49S.E. of regression11743.08 Akaike info criterion21.84112Sum squared resid1.10E+09 Schwarz criterion22.00275Log likelihood-127.0467 F-statistic13.17199Durbin-Watson stat1.425642 Prob(F-statistic)0.001839Estimation Command:=LS Y C X2 X3 X4Estimation Equation:=Y = C(1) + C(2)*X2 + C(3)*X3 + C(4)*X4Substituted Coefficients:=Y = -306717.449 + 142124.3822*X2 + 570.9199106*X3 - 4222.676239*X4 Correlation Matrix X2 X3 X4X2 1.000000 0.684966 -0.226024X3 0.684966 1.000000 -0.167105X4 -0.226024 -0.167105 1.000000Y=-306717+142124X2+570.9X3-4223X4 (2.738) （2.102）(-0.5073) R2=0.8316 F=13.17 S=11743 DW=1.426 查表得F(r,n-k)=F0.05(4,8)=3.84,t/2(n-k)=t0.025(8)=2.306,由于F F0.05(4,8)=3.84,所以拒絕假設(shè)H0:=0,模型在總體上顯著。但是通過(guò)t值可以看出X3和X4無(wú)法通過(guò)顯著性檢驗(yàn),說(shuō)明這個(gè)模型建立的不是十分理想。我們進(jìn)而考慮分別建立一個(gè)解釋變量和兩個(gè)解釋變量的模型，利用Eviews可以得到如下估計(jì)結(jié)果：1）對(duì)X2Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 17:43Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C-180859.942190.69-4.2867250.0016X2220364.442122.475.2315180.0004R-squared0.732397 Mean dependent var38953.65Adjusted R-squared0.705637 S.D. dependent var24406.49S.E. of regression13241.81 Akaike info criterion21.97116Sum squared resid1.75E+09 Schwarz criterion22.05198Log likelihood-129.8269 F-statistic27.36878Durbin-Watson stat0.716502 Prob(F-statistic)0.000383Estimation Command:=LS Y C X2Estimation Equation:=Y = C(1) + C(2)*X2Substituted Coefficients:=Y = -180859.8861 + 220364.4473*X2Y=-180860+220364X2 （a） （5.232）R2=0.7324 F=27.37S=13242 DW=0.71652）對(duì)X3Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 15:17Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C-386132.497641.28-3.9546020.0027X31103.697253.26604.3578550.0014R-squared0.655064 Mean dependent var38953.65Adjusted R-squared0.620571 S.D. dependent var24406.49S.E. of regression15033.87 Akaike info criterion22.22501Sum squared resid2.26E+09 Schwarz criterion22.30583Log likelihood-131.3501 F-statistic18.99090Durbin-Watson stat1.466938 Prob(F-statistic)0.001426Estimation Command:=LS Y C X3Estimation Equation:=Y = C(1) + C(2)*X3Substituted Coefficients:=Y = -386132.4019 + 1103.69677*X3Y=-386132+1104X3 （b） (4.538)R2=0.6551 F=18.99S=15034 DW=0.71653）對(duì)X4Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 15:18Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C96133.6064802.431.4834880.1688X4-15103.6617013.62-0.8877400.3955R-squared0.073051 Mean dependent var38953.65Adjusted R-squared-0.019644 S.D. dependent var24406.49S.E. of regression24645.04 Akaike info criterion23.21355Sum squared resid6.07E+09 Schwarz criterion23.29437Log likelihood-137.2813 F-statistic0.788082Durbin-Watson stat0.214148 Prob(F-statistic)0.395531Estimation Command:=LS Y C X4Estimation Equation:=Y = C(1) + C(2)*X4Substituted Coefficients:=Y = 96133.60497 - 15103.66409*X4Y=96134-15104X4 (-0.8877)R2=0.07305 F=0.7881S=24645 DW=0.21414）對(duì)X2，X3Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 15:27Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C-327701.575644.37-4.3321340.0019X2146213.849110.472.9772420.0155X3573.3049260.08402.2043070.0550R-squared0.826219 Mean dependent var38953.65Adjusted R-squared0.787601 S.D. dependent var24406.49S.E. of regression11248.17 Akaike info criterion21.70612Sum squared resid1.14E+09 Schwarz criterion21.82734Log likelihood-127.2367 F-statistic21.39463Durbin-Watson stat1.247999 Prob(F-statistic)0.000380Estimation Command:=LS Y C X2 X3Estimation Equation:=Y = C(1) + C(2)*X2 + C(3)*X3Substituted Coefficients:=Y = -327701.5357 + 146213.7762*X2 + 573.304887*X3Y=-327701+146214X2+573.3X3 （c）(2.977) (2.204) R2=0.8262 F=21.39S=11248 DW=1.2485）對(duì)X2，X4Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 15:31Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C-159025.264471.72-2.4665880.0358X2215651.145047.384.7872060.0010X4-4525.5889776.199-0.4629190.6544R-squared0.738620 Mean dependent var38953.65Adjusted R-squared0.680536 S.D. dependent var24406.49S.E. of regression13794.82 Akaike info criterion22.11429Sum squared resid1.71E+09 Schwarz criterion22.23552Log likelihood-129.6858 F-statistic12.71635Durbin-Watson stat0.751053 Prob(F-statistic)0.002386Estimation Command:=LS Y C X2 X4Estimation Equation:=Y = C(1) + C(2)*X2 + C(3)*X4Substituted Coefficients:=Y = -159025.2067 + 215651.1045*X2 - 4525.587513*X4Y=-159025+215651X2-4526X4 (4.787) (-0.4629) R2=0.7386 F=12.72 S=13795 DW=0.75116）對(duì)X3，X4Dependent Variable: YMethod: Least SquaresDate: 12/13/03 Time: 15:43Sample: 1987 1998Included observations: 12VariableCoefficientStd. Errort-StatisticProb. C-344553.1115574.5-2.9812210.0154X31072.042263.30804.0714390.0028X4-7762.56110790.09-0.7194160.4901R-squared0.673822 Mean dependent var38953.65Adjusted R-squared0.601338 S.D. dependent var24406.49S.E. of regression15410.19 Akaike info criterion22.33576Sum squared resid2.14E+09 Schwarz criterion22.45699Log likelihood-131.0146 F-statistic9.296132Durbin-Watson stat1.758444 Prob(F-statistic)0.006465Estimation Command:=LS Y C X3 X4Estimation Equation:=Y = C(1) + C(2)*X3 + C(3)*X4Substituted Coefficients:=Y = -344553.0724 + 1072.042485*X3 - 7762.560522*X4Y=-34553+1072X3-7763X4(4.71) (-0.7194) R2=0.6378 F=9.296 S=15410 DW=1.758 查表得F（2，10）=4.10,F0.05(3,9)=3.86,t0.025(10)=2.228, t0.025（9）=2.262。由以上各樣本回歸方程可以看出X4（人均棉花產(chǎn)量）對(duì)Y（GNP）沒(méi)有顯著影響，應(yīng)該略去。 再比較不含X4的幾個(gè)方程（a），（b），（c），可以看出，式（a）稍微優(yōu)于式（b），在式（c）中，雖然X3沒(méi)有通過(guò)顯著性檢驗(yàn)，但是相應(yīng)的t統(tǒng)計(jì)量為2.204，很接近臨界值t0.025（9）=2.262，且式（c）的可決系數(shù)R2明顯高于式（a）中的R2，誤差項(xiàng)的標(biāo)準(zhǔn)差估計(jì)值S明顯小于式（a）中的S。因此，最后確定的總體回歸模型為 Y=1+2X2+3X3+u根據(jù)剛才的輸出結(jié)果，樣本回歸方程為Y=-327701+146214X2+573.3X3 (2.977) (2.204) R2=0.8262 F=21.39S=11248 DW=1.248A多重共線性的檢驗(yàn)：由剛才確定總體回歸模型在的分析過(guò)程可知:R2很大,F=21.39顯著大于F0.05(3,9)=3.86,而變量X2對(duì)應(yīng)的偏回歸系數(shù)t值顯著,X3的t值接近顯著,所以,這個(gè)模型是不存在多重共線性的。B異方差性的檢驗(yàn)：對(duì)X2，X3ARCH Test:F-statistic0.431993 Probability0.739434Obs*R-squared1.852580 Probability0.603560Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/13/03 Time: 17:55Sample(adjusted): 1990 1998Included observations: 9 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C1.97E+081.13E+081.7480490.1409RESID2(-1)-0.4816870.671468-0.7173640.5053RESID2(-2)-0.1386260.701171-0.1977060.8511RESID2(-3)-0.6109790.667046-0.9159480.4017R-squared0.205842 Mean dependent var1.20E+08Adjusted R-squared-0.270653 S.D. dependent var1.64E+08S.E. of regression1.85E+08 Akaike info criterion41.21034Sum squared resid1.71E+17 Schwarz criterion41.29800Log likelihood-181.4465 F-statistic0.431993Durbin-Watson stat1.241293 Prob(F-statistic)0.739434從輸出的輔助回歸函數(shù)中得到R2，計(jì)算（n-P）R2=（9-3）*0.7282=4.3692,查2分布表,給定=0.05,自由度為P=3,得臨界值20.05(3)=7.815, （n-P）R2=4.369220.05(3)=7.815,所以接受H0,表明模型中隨機(jī)誤差項(xiàng)不存在異方差性。從下面的White也可得出相同結(jié)果，模型中不存在異方差。White Heteroskedasticity Test:F-statistic4.688229 Probability0.037155Obs*R-squared8.738234 Probability0.067986Test Equation:Dependent Variable: RESID2Method: L