計量經(jīng)濟學(xué)(國債發(fā)行額數(shù)學(xué)模型)

1、精選優(yōu)質(zhì)文檔-傾情為你奉上國債，又稱國家，是國家以其信用為基礎(chǔ)，按照債的一般原則，通過向社會籌集資金所形成的債權(quán)債務(wù)關(guān)系。國債是由國家發(fā)行的債券，是中央政府為籌集財政資金而發(fā)行的一種政府債券，是中央政府向投資者出具的、承諾在一定時期支付利息和到期償還本金的債權(quán)債務(wù)憑證，由于國債的發(fā)行主體是國家，所以它具有最高的信用度，被公認(rèn)為是最安全的投資工具。售出或被個人和企業(yè)認(rèn)購的過程，它是國債運行的起點和基礎(chǔ)，核心是確定國債售出的方式即國債發(fā)行方式。 一般而言，國債發(fā)行主要有四種方式：1.固定收益出售法; 2.公募拍賣方式。 3.連續(xù)經(jīng)銷方式 4.承受發(fā)行法國債的發(fā)行額，是中國財政部必須要做出的，影響國

2、債發(fā)行額的因素多種多樣，為此，我們建立模型，研究國債發(fā)行額Y與國內(nèi)生產(chǎn)總值X1、財政赤字X2、國債還本付息額X3、居民儲蓄額X4的關(guān)系，來得到各因素國債發(fā)行的影響大小，及確定來年的國債額數(shù)。我們采集從1980年到2001年的數(shù)據(jù)進行研究，數(shù)據(jù)如下：時間YX1X2X3X4198043.0145.17868.928.583991981121.7448.624-37.3862.89524198283.8652.94717.6555.52675198379.4159.34542.5742.47893198477.3471.7158.1628.91215198589.8589.644-0.5739.56

3、16231986138.25102.02282.950.1722371987223.55119.62562.8379.8330811988270.78149.283133.9776.7638221989407.97169.092158.8872.3751961990375.45185.479146.49190.0771201991461.4216.178237.14246.892421992669.68266.381258.83438.57117591993739.22346.344293.35336.221520419941175.25467.594574.52499.36215191995

4、1549.76584.781581.52882.962966219961967.28678.846529.561355.033852119972476.82744.626582.421918.374628019983310.93783.452922.232352.925340819993715.03820.67461743.591910.535962220004180.1894.4222491.271579.826433220014604959.3332516.542007.7373762由數(shù)據(jù)，我們進行第一次擬合：Dependent Variable: YMethod: Least Squa

5、resDate: 10/25/11 Time: 16:54Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C14.4348135.409080.0.6886X10.0.0.0.6784X20.0.6.0.0000X30.0.4.0.0001X40.0.0.0.7182R-squared0. Mean dependent var1216.395Adjusted R-squared0. S.D. dependent var1485.993S.E. of regressio

6、n53.18111 Akaike info criterion10.98200Sum squared resid48079.92 Schwarz criterion11.22996Log likelihood-115.8020 F-statistic4094.752Durbin-Watson stat2. Prob(F-statistic)0.得到線性擬合方程為：Y=14.43481+0.X1+0.X2+0.X3+0.X4 O. 0. 6. 4. 0.R2=O. R-2=0. F=4094.752從總體上看，模型中國債發(fā)行額與各解釋變量線性關(guān)系顯著。檢驗： 計算解釋變量之間的簡單相關(guān)系數(shù)X1X

7、2X3X4X1 1. 0. 0. 0.X2 0. 1. 0. 0.X3 0. 0. 1. 0.X4 0. 0. 0. 1.從表中，可以發(fā)現(xiàn)，解釋變量存在著高度線性相關(guān)，雖然在整體上線性回歸擬合較好，但X1,X4的參數(shù)t值并不顯著，表明模型中解釋變量存在嚴(yán)重多重線性共線性。修正：1、 Y與X1線性回歸：Dependent Variable: YMethod: Least SquaresDate: 10/25/11 Time: 17:16Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-Statisti

8、cProb. C-388.3980124.1492-3.0.0053X14.0.17.180410.0000R-squared0. Mean dependent var1216.395Adjusted R-squared0. S.D. dependent var1485.993S.E. of regression383.5804 Akaike info criterion14.82348Sum squared resid. Schwarz criterion14.92267Log likelihood-161.0583 F-statistic295.1665Durbin-Watson stat

9、0. Prob(F-statistic)0.Y=-388.3980+4.X1 -3. 17.18041R2=0. R-2=0. F=295.16652、 Y與X2擬合：Dependent Variable: YMethod: Least SquaresDate: 10/25/11 Time: 17:21Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C249.5863129.59951.0.0685X21.0.12.952960.0000R-squared0. Mea

10、n dependent var1216.395Adjusted R-squared0. S.D. dependent var1485.993S.E. of regression496.9387 Akaike info criterion15.34132Sum squared resid. Schwarz criterion15.44050Log likelihood-166.7545 F-statistic167.7791Durbin-Watson stat0. Prob(F-statistic)0.Y=249.5863+1.X2 1. 12.95296R2=0. R-2=0. F=167.7

11、7913、Y與X3擬合：Dependent Variable: YMethod: Least SquaresDate: 10/25/11 Time: 17:27Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C80.25663138.50020.0.5687X31.0.12.857500.0000R-squared0. Mean dependent var1216.395Adjusted R-squared0. S.D. dependent var1485.993S.

12、E. of regression500.2312 Akaike info criterion15.35453Sum squared resid. Schwarz criterion15.45371Log likelihood-166.8998 F-statistic165.3154Durbin-Watson stat0. Prob(F-statistic)0. Y=80.25663+X3 0. 12.85750R2=0. R-2=0. F=165.3154 因常數(shù)項t=0.<2.306 則省略常數(shù)項，得到擬合方程為： Y=X34、 Y與X4擬合：Dependent Variable: Y

13、Method: Least SquaresDate: 10/25/11 Time: 17:30Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C-32.4313144.08887-0.0.4705X40.0.43.303940.0000R-squared0. Mean dependent var1216.395Adjusted R-squared0. S.D. dependent var1485.993S.E. of regression156.4211 Akaike

14、 info criterion13.02949Sum squared resid.3 Schwarz criterion13.12867Log likelihood-141.3244 F-statistic1875.231Durbin-Watson stat0. Prob(F-statistic)0.Y=-32.43131+0.X4-0. 43.30394 R2= R-2=0. F=1875.231因常數(shù)項t=-0.<2.306 則省略常數(shù)項，得到擬合方程為：Y=0.X4 在四個擬合方程中，X4的t檢驗值最大，則選出X45、 Y與X4、X1擬合：Dependent Variable: Y

15、Method: Least SquaresDate: 10/25/11 Time: 17:40Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C176.706545.534463.0.0010X1-2.0.-5.0.0000X40.0.17.136510.0000R-squared0. Mean dependent var1216.395Adjusted R-squared0. S.D. dependent var1485.993S.E. of regression9

16、7.01420 Akaike info criterion12.11372Sum squared resid.4 Schwarz criterion12.26249Log likelihood-130.2509 F-statistic2453.999Durbin-Watson stat1. Prob(F-statistic)0.Y=176.7065-2.X1+0.X4 3. -5. 17.13651R2=0. R-2=0. F=2453.9996、 Y與X2、X4擬合： Dependent Variable: YMethod: Least SquaresDate: 10/25/11 Time:

17、 17:44Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C-6.30.06927-0.0.8339X20.0.5.0.0001X40.0.20.693360.0000R-squared0. Mean dependent var1216.395Adjusted R-squared0. S.D. dependent var1485.993S.E. of regression105.0896 Akaike info criterion12.27363Sum square

18、d resid.5 Schwarz criterion12.42241Log likelihood-132.0099 F-statistic2089.942Durbin-Watson stat1. Prob(F-statistic)0. Y=-6.+0.X2+0.X4 -0. 5. 20.69336 R2=0. R-2=0. F=2089.942 因常數(shù)項的t=-0.<2.306,則省略常數(shù)項，得到擬合方程為： Y=0.X2+0.X47、 Y與X3、X4的擬合： Dependent Variable: YMethod: Least SquaresDate: 10/25/11 Time:

19、17:49Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C-32.7135742.26045-0.0.4484X3-0.0.-1.0.1125X40.0.14.269790.0000R-squared0. Mean dependent var1216.395Adjusted R-squared0. S.D. dependent var1485.993S.E. of regression149.9329 Akaike info criterion12.98438Sum

20、 squared resid.9 Schwarz criterion13.13316Log likelihood-139.8281 F-statistic1021.904Durbin-Watson stat0. Prob(F-statistic)0. Y=-32.71357-0.X3+0.X4 -0. -1. 14.26979 R2=0. R-2=0. F=1021.904因常數(shù)項和X3系數(shù)絕對值的t值都小于2.306，先省略常數(shù)項，由X3與X4與Y進行擬合：Dependent Variable: YMethod: Least SquaresDate: 10/25/11 Time: 17:57

21、Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. X3-0.0.-1.0.1090X40.0.14.525610.0000R-squared0. Mean dependent var1216.395Adjusted R-squared0. S.D. dependent var1485.993S.E. of regression148.4231 Akaike info criterion12.92452Sum squared resid.3 Schwarz criteri

22、on13.02370Log likelihood-140.1697 F-statistic2084.990Durbin-Watson stat0. Prob(F-statistic)0.此時，發(fā)現(xiàn)X3系數(shù)的t值依然小于2.306，則省略X3,得到擬合方程為： Y=0.X4比較后三個擬合方程，選出最優(yōu)為Y與X1、X4的擬合。8、 Y與X1、X2、X4擬合：Dependent Variable: YMethod: Least SquaresDate: 10/25/11 Time: 18:03Sample: 1980 2001Included observations: 22VariableCoef

23、ficientStd. Errort-StatisticProb. C124.504341.072913.0.0072X1-1.0.-3.0.0012X20.0.3.0.0056X40.0.11.055320.0000R-squared0. Mean dependent var1216.395Adjusted R-squared0. S.D. dependent var1485.993S.E. of regression80.05422 Akaike info criterion11.76625Sum squared resid.2 Schwarz criterion11.96462Log likelihood-125.4288 F-statistic2405.922Durbin-Watson stat2. Prob(F-statistic)0.Y=124.5043-1.X1+0.X2+0.X4 3. -3. 3. 11.05532 R2=0. R-2=0. F=2405.9229、Y與X1、X3、X4擬合：Dependent Varia