计量经济学(国债发行额数学模型)

1、精选优质文档-倾情为你奉上国债，又称国家，是国家以其信用为基础，按照债的一般原则，通过向社会筹集资金所形成的债权债务关系。国债是由国家发行的债券，是中央政府为筹集财政资金而发行的一种政府债券，是中央政府向投资者出具的、承诺在一定时期支付利息和到期偿还本金的债权债务凭证，由于国债的发行主体是国家，所以它具有最高的信用度，被公认为是最安全的投资工具。售出或被个人和企业认购的过程，它是国债运行的起点和基础，核心是确定国债售出的方式即国债发行方式。 一般而言，国债发行主要有四种方式：1.固定收益出售法; 2.公募拍卖方式。 3.连续经销方式 4.承受发行法国债的发行额，是中国财政部必须要做出的，影响国

2、债发行额的因素多种多样，为此，我们建立模型，研究国债发行额Y与国内生产总值X1、财政赤字X2、国债还本付息额X3、居民储蓄额X4的关系，来得到各因素国债发行的影响大小，及确定来年的国债额数。我们采集从1980年到2001年的数据进行研究，数据如下：时间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由数据，我们进行第一次拟合：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.得到线性拟合方程为：Y=14.43481+0.X1+0.X2+0.X3+0.X4 O. 0. 6. 4. 0.R2=O. R-2=0. F=4094.752从总体上看，模型中国债发行额与各解释变量线性关系显著。检验： 计算解释变量之间的简单相关系数X1X

7、2X3X4X1 1. 0. 0. 0.X2 0. 1. 0. 0.X3 0. 0. 1. 0.X4 0. 0. 0. 1.从表中，可以发现，解释变量存在着高度线性相关，虽然在整体上线性回归拟合较好，但X1,X4的参数t值并不显著，表明模型中解释变量存在严重多重线性共线性。修正：1、 Y与X1线性回归：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与X2拟合：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与X3拟合：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 因常数项t=0.<2.306 则省略常数项，得到拟合方程为： Y=X34、 Y与X4拟合：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因常数项t=-0.<2.306 则省略常数项，得到拟合方程为：Y=0.X4 在四个拟合方程中，X4的t检验值最大，则选出X45、 Y与X4、X1拟合：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与X2、X4拟合： 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 因常数项的t=-0.<2.306,则省略常数项，得到拟合方程为： Y=0.X2+0.X47、 Y与X3、X4的拟合： 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因常数项和X3系数绝对值的t值都小于2.306，先省略常数项，由X3与X4与Y进行拟合：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.此时，发现X3系数的t值依然小于2.306，则省略X3,得到拟合方程为： Y=0.X4比较后三个拟合方程，选出最优为Y与X1、X4的拟合。8、 Y与X1、X2、X4拟合：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与X1、X3、X4拟合：Dependent Varia