计量经济学国债发行额数学模型.docx

1、计量经济学国债发行额数学模型国债，又称国家公债，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。国债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环节，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

2、做出的，影响国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.

3、5739.5616231986138.25102.02282.950.1722371987223.55119.62562.8379.8330811988270.78149.283133.9776.7638221989407.97169.092158.8872.3751961990375.45185.479146.49190.0771201991461.4216.178237.14246.892421992669.68266.381258.83438.57117591993739.22346.344293.35336.221520419941175.25467.594574.52499.3621

4、51919951549.76584.781581.52882.962966219961967.28678.846529.561355.033852119972476.82744.626582.421918.374628019983310.93783.452922.232352.925340819993715.03820.67461743.591910.535962220004180.1894.4222491.271579.826433220014604959.3332516.542007.7373762由数据，我们进行第一次拟合：Dependent Variable: YMethod: Lea

5、st SquaresDate: 10/25/11 Time: 16:54Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C14.4348135.409080.4076580.6886X10.1902360.4509900.4218180.6784X20.9402010.1538776.1100720.0000X30.8208700.1683064.8772340.0001X40.0054810.0149370.3669690.7182R-squared0.998963

6、 Mean dependent var1216.395Adjusted R-squared0.998719 S.D. dependent var1485.993S.E. of regression53.18111 Akaike info criterion10.98200Sum squared resid48079.92 Schwarz criterion11.22996Log likelihood-115.8020 F-statistic4094.752Durbin-Watson stat2.072804 Prob(F-statistic)0.000000得到线性拟合方程为：Y=14.434

7、81+0.190236X1+0.940201X2+0.820870X3+0.005481X4 O.407658 0.421818 6.110072 4.877234 0.366969=O.998963 0.998719 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X1X2X3X4X1 1.000000 0.869643 0.954508 0.986413X2 0.869643 1.000000 0.787957 0.919614X3 0.954508 0.787957 1.000000 0.959852X4 0.986413

8、0.919614 0.959852 1.000000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-StatisticProb. C-388.3980124.1492-3.1284790

9、.0053X14.4943130.26159517.180410.0000R-squared0.936541 Mean dependent var1216.395Adjusted R-squared0.933369 S.D. dependent var1485.993S.E. of regression383.5804 Akaike info criterion14.82348Sum squared resid2942679. Schwarz criterion14.92267Log likelihood-161.0583 F-statistic295.1665Durbin-Watson st

10、at0.248664 Prob(F-statistic)0.000000Y=-388.3980+4.494313X1 -3.128479 17.18041=0.936541 0.933369 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. C249.5863129.59951.9258270.0

11、685X21.8551330.14322112.952960.0000R-squared0.893492 Mean dependent var1216.395Adjusted R-squared0.888166 S.D. dependent var1485.993S.E. of regression496.9387 Akaike info criterion15.34132Sum squared resid4938962. Schwarz criterion15.44050Log likelihood-166.7545 F-statistic167.7791Durbin-Watson stat

12、0.617461 Prob(F-statistic)0.000000Y=249.5863+1.855133X2 1.925827 12.95296=0.893492 0.888166 F=167.77913、Y与X3拟合：Dependent Variable: YMethod: Least SquaresDate: 10/25/11 Time: 17:27Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C80.25663138.50020.5794690.5687X3

13、1.7533690.13636912.857500.0000R-squared0.892076 Mean dependent var1216.395Adjusted R-squared0.886680 S.D. dependent var1485.993S.E. of regression500.2312 Akaike info criterion15.35453Sum squared resid5004625. Schwarz criterion15.45371Log likelihood-166.8998 F-statistic165.3154Durbin-Watson stat0.652

14、788 Prob(F-statistic)0.000000 Y=80.25663+1753369X3 0.579469 12.85750=0.892076 0.886680 F=165.3154 因常数项t=0.5794692.306 则省略常数项，得到拟合方程为： Y=1753369X34、 Y与X4拟合：Dependent Variable: YMethod: Least SquaresDate: 10/25/11 Time: 17:30Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-Stat

15、isticProb. C-32.4313144.08887-0.7355900.4705X40.0610410.00141043.303940.0000R-squared0.989447 Mean dependent var1216.395Adjusted R-squared0.988920 S.D. dependent var1485.993S.E. of regression156.4211 Akaike info criterion13.02949Sum squared resid489351.3 Schwarz criterion13.12867Log likelihood-141.3

16、244 F-statistic1875.231Durbin-Watson stat0.629259 Prob(F-statistic)0.000000Y=-32.43131+0.061041X4-0.735590 43.30394 =0989447 0.988920 F=1875.231因常数项t=-0.7355902.306 则省略常数项，得到拟合方程为：Y=0.061041X4 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: YMethod: Least SquaresDate: 10/25/11 Time: 17:40Sa

17、mple: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C176.706545.534463.8807210.0010X1-2.3132740.402728-5.7440080.0000X40.0911920.00532217.136510.0000R-squared0.996144 Mean dependent var1216.395Adjusted R-squared0.995738 S.D. dependent var1485.993S.E. of regression97

18、.01420 Akaike info criterion12.11372Sum squared resid178823.4 Schwarz criterion12.26249Log likelihood-130.2509 F-statistic2453.999Durbin-Watson stat1.819363 Prob(F-statistic)0.000000Y=176.7065-2.313274X1+0.091192X4 3.880721 -5.744008 17.13651=0.996144 0.995738 F=2453.9996、 Y与X2、X4拟合： Dependent Varia

19、ble: YMethod: Least SquaresDate: 10/25/11 Time: 17:44Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C-6.39478830.06927-0.2126690.8339X20.3878920.0771025.0309030.0001X40.0498870.00241120.693360.0000R-squared0.995475 Mean dependent var1216.395Adjusted R-squared

20、0.994999 S.D. dependent var1485.993S.E. of regression105.0896 Akaike info criterion12.27363Sum squared resid209832.5 Schwarz criterion12.42241Log likelihood-132.0099 F-statistic2089.942Durbin-Watson stat1.199846 Prob(F-statistic)0.000000 Y=-6.394788+0.387892X2+0.049887X4 -0.212669 5.030903 20.69336

21、=0.995475 0.994999 F=2089.942 因常数项的t=-0.2126692.306,则省略常数项，得到拟合方程为： Y=0.387892X2+0.049887X47、 Y与X3、X4的拟合： Dependent Variable: YMethod: Least SquaresDate: 10/25/11 Time: 17:49Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C-32.7135742.26045-0.7740940.4484X3-0.

22、2424450.145713-1.6638520.1125X40.0687330.00481714.269790.0000R-squared0.990789 Mean dependent var1216.395Adjusted R-squared0.989820 S.D. dependent var1485.993S.E. of regression149.9329 Akaike info criterion12.98438Sum squared resid427117.9 Schwarz criterion13.13316Log likelihood-139.8281 F-statistic

23、1021.904Durbin-Watson stat0.804370 Prob(F-statistic)0.000000 Y=-32.71357-0.242445X3+0.068733X4 -0.774094 -1.663852 14.26979 =0.990789 0.989820 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: 17:57Sample: 1980 2001Included observati

24、ons: 22VariableCoefficientStd. Errort-StatisticProb. X3-0.2419920.144245-1.6776530.1090X40.0680350.00468414.525610.0000R-squared0.990499 Mean dependent var1216.395Adjusted R-squared0.990024 S.D. dependent var1485.993S.E. of regression148.4231 Akaike info criterion12.92452Sum squared resid440588.3 Sc

25、hwarz criterion13.02370Log likelihood-140.1697 F-statistic2084.990Durbin-Watson stat0.781478 Prob(F-statistic)0.000000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=0.068035X4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 2001Includ

26、ed observations: 22VariableCoefficientStd. Errort-StatisticProb. C124.504341.072913.0313010.0072X1-1.5673030.408203-3.8395220.0012X20.2270360.0721453.1469530.0056X40.0749410.00677911.055320.0000R-squared0.997512 Mean dependent var1216.395Adjusted R-squared0.997098 S.D. dependent var1485.993S.E. of r

27、egression80.05422 Akaike info criterion11.76625Sum squared resid115356.2 Schwarz criterion11.96462Log likelihood-125.4288 F-statistic2405.922Durbin-Watson stat2.010999 Prob(F-statistic)0.000000Y=124.5043-1.567303X1+0.227036X2+0.074941X4 3.031301 -3.839522 3.146953 11.05532 =0.997512 0.997098 F=2405.9229、Y与X1、X3、X4拟合：Dependent Variable: YMethod: Least SquaresDate: 10/25/11 Time: 18:04Sample: 1980 2001Included observations: 22VariableCoefficientStd. Errort-StatisticProb. C166.439343.777343.8019500.0013X1-2.2017210.389023-5.6596210.0000X3-0.1563430.091075-1.71