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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
2、须要做出的，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-
3、0.5739.5616231986138.25102.02282.950.1722371987223.55119.62562.8379.8330811988270.78149.283133.9776.7638221989407.97169.092158.8872.3751961990375.45185.479146.49190.0771201991461.4216.178237.14246.892421992669.68266.381258.83438.57117591993739.22346.344293.35336.221520419941175.25467.594574.52499.36
4、2151919951549.76584.781581.52882.962966219961967.28678.846529.561355.033852119972476.82744.626582.421918.374628019983310.93783.452922.232352.925340819993715.03820.67461743.591910.535962220004180.1894.4222491.271579.826433220014604959.3332516.542007.7373762由数据，我们进行第一次拟合：Dependent Variable: YMethod: L
5、east 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-squared0.9989
6、63 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=14.4
7、3481+0.190236X1+0.940201X2+0.820870X3+0.005481X4 O.407658 0.421818 6.110072 4.877234 0.366969R2=O.998963 R-2=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
8、.986413 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
9、.1284790.0053X14.4943130.26159517.180410.0000R-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-W
10、atson stat0.248664 Prob(F-statistic)0.000000Y=-388.3980+4.494313X1 -3.128479 17.18041R2=0.936541 R-2=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. C249.5863129.5
11、9951.9258270.0685X21.8551330.14322112.952960.0000R-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-statistic167.7791Durb
12、in-Watson stat0.617461 Prob(F-statistic)0.000000Y=249.5863+1.855133X2 1.925827 12.95296R2=0.893492 R-2=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.
13、50020.5794690.5687X31.7533690.13636912.857500.0000R-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 stat0.652788 Prob(F-statistic)0.000000 Y=80.25663+1753369X3 0.579469 12.85750R2=0.892076 R-2=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=1753369X
