計量經(jīng)濟學(國債發(fā)行額數(shù)學模型)

1、國債，又稱國家公債，是國家以其信用為基礎，按照債的一般原則，通過向社會籌集資金所形成的債權債務關系。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債務憑證，由于國債的發(fā)行主體是國家，所以它具有最高的信用度，被公認為是最安全的投資工具。國債售出或被個人和企業(yè)認購的過程，它是國債運行的起點和基礎環(huán)節(jié)，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，影響國債發(fā)行額的因素多種多

2、樣，為此，我們建立模型，研究國債發(fā)行額Y與國內生產(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：由數(shù)據(jù)，我們進行第一次擬合：Dependent Variable: Y Method: Least SquaresDate: 10/25/11 Time: 16:54 Sample: 1980 2001C X1 X2 X3 R-squared14.43481 0.190236 0.940201 0.820870 35.40908 0.450990 0.153877 0.

3、168306 0.407658 0.421818 6.110072 4.877234 0.6886 0.6784 0.0000 0.0001 1216.395 1485.993 10.98200 11.22996 4094.752 0.998963 Mean dependentvarAdjusted R-squared 0.998719 S.D. dependent var S.E. of regression 53.18111 Akaike info criterion Sum squared resid 48079.92 Schwarz criterion Log likelihood -

4、115.8020 F-statistic得到線性擬合方程為：Y=14.43481+0.190236X1+0.940201X2+0.820870X3+0.005481X4 O.407658 0.421818 6.110072 4.877234 0.366969 R2=O.998963 R2=0.998719 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系顯著。 檢驗：計算解釋變量之間的簡單相關系數(shù) X1 X2 X3X1 1.000000 0.869643 0.954508 X2 0.869643 1.000000 0.787957 X3 0.954508 0.787957

5、1.000000 X4 0.986413 0.919614 0.959852X40.986413 0.919614 0.959852 1.000000從表中，可以發(fā)現(xiàn)，解釋變量存在著高度線性相關，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重多重線性共線性。修正：1、 Y與X1線性回歸：Dependent Variable: Y Method: Least Squares Date: 10/25/11 Time: 17:16 Sample: 1980 2001 C R-squaredAdjusted R-squared S.E. of regressi

6、on Sum squared resid Log likelihood -388.3980 124.1492 -3.128479 0.0053 1485.993 14.82348 14.92267 295.1665 0.936541 Mean dependent var 1216.395 0.933369 S.D. dependent var 383.5804 Akaike info criterion 2942679. Schwarz criterion -161.0583 F-statistic Y=-388.3980+4.494313X1-3.128479 17.18041R2=0.93

7、6541 R2=0.933369 F=295.16652、 Y與X2擬合：Dependent Variable: Y Method: Least Squares Date: 10/25/11 Time: 17:21 Sample: 1980 2001 Included observations: 22C X2R-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat249.5863 1.855133129.5995 0.1432211.925827 12.9

8、52960.0685 0.0000 1485.993 15.34132 15.44050 167.7791 0.0000000.893492 Mean dependent var 1216.395 0.888166 S.D. dependent var 496.9387 Akaike info criterion 4938962. Schwarz criterion -166.7545 F-statistic 0.617461 Prob(F-statistic)Y=249.5863+1.855133X2 1.925827 12.95296R2=0.893492 R2=0.888166 F=16

9、7.77913、Y與X3擬合：Dependent Variable: Y Method: Least Squares Date: 10/25/11 Time: 17:27 Sample: 1980 2001 C R-squared80.25663 138.5002 0.579469 0.5687 0.892076 Mean dependent var 1216.395Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat0.886680 S.D. dependent va

10、r 500.2312 Akaike info criterion 5004625. Schwarz criterion -166.8998 F-statistic 0.652788 Prob(F-statistic)1485.993 15.35453 15.45371 165.3154 0.000000Y=80.25663+1753369X3 0.579469 12.85750R2=0.892076 R2=0.886680 F=165.3154因常數(shù)項t=0.579469<2.306 則省略常數(shù)項，得到擬合方程為： Y=1753369X34、 Y與X4擬合：Dependent Varia

11、ble: Y Method: Least Squares Date: 10/25/11 Time: 17:30 Sample: 1980 2001 Included observations: 22C R-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat-32.43131 44.08887 -0.735590 0.4705 0.989447 Mean dependent var 1216.395 0.988920 S.D. dependent var

12、156.4211 Akaike info criterion 489351.3 Schwarz criterion -141.3244 F-statistic 0.629259 Prob(F-statistic)1485.993 13.02949 13.12867 1875.231 0.000000Y=-32.43131+0.061041X4-0.735590 43.30394R2=0989447 R2=0.988920 F=1875.231因常數(shù)項t=-0.735590<2.306 則省略常數(shù)項，得到擬合方程為：Y=0.061041X4在四個擬合方程中，X4的t檢驗值最大，則選出X45

13、、 Y與X4、X1擬合：Dependent Variable: Y Method: Least Squares Date: 10/25/11 Time: 17:40 Sample: 1980 2001 Variable C X1 R-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood Coefficient 176.7065 -2.313274 Std. Error 45.53446 0.402728 t-Statistic 3.880721 -5.744008 Prob. 0.0010 0

14、.0000 1485.993 12.11372 12.26249 2453.999 0.996144 Mean dependent var 1216.395 0.995738 S.D. dependent var 97.01420 Akaike info criterion 178823.4 Schwarz criterion -130.2509 F-statistic Y=176.7065-2.313274X1+0.091192X4 3.880721 -5.744008 17.13651 R2=0.996144 R2=0.995738 F=2453.9996、 Y與X2、X4擬合：Depen

15、dent Variable: Y Method: Least Squares Date: 10/25/11 Time: 17:44 Sample: 1980 2001 Included observations: 22C X2 X4R-squaredAdjusted R-squared-6.394788 0.387892 0.04988730.06927 0.077102 0.002411-0.212669 5.030903 20.693360.8339 0.0001 0.0000 1485.9930.995475 Mean dependent var 1216.395 0.994999 S.

16、D. dependent varS.E. of regression Sum squared resid Log likelihood 105.0896 Akaike info criterion 209832.5 Schwarz criterion -132.0099 F-statistic 12.27363 12.42241 2089.942 Y=-6.394788+0.387892X2+0.049887X4 -0.212669 5.030903 20.69336 R2=0.995475 R2=0.994999 F=2089.942因常數(shù)項的t=-0.212669<2.306,則省略

17、常數(shù)項，得到擬合方程為： Y=0.387892X2+0.049887X47、 Y與X3、X4的擬合：Dependent Variable: Y Method: Least Squares Date: 10/25/11 Time: 17:49 Sample: 1980 2001 Variable C X3 R-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood Coefficient -32.71357 -0.242445 Std. Error 42.26045 0.145713 t-Stat

18、istic -0.774094 -1.663852 Prob. 0.4484 0.1125 0.990789 Mean dependent var 1216.395 0.989820 S.D. dependent var 149.9329 Akaike info criterion 427117.9 Schwarz criterion -139.8281 F-statistic 1485.993 12.98438 13.13316 1021.904 Y=-32.71357-0.242445X3+0.068733X4 -0.774094 -1.663852 14.26979 R2=0.99078

19、9 R2=0.989820 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: Y Method: Least Squares Date: 10/25/11 Time: 17:57 Sample: 1980 2001 X3 R-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood -0.241992 0.144245 -1.677653 0.1090 1485.993 12.92452 13.023

20、70 2084.990 0.990499 Mean dependent var 1216.395 0.990024 S.D. dependent var 148.4231 Akaike info criterion 440588.3 Schwarz criterion -140.1697 F-statistic 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=0.068035X4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: Y Method: Least Squares Date: 10

21、/25/11 Time: 18:03 Sample: 1980 2001 Included observations: 22C X1 X2 R-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood 124.5043 -1.567303 0.227036 41.07291 0.408203 0.072145 3.031301 -3.839522 3.146953 0.0072 0.0012 0.0056 0.997512 Mean dependent var 1216.395 0.997098

22、S.D. dependent var 80.05422 Akaike info criterion 115356.2 Schwarz criterion -125.4288 F-statistic 1485.993 11.76625 11.96462 2405.922Y=124.5043-1.567303X1+0.227036X2+0.074941X4 3.031301 -3.839522 3.146953 11.05532 R2=0.997512 R2=0.997098 F=2405.9229、Y與X1、X3、X4擬合：Dependent Variable: Y Method: Least Squares Date: 10/25/11 Time: 18:04 Sample: 1980 2001 Included observations: 22C X1 X3 R-squaredAdjusted