计量经济学国债发行额数学模型.docx

计量经济学国债发行额数学模型.docx

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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

Y

X1

X2

X3

X4

1980

43.01

45.178

68.9

28.58

399

1981

121.74

48.624

-37.38

62.89

524

1982

83.86

52.947

17.65

55.52

675

1983

79.41

59.345

42.57

42.47

893

1984

77.34

71.71

58.16

28.9

1215

1985

89.85

89.644

-0.57

39.56

1623

1986

138.25

102.022

82.9

50.17

2237

1987

223.55

119.625

62.83

79.83

3081

1988

270.78

149.283

133.97

76.76

3822

1989

407.97

169.092

158.88

72.37

5196

1990

375.45

185.479

146.49

190.07

7120

1991

461.4

216.178

237.14

246.8

9242

1992

669.68

266.381

258.83

438.57

11759

1993

739.22

346.344

293.35

336.22

15204

1994

1175.25

467.594

574.52

499.36

21519

1995

1549.76

584.781

581.52

882.96

29662

1996

1967.28

678.846

529.56

1355.03

38521

1997

2476.82

744.626

582.42

1918.37

46280

1998

3310.93

783.452

922.23

2352.92

53408

1999

3715.03

820.6746

1743.59

1910.53

59622

2000

4180.1

894.422

2491.27

1579.82

64332

2001

4604

959.333

2516.54

2007.73

73762

由数据，我们进行第一次拟合：

DependentVariable:

Y

Method:

LeastSquares

Date:

10/25/11Time:

16:

54

Sample:

19802001

Includedobservations:

22

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

14.43481

35.40908

0.407658

0.6886

X1

0.190236

0.450990

0.421818

0.6784

X2

0.940201

0.153877

6.110072

0.0000

X3

0.820870

0.168306

4.877234

0.0001

X4

0.005481

0.014937

0.366969

0.7182

R-squared

0.998963

Meandependentvar

1216.395

AdjustedR-squared

0.998719

S.D.dependentvar

1485.993

S.E.ofregression

53.18111

Akaikeinfocriterion

10.98200

Sumsquaredresid

48079.92

Schwarzcriterion

11.22996

Loglikelihood

-115.8020

F-statistic

4094.752

Durbin-Watsonstat

2.072804

Prob（F-statistic）

0.000000

得到线性拟合方程为：

Y=14.43481+0.190236X1+0.940201X2+0.820870X3+0.005481X4

O.4076580.4218186.1100724.8772340.366969

=O.998963

0.998719F=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

X1

X2

X3

X4

X1

1.000000

0.869643

0.954508

0.986413

X2

0.869643

1.000000

0.787957

0.919614

X3

0.954508

0.787957

1.000000

0.959852

X4

0.986413

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：

DependentVariable:

Y

Method:

LeastSquares

Date:

10/25/11Time:

17:

16

Sample:

19802001

Includedobservations:

22

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

-388.3980

124.1492

-3.128479

0.0053

X1

4.494313

0.261595

17.18041

0.0000

R-squared

0.936541

Meandependentvar

1216.395

AdjustedR-squared

0.933369

S.D.dependentvar

1485.993

S.E.ofregression

383.5804

Akaikeinfocriterion

14.82348

Sumsquaredresid

2942679.

Schwarzcriterion

14.92267

Loglikelihood

-161.0583

F-statistic

295.1665

Durbin-Watsonstat

0.248664

Prob（F-statistic）

0.000000

Y=-388.3980+4.494313X1

-3.12847917.18041

=0.936541

0.933369F=295.1665

2、Y与X2拟合：

DependentVariable:

Y

Method:

LeastSquares

Date:

10/25/11Time:

17:

21

Sample:

19802001

Includedobservations:

22

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

249.5863

129.5995

1.925827

0.0685

X2

1.855133

0.143221

12.95296

0.0000

R-squared

0.893492

Meandependentvar

1216.395

AdjustedR-squared

0.888166

S.D.dependentvar

1485.993

S.E.ofregression

496.9387

Akaikeinfocriterion

15.34132

Sumsquaredresid

4938962.

Schwarzcriterion

15.44050

Loglikelihood

-166.7545

F-statistic

167.7791

Durbin-Watsonstat

0.617461

Prob（F-statistic）

0.000000

Y=249.5863+1.855133X2

1.92582712.95296

=0.893492

0.888166F=167.7791

3、Y与X3拟合：

DependentVariable:

Y

Method:

LeastSquares

Date:

10/25/11Time:

17:

27

Sample:

19802001

Includedobservations:

22

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

80.25663

138.5002

0.579469

0.5687

X3

1.753369

0.136369

12.85750

0.0000

R-squared

0.892076

Meandependentvar

1216.395

AdjustedR-squared

0.886680

S.D.dependentvar

1485.993

S.E.ofregression

500.2312

Akaikeinfocriterion

15.35453

Sumsquaredresid

5004625.

Schwarzcriterion

15.45371

Loglikelihood

-166.8998

F-statistic

165.3154

Durbin-Watsonstat

0.652788

Prob（F-statistic）

0.000000

Y=80.25663+1753369X3

0.57946912.85750

=0.892076

0.886680F=165.3154

因常数项t=0.579469<2.306则省略常数项，得到拟合方程为：

Y=1753369X3

4、Y与X4拟合：

DependentVariable:

Y

Method:

LeastSquares

Date:

10/25/11Time:

17:

30

Sample:

19802001

Includedobservations:

22

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

-32.43131

44.08887

-0.735590

0.4705

X4

0.061041

0.001410

43.30394

0.0000

R-squared

0.989447

Meandependentvar

1216.395

AdjustedR-squared

0.988920

S.D.dependentvar

1485.993

S.E.ofregression

156.4211

Akaikeinfocriterion

13.02949

Sumsquaredresid

489351.3

Schwarzcriterion

13.12867

Loglikelihood

-141.3244

F-statistic

1875.231

Durbin-Watsonstat

0.629259

Prob（F-statistic）

0.000000

Y=-32.43131+0.061041X4

-0.73559043.30394

=0989447

0.988920F=1875.231

因常数项t=-0.735590<2.306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X4

5、Y与X4、X1拟合：

DependentVariable:

Y

Method:

LeastSquares

Date:

10/25/11Time:

17:

40

Sample:

19802001

Includedobservations:

22

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

176.7065

45.53446

3.880721

0.0010

X1

-2.313274

0.402728

-5.744008

0.0000

X4

0.091192

0.005322

17.13651

0.0000

R-squared

0.996144

Meandependentvar

1216.395

AdjustedR-squared

0.995738

S.D.dependentvar

1485.993

S.E.ofregression

97.01420

Akaikeinfocriterion

12.11372

Sumsquaredresid

178823.4

Schwarzcriterion

12.26249

Loglikelihood

-130.2509

F-statistic

2453.999

Durbin-Watsonstat

1.819363

Prob（F-statistic）

0.000000

Y=176.7065-2.313274X1+0.091192X4

3.880721-5.74400817.13651

=0.996144

0.995738F=2453.999

6、Y与X2、X4拟合：

DependentVariable:

Y

Method:

LeastSquares

Date:

10/25/11Time:

17:

44

Sample:

19802001

Includedobservations:

22

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

-6.394788

30.06927

-0.212669

0.8339

X2

0.387892

0.077102

5.030903

0.0001

X4

0.049887

0.002411

20.69336

0.0000

R-squared

0.995475

Meandependentvar

1216.395

AdjustedR-squared

0.994999

S.D.dependentvar

1485.993

S.E.ofregression

105.0896

Akaikeinfocriterion

12.27363

Sumsquaredresid

209832.5

Schwarzcriterion

12.42241

Loglikelihood

-132.0099

F-statistic

2089.942

Durbin-Watsonstat

1.199846

Prob（F-statistic）

0.000000

Y=-6.394788+0.387892X2+0.049887X4

-0.2126695.03090320.69336

=0.995475

0.994999F=2089.942

因常数项的t=-0.212669<2.306,则省略常数项，得到拟合方程为：

Y=0.387892X2+0.049887X4

7、Y与X3、X4的拟合：

DependentVariable:

Y

Method:

LeastSquares

Date:

10/25/11Time:

17:

49

Sample:

19802001

Includedobservations:

22

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

-32.71357

42.26045

-0.774094

0.4484

X3

-0.242445

0.145713

-1.663852

0.1125

X4

0.068733

0.004817

14.26979

0.0000

R-squared

0.990789

Meandependentvar

1216.395

AdjustedR-squared

0.989820

S.D.dependentvar

1485.993

S.E.ofregression

149.9329

Akaikeinfocriterion

12.98438

Sumsquaredresid

427117.9

Schwarzcriterion

13.13316

Loglikelihood

-139.8281

F-statistic

1021.904

Durbin-Watsonstat

0.804370

Prob（F-statistic）

0.000000

Y=-32.71357-0.242445X3+0.068733X4

-0.774094-1.66385214.26979

=0.990789

0.989820F=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：

DependentVariable:

Y

Method:

LeastSquares

Date:

10/25/11Time:

17:

57

Sample:

19802001

Includedobservations:

22

Variable

Coefficient

Std.Error

t-Statistic

Prob.

X3

-0.241992

0.144245

-1.677653

0.1090

X4

0.068035

0.004684

14.52561

0.0000

R-squared

0.990499

Meandependentvar

1216.395

AdjustedR-squared

0.990024

S.D.dependentvar

1485.993

S.E.ofregression

148.4231

Akaikeinfocriterion

12.92452

Sumsquaredresid

440588.3

Schwarzcriterion

13.02370

Loglikelihood

-140.1697

F-statistic

2084.990

Durbin-Watsonstat

0.781478

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：

DependentVariable:

Y

Method:

LeastSquares

Date:

10/25/11Time:

18:

03

Sample:

19802001

Includedobservations:

22

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

124.5043

41.07291

3.031301

0.0072

X1

-1.567303

0.408203

-3.839522

0.0012

X2

0.227036

0.072145

3.146953

0.0056

X4

0.074941

0.006779

11.05532

0.0000

R-squared

0.997512

Meandependentvar

1216.395

AdjustedR-squared

0.997098

S.D.dependentvar

1485.993

S.E.ofregression

80.05422

Akaikeinfocriterion

11.76625

Sumsquaredresid

115356.2

Schwarzcriterion

11.96462

Loglikelihood

-125.4288

F-statistic

2405.922

Durbin-Watsonstat

2.010999

Prob（F-statistic）

0.000000

Y=124.5043-1.567303X1+0.227036X2+0.074941X4

3.031301-3.8395223.14695311.05532

=0.997512

0.997098F=2405.922

9、Y与X1、X3、X4拟合：

DependentVariable:

Y

Method:

LeastSquares

Date:

10/25/11Time:

18:

04

Sample:

19802001

Includedobservations:

22

Variable

Coefficient

Std.Error

t-Statistic

Prob.

C

166.4393

43.77734

3.801950

0.0013

X1

-2.201721

0.389023

-5.659621

0.0000

X3

-0.156343

0.091075

-1.71