計(jì)量經(jīng)濟(jì)學(xué)案例分析

計(jì)量經(jīng)濟(jì)學(xué)案例分析

姓名：學(xué)號(hào)：

學(xué)院：管理學(xué)院

專業(yè)：10級(jí)工程管理

計(jì)量經(jīng)濟(jì)學(xué)案例分析

案例：研究從1989-2022年，影響我國(guó)國(guó)債發(fā)行總量的主要因素。當(dāng)年的國(guó)債發(fā)行總

量（Y）,國(guó)內(nèi)生產(chǎn)總值（XI）、城鄉(xiāng)居民儲(chǔ)蓄存款（X2）、國(guó)家財(cái)政收入（X3）、國(guó)家財(cái)政赤字

（X4）、國(guó)債余額（X5）。在這里，國(guó)債發(fā)行總量作為被解釋變量，其余為解釋變量。數(shù)據(jù)

如下：

國(guó)債發(fā)行總國(guó)內(nèi)生產(chǎn)總城鄉(xiāng)居民儲(chǔ)

財(cái)政收入財(cái)政赤字X4國(guó)債余額X5

年份量Y（億值Xl（億蓄額X2

X3（億元）（億元）（億元）

元）元）（億元）

1989138.9116992.35196.42664.9158.88769.33

1990197.2418667.87119.82937.16922.56890.34

1991281.2721781.59244.93149.488963.631059.99

1992460.7726923.511757.33483.3711296.531282.72

1993381.3235333.915203.54348.9514822.181540.74

19941137.5548197.9215L8.85218.120381.252286.4

19951510.960793.729662.36242.228151.43300.3

19961847.7771176.638520.87407.9936673.034361.43

19972411.797897346279.88651.1443868.015508.93

19983808.7784402.353407.59875.9549598.737765.7

1999401589677.159621.811444.0855606.810542

2000465799214.664332.413395.2359675.413020

20014884109655.273762.416386.0468878.415618

20025934.3120332.786910.718903.6480976.419336.1

20036280.1135822.8103617.721715.2597337.622603.6

20046923.9159878.3119555.426396.47112631.525777.6

20057042184937.414105131649.2913400928774

20228883.3216314.4161587.338760.215270431448.7

202223483.28265810.3172534.251321.78149050.9248741

20228615314045.4217885.461330.35209270.449767.83

202216229.2340506.9260771.768518.3244542.562708.35

注：所有數(shù)據(jù)均來自2022年《中國(guó)統(tǒng)計(jì)年鑒》

作散點(diǎn)圖觀察各變量的增長(zhǎng)趨勢(shì)，如圖所示:

OGraph:UNTITLEDWorkfile:曲■計(jì)量經(jīng)不學(xué)案免淅三U百

Y

X1

X2

X3

X4

X6

從上面的散點(diǎn)圖可以看出Y,X1,X2,X3,X4,X5都是逐年增長(zhǎng)的，但增長(zhǎng)速率并

不相同，是曲線增長(zhǎng)，為便于研究，將模型設(shè)置如下:

InYt=|}o+|MInXit+p2InXzt+p3InX3t+p4InX4t+fislnXst+nt

其中，u為隨機(jī)誤差項(xiàng)。

進(jìn)行普通最小二乘回歸，結(jié)果如下所示:

Equation:UNTITLEDNorkfile:陳葉計(jì)量經(jīng)濟(jì)學(xué)案例分析\Un.'G

ViewProcObjectPrinlNameFreezeEstinnteForecastStatsResids

DependentVariable:LOG(Y)

Method:LeastSquares

Date:12/15/12Time:21:46

Sample:19892022

Includedobservations:21

VarableCoefficientStd.Errort-StatisticProb.

C-5.9504632.023127-2.9412200.0101

LOG(XI)3.2045090.9506093.3710060.0042

L0GCX2-2.1701620.982507-2.2087990.0432

L0G(X3)-2.0073890.420934-4.7688950.0002

L0G(X4)0.1876840.0936122.0049220.0634

LOG(X5)1.97G2800.4401614.4899040.0004

R-squared0.986336Meandependentvar7.815790

AdjustedR-squared0.981782S.D.dependentvar1.475374

S.Lofregression0.199139Akaik。infocriterion-0.154668

Sumsquaredresid0.594847Schwarzcriterion0.143767

laglikelihood7.624009F-statistic216.5585

Durbin-Watsonstat2.519594Prob(F-statis:ic)0.000000

InY=-5.950463+3.204509lnXi-2.1701621nX2-2.007389lnX3+0.18762801nX4

+1.9762801nX5

2

模型估計(jì)結(jié)果說明，在假定其他條件不變的情況下，當(dāng)年國(guó)內(nèi)生產(chǎn)總俏每噌長(zhǎng)1雙

國(guó)債發(fā)行總量會(huì)增加3.204509機(jī)在假定其他條件不變的情況下，當(dāng)年城鄉(xiāng)居民儲(chǔ)蓄額每

增長(zhǎng)1%,國(guó)債發(fā)行總量會(huì)減少2.170162%;在假定其他條件不變的情況下，當(dāng)年財(cái)政收

入每增長(zhǎng)1%,國(guó)債發(fā)行總量會(huì)減少2.007389枇在假定其他條件不變的情況下，當(dāng)年財(cái)

政赤字每增長(zhǎng)1乳國(guó)債發(fā)行總量會(huì)增加0.1876280船在假定其他條件不變的情況下，

當(dāng)年國(guó)債余額每增加1%,國(guó)債發(fā)行總量會(huì)增加1.976280%。上述分析與實(shí)際不符，模型

需要進(jìn)一步調(diào)整。

多重共線性檢驗(yàn)

由普通最小二乘回歸結(jié)果知R2=0.986336,修正后的可決系數(shù)為0.981782,這說明模

型對(duì)樣本的擬合較好。F值為216.5585,很顯著，即〃國(guó)內(nèi)生產(chǎn)總值”、“城鄉(xiāng)居民儲(chǔ)蓄

額"、“財(cái)政收入”、〃財(cái)政赤字〃和“國(guó)債余額”5個(gè)變量聯(lián)合起來對(duì)“國(guó)債發(fā)行總量”

有顯著影響。但是當(dāng)a=0.05時(shí),to.o2s(21-6)=2.131,X3的系數(shù)I檢驗(yàn)不顯著，而且X3

X3的符號(hào)與預(yù)期相反，這表明很可能存在嚴(yán)重的多重共線性。

查看解釋變最的相關(guān)系數(shù)矩陣，如卜.:

Group:UNTITLEDWorkfile:陳葉-計(jì)量經(jīng)濟(jì)學(xué)案例分析\Untitled

ProcObjectPrintName〔FreezeSample|Sheet|Stats|Spec|

CorrelationMatrix

XIX2X3X4Xb

XI1.0000000.9946840.9928000.9914640.989034

X20.99468L1.0000000.9875450.9988780.987698

X30.9928000.9875451.0000000.9832730.992775

X40,9914640.9988780.9832731.0000000.960840

X5_____0.989034-0.9876980.9927250.980840L000000

由上圖發(fā)現(xiàn)，XI和X2的相關(guān)系數(shù)為0.994684,高度相關(guān)，這符合普通的經(jīng)濟(jì)規(guī)律，

即城鄉(xiāng)居民儲(chǔ)蓄額和國(guó)內(nèi)生產(chǎn)總值存在高度的相關(guān)性“5個(gè)解釋變量之間的相關(guān)系數(shù)都較

高，證實(shí)存在嚴(yán)重的多重共線性。

卜面用逐步回歸的方法對(duì)其進(jìn)行檢驗(yàn)。首先找出最符單的回歸形式。

(l)mY=-10.11493+1.5811891nX1

Equation:UNTITLEDWorkfile:陳葉-計(jì)量經(jīng)濟(jì)學(xué)案例分析\Un…

View3rocObjectPrinttamokrcozoEstimateForecastStatsResids

DependentVariable:LOG(Y)

Method:LeastSquares

Date:12/15/12Time:22:46

Sample:19892022

Includedobservations:21

VariableCoefficientStd.Errort-StatisticProb.

C-10.114930.944073-10.714130.0000

LOG(XI)1.5811890.08299819.051030.0000

R-squared0.950254Meandependentvar7.815790

AdjustedR-squared0.947636S.D.dependentvar1.475374

S.E.ofregression0.337613Akaikeinfccriterion0.756558

Sumsquaredresid2.165664Schwarzcriterion0.856036

Log1ikelihood-5.913858F-statistic362.9416

Durbin-Watsonstat1.547126Prob(F-statiStic)0.000000

3

(2)mY=-5.618505+1.2451181nX2

Equation:UNTITLEDWorkfile:陳葉-計(jì)點(diǎn)經(jīng)濟(jì)學(xué)案例分析\Un..

ew[Proc](bi?i|print|NamekreezcEstim;itc|Forecast{Stat或esidsj

l>epandertVariable:LOG(Y)

Method:LeastSquares

Date:12/15/12Time:22:49

Sample:19892022

Includedobservations:21

VariableCoefficientStd.Errort-StatisticProb.

C-5.6185050.6011369.2954560.0000

L0G(X2)1.2451180.05571322.348810.0000

R-squared0.963354Meandependentvar7.815790

AdjustedR-squared0.961425S.D.dependentvar1.475374

S.E.orregression0.289772Akaikeinfocriterion0.450945

Sumsquaredresid1.595383Schwarzcriterion0.550423

l-oglike!ihood-2.734921F-statistic499.4693

IhirbinTatsonstat2.240811Prob(F-slatistic)0.000000

(3)mY=-4.830354+1.3451131nX3

Equation;UNTITLEDWorkfile:陳葉-計(jì)星經(jīng)濟(jì)學(xué)案例分析\Un..

VicwPro)ObjectPmtMw?卜二義文「ForucaatSlulsResids

DependentVanable:LOG(Y)

Method:LeastSquares

Date:12/15/12Time:22:49

Sample:19892022

Includedobservations.21

VariableCoefficientStd.Errort-StatisticProb.

c4.8303541.0057524.8027310.0001

L0G(X3)1.3451130.10636312.646460.0000

R-squared0.893S15如andependetitvar7.815790

AdjustedR-squared0.688226S.D.dependentvar1.475374

S.E.ofregression0.493256Akaikeinfocriterion1.514815

bumsquaredresid4.622725Schwarzcriterion1.614293

LoglikelihoodT3.90556F-statistic159.9329

Durbin-Watsonstat0.776447Prob(F_statistic)0.000000

(4)hY=-0.777112+0.813131

Equalion:UNTITLEDWorkfl。:陳葉一計(jì)量經(jīng)濟(jì)學(xué)案例分析\Un.|

VicwlproJobjiect|UciFreezelEsiinat」F°ri?casi(Sta』Resds|

DependentVariable:l.0G(Y)

Method:LeastSquares

Date:12/15/12Time:2250

Sample:19892022

Includedobservations.21

VariableCoefficientStd.Error1-StatisticProb.

C-0.7771120.980784-0.7923370.4379

L0G(X4)0.8131310.0917788.8597220.0000

R-squaied0.805118Meandependentvar7.815790

AdjustedR-squared0.794861S.D.dependentvar1.475374

S.E.ofregression0.668231Akaikeinfocriterion2.122028

Sumsquaredresid8.484128Schwarzcriterion2.221506

Loglikelihood20.28129F.statistic78.49468

Durbin-Watsonstat1.349054Prob(F-$lalisil.：>0.000000

(5)mY=-l.l40406+0.998228lnXs

Equation:UNTITLEDWorkfile;陳葉一計(jì)量經(jīng)濟(jì)學(xué)案例分析\Un

ViewProcObjectprintNameFreezeEstimateForecastSialsResids

DependentVariable:LOG(Y)

Methad:LeastSquares

Date:12/15/12Time:23:08

Sample:19892022

Includedobservations:21

VariableCoefficientStd.Errcrt-StatisticProb.

C-1.1404060.459559-2.4815240.0226

L0G(X5)0.9982280.05060119.727340.0000

R-squared0.953451Meandependentvar7.815790

AdjustedR-squared0.951001S.D.dependentvar1.475374

S.E.ofregression0.326586Akaikeinfocriterion0.690147

Sumsquaredresid2.026513Schwarzcriterion0.789626

Log1ikelihood

-5.246545F-statistic389.1679

Durbin-Watsonstat1.205226Prob(F-statiStic)0.000000

可見，國(guó)債發(fā)行總量受城鄉(xiāng)居民儲(chǔ)蓄額的影響最大，因此選(2)為初始的回歸模型。

接著進(jìn)行逐步回歸。將其他解釋變量分別導(dǎo)入上述初始回歸模型，尋覓最佳回歸方程。

如下表所示：

cInX,InX'InX3InX4InX5R2D.W.

Y=f(X2)-5.621.250.9633542.241

t值(-9.3)(22.35)

Y=f(X2,X,)-4.21.62-0.480.9601132.379

t值(-1.76)⑵54)(-0.61)

Y=f(X2,X3)-5.621.61-0.420.9637322.611

t值(-9.58)(6.37)(-1.49)

Y=f(X2,X4)-5.511.220.0260.9635852.272

t值(-7.94)(13.87)(2.33)

Y=f(X2,X4,Xs)-3.630.640.090.400.9593302.078

t值(-1.75)(1.37)(0.76)(0.98)

討論：

第一步，在初始模型中引入足，模型擬合優(yōu)度下降，同時(shí)&的參數(shù)未能通過t檢驗(yàn)。

第二步，去掉XI,引入X3,擬合優(yōu)度雖有提高，但X3的參數(shù)未能通過t檢驗(yàn)。

第三步，去掉X3,引入兒，擬合優(yōu)度提高，且的參數(shù)通過t檢驗(yàn)。

第四步，引入Xs,擬合優(yōu)度下降，同時(shí)所有參數(shù)都不能t通過檢驗(yàn)。

因此，最終的國(guó)債發(fā)行總量函數(shù)應(yīng)以Y=f(Xz,X4)為最優(yōu)，擬合結(jié)果如卜.：

InY=-5.512199+1.222419hX2+0.0134221lnX4

這說明，在其他因素不變的情況下，當(dāng)居民儲(chǔ)蓄額X2每增加1億元，財(cái)政赤字增加1

億元時(shí)，國(guó)債總發(fā)行量將分別增加1.22億元和0.013億元。

5

序列相關(guān)性檢驗(yàn)

從修正多重共線性后的模型看殘差圖如卜.:

D.W.檢驗(yàn)結(jié)果表明，在5%顯著性水平下，n=21,k=3（包含常數(shù)項(xiàng)），查表得

dL=l.13,du=l.54,4-du=4-l.54=2.46,即du<D.W.<4-du,說明該模型不存在一階自相

關(guān)，上圖所示的殘差圖也可表明該情況。

川拉格朗日乘數(shù)法進(jìn)一步檢驗(yàn)是否存在二階自相關(guān)，結(jié)果如下圖所示:

Equation:UNTITLEDNcrkfie:陳葉-計(jì)量經(jīng)濟(jì)學(xué)案例分析\Unlitled

VowPracnhjprfPrimNamelrroozcF?cfStatqReeids

Breusch-GodfreySerialCorrelationLMTest:

E-statistic0.208765Probability0.813762

Obs*R-squared0.531071Probability0.765646

TestEquation:

DependentVariable:RESID

Method:LeastSquares

Date:12/16/12Time:01:16

Presanplemissingvaluelaggedresidualssettozero.

VariableCoefficientStd.Errort-StatisticProb.

C-0.0697780.7572560.0921460.9277

L0G(X2)0.0097150.1468610.0661530.9481

L0G(X，D-0.0028910.103029-0.0280560.9780

^ESID(-l)-0.1701660.2635660.6456290.5277

RESID(-2)-0.0716170.319931-0.2238520.8257

R-squtred0.025132Meandep(?nderilvar-5.25E.16

AdjustedR-squared0.218210S.D.dopencentvar0.281879

S.E.ofregression0.311117Akaikeinfocriterion0.706961

Sumsquaredresid1.548701Schwarzcriterion0.955659

LOK1kelihood-2.423118F-statistic0.104362

Durbir-Watsonstat1.920002Prob(F-statistic)0.979326

從上圖中可以看出resid(-2)的參數(shù)估計(jì)值通過檢驗(yàn)，不拒絕原假設(shè)，即不存在二階

自相關(guān)。所以修正后的模型不存在序列相關(guān)性。

異方差性檢驗(yàn)

用懷特檢驗(yàn)查看是否存在異方差性，結(jié)果如下圖所示:

Equation:UNTITLEDUorkfile:陳葉-計(jì)量經(jīng)濟(jì)學(xué)案例分析Untitled

VenObjccPit廂neFcczcEslateFoecasSlotsResid

WhitelloteroskodasticityTest:

Fstatistic2.380115Probability0.068569

Obs*R-squared9.290213Probabi1ity0.098034

TestEcuation:

DependeitVariable:RESID*2

Method:LeastSquares

Date:12/16/12Time:01:23

Sample:19892022

Includecobservations: